Particle Physics At The Tercentenary Of Mikhail Lomonosov - Proceeding Of The Fifteenth Lomonosov Conference On Elementary Particle Physics: Proceedings of the Fifteenth Lomonosov Conference on Elementary Particle Physics 9789814436830, 9789814436823

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PARTICLE PHYSICS at the Tercentenary of Mikhail Lomonosov

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Faculty of Physics of Moscow State University

INTERREGIONAL CENTRE FOR ADVANCED STUDIES

Proceedings of the Fifteenth Lomonosov Conference on Elementary Particle Physics

PARTICLE PHYSICS at the Tercentenary of Mikhail Lomonosov Moscow, Russia

18 – 24 August 2011

Editor

Alexander I. Studenikin Moscow State University, Russia

World Scientific NEW JERSEY

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LONDON

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BEIJING

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TA I P E I

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PARTICLE PHYSICS AT THE TERCENTENARY OF MIKHAIL LOMONOSOV Proceedings of the Fifteenth Lomonosov Conference on Elementary Particle Physics Copyright © 2013 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher.

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Moscow State University Faculty of Physics Interregional Centre for Advanced Studies

FIFTEENTH LOMONOSOV CONFERENCE ON ELEMENTARY PARTICLE PHYSICS Moscow, August 18-24, 2011

Mikhail Lomonosov 1711-1765

Sponsors Russian Ministry of Education and Science Russian Foundation for Basic Research Interregional Centre for Advanced Studies Supporting Institutions Faculty of Physics of Moscow State University Joint Institute for Nuclear Research (Dubna) Institute for Nuclear Research (Moscow) Skobeltsyn Institute of Nuclear Physics (MSU) Bruno Pontecorvo Neutrino and Astrophysics Laboratory (MSU)

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International Advisory Committee E.Akhmedov (Max Plank, Heidelberg), S.Belayev (Kurchatov Inst.,Moscow), V.Belokurov (MSU), V.Berezinsky (LNGS, Gran Sasso), S.Bilenky (JINR, Dubna), J.Bleimaier (Princeton), M.Danilov (ITEP, Moscow), G.Diambrini-Palazzi (Univ. of Rome), A.Dolgov (INFN, Ferrara & ITEP, Moscow), N.Fornengo (INFN, Turin), C.Giunti (INFN, Turin), M.Itkis (JINR, Dubna), V.Kadyshevsky (JINR, Dubna), A.Logunov (IHEP, Protvino), A.Masiero (INFN, Padua), V.Matveev (INR, Moscow), L.Okun (ITEP, Moscow), M.Panasyuk (SINP MSU), V.Rubakov (INR, Moscow), D.Shirkov (JINR, Dubna), J.Silk (Univ. of Oxford), A.Skrinsky (INP, Novosibirsk), A.Slavnov (MSU & Steklov Math.Inst, Moscow) A.Smirnov (ICTP, Trieste & INR, Moscow), P.Spillantini (INFN, Florence), A.Starobinsky (Landau Inst., Moscow), V.Trukhin (MSU) Organizing Committee V.Bagrov (Tomsk State Univ.), I.Balantsev (MSU), V.Bednyakov (JINR, Dubna), V.Braginsky (MSU), A.Egorov (ICAS, Moscow), D.Galtsov (MSU), A.Grigoriev (MSU & ICAS, Moscow), S.Kapitza (EAPS), A.Kataev (INR, Moscow), A.Lokhov (MSU), V.Mikhailin (MSU & ICAS, Moscow), N.Nikiforova (MSU), A.Nikishov (Lebedev Physical Inst., Moscow), V.Ritus (Lebedev Physical Inst., Moscow), M.Polyakova (ICAS), Yu.Popov (MSU) , V.Savrin (MSU), A.Studenikin (MSU & ICAS, Moscow)

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Moscow State University Interregional Centre for Advanced Studies

NINTH INTERNATIONAL MEETING ON PROBLEMS OF INTELLIGENTSIA “The INTELLIGENTSIA: Custodial of Civilization” Moscow, August 24, 2011

Presidium of the Meeting V.A.Sadovnichy (MSU) - Chairman V.V.Belokurov (MSU) J.Bleimaier (Princeton)

G.Diambrini-Palazzi (Universiry of Rome) V.G.Kadyshevsky (JINR)

S.P.Kapitza (Russian Academy of Sciensies) V.V.Mikhailin (MSU)

A.I.Studenikin (MSU & ICAS) - Vice Chairman V.I.Trukhin (MSU)

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FOREWORD th

The 15 Lomonosov Conference on Elementary Particle Physics was held at the Moscow State University (Moscow, Russia) on August 18-24, 2011 under the Patronage of the Rector of the Moscow State University Victor Sadovnichy. The conference was organized by the Faculty of Physics of the Moscow State University in cooperation with the Interregional Centre for Advanced Studies and supported by the Joint Institute for Nuclear Research (Dubna), the Institute for Nuclear Research (Moscow), the Skobeltsyn Institute of Nuclear Physics of MSU and the Bruno Pontecorvo Neutrino and Astrophysics Laboratory (MSU). The Ministry of Education and Science of Russia and the Russian Foundation for Basic Research sponsored the conference. It was more than twenty years ago when the first of the series of conferences (from 1993 called the “Lomonosov Conferences”), was held at the Department of Theoretical Physics of the Moscow State University (June 1983, Moscow). The second conference was held in Kishinev, Republic of Moldavia, USSR (May 1985). After the four years break this series was resumed on a new conceptual basis for the conference programme focus. During the preparation of the third conference (that was held in Maykop, Russia, 1989) a desire to broaden the programme to include more general issues in particle physics became apparent. During the conference of the year 1992 held in Yaroslavl it was proposed by myself and approved by numerous participants that these irregularly held meetings should be transformed into regular events under the title “Lomonosov Conferences on Elementary Particle Physics”. Since then at subsequent meetings of this series a wide variety of interesting things both in theory and experiment of particle physics, field theory, astrophysics, gravitation and cosmology were included into the programmes. It was also decided to enlarge the number of institutions that would take part in preparation of future conferences. The 15th Lomonosov Conference on Elementary Particle Physics was dedicated to tercentenary of Mikhail Lomonosov (1711-1765). Mikhail Lomonosov is a brilliant Russian encyclopaedias of the era of the Russian Empress Catherine the 2nd, was world renowned for his distinguished contributions in the fields of science and art. He also helped establish the high school educational system in Russia. The Moscow State University was founded in 1755 based on his plan and initiative, and the University now bears the name of Lomonosov. The 6th Lomonosov Conference on Elementary Particle Physics (1993) and all of the subsequent conferences of this series were held at the Moscow State University on each of the odd years. Publication of the volume "Particle Physics, Gauge Fields and Astrophysics" containing articles written on the basis of presentations at the 5th and 6th Lomonosov Conferences was supported by the Accademia Nazionale dei Lincei (Rome, 1994). Proceedings of the 7th and 8th Lomonosov Conference (entitled “Problems of Fundamental Physics” and

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“Elementary Particle Physics”) were published by the Interregional Centre for Advanced Studies (Moscow, 1997 and 1999). Proceedings of the 9th, 10th, 11th, 12th, 13th and 14th Lomonosov Conferences (entitled “Particle Physics at the Start of the New Millennium”, “Frontiers of Particle Physics”, “Particle Physics in Laboratory, Space and Universe”, “Particle Physics at the Year of 250th Anniversary of Moscow University”, “Particle Physics on the Eve of LHC” and “Particle Physics at the Year of Astronomy”) were published by World Scientific Publishing Co. (Singapore) in 2001, 2003, 2005, 2006, 2009 and 2011, correspondently. The physics programme of the 15th Lomonosov Conference on Elementary Particle Physics (August 18-24, 2011) included review and original talks on wide range of items such as neutrino and astroparticle physics, electroweak theory, fundamental symmetries, tests of standard model and beyond, heavy quark physics, non-perturbative QCD, quantum gravity effects, physics at the future accelerators. Totally there were more than 350 participants with 147 talks including 53 plenary (30-25 min) talks, 43 session (20 min) talks, 36 brief (1510 min) reports and 15 poster presentations. One of the goals of the conference was to bring together scientists, both theoreticians and experimentalists, working in different fields, so that no parallel sessions were organized at the conference. The Round table discussion on “Frontiers of Particle Physics: News from High Energies, Neutrinos and Cosmology” was held during the last day of the 15th Lomonosov Conference. Following the tradition that has started in 1995, each of the Lomonosov Conferences on particle physics has been accompanied by a conference on problems of intellectuals. The 9th International Meeting on Problems of Intelligentsia held during the 15th Lomonosov Conference (August 24, 2011) was dedicated to discussions on the issue “The Intelligentsia: Custodial of Civilization”. The success of the 15th Lomonosov Conference was due in a large part to contributions of the International Advisory Committee and Organizing Committee. On behalf of these Committees I would like to warmly thank the session chairpersons, the speakers and all of the participants of the 15th Lomonosov Conference and the 9th International Meeting on Problems of Intelligentsia. We are grateful to the Rector of the Moscow State University, Victor Sadovnichy, the Vice Rector of the Moscow State University, Vladimir Belokurov, the Dean of the Faculty of Physics, Vladimir Trukhin, the Directors of the Joint Institute for Nuclear Research, Victor Matveev, the Director of the Budker Institute of Nuclear Physics, Alexander Skrinsky, Vice Director of JINR, Mikhail Itkis and the Vice Dean of the Faculty of Physics of the Moscow State University, Anatoly Kozar for the support in organizing these two conferences. We extremely appreciate continuous support of the Lomonosov Conferences from Nikolay Sysoev, the Dean of Faculty of Physics since 2011. I would like to thank Federico Antinori, Gianpaolo Bellini, Kerstin Borras, Tom Browder, Mark Chen, Giorgio Chiarelli, Dmitry Denisov, Guido Drexlin,

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Antonio Ereditato, Vincenzo Flaminio, Nicolao Fornengo, Paolo Franzini, Marek Gazdzicki, Fabiola Gianotti, Carlo Giunti, Maury Goodman, Francis Halzen, Werner Hofmann, Peter Jenni, Anna Kaszmarska, Takashi Kobayashi, Yury Kudenko, Gaia Lanfranchi, Luca Latronico, Cristina Lazzeroni, Tsuyoshi Nakaya, Popat Patel, Daniel Pitzl, David Reitze, Yoishiro Suzuki, Ermanno Vercelli, Horts Wahl, Richard van de Water, Bolek Wyslouch and Kai Zuber for their help in planning of the scientific programme of the meeting and inviting speakers for the topical sessions of the conference. We are also very thankful to Dr Christine Sutton, the Editor of “CERN Courier”, for providing informational support of the event. Furthermore, I am very pleased to mention Ilya Balantsev, Alexey Lokhov and Ilya Tokarev, the Scientific Secretaries of the conference, Alexander Grigoriev, Maxim Gromov, Andrey Egorov, Hamid Gadimi, Konstantin Kiselev, Mila Polyakova, Olga Shustova and Lisa for their very efficient work in preparing and running the meeting. These Proceedings were prepared for publication at the Interregional Centre for Advanced Studies with support by the Russian Foundation for Basic Research and the Russian Ministry of Education and Science.

Alexander Studenikin

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xiii CONTENTS

Fifteenth Lomonosov Conference on Elementary Particle Physics – Sponsors and Committees

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Ninth International Meeting on Problems of Intelligentsia – Presidium

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Foreword

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Physics at Accelerators and Studies in SM and Beyond

1

Searches for the Higgs boson with the CMS A.V. Gritsan, on behalf of the CMS Collaboration

3

ATLAS status and recent results A. Cheplakov, on behalf of the ATLAS Collaboration

9

Higgs searches at ATLAS C. Solans, on behalf of the ATLAS Collaboration

13

The MPD@NICA project at JINR A. Litvinenko, for the NICA/MPD Collaboration

18

Recent results from HERA collider S. Levonian

24

Electroweak and QCD Physics with the Tevatron A. Alton, for the D0 and CDF Collaborations

30

Anomalous like-sign dimuon charge asymmetry G. Borissov, on behalf of D0 Collaboration

35

First LHC constraints on anomalously interacting new vector bosons M. Chizhov, V. Bednyakov, I. Boyko, J. Budagov, M. Demichev and I. Yeletskikh

38

Jets at TEVATRON and LHC M. V. Tokarev and T. G. Dedovich

42

SUSY searches at ATLAS M. Primavera, on behalf of the ATLAS Collaboration

46

Searches for supersymmetry with the CMS experiment A. Cakir, on behalf of the CMS Collaboration

51

Photon and di-photon production at ATLAS M. Delmastro

57

xiv Soft QCD with the ATLAS detector at the LHC S. Ferrag, on behalf of the ATLAS Collaboration

61

Exotic physics searches with the ATLAS detector J. Frost, on behalf of the ATLAS Collaboration

67

Boson and diboson production at ATLAS M. Venturi, on behalf of the ATLAS Collaboration

71

Heavy flavour production at ATLAS S. Sivoklokov, on behalf of the ATLAS Collaboration

76

A search for WR and heavy neutrinos in the dileptons+jets final state with the ATLAS detector R. Yoosoofmiya, on behalf of the ATLAS Collaboration

79

Diffraction at CMS A. Proskuryakov, on behalf of the CMS Collaboration

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Measurements of forward energy flow with CMS A.-K. Sanchez, for the CMS Collaboration

87

Search for a heavy neutrino and right-handed W of the left-right symmetric model with CMS detector D. Tlisov, on behalf of the CMS Collaboration

90

Search for microscopic black hole signatures in the CMS experiment at the LHC M. Savina, on behalf of the CMS Collaboration

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Neutrino Physics

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ICARUS: a powerful detector for ν physics A. Guglielmi

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The ANTARES undersea neutrino telescope M. Anghinolfi, on behalf of the ANTARES Collaboration

105

Tritium-β-decay experiments - the direct way to the absolute neutrino mass L. Bornschein, for the KATRIN Collaboration

110

Search for ντ interactions with the nuclear emulsion films of the OPERA experiment F. Pupilli, on behalf of the OPERA Collaboration The electronic detectors of the hybrid OPERA neutrino experiment R. Rescigno, on behalf of the OPERA Collaboration

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xv Recent results from Super-Kamiokande Y. Obayashi

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Next generation water Cherenkov detector Hyper-Kamiokande ~ R&D status ~ Y. Obayashi

128

The DAEδALUS experiment Z. Djurcic

132

The NOνA experiment Z. Djurcic

138

Opportunities of SAGE with artificial neutrino source for investigation of active-sterile transitions V. Gavrin

144

Results and implications from MiniBooNE: neutrino oscillations W. Huelsnitz, for the MiniBooNE Collaboration

149

New oscillation results from the T2K experiment A. Izmaylov, for T2K Collaboration

154

T2K non-oscillation neutrino physics with near detectors M. Ieva, on behalf of the T2K Collaboration

159

The MAJORANA double beta decay experiment: present status A. Barabash, on behalf of MAJORANA Collaboration

164

Low energy neutrino and dark matter physics with sub-keV germanium detector Shin-Ted Lin, for the TEXONO Collaboration

169

Study of solar and geo-neutrinos with the Borexino detector E. Litvinovich, on behalf of the Borexino Collaboration

173

Study of the rare processes with the BOREXINO detector A. Derbin and K. Fomenko, on behalf of the Borexino Collaboration

177

Recent results from the IceCube neutrino telescope E. Strahler, for the IceCube Collaboration

181

Double CHOOZ project: status of a reactor experiment aimed at search for neutrino oscillations S. Sukhotin, on behalf of the Double Chooz Collaboration

186

Search for neutrino radiation from collapsing stars and the sensitivity of experiments to the different types of neutrinos V. Dadykin and O. Ryazhskaya

190

xvi Supernova neutrino type identification with adding sodium chloride in LVD V. V. Ashikhmin, K. V. Manukovskiy, O. G. Ryazhskaya, I. R. Shakiryanova and A. V. Yudin, for LVD Collaboration

199

Recalculation of the day–night flavor asymmetry for solar neutrinos S. Aleshin, O. Kharlanov and A. Lobanov

201

Neutrino emission from a strongly magnetized degenerate electron gas: the Compton mechanism via a neutrino magnetic moment A. Borisov, B. Kerimov and P. Sizin Phenomenological relations for neutrino mixing angles and masses V. V. Khruschov

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206

Neutrino-triggered asymmetric magnetorotational pulsar natal kick (“Cherry-Stone Shooting” mechanism) A. V. Kuznetsov and N. V. Mikheev

208

Contribution to the neutrino form factors coming from the charged Higgs of a two Higgs doublet model C. G. Tarazona, R. A. Diaz and J. Morales

210

Interference of the solar neutrinos K. A. Akmarov

212

Astroparticle Physics and Cosmology

217

Particle Dark Matter: DAMA/LIBRA results and perspectives R. Bernabei, P. Belli, A. Di Marco, F. Montecchia, F. Cappella, A. d'Angelo, A. Incicchitti, D. Prosperi, R. Cerulli, C. J. Dai, H. L. He, X. H. Ma, X. D. Sheng, R. G.Wang and Z.P.Ye

219

Dark matter indirect detection phenomenology: status circa 08.2010 M. Cirelli

226

Recent results of the High Energy Stereoscopic System (H.E.S.S.) H. Gast, for the H.E.S.S. Collaboration

232

Selected issues in leptogenesis E. Nardi

238

Five years of PAMELA in orbit P. Spillantini

244

Exotic effects in cosmic rays and experiments at LHC L. I. Sarycheva

252

xvii Relic gravitational waves from primordial black holes A. Dolgov

256

Singularities in models of modified gravity E. V. Arbuzova and A. D. Dolgov

262

Life inside black holes V. Dokuchaev

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Superdense dark matter clumps from nonstandard perturbations V. Berezinsky, V. Dokuchaev and Y. Eroshenko

267

On the simplified tree graphs in gravity A. I. Nikishov

270

Loop quantum cosmology corrections to Friedmann's model M. Fil'chenkov and Y. Laptev

273

Construction of the curvature radiation profiles from pulsars V. A. Bordovitsyn and E. A. Nemchenko

275

On spectrum and mass composition of ultrahigh-energy cosmic rays from nearby sources O. P. Shustova

277

Noncommutative braneworld inflation K. Nozari and S. Akhshabi

280

CP Violation and Rare Decays

289

The physics programme at SuperB A. Bevan, on the behalf of the SuperB Collaboration

291

Status and prospects of SuperKEKB collider and BELLE II experiment T. Aushev

296

Rare B-meson decays M. Misiak

301

Recent results on rare kaon decays from NA48/2 and NA62 experiments at CERN SPS A. Bizzeti LHCb results E. Gushchin

306

312

xviii Search for the new physics in rare heavy flavour decays at LHCb D. Savrina, on behalf of the LHCb Collaboration

316

Search for charged lepton flavor violation Y. Kuno

319

Status and perspectives of the KLOE-2 experiment M. Martemianov, on behalf of the KLOE-2 Collaboration

324

Search for heavy neutrino in rare kaon decays A. Shaikhiev

328

Hadron Physics

333

Onset of deconfinement and critical point: news from NA49 and NA61 at the CERN SPS M. Gazdzicki

335

Proton-proton physics with ALICE E. Vercellin

340

Recent ALICE results from heavy-ion collisions at the LHC G. Feofilov, for the ALICE Collaboration

345

Results from heavy-ion collisions with the CMS detector O. Kodolova, on behalf of the CMS Collaboration

351

Elliptic flow in heavy-ion collisions with the CMS detector at the LHC: first results S. Petrushanko, for the CMS Collaboration

355

Forward jets and forward-central jets at CMS G. Safronov, for the CMS Collaboration

359

Hadronization effects in inclusive τ decay A. V. Nesterenko

363

Experimental signatures of superstrong magnetic fields in heavy-ion collisions P. Buividovich, M. Polikarpov and O. Teryaev

367

Observation of correlations of the double φ-meson system in the SELEX experiment G. Nigmatkulov and D. Romanov, on behalf of the SELEX Collaboration

374

xix New Developments in Quantum Field Theory

377

The “spin-charge-family-theory”, which offers the mechanism for generating families, predicts the fourth family and explains the origin of the dark matter N. S. Mankoč Borštnik

379

A new look at some general puzzles of Universe P. Fiziev and D. Shirkov

387

Vacuum energy decay E. Alvarez and R. Vidal

392

Problems in theory of the Casimir effect V. M. Mostepanenko

396

Constraints on light elementary particles and extra dimensional physics from the Casimir effect G. L. Klimchitskaya

402

Spherical Casimir effect within D = 3 + 1 Maxwell–Chern–Simons electrodynamics O. Kharlanov and V. Zhukovsky

405

General relativity and Weyl geometry: towards a new invariance principle C. Romero and J. B. Fonseca-Neto

408

Derivation of the NSVZ beta-function in N=1 SQED regularized by higher derivatives by summation of diagrams K. Stepanyantz

412

Post-exponential decay of unstable particles: possible effects in particle physics and astrophysics K. Urbanowski and J. Piskorski

414

More on noncommutative magnetic moment and lepton size T. Adorno, D. Gitman and A. Shabad Analytical account for the constant magnetic field effect on the undulator radiation spectrum K. V. Zhukovsky

417

422

Numerical investigation of lattice Weinberg-Salam model M. A. Zubkov

425

Chiral density waves in 2D Nambu-Jona-Lasinio model D. Ebert, N. Gubina, K. Klimenko, S. Kurbanov and V. Zhukovsky

427

xx Finite size effects in the Gross–Neveu model with isospin and baryonic chemical potentials T. Khunjua, V. Zhukovsky, D. Ebert and K. Klimenko

429

Probing Lorentz violation P. Satunin

432

Classical spin light theory V. Bagrov, V. Bordovitsyn and O. Konstantinova

434

“Sterile” neutrinos and extended gauge formalism V. Koryukin

436

Dirac algorithm and elementary particle physics O. Kosmachev

438

Problems of Intelligentsia

441

The Intelligentsia: Guardian of National Culture J. K. Bleimaier

443

Conference Programme

449

List of Participants

457

Physics at Accelerators and Studies in SM and Beyond

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3 SEARCHES FOR THE HIGGS BOSON WITH THE CMS Andrei V. Gritsan a on behalf of the CMS collaboration Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, USA Abstract. We test the nature of Electroweak Symmetry Breaking by searching for the Higgs boson with the CMS detector at the Large Hadron Collider. We report results with both the high-mass final states with weak bosons (W W , ZZ) and the low-mass final states with photons, taus, or beauty quarks. Higgs searches performed in sub-channels are further combined to extract the best overall sensitivity in the range of Higgs masses from 110 to 600 GeV.

1

Introduction

A primary goal of the Large Hadron Collider (LHC) [1] experiments is to study the mechanism of electroweak symmetry breaking where the weak W and Z bosons acquire mass while the photon, γ, remains massless. The standard model (SM) of particle physics postulates the mechanism of electroweak symmetry breaking with the Higgs field as a possible explanation [2]. A consequence of the Higgs field would be existence of the spin-zero Higgs boson (H) with quantum numbers of the vacuum, J P C = 0++ . Indirect measurements [3] suggest that the mass of a SM Higgs boson would most likely fall in the range below 200 GeV with part of this range already excluded by direct limits from experimental searches at LEP [4] and the Tevatron [5]. However, these constraints are either of limited scope or rely on detailed theoretical assumptions and therefore the aim of the LHC experiments is to explore all accessible masses. 2

Data analysis

The search is√ performed with a sample of proton-proton collisions at a center-ofmass energy s = 7 TeV corresponding to an integrated luminosity of 4.7 fb−1 recorded by the CMS experiment [6] at the LHC during 2011. Several decay channels are studied, the high-mass final states with weak bosons (W W , ZZ) and the low-mass final states with photons, taus, or beauty quarks. Table 1 lists individual analyses used in the combination [7]. Examples of reconstructed variables in four representative analyses are shown in Fig. 1. The H → γγ analysis [8] is a search for a narrow peak in the di-photon mass distribution. All selected di-photon candidates are split into four categories based on whether both photons are in the central part of the CMS detector and whether both photons have produced compact electromagnetic showers. This is motivated by the differences in the photon energy resolutions of the a e-mail:

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4 barrel/endcap electromagnetic calorimeters and for photons showering or nonshowering in the detector volume before the electromagnetic calorimeters. The background under the expected signal peak is extrapolated from sidebands. The H → bb search [9] relies on Higgs boson production in association with W or Z bosons (V ). We use the following W and Z boson decay modes: W → eν/µν and Z → ee/µµ/νν. The presence of neutrinos is tagged by requiring a missing transverse energy ETmis defined as a vector opposite to the vector sum of transverse momenta of all reconstructed objects. The dijet system, with both jets being b-tagged, is required to be boosted in the transverse plane. The main backgrounds V +jets, V b¯b, and tt¯ are derived from data control samples. The W Z and ZZ backgrounds with a Z boson decaying to b¯b as well as the single top background are predicted via simulation. A cut is placed on the MVA output and we count the number of events passing the cut in the five channels. The H → τ τ search [10] is performed using the di-tau final state signatures eµ, eτh , µτh , where τh stands for a τ decaying hadronically. Each of these three categories is further divided into exclusive sub-categories according to the associated jet activity: events with two VBF-like jets, events with at least one high ET jet, and events with no or exactly one low ET jet. We search for a broad excess in the di-tau mass mτ τ distribution. The main irreducible background is Z → τ τ derived from data by using Z → µµ events using simulated taus. The reducible backgrounds (W + jets, QCD, Z → ee) are evaluated using data driven techniques. In the H → W W (∗) → 2ℓ2ν search [11], we look for an excess of events with two leptons of opposite sign, missing transverse energy, and 0/1/2 jets. All events are split into five categories. For events with 0 jets, the main background is W W production. For events with 1 jet, W W and tt¯ are the main backgrounds. Both 0- and 1-jet categories are further split into same-flavour and opposite-flavor dilepton sub-channels. The 2-jet category is optimized to take advantage of the VBF production signature. The main background for

Table 1: Summary information on the analyses included in the combination (ℓ = e, µ).

Channel H H H H H H H H

→ γγ → ττ → bb → W W (∗) → ℓνℓν → ZZ (∗) → 4ℓ → ZZ → 2ℓ2τ → ZZ → 2ℓ2ν → ZZ (∗) → 2q2ℓ

mH range (GeV) 110 − 150 110 − 145 110 − 135 110 − 600 110 − 600 190 − 600 250 − 600 130 − 164 & 200 − 600

Lumi (fb−1 ) 4.7 4.6 4.7 4.6 4.7 4.7 4.6 4.6

subchannels 4 9 5 5 3 8 2 6

mH resolution 1–3% 20% 10% 20% 1–2% 10–15% 7% 3%

5 this channel is tt¯. We search for an excess of events in the MVA output distributions. All backgrounds, except for very small contributions from W Z, ZZ, and W γ are evaluated directly from data using various control samples. In the H → ZZ (∗) → 4ℓ search [12], we look for a four-lepton mass peak. The 4e, 4µ, 2e2µ sub-channels are tracked individually. The dominant irreducible background is electroweak ZZ diboson production (with both Zs decaying to either 2e, 2µ, or 2τ ) and taken from simulation. The smaller backgrounds with jets faking leptons (e.g. Z + jets, Zb¯b, tt¯) are evaluated all together from data. In the H → ZZ → 2ℓ2τ search [13], one Z boson is required to decay to a dilepton pair (e+ e− or µ+ µ− ) forming an on-shell Z boson. The other Z boson is required to decay to τ τ , with the following four final state signatures used in the analysis: eµ, eτh , µτh , τh τh . We search for a broad excess in the visible mass distribution. The dominant background is electroweak ZZ diboson production and taken from simulation. The main sub-leading backgrounds with jets faking τ -leptons come from Z + jets (including ZW ) and tt¯. In the H → ZZ → 2ℓ2ν search [14], we select events with Z → e+ e− or + − µ µ and a large missing transverse energy ETmis . We then build the transverse invariant mass mT from the dilepton pair momenta and ETmis , assuming that ETmis arises from a Z → νν decay. We search for a correspondingly broad excess of events in the mT distribution. The ZZ and W Z backgrounds are taken from simulation, while all other backgrounds, Z + jets and a cumulative sum of the rest, are evaluated from control samples in data. In the H → ZZ (∗) → 2q2ℓ search [15], we select events with two leptons and with two jets including two, one, or no b-tags. Motivation for b-tagging is driven by the high rate of b-jets in Z → q q¯ decays in comparison to general QCD jets produced in association with a Z boson. The two jets are required to form an invariant mass consistent with the Z boson mass. For the search in the mass range 200–600 GeV, the mass of the dilepton pair is also required to be consistent with the Z boson mass. For the search in the mass range 130–164 GeV, the requirement on the mass of the dilepton pair is relaxed. In the high mass range, events are further selected using a cut on a multivariate angular likelihood constructed from the kinematic variables of the two leptons and two jets. In this search we look for a peak in the dilepton-dijet invariant mass distribution, with the dijet mass constrained to the mass of the Z boson. The background dilepton-dijet mass distribution is derived using sideband regions in data. 3

Results

Figure 2 shows the CLs value for the SM Higgs boson as a function of its mass. The observed values are shown by the solid line. The dashed line indicates the median expected value of CLs . We exclude the SM Higgs boson at 95%

6 C.L. in the mass range 127–600 GeV. To quantify the consistency of the observed excesses with the background-only hypothesis, Fig. 3 shows a scan of the observed combined local p-value in the low mass range. One can see that the p-value curve dips downward over a large range of masses, driven by the broad excesses in the channels with poor mass resolution, with two narrower features corresponding to the ZZ → 4ℓ and H → γγ channels. The second dip is mostly driven by the γγ excess around di-photon mass mγγ ∼ 124 GeV . The local significance of the minimum p-value is 2.6σ. The global significance of the excess, taking into account the look-elsewhere effect for the entire search mass range 110–600 GeV, has been approximately evaluated directly from the data as 0.6σ. For a restricted range of interest, the global p-value can be evaluated by generating pseudo-data. If this is done, by way of illustration, for the mass range 110–145 GeV, we obtain a global significance of 1.9σ. Acknowledgments We would like to thank our CMS colleagues for making these results happen and wish to congratulate LHC colleagues for the excellent machine performance. References [1] L. Evans and P. Bryant (eds.), JINST 3, S08001 (2008). [2] F. Englert and R. Brout, Phys. Rev. Lett. 13, 321 (1964); P. Higgs, Phys. Rev. Lett. 13, 508 (1964); G. S. Guralnik, C. R. Hagen, T. W. B. Kibble, Phys. Rev. Lett. 13, 585 (1964). [3] ALEPH, CDF, D0, DELPHI, L3, OPAL, SLD Collaborations, the LEP Electroweak Working Group, the Tevatron Electroweak Working Group, and the SLD electroweak and heavy flavour groups, CERN-PH-EP-201009 (2010). [4] ALEPH, DELPHI, L3, OPAL Collaborations, Phys. Lett. B565, 61 (2003). [5] CDF, D0, and the TEVNPHWG Working Group, arXiv:1103.3233. [6] CMS Collaboration, JINST 0803, S08004 (2008). [7] CMS Collaboration, preprint CMS-HIG-11-032. [8] CMS Collaboration, preprint CMS-HIG-11-030. [9] CMS Collaboration, preprint CMS-HIG-11-031. [10] CMS Collaboration, preprint CMS-HIG-11-029. [11] CMS Collaboration, preprint CMS-HIG-11-024. [12] CMS Collaboration, preprint CMS-HIG-11-025. [13] CMS Collaboration, preprint CMS-HIG-11-028. [14] CMS Collaboration, preprint CMS-HIG-11-026. [15] CMS Collaboration, preprint CMS-HIG-11-027.

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8

Figure 2: The observed (solid) and expected (dashed) 95% C.L. upper limits on the ratio of the production cross section to the SM expectation for the Higgs boson as a function of its mass for eight analyses and the combination.

Figure 3: The observed local p-value as a function of the SM Higgs boson mass.

9 ATLAS STATUS AND RECENT RESULTS Alexander Cheplakov a , on behalf of the ATLAS collaboration Laboratory of High Energy Physics, JINR, 141980 Dubna, Russia Abstract.The Large Hadron Collider at CERN has resumed its operation in 2011 by showing a stable world-record-breaking performance at 3.5 TeV per proton beam energy. ATLAS is one of four major experiments accumulating data since the LHC start-up. The status of the detector and its performance are presented in this talk. The main results are summarized, including soft- and hard-QCD processes, W and Z boson production, as well as search for new physics.

1

ATLAS detector

The ATLAS is a general-purpose detector designed to explore the full discovery potential of the Large Hadron Collider (LHC), including searches for the Higgs Boson, SUSY particles, new heavy Gauge bosons (W, Z), etc. The detector consists of two cylindrical magnetic spectrometers, electromagnetic and hadronic calorimeters with a pseudorapidity coverage up to 4.9 as can be seen in Fig. 1 [1]. The vertices and tracks of charged particles are reconstructed in the inner detector consisted of silicon pixel, silicon strip and transition radiation detectors located in a 2 T magnetic field provided by a superconducting solenoid. The tracking detector covers pseudorapidity range ±2.5. It is surrounded by a calorimeter system. Highly granular liquid argon (LAr) electromagnetic sampling calorimetry together with LAr hadronic end-caps and Fe-scintillating tiles provide an excellent performance for reconstruction of electromagnetic and hadronic showers. The muon spectrometer is positioned outside the calorimeters. The air-core toroid system has a strong bending power with an average magnetic field integral of about 3 Tm. The drift tubes and cathode strip chambers provide a precise coordinate measurements while the resistive-plate chambers are used for triggering. 2

Physics performance

Thanks to the excellent work of the LHC machine the experiment has recorded about 3 fb−1 of integrated luminosity at a center of mass energy of 7 TeV by the end of summer 2011. Since the start of LHC at the end of 2009 the ATLAS data taking efficiency has been higher than 95% and the fraction of operational channels is very close to 100%. The ATLAS detector physics performance is illustrated in Figs. 2 and 3 by the agreement between the data and Monte-Carlo simulation for J/Ψ and Z-boson decays. These plots show a good linearity and accuracy of the momentum and energy measurements in the ATLAS detector from the Z mass scale down to a few GeV. a e-mail:

[email protected]

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21

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Time-of-Flight system

The Time-of-Flight (ToF) system is intended to perform particle identification for total momentum up to 2 GeV/c. The system includes the barrel part and two end-caps and covers the pseudorapidity interval |η| < 2. The ToF is based on Multigap Resistive Plate Counters (mRPC) with satisfactory timing properties and efficiency in particle fluxes up to 103 cm−2 s−1 [4]. The 2.5 m diameter barrel of ToF has a length of 500 cm to cover the pseudorapidity region |η| < 1.4. The basic element of ToF is a 7 cm × 62 cm mRPC built of 12 glass plates which are separated by 220 µm thick spacers forming 10 equal gas gaps. All the counters are assembled in 12 azimuthal modules providing an overall geometric efficiency of about 95 %. In Fig. 4 (a) the particle identification is based on the TPC only. In Fig. 4 (b) the particle identification based on TPC and ToF system. From these pictures one can conclude that ToF system essentially improves particle separation (especially for pions and kaons).

22

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Figure 5: a)Conceptual layout of ITS with a side view of its quarter. Notations: 1 - silicon strip detectors of the cylindrical part of ITS; 2 - carbon fiber support; 3 - front end electronics; 4 -disc detectors; 5 - cooling system elements; 6 - accelerator chamber; 7 - collider beams (see [4]). b)An example of decay of a 0.5 GeV/c multistrange hyperon in the interaction region of MPD. Notations: 1 - collider vacuum chamber; 2 - beams intercept region; 3 - region of uncertainty of tracks extrapolation based on TPC measurements (11 mm); 4 - region of uncertainty of tracks extrapolation obtained with the IT (40 um); 5 - silicon strip detectors of the ITS (see [4]).

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Electro Magnetic Calorimeter

The main goal of the Electro Magnetic Calorimeter (EMC) is to identify electrons, photons, neutral hadrons and measure their energy and position. The high-multiplicity environment of heavy-ion collisions requires for a fine EMC segmentation .In order to provide π 0 – 2γ registration, the transverse size of the cells must be of the order of the Molier radius. Moreover, as Monte-Carlo simulations indicate, the EMC occupancy should not exceed 5% to reconstruct photons with high accuracy. Our chosen is a Pb-scintillator sampling calorimeter of the shashlyk-type ,which can provide an energy resolution better than 6% at Eγ >200 MeV. The EMC is proposed to be built of towers as basic building elements (e.g. 3 cm squared). Each Pb-scintillator-based tower contains sampling cells consisting of 250 to alternating tiles of Pb (0.275 mm) and plastic scintillator (1.5 mm). The module with a thickness of 18 radiation lengths will be approximately 40 cm long. The cells of each tower are optically combined by nine longitudinally penetrating Wave Length Shifting fibers (WLS) for light collection. The light collected with nine fibers is readout by Microstrip Avalanche Photodiodes (MAPD) units having 3 × 3 mm2 sensitive areas. The towers, mechanically grouped together, form a trapezium-shape module. 2.4

Inner Tracker System

The inner tracking system consists of a silicon cylinder (see Fig. 5 (a)) and silicon disks. Supporting structures and cooling elements are optimized in order to reduce Coulomb scattering. The main objectives of ITS are the exact

23 recovery interaction vertex and reconstruction of secondary vertices in the study of hyperon production as it is shown in Fig. 5 (b). 2.5

The Other Detector Subsystem

Since the collision of heavy nuclei has a complicated space-time structure, the MPD contains a number of detector subsystems (see Fig. 1 (a)), and is specific for research in the field of heavy-ion collisions. Below the parameters and aims of some of these subsystems are discussed: 1. Zero Degree Calorimeter (ZDC) – will be used to classify of events on the centrality and for the trigger; 2. Beam-Beam Counter – is intended to use in the zero level trigger; 3. Fast Forward Detector – is intended for use for the zero level trigger and the driving signal for Time-of-Flight measurements. The MpdRoot framework [10] is used for simulation and further for data analysis. 3

Conclusion

This work was supported in part by RFBR grants No. 10 - 02 - 01 036-A and No. 11-02 - 01 026-a. References [1] I.G.Bearden et al. Phys.Rev., 93, 102301 (2005). [2] A.N.Sissakian, V.D.Kekelidze and A.S. Sorin for the NICA collaboration Nucl.Rhys. A827, p.630c (2009). [3] M.Gorenshtein et al., Phys.Lett., B567, 175 (2003). [4] < http : //nica.jinr.ru/f iles/CDR M P D/M P D CDR en.pdf >. [5] Kh.U.Abraamyam et al., NIM, A628, 99 (2011). [6] M. Anderson et al., NIM, A499, 659 (2003), nucl-ex/0301015. [7] The STAR Collaboration, “Conceptual Design Report for the Solenoidal Tracker at RHIC” , June 1992, Pub-5347. [8] ALICE Collaboration, ALICE TDR 7 “Time projection chamber” , CERN/LHCC 2000-001, January 2000. [9] ALEPH Collaboration, NIM,A294, 121 (1990). [10] < http : //nc10.jinr.ru/drupal/ >.

24 RECENT RESULTS FROM HERA COLLIDER Sergey Levonian a DESY, Notkestraße 85, 22607 Hamburg, Germany Abstract. HERA collaborations H1 and ZEUS are publishing final analyses based on complete e± p statistics of ∼ 0.5 fb−1 per experiment and using combinations of their data sets. Here selected recent results are presented from three areas: structure of the proton, searches for new physics and investigations of QCD phenomena at low Bjorken x.

1

Introduction

HERA – so far unique ep collider – ended its operation in June 2007. Since then two general purpose experiments H1 and ZEUS are finalising physics analyses using full e+ p and e− p data samples collected with unpolarised (1993-2000) and longitudinally polarised (2003-2007) lepton beams. Rich physics landscape of HERA is based upon its unique capabilities in three areas. First, it is a super-microscope with a record resolution power allowing a structure of matter to be probed down √ to 10−18 m. Second, it is a high energy frontier machine with c.m.s. energy of s = 319 GeV, which permits a search of new physics beyond the Standard Model (SM) in a way complementary to e+ e− and pp colliders. Third, it proved to be a powerful QCD laboratory, putting the theory of strong force into stringent tests, especially in low Bjorken x regime, which is one of the specifics at HERA. In this brief overview recent results from all three areas are presented. Although they represent by far not complete account of all latest HERA results, two important aspects of HERA analyses are nevertheless covered: a) precision measurements and b) search for novel phenomena, both within and beyond the SM. 2

Inclusive measurements and proton structure

Inclusive deep inelastic scattering (DIS) cross sections are measured at HERA over six orders of magnitude in negative four-momentum-transfer squared, Q2 , and in Bjorken x and used to determine proton PDFs. Combination of H1 and ZEUS data allows not only to achieve better statistical precision, but also to improve accuracy due to cross calibration of both experiments properly taking into account correlated and uncorrelated systematic uncertainties. As a result 1% precision is achieved in the bulk region for combined neutral current (NC) cross section. Combined HERA I data are used to extract the HERAPDF1.0 set [1]. Adding HERA II cross sections improved accuracy especially at high Q2 and high x domain. This combination provides HERAPDF1.5 set [2]. Figure 1 a e-mail:

[email protected]

25 illustrates inclusive NC cross sections, extracted HERAPDF1.5 at a certain scale (Q2 = 10 GeV2 ) and confronts the predictions based on those PDFs with recent LHC data on lepton asymmetry. Comparison of jets cross sections measured at Tevatron [3] with NLO QCD prediction using HERAPDF1.0 is also shown. Both comparisons show fair agreement with the data. Improvement in low x gluon density determination due to HERA data is crucial for hadron colliders. It allows to constrain basic SM processes calculation much better than before. Next step under work now is adding jet and charm data into final simultaneous global fit of proton PDFs and αs .

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26 3

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A search for new physics in most promising specific final state topologies has been recently published using ∼ 1 fb−1 of combined H1 and ZEUS data [4, 5]. Overall good agreement with the SM is found. The largest deviation of 2.6σ ∑ has been observed for multilepton events with high transverse momentum, PTl > 100 GeV, in e+ p collisions. Here new results are presented on search of contact interactions [6, 7] and leptoquarks [8] at HERA using full high Q2 NC and CC e± p statistics. New physics phenomena in l − q scattering experiments may manifest themselves in deviations of the differential cross section dσ/dQ2 from the SM expectation, and may be related to new heavy particles with √ masses MX much larger than the electroweak scale. In the low energy limit s ≪ MX such phenomena can be described by an effective four-fermion CI model. Since the data are found to be consistent with the expectation from the SM alone lower limits on the compositeness scale Λ at 95% CL are set in the range 3.6 TeV to 8.9 TeV depending on the model and the sign of the coupling coefficient. Also, search for possible quark substructure manifestations are performed using standard form factor approximation f (Q2 ) = 1 − ⟨R2 ⟩Q2 /6 (see Fig. 2). Best limit of 0.63 × 10−3 fm is set by ZEUS [6].

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New exclusion limits for 14 types of first generation scalar and vector leptoquarks are derived by H1 collaboration (see an example on the right part of Fig. 2). Assuming coupling strength of λ = 0.3 leptoquarks are ruled out up to masses of 800 GeV, which is beyond the current limits from hadron colliders.

27 4

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HERA provides wide variety of processes to study QCD dynamics in low x regime. An incomplete list includes diffraction, exclusive vector meson production, jets, heavy flavours. An interesting question is whether perturbative QCD at next-to-leading order exploiting DGLAP evolution equations is sufficient to describe HERA data, or there are experimental evidences on new dynamics beyond DGLAP. Here we present some results on multijet production in various topologies. These processes are also important because they allow a direct measurement of the strong coupling αs . On Fig. 3 measurements of inclusive

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This observation has an important impact on the hadron collider physics programme, requiring to implement alternative parton evolution schemes into Monte Carlo models, used to simulate QCD final states at the LHC. 5

Conclusions

The Standard Model survived full combined HERA data and is now waiting for next challenges expected at the LHC. Combined high precision H1 and ZEUS inclusive neutral-current and charged-current DIS cross sections provide

29 new proton PDF, in particular constraining gluon and sea quarks at low x, which allow for better precision of SM background estimate in pp collisions, thus improving the sensitivity to new physics at the LHC. NLO DGLAP QCD is surprisingly successful down to low Q2 and low x in describing bulk of HERA data. Although some room for novel parton evolution beyond DGLAP is found at specific corners of phase space, there are no unambiguous evidence for parton saturation at low x yet. References [1] [2] [3] [4] [5] [6] [7] [8] [9]

H1 and ZEUS Collab., F.D. Aaron et al., JHEP 01, 109 (2010). H1 and ZEUS Collab., H1prelim-10-142, ZEUS-prel-10-018 (2010). D0 Collab., V.M. Abazov et al., Phys. Rev. Lett. 101, 062001 (2008). H1 and ZEUS Collab., F.D. Aaron et al., JHEP 10, 013 (2009). H1 and ZEUS Collab., F.D. Aaron et al., JHEP 03, 035 (2010). ZEUS Collab., H. Abramowicz et al., ZEUS-prel-09-013 (2009). H1 Collab., F.D. Aaron et al., Phys. Lett. B 705, 52 (2011). H1 Collab., F.D. Aaron et al., Phys. Lett. B 704, 388 (2011). W. Buchm¨ uller, R. R¨ uckl and D. Wyler, Phys. Lett. B 191, 422 (1987); [Erratum-ibid. B 448, 320 (1999)]. [10] ZEUS Collab., H. Abramowicz et al., ZEUS-prel-11-005 (2011). [11] H1 Collab., F.D. Aaron et al., H1prelim-11-032 (2011). [12] H1 Collab., F.D. Aaron et al., Eur.Phys.J. C 67, 1 (2010). [13] H1 and ZEUS Collab., H1prelim-07-132, ZEUS-prel-07-025 (2007). [14] H1 Collab., F.D. Aaron et al., Eur.Phys.J. C 54, 389 (2008). [15] Z. Nagy, Z. Trocsanyi, Phys. Rev. Lett. 87, 082001 (2001).

30 ELECTROWEAK AND QCD PHYSICS WITH THE TEVATRON Andrew Alton a , for the D0 and CDF collaborations Department of Physics, Augustana College, Sioux Falls, SD, 57197, USA Abstract. New results from the CDF and D0 experiments in the topics of QCD and Electroweak physics are presented. We focus on results with photons and multiple bosons in the final state.

1

Introduction

The Tevatron allows the D0 and CDF experiments to make very precise measurements of Electroweak and QCD processes. These precision measurements allow us to test the standard model, explore for new physics and provide inputs for parton distribution functions. These measurements also allow us to constrain standard model backgrounds for other new physics searches. Due to the limited space available we only cover a handful of results by focusing on measurements with photons or multiple bosons in the final state. In addition, we include a recent and very precise measurement of sin2 θW , which was extracted from the forward-backward asymmetry of electrons in the decays of Z bosons. 2

QCD results

Our QCD result will focus on events with one or more photons in the final state. 2.1

Multiparton interactions

At hadron colliders, parton interactions are primarily due to 2-to-2 processes, where a pair of partons interact and produce a pair of resultants. The Tevatron experiments are sensitive to double parton interactions (DP), where two (or more) partons from the proton interact with two (or more) partons in the anti-proton [1]. Understanding DP can be very important for understanding backgrounds to processes such as associated Higgs production. In order to be sensitive to DP process the D0 experiment selects events which are triggered by a high energy photon and have at least two jets. For this discussion we focus on events with 3 or more jets. The photon and most energetic jet are presumed to have been initiated by the same hard scattering, while the lower energy jets are presumed to be from the less energetic scattering. Given this interpretation, we can define the ∆S variable, as shown in Fig. 1, as the separation angle between the total transverse momentum balance vectors defined by the final state products of each hard scatter. In Fig. 2 you can see a e-mail:

[email protected]

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∆S (rad)

Figure 1: This figure is used to define the varriable ∆S which is sensitive to DP events.

Figure 2: This figure shows how well different simulations model the data for ∆S

how well different models of MPI describe the data for ∆S. Generally Pythia with tune Perugia-0 and Sherpa with default MPI model work well. 2.2

Di-photon results

Processes that produce two photons can occur directly or they can happen through quark fragmentation. Both CDF and D0 [2, 3] have recently produced new measurements based on di-photon events. CDF removes background events based on tracks near the candidate photon, while D0 uses a neural net (NN) to separate photons from backgrounds. Figure 3 shows the NN output compared to Monte Carlo fake photons and real photons, as well as a pure sample of data photons from Z and photon events. The di-photon mass plot for D0 is shown in Fig. 4 and CDF’s equivalent is shown in [2]. It is clear that low mass data is not described well by any theory. The CDF experiement also examined exclusive di-photon events where the two electromagnetic (EM) objects were produced exclusively without any other objects in the event. Understanding exclusive processes may be useful for observing the Higgs boson in it’s b¯b final state. CDF observed 43 exclusive di-photons and 34 di-electron. These EM objects had a low energy threshold at 2.5 GeV. In Fig. 5 through 7 you can see a few distributions for the di-photon events and Fig. 8 shows the di-electrons mass distribution.

Events/0.05

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Figure 3: This shows the NN output of Monte Carlo fake photons and MC real photons, as well as a pure sample of data photons from Z and photon events.

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Figure 4: This figure shows the diphoton mass for D0’s data and a collection of theory discriptions.

Electroweak physics

Our electroweak results will include the extraction of sin2 θw from the forwardbackward asymmetry of di-electron pairs and studying di-boson events. 3.1

Forward-Backward asymmetry

The sample of events described as the “Z to ee” sample is actually a combination of coupling to the γ ∗ which is purely vectoral, and coupling to the Z-Boson which also has an axial component. This allows examination of the forwardbackward asymmetry to be sensitive to sin2 θw . D0 extracted a value of 0.2309± 0.0016 [4] and CDF used a different method to measure 0.2329 ± 0.0012 [5]. 3.2

Z-Boson pair production

Both experiments have made recent measurements of Z-Boson pair production. D0 has observed 10 four-lepton candidates, while CDF observed 14 four-lepton candidates. These resulted in new cross section measurements [6]. The D0 measurement in the four-lepton channel is 1.26 ± 0.49 pb, while the CDF measurement is 2.18 ± 0.70. The CDF four lepton candidate events had a cluster of events at high mass, so they examined their di-lepton and missing transverse energy sample and their di-lepton plus di-jet sample to see if they could confirm the clustering in other channels, but did not find the structure in these samples. In Fig. 9 you can find D0’s four-lepton mass distribution, while Fig. 10 shows CDF’s di-lepton mass compared to the other di-lepton mass.

33

IP IP → γ γ Data SuperCHIC MC (Normalized to data)

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CDF Run II Preliminary

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Figure 5: Exclusive di-photon mass.

22 20 18 16 14 12 10 8 6 4 2 0 0

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0.1 0.2 0.3 0.4 0.5 0.6 0.7 |π - ∆φ| (rad)

Figure 6: Exclusive di-photon angular separation.

T

Figure 7: Exclusive di-photon transverse momentum.

3.3

CDF Run II Preliminary

Events per GeV/c2

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IP IP → γ γ 18 Data 16 SuperCHIC MC (Normalized to data) 14 12 10 8 6 4 2 0 0 0.5 1 1.5 2 2.5 3 3.5 4 p of central system (GeV/c)

γ γ → e+e-

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Figure 8: Exclusive di-electron mass.

W-Boson production in association with di-jets

The CDF experiment recently [7] reported evidence for an unexpected resonance in the di-jet mass distribution when observed in conjunction with a W-boson. The D0 experiement attempted to confirm this result [8], but their results were consistent with the standard model expectation. However CDF also released an updated result and their significance has grown more substantial with new data. The D0 results exclude a resonance at a mass of 145 GeV/c2 with a cross section of more than 1.9 pb at 95 % confidence level. The CDF experiment estimates their cross section at 3.0 ± 0.7 pb. 4

Conclusions

We have presented many new QCD and Electoweak results, most of which used about half the luminosity available from the Tevatron and updates should be

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Figure 10: Di-lepton mass compared to the other di-lepton mass.

expected. Our results cover many orders of magnitude in cross sections and some have provided interesting discrepancies, while other provide possible signs of new physics. Acknowledgments The author would like to thank both experiments and the Fermilab staff. In addition we would like to acknowledge Research Corporation, the Augustana College RSA fund, and the South Dakota CUBED center for support. References [1] V. M. Abazov et al [D0 Collaboration],Phys.Rev. D83 052008(2011). [2] T.Aaltonen et al [CDF Collaboration],Phys.Lett. B690 108(2011) and http://wwwcdf.fnal.gov/physics/new/qcd/abstracts/exclusive diphoton.html [3] V. M. Abazov et al [D0 Collaboration],Phys.Lett. B690 108(2010). [4] V. M. Abazov et al [D0 Collaboration],Phys.Rev. D84 012007(2011). [5] T. Aaltonen et al [CDF Collaboration],Phys.Rev.Lett. 106 241801(2011). [6] V. M. Abazov et al [D0 Collaboration],Phys.Rev. D84 011103(2011), http://www-cdf.fnal.gov/physics/ewk/2011/zzpenn/, and http://wwwcdf.fnal.gov/physics/exotic/r2a/20110718.highmasszz/ [7] T. Aaltonen et al [CDF Collaboration],Phys.Rev.Lett. 106 171801(2011). [8] V. M. Abazov et al [D0 Collaboration],Phys.Rev.Lett. 107 011804(2011).

35 ANOMALOUS LIKE-SIGN DIMUON CHARGE ASYMMETRY Guennadi Borissov a On behalf of D0 collaboration Physics Department, Lancaster university, Lancaster, LA1 4YB, UK Abstract. I present an updated measurement of the anomalous like-sign dimuon −1 charge asymmetry Absl for semi-leptonic b-hadron decays in 9.0 fb √ of pp collisions recorded with the D0 detector at a center-of-mass energy of s = 1.96 TeV at the Fermilab Tevatron collider. The D0 collaboration obtains Absl = (−0.787 ± 0.172 (stat) ± 0.093 (syst))%. This result differs by 3.9 standard deviations from the prediction of the standard model and provides evidence for anomalously large CP violation in semi-leptonic neutral B decay. The dependence of the observed asymmetry on the muon impact parameter is consistent with the hypothesis that it originates from semi-leptonic b-hadron decays.

The D0 collaboration reported last year [1] the evidence of anomalous likesign dimuon charge asymmetry Absl using 6.1 fb−1 of data: Absl = (−0.957 ± 0.251 (stat) ± 0.146 (syst))%.

(1)

This result differs by 3.2 standard deviations from the Standard Model prediction [3] Absl (SM) = (−0.028+0.005 (2) −0.006 )%, In this talk I present the new result of the dimuon charge asymmetry using 9.0 fb−1 of data [2]. For this new measurement we improved the muon selection, which resulted in 13% increase of statistics for the same integrated luminosity and simultaneous 20% reduction of background from K → µ and π → µ decays. We also improved the measurement technique. In addition, we studied the dependence of the Absl on the muon impact parameter. The new result for 9.0 fb−1 of data is: Absl = (−0.787 ± 0.172 (stat) ± 0.093 (syst))%.

(3)

It is consistent with our previous measurement given in Eq. (1) and deviates from the Standard Model prediction by 3.9 standard deviation. The asymmetry Absl contains contributions from the semi-leptonic charge asymmetries adsl and assl of B 0 and Bs0 mesons [4], respectively: Absl = Cd adsl + Cs assl , with aqsl =

∆Γq tan ϕq , ∆Mq

(4)

where ϕq is a CP-violating phase, and ∆Mq and ∆Γq are the mass and width differences between the eigenstates of the propagation matrices of the neutral a e-mail:

[email protected]

asls

0.02

0.02

SM

Standard Model

-0.02

DØ, 9.0 fb-1

) P >120

120 µm, = (0.397 ± 0.022)adsl + (0.603 ± 0.022)assl for IP < 120 µm.

(6) (7)

The change of these contributions is influenced by the significant difference in the oscillation frequency of B 0 and Bs0 mesons. We obtain Absl Absl

= (−0.579 ± 0.210 (stat) ± 0.094 (syst))% for IP > 120 µm, (8) = (−1.14 ± 0.37 (stat) ± 0.32 (syst))% for IP < 120 µm. (9)

From these results we obtain the separate values of adsl and assl : adsl = (−0.12 ± 0.52)%, assl = (−1.81 ± 1.06)%,

(10)

which are consistent with the world average values of these quantities [5]. Figure 1(right) presents the results of the IP study in the (adsl , assl ) plane together with the result (3) of the Absl measurement using all like-sign dimuon events. The ellipses represent the 68% and 95% two-dimensional C.L. regions, respectively, of assl and assl values obtained from the measurements with IP selections. In conclusion, the new measurement of the like-sign dimuon charge asymmetry Absl is performed by the D0 experiment using 9 fb−1 of data. The obtained result deviates from the SM prediction by 3.9 standard deviations. The dependence of Absl on muon impact parameter is consistent with the hypothesis that the dimuon charge asymmetry arises from semileptonic b-hadron decays. [1] V.M. Abazov et al. (D0 Collaboration), Phys. Rev. D82, 032001 (2010); V.M. Abazov et al. (D0 Collaboration), Phys. Rev. Lett. 105, 081801 (2010). [2] V. M. Abazov et al. (D0 Collaboration), Phys. Rev. D84 052007 (2011). [3] A. Lenz and U. Nierste, J. High Energy Phys. 0706, 072 (2007). [4] Y. Grossman et al., Phys. Rev. Lett. 97, 151801 (2006). [5] D. Asner et al., Heavy Flavor Averaging Group (HFAG), arXiv:1010.1589 [hep-ex] (2010). [6] V.M. Abazov et al. (D0 Collaboration), Phys. Rev. D 82, 012003 (2010). [7] M. Gronau, J. L. Rosner, Phys. Rev. D 82, 077301 (2010).

38 FIRST LHC CONSTRAINTS ON ANOMALOUSLY INTERACTING NEW VECTOR BOSONS Mikhail Chizhov Centre for Space Research and Technologies, University of Sofia, Bulgaria Vadim Bednyakov a , Igor Boyko, Julian Budagov, Mikhail Demichev, and Ivan Yeletskikh Dzhelepov Laboratory of Nuclear Problems, Joint Institute for Nuclear Research, 141980, Dubna, Russia Abstract. It was recently proposed to extend the Standard Model by means of new spin-1 chiral Z ∗ and W ∗± bosons with the internal quantum numbers of the electroweak Higgs doublets. These bosons have unique signatures in transverse momentum, angular and pseudorapidity distributions of the final leptons, which allow one to distinguish them from other heavy resonances. With 40 pb−1 of the LHC proton-proton data at the energy 7 TeV, the ATLAS detector was used to search for narrow resonances in the invariant mass spectrum of e+ e− and µ+ µ− final states and high-mass charged states decaying to a charged lepton and a neutrino. From the search exclusion mass limits of 1.15 TeV/c2 and 1.35 TeV/c2 were obtained for the chiral neutral Z ∗ and charged W ∗ bosons, respectively. These are the first direct limits on the W ∗ and Z ∗ boson production.

1

Chiral boson model

New heavy neutral gauge bosons are predicted in many extensions of Standard Model (SM). They are associated with additional U(1)′ gauge symmetries and are generically called Z ′ bosons. The minimal gauge interactions of these bosons with matter lead to the well-known angular distribution of outgoing leptons (the Z ′ decay product) in the dilepton center-of-mass reference frame. In addition, another type of spin-1 bosons may exist, which leads to a different signature in the angular distribution. This follows from the presence of different ¯ µ (1±γ 5 )ψ and ∂ν [ψσ ¯ µν (1±γ 5 )ψ], types of relativistic spin-1 fermion currents ψγ which can couple to the corresponding bosons. The mesons assigned to the tensor quark states are some types of “excited” states as far as the only orbital angular momentum with L = 1 contributes to the total angular momentum, while the total spin of the system is zero. This property manifests itself in their derivative couplings to matter and a different chiral structure of the anomalous interactions in comparison with the minimal gauge ones. Let us assume that the electroweak gauge sector of the SM is extended by a doublet of new spin-1 chiral bosons Wµ∗ with the internal quantum numbers of the SM Higgs boson. There are at least three different classes of theories, all motivated by the Hierarchy problem, which predict new vector weak doublets with masses not far from the electro-weak scale [1]. It is possible to point out several model-independent and unique signatures which allow one to identify production of such bosons at the hadron colliders [2]. a e-mail:

[email protected]

39 Since the tensor current mixes the left-handed and right-handed fermions, which in the SM are assigned to different representations, the gauge doublet should have only anomalous interactions ( ) ( ) ) ) µν g ( g ( ∗0 ∂µ Wν∗+ ∗ ∗− µν UL L = ∂µ Wν ∂µ W ν DR σ UL DL σ DR + , (1) DL ∂µ Wν∗0 M M where M is the boson mass, g is the coupling constant of the SU(2)W weak gauge group, and U and D generically denote up-type and down-type leptons and quarks. These bosons, coupled to the tensor quark currents, can be considered as excited states. For comparison we will consider topologically analogous gauge interactions of the Z ′ boson ) g (¯ µ ¯ µd Z ′ L′N C = ℓγ ℓ + dγ (2) µ 2 with the same mass M . The coupling constants are chosen in such a way that all fermionic decay widths in the Born approximation of the both neutral bosons are identical. It means that their total production cross sections at the hadron colliders are nearly equal up to next-to-leading order corrections. Their g2 total fermionic decay width Γ = 4π M ≈ 0.034M is sufficiently narrow and they can be identified as resonances in the Drell–Yan process. Up to now, any excess in the yield of the Drell–Yan process with highenergy invariant mass of the lepton pairs remains the clearest indication of possible production of a new heavy neutral boson at the hadron colliders. The peaks in the dilepton invariant mass distributions originate from the Breit– Wigner propagator form, which is the same for both the gauge and chiral neutral bosons in the Born approximation. Concerning discovery of the charged heavy boson at the hadron colliders one believes that the cleanest method is detection of its subsequent leptonic decay into an isolated high transversemomentum charged lepton. In this case the heavy new boson can be observed through the Jacobian peak in the transverse pT (or mT ) distribution. It has become proverbial that the Jacobian peak is an inevitable characteristic of any two-body decay. However, it is not the case for decays of the new chiral bosons [3]. It has been found in [4] that tensor interactions lead to a new angular distribution of the outgoing fermions dσ(q q¯ → Z ∗/W ∗ → f f¯) ∝ cos2 θ, d cos θ

(3)

in comparison with the well-known vector interaction result dσ(q q¯ → Z ′/W ′ → f f¯) ∝ 1 + cos2 θ . d cos θ

(4)

The absence of the constant term in the first case results in very new experimental signatures [3]. The angular distribution for vector interactions (4)

40 includes a nonzero constant term, which leads to the kinematical singularity in the pT distribution of the final fermion. This singularity is transformed into a well-known Jacobian peak due to a finite width of the resonance. In contrast, the pole in the decay distribution (3) of the Z ∗ /W ∗ bosons is canceled out and the fermion transverse momentum pT distribution even reaches zero at the kinematical endpoint pT = M/2. A crucial difference between the neutral chiral bosons and other resonances should come from the analysis of the angular distribution of the final-state leptons with respect to the boost direction of the heavy boson in the rest frame of the latter (the Collins–Soper frame [5]). Instead of a smoother angular distribution for the gauge interactions a peculiar “swallowtail” shape of the chiral boson distribution occurs with a dip at ∗ cos θCS = 0. Neither scalars nor other particles possess such a type of angular behavior (see also [6]). 2

The first experimental constraints on the chiral bosons

ATLAS

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The first direct experimental search for the excited chiral vector bosons was performed by the ATLAS collaboration [7, 8] in 2010. At the LHC energy of 7 TeV with the integral luminosity around 40 pb−1 the ATLAS detector was used for searching for narrow resonances in the invariant mass spectrum above 110 GeV/c2 of e+ e− and µ+ µ− final states [9]. The main physical results relevant to our discussion are presented in Fig. 1. It is seen that both the

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Figure 1: Dielectron (left) and dimuon (right) invariant mass distribution, compared to the stacked sum of all expected backgrounds and with three example Z ∗ signals overlaid.

dielectron and dimuon invariant mass distributions are well described by the prediction from SM processes. Nevertheless, these distributions were for the first time used to obtain a lower direct mass limit of 1.152 TeV/c2 for the neutral chiral Z ∗ boson. This is the first direct mass limit on this particle. The Z ∗ limits are about 100–200 GeV/c2 more stringent than the corresponding limits on all considered Z ′ bosons.

41

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σB [pb]

Events

Furthermore, the ATLAS collaboration searched for high-mass states, such as heavy charged gauge bosons, decaying to a charged lepton and a neutrino [10]. The search for heavy charged resonances inclusively produced at the LHC looks more complicated than the search for neutral states due to the absence of the second decay particle — the undetectable neutrino. In this case the kinematic variable used to identify the W ′ /W ∗ is the transverse mass mT = √ miss miss 2pT ET (1 − cos ϕlν ). Here pT is the lepton transverse momentum, ET is the magnitude of the missing transverse momentum, and ϕlν is the angle between the pT and missing ET vectors. The main physical results relevant to our consideration are given in Fig. 2. The agreement between the data and

W Z ttbar Diboson QCD

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Figure 2: Spectra of mT for the muon decay channel (left panel). Limits at 95% C.L. for W ∗ production in the combination of both lepton decay channels (right panel). The solid lines show the observed limits with all uncertainties. From [10].

the expected background is rather good. The lower mass limits expected and obtained from these measurements are depicted in the right panel of Fig. 2. The intersection between the central theoretical prediction and the observed limits provides the 95% C.L. lower limit on the mass. It was found that the charged chiral W ∗ boson was excluded for masses below 1.350 TeV/c2 . These are the first direct limits on the W ∗ boson production. References [1] M.V.Chizhov and G.Dvali, Phys. Lett. B 703, 593 (2011). [2] M.V.Chizhov, V.A.Bednyakov, and J.A Budagov, Phys. Atom. Nucl. 71, 2096 (2008). [3] M.V.Chizhov, hep-ph/0609141. [4] M.V.Chizhov, hep-ph/0008187. [5] J.C.Collins and D.E.Soper, Phys. Rev. D 16, 2219 (1977). [6] M.V. Chizhov et al., hep-ph/1110.3149. [7] G.Aad et al., JINST 3, S08003 (2008). [8] G.Aad et al., JHEP 09, 056 (2010). [9] G.Aad et al., Phys. Lett. B 700, 163 (2011). [10] G.Aad et al., Phys. Lett. B 701, 50 (2011).

42 JETS AT TEVATRON AND LHC M.V. Tokareva , T.G. Dedovich Joint Institute for Nuclear Research, 141980 Dubna, Moscow region, Russia Abstract. Self-similarity of jet production in pp and p¯p collisions is studied in the framework of z-scaling. Inclusive transverse momentum spectra measured by CDF and D0 Collaborations at Tevatron and CMS and ATLAS Collaborations at LHC are analyzed. New results on asymptotic behavior of scaling function ψ(z) are presented. It could be interesting for study of fractal structure of momentum space at small scales.

1

Introduction

Jets are traditionally considered as a best probe of constituent interactions at high energies. It is of interest both jet production itself and search for new particles identified by the jets. New data on inclusive cross sections of jet production in pp collisions at LHC [1, 2] are analysed in the framework of zscaling [3]. The obtained results are compared with data of jet production in p¯p collisions at Tevatron [4–7]. 2

z-Scaling

The method of phenomenological description of high-pT particle production cross sections in inclusive reactions (z − scaling) developed in [3, 8] was use in the present analysis. It is based on the principles of locality, self-similarity and fractality reflecting properties of particle structure, their constituent interactions and particle formation. The collision of hadrons is assumed to be an ensemble of individual self-similar interactions of their constituents. The structures of the colliding objects (M1 ) and (M2 ) are characterized by the parameters (fractal dimensions) δ1 and δ2 . The interacting constituents carry the fractions x1 , x2 of the incoming momenta P1 , P2 . The inclusive particle (m1 ) carries the momentum p. The elementary sub-process is considered as a binary collision of the constituents (x1 M1 ) and (x2 M2 ) resulting in the scattered (m1 ) and recoil (MX ) objects in the final state. The momentum conservation law of the sub-process is written as follows 2 (x1 P1 + x2 P2 − p)2 = MX ,

(1)

where MX = x1 M1 + x2 M2 + m2 is the recoil mass. This equation is expression of the locality of the hadron interaction at a constituent level. The structural parameters δ1 , δ2 are connected with the corresponding momentum fractions by the function Ω(x1 , x2 ) = (1 − x1 )δ1 (1 − x2 )δ2 . (2) a e-mail:[email protected]

43 The quantity Ω is proportional to relative number of all such constituent configurations which contain the state defined by the fractions x1 and x2 . We use δ1 = δ2 ≡ δ, M1 = M2 , and m2 = m1 ≡ 0 in the analysis of jet production in proton-(anti)proton interactions. The parameters δ1 and δ2 were found to be constant values [3]. They are interpreted as the fractal dimensions in the space of the momentum fractions {x1 , x2 }. The scaling variable z has the form z = z0 Ω−1 . The quantity z0 are ex1/2 pressed via the transverse kinetic energy s⊥ of the sub-process consumed on the production of (m1 ) and (m2 ) and the multiplicity density dN/dη|0 at η = 0. The scaling function ψ(z) = −

πs d3 σ J −1 E 3 . (dN/dη)σin dp

(3)

is expressed in terms of the inclusive cross section, multiplicity density dN/dη, and total inelastic cross section σin . Here s is the square of the center-of-mass energy, and J is the corresponding Jacobian. The function ψ(z) is normalized to unity.

a) b) √ Figure 1. Inclusive spectra of jet production in pp collisions at s = 7000 GeV √ Figure 1: √ Inclusive spectra of jet production in pp collisions at s = 7000 GeV and in p¯p col0 lisions at s = 630, 1800, 1960 GeV and θ ≃ 90 measured by the CMS [1] and the D0 [4, 5] (a) and CDF [6, 7] (b) Collaborations in z-presentation, respectively.

3

Self-similarity of jet production at LHC

The inclusive jet cross section measures the probability of observing a hadronic jet produced in a hadron-hadron collisions. A jet is a direct evidence of hard interaction of hadronic constituents (quarks and gluons). New LHC √ data [1, 2] on inclusive cross sections of jet production in pp collisions at s = 7000 GeV are analized in framework of z-scaling and compared with Tevatron data [4–7]. These data allow √ us to study the energy dependence of the function ψ(z) over a wide range of s = 630−7000 GeV. Figure 1 shows the z-presentation of jet spectra measured by CMS Collaboration at LHC and by D0 (a) and CDF (b) Collaborations at Tevatron. All data demonstrate the

44

with Tevatron data [4–7]. These data allow √us to study the energy dependence of the function ψ(z) over a wide range of s = 630 − 7000 GeV.

a)

b)

√

√

Figure 2: Inclusive spectra of jet production in pp collisions at s = 7000 GeV and different pseudorapidity intervals in z-presentations. Experimental data obtained by the CMS and ATLAS Collaboration are taken from [1, 2].

energy independence of the scaling function. The power behavior of ψ(z) is observed over a wide range of z. The function ψ(z) changes more than on twelve orders of magnitude. The dashed line corresponds to asymptotic behavior of ψ(z). Some deviation of data from the asymptotic behavior of the scaling function for z < 102 is observed. The collected by the CMS Collaboration the data correspond to the integrated luminosity of 34 pb−1 . The jet spectra are measured up to transverse momentum pT = 1000 GeV/c. Nevertheless the minimal value of ψ(z) at √ z ≃ 7 · 103 is reached at Tevatron energy s = 1960 GeV. Figure 2 demonstrates inclusive spectra [1,2] of jet production in pp collisions √ at a center-of-mass energy s = 7000 GeV, over the momentum pT = 20 − 1350 GeV/c and pseudorapodity |η| < 4.4 range in z-presentations. Both CMS and ATLAS data demonstrate the angular independence of ψ(z). The function is described by the power law, ψ(z) ∼ z −β , with a constant value of the slope parameter β. The results of analysis of LHC data are in a good agreement with CDF and D0 data on angular dependence of jet spectra [9]. The collected by the ATLAS Collaboration the data correspond to the integrated luminosity of 37 pb−1 . The spectra are measured over the range of pT = 25 − 1350 GeV/c. The minimal value of ψ(z) at z ≃ 104 is reached. The obtained results give us new confirmation that self-similarity of jet production is valid up to 10−4 fm. In [9] was found that the NLO QCD predictions demonstrate dramatic deviation from the asymptotic behavior of ψ(z) predicted by the z-scaling. The behavior was not reproduced by the NLO QCD evolution of cross sections with the phenomenological parton distribution functions used in the analysis [9]. We conclude that the asymptotic behavior of ψ(z) could be used as the additional constraint on a gluon distribution function in the global QCD analysis of √ experimental data including new LHC data on spectra of jet production at s = 7000 GeV.

45 4

Conclusions

New data on jet spectra obtained by CMS and ATLAS Collaborations at LHC up to highest jet transverse momentum pT ≃ 1350 GeV/c confirm the energy and angular independence of the z-scaling found at Tevatron energies. The observed power behavior of the scaling function indicates that properties of mechanism of jet production reflect the self-similarity, locality and fractality of the hadron interactions at a constituent level. We assume that the verification of the asymptotic behavior of the scaling function, ψ(z) ∼ z −β , of jet production at higher transverse momentum pT > 2000 GeV/c could give information on fractal structure of momentum space. References [1] C. Dragoiu (for CMS Collab.), XIX Int. Workshop DIS2011, April 11-15, 2011, Newport News, VA, USA; http://conferences.jlab.org/DIS2011/; arXiv:1106.0208v1 [hep-ex] 1 Jun 2011. [2] J. Zhang (for ATLAS Collab.), XIX Int.Workshop DIS2011, April 11-15, 2011, Newport News, VA, USA; http://conferences.jlab.org/DIS2011/ [3] M.V. Tokarev, T.G. Dedovich, Int. J. Mod. Phys. A 15, 3495 (2000). [4] B. Abbott et al., Phys. Rev. Lett. 82, 2451 (1999);Phys. Rev. D 64, 032003 (2001). D. Elvira, Ph.D Thesis Universodad de Buenos Aires, Argentina (1995). V.M. Abazov et al., Phys. Lett. B 525, 211 (2002); Phys. Rev. Lett. 101, 062001 (2008). [5] M. Begel et al. (D0 Collab.), hep-ex/0305072. M. Voutilainen (for D0 Collab.) XIV Int.Workshop DIS2006, April 20-24, 2006, Tsukuba, Japan; http://www-conf.kek.jp/dis06/ J. Commin (for D0 Collab.) XV Int. Workshop DIS2007, April 16-20, 2007, Munich, Germany; http://www.mppmu.mpg.de/dis2007/ [6] F. Abe et al., Phys. Rev. Lett. 77, 438 (1996). T. Affolder et al., Phys. Rev. D 64, 032001 (2001). [7] A. Abulencia et al., Phys. Rev. Lett. 96, 122001 (2006); Phys.Rev. D 74, 071103 (2006); Phys.Rev. D 75, 092006 (2007). [8] I. Zborovsk´ y, M. V. Tokarev, Phys. Rev. D 75, 094008 (2007). [9] M. V. Tokarev, T. G. Dedovich, in “Relativistic Nuclear Physics and Quantum Chromodynamics” (Proceedings of the XIX International Baldin Seminar on High Energy Physics Problems, September 29 - October 4, 2008, Dubna, Russia), ed. by A. N. Sissakian, V. V. Burov, A. I. Malakhov, S. G. Bondarenko, E. B. Plekhanov, JINR, Vol.2, pp.187-197, 2008.

46 SUSY SEARCHES AT ATLAS Margherita Primavera a on behalf of the ATLAS Collaboration INFN Section of Lecce, Department of Physics, University of Salento, 73100 Lecce, Italy Abstract. Supersymmetry (SUSY) predicts a new symmetry between fermions and bosons and it is one of the most favoured theories to describe physics beyond the Standard Model (SM). If SUSY particles are not too heavy, but accessible at TeV scale energies, LHC provides an excellent opportunity to test the validity of SUSY √ models. Searches for SUSY signals in proton-proton collisions at s =7 TeV with the ATLAS detector [1] are presented.

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Introduction

SUSY is one of the most popular extensions of the Standard Model of particle physics. It postulates that every fundamental Standard Model fermion has a boson partner and vice versa and defines the R-parity quantum number as (−1)2s+3B+L . It naturally solves the mass hierarchy problem and, in the case in which R-Parity is conserved, provides a candidate for dark matter in the form of the Lightest Supersymmetric Particle (LSP), produced at the end of all sparticle cascade-decay and which must be stable. Since the LSP is a weakly interacting particle, it escapes detection giving rise to large missing transverse energy (ETmiss ). Due to the fact that the production of coloured sparticles should be favoured at the LHC, high-pT jets are also expected in the final state. In addition, different numbers of high-pT leptons, which can arise from model-dependent cascades to the LSP, can be produced. Searches are then performed in events with large ETmiss and jets, in association with ≥ 0 leptons or 2 photons. Other searches are also performed for various R-Parity violating SUSY scenarios, which can produce different experimental signatures like electron-muon resonances, and for metastable massive particles like R-hadrons.

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In the 0-lepton search [2], updated with ∼1 fb−1 of 2011 data, events which contain leptons with pT > 20(10 for muons) GeV are explicitly vetoed. Events are accepted in the selection if they have large ETmiss (> 130 GeV), a high-pT leading jet (> 130 GeV) and at least two, three or four jets in the final state. The discriminating variable mef f is defined as the scalar sum of the pT of the a e-mail:

[email protected]

47 jets plus ETmiss , and five signal regions are identified, mainly by cutting on different values of mef f . The SM processes contributing to the background are: the irreducible Z → νν + jets, W → lν in which the lepton candidate falls outside the detector acceptance, tt and QCD, where misreconstruction of jet energies in calorimeters leads to fake missing transverse momentum, or neutrinos are produced in the semileptonic decay of heavy quarks. To estimate the background, several control regions are defined for each of the signal regions, optimized to provide data samples enriched in specific background sources. No excess of events over the background expectation is seen in any of the five signal regions, and exclusion limits have been set in the (m0 ,m1/2 ) mSUGRA/CMSSM plane [3, 4] (Fig. 1). Squarks and gluinos of equal mass have been excluded at 95% C.L. for masses below 980 GeV. m1/2 [GeV]

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1-lepton search

In the one-lepton analysis [5], updated with 165 pb−1 of 2011 data, selected events are required to contain exactly one electron (pT > 25 GeV) or muon (pT > 20 GeV), and at least three jets with energy greater than 25 (60 for the leading jet) GeV. The main backgrounds are expected to come from tt and W+jets. The signal region is defined in terms of the effective mass, that includes the lepton pT in the calculation. In absence of any excess in mef f > 500 GeV region, the result has been interpreted as a limit in the mSUGRA/CMSSM plane (Fig. 1). In the specific case in which the gluino and the squark have equal mass, masses below 750 GeV have been excluded at 95% C.L.

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2.4

2-lepton search.

SUSY searches for events with ETmiss and two high-pT leptons in the final state were carried out in ATLAS using the full 2010 dataset [7]. Three analyses are performed: same-sign and opposite-sign searches, looking for pairs of leptons with same or opposite charge but no requirement on flavour (electron or muon), and the flavour subtraction analysis [8], looking for any excess beyond the SM expectations of high ETmiss (> 100 GeV) events containing opposite charge identical flavor lepton pairs, which could prove a signal of new physics. The main background sources are tt events for the opposite-sign analysis, and events

49 containing fake or misidentified leptons for the same-sign analysis. No excess has been observed in the signal regions for all three analyses. For each analysis, these results have been interpreted as limits in the parameter spaces of three different SUSY models: the mSUGRA/CMSSM, and two classes of MSSM models, one with a compressed SUSY particle mass spectrum and another with a light neutralino. Depending on model assumptions, squarks with masses between 450 and 690 GeV have been excluded, in the case where squarks are approximately mass degenerate and lighter than gluinos. 2.5

2-photon search

In Gauge Mediated SUSY Breaking (GMSB) models the LSP is the gravitino ˜ In the case in which the next-to-LSP is bino-like, the final decay in a chain G. could be dominated by a neutralino decaying to a photon and a gravitino, leading to final states with two photons. Similar topologies are also expected in Universal Extra Dimension (UED) models. ATLAS looks for events with two photons and large ETmiss (> 125 GeV) in the final state [9]. No excess of events above the SM prediction is, and a 95% C.L. limit of 560 GeV has been set on the gluino mass in the context of a Generalized GMSB model with a bino-like χ01 with mass > 50 GeV. 3

eµ resonance search

In some R-Parity violating SUSY models which do not conserve flavour, a ν˜τ can decay into e± µ∓ , a clean experimental signature with low background. ATLAS performs searches for these events using the 2010 and a part (870 pb−1 ) of 2011 datasets [10]. No excess of events above the expected SM background is observed analyzing the meµ spectrum. For a tau sneutrino with a mass of 100 GeV (1 TeV) the limit at 95% C.L. on the production cross section times branching ratio is set to 130(11) fb. 4

Stable massive particle search

Massive Long-Lived Particles (LLP) are predicted in several SUSY models and in other BSM theories. These particles are slow (β < 1) and highly ionizing, and their mass could be measured from β and the momentum p. While coloured LLPs could hadronize forming R-hadrons, i.e. bound hadronic states of squarks or gluinos and light quarks or gluons which could be electrically charged or neutral, or could even change charge due to interactions with detector material, long-lived sleptons could interact like heavy muons. ATLAS has produced final results on two separate analyses that look for LLPs. A first analysis [11] primarily uses muon signals, searching for: a) long-lived sleptons identified in both the inner detector and in the muon spectrometer and b) R-hadrons candidates in the muon spectrometer, with inner detector and calorimeter signals

50 used if available. Neither a) or b) observe an excess above the SM estimated background: stable τ˜ sleptons have been excluded and 95% C.L. limits up to a mass of 136 GeV in specific GMSB models and gluino R-hadrons have been excluded, in a Split SUSY model, up to masses of 530 to 544 GeV depending on the fraction of R-hadrons produced as g˜-balls. A second analysis [12], complementary to the first one, searches for R-hadrons which could be neutral in the muon spectrometer, looking for a large dE/dx deposition in the pixel detector and long time of flight in tile calorimeter, both used to compute R-hadron β and mass. At 95% C.L. lower limits on the masses of stable sbottoms, stops and gluinos were set respectively to 294, 309, and from 562 to 586 GeV depending on the model of hadronic scattering in matter (Fig. 2). 5

Conclusions

The excellent LHC and ATLAS performance in 2010 and 2011 data taking campaign has allowed to perform many searches for Supersymmetry, optimized for different signatures. No deviation from the Standard Model prediction have been observed in data, and both new limits on the masses of the SUSY particles and larger exclusion regions in the parameter space of different models have been set. Several factors larger dataset are already available to be analyzed, and a broader reach to new phenomena is expected soon. References [1] The ATLAS Collaboration, JINST 3, S08003 (2008). [2] The ATLAS Collaboration, Phys. Lett. B701, 186 (2011). [3] A.H. Chamseddine, R.L. Arnowitt, P. Nath, Phys. Rev. Lett. 49, 970 (1982); R. Barbieri, S. Ferrara, C.A. Savoy, Phys. Lett. B119, 343 (1982); L.E. Ibanez, Phys. Lett. B118, 73 (1982); L.J. Hall, J.D. Lykken, S. Weinberg, Phys. Rev. D27, 2359 (1983); N. Ohta, Prog. Theor. Phys. 70, 542 (1983) 48. [4] G.L. Kane et al., Phys. Rev. D49, 6173 (1994) [5] The ATLAS Collaboration, Phys. Rev. Lett. 106, 131802 (2011). [6] The ATLAS Collaboration, Phys. Lett. B701, 398 (2011). [7] The ATLAS Collaboration, Eur. Phys. J. C71, 1682 (2011). [8] The ATLAS Collaboration, Eur. Phys. J. C71,1647 (2011). [9] The ATLAS Collaboration, Eur. Phys. J. C71, 1744 (2011). [10] The ATLAS Collaboration, Phys. Rev. Lett. 106, 251801 (2011); the ATLAS Collaboration, ATLAS-CONF-2011-109. [11] The ATLAS Collaboration, Phys. Lett. B701, 428 (2011). [12] The ATLAS Collaboration, Phys. Lett. B703, 1 (2011).

51 SEARCHES FOR SUPERSYMMETRY WITH THE CMS EXPERIMENT Altan Cakir a , on behalf of the CMS Collaboration Deutsches Elektronen-Synchrotron, 22607, Hamburg, Germany Abstract. After a very successful startup of the LHC in 2010, the CMS experiment has already accumulated significantly more data in 2011. After the successful rediscovery of the Standard Model, the search for signs of new physics has already reached, and in most cases enlarged, the limits from previous experiments. In this conference report I review the recent discovery reach of SUSY searches that will be performed with the 2011 data.

1

Introduction

High energy and particle physics enter a new era with the start-up of the Large Hadron Collider (LHC) at CERN, a proton-proton accelerator located at the Swiss-French border with a circumference of 27 km. The LHC provides a new energy regime to explore the origin of the electroweak symmetry breaking, search for and study Supersymmetry (SUSY) or other Beyond the Standard Model (BSM) physics scenarios. Physics beyond the SM is expected to consist of new heavy particles, otherwise these particles would have been discovered already at previous accelerators. These heavy particles decay to lighter particles, which will have higher transverse momentum (PT ) with respect to the beam axis than decay products of light particles. In addition, SUSY is expected to produce missing transverse energy (ETM iss ) due to the escaping the lightest supersymmetric particle (LSP), √ neutralinosb , candidate for dark matter [1]. At s = 7 TeV center-of-mass energy, the production cross-sections may be sufficient such that a data sample of modest integrated luminosity, 1.1fb−1 could contain a large number of new particles. The Compact Muon Solenoid (CMS) is an experiment [2] designed to find evidence for new physics beyond SM using a signature of high-energy objects in the final state. The signatures expected for new physics have been taken into consideration extensively in the design of the experiment. In this report various SUSY analyses based on signatures involving jets, leptons, and missing transverse momentum are discussed. These analyses are designed to be simple and generic, focusing on basic topological and kinematic properties that typically characterize SUSY signatures at the LHC. This conference report is organized as follows: the search for a missing energy signature in di-jet and multi-jet events using the αT variable is discussed a e-mail:

[email protected] R-parity, R=(−1)3(B−L)+2S where B and L are baryon- and lepton numbers, respectively and S is the spin, is conserved. All SM particles have even R-parity, while SUSY particles are R-odd. b Assuming

52 for Hadronic SUSY searches. In the following sub-section two analyses with leptonic signature, one requiring two same-charge leptons and the other requiring opposite-charge leptons are presented, respectively. To interpret the results, a practical model of SUSY breaking, the constrained minimal SUSY model (cMSSM c ) is discussed. 2 2.1

SUSY searches Results for hadronic SUSY searches with αT parameter

The kinematic variable αT was first defined for di-jet [3] and subsequently extended to n-jet events [4]. In hadronic SUSY searches it is based on the assumption that colored particle (squark-squark, gluino-gluino, or gluino-squark) are pair-produced and subsequently decay directly to a quark and neutralino. The extension to n-jets allows sensitivity to beyond the direct decay. This approach is the most promising for points in a SUSY parameter space where squarks have large branching ratios to decay directly to the LSP.

Figure 1: Comparison of the αT (left) and HT (right) distribution between data and MC.

The data sample used in this analysis is recorded with a trigger based on the scalar sum of the transverse energy ET of jets, defined in general as HT jet ji = ΣN i=1 ET , where Njet is the number of jets. Events are selected if they satisfy HTtrigger > 375 GeV. The expected event topology consists of two or more high pT jets and two invisible neutralinos leading to a missing transverse energy signature. The main background processes for this topology are QCD di-jet events and Z+jets where Z decays into two invisible neutrinos. Figure 1 demonstrates that the αT variable is an excellent discriminator between QCD c The cMSSM is described by five parameters: the universal scalar and gaugino mass parameters (m0 and m1/2 , respectively), the universal trilinear soft SUSY breaking parameter A0 , and two low-energy parameters, the ratio of the two vacuum expectation values of the two Higgs doublets, tanβ, and the sign of the Higgs mixing parameter, sign(µ). The parameter values defining LM4 are 210, 285, 0, 10, + and LM6 are 85, 400, 0, 10, +, respectively.

53 background and signal. Though the Monte-Carlo (MC) simulation describes the data reasonably well, the background yields are obtained from data control samples. The ratio RαT = NαT >θ /NαT 0.55 is chosen such that the numerator of the ratio in all HT bins is dominated by tt¯, W +jets and Z→ ν ν¯ + jets events. Figure 2 shows that data are consistent with SM by predictions. Data-driven techniques are also used to estimate the tt¯ by W→lν, and the Z background from γ+jets events.

Figure 2: The dependence of RαT (left) on HT for events with Njets ≥ 2. HT (right) distribution for the events observed in data, the outcome of the fit (light blue line) and a breakdown the individual background contributions as predicted by the control samples.

The results are currently based on an integrated luminosity of 1.1fb−1 . The observed yield is consistent with the predictions from MC and from the datadriven background estimates, so that no evidence for SUSY signal is observed. 2.2

Results for leptonic SUSY searches

Dileptonic events with Same Charge The requirement of same-sign, isolated, dileptons, as the Standard Model backgrounds are naturally expected to be small, makes this a very appealing channel to study [5]. Muon, electron, and tau candidates with pT as low as 5, 10, and 15 GeV respectively, and with |η| < 2.4, are used to define the dilepton final states. All events considered for search regions are required to have two leptons with the same charge, at least two jets, and ETM iss above 30 GeV. The requirement of at least two jets provides a universal requirement of HT > 80 GeV. The following selection cuts for four different search regions are defined: 1. The requirement of HT > 400 GeV and ETM iss > 120 GeV, provides a high sensitivity to the low values of m0 , as in LM6. 2. The requirement of HT > 200 GeV and ETM iss > 50 GeV, provides a high sensitivity to mass-splittings between gluinos/squarks and charginos/ neutralinos.

54

Figure 3: Summary of background predictions and observed yields in the search regions for the inclusive (left) selections, dilepton candidates with HT > 200 GeV, and and high-pT dilepton selections (right), dilepton candidates with both leptons having pT > 10 GeV, at least one lepton having pT > 20 GeV and no HT requirement beyond HT > 80 GeV.

3. The requirement of HT > 400 GeV and ETM iss > 50 GeV, provides a high sensitivity the high values of m0 . 4. The requirement of HT > 80 GeV and ETM iss > 100 GeV, provides a high sensitivity to models predicting low hadronic activity with a high ETM iss . Figure 3 summaries the result of searches for new physics with same-sign dilepton events in the ee, µµ, eµ, eτ , µτ , and τ τ final states. No evidence for an excess over the background prediction has been seen at L=0.98fb−1 . Dileptonic events with opposite charge This analysis focuses on events with opposite charge leptons pairs (e+ e− , e+ µ− , e− µ+ , µ+ µ− ) jets and ETM iss in the final state [6]. Due to the decay χ02 → ˜ χ0 ℓ± ℓ± in the cMSSM, a characteristic kinematic edge is expected in the ℓ˜ℓ→ 1 invariant dilepton mass distributions. In the following two signal regions are defined by motivating requirements of large ETM iss and HT : 1. High ETM iss signal region: HT > 300 GeV and ETM iss > 275 GeV 2. High HT signal region: HT > 600 GeV and ETM iss > 200 GeV Three independent data-driven estimation methods are used to perform counting experiments in these signal regions. For both signal regions, the observed yield is consistent with the predictions from MC and from the data-driven background estimates based on observed data (Figure 4). It is concluded that no evidence for non-SM contributions to the signal regions is observed at L=0.98fb−1 data.

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Figure 4: Summary of background predictions and observed yields in the search regions for the ETM iss distributions that signal regions are indicated by the vertical lines in the plots.

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Interpretation of results and outlook

The results of the hadronic (αT ) and leptonic (same-sign and opposite-sign) SUSY searches are interpreted in the context of cMSSM model [7]. In the absence of a signal, limits on the allowed parameter space in the cMSSM were set which exceed those set by previous analyses.

Figure 5: Exclusion regions in the cMSSM corresponding to the observed limit from SUSY searches. The exclusion contours based on 34pb−1 2010 data are also displayed.

No evidence for SUSY signature has yet been observed at L=1.1fb−1 data. The CMS collaboration expects to collect L=5fb−1 of data by the end of 2011. References [1] [2] [3] [4]

S. P. Martin, arXiv:hep-ph/9709356. The CMS Collaboration JINST 3 (2008) S08004 doi:10.1088/1748-0221 L. Randall and D. Tucker-Smith, Phys. Rev. Lett. 101, 221803 (2008). The CMS Collaboration, PAS SUSY-11-003.

56 [5] The CMS Collaboration, PAS SUSY-11-010. [6] The CMS Collaboration, PAS SUSY-11-011. [7] The CMS Collaboration, PAS SUSY-11-016.

57 PHOTON AND DI-PHOTON PRODUCTION AT ATLAS Marco Delmastro a b CERN c Abstract. The latest ATLAS measurements of the cross section for the inclusive production of isolated prompt photons in pp collisions at a centre-of-mass energy √ s = 7 TeV at the LHC are presented, as well as the measurement of the di-photon production cross section.

1

Overview

The production of prompt photons at hadron colliders provides means for testing perturbative QCD predictions, providing a colorless probe of the hard scattering process. The dominant production mechanism of single photons in pp collisions at the Large Hadron Collider (LHC) energies is qg → qγ, while the production of di-photon final states mainly occurs through quark-antiquark annihilation, q q¯ → γγ, and gluon-gluon interaction gg → γγ mediated by a quark box diagram. In both single and di-photon final states, parton fragmentation to photon also contributes. Because of the main production mechanism, the measurement of the inclusive photon cross section at the LHC can constrain the gluon density in protons. The study of the distribution of the azimuthal separation between the two photons in di-photon events can provide insight on the fragmentation model, while for balanced back-to-back di-photons the di-photon cross section is sensitive to soft gluon emission, which is not accurately described by fixed-order perturbation theory. Di-photon production is also an irreducible background for some new physics processes, such as the Higgs decay into photon pairs. We present here two measurements of the inclusive isolated prompt photon γ , production cross section as a function of the photon transverse energy ET using pp collision data collected in 2010 with the ATLAS detector [4] at the LHC at a center-of-mass energy of 7 TeV. The former is based on an integrated ∫ luminosity L dt = (0.88 ± 0.1) pb−1 [1], and provides a measurement of the γ < 100 GeV in the photon pseudorapidity η intervals cross section for 15 ≤ ET [0,0.6), [0.6,1.37) and [1.52,1.81). The latter uses the full 2010 data sample ∫ γ γ range L dt = (36.4 ± 1.2) pb−1 [2], covering the 40 ≤ ET < 400 GeV ET and extending to the [1.81,2.37) pseudorapidity region. We also present the measurement of the inclusive di-photon cross section as a function of the di-photon invariant mass mγγ , the di-photon system momentum pT,γγ and the azimuthal ∫ separation between the two photons ∆ϕγγ , using an integrated luminosity L dt = (36.0 ± 0.1) pb−1 [3]. a e-mail:

[email protected] behalf of the ATLAS Collaboration c The author is now at LAPP (IN2P3/CNRS, France). b On

58 2

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Single photon events are triggered in ATLAS using a high-level trigger with a nominal transverse energy threshold of 10 GeV [1] or 40 GeV [2]; di-photon γ events are triggered by two photon candidates having ET > 15 GeV [3]. Using unbiased or lower-threshold triggers, these triggers are found to be fully efficient for photons and di-photons passing the selection criteria of the analyses. Photon candidates depositing their energy in the ATLAS Liquid Argon (LAr) electromagnetic calorimeter (EMC) in the regions |η| 5.10−6 . The main uncertainty on this measurement comes from the luminosity calibration which has a precision of 3.7%. The figure also shows the result for the model-dependent extrapolation to the full inelastic cross-section: σinel = 69.4 ± 2.4(exp.) ± 6.9(extr.), where extr. expresses the additional uncertainty obtained using different model extrapolations. Data values are found to be lower than MC predictions, but the extrapolated value agrees with most analytic models.

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√ Figure 4: The inelastic cross-section versus s . The ATLAS measurement for ξ > 5.10−6 is shown as the red filled circle and compared with the predictions of Schuler and Sjostrand and Phojet for the same phase space. Data (filled circles for pp data and unfilled circles for p¯p data) from several experiments are compared with the predictions of the pp inelastic cross-section from Schuler and Sjostrand (as used by Pythia), by Block and Halzen and by Achilli et al. An extrapolation from the measured range of ξ > 5.10−6 to the full inelastic cross-section using the acceptance of 87±10% is also shown (blue filled triangle). The experimental uncertainty is indicated by the error bar while the total (including the extrapolation uncertainty) is represented by the blue shaded area.

66 5

Summary

In the first years of LHC running, ATLAS successfully performed a number of different soft QCD measurements. An inelastic cross-section of 60.3 ± 2.1 √ is measured for ξ > 5.10−6 at s=7 TeV, setting a new reference for the inelastic cross-section at this collision energy. Charged particle distributions, underlying event distributions, two-particle correlations in pp collisions at 900 GeV and 7 TeV have been presented. These are important inputs for MC tuning purposes, since most of the pre-LHC models do not show satisfactory agreement with data. The new AMBT1 and subsequent tunes represent first improvements for soft QCD results. Overall these studies show that there is still room for improvement of the phenomenological models that describe soft QCD at the new energy-scale accessible by the LHC. References [1] ATLAS Collaboration,“The ATLAS Experiment at the CERN Large Hadron Collider,” JINST 3, S08003 (2008). [2] ATLAS Standard Model Public Results twiki page: https://twiki.cern.ch/ twiki/bin/view/AtlasPublic/StandardModelPublicResults

[3] ATLAS Collaboration, “Charged-particle multiplicities in pp interactions measured with the ATLAS detector”, New J. Phys. 13, 053033 (2011). [4] ATLAS Collaboration,“ Measurement of underlying event characteristics √ using charged particles in pp collisions at s = 900 GeV and 7 TeV with the ATLAS detector,” Phys. Rev. D 83, 112001 (2011). [5] ATLAS Collaboration, “Measurements of underlying-event properties using neutral and charged particles in pp collisions at 900 GeV and 7 TeV with the ATLAS detector” Eur. Phys. J. C71, 1636 (2011). [6] ATLAS Collaboration,“ATLAS tunes of PYTHIA6 and PYTHIA8 for MC11”, ATLAS public note, ATL-PHYS-PUB-2011-009 (2011) [7] ATLAS Collaboration “Charged particle multiplicities in pp interactions with ATLAS and AMBT1 tune”,ATLAS-CONF-2010-031 (2010) [8] ATLAS Collaboration, “Measurement of Inclusive Two-Particle Angular √ Correlations in pp Collisions at s=900 GeV and 7 TeV”, 2011. ATLASCONF-2011-055. [9] Sjostrand, T. Mrenna, S. Skands, P. “A brief introduction to Pythia 8.1”. Comput. Phys. Commun. 178, 852-867 (2008) [10] Engel, R. “Photoproduction within the two component dual parton model: amplitudes and cross-sections”. Z. Phys. C66, 203-214 (1995) [11] Field, R. “Min-bias and the underlying event at the Tevatron and the LHC”. Talk presented at the Fermilab MC Tuning Workshop, Oct (2002). [12] √ ATLAS Collaboration, “Measurement of the inelastic pp cross-section at s=7 TeV with the ATLAS detector” , Nature. Com. 2 463 (2011)

67 EXOTIC PHYSICS SEARCHES WITH THE ATLAS DETECTOR James Frost a , (On behalf of the ATLAS Collaboration) Department of Physics, Cavendish Laboratory, JJ Thomson Avenue, Cambridge, CB3 0HE, UK Abstract. A selection of the most recent ATLAS results of searches for new physics phenomena are detailed. The proton-proton collision data were collected up to the first half of 2011 with the ATLAS detector at 7 TeV centre-of-mass energy produced by the LHC. Summaries are given of leptonic search signatures, of dilepton resonances, and of a charged lepton and neutrino, interpreted in the context of heavy gauge bosons and Randall-Sundrum gravitons. A search for monojet final states is detailed, and limits placed on large extra-dimensional models. The most recent ATLAS results for dijet resonances are described. Two other search results are outlined: a study of the dijet invariant mass in events with an associated W boson, and a search for first or second generation scalar leptoquarks.

1

Search for dilepton resonances

Several extensions of the Standard Model predict narrow high-mass resonances, which decay into e+ e− or µ+ µ− pairs. Such models include new heavy spin1 neutral gauge bosons, such as Sequential Standard Model Z ′ [1] or excited boson Z ∗ [2], in adition to spin-2 Randall-Sundrum gravitons, G∗ [3]. The ATLAS detector has been used to search for such resonances in the dilepton invariant mass spectrum [4]. Integrated luminosities of 1.08 fb−1 and 1.21 fb−1 of proton-proton collision data has been used for the e+ e− and µ+ µ− channels respectively. The predominant Standard Model background is the Drell-Yan process, Z/γ ∗ , resulting in the same final state. No deviations from Standard Model expectations are observed; consequently limits are set on the cross section times branching fraction, σB. The resulting combined limits at 95% C.L. using a Bayesian approach are 1.83 TeV for the Sequential Standard Model Z ′ boson, and in the range 0.71 − 1.63 TeV for a Randall-Sundrum ¯ P l , in the range 0.01−0.1. These Z ′ boson limits graviton with couplings, k/M are the most stringent set to date. 2

Search for a heavy neutral particle decaying into an electronmuon pair

The ATLAS Collaboration has searched for neutral new particles which decay into two leptons of differing flavour and opposite charge [5]. Examples include sneutrinos in R-parity violating supersymmetric theories and new gauge bosons (Z ′ ) with lepton-flavour violating interactions. The eµ final state provides a clean detector signature, with little Standard Model background in the high meµ signal region. A luminosity of 0.87 fb−1 of 7 TeV collision data is analysed a e-mail:

[email protected]

68 and no deviations from Standard Model predictions are observed. At 95% C.L., an upper limit, σB(Z ′ → eµ) < 11 fb is set for Z ′ masses above 700 GeV. Exclusion limits are also placed on the production cross section and R-parity violating couplings for τ -sneutrinos. 3

Search for a heavy gauge boson decaying into a charged lepton and a neutrino

Extensions to the Standard Models predicting new heavy gauge bosons [6] can also be investigated through the decay signature of the new charged bosons (W ′ ) to a charged lepton, e or µ, and a neutrino. The ATLAS Collaboration has recently completed such a search, using 1.04 fb−1 of 7 TeV pp collision √ data [7]. The discriminating variable used is the transverse mass, mT = 2pT ETmiss (1 − cos ϕlν ), with a signal manifest as a Jacobian peak lying at high mass on the irreducible background formed by the tail of the Standard Model W boson decay to the same final state. In the absence of an excess, 95% C.L. limits are placed upon the cross section times branching fraction; Sequential Standard Model W’ bosons with masses up to 2.15 TeV are excluded. These are the best available limits for mW ′ > 600 GeV. 4

Searches in dijet mass distributions

Dijet mass distributions have shown themselves to be useful tools for investigating new phenomena, and for searching for resonances indicative of new physics. The most recent ATLAS results [8] are obtained from the analysis of 0.81 fb−1 of 2011 pp collision data. Data events with dijet masses up to 4 TeV are observed, and no evidence of resonant production is found. Limits are set for several new physics scenarios: excluded at 95% C.L. are excited quarks with masses below 2.91 TeV, axigluon masses up to 3.21 TeV and color octet scalar resonances lighter than 1.91 TeV. 5

Searches in monojet plus missing transverse momentum final states

The ATLAS experiment has recently reported a search for new physics in the monojet plus large missing transverse energy final state, which has been updated to a 2011 data sample corresponding to an integrated luminosity of 1.00 fb−1 [9]. The dominant Standard Model backgrounds, are electroweak gauge boson decays to neutrinos. Model-independent 95% C.L. upper limits are set on the fiducial cross section for the non-Standard Model production of these final states, varying between 2.02 pb and 0.045 pb. Additionally, an

69 interpretation is made in terms of the Large Extra Dimensions model [10]. Values of the fundamental (4+n)-dimensional Planck scale, MD , between 3.2 and 2.0 TeV are excluded for 2 − 6 extra dimensions. 6

Invariant mass distribution of jet pairs produced in association with a leptonically decaying W boson

ATLAS has performed a study of the invariant mass of jet pairs produced in association with a W boson which decays leptonically, using 1.02 fb−1 of 2011 collision data [11]. The CDF Collaboration has published a study of such events, using a 4.3 fb−1 sample of TeVatron data, and observes an excess of events in the 120 − 160 dijet mass range [12]. The D0 Collaboration find no evidence for such an effect in an equivalent data sample [13]. Both electron and muon channels are analysed, and no significant excess over Standard Model expectations is observed at any mass in the 100 − 300 GeV search region. 7

Search for first or second generation leptoquarks

The ATLAS Collaboration has recently published a search for the pair production of first or second generation scalar leptoquarks using 35 fb−1 of 2010 pp collision data [14]. The data are in good agreement with the Standard Model expectation, with no evidence of an excess. Limits at 95% C.L. are set in the 2-D plane of the leptoquark mass and the branching fraction, β, for leptoquark decay into a charged lepton and quark. Lower bounds are set on first and second generation leptoquark masses of 376 GeV and 422 GeV for β = 1. For β = 0.5, the corresponding bounds are 319 GeV and 362 GeV. 8

Summary

The Exotic physics programme of the ATLAS Collaboration has searched for a wide range of new physics phenomena; Figure 1 summarises a subset of these limits, many of which are world-leading and in excess of 1 TeV. No evidence of beyond Standard Model physics has been observed, however the increasing luminosity is opening up new model phase space for searches rapidly. With the superb performance of the LHC during 2011, an end-of-year dataset with at least four times the luminosity of these searches is anticipated. References [1] P. Langacker, arXiv:0911.4294 [hep-ph]. [2] M. Chizhov et al., Physics of Atomic Nuclei 71, 2096 (2008). [3] L. Randall and R. Sundrum, Phys. Rev. Lett. 83 3370 (1999).

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[4] ATLAS Collaboration, accepted by Phys. Rev. Lett., arXiv:1108.1582 [hep-ex]. [5] ATLAS Collaboration, ATLAS-CONF-2011-109, http://cdsweb.cern.ch/record/1373411. [6] K. Nakamura, et al., J. Phys. G 37 075021 (2010). [7] ATLAS Collaboration, Phys. Lett. B 705 (2011) 28. [8] ATLAS Collaboration, ATLAS-CONF-2011-095, http://cdsweb.cern.ch/record/1369186. [9] ATLAS Collaboration, ATLAS-CONF-2011-096, http://cdsweb.cern.ch/record/1369187. [10] N. Arkani-Hamed, et al., Phys. Lett. B 429 263 (1998). [11] ATLAS Collaboration, ATLAS-CONF-2011-097, http://cdsweb.cern.ch/record/1369206. [12] CDF Collaboration, Phys. Rev. Lett. 106 (2011) 171801. [13] D0 Collaboration, arXiv:1106.1921 [hep-ex]. [14] ATLAS Collaboration, Phys. Rev. D 84 011101(R) (2011).

71 BOSON AND DIBOSON PRODUCTION AT ATLAS Manuela Venturi a On behalf of the ATLAS Collaboration Fakult¨ at f¨ ur Mathematik und Physik, Albert-Ludwigs-Universit¨ at, Freiburg im Breisgau, Germany Abstract. Results obtained with the ATLAS detector [1] at the LHC, with 7 TeV pp-collisions and an integrated luminosity up to 1 fb−1 , are presented for many electroweak processes. In particular, W and Z cross section measurements are discussed, along with W charge asymmetry, W + jets production, W W , ZZ and W Z cross sections and their gauge couplings.

1

Introduction

In the LHC era, it is crucial to gain a good understanding of the electroweak (EWK) sector of the Standard Model (SM), both in its own right and as a prerequisite to discovery searches. In the following, the most up-to-date measurements of W , Z, W + jets, W W , ZZ and W Z cross sections will be reviewed, along with that of the W charge asymmetry. There are both theorethical and experimental motivations for studying these processes. From an experimental point of view, W and Z leptonic decays are used to benchmark the detector, i.e. to establish efficiencies of lepton triggers and reconstruction, energy and angular resolution, energy scales, etc. On the other hand, from a theorethical perspective, these processes represent a stringent test of perturbative QCD (pQCD) at the TeV scale, allowing to compare the measured quantities with their predictions at next-to-leadingorder (NLO) or next-to-next-to-leading-order (NNLO). Some of the EWK measurements, namely W charge asymmetry and Z rapidity spectrum, allow the determination of parton distribution functions (PDFs) in a new energy regime, and are being used already to diminish PDF uncertainties. Moreover, diboson cross sections are expected to be sensitive to physics beyond the SM. Lastly, searches like that for the Higgs boson and for Supersymmetry require a precise knowledge of the EWK SM sector, since it represents an important background. 2

Boson physics

2.1

W and Z cross section measurements

The analysis [2] uses data collected by ATLAS during 2010, corresponding to around 35 pb−1 of integrated luminosity, to determine the cross sections times leptonic branching ratios, σW ± · BR(W → ℓν) and σZ/γ ∗ · BR(Z/γ ∗ → ℓℓ), where ℓ = e, µ. The integrated and differential cross sections are measured in the fiducial volume of the ATLAS detector, using the equation: σfid = a e-mail:

[email protected]

72 (N − B)/(CW,Z · L), where N is the number of candidate events observed in data, B the number of background events and L the integrated luminosity corresponding to the run selections and trigger employed. The efficiency factor CW,Z determines the fiducial region of the detector, defined as a function of the transverse momentum, pT , and pseudorapidity, η, of the final state leptons. Muons are required to be combined, i.e. reconstructed using both the Inner Detector (ID) and the Muon Spectrometer (MS). They are requested to satisfy quality cuts, have pT > 20 GeV and |η| < 2.4. Electrons are reconstructed from their ID tracks and calorimeter informations, with quality cuts applied on both. An electron candidate has pT > 20 GeV and |η| < 2.47, excluding the region 1.37 < |η| < 1.52, where the transition between the barrel and the end-cap calorimeters is. For Z → ee, the range up to η = 4.9 is added to the analysis, allowing one of the electrons to be in the forward region. Additional selection criteria are applied to reduce the background and define the signal regions. For W → ℓν, transverse missing energy and mass miss have > 25 GeV and mT > 40 GeV, where mT = √ to be respectively ET

2 pℓT ETmiss (1 − cos(ϕl − ϕν )). For Z → ℓℓ, leptons are required to have same flavour and opposite charge, while their invariant mass has to be 66 < mℓℓ < 116 GeV. In all analyses, QCD multijet background is determined from data, with methods varying according to the analysis (template fit to the ETmiss distribution for W → eν, control regions for the others). EWK and tt backgrounds are negligible and are constrained via MC simulations. Figure 1 [2] shows the measured W + , W − , W ± and Z cross sections in the fiducial regions, compared with theorethical predictions using different PDF sets. The agreement is good in all cases. 2.2

W charge asymmetry

The same selection shown in (2.1) is used to determine the charge asymmetry A for the lepton from the W decay, in bins of pseudorapidity, defined as: A = (dσWℓ+ /dηℓ − dσWℓ− /dηℓ )/(dσWℓ+ /dηℓ + dσWℓ− /dηℓ ). This is a powerful measurement to probe the inner structure of the proton since many systematic uncertainties cancel in the ratio, while the dependence on ηℓ allows to explore different regions of x. Results are shown in Fig. 2 (left) [2], with a comparison to NNLO calculations. 2.3

W + jets

Another measurement performed with the selection described in (2.1), is the production cross section for a W boson in association with jets [3]. Jets are reconstructed using an anti-kT algorithm with a radius parameter R = 0.4.

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These jets are required to have ET > 20 GeV, rapidity |y| < 2.8 and not to be close (∆R > 0.5) to any lepton candidate. Figure 2 (right) shows the cross section ratio as a function of jet multiplicity for the muon channel. MC predictions agree with data at NLO, but not at LO (Pythia), as expected. 3 3.1

Diboson physics WW cross section measurement

The measurement of the W W production cross section at the LHC provides an important test of the SM through its sensitivity to triple gauge boson couplings (TGCs), which result from the non-Abelian structure of the gauge symmetry group, SU(2)L × U(1)Y . Furthermore, non-resonant W W production is an irreducible background in searches for the Higgs boson in the same final state. The analysis [4] uses an integrated luminosity of 1.02 fb−1 ; W W events are reconstructed using leptonic (ℓ = e, µ) decays of the W boson. The resulting final state has two high-pT charged leptons and substantial ETmiss . The major backgrounds are Drell-Yan, top quark, W + jet and diboson (W Z, ZZ and W γ) production. Muons and electrons are defined as in the standard W analysis, described in (2.1), apart from a more stringent cut on the pT of the leading electron, pT > 25 GeV. Jets, reconstructed using an anti-kT algorithm as in (2.3), are required to have ET > 30 GeV and |y| < 4.5. The selection is divided into three channels: ee, µµ and eµ. After requiring two leptonic candidates with opposite charge, originating from the primary

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vertex of the event, cuts are applied on the dilepton invariant mass (mll > 10 GeV for eµ, mll > 15 GeV and |mll − mZ | > 15 GeV for ee and µµ) and miss on the relative missing transverse energy (ET,Rel > 25, 40, 45 for eµ, ee, µµ respectively). Jets are fully vetoed, in order to reduce the tt background. The total cross section is extrapolated from the fiducial region, with a combination of the three channels, yielding 48.2 ± 4.0(stat) ± 6.4(syst) ± 1.8(lumi) pb, which agrees nicely with the theoretical NLO prediction of 46 ± 3 pb. 3.2

ZZ and WZ cross section measurements

In the SM, ZZ production proceeds predominantly via the t-channel, while the s-channel vertices (ZZZ, ZZγ) - also known as neutral Trilinear Gauge Couplings (nTGCs) - are forbidden. Non-zero nTGCs would lead to an enhancement of the ZZ cross section, and their observation would be an hint of physics beyond the SM. We also note that this process is an irreducible background for the search H → ZZ, and thus crucial to be constrained. Three final states are considered in the analysis (eeee, µµµµ, eeµµ), which also employs 1.02 fb−1 [5]. Leptons are defined closely to the W W selection, as described in (3.1); they are then associated in pairs of same flavour and opposite charge to form Z candidates, with |mℓℓ − mZ | < 15 GeV. The cross section resulting from the combination of all the channels, for a +0.4 total of 12 ZZ candidates, is found to be 8.4+2.7 −2.3 (stat)−0.7 (syst) ± 0.3(lumi) pb, which is statistically consistent with the SM NLO expectation of 6.5+0.3 −0.2 pb. The corresponding exclusion limits for nTGCs ̸= 0 are shown in Figure 3

75 (left), and are found to be already competitive with those obtained from CDF and LEP, after a much longer data taking period. With a similar selection, the W Z cross section is also measured, yielding 21.1+3.1 −2.8 (stat) ± 1.2(syst) pb, compatible with the SM NLO expectation of 17.2+1.2 −0.8 pb. Limits on the anomalus gauge couplings (aTGCs) are also derived, no hint of physics beyond the SM is found (Figure 3 (right)). ∫

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4

Conclusions

Measurements performed by the ATLAS experiment with collision data collected in 2010 and in the first half of 2011 have been shown, namely the cross sections for W , Z, W + jets, W W , ZZ and W Z leptonic decays, along with the W charge asymmetry. Others – such as Z rapidity spectrum, Z + jets, W γ, Zγ – could not be discussed here for brevity’s sake. All results are found to be in nice agreement with the SM NLO expectation, with no deviation from the SM observed. References [1] [2] [3] [4] [5] [6]

The The The The The The

ATLAS ATLAS ATLAS ATLAS ATLAS ATLAS

Collaboration, Collaboration, Collaboration, Collaboration, Collaboration, Collaboration,

JINST 3 (2008) S08003. arXiv:1109.5141 [hep-ex]. arXiv:1109.5141 [hep-ex]. ATLAS-CONF-2011-110 ATLAS-CONF-2011-107. ATLAS-CONF-2011-099.

76 HEAVY FLAVOUR PRODUCTION AT ATLAS Sergey Sivoklokov a on behalf of the ATLAS Collaboration Lomonosov Moscow State University Skobeltsyn Institute of Nuclear Physics,119991 Moscow, Russia Abstract. The production of heavy flavours at LHC provides an opportunity for a new insight into QCD. The ATLAS detector provides data at higher transverse momenta and wider rapidity ranges than have previously been studied. Both Charmonia [2] and Bottomonia [3] production cross sections have been measured in proton-proton collisions at centre of mass energy of 7 TeV as a function of transverse momemtum and rapidity. Exclusive B and D meson states have been also reconstructed ( [4–6]). Results are compared to theoretical predictions of various QCD models.

1

The ATLAS detector

ATLAS [1] is a multi-purpose experiment at the LHC designed primarily to search for Higgs bosons and signs of new physics beyond the Standard Model. In addition it has a broad flavour physics program. The key elements of the detector for this study are the Inner Detector and Muon Spectrometer. The Inner Detector provides precise tracking information measuring charged particles with silicon pixels, silicon strips detectors and a transition radiation tracker, immersed in a 2T solenoidal magnetic field and covers the pseudorapidity range |η| < 2.5 . The Muon Spectrometer consists of several types of detecors sitting in a toroidal magnetic field with a strength ∼ 0.5 T and covers |η| < 2.7. It can masure muon transverse momentum with a relative uncertainty of 10% up to momenta of ∼ 1 TeV.The Muon Spectrometer also provides information for muon triggers — a key to the most of heavy flavour studies as muons are the clean signature of heavy flavours involved processes. 2

Quarkonia production

Measurements of J/ψ and Υ production and properties in ATLAS are important steps both for understanding the detector performance and for performing measurements of various B-physics channels. It also provides a testing ground for studies of the muon trigger and identification efficiencies and momentum scale and resolution. The resulting dimuion invariant mass spectra obtained with 0.24 fb−1 of data recorded on 2010-2011 are shown at Fig. 2. The plots show all oppositely charged di-muon pairs, passing vertexing, in the J/ψ and ψ(2S) mass range (left) and in the Υ(1S, 2S, 3S) mass range (right). Events which fire a variety of di-muon triggers, with one or two muons at level 1 confirmed at the high level trigger (HLT), are included. The pair of muons are a e-mail:

[email protected]

77 required to have a minimum pT of (2.5, 4) GeV as calculated by the offline reconstruction. The fitted mass values are in the good agreement with the PDG averages. 300 ×10 ATLAS Preliminary 250 s = 7 TeV

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ATLAS has measured the inclusive J/ψ production cross section and the production fraction of non-prompt J/ψ (produced via the decay of a B-hadron) to inclusively produced J/ψ. The 2.3 pb−1 of data collected in 2010 has been used in the analysis. The low luminosity 2010 data was employed to allow loose trigger selections in order to obtain a sufficient statistics at lower pT . The doubly differential cross-sections for J/ψ production in bins of rapidity and pT has been derived. Details of analysis can be found in [2]. The resulting inclusive differential cross-section for one of the four rapidity bins is shown in Fig. 2 as a function of J/ψ pT . Differential production cross-sections of prompt and non-prompt J/ψ was separately determined and compared to several QCD models predictions predictions. ATLAS also provides a measurement of the fiducial differential production cross-section of Υ(1S) mesons decaying into two muons with pT > 4GeV and |η| < 2.5 . Figure 3 shows Υ(1S) cross-section Υ(1S) as a function of pT for the central rapidity bin in comparison with theory predictions (details can be found in [3]). 3

D and B-mesons study

Open charm mesons have been reconstructed in ATLAS via the channels Ds+ → ϕπ → (KK)π and D+ → Kππ. The fitted mass are in a good agreement with PDG values. The differential cross section for D∗± derived from this signals are shown at Fig. 4 with respect to the D-meson pT [5]. The inclusive Bmesons study is an important step for future studies of CP-violation effects and rare b-hadron decays. Several important modes has been reconstructed ( B ± → Jψ(µµ)K ± , B 0 → Jψ(µµ)K ∗ (Kπ) (Fig. 5 B ± → Jψ(µµ)ϕ(KK))(

78 [5–7]). The life-time measurements are in agreement with world averages. 4

Conclusion

d2σ/dpTdy × BR(ϒ (1S) → µ+ µ-) [pb/GeV]

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102

Inclusive cross-section ATLAS |y | 20 GeV and |η| < 2.8 are considered. Jets closest to electron candidates (within a distance ∆R < 0.5) are discarded. Details of the object selection can be found elsewhere [1]. Events are required to have at least one reconstructed primary vertex with five or more tracks consistent with this vertex. At least one of the lepton candidates must trigger the event at the last stage of the single-lepton trigger decision. Additionally, to suppress Drell-Yan and heavy flavor backgrounds, while keeping sufficient statistics needed to validate the relevant SM background estimates, the dilepton invariant mass, mll , is required to be greater than 110 GeV. The signal region is then subdivided into same-sign (SS) and opposite-sign (OS) dilepton events. The invariant mass mlljj (which represents the final state for WR candidates’ decays) is required to be greater than 400 GeV. To further reduce the larger SM background contribution in the OS dilepton channels, the scalar sum of the transverse energies of the leptons and two highest pT jets, denoted by ST , is required to be greater than 400 GeV. b ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the center of the detector and the z-axis coinciding with the axis of the beam pipe. The x-axis points from the IP to the center of the LHC ring, and the y axis points upward. Cylindrical coordinates (r,ϕ) are used in the transverse plane, ϕ being the azimuthal angle around the beam pipe. The pseudorapidity is defined in terms of the polar angle θ as η = −ln(tan(θ/2)).

81

Figure 1: Combined exclusion limit for all channels (ee, µµ and eµ) [2] for the mass of Heavy Majorana Neutrino for four-fermion operator V, assuming Λ = 1 TeV, α = 1

3

Experimental results

The numbers of events observed in data and expected according to the SM backgrounds in signal region in the SS and OS final states after preselection and final selection are shown in Table 1. A good agreement is observed between the numbers of data events and the predicted backgrounds. Figures 1 and 2 show limits obtained in the context of Effective Lagrangian Operators and LRSM, respectively. Table 1: A summary of the expected and observed numbers of events for the SS and OS dilepton channels [1]. The top of the table gives the numbers of events obtained for events with two leptons, at least one jet and mll > 110 GeV . The bottom part of the table shows the numbers of events satisfying also requirements Mlljj > 400 GeV and, for the OS channel, ST > 400 GeV . For each entry the statistical uncertainty is followed by the systematic uncertainty (the integrated luminosity uncertainty is not included). The uncertainty due to the integrated luminosity is 3.4% for all backgrounds except for the fake (i.e. heavy flavor) lepton background, which is measured from data.

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OS Preselection 0.18 ± 0.01 ± 0.01 4.0 ± 0.1 ± 0.4 0.39 ± 0.01 ± 0.06 56.3 ± 0.6 ± 8.0 0.81 ± 0.06 ± 0.15 106.6 ± 3.2 ± 14.0 5.81 ± 1.27 ± 2.06 6.9 ± 2.3 ± 2.7 7.2 ± 1.3 ± 2.1 173.8 ± 3.9 ± 16.7 5 177 Final selection 1.9 ± 0.4 ± 0.5 13.3 ± 1.2 ± 2.1 2 10

82

Figure 2: Observed and expected 95% CL lower limits [1] on masses for the heavy Majorana neutrino and WR for the combined SS+OS channels obtained from the cross-section times branching ratio predictions. The no-mixing and maximal mixing scenarios are shown on the left and on the right, respectively. The exclusion region is inside solid-hatched boundary. The contours show the observed upper limit on σ × BR [pb] as the function of masses of heavy Majorana neutrino and WR , where σ is the production cross-section for the WR , and BR is the branching ratio to ee, µµ in the no-mixing scenario and ee, µµ, eµ in the maximal mixing scenario.

4

Conclusion

Events observed in (34 pb−1 ) of pp data are consistent with the expectations for the SM backgrounds. New limits are placed on WR mass in the context of Left Right Symmetric Model. In the context of effective Lagrangian framework, for V operator (assuming α = 1 , Λ = 1 TeV), heavy neutrinos of masses up to 460 GeV are excluded at 95% CL. References [1] ATLAS Collaboration, ATLAS-CONF-2011-115 (2011). http://cdsweb.cern.ch/record/1375552 [2] ATLAS Collaboration, arXiv:1108.0366v1 [hep-ex] (2011). [3] R. N. Mohapatra, Unification and Supersymmetry. Springer-Verlag, 3rd ed., 2002. [4] R. N. Mohapatra and P. B. Pal, ISBN 981-238-070-1, Massive Neutrinos in Physics and Astrophysics. World Scientific, 3rd ed., 2004. [5] F. Aguila, S. Bar-Shalom, A. Soni et al., Phys. Lett. B 670, 399-402 (2009). [6] ATLAS Collaboration, JINST 3 (2008) S08003. [7] ATLAS Collaboration, JHEP 12 (2010) 060. [8] M. Cacciari and G. P. Salam, Phys. Lett. B 641 (2006) 57.

83 DIFFRACTION AT CMS Alexander Proskuryakov a , on behalf of the CMS collaboration SINP, Moscow State University, 119991 Moscow, Russia Abstract. The measurement of the inelastic cross section and the observation of diffraction at 7 TeV with the CMS detector are presented. The results are compared with the predictions of the PYTHIA6, PYTHIA8 and PHOJET generators.

1

Introduction

This paper presents the results on the measurement of the pp inelastic cross section [1], as well as the observation of a diffractive signal dominated by the inclusive single-diffractive reaction pp → Xp [2,3]. The analysis is based on the data collected by the CMS experiment during the year 2010, at a centre-of-mass energy of 7 TeV. The data are compared to simulated events obtained from the PYTHIA6 [4], PYTHIA8 [5] and PHOJET [6]. event generators. Diffractive events with a hard sub-process are simulated with the POMPYT generator [7]. 2

CMS detector

A detailed description of the Compact Muon Solenoid (CMS) experiment can be found elsewhere [8]. The central feature of the CMS apparatus is a superconducting solenoid, of 6 m internal diameter. Within the field volume are the silicon pixel and strip tracker, the crystal electromagnetic calorimeter (ECAL) and the brass-scintillator hadronic calorimeter (HCAL). Muons are measured in gaseous detectors embedded in the iron return yoke. CMS has extensive forward calorimetry. The forward part of the hadron calorimeter, HF, covers the pseudorapidity region 2.9 < |η| < 5.2. Two elements of the CMS monitoring system, the Beam Scintillator Counters (BSC) and the Beam Pick-up Timing eXperiment (BPTX) devices, were used to trigger the CMS readout. The two BSC are sensitive in the |η| range from 3.23 to 4.65. 3

Inelastic cross section measurement

A new method to measure the inelastic pp cross section has been developed based on the assumption that pile-up events are randomly distributed according to a Poisson probability. This method relies only on the accurate knowledge of the CMS tracking system and it does not depend upon a specific Monte Carlo simulation. The number of inelastic proton-proton (pp) interactions in a given bunch crossing follows a Poisson probability distribution: P (n) = a e-mail:

(L · σ)n −L·σ e , n!

[email protected]

(1)

84

Figure 1: Fraction of events with n pile-up events as a function of luminosity. The dotted line is a Poisson fit.

Figure 2: Compilation of total inelastic pp and p¯ p cross section values. CMS analysis uncertainty is shown in dark blue while the model-dependent extrapolation is shown in light blue (dark green and light blue for ATLAS). Picture layout and data points courtesy of [10].

where L is the bunch crossing luminosity and σ the total inelastic pp cross section. The true pile-up distributions are obtained by performing a bin-by-bin correction of the measured vertex distributions with the efficiency values obtained with Monte Carlo. Then, each pile-up distribution is fitted with a Poisson function, Eq. 1, as shown in Fig. 1. The measurements obtained in this analysis can be used to estimate the value of the total inelastic pp cross section using MC dependent extrapolation factors: σinel (pp) = 68 ± 2.0(syst.) ± 2.4(lumi) ± 4(ext.) mb.

(2)

Figure 2 shows how this value compares with previous pp and p¯ p measurements and with the ATLAS results [9].

85 4

Observation of diffraction

Figure 3 (left) shows the distribution of the selected events as a function of ∑ (E ± pZ ), where the sum runs over all calorimeter towers, including HF. This variable approximately equals twice the Pomeron energy; the plus (minus) sign applies to the case in which the proton emitting the Pomeron moves in the +z (z) direction. Diffractive events cluster at very small values of E ±pZ , reflecting the peaking of the cross section at small ξ, the proton fractional energy loss in single-diffractive events. Diffractive events also appear as a peak in the zeroenergy bin of the deposited energy distribution in HF (EHF ), on either the HF at forward rapidities (HF+) or the HF at negative rapidities (HF-), reflecting the presence of a large rapidity gap (LRG) extending over HF+ or HF- (Fig. 3, right panel). The data are compared with the predictions of PYTHIA6 and PYTHIA8, as well as PHOJET. A clear diffractive contribution is evident. The bands in all cases illustrate the effect of a 10% energy scale uncertainty in the calorimeters and should be taken as a rough estimate of the systematic uncertainty due to the current imperfect understanding and simulation of the detector.

Figure 3: Distributions of the accepted events as a function of E + pZ (left) and EHF + (right). The predictions of PYTHIA6, PYTHIA8 and PHOJET are also shown, normalised to the data. The distributions are uncorrected. The vertical bars indicate the statistical uncertainty of the data. The bands illustrate the effect of a 10% energy scale uncertainty in the calorimeters.

The selected sample of W events with a LRG is shown in Fig. 4, as a function of the signed charged lepton rapidity ηlepton , defined to be positive when the observed gap and the lepton are in the same hemisphere and negative otherwise. The data show that charged leptons from W decays are found more often in the hemisphere opposite to the gap. 5

Summary

A new method to measure the inelastic pp cross section has been developed based on the assumption that pile-up events are randomly distributed according

86

Figure 4: Signed lepton rapidity distribution in W events with a LRG. Electron and muon channels are combined. The fit result for the combination of the PYTHIA6 (ProQ20 tune) and POMPYT predictions is shown as the dotted line. Fit results of the non-diffractive component using different PYTHIA6 tunes are also shown.

to a Poisson probability.The model-dependent value of the extrapolated total inelastic pp cross section is σinel (pp) = 68 ± 2.0(syst.) ± 2.4(lumi) ± 4(ext.) mb Evidence of the observation of diffraction at the LHC, at 7 TeV center-ofmass energy, has been presented. Diffractive events appear as a peak at small values of the variable E ± pZ , which is proportional to ξ, the proton fractional energy loss, reflecting the 1/ξ behaviour of the diffractive cross section. Diffractive events also appear as a peak in the energy distribution of the forward calorimeter HF, reflecting the presence of a rapidity gap over HF. A large asymmetry is observed when comparing the number of events with the charged lepton (from the W ( Z ) decay) in the opposite and same hemisphere as the rapidity gap. Such an asymmetry is predicted by the diffractive POMPYT MC, in contrast to the various non-diffractive PYTHIA MC tunes. References [1] [2] [3] [4] [5]

CMS Collaboration, PAS-FWD-11-001 (2011). CMS Collaboration, PAS-FWD-10-007 (2010). CMS Collaboration, PAS-FWD-10-008 (2010). T. Sjostrand, S. Mrenna and P.Z. Skands, JHEP 0605 (2006) 026. T. Sjostrand, S. Mrenna and P.Z. Skands, Comput. Phys. Commun. 178 (2008) 852. [6] F.W. Bopp, R. Engel and J. Ranft, arXiv:hep-ph/9803437. [7] P. Bruni and G. Ingelman, Phys. Lett. B 311, 317 (1993). [8] CMS Collaboration, JINST 3 (2008) S08004. [9] ATLAS Collaboration, arXiv:1104.0326. [10] A. Achilli et al., “Total and inelastic cross-sections at LHC at CM energy of 7 TeV and beyond”, arXiv:1102.1949.

87 MEASUREMENTS OF FORWARD ENERGY FLOW WITH CMS Ann-Karin Sanchez a for the CMS Collaboration Institute for Particle Physics, ETH Zurich, Schafmattstrasse 20, CH-8093 Zurich Abstract. Measurements of the forward energy flow in minimum bias events and in events with either hard jets or W and Z bosons produced at central rapidities are presented. Results are compared to MC models with different parameter tunes for the description of the underlying event.

1

Introduction and motivation

Quantum Chromodynamics processes can be investigated through the measurement of the average energy per event (energy flow) in specific angular regions. Such a measurement is useful in examining the complex final states that result from a hadron-hadron interaction. The LHC with its large centre-of-mass energy allows to study final states from the proton-proton interaction with large contributions from multiple-parton interactions (MPI). Multiple-parton interactions are not well understood theoretically and a systematic description in QCD remains challenging. Phenomenological approaches to multi-parton dynamics rely strongly on parameterised models and tuned parameters (tunes) to describe data. Measurements of the underlying event structure have been performed for central values of the pseudorapidity. The extension of the measurements to large pseudorapidities and higher centre-of-mass energies is a challenge for the models since, in this region of phase space, parton showers (initial-state radiation), as well as MPI, are expected to play a significant role. Exploiting the large calorimeter coverage of the Compact Muon Solenoid (CMS) detector [1] allows the energy flow to be measured over a wider range than was accessible in previous analyses. The measurement of the energy flow in the pseudorapidity range 3 < |η| < 5 is presented at two different centreof-mass energies, 0.9 and 7 TeV and for different event classes: minimum-bias events and events with central high-transverse-momenta dijets and events with a centrally produced W or Z boson. 2

Minimum-bias and dijet events

The energy flow was measured with the CMS hadronic forward (HF) calorimeters and corrected to the stable-particle level. A detailed description of the √ event selection can be found in [2]. The results for s = 7 TeV are shown in Fig. 1. We observe three distinct features of the data. The first is that the energy flow in both minimum-bias and dijet events increases with pseudorapidity, and the increase is found to be steeper for minimum-bias events. The second is that the energy flow increases with centre-of-mass energy, being a factor of a e-mail:

[email protected]

88 √ √ two to three higher at s = 7 TeV than at s = 0.9 TeV. Finally, the average energy flow is significantly higher in dijet events than in the minimum-bias sample. The data are compared to different MC predictions. The shape of the energy-flow distribution, both in minimum-bias and dijet events, is reproduced by all the MC event generators that include a contribution from MPI. The measured energy flow is also compared to predictions derived from the event generators used in cosmic-ray air shower simulations and the description of the data by all these models is good.

√ Figure 1: Energy flow as a function of η for minimum-bias and dijet events at s = 7 TeV. The systematic uncertainties are indicated as error bars, the statistical errors are negligible. The yellow bands illustrate the spread of the predictions from the considered pythia6 tunes.

3

W and Z boson events

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89 description can be found in [3]. The results for the measured forward energy flow in the HF detectors are shown in Fig. 2. Besides the ProQ20 tune, none of the MC models considered provide a good description of the HF energy distribution observed in the data. The forward/backward correlations of the measured forward energy flow is highly sensitive to the underlying event. In Fig. 3 different energy intervals are shown and we observe a strong positive correlation between forward and backward energy deposits in data as well as in MC. The distributions for the medium energy interval are in better agreement with the predictions of the various tunes than the inclusive HF distributions, while for the low and high energy intervals it is worse. -1

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4

Conclusions

The energy flow at large pseudorapidities has been measured in pp collisions for minimum-bias events and events with a dijet system or a W or Z boson in the central region. The results indicate the importance of the MPI in the description of the data with the MC models. The variation of the energy flow with η, both in minimum-bias and dijet events, is reasonably well reproduced by all Monte Carlo event generators with multiple-parton interactions included. However, in the W (Z) events larger discrepancies are observed and large efforts are needed especially for a simultaneous description of the forward/backward correlations. As can be seen by the large spread in the theoretical predictions, the magnitude of the average energy strongly depends on the parameter settings of the different MC tunes. Thus, the measured energy flow can be used for further constraints on the modeling of multiple-parton interactions. References [1] CMS Collaboration, JINST 0803 (2008), S08004. [2] CMS Collaboration, arXiv:1110.0211 [hep-ex] (2011) [3] CMS Collaboration, arXiv:1110.0181 [hep-ex] (2011)

90 SEARCH FOR A HEAVY NEUTRINO AND RIGHT-HANDED W OF THE LEFT-RIGHT SYMMETRIC MODEL WITH CMS DETECTOR Danila Tlisov on behalf of the CMS Collaboration a INR RAS, Prospekt 60-letiya Oktyabrya 7a, Moscow 117312, Russia Abstract. This work describes the first search for signals from the production of right-handed WR bosons and heavy neutrinos Nℓ (ℓ = e, µ), that arise naturally in the left-right symmetric extension to the Standard Model, with the CMS Experiment at the LHC using the 7 TeV pp collision data collected in 2010 and 2011 corresponding to an integrated luminosity of 240 pb−1 . No excess over expectations from Standard Model processes is observed. For models with exact left-right symmetry (the same coupling in the left and right sectors) we exclude the region in the two-dimensional parameter space that extends to (MWR , MNℓ ) = (1700 GeV, 600 GeV).

1

The left-right (LR) symmetric model

The left-right (LR) symmetric extension to the Standard Model model [1–3] is attractive because it naturally explains the parity violation seen in weak interactions as a result of spontaneously broken parity. The model necessarily incorporates additional WR± and Z ′ gauge bosons and heavy right-handed neutrino states Nℓ and thus can also explain the smallness of the ordinary neutrino masses through the see-saw mechanism [4]. The strength of gauge interactions of WR± bosons is described by the coupling constants gR . Strict LR symmetry leads to the relation gL = gR at MWR , which will be assumed throughout this paper. To simplify our study, we further assume that the mixing angles (WR − WL , Z ′ − Z, and Nℓ − Nℓ′ ) are small. The existing experimental limit on the WR mass is in the range 739 − 768 GeV and depends on the heavy neutrino mass (the smaller number corresponds to the case when all three Nℓ have masses smaller than MWR ) [5]. We consider the leading production reaction at the LHC: pp → WR + X → Nℓ + ℓ + X. The right-handed neutrino decays into a charged lepton ℓ± and an off-shell WR∗ which subsequently decays into a pair of quarks which hadronize into jets (j). This produces the final state WR → ℓ1 Nℓ → ℓ1 ℓ2 WR∗ → ℓ1 ℓ2 jj (ℓ = e, µ), where ℓ1 , ℓ2 have the same flavor. We use PYTHIA [6], with default CTEQ6L1 parton distribution functions [7], for the signal event generation and calculation of cross sections. We also study relevant background samples generated using PYTHIA, ALPGEN [8], and MADGRAPH [9]. a e-mail:

[email protected]

91 2

The CMS detector and object reconstrution

This measurement was performed using 240 pb−1 of pp collision data collected in 2010 and 2011 by the CMS detector at a center-of-mass energy of 7 TeV. The central feature of the CMS apparatus is a superconducting solenoid, of 6 m internal diameter, providing a field of 3.8 T. Within the field volume are the silicon pixel and strip tracker, the crystal electromagnetic calorimeter (ECAL) and the brass/scintillator hadronic calorimeter (HCAL). Muons are measured in gas-ionization detectors embedded in the steel return yoke. In addition to the barrel and endcap detectors, CMS has extensive forward calorimetry. A detailed description of the CMS detector can be found elsewhere [10]. 3

Object reconstrution and events selection

Information about electron reconstruction and identification in CMS during this running period can be found in [11]. The muon identification strategy is based on both the muon detectors and the inner tracker, as described in [12]. We reconstruct jets from calorimeter towers using the anti-kt clustering algorithm [13] with a cone of radius R = 0.5 and impose a minimum transverse momentum requirement of 40 GeV/c on the jet candidates. We select WR → ℓNℓ candidates using the two highest ET /pt same-flavor (e or µ) leptons, and the two highest pt jets that satisfy the above criteria. As the WR → ℓNℓ decay tends to produce high momentum leptons, we require ET (pt ) > 60 GeV(/c) for at least one of the lepton candidates and ET (pt ) > 30 GeV/c for another. In the electron channel, we reject the event if no electron candidate is found in the ECAL barrel region (|η| < 1.44). 4

Backgrounds

The background for WR → ℓNℓ decay primarily consists of events from Standard Model processes with two real leptons, such as tt¯ and Z+jets. It is also possible for jets to be misidentified as leptons, which allows QCD multijet processes to contribute background events. We estimate the tt¯ contribution using simulated events, normalizing it to the cross section measured by CMS [16]. We cross check this normalization using a sample of reconstructed eµjj events in data and simulation. Our estimate of the Z+jets background contribution is based on observation of Z → ee, µµ decays in simulation and data. We normalize the Z+jets contribution to the inclusive NNLO calculation [14, 15], and then rescale the expected distribution to data (accounting for background contributions) using the reconstructed dilepton mass region near the Z peak. We take the remaining electroweak and top background estimates directly

92 from simulation, as their small cross sections severely limit their impact on the background level. We determine the QCD multijet background from data using an estimate of the lepton fake rate. For each channel, we examine a sample of dijet events in data in order to determine the lepton fake rate. 5

Results

We limit contributions from Standard Model backgrounds by imposing requirements on the dilepton mass (Mℓℓ ) and the mass of the reconstructed WR candidate (Mℓℓjj > 520 GeV). Electroweak backgrounds, primarily from Z+jets, are suppressed by requiring Mℓℓ > 200 GeV. We show the 95% C.L mass regions excluded for both channels in Fig. 1, where we obtain these plots by comparing the observed (expected) upper limit using a single-bin Bayesian approach [17] with a flat prior and the expected cross section for each mass point. These limits extend to MWR = 1700 GeV, and exclude a wide range of heavy neutrino masses for MWR =1500 GeV. Good agreement is seen between the observed and expected limits. More this analisys details can be found in [18].

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6

Conclusions

We have presented a search for right-handed bosons (WR ) and heavy neutrinos (Nℓ ) of the Left-Right symmetric extension of the Standard Model. The contribution from background top and electroweak processes is determined from simulated event samples and the expected rate is normalized to data whenever

93 possible. The background from QCD multijet events is estimated from data. The uncertainty for the backgrounds is estimated using data-driven methods. We find that our data sample is in good agreement with expectations from Standard Model processes. We use a Bayesian approach to set a limit on the WR and Nℓ masses that includes treatment of the systematic uncertainties as nuisance parameters. For models with exact left-right symmetry (the same coupling in the right sector) we exclude the region in the two-dimensional parameter space (MWR , MNℓ ) that extends to MWR = 1700 GeV. Acknowledgments We would like to thank Chris Hill, Greg Landsberg, the Exotica LQ working group, particularly Paolo Rumerio, Francesco Santanastasio, Sarah Eno, for the useful discussions and suggestions.We thank the technical and administrative staff at CERN and the other CMS Institutions. References [1] [2] [3] [4] [5]

J. C. Pati and A. Salam, Phys.Rev. D 10, 275 (1974). R. N. Mohapatra and J. C. Pati, Phys.Rev. D 11, 366 (1975). G.Senjanovic and R.N.Mohapatra, Phys.Rev. D 12, 1502 (1975). R.N. Mohapatra and G. Senjanovic, Phys.Rev.Lett. 44, 912 (1980). V.M.Abazov and others, D0 collaboration, Phys.Rev.Lett. 100, 211803 (2008). [6] T.Sjostrand and others, JHEP 001, 026 (2006). [7] J.Botts and others, Phys. Lett. B 304, 159 (1993). [8] J.Alwall and others, JHEP 0307, 001 (2003). [9] T.Sjostrand and others, JHEP 09, 028 (2007). [10] J.Botts and others, CMS collaboration JINST 3, S08004 (2008). [11] J.Botts and others, CMS collaboration, CMS PAS EGM-10-004 (2010). [12] J.Botts and others, CMS collaboration, CMS PAS MUO-2010-002 (2010). [13] M. Cacciari and G. Salam and G. Soyez, JHEP 04 (2008). [14] Ryan Gavin and Ye Li and Frank Petriello and Seth Quackenbush,“FEWZ 2.0: A code for hadronic Z production at next-to-next-toleading order”, eprint 1011.3540. [15] P.Nadolsky, “Theory of W and Z production”, arXiv:hep-ph/0412146. [16] J.Botts and others, CMS collaboration, CMS PAS TOP-10-005 (2010). [17] I.Bertram and others, “ A Recipe for the Construction of Confedence Limits”, FERMILAB TM-2104 (2000). [18] J.Botts and others, CMS collaboration, CMS PAS EXO-11-002 (2011).

94 SEARCH FOR MICROSCOPIC BLACK HOLE SIGNATURES IN THE CMS EXPERIMENT AT THE LHC Maria Savina a on behalf of the CMS Collaboration Joint Institute for Nuclear Research, 141980 Dubna, Russia Abstract. The recent results on a search for microscopic black hole production in pp collisions at a center-of-mass energy of 7 TeV by the CMS experiment at the LHC is presented using a 2011 data set corresponding to an integrated luminosity of one inversed fb.

Scenarios predicting large extra dimensions [1, 2] appeared more than ten years ago as an attempt at solving the scale-hierarchy problem associated with a formidable difference between the electroweak scale (about 1 TeV) and the Planck scale, MPl (about 1019 GeV), which determines the limit of applicability of quantum field theory, where it gives way to quantum gravity. The reduction of the fundamental gravity scale from the value of 1019 GeV in four-dimensional theory to a much smaller value in multidimensional models is a feature peculiar to such models. This immediately entails a number of important implications, in particular, the production of Kaluza-Klein excitations of the graviton and the fields of the Standard Model and, secondly, the production of microscopic black holes at accelerators that is followed by their fast evaporation. A correct description of the process involving the formation of black holes and their further evolution requires invoking quantum gravity as a full theory. If, however, one moves rather far upward in energy from the fundamental multidimensional scale, then black-hole production admits an asymptotic treatment in terms of a classical process described by the geometric production cross section determining the size of the region below the gravitational radius. Since the geometric cross section for black-hole production is not suppressed by coupling constants smaller than unity, it grows with primary-particle collision energy. The production cross section for black holes depends on the number of extra dimensions and on the geometry of the total multidimensional space. The evaporation stage can be characterized by equilibrium (thermal) emission of particles of all types existing in the Standard Model. For all these and some other questions see, for example [3] or the review [4]. In this analysis we focus on black hole production in a model with large, flat, extra spatial dimensions (ADD type scenarios) [3]. The first search for microscopic black holes at a particle accelerator was carried out by the CMS Collaboration in 2010 [5] in pp collisions at a center-of-mass energy of 7 TeV, using a data sample corresponding to an integrated luminosity of 35 pb−1 . Sufficiently increased statistics of 1.09 fb−1 collected during year of 2011 one allows to extend the sensitivity of the 2010 analysis [6]. Using simple semiclassical approximation, as realized as a option in BlackMax event generator [7], a e-mail:

[email protected]

95 comparison with different black hole models had been done and some limits derived.

Figure 1: Total transverse energy, ST , for events with: N = 2 (top left); N ≥ 4 (top right); N ≥ 6 (bottom left); and N ≥ 8 (bottom right) objects in the final state. Data are depicted as solid circles with error bars; shaded band is the background prediction (solid line) with its uncertainty. Also shown are black hole signals for three different parameter sets.

The total transverse energy (ST ) of the event is used to separate black hole events from the backgrounds. The ST variable is defined as a scalar sum of the ET of individual jets, electrons, photons, and muons passing the above selections. Only photons, leptons (e and µ) and jets with ET > 50 GeV are counted toward the ST in order to suppress the SM backgrounds and to be insensitive to jets from pile-up, while being fully efficient for black hole decays. The missing ET in the event is also added to ST , if missing ET > 50 GeV. The main background to black hole signals arises from QCD multijet events. Other backgrounds from direct photon, W/Z+jets, and ttbar production were estimated from MC simulations. The dominant QCD background, however, we estimate from data using the ST multiplicity invariance technique (data-driven method) of Ref. [5].

96 The ST distributions for data events with multiplicities N ≥ 2, 4, 6, and 8 are shown in Fig. 1. The data agree well with the background shapes from the low-multiplicity samples and do not exhibit any evidence for new physics. Since no excess is observed above the predicted background, upper limits on the black hole production cross section in a few tested scenarios have been set using the Bayesian method with flat signal prior and log-normal prior for integration over the nuisance parameters (background, signal acceptance, luminosity). Translating these upper limits into lower limits on the parameters of the ADD model, the production of black holes with minimum mass of 4 to 5 TeV for a large variety of model parameters at 95% C.L. can be excluded (Fig. 2).

Figure 2: The 95% confidence level limits on the black hole mass as a function of the multidimensional Planck scale MD for several benchmark scenarios. The area below each curve is excluded by this search.

References [1] N.Arkani-Hamed, S.Dimopoulos, and G.Dvali, Phys. Lett. B 429, 263 (1998). [2] L.Randall and R.Sundrum, Phys. Rev. Lett. 83, 3370, 4690 (1999). [3] S.Dimopoulos and G.Landsberg, Phys.Rev.Lett. 87, 161602 (2001). [4] M.Savina, Phys.At.Nucl. 74, No.3, 496 (2011). [5] CMS Collaboration. Phys. Lett. B 697, 434 (2011), arXiv:1012.3375. [6] CMS Collaboration. CMS PAS EXO-11-071. [7] D.C.Dai, G.Starkman, D.Stojkovic, C.Issever, E.Rizvi, and J.Tseng, Phys.Rev. D 77, 076007 (2008), arXiv:0711.3012.

Neutrino Physics

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99 ICARUS: A POWERFUL DETECTOR FOR

ν

PHYSICS

Alberto Guglielmi a INFN Sezione di Padova, Department of Physics, 35131 Padova, Italy Abstract. Fundamental contributions to neutrino physics are expected from ICARUS, the novel 770 t liquid Argon TPC presently taking data at LNGS with CNGS beam. This detector will be moved to CERN PS after the completion of LNGS physics programme in order definitely clarify the presence of new extra sterile neutrinos as suggested by anomalies observed in different present experiments.

1

Introduction

The possible presence of sterile neutrinos was originally proposed by B. Pontecorvo in a seminal paper where he considered the existence of right-handed neutrinos, neutrino oscillations, lepton number violation, 0ν − ββ decays, and other fundamental queries that dominated neutrino physics up to now [1]. Two distinct classes of phenomena have been analyzed, namely a) the apparent reduction in the ν e low energy neutrinos events from nuclear reactors (Fig. 1) [2] and from the signal from Mega-Curie calibration sources in GALLEX and Sage experiments (R = 0.86 ± 0.05 ∼ 2.7σ away from R = 1 expectation) [3,4], and b) evidence for a ν e event excess in neutrino beam from particle accelerators (Fig. 2) as observed in LSND and MiniBooNe experiments [5, 6].

Figure 1: Experimental results at nuclear reactors compared to ν new flux calculations. Fits are performed in different scenarios, including also the presence of a sterile neutrino. a e-mail:

[email protected]

100 This second anomaly, completely different from the claimed disappearance rate in the ν e channel, may indicate a more complex physics situation. These experiments may all point out the possible existence of the fourth non standard neutrino state driving neutrino oscillations at a small distance, with typically |∆m2new | ≥ 1 eV2 and relatively large mixing angle sin2 θnew ≃ 0.1 [7]. The existence of a fourth neutrino state may be also hinted or at least not excluded by cosmological data mainly coming from WMAP [8].

!"#"$%%&'()#*+#,-./"#%01( 2342(5676(8%.(

PRELIMINARY JULY 2011

Figure 2: P (νµ → νe ) versus L/Eν as measured by LSND (black) and MiniBooNE (red).

In order to definitely clarify the existence of such phenomena, a new experiment at the CERN PS based on the search for spectral differences in electronlike signatures in two identical large mass liquid Argon TPCs (LAr-TPC) but at different distance from the source has been proposed [10]. According to the present proposal the ICARUS T600 detector, presently in operation underground at LNGS with the CNGS neutrino beam from CERN-SPS, will be moved in 2013 into the Far position of the CERN-PS neutrino beam-line after the completion of the presently running experiment. 2

ICARUS-T600 LAr-TPC: a powerful detector for neutrino physics

The ICARUS detector, the largest LAr-TPC ever built [9], consists of two identical adjacent cryostats filled with 770 t of ultra-pure liquid Argon, each housing 2 TPCs separated by a central common cathode, with 1.5 m drift length. Ionization electrons, abundantly produced by charged particles along their path are drifted under uniform electric field (ED = 500 V/cm) towards the TPC anode made of 3 parallel wire planes (3 mm pitch), facing the drift volume, oriented on each plane at 00 , ±600 with respect to the horizontal direction.The relative time of each ionization signal, combined with the electron drift velocity information (vD ∼1.6 mm/µs), provides the position of the track along the drift coordinate. Globally a remarkable 1 mm3 spatial resolution has been measured. Absolute event time is determined by the scintillation light signal from arrays of photo-multipliers installed in LAr behind the wire planes.

101 ICARUS is very suited for rare event studies, such as neutrino oscillation physics from CNGS beam and atmospheric neutrinos, and search for nucleon decay, since they combine large mass and good spatial granularity and calorimetric accuracy. The calorimetric √ response allows a precise measurement of e.m. energy (σE /E ≈ 11%/ E(GeV))for contained events, while the momentum of non-contained particles (mainly muons) can be measured within ∼ 15% resolution from the deflection angle along the track due to multiple scattering. At √ higher energies the estimated resolution for hadronic showers is σE /E = 0.30/ E(GeV). The measured dE/dx energy allows a clear pion to proton separation as obtained from the last part of the residual range. Moreover π 0 → 2γ are recognized by detecting γ conversion, measuring dE/dx and the 2γ invariant mass. As a result a very efficient e/π 0 discrimination allows to reject the neutrino NC interactions by a factor ≈ 103 in the νe appearance search, while keeping more than 90% of νe CC events. A typical νµ CC event, fully reconstructed, is shown in Fig. 3.

Figure 3: A reconstructed νµ CC event in ICARUS. The neutrino produces a long muon (1), a charged pion (3) and an e.m. shower (2). At a closer look the shower can be identified as generated by a π 0 ; two e− e+ pairs can be resolved, especially in Induction2 view, and the ∗ = 125 ± 15 MeV, consistent with the invariant mass of the 2γ system is measured as Mγγ 0 π mass. The momentum of the escaping muon measured by multiple scattering, is 10.5±1.8 GeV. In the secondary vertex, the π interaction produces several hadrons; a K → µ → e is observed (5). The 250 MeV/c total pT is consistent with the nucleon Fermi momentum.

The experiment collected in 2010 168 CNGS beam neutrino events (5.8×1018 pot, 169 events expected) triggering on the photomultiplier signals in coincidence with the early-warning signal sent from CERN at each proton extraction. Preliminary results on reconstruction of 2010 data sample show that the main

102 ingredients (calorimetry, multiple scattering and directional reconstruction) of the event reconstruction are measured in an unbiased way in agreement with expectations, allowing to reconstruct the neutrino energy spectrum (Fig.4).

Figure 4: Reconstructed energy spectrum of νµ CC (left) and corresponding muon momentum as measured by multiple scattering (right) compared with MonteCarlo.

3

A more direct, new approach to neutrino oscillations

The proposed experiment at CERN PS 1.5 GeV νµ beam from 19.2 GeV/c proton, is based on two similar LAr-TPCs, i.e. a new T150 (150 tons) and ICARUS-T600 to observe the νe signal in the Near and Far positions, at 127 m and 850 m from the proton target (Fig. 5) [10]. As an important feature of the present proposed experiment, the possibility to run with anti-neutrino beam has been considered in order to further check the LSND claim, which is mainly based on ν e data. The adopted neutrino beam energy allows, unlike lower energy beams, to obtain useful event rates, also operating in antineutrino mode.

T150

I216/P311 proposal

T600

Figure 5: (Left) Experimental set-up proposed at the CERN PS neutrino beam with two LAr-TPC detectors. (Right) Expected νe fluence at Near/Far detector positions.

The ∼ 0.5% intrinsic νe contamination spectra of the neutrino beam, mainly from the K and µ 3-body decays, are expected to be closely identical in the

103 Near and Far positions (Fig. 5). In this way, all cross sections and experimental biases cancel out. In absence of oscillations, after some beam related small spatial corrections, the two electron neutrino energy spectra should be a precise copy of each other, independently of the specific experimental event signatures and without any need of Monte Carlo comparisons. Therefore any resulting νe difference between the two locations, if observed, must be inevitably attributed to the time evolution of the neutrino species, and both the mixing angle sin2 θnew and the mass difference |∆m2new | can be separately measured.

Figure 6: Expected 90% C.L. νµ → νe sensitivity for neutrino (top, left) and antineutrino (top, right) beams, and the corresponding νe disappearance sensitivity (bottom).

A key issue of the proposed experiment is the LAr-TPC detection capability of all the genuine νe events, allowing the reconstruction of the totality of neutrino events without restricting to the QE interactions, and the very high level of rejection of the associated background events, in primis from the π 0 decay. Quasi-elastic neutrino events in the 50 litre ICARUS LAr-TPC exposed to the CERN-WANF beam in coincidence with the NOMAD experiment have been reconstructed in 3D with particle identification, momentum balance and π 0 rejection in a energy range which is relevant for the proposed experiment [9].

104 Globally more 106 muon neutrino events will be collected with the Far detector in ν focusing mode for 2.5 × 1020 pot (2 year exposure, 30 KWatt of beam power) and 0.7 × 105 in ν mode with twice more exposure. The expected sensitivity to νµ → νe oscillation appearance for both neutrino and antineutrino beam will fully cover the parameter space region allowed by the LSND except for the highest ∆m2 values (Fig. 6). Globally about 106 νµ CC will Moreover the νe disappearance sensitivity from 6900 νe will fully enclose the “anomalies” from the combination of the published reactor neutrino experiments, GALLEX and Sage calibration sources experiments for 2.5 · 1020 pot. A 3% systematic uncertainty has been considered in the Far to Near ratio prediction. The disappearance signal in the same sin2 2θnew − ∆m2new range may also be studied independently with the dominant νµ and ν µ . As an additional bonus, the large statistics of excellent quality data will also profit to the knowledge of neutrino cross-sections in the 0-5 GeV energy range. Acknowledgments It’s a real pleasure to thanks the Organizing Committee of the 15th Lomonosov Conference on Elementary Particle Physics, in particular the Chairman Professor Alexander Studenikin, for the pleasant and fruitful atmosphere during the Conference. References [1] [2] [3] [4] [5] [6]

B.M. Pontecorvo Zh. Eksp. Teor. Fiz. 53, 1717 [JETP 26, 984] (1967). G. Mention et al. Preprint arXiv:1101.2755v1 [hep-ex]. J.N. Abdurashitov et al. Phys. Rev. C 59, 2246 (1999). F. Kaether et al. Phys. Lett. B 685, 47 (2010). A. Aguilar et al. Phys. Rev. D 64, 112007 (2001). A.A. Aguilar-Arevalo Phys. Rev. Lett. 102, 101802 (2009); E. Zimmerman “Short-Baseline Neutrino Physics at MiniBooNE”, PANIC11 Cambridge (2011). [7] C. Giunti, M. Laveder Phys. Rev. D 82, 053005 (2010). [8] E. Komatsu et al. Preprint arxiv.org/abs/1001.4538. [9] S. Amerio et al, Nucl. Instr. and Meth. A 527, 329 (2004); F. Arneodo F. et al. Phys. Rev. D 74, 112001 (2006); C. Rubbia et al. JINST 6, 7011 (2011). [10] C. Rubbia et al., CERN-SPSC-2011-033, SPSC-P-345 (2011).

105 THE ANTARES UNDERSEA NEUTRINO TELESCOPE. Marco Anghinolfi a on behalf of the ANTARES collaboration. INFN Sezione di Genova, via Dodecaneso 33, 16146 Genoa, Italy Abstract. Neutrino astronomy is a very promising field of investigation representing a complementary source of information with respect to photon-astronomy. ANTARES, operating off the French Mediterranean coast, is the worlds largest operational underwater neutrino telescope. In these proceedings, in addition to a short detector description, the results of recent analysis will be discussed. The ANTARES project is an important physics experiment but also represents a bench mark for a future large detector of the km3 scale.

1

Introduction

One of the questions concerning the origin of the cosmic rays is to locate the sources and to study the acceleration mechanisms able to produce the observed particles with energies orders of magnitude above the level which can be reached with man-made accelerators. Over the last years it became evident that multimessengers searches can help to achieve this task. The construction of large neutrino telescopes at the South Pole (IceCube) and in the Mediterranean Sea (where ANTARES is operating and KM3NeT is proposed) are important steps in this direction. Underwater neutrino telescopes are optimized to detect the Cherenkov light from the muons produced by the neutrino interaction in the medium surrounding the detector: the high energy neutrino momentum is transferred to the muon allowing for the reconstruction of the initial direction. 2

ANTARES

The ANTARES detector is fully equipped and operational since May 2008 [1]. The detector is composed of 12 detection lines placed at a depth of 2475m off the shore near Toulon, South of France, plus an instrumented line for the monitoring of the environment. The detector lines are about 450m long and hold a total of 885 optical modules (OM), 17”glass spheres housing each a 10” photomultiplier tube [2]. A schematic layout of the detector is shown in Fig. 1. The OMs look downward at 45o in order to optimize the detection of upgoing, i.e. neutrino induced, tracks. All detected signals are transmitted via an optical cable to the shore station, where a data - filter selects coincident signals or hits, in several adjacent OMs. The muon direction is then determined by means of a maximum like-lihood procedure in which the position and arrival time of the hits are compared to the expectation from a Cherenkov signal of a muon track. The detection of upgoing (atmospheric) neutrinos is of the order of a few events per day. a e-mail:

[email protected]

106

Figure 1: Schematic view of the ANTARES detector.

3

Search for point sources

The search for point sources of astrophysical high energy neutrinos represents one of the major challenges of the experiment. At present, the analysis has been performed on the data collected in the period from the 2007 to 2010 for a total integrated livetime of 813 days. The search method is based on the likelihood of the observed events [3] where a probability density function which allows to distinguishing between low and high energy events has been included. Two different analysis have been performed: the full sky search for an excess of events over the background anywhere in the observable sky and the fixed search for an excess of events at a number of 24 predefined candidate sources in the sky. In the full sky search, no significant clusters of neutrino candidates were found. The most signal-like cluster is located at αs, δs = (-47o ,65o ) equatorial coordinates, the test statistic for this cluster being still compatible with background. The results of the search in the direction of 24 pre-defined candidate sources have shown that none of the sources have a significant excess of events. The 90% confidence level limits on the neutrino flux using the FeldmanCousins prescription [4] and assuming an Eν−2 neutrino spectrum for each of the source candidates as a function of the source declination is shown in fig 2 together with the results from other experiments. The sensitivity of this analysis, defined as the median expected limit, is also shown in the figure. One should note that these partial ANTARES results represent the best limits of the neutrino flux in the 10 TeV energy regime for the Southern Hemisphere (the limits in the same sky region published by the IceCube Collaboration [5] refer to a neutrino flux in the PeV region).

107

Figure 2: Flux limits from selected candidates (blue dots) with an Eν−2 energy spectrum. The sensitivity, which is defined as the median expected limit is the blue dotted line. Results from other experiments are also shown.

4

Diffuse flux

A search for a diffuse flux of astrophysical muon neutrinos has been done in the data collected during the period from December 2007 to December 2009 for a total of 334 days of equivalent live time. The atmospheric neutrinos that have traversed the Earth and have been detected as up-going neutrino in the ANTARES telescope are an irreducible background for the study of cosmic neutrinos. However the spectrum of cosmic neutrinos is expected to be harder (∼ Eν−2 ) than that of atmospheric neutrinos and a possible method to distinguish the cosmic diffuse flux is to search for an excess of high energy events in the measured energy spectrum. To this purpose an energy estimator was defined [6]. As for the point like search the selection of the candidate tracks was obtained by applying requirements on the geometry of the event and on the track reconstruction quality parameter. First, with a proper choice of cuts, all the atmospheric muons were removed from the sample. Then, to separate atmospheric and astrophysical neutrinos, a suitable cut on the energy estimator was applied. Being the number of observed events compatible with the number of expected background events, the upper limit for the flux at a 90% confidence level was calculated using the FeldmanCousins approach as shown in fig.3. Here the results of Frejus, MACRO, Amanda-II 2000-03 refer to the limits of the same νµ + ν¯µ flux while Baikal and Amanda-II UHE 2000-02 refer to neutrinos and antineutrinos of all flavors, and are divided by 3. For reference, the W&B [7] and the MPR [8] upper bounds for transparent sources are also shown: they have been divided by two, to take into account neutrino oscilla-

108

Figure 3: The ANTARES 90% c.l. upper limit for a E −2 diffuse high energy νµ + ν¯µ flux, compared to results from other experiments and theoretical estimates.

tions. The grey band represents the expected variation of the atmospheric νµ flux. 5

On-going physics analysis

The ANTARES project is an important physics experiment and the continuous data taking started in 2007 is expected to continue at least until 2016. A detailed planning of various analyses has been agreed within the collaboration: in addition to the point like and diffuse searches already described, various physics analyses are in progress. In the following we give the highlights of some of the most significant. A correlation between Ultra High Energy Cosmic Ray (UHECR) events detected by AUGER [9] and neutrino events candidates detected by ANTARES is being studied with a stacking analysis: in this approach the arrival directions of neutrino events observed by the neutrino telescope ANTARES in 2007 and 2008 with 5 to 12 lines and 69 ultra-high energy cosmic rays (UHECRs) detected by AUGER are correlated. The analysis looks for a cumulative excess in the directions of all of the UHECR events allowing for a possible deflection of 3o of charged particles in the magnetic fields. For the given period no correlated neutrino events have been found Concerning the analyses related to the indirect search for Dark Matter the work has mainly concentrated on the search for neutrino candidates coming from the Sun using a special reconstruction algorithm optimized for low energies (∼ 100 GeV). This analysis extended to the 2007-2008 period is in progress. Since the start of operation of ANTARES an online connection of the DAQ system to the satellites of Gamma-ray Burst Coordination Network has been

109 established. Currently GRB data analyses are being performed on the 2007 and 2008 data sets, both for muon and electron shower reconstruction. The unblinding of the data corresponding to 37 selected GRBs of 2007 has taken place. No events were found from the direction of any of these GRBs, allowing a limit to be placed on the corresponding flux of muon neutrinos. Neutrino telescopes are also well suited for the search of magnetic monopoles; these particles are expected to deliver a conspicuous signal in the detector in a wide variety of conditions. To this extent, a dedicated version of the reconstruction algorithm in which the particle velocity is left free and fitted as an additional track parameter has been developed. A further cut on the number of hits produced by the monopole gives a good discrimination power for β ≥ 0.65 The unblinding of the whole 2008 data sample did not show any signal and the corresponding 90% C.L. limits for the monopole flux have been determined. 6

Conclusion

ANTARES is the largest neutrino telescope taking data in the Northern hemisphere. The search of point like sources and diffuse flux for the data collected in the 2007-2010 period shows no significant excess of events from the atmospheric neutrino background. The detection of dark matter from the Sun, the signal from the magnetic monopole and many other physics analysis are in progress and benefit from the excellent angular resolution and acceptance of the detector which is expected to operate at least until 2016. References [1] A. Aguilar et al. Nucl. Inst. and Methods, A 656 (2011), 11 [2] A. Aguilar et al. Nucl. Inst. and Methods, A 555 (2005),132 [3] Aart Heijboer: The ANTARES Collaboration, contributions to the 31st International Cosmic Ray Conference (ICRC 2009), Lodz, Poland, July 2009,arXiv:1002.0701v1. [4] G. J. Feldman and R. D. Cousins, Phys. Rev. D, 1998, 57(7):3873-3889 [5] R. Abbasi et al., Astrophys. J., 2011, 732, 18. [6] J.A. Aguilar et al. Phys. Letter B 696 (2011) 16-22 [7] E. Waxman and J. Bahcall, Phys. Rev. D 59 (1998) [8] K. Mannheim, R. J. Protheroe, J. P. Rachen, Phys. Rev. D 63 (2000) [9] J. Abraham et al., Nucl. Inst. and Methods, A 523, (2004), 50

110 TRITIUM-β-DECAY EXPERIMENTS - THE DIRECT WAY TO THE ABSOLUTE NEUTRINO MASS Lutz Bornschein a , for the KATRIN collaboration Institute for Nuclear Physics, Karlsruhe Institute of Technology, Postfach 3640, D-76021 Karlsruhe, Germany Abstract. Tritium-β-decay experiments provide the most sensitive approach to measure the absolute neutrino mass in a model independent way. The Karlsruhe Tritium Neutrino experiment KATRIN will measure the neutrino mass scale with an expected sensitivity of 0.2 eV/c2 (90% C.L.) and so will help to clarify the roles of neutrinos in the early universe. KATRIN investigates spectroscopically the electron spectrum from tritium β-decay 3 H →3 He + e− + ν e close to the kinematic endpoint of 18.6 keV. It will use a windowless gaseous tritium source in combination with an electrostatic filter for energy analysis. KATRIN is currently under construction at the Karlsruhe Institute of Technology (KIT) Campus North. This proceeding will give an overview of the status of the main components of the KATRIN experiment.

1

Introduction

Recent results of the measurement of the cosmic microwave background fit remarkably well with the simplest cosmological ΛCDM model [1]. The model predicts a fraction of about 23% of the total matter density Ωtot given by matter density of dark matter ΩDM while the majority of about 73% is given by the cosmological constant ΩΛ . There are even hints that a warm dark matter model (ΛWDM) could explain the observations on small (galactic) scales where the current ΛCDM model seems to fail [2]. Although great efforts are done to directly detect WIMPs [3] the still only proven (hot) dark matter particle is the neutrino. With the discovery of massive neutrinos from ν-oscillation experiments about a decade ago (e.g. [4–8]), one of the most fundamental tasks over the next years will be the determination of the absolute mass scale of neutrinos. We know today from direct measurements [9] as well as from cosmological bounds [10] that the neutrino masses are definitely so small that they provide only a subdominant fraction of the cosmological dark matter. However the interpretation of cosmological data leads to inconclusive statements on neutrino masses. Therefore, it is essential to probe neutrino masses with laboratory experiments. The spectroscopy of β-decay just below the kinematic endpoint is the only direct and model independent way to investigate neutrino masses with a sensitivity in the (sub-) eV range [11]. a e-mail:

[email protected]

111 2

Tritium β–decay experiments

The most sensitive method to study the electron neutrino mass is the investigation of the tritium β decay 3 H → 3 He + e− + ν¯e where a non-zero “effective” neutrino mass mν causes a distortion of the β spectrum. The energy spectrum of the β decay electrons in the case of quasi-degenerated neutrino masses with an absolute mass scale in the range of the sensitivity of future tritium β experiments is given by √ d2 N ∝ p(E+me c2 )(E0 −E) (E0 − E)2 − m2ν c4 dEdt

with m2ν =

3 ∑

2

|Uei | mi 2 .

i=1

(1) Since the influence of the experimental observable m2ν is only significant close to the β endpoint energy, these experiments require a high β–decay rate, a huge luminosity, a very high energy resolution and a very low background rate. Tritium is the isotope of choice for this kind of experiments for many decades because it has one of the lowest known β–endpoint energies of E0 = 18.6 keV, a reasonably short half life of 12.3 y, a low nuclear charge and a simple electronic shell configuration. In addition, the tritium β–decay is a super-allowed nuclear transition. In the experiments in Mainz and Troitsk [12, 13], this technique reached a new level of sensitivity with the use of the so called MAC-E-Filter (Magnetic Adiabatic collimation combined with an Electrostatic Filter) [14, 15]. It consists essentially of two superconducting solenoids separated by ring electrodes. Source and detector are placed in high-field regions of the magnets. The magnetic guiding field enables the acceptance of up to full forward solid angle of 2π and the transformation of the transverse cyclotron motion into longitudinal motion parallel to the magnetic field. The retarding electrostatic potential of the electrodes reaches its maximum at the minimum of the magnetic field. The energy resolution of the MAC-E-Filter is given by the ratio of the minimum and maximum of the magnetic fields the electrons pass on their way between source and detector. The results of the measurements in Mainz (using a quench condensed source) and Troitsk (using a windowless gaseous source) for m2ν were within the experimental sensitivity compatible with zero [16–18]. Meanwhile both experiments reached their intrinsic sensitivity limit. From their results the Particle Data Group derives an upper limit on the “effective” neutrino mass of mν < 2 eV [9]. 3

The Karlsruhe Tritium Neutrino Experiment – KATRIN

In 2001 the leading groups in the field of tritium β–decay experiments came together to initiate the Karlsruhe Tritium Neutrino Experiment (KATRIN)

112 CMS

WGTS

Transport Section

Spectrometer Section

Detector

Figure 1: Overview of the KATRIN experiment. For further details see main text.

on site of the Forschungszentrum Karlsruhe (now KIT Campus North). This is an ultimate experiment with an at least one order of magnitude improved sensitivity on mν . Since the measurements in Mainz showed that an enlarged quench condensed tritium source was not an option for the new experiment due to self charging of the tritium films [19], a windowless gaseous tritium source (WGTS), similar to the one used in Troitsk but much stronger, was chosen. For this source a throughput of 40 g per day of almost pure tritium gas (≥ 95 %) will be needed. Therefore KATRIN makes use of the unique expertise of the Tritium Laboratory Karlsruhe (TLK), which is the only scientific laboratory with a closed tritium cycle and a license to handle the required amount of tritium. The KATRIN experiment consists of five main sections (Fig. 1): Beta electrons are produced in the windowless gaseous tritium source. The transport section, which reduces the tritium flow rate by at least 14 orders of magnitude, adiabatically guides the electrons to the spectrometer section, where the energy analysis is performed, and the detector where the electrons are counted. The calibration and monitoring system (CMS) monitors the activity of the WGTS and performs systematic studies. In the following an overview of the status of these main sections will be given. Windowless gaseous tritium source In order to reach the design sensitivity of 0.2 eV/c2 , the main parameters of the windowless gaseous tritium source (WGTS), i.e. the source temperature, the gas inlet and outlet flow rate and the isotopic composition of the inlet gas, have to be stabilized to the per mill level. The results of the test experiment “Demonstrator” have shown that the cooling concept of the WGTS cryostat can achieve a temperature stabilization of the 30 K beam tube in the mK range, which is more than one order of magnitude better than specifications [20]. After completing the tests, the Demonstrator will be upgraded to the final WGTS by installing the superconducting magnets and other related tritium-handling components.

113 The stabilization of the gas inlet and outlet flow rate is performed by the Inner Loop System. It injects Tritium gas from a pressure controlled buffer vessel via a capillary with constant conductivity into the center of the source beam tube from where the tritium diffuses to both sides. At the end of the source beam tube the gas is removed by turbomolecular pumps (TMPs), cleaned by a palladium membrane filter and pumped into a storage vessel. From there the tritium gas is led through a Laser Raman cell back into the pressure controlled buffer vessel. A four week test run of the Inner Loop System with a capillary of similar conductance as the KATRIN injection capillary and the source tube showed a five times better stability of the pressure profile than required for the design values of KATRIN [21]. The precise knowledge of the composition of the tritium inlet gas of the WGTS is necessary to account for systematic effects in the WGTS, e.g. Doppler broadening, elastic scattering, nuclear recoil and the final state distribution of the (3 HeT)+ daughter molecules. The gas composition for KATRIN is monitored in the Inner Loop System with Laser Raman spectroscopy (LARA). This allows the simultaneous monitoring of all hydrogen isotopologues (T2 , DT, HT, D2 , HD, H2 ) [22]. A test of the LARA system in the closed tritium loop LOOPINO for 3 weeks of non-stop operation showed that the required 0.1% precision is achievable under KATRIN conditions [23]. Further improvement of precision due to an optimization of the laser beam path and the read-out mechanism of the optical detector are expected. Transport section The transport section consists of the differential pumping sections (DPS1-F and DPS2-F) and the cryogenic pumping section (CPS). After commissioning of the DPS2-F, the gas reduction factor has been measured for D2 , He and other noble gases at room temperature. The measured reduction factors vary between (1.86 ± 0.37) × 104 (for D2 ) and (5.6 ± 1.1) × 104 (for Kr), which are in good agreement with simulations [24]. A further improvement of the gas reduction factor can be expected when the instrumentation of the DPS2-F beam tube is completed. The manufacturing of the CPS is ongoing and the delivery to KIT is expected for 2012. Spectrometer section Two electrostatic filters, based on the MAC-E principle, are used for the energy analysis of the β-decay electrons. The pre-spectrometer will reject those electrons with energies more than about 300 eV below the endpoint, i.e. which do not contain information on the neutrino mass. The retarding potential of the main spectrometer will be varied to measure the spectrum of the last ∼30 eV below the endpoint with an energy resolution of about 0.93 eV. The

114 pre-spectrometer has been operated as a prototype for systematic investigations and hardware developments for KATRIN. During the extended test program, a non-negligible background component for the KATRIN spectrometers was identified. 219 Rn atoms, emanating from non-evaporate getter strips, decay inside the spectrometers and produce energetic electrons that are magnetically trapped subsequently. The electrons lose their energy via collisions with residual gas molecules and produce low energetic electrons that cannot be trapped. Those electrons are guided to the end of the spectrometers where they can produce ring-like patterns on the detector [25]. A counter-measure with a LN2 cooled baffle has been successfully tested at the pre-spectrometer and a similar system was installed at the main spectrometer. The test operation of the pre-spectrometer was finished in spring 2011 and it is now ready for its final integration into the KATRIN setup. The installation of the wire frame modules [26] in the main spectrometer, which are needed for the precise forming of the electrical retarding potential and for the reduction of muon induced electron background, is almost complete. The commissioning and first measurements of the main spectrometer are scheduled for 2012. Detector The detector system, designed and built by the University of Washington in Seattle, USA, has arrived in Karlsruhe in summer 2011. It has been commissioned successfully at the KATRIN beam line. Calibration and monitoring system The feasibility of source activity monitoring using β induced X-ray spectroscopy has been successfully demonstrated at Tritium Laboratory Karlsruhe. A technical design of the calibration and monitoring section has been developed. 4

Conclusion

Tritium-β-decay experiments provide the most sensitive approach to measure the absolute neutrino mass in a model independent way. With the KATRIN experiment this technique is pushed to the limit of what is technically and physically feasible. It is currently under construction at the KIT Campus North. Test measurements of several main components of KATRIN have been successfully performed and important milestones were achieved, other main components have been commissioned or are in the final commissioning phase. With the upcoming measurements at the main spectrometer in 2012 the commissioning of KATRIN main components will continue.

115 Acknowledgments The author has dedicated his presentation at the 15th Lomonosov Conference on Elementary Particle Physics to Academician Prof. Vladimir M. Lobashev, Head of the Experimental Physics Department of the Institute for Nuclear Research in Troitsk and Head of the Troitsk Neutrino Mass Experiment. Academician Prof. Vladimir M. Lobashev died on August, 3rd 2011 at the age of 78. The audience paid tribute to Academician Prof. Vladimir M. Lobashev with a minute of silence. References [1] E. Komatsu et al., The Astrophys. Jour. Suppl. Series, 192:18 (47pp), 2011. [2] H.J. de Vega, N.G. Sanchez, arXiv:1109.3187v1 [astro-ph.CO] 14 Sep 2011. [3] D. Akimov, Nucl. Inst. and Meth. A 628, (2011) 5058. [4] T. Kirsten, Rev. Mod. Phys. 71 (1999) 1213. [5] Q.R. Ahmad et al., Phys. Rev. Lett. 81 (2001) 071301. [6] Y. Fukuda et al., Phys. Rev. Lett. 85 (2000) 3999. [7] K. Eguchi et al., Phys. Rev. Lett. 90 (2003) 021802. [8] M.H. Ahn et al., Phys. Rev. Lett. 90 (2003) 041801. [9] K. Nakamura et al. (Particle Data Group), J. Phys. G 37, 075021 (2010) and 2011 partial update for the 2012 edition. [10] S. Hannestad, arXiv:1007.0658v2 [hep-ph] 11 Aug 2010 [11] E.W. Otten, Ch. Weinheimer, Rep. Prog. Phys. 71 (2008) 086201 (36pp). [12] A. Picard et al., Nucl. Inst. and Meth. B 63, 345 (1992). [13] V.M. Lobashev, P.E. Spivak, Nucl. Inst. and Meth. A 240 (1985) (6pp). [14] P. Kruit, F.H. Read, J. Phys. E: Sci. Instrum. 16 313 (1983). [15] G Beamson et al, J. Phys. E: Sci. Instrum. 13 64 (1980). [16] V.M. Lobashev et al., Phys. Lett. B 460 (1999) 227-235. [17] V.M. Lobashev, Nucl. Phys. A 719 (2003) C153-C160. [18] Ch. Kraus et al., Eur. Phys. J. C 40 (2005) 447-468. [19] B. Bornschein et al., Jour. of Low Temp. Phys. Vol. 131, 1/2, (2003). [20] S. Grohmann, Cryogenics 49 (2009) 413420. [21] M. Sturm, Dissertation (2010), KIT. [22] M. Sturm et al., Laser Phys. 20 2, 493 (2010). [23] S. Fischer et al., Fusion Sci. Technol. 60 3 (2011) 925-930. [24] S. Lukic et al., Vacuum (2011), article in press, arXiv:1107.0220v1 [physics.ins-det] (2011). [25] F.M. Fr¨ ankle et al., Astropart. Phys. 35 3 (2011). [26] K. Valerius, Prog. in Part. and Nucl. Phys. 64 2 291-293 (2010).

116 SEARCH FOR ντ INTERACTIONS WITH THE NUCLEAR EMULSION FILMS OF THE OPERA EXPERIMENT Fabio Pupilli a , on behalf of the OPERA Collaboration INFN - Laboratori Nazionali del Gran Sasso, I-67100 Assergi (L’Aquila), Italy Abstract. The OPERA experiment aims at measuring the νµ → ντ oscillation through the ντ appearance in an almost pure νµ beam (CNGS). For the direct identification of the short-lived τ lepton, produced in ντ CC interactions, a micrometric detection resolution is needed. Therefore the OPERA detector makes use of nuclear emulsion films, the highest spatial resolution tracking device, combined with lead plates in an emulsion cloud chamber (ECC) structure called ’brick’. In this paper the nuclear emulsion analysis chain is reported; the strategy and the algorithms set up will be described together with their performances.

1

Introduction

In the past decades several experiments provided compelling evidences supporting the neutrino oscillation hypothesis. For what concerns the atmospheric neutrino sector, the disappearance of muonic neutrinos have been convincingly observed in different experiments [1], exploiting both natural and artificial neutrino sources. Nevertheless, the confirmation of the νµ → ντ oscillation as the leading channel, through the direct observation of the ντ appearance is still missing. The OPERA experiment [2], located in the underground Gran Sasso National Laboratory, is aiming at the first direct observation of neutrino oscillations in appearance mode by the identification of the τ lepton produced in ντ CC interactions, in an almost pure νµ beam (CNGS [3]) produced by the CERN SPS, 730 km far away from the detector. The τ detection is accomplished by an event-by-event topological and kinematical reconstruction, and the micrometric resolution needed to identify the short-lived τ particle is provided by nuclear emulsions. 2

The detector

OPERA is a hybrid detector [4] made of two indentical sections called Super Modules (SM), each one composed of a muon spectrometer and a target section hosting the core of the apparatus, highly modular sandwiches of emulsion and lead plates (bricks). The bricks are arranged in vertical structures called walls transverse to the beam direction; each wall is followed by a pair of tracker planes (TT) made of plastic scintillator strips and providing bi-dimensional information used to identify the brick where the neutrino interaction occurred and to generate the trigger. The muon spectrometer at the downstream end of each SM allows measuring charge and momentum of penetrating tracks. a e-mail:

[email protected]

117 3

OPERA bricks and emulsion automatic scanning

The OPERA bricks exploit the ECC (Emulsion Cloud Chamber) technique: emulsion films are interspaced with lead plates, providing high tracking resolution and large target mass in a modular way. Each brick is composed of 57 emulsion films interleaved with 56 lead plates of 1 mm thickness. The transverse dimension of a brick are 12.5 × 10.0 cm2 and the thickness along the beam direction is 7.9 cm, corresponding to about 10 radiation lengths. The weight is about 8.3 kg. A tightly packed removeable doublet of emulsion films, called Changeable Sheets (CS) [5], is attached to the downstream face of each brick; CS act as offline “triggers” and interfaces between the TT and the brick, with the task of validating the result of the algorithm for the selection of bricks and allowing the transition from the centimeter resolution of the electronic detectors to the micrometric resolution of nuclear emulsions. A total amount of 150000 bricks have been produced and placed in the walls of the detector, for a total target mass of ∼ 1.25 ktons; this translates in an overall emulsion surface larger than 100000 m2 . The industrial production of such a large amount of films was carried out, after a joint R&D program [6], by the Fuji Film company. An OPERA film has 2 emulsion layers (each 44 µm thick) on both sides of a transparent triacetylcellulose base (205 µm thick). The total thickness is 293±5 µm; the sensitivity of a film amounts to ∼ 36 grains/100 µm for minimum ionising particles. Given the rate of ∼ 20 neutrino interactions/day and the corresponding large emulsion surface to be analysed, a dedicated R&D project was pursued in OPERA leading to the development of fully automated high-speed scanning systems [7]. The systems are based on a motorised stage, holding the emulsion film, and on an optics equipped with a camera, moving along the Z direction and focusing different depths in emulsion: in this way, while the area to be scanned is spanned in the X-Y direction, the camera produces optical tomographic image sequences of each emulsion layer. The acquired images are digitized and processed by a control workstation to reconstruct aligned sequences of grains through an emulsion layer (micro-tracks). The linking of two matching micro-tracks produces the so-called base-track (see Figure 1); this reduces the instrumental background due to fake combinatorial alignments. The analysis of an emulsion stack continues with the film-to-film alignment, computing the six parameters of an affine transformation by a suitable alignment pattern (as described in the following section), and with the volume-track formation by fitting aligned base-tracks in the analysed volume. The performances of this analysis procedure have been evaluated in a 10 GeV pion exposure of an OPERA emulsion stack without lead, to test intrinsic resolutions and efficiencies [8]: the position resolution is sub-micrometric, while the angular resolution is of the order of a mrad; the base-track finding efficiency is on average ∼ 90%.

118

Figure 1: Micro-track connection across the plastic base (base-track)

4

Event analysis

Once signals in the electronic detectors are compatible with an interaction inside a brick, data are processed by a software reconstruction program that selects the brick with the highest probability to contain the neutrino interaction vertex [9]. The impact point on CS of the muon (for CC-like events) or of the barycenter of the shower (for NC-like events) is also predicted. The brick is extracted from the detector and is stored in a shielded area underground, waiting for confirmation by the CS films analysis. Given the measured position resolution of the TT reconstruction (∼ 8 mm), a large area around the prediction is scanned on each CS film; the films are roughly aligned exploiting four X-ray marks printed before the development of the doublet (with a precision of ∼ 10 µm) and finely aligned using tracks from low energy electrons emitted in the decay of natural radioactive isotopes (∼ 2 µm precision). If tracks compatible with an interaction in the brick and with electronic detector data are found in the CS films, the corresponding brick undergoes an exposure to X-rays, to produce lateral marks on the film edges for a coarse alignment, and to high energy cosmic rays, to provide a pattern of tracks for a refined film-to-film alignment; then it is dismantled and the emulsion films are developed. If no signal is detected in the CS films, the brick is reinserted in the detector with a fresh CS doublet and the next most probable brick is extracted. All tracks found in the CS films are looked for in the most downstream film of the brick and then followed back from film to film (scan-back), exploiting the lateral X-ray mark alignment, until they are not found in five consecutive films. The stopping point is considered as the signature either for a primary or a secondary vertex. The vertex confirmation is performed by scanning an area of 1 cm2 on 5 upstream and 10 downstream films with respect to the stopping point (volume-scan). All base-tracks are reconstructed and aligned with a micrometric precision, thanks to the cosmic ray alignment tracks, and the volume tracks are constructed. The interaction point is identified by an automated algorithm as the minimum distance point of two or more tracks and the vertex is fully reconstructed. A dedicated procedure, called decay search, is performed with the aim of finding eventual decay topologies, secondary interactions or γ-ray conversions, searching for large kink angles or for tracks

119 with large impact parameter (IP) with respect to the vertex (since the IP for primary tracks is not larger than 10 µm). When a secondary vertex is found, a kinematical analysis is performed, exploiting the high resolution ensured by nuclear emulsions: momenta of charged particles are estimated through the angular deviations due to the Multiple Coulomb Scattering of particles in lead plates (with a resolution of ∼ 22%) [10]; the energy of electromagnetic showers is measured by a Neural Network shower shape analysis, which takes into account also the Multiple Coulomb Scattering of the leading tracks. This analysis chain led to the reconstruction of ∼ 2800 neutrino interactions in the first two physics runs [11], and to the observation of a first ντ candidate event [12]. 5

Conclusions

Thanks to their high resolution, nuclear emulsions play a key role for the purposes of the OPERA experiment. High speed automatic scanning systems and dedicated procedures have been developed for each analysis step, to ensure a micrometric resolution in position and an angular resolution of the order of a mrad, needed for the τ decay topological identification.Nuclear emulsion films are also used in kinematical analysis of decay topologies. The OPERA nuclear emulsion analysis chain has proven to be successful, leading to the reconstruction of ∼ 2800 neutrino interactions and of a first ντ candidate. References [1] Y. Fukuda et al. [Super-K Coll.], Phys. Rev. Lett. 81, 1562 (1998). M. H. Ahn et al. [K2K Coll.], Phys. Rev. D 74, 072003 (2006). P. Adamson et al. [MINOS Coll.], Phys. Rev. Lett. 101, 131802 (2008). [2] M. Guler et al. [OPERA Coll.], CERN-SPSC-2000-028. [3] CNGS project: http://proj-cngs.web.cern.ch/proj-cngs/. [4] R. Acquafredda et al. [OPERA Coll.], JINST 4, P04018 (2009). [5] A. Anokhina et al. [OPERA Coll.], JINST 3, P07005 (2008). [6] T. Nakamura et al., Nucl. Instrum. Meth. A 556, 80 (2006). [7] L. Arrabito et al., Nucl. Instrum. Meth. A 568, 578 (2006). K. Morishima and T. Nakano, JINST 5 P04011 (2010). [8] L. Arrabito et al., JINST 2, P05004 (2007). [9] N. Agafonova et al. [OPERA Coll.], New J. Phys. 13, 053051 (2011). R. Rescigno, The electronic detectors of the hybrid OPERA neutrino experiment, these proceedings. [10] N. Agafonova et al. [OPERA Coll.], arXiv:1106.6211v1 [physics.ins-det], submitted to New J. Phys. [11] N. Agafonova et al. [OPERA Coll.], arXiv:1107.2594v1 [hep-ex]. [12] N. Agafonova et al. [OPERA Coll.], Phys. Lett. B 691, 138 (2010).

120 THE ELECTRONIC DETECTORS OF THE HYBRID OPERA NEUTRINO EXPERIMENT R. Rescigno a on behalf of the OPERA collaboration Department of Physics, Salerno University, I- 84084 Fisciano, Salerno, Italy Abstract. OPERA is an hybrid detector for neutrino oscillation detection in appearance mode; the Electronic Detectors (EDs) have the crucial role of triggering for neutrino events and predicting the position of the interaction vertex in the target. The EDs consist of a target tracker (scintillator strips) and a spectrometer (RPC and drift tubes). The various sub-detectors are described in the paper as well as their performance as estimated by Monte-Carlo simulation and measured from real data.

1

Introduction

The OPERA experiment aims at observing ντ appearance in an almost pure νµ beam [1] . The ντ particle is indirectly observed by the detection of the τ lepton produced in its CC interaction and identified through the topology and the kinematics at both the interaction and decay vertices. The OPERA apparatus features Electronic Detectors (EDs) to provide a trigger for neutrino interactions, locate the interaction target unit and measure the muon momentum and charge [2]. The data collected during the 2008 and 2009 runs are reviewed and several kinematical variable distributions obtained using the EDs are compared to the Monte-Carlo (MC) simulation. 2

OPERA electronic detectors

Figure 1: Side view of the OPERA detector

The detector [2] is composed of two identical super-modules (SM1 and SM2, see Figure 1), each made of a muon spectrometer and a target section. The a e-mail:

[email protected]

121 veto system is placed upstream of the first SM. The detector has a total length of 20 m, is 10 m high and 10 m wide. The VETO System The first part of the OPERA apparatus crossed by the neutrino beam is the veto system. It consists of two layers of glass RPC with an overall sensitive area of about 200 m2 . The purpose of this device is to tag charged particles produced in interactions occurring in the rock in front of the OPERA target. It is operated in streamer mode, reaching an efficiency of about 97%. The Target Section Each target section is composed of lead-emulsion units, named bricks, arranged in walls interleaved with pairs of planes of plastic scintillator strips that constitute the Target Tracker (TT). A brick is a stack of 57 emulsion films, providing the sub-micrometric resolution, interleaved with 56 lead plates, each 1 mm thick and providing the mass. More information on this can be found in [6]. The insertion and extraction of bricks into/from the OPERA target is handled by the Brick Manipulator System (BMS). The TT provides a real time detection of charged particles produced in neutrino interactions, complementing emulsion films with time resolution. It allows locating the brick in which the interaction took place by defining a probability map; about 60% of the events are located in the most probable brick, and 80% are in the first two bricks. The TT also works as sampling calorimeter. The scintillator strips in each pair of planes are oriented horizontally and vertically. Each plane spans 6.7 x 6.7 m2 and is made of 4 modules of 64 strips each read at both ends via wavelength shifting (WLS) fibers connected to multi-anode photomultiplier tubes. For a minimum ionizing particle (m.i.p) the sum of the numbers of photo-electrons collected at both ends of the fibres exceeds 15, with an efficiency of about 99 %. The position accuracy is 10 mm and the angular accuracy is 23 mrad [3]. Each target section is equipped with 32 double planes of vertical (X) and horizontal (Y) strips. The trigger for neutrino event is defined by the requirement of at least 2 XY coincidences in the TT with a threshold of 1 photo-electron, in a time window around the CNGS neutrino spill of 10.5 µs. The Muon Spectometers The muon spectrometers identify muons and measure their momentum and the sign of their charge. Each spectrometer consists of a dipolar magnet with arms made of 12 iron slabs. The measured magnetic field strength is 1.52 T. The two arms are interleaved with 6 drift tube stations called HPT (High Precision Tracker) for precise measurement of muon bending. The spatial single-tube resolution is better than 300 µm. Planes of bakelite Resistive Plate Chamber (RPC) are interleaved with the iron slabs (11 RPC planes in each arm), providing a coarse tracking inside the

122

Figure 2: Muon momentum reconstruction for Monte-Carlo (pink) and real data (black). Normalization for the MC sample is provided by real data.

Figure 3: Reconstructed momentum × charge: real data (black dots with error bars) and MC (solid histogram) are both normalized to unity.

Figure 4: Energy deposited in the TT for events with at least one reconstructed muon. Dots corresponds to data and solid histogram to MC. The MC distribution is normalized to data.

Figure 5: Transverse hadronic shower profile in the X and Y projections. Dots with error bars denote data, solid histogram denotes MC. The MC sample is normalized to data.

magnet, range measurement of stopping particles and a calorimetric information of hadron showers. The total area covered is 3500 m2 [4]. 3

Performance of the OPERA ED

This section presents a comparison between MC simulation and data collected during years 2008 and 2009 [5]. Muon momentum and charge The momentum measurement is performed by using a Kalman filter-based algorithm. The momentum resolution is better than 20 % for momentum lower than 30 GeV/c. The reconstructed muon momentum distribution is shown in Fig. 2 and compared to MC expectations: a very good agreement is observed.

123 The efficiency of the algorithm used to determine the sign of the muon has been studied using CC MC events. Wrong charge assignment occurs for about 1.2% of muons with momenta between 2.5 and 45 GeV/c. Figure 3 shows the momentum times charge distribution for data and MC both normalized to unity. Visible energy and hadronic shower profile The energy deposited in the TT can be estimated by converting the photo-electron signal picked up at each end of the scintillator strips, as explained in [5]. The results of the comparison between data and MC are reported in Fig. 4: the two distributions are in good agreement. The profile of hadron showers is studied by weighting the position of TT hits by the number of collected photo-electrons. The transverse profile distribution is shown in Fig. 5. NC-to-CC ratio The NC/CC ratio obtained with MC is equal to 0.257 ± 0.031 whereas the data collected give a ratio of 0.228 ± 0.008. The two estimates agree within statistical errors. 4

Conclusions

OPERA is the first experiment designed to search for ντ appearance in a νµ beam. It uses an hybrid detector with a lead-emulsion target and electronic detectors. Specific results from the emulsion analysis are presented in [6]. The data collected during the 2008 and 2009 runs with the EDs fully operating for more than 98% of the active beam time are compared to expectations from MC simulation. Simulation and real data agree in terms of energy deposition, shower profile and muon reconstruction and momentum measurement. The agreement between the expected and found NC/CC ratio indicates a good understanding and control of the detector performance. References [1] [2] [3] [4] [5] [6]

M. Guler et al., CERN-SPSC-2000-028 (2000) R. Acquafredda et al., J. Instrum 4 P04018 (2009). T. Adam et al., Nucl. Instrum. Methods A 557, 523 (2007). M. Ambrosio et al., IEEE Trans. Nucl. Sci 51, 975 (2004). N. Agafonova et al., New J. Phys 13, 053051 (2011). F.Pupilli, “Search for ντ interaction with the nuclear emulsions of the OPERA experiment”, these proceedings.

124 RECENT RESULTS FROM SUPER-KAMIOKANDE Yoshihisa Obayashi a Kamioka Observatory, Institute for Cosmic Ray Research(ICRR), The University of Tokyo, 456 Higashimozumi, Kamiokacho, Hidashi, Gifu 506-1205 JAPAN, and Institute for the Physics and Mathematics of the Universe(IPMU), Todai Institutes for Advanced Study(TODIAS), The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwashi, Chiba 277-8583 Japan Abstract. Super-Kamiokande(SK) is a large water Cerenkov detector which consists of 50 kton pure water. Atmospheric and solar neutrino oscillation analysis results, nucleon decay search results and search for neutrinos from supernovae in SKI+II+III (before electronics upgrade) data and preliminary results on neutrino observation in SK-IV are reported.

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Introduction

Super-Kamiokande(SK) is a large water Cerenkov detector which consists of 50 kton pure water as a target of observation of atmospheric, solar, supernovae and accelerator neutrino and as a source of nucleon decay. Cherenkov lights emitted by charged particles from neutrino interaction at 22.5 kton of fiducial volume are viewed by 11,146 inward-facing 20-inch photomultiplier tubes(PMTs) during the first run of the detector, SK-I. The two subsequent run periods, SK-II and SK-III had 5,182 and 11,129 PMTs respectively. The outer detector surrounding the inner volume has been instrumented with 1,885 outward-facing 8-inch PMTs and used primarily as a veto. Although Super-Kamiokande has provided enormous amount of data and physics results [1] for more than 10 years since the observation started in 1996, DAQ electronics and computers are upgraded, then, SK started its physics data taking as SK-IV in October 2008. Atmospheric and solar neutrino oscillation analysis results, nucleon decay search results and search for neutrinos from supernovae in SK-I+II+III (before electronics upgrade) data and preliminary results on neutrino observation in SK-IV are reported in the following sections. 2

Atmospheric neutrino oscillation analysis

The atmospheric neutrino data are divided into three categories. Fully contained (FC) events deposit all of their Cherenkov light in the inner detector (ID), Partially contained (PC) events additionally have an exiting particle that deposes energy in the outer detector (OD), and upward-going muon (Up-µ) events are produced by neutrino interactions in the rock below the detector. FC events are separated into Sub-GeV (Evis < 1.33 GeV) and MultiGeV (Evis > 1.33 GeV) then further separated based on their number of rea e-mail:[email protected]

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constructed Cherenkov rings and their particle identification. The sub-GeV single-ring e- and µ- like samples are further divided based upon their number of decay-electrons and whether or not they are π 0 -like. Details of this selection procedure is found in [2]. The atmospheric neutrino data and MC expectation for the first three SK run period is shown in Figure1. A standard oscillation analysis based on the zenith angle distribution and L/E distribution is performed for SK-I+II+III atmospheric neutrino data. The details of the analysis may be found in [3], [4]. The obtained allowed regions are shown in the Figure 2. The best fit oscillation parameters obtained by the Zenith and L/E analysis are ( ∆m223 , sin2 2θ23 ) = ( 2.11 × 10−3 (eV2 ), 1.0 ) and ( 2.19 × 10−3 (eV2 ), 1.0 ), respectively. Both results of zenith angle and L/E analysis give consistent results. Recent Result from T2K is shown in Figure 2 as well. A search for non-zero θ13 and deviations of sin2 θ23 from 0.5 in the threeflavor oscillation framework has been also performed. Since the analysis is also sensitive for the hierarchy of neutrino mass, analysis are performed for both normal and inverted mass hierarchy. Additionally, a CP phase δ is also considered in the analysis. Detail of the analysis may be found in [2], but here all oscillation parameters are considered at a time. As a result of the analysis, consistent result to the two-flavor analysis and no significant preference on hierarchy, no significant constraint on CP phase at 90% C.L. are obtained.

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Figure 3: Allowed regions for the antineutrino mixing parameters for the SKI+II+III data set. The blue, red and green contours represent the 68%, 90%, and 99% allowed regions. The shaded region shows the 90% CL allowed region of ν¯µ disappearance measurement from MINOS [5].

3

0

5

10 15 20 Total electron energy (MeV)

Figure 4: Ratio of ovserved and expected energy spectra of solar neutrino. The dashed line represents the SK-III average.

A search for CPT-violation

A search for differences in the oscillations of anti neutrinos and neutrinos in the SK-I+II+III atmospheric neutrino data has been performed. Though SK cannot distinguish ν from ν¯ on an event by event basis, potential difference in their oscillations would appear at a statistical level. Here, we consider ad-hoc CPT violations by testing separate two-neutrino disappearance models for ν ¯ 2 , sin2 2θ, ¯ ∆m2 , and ν¯. The best fit oscillation parameters is found at ( ∆m 2 −3 2 −3 2 2 sin 2θ ) = ( 2.0 × 10 eV , 1.0, 2.1 × 10 eV , 1.0 ) with χ = 470.6 for 416 degrees of freedom. Allowed regions for the antineutrino oscillation parameters are shown in Figure 3 with antineutrino results from MINOS [5]. No difference in ν and ν¯ mixing is found in the data and the best fit in the neutrino parameters is consistent with standard two flavor results.

4

Atmospheric neutrino data from SK-IV

Atmospheric neutrino data is successfully accumulated after the all electronics upgrade as SK-IV. Oscillation analysis results including SK-IV data will be published soon.

127 5

Solar neutrino

Since solar neutrino has small kinetic energy compare to atmospheric neutrino, reducing the background hits is essential to improve its analysis. In the SK-III period, by lowering radon level emanated in the water and controling water flow in the SK tank, background level is lowered down to about 60% compare to SK-I period. Additionaly, analysis method also improved for event reconstruction and inventing new event selection cut, and by understanding water transparency and reflectivity of black sheet on the tank wall, systematic error could be reduced at about 2/3 of SK-I period. Obtained 8 B flux of 2.32 ± 0.04(stat) ± 0.05(syst)(×106 /cm2 s) from SK-III solar neutrino data is well consistent with SK-I and II results. Day/Night ratio (Φ −ΦNight ) = −0.056 ± 0.031(stat) ± 0.013(syst) from SK-III is of ADN = (ΦDay Day +ΦNight ) also consistent with SK-I and II results. Observed spectra with respect to the expectation is shown in Figure 4. In the SK-IV solar neutrino analysis, energy threshold is lowered down to 4.0MeV and the analysis results will be published soon. 6

Nucleon decay search

The nucleon decay search is one of the most important physics targets at SuperKamiokande. Since expected energy region and event topology is quite similar as atmospheric neutrino, nucleon decay search has been performed on same dataset as atmospheric neutrino analysis. The nucleon decay search for major decay modes are performed on SK-I, II, III and early dataset from SK-IV but still no positive signal has been detected. Therefore, we have updated lifetime limit of nucleon decay as follows: τ /BR > 1.3 × 1034 year for p → e+ π 0 mode, τ /BR > 1.1 × 1034 year for p → µ+ π 0 mode, τ /BR > 4.0 × 1033 year for p → νK + mode. References [1] [2] [3] [4] [5] [6]

Y. Fukuda et al., Phys. Rev. Lett. 81, 1562(1998) R. Wendell et al., Phys. Rev. D 81, 092004 (2010). Y. Ashie et al., Phys. Rev. D 71, 112005(2005). Y. Ashie et al., Phys. Rev. Lett. 93, 101801(2004). P. Adamson et al, Phys. Rev. Lett. 107, 021801 (2011) K. Abe et al, Phys. Rev. D 81, 052010(2011)

128 NEXT GENERATION WATER CHERENKOV DETECTOR HYPER-KAMIOKANDE ∼ R&D STATUS ∼ Yoshihisa Obayashi a Kamioka Observatory, Institute for Cosmic Ray Research(ICRR), The University of Tokyo, 456 Higashimozumi, Kamiokacho, Hidashi, Gifu 506-1205 JAPAN, and Institute for the Physics and Mathematics of the Universe(IPMU), Todai Institutes for Advanced Study(TODIAS), The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwashi, Chiba 277-8583 Japan Abstract. Hyper-Kamiokande(Hyper-K) working group is now desiging [1] a next generation underground water Cherenkov detector, which will serve as a long baseline neutrino oscillation experiment and as a detector for atomospheric neutrinos, and neutrinos from astronomical origins. Status of R&D for the detector construction and its physics capability is described.

1

Introduction

We propose the Hyper-Kamiokande (Hyper-K) detector as a next generation underground water Cherenkov detector. The baseline design of Hyper-K is based on the well-proven technologies employed and tested at SuperKamiokande. Hyper-K consists of two cylindrical tanks lying side-by-side, the outer dimensions of each tank being 48 (W) × 54 (H) × 250 (L) m3 . The total (fiducial) mass of the detector is 0.99 (0.56) million metric tons, which is about 20 (25) times larger than that of Super-K. A proposed location for Hyper-K is about 8 km south of Super-K (and 295 km away from J-PARC) and 1,750 meters water equivalent (or 648 m of rock) deep. The inner detector region is viewed by 99,000 20-inch PMTs, corresponding to the PMT density of 20% photo-cathode coverage (one half of that of Super-K). Table 1 summarizes the baseline design parameters of the Hyper-K detector. 2

Physics targets

Hyper-K provides rich neutrino physics programs. In particular, it has unprecedented potential for precision measurements of neutrino oscillation parameters and discovery reach for CP violation in the lepton sector. With a total exposure of 5 years (1 year being equal to 107 sec) to a 2.5-degree off-axis neutrino beam produced by the 1.66 MW J-PARC proton synchrotron, it is expected that the CP phase δ can be determined to better than 18 degrees for all values of δ and that CP violation can be established with a statistical significance of 3σ for 74% of the δ parameter space if sin2 2θ13 > 0.03 and the mass hierarchy is known. If the mass hierarchy is unknown, the sensitivity to the CP violation is somewhat reduced due to degeneracy. For a large value of sin2 2θ13 , it is a e-mail:[email protected]

129 Table 1: Detector parameters of the baseline design.

Candidate site Address Lat. Long. Alt. Overburden Cosmic Ray Muon flux Off-axis angle for the J-PARC ν Distance from the J-PARC Detector geometry Total Volume Inner Volume (Fiducial Volume) Outer Volume Photo-multiplier tubes Inner detector Outer detector Water quality light attenuation length Rn concentration

Tochibora mine Kamioka town, Gifu, JAPAN 36◦ 21′ 08.928′′ N 137◦ 18′ 49.688′′ E 508 m 648 m rock (1,750 m water equivalent) 1.0 ∼ 2.3 × 10−6 sec−1 cm−2 2.5◦ (same as Super-Kamiokande) 295 km (same as Super-Kamiokande) 0.99 Megaton 0.74 (0.56) Megaton 0.2 Megaton 99,000 20-inch ϕ PMTs 20% photo-coverage 25,000 8-inch ϕ PMTs > 100 m @ 400 nm < 1 mBq/m3

also possible to determine the mass hierarchy for some of δ with this program alone. If sin2 2θ13 = 0.1, the mass hierarchy can be determined with more than 3σ statistical significance for 46% of the δ parameter space. The recent result of sin2 2θ13 > 0.03 obtained by the T2K experiment [2] boosts the expectation of discovery of CP violation by Hyper-K. The high statistics data sample of atmospheric neutrinos obtained by HyperK will allow us to extract information on the mass hierarchy and the octant of θ23 . With a full 10 year period of data taking, the significance for the mass hierarchy determination is expected to reach 3σ or greater if sin2 2θ13 > 0.04 and sin2 θ23 > 0.4. If sin2 2θ23 is less than 0.99, it is possible to identify the octant of θ23 , i.e. discriminate sin2 θ23 < 0.5 from > 0.5. Hyper-K extends the sensitivity to nucleon decays far beyond that of SuperK. The sensitivity to the partial lifetime of protons for the decay mode p → e+ π 0 , the mode considered to be most model independent, is expected to be 1.3 × 1035 years. It is the only realistic detector option known today able to reach this sensitivity. The sensitivity for the decay mode p → ν¯K + , the mode favored by super symmetry (SUSY) models, reaches 2.5 × 1034 years, and

130 therefore Hyper-K would discover proton decay if some of the SUSY models are correct. Table 2: Physics targets and expected sensitivities of the Hyper-Kamiokande experiment. σSD is the WIMP-proton spin dependent cross section.

Physics Target Neutrino study w/ J-PARC ν − CP phase precision − CP V 3σ discovery coverage

Atmospheric neutrino study − MH determination − θ23 octant determination Nucleon Decay Searches − p → e+ + π 0 − p → ν¯ + K + Solar neutrinos − 8 B ν from Sun − 8 B ν day/night accuracy Astrophysical objects − Supernova burst ν − Supernova relic ν − WIMP annihilation at Sun

Sensitivity / Conditions 1.66 MW × 5 years (1 year ≡ 107 sec) < 18◦ @ s2 2θ13 (≡ sin2 2θ13 ) > 0.03 and mass hierarchy (MH) is known 74% @ s2 2θ13 = 0.1, MH known 74% @ s2 2θ13 = 0.03, MH known 66% @ s2 2θ13 = 0.01, MH known 10 years observation > 3σ CL @ 0.4 < s2 θ23 and 0.04 < s2 2θ13 > 90% CL @ s2 2θ23 < 0.99 and 0.04 < s2 2θ13 10 years data 1.3 × 1035 yrs (90% CL) 5.7 × 1034 yrs (3σ CL) 2.5 × 1034 yrs (90% CL) 1.0 × 1034 yrs (3σ CL) 200 ν’s / day @ 7.0 MeV threshold w/ osc. < 1% @ 5 years, only stat. w/ SK-I BG ×20 170,000∼260,000 ν’s @ Galactic center 30∼50 ν’s @ M31 (Andromeda galaxy) 830 ν’s / 10 years 5 years observation σSD = 10−39 cm2 @ MWIMP = 10 GeV, χχ → b¯b dominant σSD = 10−40 cm2 @ MWIMP = 100 GeV, χχ → W + W − dominant

Hyper-Kamiokande functions as an astrophysical neutrino observatory. If a core collapse supernova explosion occurs halfway across our galaxy, the HyperK detector would detect approximately 170,000∼260,000 neutrinos as a ∼ 10 second long burst. This very large statistical sample should at last reveal the detailed mechanism of supernova explosions. For instance, the onset time of the explosion can be determined with an accuracy of 0.03 milliseconds, which is a key information to study the first physical process of the explosion (p + e− → n + νe ), allowing examination of the infall of the core and the ability to see the precise moment when a new neutron star or black hole is born. The sharp risetime of the burst in Hyper-K can also be used to make a measurement of the

131 absolute mass of neutrinos. Because of non-zero masses, their arrival times will depend on their energy. The resulting measurement of the absolute neutrino mass would have a sensitivity of 0.5 − 1.3 eV/c2 , and does not depend on whether the neutrino is a Dirac or Majorana particle. Hyper-K is also capable of detecting supernova explosion neutrinos from galaxies outside of our own Milky Way; about 7,000-10,000 neutrinos from the Large Magellanic Cloud and 30-50 even from the Andromeda galaxy. Detection of supernova relic neutrinos (SRN) is of great interest because the history of heavy element synthesis in the universe is encoded in the SRN energy spectrum. With gadolinium added to water, a neutron produced by the inverse beta process (¯ νe + p → e+ + n), which is the predominant interaction mode for the SRNs, can be tagged by detecting gammas from the Gd(n,γs)Gd reaction. Doing so greatly reduces backgrounds and opens up the SRN energy window, improving the detector’s response to this important signal. Our study shows that Hyper-K with 0.1% by mass of gadolinium dissolved in the water is able to detect as many as 830 SRNs in the energy range of 10-30 MeV for 10 years of livetime. This large sample will enable us to explore the evolution of the universe. Dark matter can be searched for in Hyper-K as was done in Super-K. Neutrinos emitted by weakly interacting massive particles (WIMPs) annihilating in the Sun, Earth, and galactic halo can be detected using the upward-going muons observed in Hyper-K. A sensitivity to the WIMP-proton spin dependent cross section would reach 10−39 (10−40 ) cm2 for a WIMP mass of 10 (100) GeV and 5 years of livetime. 3

Summary

Table 2 summarizes the physics potential of Hyper-K. A realistic design of the detector with cost estimation is ongoing. Inspection of rock condition around the candidate site is also ongoing. The detailed report after those inspection and discussion will be appear near future. References [1] K. Abe et al. (Hyper-K), arXiv:1109.3262v1 [hep-ex]. [2] K. Abe et al. (T2K), Phys. Rev. Lett. 107, 041801 (2011), arXiv:1106. 2822 [hep-ex].

132 THE DAEδALUS EXPERIMENT Zelimir Djurcic a Argonne National Laboratory, 9700 South Cass Avenue, Argonne, IL 60439, USA Abstract. The DAEδALUS experiment follows a new approach to search for the CP-violation in the neutrino sector. It is envisioned to utilize multiple intense neutrino beams with energy up to 52.8 MeV from pion and muon decay-at-rest, near a very large water Cherenkov or a large liquid scintillator detector. Therefore, the experiment would search for ν¯µ → ν¯e oscillations at short baselines corresponding to the atmospheric ∆m2 region. Such experiment would have much different systematics than, for example, proposed long baseline neutrino experiment (LBNE) using a beam from Fermilab to DUSEL, and would rely on the recent and ongoing development of compact, superconducting cyclotron technology.

Introduction The DAEδALUS is a Decay-At-rest Experiment for δCP studies At the Laboratory for Underground Science. The primary goal of the experiment is a search for CP-violation in ν¯µ → ν¯e oscillation channel at the atmospheric ∆m2 by measuring absolute neutrino rates in a single detector that is exposed to neutrino beam sources at three distances [1], [2], [3]. In this way the search exploits the L-dependence of the CP-violating interference term in the oscillation formula, rather that direct comparison of measurements performed with neutrino and anti-neutrino beams as planned in several proposed long-baseline experiments. Cyclotrons will be used to deliver protons into a beam stop to produce pion and muon decay-at-rest (DAR) anti-neutrino beams of a high intensity. Such DAR neutrino beam arrises from the stopped pion decay chain π + → νµ + µ+ , µ+ → e+ ν¯µ νe . The resulting ν¯µ flux rises with the energy to the 52.8 MeV endpoint with well-known energy dependence. Given that most π − capture before decay, the intrinsic ν¯e fraction in the beam is only about 4 x 10−4 of the total. Experimental configuration under consideration assumes neutrino sources positioned at distnce (L) of 1.5 km, 8 km, and 20 km from a large Water Cherenkov detector [4]. Here the advantage of the DAR coming from the nature of the weak interaction provides identical (up to the relative normalization) energy dependence of thee fluxes. The large water detector provides free protons as the target for the inverse beta decay interaction (IBD): ν¯e + p → n + e+ . The IBD interaction is identified with a coincidence signal consisted of the Cherenkov ring produced by the positron followed by the capture of neutron. Water doped with gadolinium (Gd) is desired to enhance the neutron capture signal. In principle, the DAEδALUS can be installed near any ultra-large detector with free protons such as LBNE with a potential Water Cherenkov detector in US [5], Hyper-K experiment in Japan [6] or an experiment with a neutrino beam from CERN to either very large water Cherenkov a e-mail:

[email protected]

133 detector [7] or liquid scintillator [8] in Europe. The cyclotrons at three sites will be run at alternating periods: detected neutrino events will have L defined by timing. CP-violation reach It is the most likely that CP-violation search will be a two phase measurement. In this report one may assume that the first phase will use 1MW, 2MW and 3MW accelerators at the near, mid and far locations to explore the oscillation space at ∼3σ level. Based on the first phase results, one may deploy additional neutrino sources at appropriate locations in the second phase to achieve an optimal measurement. Here we assume the second phase configuration realized with 1MW, 2MW and 7MW accelerators at the near, mid and far locations. In addition, we assume each phase extending over a five year period.

Figure 1: One (inner contour) and two (outer contour) σ sensitivities for DAEδALUS for 10 years of DAEδALUS running.

134 To evaluate the CP-violation sensitivity the following three steps are needed: • The absolute normalization of the flux from near accelerator is measured using ν-e scatters in the detector for which the cross-section is known to 1%. • The relative flux normalization between the neutrino sources (accelerators) is determined by comparison of electron-neutrino-oxygen interaction rates in the detector. • When the normalization of the accelerators is determined the IBD events from three sites can be fit to extract the CP-violating parameter δCP . Given that the oscillation probability also depends on the mixing angle θ13 the resulting measurement is described in a sin2 2θ13 − δCP plane. Fig. 1 shows the CP-violation sensitivity when two phases are combined in a 10 year measurement, with use of a 300kTON Gd-doped Water Cherenkov detector. DAEδALUS is not sensitive to matter effects and, therefore, has a degeneracy between the two mass hierarchies. This can be represented by showing the δCP scale for normal hierarchy on the left and inverted on the right of Fig 1. DAEδALUS can determine if there is CP violation (i.e. δCP 6= 0 or 180◦ ) without knowing the hierarchy. The capabilities of the DAEδALUS are enhanced when combined with a long-baseline experiment such as proposed LBNE experiment which uses a conventional long-baseline neutrino beam from Fermilab to DUSEL. Studies of detector configurations for the CP-violation searches combining LBNE and DAEδALUS [4] show that the CP-violation sensitivity is outstanding when the DAEδALUS 10 year run (¯ ν -only mode) is combined with a 10 year LBNE run (ν-only mode, 30 × 1020 protons-on-target) and a 300kTON Water Cherenkov detector at DUSEL, as shown in Fig. 2. The LBNE-alone and the DAEδALUSalone have comparable capabilities. However, combined LBNE and DAEδALUS experiments exceed the sensitivity of ProjectX, consistent with other published studies [9]. Cyclotron requirements and status The antineutrinos would be created using a high-power (MW class) proton cyclotron with ≈800 MeV beam energy that sends a beam into a beam dump. The DAEδALUS will benefit from high-power cyclotrons under development for commercial purposes. In fact, no special beam qualities are needed beside the high power at appropriate energy within a broad time window. However, machines should be reliable to run with adequate up-time over the 10 year period at a low operations cost. Three potential cyclotron designs are under consideration for the DAEδALUS [10], [11]. One design is the Multi-MegaWatt Cyclotron (MMC) under development as an technology for Accelerator Driven

135

Exclusion of GCP= 00 or 1800 at 3V in 10 yrs

Fraction of GCP

1.0 0.8 0.6 0.4 0.2 0.0 0.001

0.01

0.1

sin2(2T13) Daedalus(100kt Gd) + LBNE_nu_only(300kt WC) Daedalus(200kt Gd) + LBNE_nu_only (200kt_WC+17kt_LAr) Daedalus(300kt Gd) + LBNE_nu_only (300kt WC) LBNE (300kt WC) nu_30e20 + nubar_30e20 LBNE ProjectX (300kt WC) nu_100e20 + nubar_100e20 Figure 2: Fraction of δCP space over which a measurement can be differentiated from δCP = 0◦ or 180◦ at 3σ in 10 years, assuminga known normal hierarchy.

136 Systems (ADS) for Thorium Reactors. Fig shows the cyclotron, with the beam injected from the right, accelerated and stripped with two extraction paths. It consists of an injector and a booster cyclotron. The MMC would

Figure 3: Preliminary design of a DAEδALUS Multi-MegaWatt Cyclotron. An injector and a booster cyclotron are shown.

accelerate H+ 2 ions with to meet design goals of 12 mA of beam at 800 MeV. Current approach is based on commercially available equipment to provide a cost-effective solution. Beam dumps are expected to be simple graphite targets. The ion source may be adapted from the ECR Visible Ion Source at Catania, while the injector cyclotron is planned to be a modified commercial model. The three sources will have beam-on times synchronized. In such scheme the detector will receive the 100 msec beam bunch from each source within 500 msec period. During 200 msec time interval (40% of the total cycle time) we plan to have all sources off, to allow measurement of cosmogenic and other backgrounds. A description of all aspects of the system from the ion source to the extracted beam is provided in [12].

137 Conclusion DAEδALUS is experiment that will improve CP-violation sensitivity in the way complementary to long-baseline experiments and which may be possible for an inverse-beta-decay-sensitive far detector. Combining data from decay-at-rest sources at 20 km, 8 km, and 2 km from a large water Cherenkov detector with Gd doping has oscillation sensitivity similar to planned long-baseline experiments. DAEδALUS requires development of new high-power cyclotrons (which may have industrial applications). Combining decay-at-rest (DAEδALUS ) antineutrino data with a neutrino data from an experiment such as LBNE would result in a sensitivity much better than what would Project-X upgrade provide with LBNE-alone. References [1] J. M. Conrad and M. H. Shaevitz, Phys. Rev. Lett 104, 141802 (2010). [2] J. Alonso et. al., “Expression of Interest for A Novel Search for CP Violation in the Neutrino Sector: DAEδALUS”, arXiv: 1006.0260 (2010). [3] J. M. Conrad, “The DAEδALUS Experiment”, arXiv:1012.4853 [hep-ex]. [4] J. Alonso et. al., “A Study of Detector Configurations for the DUSEL CP Violation Searches Combining LBNE and DAEδALUS”, arXiv: 1008.4967 (2010). [5] Long-Baseline Neutrino Experiment (http://lbne.fnal.gov/), T. Akiri et. al., arXiv:1110.6249. [6] K. Abe et. al., arXiv:1109.3262 hep-ex]. [7] A. de Bellefon et. al., arXiv:hep-ph/0603172. [8] M. Wurm et. al., arXiv:1104.5620 [hep-ex]. [9] S. K. Agarwalla et. al. “A new approach to anti-neutrino running in long-baseline neutrino oscillation experiments”, arXiv: 1005.4055 (2010). [10] J. Alonso, “The DAEδALUS Project: Rationale and Beam Requirements”, arXiv: 1010.0971 (2010). [11] L. Calabretta et. al., “A Multi Megawatt Cyclotron Complex to Search for CP Violation in the Neutrino Sector”, arXiv:1010.1493 (2010). [12] L. Calabretta et. al., “Preliminary Design Study of High-Power H2+ Cyclotrons for the DAEdALUS Experiment”, arXiv:1107.0652v1 [physics.acc-ph].

138 THE NOνA EXPERIMENT Zelimir Djurcic a Argonne National Laboratory, 9700 South Cass Avenue, Argonne, IL 60439, USA Abstract. The NOνA experiment is designed to search for a non-vanishing mixing angle θ13 with unprecedented sensitivity and has the potential to resolve the neutrino mass hierarchy and constrain CP-violation phase. NOνA will use two functionally identical detectors at near and far locations to eliminate sensitivity to modeling of neutrino flux and cross-sections. The near detector will measure neutrino rate to constrain backgrounds expected in the far detector which will search for appearance of electron neutrinos and/or anti-neutrinos using Fermilab NuMI neutrino beam. The NOνA prototype near detector on the surface started running at Fermilab in October 2010 and registered its first neutrino interactions from the NuMI beam in December 2010. Current status of experiment is described.

1

Introduction

Recent years have seen enormous progress in the physics of neutrino mixing, but several critical questions remain: What is the value of θ13 , the last unmeasured mixing angle in the neutrino mixing matrix? What is the mass hierarchy? Do neutrino oscillations violate CP symmetry? Why are the quark and neutrino mixing matrices so different? A major motivation to search for CP-violation in neutrino oscillations is that its observation would make it more likely that the baryon-antibaryon asymmetry of the universe arose through leptogenesis [1]. The theory of leptogenesis is linked to the see-saw theory and as a consequence the light neutrinos are Majorana and have GUT-scale partners. Then the matter-antimatter asymmetry of the universe may be explained through CPviolating decays of the heavy partners, producing a state with unequal numbers of Standard Model leptons and antileptons. Furthermore, the Standard Model processes convert such a state into the world around us with an unequal number of baryons and antibaryons. It is thought that CP-violation would be very unlikely to appear in the heavy sector without happening in light neutrinos [2]. The value of θ13 is central to each of these questions. Measurement of non-zero value of θ13 would open a wide range of possibilities to explore CP-violation and the mass hierarchy. In addition, the size of θ13 with respect to the other mixing angles may give insights into the origin of these angles and the source of neutrino mass. Experimental methods to measure the currently unknown mixing angle θ13 include accelerator searches for νe appearance and precise measurements of reactor antineutrino disappearance. While both accelerator and reactor experiments hold the promise of unambiguously determining the θ13 mixing angle, the NOνA (NuMI Off-Axis νe Appearance) Experiment is an accelerator based experiment that will help address all of the questions listed above [3]. a e-mail:

[email protected]

139 2

NOνA Description

The measurement of θ13 at NOνA will be conducted by searching for an appearance of electron neutrinos and/or anti-neutrinos in the NuMI (Neutrinos at the Main Injector) neutrino beam at Fermilab. Neutrinos for NOνA will be produced by 120 GeV protons incident on a graphite target. The Fermilab accelerator complex is currently capable of delivering 400 kilowatts of power to the NuMI beam, but part of the NOvA project will include an upgrade to the accelerator to provide 700 kilowatts of power to NuMI. The experiment will use two functionally identical detectors: a 222 ton “Near” detector at a distance of about a 1000 m from the NuMI beam target and a large 14 kilo-ton “Far” detector at a distance of 810 km located in Ash River, Minnesota. Fig. 1 shows NOνA near and far detectors with corresponding dimensions. The detectors

Figure 1: NOνA near and far detectors with corresponding dimensions.

will be located at an off-axis angle of 0.8◦ with respect to the NuMI beam axis resulting in the neutrino flux confined to a relatively narrow band of energy around 2 GeV, which is useful in limiting backgrounds in νµ → νe searches. The detectors have a cell structure made of highly reflective extruded plastic PVC filled with liquid scintillator. The Far detector cells are 3.9 cm wide, 6.0 cm deep and 15.5 meters long. The Near detector cells are shorter with the same width and depth. Neutrinos interacting in the liquid produce charged particles

140 with energy collected with wavelength-shifting fibers connected to avalanche photo-diodes (APDs) as photo-detectors. Such a scheme allows a very precise measurement of neutrino energy and an efficient separation of νe from νµ . The construction of the detectors is underway and the first neutrino detection has already been achieved with the Near detector prototype located in a surface building at Fermilab. For the final location of the Near detector, a tunnel at the NuMI beam at 0.80 off-axis location will be excavated. The use of two detectors eliminates sensitivity to modeling of the neutrino flux and cross-sections, and only requires a knowledge of the relative acceptance of the two detectors. The cancellation of these important systematic errors will allow NOνA to explore the range of sin2 2θ13 at the 0.01 level. The neutrino beams at hand and initial thoughts on how we plan to use these beams with available detectors to reach the NOνA goals is described in [4].

3

NDOS and current status of NOνA experiment

The Near Detector On the Surface (NDOS) is the prototype of NOνA Near detector. The NOνA NDOS started running at Fermilab in October 2010 and registered its first neutrino interactions from the NuMI beam in December 2010. The NDOS location at Fermilab was chosen to provide the prototype to simultaneously detect neutrino interactions from both the NuMI neutrino beam (110 mrad or 6.4o off-axis) and the Booster neutrino beam (on-axis). Constructing and operating the NDOS allowed the collaboration to exercise preparation for production of full far detector. It was found that ∼22% of the manifold covers that close detector cells cracked after assembly into a block. These manifolds have been fixed and a new design was adopted for final production. In addition, it was discovered that surface cleanliness and sealing issues have led to many of the NDOS APDs behaving unusably noisy. A total of 274 installed APD units have been removed from the NDOS detector for additional cleaning and testing. To alleviate these issues the collaboration is investigating new surface coating and installation techniques. Despite all challenges listed above the NDOS provided extremely valuable preparation for construction of Far detector. It also allowed collaboration to collect and analyze real cosmic rays and neutrinos and enabled early development of calibration techniques and physics analyses. Fig. 2 shows the NDOS event display with cosmic ray muon tracks and Fig. 3 is showing the display of a candidate neutrino event from NuMI beam. The Far detector laboratory is complete and the detector construction will commence in 2012. Construction of the full 14 kilo-ton detector is expected to be completed in 2014. The NuMI beam upgrades are on schedule to begin during the accelerator shutdown in March 2012. In the same time the Near detector cavern will be prepared.

141

Figure 2: NDOS event display showing cosmic ray muon tracks. The top and side views of the display represent vertical and horizontal detector modules. Indicated are sections that are not fully instrumented.

Expected raw signal and background rates at the Far detector are shown in Fig. 4 (Left). The NOνA detectors will be able to reject the νµ CC and NC events at a level sufficient to make the hashed signal structure detectable. The expected sensitivity of the NOvA experiment to νµ → νe transition expressed as a combination of θ13 and θ23 mixing angles with respect to δCP is shown in Fig. 4 (Right), assuming a conservative 10% systematic error on the backgrounds, and 6 years of running evenly split between neutrino and anti-neutrino horn polarities. 4

Summary and conclusion

Currently there are two long-baseline experiments running: T2K [5] and MINOS [6]. Both recently reported indications of νµ → νe appearance. Several of the reactor antineutrino experiments, designed to search for a non-vanishing mixing angle θ13 with unprecedented sensitivity, recently reported first results. The Double Chooz collaboration presented results of the first oscillation search performed with the far-only detector [7], and the Daya Bay Collaboration performed the first θ13 search with a near/far detector combination [8]. The results

142

Figure 3: NDOS event display showing a candidate neutrino event from NuMI beam.

provide a strong evidence of reactor electron antineutrino disappearance consistent with neutrino oscillations [9]. Recent global fits combining these results favor value of sin2 2θ13 ∼ 0.08 with a high confidence. This is the beginning in our multi-year program to establish the magnitude of θ13 that will culminate with the NOνA oscillation searches. The upcoming NOνA [3] experiment will be operational in 2014. It will be the first precision experiment to probe oscillations with neutrinos propagating through signifiant matter. References [1] B. Kayser, Proceedings of the 22nd Recontres de Blois, eds. L. Celnikier, J. Durarchez, B. Klima, and J. Tran Trahn Van (Gioi Publishers, Viernam, 2011) p.91. [2] C. Amsler, et al., Review of particle physics, see chapter 13, Neutrino Mixing, Phys. Lett. B667 (2008) 1. doi:10.1016/j. physletb.2008.07.018. [3] D. Ayres et al., FERMILAB-DESIGN-2007-01.; G. S. Davies, arXiv:1110.0112; M. Betancourt, arXiv:1109.6692; [4] Z. Djurcic, AIP Conf.Proc.1382:132-134,2011, FERMILAB-CONF-11655; [5] K. Abe et al., Phys.Rev.Lett. 107, 041801 (2011), 1106.2822. [6] P. Adamson et al., Phys. Rev. Lett. 107, 181802 (2011), hep-ex/1108. 0015v1.

143

δ (π)

90% CL Sensitivity to sin2(2θ13) ≠ 0 2 NOνA 1.8 1.6

10

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[7] Y. Abe et al, arXiv:1112.6353[hep-ex]. [8] F. P. An et al, arXiv:1203.1669 [hep-ex]. [9] Talk given by Z. Djurcic at NuFact 2011; Z. Djurcic, arXiv:1201.1522 [hep-ex] .

144 OPPORTUNITIES OF SAGE WITH ARTIFICAL NEUTRINO SOURCE FOR INVESTIGATION OF ACTIVE-STERILE TRANSITIONS Vladimir Gavrina Institute for Nuclear Research RAS,Moscow 117312 Russia Abstract. SAGE with very intense artificial neutrino source provides a unique possibility to search of transitions of electron neutrino to sterile states. We propose to place a very intense source of 51 Cr at the center of a 50-tonne target of gallium metal that is divided into two concentric spherical zones and to measure the neutrino capture rate in each zone. This experiment can set limits on transitions from active to sterile neutrinos with ∆m2 ≈ 1 eV2 with a sensitivity to disappearance of electron neutrinos of a few percent.

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Introduction

The search for sterile neutrino is now a field of active investigation. The idea of the sterile neutrino was first proposed by B. Pontecorvo [1] and has been used repeatedly to explain a variety of different neutrino observations [2]. To the experiments that can be interpreted in terms of neutrino oscillations belong also the capture rate measurements in the Ga detectors SAGE [3, 4] and GALLEX [5]. These four experiments used intense reactor-produced 51 Cr or 37 Ar neutrino sources and their weighted-average value, expressed as the ratio R of the measured production rate to the expected production rate based on the measured source strength, is 0.87±0.05, considerably less than the expected value of unity. All possible explanations for this unexpectedly low result are discussed in detail in Ref. [6]. Foremost among these is overestimation of the cross section for neutrino capture to the lowest two excited states in 71 Ge. The interpretation of the Ga source experiments in terms of oscillations to a sterile neutrino with ∆m2 ≈ 1 eV2 , as well as the agreement of these results with the reactor experiments Bugey, Chooz, and G¨osgen and the accelerator experiments LSND and MiniBooNE is considered in detail in Ref. [7]. If transitions to a sterile neutrino are occurring, the region of allowed oscillation parameters inferred from the four Ga source experiments is shown in Figure 1. We believe that new experiments are necessary to understand the low result of the Ga source measurements. One such experiment at the Research Center of Nuclear Physics (RCNP), Osaka, that should provide information to better determine the cross section for neutrino capture at low energy is completed [8]. The result is the measured cross section which gave a slightly larger value than was roughly estimated by Bahcall and therefore it slightly amplifies the discrepancy observed in calibration measurements. Another experiment which we intend to pursue is an improved version of Ga source experiments [9]. a e-mail:

[email protected]

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The new Ga source experiment

Our plan, as schematically pictured in Figure 2, is to place a 51 Cr source with initial activity of 3 MCi at the center of a 50-tonne target of liquid Ga metal that is divided into two concentric spherical zones, an inner 8-tonne zone and an outer 42-tonne zone.

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146 After an exposure period of a few days, the Ga in each zone is transferred to reaction vessels and the 71 Ge atoms produced by neutrino capture are extracted. If oscillations to a sterile neutrino are occurring with mass squared difference of ∆m2 and mixing parameter sin2 (2θ) then the rates in the outer and inner zones of gallium will be different and their ratio, for the specific case of sin2 (2θ) = 0.3, will be as shown in Figure 3.

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Expected results and uncertainty

In the absence of oscillations and using the neutrino capture cross section on Ga calculated by Bahcall [10], a mean of ∼ 65 atoms of 71 Ge produced by the source per day is expected in each zone at the beginning of irradiation. 10 exposures will be made, each of 10 days duration with a dead time of 1 day between the irradiations. The extracted 71 Ge atoms from each zone will be measured in individual counters. One of the background components will be from solar neutrinos, which flux is now known with high accuracy from SAGE measurements since 1990. Production rate from solar neutrinos is 64 times lower than from the source at the start of the first exposure in the outer zone and ∼ 340 times lower in the inner zone. A Monte Carlo simulation based on the extraction schedule and value of the total extraction and counting efficiency 53% and background rates gives the value of statistical uncertainty 3.7% in each zone and 2.6% in the entire target. The sum of all systematic uncertainties is ±2.6% in each zone and in the entire target. The total uncertainty, statistical

147 and systematic combined in quadrature, is 4.5% for each zone and 3.7% for entire target; the theoretical uncertainty in the cross section has been neglected. The total number of the events of 71 Ge decays with statistical and systematic uncertainty is expected to be 840 ± 4.5% atoms in each zone and 1680 ± 3.7% atoms for the entire target mass. 2.2

Conclusion

The proposed experiment has the potential to test neutrino oscillation transitions with a mass-squared difference ∆m2 > 0.5 eV2 . In contrast, experiments with reactor and accelerator neutrinos suffer from several disadvantages. The neutrino energy E is distributed over a wide spectrum and the dimensions L of the sources and detectors are on the scale of several meters. Other disadvantages of a reactor or accelerator experiment are that the knowledge of the neutrino flux incident on the target is usually significantly worse than with a neutrino source and that, with some targets, there are appreciable uncertainties in the cross section for neutrino interaction. If in new experiment in which a very-intense 51 Cr source irradiates a target of Ga metal that is divided into two zones there is either a significant difference between the capture rates in the two zones, or the average rate in both zones is considerably below the expected rate, then there is evidence of nonstandard neutrino properties. The proposed experiment has the potential to test neutrino oscillation transitions with mass-squared difference ∆m2 > 0.5 eV2 . This capability exists because the experiment uses a compact nearly monochromatic neutrino source with well-known activity, the dense target of Ga metal provides a high interaction rate, and the special target geometry makes it possible to study the dependence of the rate on the distance to the source. Acknowledgments We are grateful to the Russian Foundation of Basic Research for support under grants 05-02-17199, 08-02-00146 and 11-02-00-806-a, 11-02-12130-ofi-m-2011. The research was supported by Grants of President of Russian Federation NS1782.2003.2 and NS-3517.2010. References [1] B. Pontecorvo, Zh. Eksp. Teor. Fiz. 53, 1717 (1967) [Sov. Phys. JETP 26, 984 (1968)]. [2] A. Kusenko, Phys. Rept. 481, 1 (2009); [arXiv:0906.2968]. [3] J. N. Abdurashitov et al. [SAGE coll.], Phys. Rev. C 59, 2246 (1999). [4] J. N. Abdurashitov et al. [SAGE coll.], Phys. Rev. C 73, 045805 (2006).

148 [5] F. Kaether, W. Hampel, G. Heusser, J. Kiko, and T. Kirsten, Phys. Lett. B 685, 47 (2010). [6] J. N. Abdurashitov et al. [SAGE coll.], Phys. Rev. C80, 015807 (2009); [arXiv:nucl-ex/0901.2200v3]. [7] C. Giunti and M. Laveder, Mod. Phys. Lett. A 22, 2499 (2007); [arXiv:hep-ph/0610352v2]; M. A. Acero, C. Giunti, and M. Laveder, Phys. Rev. D 78, 073009 (2008); [arXiv:0711.4222v3]; C. Giunti and M. Laveder [arXiv:0902.1992v2]; C. Giunti and M. Laveder [arXiv:1005.4599v2]. [8] D. Frekers, H. Ejiri et al. should be published in Phys. Rev. Let. (2011). [9] V. N. Gavrin, V. V. Gorbachev, E. P. Veretenkin and B. T. Cleveland, [arXiv:nucl-ex/1006.2103v2] (2011). [10] J. N. Bahcall, Phys. Rev. C 56, 3391 (1997); [arXiv:hep-ph/9710491].

149 RESULTS AND IMPLICATIONS FROM MINIBOONE: NEUTRINO OSCILLATIONS Warren Huelsnitz, for the MiniBooNE Collaboration a Los Alamos National Laboratory, Los Alamos, NM Abstract. The MiniBooNE experiment at Fermilab reported an excess of electron antineutrino-like events in a muon antineutrino beam, consistent with evidence for antineutrino oscillations in the 0.1 to 1.0 eV2 ∆m2 range from the Liquid Scintillator Neutrino Detector experiment at Los Alamos National Laboratory. Results from an updated ν¯e appearance analysis, based on 50% more data taken in antineutrino mode, will be discussed. Models involving sterile neutrinos have been proposed to explain these observations, with some models predicting large muon antineutrino disappearance. Joint analyses using data from the MiniBooNE and SciBooNE detectors to extend the sensitivity to muon neutrino and antineutrino disappearance will be discussed.

1

The MiniBooNE experiment

The MiniBooNE experiment [1] was built at Fermi National Accelerator Laboratory to test evidence for neutrino oscillations at the ∆m2 ≈ 1eV2 scale seen in the LSND experiment at Los Alamos National Laboratory [2]. MiniBooNE uses the booster neutrino beamline at FNAL; 8 GeV protons strike a beryllium target, positive or negative pions and kaons are then either focused or defocused as determined by the polarity of a focusing horn, resulting in a beam with an enhanced flux of either muon neutrinos or antineutrinos. Neutrino interactions are then detected in a 12 m diameter, mineral oil Cherenkov detector at a distance of 540 m from the target. The detector is instrumented with 1280 8-inch PMTs in the active region, and 240 8-inch PMTs in an outer, veto region. The MiniBooNE oscillation search has the same L/E ≈ 1 as LSND, but independent systematic uncertainties. 2

Updated electron antineutrino appearance measurement

MiniBooNE neutrino mode results, based on 6.5 × 1020 protons on target (POT), were reported in Ref. [3]. Above 475 MeV, the neutrino mode results showed good agreement with the background-only hypothesis and, assuming CP conservation, were inconsistent with LSND-type oscillations at the 98% confidence level (CL). Below 475 MeV, however, the data showed a 3σ excess over background. The shape of this excess, as a function of reconstructed neutrino energy, was not consistent with a simple two neutrino oscillation model. The neutrino mode low energy excess is further discussed in [4]. Figure 1 shows the updated ν¯e event distribution, using data taken in antineutrino mode through May, 2011. This data included 8.58 × 1020 POT, a e-mail:

[email protected]

150

Figure 1: Data, with statistical uncertainty, versus reconstructed neutrino energy for updated ν¯e analysis. Also shown are the predicted backgrounds with systematic uncertainty.

about 50% more data than that used in the previously published ν¯e appearance results [5]. The reconstructed neutrino energy is computed assuming that all events in the final event sample are charged current quasi-elastic (CCQE), νN → eN ′ . Figure 2 shows the observed event excess, relative to expected backgrounds, as a function of energy. This data shows an excess of 38 ± 18.5 events in the low energy region, below 475 MeV. With the addition of the new data, the low energy excess in antineutrino mode looks more similar to the low energy excess in the νe event sample in neutrino mode [3, 4]. However, the origin of the low energy excess, whether it is due to a more complicated oscillation signal, misunderstood background, or new physics, remains unresolved and is one of the physics motivations for the MicroBooNE detector [6]. The ν¯e appearance analysis of Ref. [5] was repeated using additional data taken in antineutrino mode through May, 2011. In addition to reduced statistical uncertainties in the internally constrained backgrounds, the results of a recent SciBooNE measurement of K + production in the beam [7] were included in background predictions. The results are shown in Fig. 3. Consistent with the analysis reported in [5], the region above 475 MeV was fit to a two-neutrino oscilaltion model. Above 475 MeV, there is an excess of 16 ± 19 events with an expected background of 152 events. The two-neutrino oscillation hypothesis is

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Figure 2: ν¯e appearance data minus expected background. Error bars include statistical and systematic uncertainties. The best fit to the two-neutrino oscillation model and two other oscillation hypotheses consistent with the LSND result are shown.

favored over the null (background only) hypothesis at a 91.1% CL. Although significance relative to the null hypothesis is lower than the 99.4% CL reported for the earlier ν¯e appearance result [5], compatibility with neutrino oscillations is improved. The χ2 probability is 35.5% for the oscillation fit and 14.9% for the null fit. For the previous result, the χ2 probability was 8.7% for the oscillation fit and 0.5% for the null fit. If the entire region above 200 MeV is used in the updated analysis, then LSND-like oscillations are favored at the 97.6% CL, with a χ2 probability of 50.7% for the oscillation fit. 3

Joint MiniBooNE/SciBooNE disappearance analysis

Sterile neutrino models have been invoked to explain the short baseline appearance results of MiniBooNE and LSND [8]. If these models are correct, then the appearance of νe (¯ νe ) in a νµ (¯ νµ ) beam is the result of one or more sterile neutrinos acting as an intermediary. Hence, observation of the short baseline disappearance of νµ (¯ νµ ) in an experiment such as MiniBooNE would be the ”smoking gun” to confirm or exclude these models. Such a search was performed in MiniBooNE [9], and no evidence for νµ or ν¯µ disappearance was found. However, the sensitivity of the analyses was limited by neutrino flux and cross section uncertainties. The search for νµ disappearance was recently

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Figure 3: Preliminary results for the updated ν¯e oscillation analysis.

revisited with the inclusion of data from the SciBooNE detector [10]. SciBooNE operated in the same beamline as MiniBooNE during 2007 and 2008, collecting data while the beam was operating in neutrino mode as well as antineutrino mode. SciBooNE was at a distance of 100 m from the target. Two complimentary disappearance analyses were performed using the same data. In the simultaneous fit method, the data from both detectors were fit simulataneously to a two neutrino oscillation model. In the spectrum fit method, SciBooNE data were used to determine energy dependent scale factors that were then applied to the MiniBooNE simulation. The results can be seen in Fig. 3 of Ref. [11]. No evidence for νµ disappearance was found, however limits on sin2 2θ were improved, relative to previous results, in the region 10 → 30 eV2 . A joint search for ν¯µ disappearance using data from MiniBooNE and SciBooNE is underway. This new analysis will take advantage of neutrino cross section measurements [12], background measurements [7, 12], and constraints on neutrino background in the antineutrino beam [13]. 4

Summary and future plans

MiniBooNE’s ν¯e appearance analysis has been updated using 50% more data. The result remains consistent with evidence from LSND for ∆m2 ≈ 1 eV2

153 oscillations, however with reduced significance but higher compatability with neutrino oscillations. The excess at low energy now appears more consistent between neutrino and antineutrino modes, however the origin is still unresolved. An analysis that will simultaneously fit MiniBooNE’s νe and ν¯e appearance data is in progress, with and without allowing CP violation. A joint MiniBooNE/SciBooNE search for νµ disappearance has been completed and a search for ν¯µ disappearance is underway. The MiniBooNE Collaboration anticipates running into the summer of 2012, increasing the current antineutrino data set by another 50%. References [1] A.A. Aguilar-Arevalo et al., (MiniBooNE Collaboration), Nucl. Instrum. Meth. A, 599:28-46 (2009). [2] A. Aguilar et al., (LSND Collaboration), Phys. Rev. D 64, 112007 (2001). [3] A.A. Aguilar-Arevalo et al., (MiniBooNE Collaboration), Phys. Rev. Lett. 98, 231801 (2007). [4] A.A. Aguilar-Arevalo et al., (MiniBooNE Collaboration), Phys. Rev. Lett. 102, 101802 (2009). [5] A.A. Aguilar-Arevalo et al., (MiniBooNE Collaboration), Phys. Rev. Lett. 105, 181801 (2010). [6] H. Chen et al., (MicroBooNE Collaboration), Proposal for a New Experiment Using the Booster and NuMI Neutrino Beamlines: MicroBooNE. FERMILAB-PROPOSAL-0974. [7] G. Cheng et al., (SciBooNE Collaboration), Phys. Rev. D 84, 012009 (2011). [8] G. Karagiorgi, et al., Phys. Rev. D 80, 073001 (2009); J. Kopp, M. Maltoni, and T. Schwetz, Phys. Rev. Lett. 107, 091801 (2011); C. Giunti and M. Laveder, arXiv: 1107.1452; G. Karagiorgi, arXiv: 1110:3735. [9] A.A. Aguilar-Arevalo et al., (MiniBooNE Collaboration), Phys. Rev. Lett. 103, 061802 (2009). [10] A.A. Aguilar-Arevalo et al., (SciBooNE Collaboration), arXiv: hepex/0601022. [11] K.B.M. Mahn et al., (MiniBooNE and SciBooNE Collaborations), arXiv:.1106.5685, (submitted to Phys. Rev. Lett.). [12] A.A. Aguilar-Arevalo et al., (MiniBooNE Collaboration), Phys. Rev. D 81, 092005 (2010). [13] A.A. Aguilar-Arevalo et al., (MiniBooNE Collaboration), Phys. Rev. D 84, 072005 (2011); J. Grange, arXiv: 1107.5327.

154 NEW OSCILLATION RESULTS FROM THE T2K EXPERIMENT Alexander Izmaylov a (for T2K Collaboration) Institute for Nuclear Research RAS, 117312 Moscow, Russia Abstract. The T2K (Tokai to Kamioka) experiment is a second generation long baseline neutrino oscillation experiment located in Japan. The main goal is to probe the θ13 neutrino mixing parameter by looking for νµ → νe transitions in an almost pure beam of muon neutrinos. The T2K utilizes the neutirno beam produced at J-PARC (Tokai, Ibaraki) and Super-Kamiokande (Kamioka, Gifu) is used as a far detector. The experiment has been in operation since January 2010. After analyzing 1.43×1020 p.o.t. data collected six events are observed in far detector while the expected number with sin2 2θ13 =0 is 1.5±0.3. Null oscillation hypotheis leads to 7×10−3 probability to observe six or more candidate events, which so gives 2.5 σ significance to the result. Thus the current T2K result is an indication of νe appearance due to νµ → νe transitions. As for the first T2K νµ disappearance data, the null oscillation hypothesis is exluded at 4.5 σ level and the estimated atmospheric mixing parameters are consistent with the results from Super-Kamiokande and MINOS experiments.

1

Introduction

The phenomenon of neutrino oscillations established and confirmed by a number of challenging experiments in the past 20 years appears to be quite compelling. The goal for the experimentalists now is to explore the case further. The T2K (Tokai to Kamioka) [1] experiment is a second generation long baseline (LBL) neutrino oscillation experiment. The main goal is to probe the only unknown θ13 neutrino mixing parameter by looking for νµ → νe transitions in an almost pure beam of muon neutrinos. Non-zero θ13 is crucial for furhter experimental searches for CP-violation in lepton sector. The best upper limit of sin2 2θ13 < 0.15 (90% C.L.) was obtained by CHOOZ reactor experiment [2] (1999) and further slightly corrected by LBL MINOS [3] (2010). Precise measurement of the atmospheric ∆m223 and of the θ23 mixing parameters in νµ disappearance channel forms another goal of the experiment. The T2K is an international collaboration which includes about 500 members from 58 institutes of 12 countries. 2

T2K design

T2K neutrino beam is produced using 30 GeV proton synchrotron at the Japan Proton Accelerator Research Complex (J-PARC) in Tokai, Japan. The experiment layout is presented on Fig. 1. a e-mail:

[email protected]

155

Figure 1: A schematic view of the T2K LBL exepriment.

The T2K is the first neutrino experiment to utilize an off-axis neutrino beam conception. The neutrino beam at J-PARC is designed so that it is directed 2.5◦ away from the direction of the Super-Kamiokande (Super-K), located 295 km to the west. This results in forming a narrow energy band neutrino beam peaked at about 600 MeV. A peak is put on the oscillation maximum for the atmospheric ∆m2 scale at the Super-K site. At the same time the usage of the off-axis design helps to minimize the background for νe searches. The neutrino beam is monitored by a set of detectors at J-PARC: non-magnetized on-axis detector INGRID and magnetic off-axis near detector, both located at 280 m from the proton target and forming an ND280 detector complex. The main goal of the complex is to provide neutrino spectra and beam flavor composition measurements prior to oscillation process as well as to measure neutrino interactions cross-sections. 50 kton Super-K massive water Cherenkov detector is used as a T2K far detector. The Super-K performance is wellmatched at sub-GeV level and provides good µ− and e− (“fuzzy”) single rings separation with about 99% efficiency. Construction of the J-PARC neutrino beamline was started in April 2004. The complete chain of accelerator and neutrino beamline was successfully commissioned during 2009. The T2K started physics data taking in January 2010. 3

T2K neutrino oscillation analysis

The T2K data was collected in two runs RunI (Jan–Jun 2010) and RunII (Nov 2010–Mar 2011). 145 kW stable beam operation was achieved in RunII but the run was stopped in March 2011 due to the Great East Japan Earthquake. The total data set used in the present νe appearance [4] and νµ disappearance analysis corresponds to 1.43×1020 p.o.t. (2% of the T2K final goal). The beam direction stability which is a key point for an off-axis beam was checked to be well within 1 mrad (this corresponds to neutrino peak energy shift of 2%) during all the data taking. At T2K energies CCQE interactions are dominant and so corresponding leptons form Super-K νµ and νe signals. For νµ → νe search two main background

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sources are intrinsic νe contamination in νµ beam and π 0 s from NC interactions. As for νµ disappearance channel CC1π interactions form the main background. Super-K event selection criteria were optimized in order to suppress background sources. It is worth mentioning that all the selection cuts in the far detector were predefined and fixed based on Monte-Carlo (MC) simulation results prior to analysis so to avoid any biases. In order to evaluate oscillation parameters the number of events that pass exp obs Super-K selection cuts NSK is compared with the calculated expectation NSK which is based on the predicted neutrino flux, external cross-section data and νµ CC inclusive R Data rate measurement in the off-axis near detector. The latter MC one is used as a normalization factor. The present analysis is based on NEUT [6] as a neutrino interactions generator. As for the neutrino flux prediction it uses the information from proton beam monitors as an input for further FLUKA simulation. The results are then tuned to the p+C measurements from NA61/SHINE CERN experiment [5]. For some cases (horn focusing, out of target interactions) GEANT3 (GCALOR) MC is also utilized with the crosssections tuned to external data. General νµ and νe CCQE event selection cuts used in the T2K far detector are as follows: the event is accepted when its time is within -2 – +10 µsec beam trigger on-time window, it is a fully-contained (FC) event (Super-K is divided into two detectors: Outer detector (OD) and Inner detector (ID), the cut requires the vertex to be inside the ID and no activity in the OD), we then proceed with FCFV events which have vertexes inside 22.5 kton fiducial volume (FV, the vertex should be > 200 cm from the nearest ID wall), among the selected we deal with single ring events to which Super-K PID algorithms based on ring shape and opening angle are further applied. 41 total Super-K events were selected using the above criteria: 33 µ− and 8 e−like.

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Figure 3: Reconstructed neutrino energy at Super-K for selected νµ events (left) and Data/MC spectra ratio (right).

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νe appearance results

The νµ → νe appearance search is started with 8 e-like events remained after “basic” selection criteria. The further cuts are optimized to minimize intrinsic νe and NCπ 0 backgrounds, the cuts are: visible energy Evis should be > 100 MeV (7 events survived), no Michel electrons (6 events), Minv < 105 MeV (calculated under two e-like rings assumption), reconstructed neutrino energy ν < 1250 MeV (all 6 events passed two last cuts). The number of νe canErec obs didates is therefore NSK =6. The expectation gives (backgrounds + νµ → νe exp Solar term) NSK = 1.5 ± 0.3 for zero θ13 taking into account +22.8% −22.7% systematics. The probability to observe six or more events is then 0.7% which corresponds to 2.5 σ significance. The Feldman-Cousins [7] method was implemented to get confidence intervals for oscillation parameters: 0.03(0.04)< sin2 2θ13 200 MeV. 31 events survived all cuts. The null oscillation hypothesis gives 104 events with +13.2% −12.7% systematics, it is therefore exluded at 4.5 σ level. The energy spectrum distortion due to oscillations can be also clearly observed (Fig. 3). The combined analysis based on events number and energy spectrum shape allows to set more stronger limit on null oscillation hypothesis, the probability of null oscillation is limited to ∼ 10−10 . Mixing parameters were retrieved using Feldman-Cousins algorithm and two-flavor oscillation model: sin2 2θ23 > 0.85 and 2.1×10−3 < ∆m223 < 3.1×10−3 eV2 (90%

158 C.L.). The obtained values are consistent with the previous measurements by Super-Kamikande and MINOS [8, 9]. 6

Conslusions

Neutrino oscillation results from the T2K second generation long baseline experiment are presented. The T2K is the first LBL experiment to utilize off-axis conception of neutrino beam. The present analysis is based on 1.43×1020 p.o.t. collected from January 2010 to March 2011 (2% of the T2K final goal). Total six e-like single-ring events passed all the selection criteria. The probability to observe six or more events under zero θ13 hypothesis is 0.7% which is equivalent to 2.5 σ significance. The corresponding 90% C.L. intervals are 0.03(0.04)< sin2 2θ13 100 GeV) νµ candidates have been identified and the spectrum determined using unfolding techniques. The flux is consistent with previous measurements in the overlapping energy region [4]. Upcoming data will significantly increase statistics and it is expected that the energy range of study will extend beyond 1 PeV, where it will become possible to probe possible contributions from charm interactions. Although studies till now have been limited to muon neutrinos, recent work with data from DeepCore has extended our reach to lower energies, where it becomes possible to measure the contribuation from cascades (νe , neutral current νµ ). Although muon neutrino backgrounds are still present, first evidence of atmospheric neutrino induced cascades has been observed, with a measurement in agreement with the summed contribution from all flavors [5]. 4

Diffuse searches

It is possible that no single source of astrophysical neutrinos contributes enough flux at Earth to be distinguished above the atmospheric neutrino background. However, if there are many such unresolved sources, the integrated flux should be visible due to its higher energy signature. Searches have been carried out in a variety of channels, including muon neutrinos, cascades, and searches fo-

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Figure 1: Limit on the diffuse flux of muon neutrinos derived from 40-string IceCube data. [8]

Figure 2: Point source pre-trial significance skymap for the combined 40 and 59-string IceCube datasets. [10]

cusing only on extremely high energies (EHE). While these latter searches provide interesting sensitivities for upcoming datasets [6, 7], the search in the muon neutrino channel with 375.5 days of 40-string data has already provided stringent limits on the diffuse flux that fall below the Waxman-Bahcall upper bound. [8, 9]. 5

Point source searches

Data from the 40-string and 59-string configurations of IceCube were combined in a search for steady state point sources of astrophysical neutrinos. In total, 723 days of livetime were collected, with 57,460 mostly neutrino induced events in the northern hemisphere, and 87,009 events in the southern hemisphere, skewing towards higher energies (PeV − EeV). A maximum-likelihood unbinned search was conducted to search for clustering due to an astrophysical signal. The most significant deviation from background is located at 75.45◦ R.A. and −18.15◦ Dec. While the pre-trial p-value is calculated as 2.23 × 10−5 , after trials are taken into account, this result is consistent with background, occurring in 67% of scrambled skymaps [10]. 6

Dark matter searches

Weakly Interacting Massive Particles (WIMPs) are one of the most promising candiates for the universal dark matter. In the Minimally Supersymmetric Standard Model (MSSM), the WIMP can take the form of the lightest neutralino [11]. These neutralinos eventually accumulate in the center of massive objects and self-annihilate to standard model particles, including neutrinos. Event rates and energies depend on the specific model of dark matter under

184

Figure 3: Limits on the spin-dependent χp scattering cross section. The shaded region depicts the model space allowed by direct detection experiments. [12]

Figure 4: Limits on the dark matter self-annihilation cross-section, shown for an average (Einasto) galactic density profile. Limits derived from SuperK data are shown for comparison. [14]

consideration and the astrophysics of the environment. Taking these variables into consideration leads to an expectation of a few to a few 103 events per year between GeV and TeV energies, which may be searched for as a point-like source. Several such searches for WIMP annihilation in the center of the Sun have been performed using partical configurations of IceCube as well as its predecssor detector AMANDA. Recently, the results of these searches have been combined in a unified likelihood analysis [12]. All observations are in agreement with the background only hypothesis, and upper limits have been set on both the spin-dependent (SD) and spin-independent (SI) WIMP-proton scattering cross sections. While SI cross sections are well constrained by direct dark matter searches, solar capture is dominated by SD processes, and thus this IceCube combined result represents the most stringent SD limit to date over a wide energy range. IceCube can also be used to probe dark matter annihilation in the halo and galactic center. The expected neutrino flux can be derived from an assumed dark matter density profile integrated along the line of sight, convolved with a channel-dependent dark matter annihilation spectra. A search was conducted using the 22-string configuration of IceCube for such annihilations [13]. This search focused on the outer halo and looked for a large scale anisotropy in the neutrino event rate from the region surrounding the galactic center, and a region diametrically opposite. No such anisotropy was observed, and limits were set on the self-annihilation cross-section for various potential annihilation channels. With the 40-string IceCube detector, a veto was developed to select downgoing neutrino events starting within the detector volume, opening up searches to the direction of the Galactic Center. As in the 22-string search, observations were in

185 agreement with the expected backgrounds and limits were set [14]. The results of these analyses are competitive with limits derived from Super-Kamiokande data [15]. It is expected that these limits will improve substantially with the full IceCube detector and the improved vetoing capabilities introduced with DeepCore. 7

Outlook

Although no astrophysical sources of neutrinos have been observed to date, we have entered an exciting transitional period for neutrino astronomy. The IceCube detector was completed in December 2010, and datataking with the full array began in May 2011. We have presented the latest results from partial configurations of the detector, showcasing the wide range of interesting physics that can be accessed. Integral to IceCube is the densely instrumented DeepCore subarray which extends senstivity to around 10 GeV. In the future, DeepCore data will be used to extend the sensitivity of dark matter searches and conduct neutrino oscillation studies. It is anticipated that within the next few years the IceCube neutrino telescope will continue to make substantial contributions to the field, either by making the first observations of astrophysical neutrinos, or by setting strict limits on the leading theoretical models. References [1] A. Hillas, Ann. Rev. Astron. Astrophys. 22, 425 (1984) [2] A. Achterberg et al. (IceCube Coll), Astropart. Phys. 26, 155 (2006). [3] R. Abbasi et al. (IceCube Coll), Nucl. Instrum. Methods A601, 294 (2009). [4] R. Abbasi et al. (IceCube Coll), Phys. Rev. D 83, 012001 (2011). [5] C. Ha and J. Koskinen (for the IceCube Coll), Proc. of the 32nd ICRC, Beijing (2011). [6] S. Hickford and S. Panknin (for the IceCube Coll), Proc. of the 32nd ICRC, Beijing (2011). [7] H. Johansson, Ph.D. Thesis (2011) [8] R. Abbasi et al. (IceCube Coll), Phys. Rev. D 84, 082001 (2011). [9] E. Waxman and J. Bahcall, Phys. Rev. D 59, 023002 (1998). [10] J.A. Aguilar, M.Baker, J.Dumm, T.Montaruli and N.Kurahashi (for the IceCube Coll), Proc. of the 32nd ICRC, Beijing (2011). [11] M. Drees and M.M. Nojiri, Phys. Rev. D 47, 376 (1993). [12] R. Abbasi et al. (IceCube Coll), arXiv 1112.1840. [13] R. Abbasi et al. (IceCube Coll), Phys. Rev. D 84, 022004 (2011). [14] JP. Hulß, Ph.D. Thesis (2010) [15] J. Hisano, K. Nakayama, M.J.S. Yang, Phys. Lett. B 678, 101 (2009).

186 DOUBLE CHOOZ PROJECT: STATUS OF A REACTOR EXPERIMENT AIMED AT SEARCH FOR NEUTRINO OSCILLATIONS Sergey Sukhotin a on behalf of the Double Chooz collaboration National Research Centre “Kurchatov Institute” 123182 Kurchatov sq., 1,Moscow,Russia Abstract.Double Chooz is an experiment that is devoted to searches for reactorantineutrino oscillations at the CHOOZ nuclear power plant. This project is aimed at measuring the unknown mixing angle θ13 . It is assumed that the value of θ13 will be extracted from an analysis of the distortion of the antineutrino spectra obtained in relative measurements at two distances from the nuclear reactors by means of two identical detectors. The method makes it possible to minimize systematic errors of the experiment and to improve the sensitivity to the sought parameter. To date, the most stringent constraint on the parameter θ13 was obtained from the CHOOZ experiment in 1995 − 1997 (sin2 (2θ13 ) < 0.17, with the difference of the squares of the neutrino masses being ∆m213 = 2.3 × 10−3 eV2 ). The construction of the far detector was completed at the end of 2010. The commissioning period (January-March 2011) is over. The far detector is taking data.

1

Introduction

Pontecorvo’s hypothesis [1] of neutrino oscillations has been confirmed in experiments with natural and artificial sources. Experiments with solar neutrinos [2–5] and with reactor antineutrinos (KamLAND Collaboration [6]) resulted in determining the parameters of νe → νµ oscillations, which explain the deficit of solar neutrinos. From recent global analysis [7] : ∆m212 = (7.46 ± 0.2) × 10−5 eV2 tan2 (θ12 ) = 0.427 ± 0.026 The parameters of oscillations belonging to the νµ → ντ type were measured in experiments with atmospheric neutrinos [8], as well as in experiments at accelerators [9, 10]. The results are: ∆m223 = (2.5 ± 0.2) × 10−3 eV2 sin2 (2θ23 ) = 1.0 ± 0.08 The set of experiments performed thus far determined ∆m213 , thereby facilitating searches for the mixing angle θ13 , which is the last unknown parameter. Oscillations of the νe → ντ type have not yet been observed. The most stringent constraint, sin2 (2θ13 ) < 0.17 at the differences of the masses squared in the region around ∆m213 = 2.3 × 10−3 eV2 , was obtained in the CHOOZ experiment [11, 12], which was performed in 1995 − 1997. A reactor experiment that belongs to a new type and which would involve simultaneously measuring antineutrino spectra by two identical detectors positioned at different distances a e-mail:

[email protected]

187 from the reactor was proposed in 2000 [13]. In 2004, a group of physicists from France, Germany and Russia (Kurchatov Institute) announced the formation of an international collaboration with the aim of implementing such an experiment. In 2005, the project was supported by several groups from the United States of America. In 2006, laboratories from the United Kingdom, Brazil, Spain, and Japan joined the project. The project was called Double Chooz [14]. 2

Atomic power plant and detector positions

The Double Chooz experiment will be performed at the French nuclear power plant situated at the Chooz town near the border with Belgium. The nuclear power plant has two nuclear reactors of total thermal power 8.4 GW. Thus, the distances to the reactors from the far detector are already known, 997.9 and 1114.6 m. The near detector will be positioned at a mean distance of about 390 m from the reactors. The farther laboratory is arranged in a tunnel at a depth of about 300 mwe. The nearer laboratory will be situated at a depth of about 120 mwe. 3

Detector for electron antineutrinos

The discription of the Double Chooz detectors can be found at [15]. 4

Detection of reactor antineutrinos

The interactions of reactor antineutrinos in the detector will be recorded by the inverse beta-decay reaction occurring on hydrogen and resulting in the production of a positron and a neutron: νee + p → e+ + n Ethr = 1.806 MeV. (1) The delayed coincidences of signals from a positron and neutron capture in the time gate equal approximately to the tripled neutron lifetime in the detector will be used to single out events of reaction (1). A neutron, after being moderated, is captured either by gadolinium nuclei (with a probability of about 80%) or by hydrogen (with a probability of about 20%), this being accompanied by the emission of gamma rays whose total energy is about 8 MeV in the case of gadolinium or 2.2 MeV in the case of hydrogen. Owing to the presence of gadolinium in the target scintillator, the neutron lifetime decreases from 200 µs (scintillator without gadolinium) to 30 µs. The neutron detection threshold can be set to about 6 MeV. This makes it possible to reduce the background of random coincidences substantially, since the natural radioactivity spectrum does not go beyond 4 MeV, the neutron detection efficiency remaining high (about 80%). The positron-detection threshold will be set to about 0.5 MeV.

188 5

Sensitivity of the experiment to the mixing angle θ13

In the CHOOZ experiment [10,11], the search for oscillations was performed by comparing the antineutrino spectrum measured by the detector with its calculated counterpart. No effect of neutrino oscillations was discovered. The ratio (R) of the expected number of reactor-antineutrino interactions to their measured number proved to be: R =1.01 ± 2.8%(stat.) ± 2.7%(syst.) The values of the statistical and systematic errors determined the constraint on the mixing angle. In order to improve the sensitivity substantially, it is necessary to reduce the experimental errors greatly. The statistical error can easily be reduced to 0.5% by increasing the target volume and the time of data acquisition in relation to the previous CHOOZ experiment. The main systematic error in the CHOOZ experiment was associated with the determination of the flux and energy spectrum of antineutrinos corresponding to the current reactor power and fuel burnup. In the new project, it is proposed to perform simultaneous measurements with two identical detectors, whereby systematic errors related to the reactors are avoided almost completely, since the two detectors are similarly affected by any variations in the reactor power and in the composition of the reactor area. The systematic errors related to the properties of the detectors will also be removed to a considerable extent owing to the identity of the detectors. In particular, it is unnecessary to know, in the new experiment, the absolute number of hydrogen nuclei in the target, but this was a source of a significant systematic error in the first experiment. Our analysis revealed that the total systematic error related to the detectors would be about 0.6%.

6

Status of the double chooz project

The assembling and filling of the far detector is completed in December 2010. The commissioning period (January-March 2011) is over. The data taking started in May 2011. Within 1.5 years of data accumulation only with the far detector, an improvement of the sensitivity to the mixing angle θ13 and the attainment of values in the range sin2 (2θ13 ) < 0.06 are expected in the Double Chooz experiment. The construction of the nearer laboratory will have been completed in April 2012. The near detector will have been assembled at the end of 2012. Thus, it is planned to begin collecting data with two detectors starting from 2013. Within three years after that, this would make it possible to set the constraint sin2 (2θ13 ) < 0.03 on the mixing angle θ13 or to measure it, if sin2 (2θ13 ) > 0.05.

189 7

Conclusions

The Double Chooz project is aimed at measuring the mixing angle θ13 . This measurement is of importance not only for obtaining deeper insight into the nature of neutrino oscillations but also for studying phenomena that could play a significant role for developing a more fundamental theory of the subatomic world, a theory that would describe the evolution of the Universe, and so on. Acknowledgments This work was supported by the Russian Foundation for Basic Research (project 11-02-93106). References [1] B. M. Pontekorvo, Sov. Phys. JETP 6, 429 (1957)51. [2] R. Davis, D. S. Harmer, K. C. Hoffman, Phys. Rev. Lett 20, 1205(1968). [3] J. N. Abdurashitov, T. J. Bowles, C. Cattadori, et al. Astropart. Phys. 25, 349 (2006). [4] M. Altmann, M. Balata, P. Belli, et al. Phys. Lett. B 616, 174(2005). [5] SNO Collaboration., Phys. Rev. C 72, 055502 (2005). [6] K. Eguchi, S. Enomoto, K. Furuno, et al. Phys. Rev. Lett. 92, 071301 (2004). [7] SNO Collaboration arXiv:1109.0763v1 (2011). [8] Super-Kamiokande Collaboration., Phys. Rev. Lett. 97, 171801 (2006). [9] MINOS Collaboration., Phys. Rev. Lett. 97, 191801 (2006). [10] K2K Collaboration., Phys. Rev. D 74, 072003 (2006). [11] M. Apollonio, A. Baldini, C. Bemporad, et al., Phys. Lett. B 466, 415 (1999). [12] M. Appolonio et al., Eur. Phys. J. C 27, 331 (2003). [13] L. A. Mikaelyan and V. V. Sinev, Eur. Phys. J. 63, 1002 (2000). [14] Proposal Double Chooz, hep-ex/0606025. [15] S.Sukhotin, in (Proceedings of the 14th Lomonosov Conference on Elementary Particle Physics, August 19-25 2009, Moscow, Russia), ed. by A.Studenikin, World Scientific Singapore, 2011.

190 SEARCH FOR NEUTRINO RADIATION FROM COLLAPSING STARS AND THE SENSITIVITY OF EXPERIMENTS TO THE DIFFERENT TYPES OF NEUTRINOS 1

V.L. Dadykin1 ,O.G. Ryazhskaya1a Institute for Nuclear Research of RAS, prospekt 60-letiya Oktyabrya 7a,Moscow, 117312, Russia Abstract. The experiments running to search for neutrino radiation from collapsing stars up to now traditionally take one’s bearings for the detection of the e νe p → e+ n reaction and, accordingly, for the use of the hadrogenate targets. The observation of neutrino radiation from SN1987A showed that it is important to have in the composition of the targets beside the hadrogen also other nuclei suitable to neutrino radiation detection. In particular the presence of iron nuclei in the LSD provided for the sensational detection of νe flux at 2:52 UT on February 23 1987 when other more powerful detectors with their hadrogenate targets could not respond to this type of neutrino. The sensitivity of present searching experiments to different types of neutrino radiation from collapsing stars is discussed in the paper.

1

Introduction

The attemps to understand and comprehend, how the last stage of the massive main sequence stars evolution is passing, when the termonuclear reserves were already exhausted, when the macroscopic objects acquire nuclear density, when the conditions for gravitational collapse and the formation of neutron stars and black holes are created, when gravitation governs the process has the story of several years. On April 1, 2011 we could celebrate 70 years of the G. Gamov and M. Shoenberg paper publication [1], where “the role of neutrino in the vast stellar catastrophes” was discussed first time. It is nesessary to note the important achievements of the theory for the past tense. There were the elaboration of the “standard collapse model” by W. Fowler, F. Hoyle et al. [2], S.Colgate and R. White [3], W. Arnett [4], V.S. Imshennik, L.I. Ivanova, D.K. Nadyozhin, I.V. Otroshenko [5,6] R. Bowers and J. Wilson [7], Bruenn [8] et al., and the elaboration of the model of rotating collapsar by V.S. Imshennik [9]. More than 30 years the group of special detectors are ready to permanent search for neutrino radiation from collapsing stars, but the nature is miserly for the presents. During this time the neutrino radiation was measured only ones on February 23, 1987 from the Supernova SN1987A in the Large Magellanic Cloud located 50 kiloparsecs away. Due to this reason, the signals in the detectors were small, had poor statistics, and the schemes of their interpretations caused the doubt. But, the experimental results obtained in that day are unique up to now. The theoreticians constructing their models can lean only on them, and it is difficult to over-estimate the significance of the results. a e-mail:

[email protected]

191 2

On the analysis of the experimental data on the observation of neutrino radiation from SN1987A.

The information obtained on February 23, 1987 was interesting and instructive. Conserning the detection of neutrino radiation from SN1987A in KII [10] and IMB [11] there is the stable opinion formed from the beginning that these results support very well the standard collapse model. If this model realized actually the overwhelming majority of the interactions in Cherenkov detectors should be caused by the νee p → e+ n reaction , and the energy spectrum of measured positrons must correspond to the νee spectrum expected in this model and serve by the good proving base for it. In order to convince everybody in the realization of the standard collapse model, it is important to prove that the main part of pulses in KII and IMB caused exactly by inverse β-decay reactions (IBD). The identification of this reaction could be done by the analysis of angular distribution, which should be isotropic one. However, the experiment showed the rough anisotropy of particles in KII and IMB. The probability to obtain observed anisotropy for the sum of pulses in KII and IMB, as result of fluctuations, is not higher than 0.02. Therefore, we suppose that the use of main parameters of the standard collapse model, as the unique right pattern of the analisys of SN1987A experiment results, is not correct. On the whole, the experiment on February 23 includes in itself the effect at 2:52 UT, observed in LSD [12], absolutely inexplicable in the framework of this model and obtained the interpretation in the model, taking into account the rotation and strong deformation of stellar core at the stage of presupernova [13]. This model was elaborated by V.S. Imshennik to explain the envelop ejection at the final stage of the evolution of stars with a mass exceeding 8 solar masses [9], and was called by author “the model of rotating collapsar”. The data concern the correlations between the pulses in the different neutrino detectors (LSD-BUST [14]; LSD-KII), as well as the coincidences between the signals in these detectors and gravitational wave antennae [15], until now did not find the explanation in the framework of the modern models. Very close point of view on the situation, concerning the analysis of the experimental results of the observation of neutrino flux from SN 1987A, was expressed early in our papers [16–19]. 3

On the sensitivity of some underground detectors to neutrinos of different types.

The characteristics and possibilities of six detectors running to search for neutrino flux from collapsing stars are presented in the Table. Five detectors are scintillation ones, the sixth one is Cherenkov water detector. In ASD, BUST and LVD one and the same liquid scintillator (LS) of Russian production is used [20]. In KamLAND the scintillator is different, but both LS’s are similar by the composition of their nuclei, and can be describe by the formula Cn H2n ,

192

Table 1:

1 2 3 4 5 Detector Depth, Mass, Thre- Efficiency m.w.e. ktons shold, MeV

6

7

Expected number of events BackStandard model Rotating ground, collapsar s−1 model

ηe± ηn ηγ . νee p . νi e− νi C 0.970.800.85 57 2.1 9.5

ASD 0.1 Artyomovsk 570 Cn H2n 5 Russia 1.0 0.070.05 NaCl [21] BUST 0.2 0.6 - 0.2 67 Baksan 850 Cn H2n 8 Russia 0.16 Fe [14] KamLAND 1.0 0.9 500 Kamioka 2700 Cn H2n 0.35 Japan [22] Borexino 0.3 0.9 0.85 120 Gran Sasso 3300 C9 H12 0.2 Italy [23] LVD 1.0 0.9 0.6 0.55 500 Gran Sasso 3300 Cn H2n 4-6 Italy 0.95 0.45 Fe [24] Super-K 22.5 7 0.9 - - 9400 Kamioka 2700 H2 O Japan [25]

. νe A. νe Ain

19 0.16 25

2.2

4.3

8 0.033

48

85

180

12

28

60

22

55

160 0.1 250

400

-

650

193 n ≈ 9.6. The scintillator in Borexino is made on the basis of pseudocumene, the formula of that is C9 H12 . In the column 3 of the Table the figure above the formula of LS or water means the mass of the corresponding matter in kt. If in the detector or close to it there are targets for νe A interaction, the total mass of them in kt is shown above corresponding chemical simbol.Cross section for the reaction (νe A) are taken from [26–30]. In the column 5 the detection efficiency for different particles (e+ , e− , γ, n) produced in the reactions of neutrinos with the target nuclei is present. This value depends on the construction of the detector, on the sizes of the tanks, and on the energy threshold. The responses of the detectors to the neutrino radiation are shown in the column 6 for two scenarios of the last stage of massive stars evolution. There are both the standard stellar collapse model, when the rotation of the star is not taking into account, and the model of rotating collapsar, when the account for the rotation leads to the strong deformation and fragmentation of the star core at the stage of presupernova. As a result of this, gravitational collapse should have at least two stages and should be accompanied at least by two neutrino bursts. The first one mainly consists of electron neutrinos with average energy 25-55 MeV. The second one containes all types of neutrinos νe , νee , νµ , νeµ , ντ , νeτ . These two signals are separated by the time interval up to some hours. On the whole, the scenario of the final stages of stellar evolution elaborated in the rotating collapse theory [9,13,16] apparently allows more than two (three or more) neutrino bursts. In this model the amount of energy in the two neutrino bursts should approximately be in the ratio 1:3, and possibly even 1:5 [13]. It is supposed that the second stage can be developed according to standard collapse model, with the similar composition, energy spectra, and average energy of neutrino radiation. For the model of rotating collapsar in the column 6 the responses of the detectors are presented only for the first stage of the collapse, mainly to the νe signal. We pay attention to that in the Table for this model the responses of the detectors to the neutrino signal from the second collapse stage are not shown. We suppose that the values should be more or less similar to the values for the standard collapse model. The expected number of events were obtained under the assumption that 1) the collapsing star is situated in the center of Galaxy, 2) the total energy of neutrino radiation for the standard collapse model is equal to 5.3·1053 erg, 3) the total energy of neutrino radiation at the first stage of collapse for the rotating collapsar model is 8.9·1052 erg. [13]. The calculation of the responses to neutrino flux for the standard collapse model was made for Ee = 12.6MeV, E νe = 10.5MeV, E νµ,τ = 25MeV, νe and for the spectra of all these types of neutrino, according to [5,6]. Calculating the detector responses for the first stage of collapse in the rotating collapsar model we limited ourself by monoenergetic νe flux with Eνe = 40MeV leaning on the result of LSD at 2:52 on February 23, 1987A. The Table shows, how different detectors react on the neutrino flux of known composition. Here we

194 bear in mind, both the composition of neutrino different types in the flux, and their energy spectra. However, the flux composition itself is one of the main subjects of study for the searching experiments. Therefore, the experiments should have the possibility to identify the neutrino reactions responsible to the signals in the detector. Lower we will discuss some of the methods. 1. The reaction of inverse β-decay (IBD) νee + p → e+ + n, σ = 9.3Ee2+ · 10−44 cm2 , Ee+ = (Eνee − 1.3MeV)

(1)

We told already, no once, what is the place of this reaction in the searching experiments, and how it is important to be sure that the detector response was just caused by IBD. The principle of the reaction (1) identification consists in the detection, both positron, and neutron with some time delay. In this case the reaction (1) will have the characteristic signature. Since the Reines F. and Cowan C. experiment [31], in order to detect n in IBD reaction the 155 Gd salts was added in LS, and the reaction n+155 Gd →156 Gd+Σγi , ΣEγi = 8MeV, was used. The time of n capture depends on the Gd concentration and was equal to 5 ÷ 50µsec. The Gd salts are expensive, decrease the transparency of LS, and it is difficult to use them in long time experiments. In 1968 Ryazhskaya with her collaborators working in the salt mines in the low radioactivity conditions obtained that it is possible to detect the neutron capture by hadrogen of LS using the reaction n + p → d + γ, Eγ = 2.2MeV, τcapture = 170µsec. This result allowed to propose in 1973 [32] this method for the identification of IBDreaction in the experiments to search for neutrino radiation from collapsing stars using LS detectors. At the first time, we used this method in ASD(1977) and LSD(1985). Now it is used in ASD,Borexino,KamLAND and LVD. In the Cherenkov detectors for the identification of the reaction (1) it is possible to use the fact that the angular distribution of e+ in this reaction should be isotropic one. 2. The reactions of νe A interactions, both in the detector itself, and in the substance close to it. From our point of view the detector sensitivity to the electron neutrinos is very important, due to two reasons. 1) LSD has detected exactly νe ’s at 2:52 UT on February 23, 1987 from SN1987A. 2) The rotating collapsar model predicts for the first stage of collapse neutrino flux consisting mainly of νe . Moreover, it predicts that the average energies of these neutrinos should be 2 ÷ 3 times higher than these in the standard model. The Table shows that the nuclei 12 C, 16 O, 23 Na, 37 Cl and 56 Fe are the targets for νe A interactions. All possible reactions of νe with nuclei can be described as following: νe + (A, z) → e− + (A, z + 1)

(2)

νe + (A, z) → e− + (A, z + 1)∗

(3)

195

Figure 1: The probability of the interaction of electron neutrinos with different nuclei (per neutron) and with free neutrons as a function of the neutrino evergy [26].

νe + (A, z) → νe′ + (A, z)∗

(4)

where A, z are atomic number and charge of nucleus consiquently. The comparison of the reduced total cross section with the single neutron cross section for reaction 2 [26] is presented in Fig. 1. First, let us examine the νe A reactions giving the main effect in the scintillation detectors, then, the νe16 O reaction important for Cherenkov detectors. a) The 12 C nuclei are the natural target for νe interactions in LS. νe +12 C →12 N + e− , Ethr = 17.34MeV, Ee− = Eνe − Ethr , 12

(5)

N →12 C + e+ + νe′ , Ee+ = 17.34 − Eνe′ , τdecay 12 N = 15.9ms

νe +12 C →12 C∗ + νe′ ,12 C∗ →12 C + γ, Ethr = 15.11MeV, Eγ = 15.11MeV (6) If Eνe ≥ 17.34 the number of the interactions is divided between the channels (5) and (6). The reaction (5) is identified owing to the appearance of two pulses (from e− and e+ ) in the time interval about 4τ decay ≈ 64ms. The reaction (6) is identified by the detection of γ’s with energy Eγ = 15.11MeV [23]. These reactions will be the main ones in the detectors KamLAND and Borexino. b) The reactions νe A in the substance close to detectors. νe +23 Na →23 Mg∗ + e− , Ethr = 4MeV, Ee = Eνe − Ethr − Eγ 23

Mg∗ →23 Mg + γ, Eγ ∼ 7MeV

(7)

196 νe +35 Cl →35 Ar + e− , Ethr = 5MeV, Ee− = Eνe − Ethr

(8)

νe +37 Cl →37 Ar + e− , Ethr = 0.8MeV, Ee− = Eνe − Ethr The interactions with the nuclei of salt for Eνe > 25MeV can be identified thanks to the spectrum of energy losses in scintillator having the maximum in the region of 7 MeV [16, 33]. The idea to examine NaCl, as a target for νe A interactions, came from the works for the study of penetrating component of cosmic rays in the salt mines near Artyomovsk. The effects from the reactions (7,8) were calculated for the detectors ASD and LVD (to search for neutrino radiation from collapsing stars) [33]. ASD is situated in the hall made into the salt layer with the thickness of 30m. The products of νe interactions with the salt nuclei hit in the ASD and are detected with the efficiency 5-7 %, and the number of these events for Eνe > 30MeV is a little bit higher than the detected number of νe12 C interactions in LS (see Table). In future we suppose to place 300 t of NaCl on the tops of the LVD tanks to improve the detector parameters [34]. c) The reactions νe Fe. νe +56 Fe →56 Co∗ + e− , Ethr = 8.16MeV, Ee− = Eνe − Ethr − ΣEγ 56

(9)

Co∗ →56 Co + Σγ, ΣEγ = (3.6 ÷ 11)MeV νe +56 Fe →56 Fe∗ + νe′ , ∗

(10)

Fe → Fe + Σγ, ΣEγ = 3 ÷ 7MeV The energy spectrum with a maximum in the region of (7-12) MeV can indicate the identification of the reactions (9, 10) [16, 33] for Eνe > 30MeV. The tanks of LVD are situated in the iron portatanks. The total mass of Fe is about 950 t. The expected effects from νe Fe reactions in LVD for the rotating collapsar model is 1.6 times higher than that from νe12 C. There is some quantity of iron in the construction of BUST. However, due to the high energy threshold, the detection efficiency for the products of the reactions (9) and (10) is small. Due to this reason, the main effect for BUST is expected from νe12 C-reactions. d)For water Cherenkov detectors the main reaction for νe interaction with Eνe > 30MeV is the νe16 O one 56

56

νe +16 O →16 F + e− , Ethr = 15.4MeV, Ee− = Eνe − Ethr

(11)

The sign of this reaction has strong anisotropy of electron angular distribution [26, 27]. For Eνe > 30MeV the ratio of electrons coming on-out is about 3:7 and decreases with the increase of energy [27]. 3. Reactions of νµτ A, both in the detector, and in the substance close to it. The reactions of νµτ A-interactions are neutral current reactions similar to 12 (4). In the model of standard collapse E µτ = 25MeV, and the reaction of νµτ C gives the γ-line in the range of Eγ ≈ 15MeV, which can be measured in the

197 large volume detectors, and will give the information about νµτ number in the neutrino burst [35]. In the first stage of rotating collapsar model the oscillation process can transfere the part of νe into νµ with energy of 35 - 50 MeV, and it is necessary to take into account the possible reactions νµτ A for all nuclei. 4. The effect from νe e− , νi e− scattering has small part from the IBD reactions. But in the Cherenkov detectors this process gives the possibility to measure the direction to the neutrino source. 4

Conclusion

In conclusion we would like to draw the attention of specialists to the necessity of study, and carrying out the calculations of partial cross sections of charged-current and neutral-current reactions (especially with neutron and γray radiation) for the nuclei presented in the Table, and used for detection of neutrino flux with 10 < Eν < 60MeV from collapsing stars. The knowledge of these values is very important for the identification of neutrinos types. Acknowledgments We wish to thank I. Shakyrianova and N. Agafonova for help in preparing the manuscript for publication. This work was supported by the Russian Foundation for Basic Research (RFFI-12-02-00213-a), the Scientific School (SS871.2012.2) and Program for Fundamental Research of Presidium of RAS “The fundamental properties of matter and Astrophysics”. References [1] [2] [3] [4] [5]

G. Gamov, M. Shoenberg, Phys. Rev. 59,539 (1941) W. Fowler, F. Hoyle et al., Astrophys. J., 139, 909 (1964) S. Colgate and R. White, Astrophys. J., 143, 626 (1966) W. Arnet Canad, J. Phys, 44, 2553 (1966), 45, 1621 (1967) L.I. Ivanova, V.S. Imshennik, D.K. Nadyozhin, Proc. Intern. Seminar on Physics of Neutrino and Neutrino Astrophysics, 2, 180 (1969) [6] D.K. Nadyozhin, N.V. Otroshchenco , Sov. Astron., 24, 47 (1980) [7] R. Bowers and J.R. Wilson, Astrophys. J., 263, 366 (1982) [8] S.W. Bruenn, Phys. Rev. Lett., 59, 938 (1987) [9] V.S. Imshennik, Space Sci Rev., 74, 325 (1995) [10] K. Hirata et al., Phys.Rev.Lett., 58, 1490 (1987) [11] R.M. Bionta et al., Phys.Rev.Lett., 58, 1494 (1987) [12] M.Aglieta et al., Europhys.Lett. 3 1315 (1987) [13] V.S. Imshennik, O.G. Ryazhskaya, Astron. Lett., 30, 14 (2004)

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E.N. Alekseev et al., JETP.Lett., 45, 589 (1987) E. Amaldi et al., Europhys. Lett. 3, 1325 (1987) O.G. Ryazhskaya, Phys. Usp., 49, 1017 (2006) V.L. Dadykin, O.G. Ryazhskaya, Astron. Lett., 34, 581 (2008) V.L. Dadykin, O.G. Ryazhskaya, Astron. Lett., 35, 384 (2009) V.L. Dadykin, O.G. Ryazhskaya, Proc. of the Fourteenth Lomonosov Conference on Elementary Particles Physics Particle Physics at the Year of Astronomy, 177 (2010) [20] A.V. Voevodskii, V.A. Dadykin, O.G. Ryazhskaya Prib. Tekh. Eksp., 1, 85 (1970) [21] P.V. Korchagin et al. Proc. of 16th Intern. Cosmic Ray Conf. Kyoto, Japan, v.10,299 (1979) [22] P.Vogel for the KamLAND collaboration, Twenty years after SN1987A, Hawaii, February 25, 2007 [23] L. Cadonati, F.P. Calaprice and M.C. Chen, Astrop. Phys, 16, 361 (2002) [24] N.Yu. Agafonova et al. Astrop. Phys., 28, 516 (2008) [25] M. Ikeda et al. ApJ, 669, 519 (2007) [26] E.V. Bugaev et al. Nucl. Phys. A 324, 350 (1979) [27] W.C. Haxton Phus. Rev. D, 36, 2283 (1987) [28] M. Fukugita, Y. Kohyama, K. Kubodera Phys. Lett. B 212, 139 (1988) [29] E. Kolbe, K.Langanke Phys. Rev. C 63, 025802 (2001) [30] Yu. U. Gaponov, O.G. Ryazhskaya, S.V. Semenov Phys. At. Nucl. 67, 1969 (2004) [31] F. Reines, C. Cowan, Phys.Rev., 92, 830 (1953) [32] A.E. Chudakov, O.G. Ryajskaya, G.T. Zatsepin, Proc. of the 13th Intern. Conf. Cosmic Ray, ICCR, Denver, CO,USA, 17-30 August, 3, 2007 (1973) [33] V.V. Boyarkin, O.G. Ryazhskaya Bulletin of RAS: Physics, 71, v.4, 589 (2007) [34] V.V. Ashikhmin et.al. Proc. of this conference [35] O.G. Ryazhskaya, V.G. Ryasny, O. Saavedra JETP. Lett. 59, 315 (1994)

199 SUPERNOVA NEUTRINO TYPE IDENTIFICATION WITH ADDING SODIUM CHLORIDE IN LVD V.V. Ashikhmin1 ,K.V. Manukovskiy1,2 ,O.G. Ryazhskaya1 , I.R. Shakiryanova1a , A.V. Yudin1,2 (for LVD collaboration) 1 Institute for Nuclear Research of RAS, prospekt 60-letiya Oktyabrya 7a,Moscow, 117312, Russia 2

Institute for Theoretical and Experimental Physics, Bolshaya Cheremushkinskaya 25, Moscow, 117218, Russia Abstract. The main goal of LVD detector is the search for neutrino bursts from gravitational stellar collapses in our Galaxy. It is shown that the addition of kitchen salt in the structure of LVD can both significantly improve the neutrino type identification and increase the active mass of the detector.

1

Introduction

The standard gravitational collapse model (SCM) is unable to explain the envelope ejection during the star explosion as well as the signal detected by LSD experiment during SN 1987A [1]. Rotating collapsar model developed by V.S. Imshennik [2] predicts the two-stage collapse: during the first phase electron neutrinos with average energies 30-40 MeV are emitted [3], during the second one all neutrino types are radiated. To understand how the gravitational stellar collapse is developed it’s very important to have the apparata capable to distinguish the neutrino types. 2

Neutrino interactions in the LVD, experimental setup and results

LVD is scintillation-iron calorimeter and consists of 3 towers containing 840 liquid scintillation counters (tanks) with a volume of 1.5m3 each in iron portatanks [4]. Total mass of LVD is 2 kt (1 kt of scintillator (Cn H2n , n = 9.6, [5]) and 1 kt of iron).It can give a possibility to detect effectively not only νee from inverse beta-decay (IBD) from SCM: νee + p → n + e+ with the following neutron capture n + p → d + γ or n + 56 Fe → 57 Fe + γ but and νe due to ∗ νe + 56 Fe → 56 Co + e− reaction. The addition of sodium chloride to the LVD structure allows to increase the number of electron neutrino interactions via following reactions: νe + Na → e− + Mg, νe + Cl → e− + Ar and can improve the neutrino type identification [6]. 50 mm of common salt were put on the top of the portatank 113. The decay of neutron source 252 Cf situated under the salt layer on the roof of tank the 1135 was the trigger to look for the delay pulses from n-captures in the portatanks 113 and 114 in the time interval from 5 µsec up to 1 msec. Time distributions of γ-quanta from neutron capture by p, Fe or Cl nuclei were obtained. Curves were fitted by the function: y = y0 + A exp(−x/t) . The presence of salt reduces the time of a e-mail:

[email protected]

200 Table 1: R = NLET /N252 Cfdec for tanks and portatanks.

no NaCl N252 Cf dec 17551 Number of 1135 1145 tank NLET | R 10220 0.58 7039 0.40 NLET /NCf dec 0.98 Number of 113 114 portatank NLET | R 22483 1.28 15743 0.90 NLET /NCf dec 2.18

5 cm of NaCl 22727 1135 1145 16816

0.74 8139 0.36 1.1 113 114

33477

1.47 23068 2.49

1.02

neutron capture from t = (182 ± 12)µsec to (138 ± 7)µsec for portatank 113 and from t = (156 ± 11)µsec to (131 ± 10)µsec for portatank 114. The number of 252 Cf decays - (N252 Cfdec ) and number of low energy threshold pulses (LET - NLET ) are presented in the Table 1. The second column for each counter and portatank is R = NLET /N252 Cfdec . Average neutron number (Nn ) for 252 Cf decay is 3,7. For tank 1135 R increases up to 28% for this configuration with salt and efficiency of neutron detection changes from 31% to 40%. For portatank 113 this efficiency increases from 69% to 80%. 3

Conclusion

The addition of NaCl to the detector structure increases neutron (IBD) detection efficiency up to 16% for portatank 113, for tank 1135 up to 28% due to compensation of edge effect. We expect the increase of the number of electron neutrino interactions for any gravitational collapse models and significant improvement of neutrino type identification. Acknowledgement Work was supported by grants RFBR 09-02-00300, SS. 3917.2010.2 References [1] [2] [3] [4] [5]

O.G. Ryazhskaya, Physics-Uspekhi V. 49(10), 1017 (2006). V.S. V.S. Imshennik, Sp. Sci. Rev. V. 23, 779 (1995). V.S. Imshennik, O.G. Ryazhskaya, Astron.Lett. 30, 14-31 (2004). Aglietta et al., Il Nuovo Cimento A 105, 1793 (1992). A.V. Voevodskiy, V.L. Dadykin, O.G. Ryazhskaya, Prib. i Tech. Eksp. 1,143 (1970). [6] V.V. Boyarkin, O.G. Ryazhskaya (Proceedings of the 31th ICRC, 2009, Lodz, Poland)

201 RECALCULATION OF THE DAY–NIGHT FLAVOR ASYMMETRY FOR SOLAR NEUTRINOS Sergey Aleshin a , Oleg Kharlanov b , and Andrey Lobanov c Faculty of Physics, Moscow State University, 119991 Moscow, Russia Abstract. We investigate the neutrino oscillations within the two-flavor model in the presence of n jumps of the effective potential and then use the results obtained to estimate the day–night asymmetry factor for solar neurtinos.

In our investigation, we consider the neutrino oscillations in medium. The coherent weak interaction of neutrinos with the medium in the form of foward scattering leads to the so-called Wolfenstein effective potential [1]. Due to this potential, even for small vacuum mixing angle, the dense medium can produce a considerable conversion from one neurtino flavor to another [2]. This spectacular result is known as the Mikheev–Smirnov–Wolfenstein (MSW) effect. Within the two-flavor approximation, the neutrino oscillations in the isotropic medium can be described with a Schroedinger-like equation. Then the flavor evolution matrix (resolvent) R(x, x0 ), whose elements are the neutrino flavor transition amplitudes after traveling from the point x0 to x, satisfies the equation ∂R(x, x0 ) = −iλA(x)R(x, x0 ). (1) ∂x Here, the role of the Hamiltonian is played by the matrix A(x) = a(x)σ3 + bσ1 with the coefficients a(x) =

− cos 2θ0 +

b = sin 2θ0 ,

2EV (x) , ∆m2

(2) (3)

where σk are the Pauli matrices, θ0 is the vacuum mixing angle, E is the neutrino energy, ∆√m2 is the netrino mass-squared difference. The Wolfenstein potential V (x) = 2GF Ne (x) is proportional to the electron density Ne in the medium and the Fermi constant GF . The constant factor λ = ∆m2 /4E is the reciprocal vacuum oscillation length, up to a coefficient of π, losc = 4πE/∆m2 . The investigation of solutions of equation (1) is a subject of many papers. Probably the most efficient technique of finding its solutions is the so called Magnus expansion [3]. This approach leads to the approximate solution, as well as the constraints for the remainder terms. However, unfortunately, it does not have its power at the most general class of functions a(x) [4–6], and to use it, on should resort to some subclass of these functions. Nevertheless, within the problem of the neutrino oscillations, the structure of the Hamiltonian A(x) is such that the equation (1) can be unitarily transformed a e-mail:

[email protected] [email protected] c e-mail: [email protected] b e-mail:

202 to the so-called L–diagonal form [7, 8]. For L–diagonal equations, the form of the general solution is given by the Levinson theorem [8], and we only need to adjust this solution to the given initial conditions. On the other hand, the L–diagonality requires the absolute integrability of the a(x) background. We will consider the medium with n abrupt jumps of the electron density in the points xi , i = 1, n and smooth density profile between these points. It is spectacular that this model does indeed well describe the interior of the Earth [9]. Moreover, the widths of the smooth segments are large compared with the oscillation length losc , while the widths of the jumps segments are much less than losc . Then the total resolvent for such density profile is the matrix product of the resolvents for each wide and narrow segment. In each of these segments, in turn, the two small parameters arise, one of which is ρ = 2EV (x)/∆m2 . 10−2 [10,11]. The second small parameter δ is the ratio of the oscillation length to the width of the smooth segments, δ = losc /Li,i+1 , and the reciprocal value for the jump segments. Within the linear approximation in the change of the Wolfenstein potential inside the Earth, which is of the order of ρ, the dependence of the average flavor transition probabilities on the phase incursions on the smooth segments disappears. Finally, the probability of the electron/muon neutrino detection } { 1±U asun avac sin2 2θ0 2E · ∆Vn Pe,µ = , U≈ , (4) 1− 2 ωsun ωvac cos 2θ0 ∆m2 √ where ω = a2 (x) + b2 , so it is the Mikheev–Smirnov–Wolfenstein result which stands outside the brackets. We thus observe that the flavor day–night asymmetry in solar neutrino oscillations is effectively determined by the jump of the effective potential ∆Vn before the detector (i.e. on the exit from the Earth’s crust). This expression is in agreement with the recent experimental data from the Borexino collaboration [12]. Acknowledgments The authors are grateful to V. Ch. Zhukovsky and A. V. Borisov for the discussion of the results presented in the paper. References [1] [2] [3] [4] [5]

L. Wolfenstein, Phys. Rev. D 17, 2369 (1978). S. Mikheev and A. Smirnov, Sov. J. Nucl. Phys. 42, 913 (1985). W. Magnus, Commun. Pure. Appl. Math. 7, 649 (1954). J. C. D’Olivo, Phys. Rev. D 45, 924 (1992). A. D. Supanitsky, J. C. D’Olivo, and G. A. Medina-Tanco, Phys. Rev. D 78, 045024 (2008).

203 [6] A. N. Ioannisian and A. Yu. Smirnov, Nucl. Phys. B 816, 94 (2009). [7] S. S. Aleshin, O. G. Kharlanov, and A. E. Lobanov, e-Print arXiv:1110.5471 [hep-ph]. [8] E. A. Coddington and N. Levinson, “Theory of Ordinary Differential Equations” (McGraw-Hill, New York), 1955. [9] D. L. Anderson, “Theory of the Earth” (Blackwell Scientific Publications, Boston), 1989. [10] A. N. Ioannisian and A. Yu. Smirnov, Phys. Rev. Lett. 93, 241801 (2004). [11] A. N. Ioannisian, N. A. Kazarian, A. Yu. Smirnov, and D. Wyler, Phys. Rev. D 71, 033006 (2005). [12] G. Bellini et al., e-Print arXiv:1104.2150 [hep-ex].

.

204 NEUTRINO EMISSION FROM A STRONGLY MAGNETIZED DEGENERATE ELECTRON GAS: THE COMPTON MECHANISM VIA A NEUTRINO MAGNETIC MOMENT A. V. Borisov a , B. K. Kerimov b Faculty of Physics, Moscow State University, 119991 Moscow, Russia P. E. Sizin c Department of Higher Mathematics, Moscow State Mining University, 119991 Moscow, Russia Abstract. We derive relative upper bounds on the effective magnetic moment of Dirac neutrinos from comparison of the standard weak and electromagnetic mechanisms of the neutrino luminosity due to the Compton-like photoproduction of neutrino pairs in a degenerate gas of electrons on the lowest Landau level in a strong magnetic field. These bounds are close to the known astrophysical and laboratory ones.

1. Neutrino emission is the main source of energy losses of stars in the late stages of their evolution [1]. As is well known, neutron stars (NSs) can have 12 14 16 strong magnetic fields H > ∼ 10 G, the NSs with H ∼ 10 − 10 G are called magnetars [2]. In this report, we consider one of the main processes of neutrino emission in the outer regions of NSs (for a review of various neutrino processes, see [3]) that is photoproduction of neutrino pairs (γe → eν ν¯) in a degenerate gas of electrons through two mechanisms: the weak one via standard charged and neutral weak currents and the electromagnetic one via neutrino electromagnetic dipole moments arising in extended versions of the Standard Model [1,4] (for a recent review, see [5]). By comparison of the neutrino luminosities due to these two mechanism, Lw and Lem , we derive relative upper bounds on the neutrino effective magnetic moment (NEMM) µ ¯ν = (µ2ν + d2ν )1/2 , (1) restricting ourselves to the case of Dirac neutrinos. Here µν and dν are the neutrino magnetic and electric dipole moments, respectively. 2. We assume that the electron gas is degenerate and strongly magnetized: T ≪ µ − m, H > ((µ/m)2 − 1)H0 /2,

(2)

where T and µ ≃ µ(T = 0) ≡ εF = (m2 + p2F )1/2 are the temperature and chemical potential of the gas, εF and pF are the Fermi energy and momentum, H0 = m2 /e ≃ 4.41×1013 G, m and −e are the electron mass and charge (we use the units with h ¯ = c = kB = 1). Under the conditions (2), electrons occupy only the lowest Landau level in the magnetic field with pF = 2π 2 ne /(eH), where ne is the electron concentration, and the effective photon mass is generated which a e-mail:

[email protected]

b late c e-mail:

[email protected]

205 is equal to the plasmon frequency ωp = ((2α/π)(pF /εF )H/H0 )1/2 m, α is the fine-structure constant. For the nonrelativistic case, pF ≪ m and ωp ≪ T , the neutrino luminosities are expressed as follows: 2 −1 9 Lw = 3.49 × 102 H13 ρ6 T8 erg cm−3 s−1 ,

(3)

Lem = 4.06 × 1030 (¯ µν /µB )2 ρ26 T83 erg cm−3 s−1 , (4) ( ) where H13 = H/(1013 G), ρ6 = ρ/ 106 g/cm3 , T8 = T /(108 K), and µB is the Bohr magneton. Note that Eq. (3) is in agreement with the result of Ref. [6]. Assuming Lem < Lw , we obtain the upper limit on the NEMM −3/2 (1): µ ¯ν /µB < 9.3 × 10−15 H13 ρ6 T83 , and, for T = 1.8 × 108 K, H = 2.5 × 12 4 3 10 G, ρ = 5.4 × 10 g/cm , it gives µ ¯ν /µB < 1.1 × 10−12 , which is close to the known astrophysical bounds [7]. For the relativistic case, pF ≫ m and ωp ≫ T , we obtain Lw = 2.63 × 10−2 H13 ρ−6 6 T8

3/2

43/4

11/4

exp(−1.92H13 T8−1 ) erg cm−3 s−1 ,

3/2

Lem = 3.02 × 1030 (¯ µν /µB )2 H13 T8

1/2

(5)

exp(−1.92H13 T8−1 ) erg cm−3 s−1 , (6) 1/2

4 −3 ρ6 = 7.6×10−16 for H13 = and a strong relative bound µ ¯ν /µB < 9.3×10−17 H13 3 300, ρ6 = 10 . However, under these conditions, the plasmon decay (γ → ν ν¯) is a much more effective mechanism of neutrino emission [8]. Comparing the corresponding luminosity with that of Eq. (6), we derive a considerably less 1/2 stringent bound µ ¯ν /µB < 1.7 × 10−12 H13 = 2.9 × 10−11 (for H13 = 300), which is close to the conservative bound µν < 0.54 × 10−10 µB [7] and the most stringent laboratory limit µν < 3.2 × 10−11 µB [9]. We thank P. A. Eminov for useful discussions, K. V. Stepanyantz and O. G. Kharlanov for help in numerical calculations.

References [1] M. Fukugita, T. Yanagida, Physics of Neutrinos: And Applications to Astrophysics (Springer, Berlin, Heidelberg, 2003). [2] R. C. Duncan, C. Thompson, Astrophys. J. 392, L9 (1992). [3] D. G. Yakovlev, A. D. Kaminker, O. Y. Gnedin, P. Haensel, Phys. Rep. 354, 1 (2001). [4] B. K. Kerimov, S. M. Zeinalov, V. N. Alizade, A. M. Mour˜ao, Phys. Lett. B 274, 477 (1992). [5] C. Giunti, A. Studenikin, Phys. Atom. Nucl. 72, 2089 (2009). [6] V. V. Skobelev, JETP 90, 919 (2000). [7] Particle Data Group: K. Nakamura et al., J. Phys. G 37, 075021 (2010). [8] D. A. Rumyantsev, M. V. Chistyakov, JETP 107, 533 (2008). [9] A. G. Beda et al., Phys. Part. Nucl. Lett. 7, 406 (2010) [arXiv:0906.1926 [hep-ex]]; arXiv:1005.2736 [hep-ex].

206 PHENOMENOLOGICAL RELATIONS FOR NEUTRINO MIXING ANGLES AND MASSES V. V. Khruschov a NRC ”Kurchatov Institute, 1 Kurchatov Sq., 123182 Moscow, Russia Abstract. Phenomenological relations for neutrino mixing angles, CP-phases and masses are obtained by taking into account available experimental data. In the case of CP-nonconservation in the leptonic sector a possible structure of a neutrino mass matrix is investigated and values of neutrino characteristics are evaluated. The characteristics obtained can be used for interpretations of results of various neutrino experiments.

The neutrino characteristics are under active experimental and theoretical study now. It is known that neutrinos are considered as massless particles in the framework of the Standard Model (SM), but at present the oscillations of flavor neutrinos due to mixing of neutrinos of different masses are confirmed by experiments with atmospheric, solar, reactor and accelerator neutrinos [1], where measuring of differences of mass squares ∆m2ij = m2i − m2j and neutrino mixing angles is performed. However the neutrino mass values cannot be determinated in these experiments as well as the Majorana or Dirac nature of neutrinos. Three types of experiments are sensitive to the absolute mass scale of neutrinos, namely: beta decay experiments, neutrinoless double beta decay experiments, and some cosmological and astrophysical experiments. In each type of these experiments a specific neutrino mass observable (mC , mβ and m2β ) is measured, while mixing of three types of light neutrino is given with the help of the Pontecorvo-Maki-Nakagava-Sakata matrix UP M N S , which can be written in the standard parametrization with the help of mixing angles θij and phases α, β and δ. The phases α, β, and δ are not available from the data at the moment as well as the absolute scale of neutrino masses [2, 3]. Since there is only the absolute value of ∆m231 , then the neutrino mass values can be arranged in two ways: m1 < m2 < m3 , m3 < m1 < m2 , i.e. we have the normal hierarchy of the neutrino mass spectrum (NH), or the inverted hierarchy (IH). It is needed to determine experimentally as a minimum one value among neutrino mass observables mC , mβ or m2β , in order to know the absolute )1/2 (∑ ∑ 2 2 neutrino mass scale: mC = 13 i=1,2,3 |mi |, mβ = , i=1,2,3 |Uei | mi ∑ 2 m2β = | i=1,2,3 Uei mi |. The following experimental limits for neutrino mass observables are obtained: mC < 0.2eV [4], mβ < 2.2eV [5], m2β < 0.34eV [6,7], where the last limit should be increased up to 1 eV in order to include the uncertainty of nuclear matrix element values. The important question is to find out a mechanism of generation of neutrino masses. Lacking a satisfactory theory of this phenomenon, the question can be a e-mail:

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207 treated on the phenomenological level. We use the following phenomenological formula for estimations of neutrino masses [8]: mνi = ±ξ − m2li /M . Taking into account the available data, the absolute values of neutrino masses µi and characteristic scales ξ and M in eV have been obtained in the NH- and IH-cases: µ1 ≈ 0.06926, µ2 ≈ 0.06981, µ3 ≈ 0.08513, ξ ≈ 0.069259, M ≈ 2.0454 · 1019 , µ1 ≈ 0.07751, µ2 ≈ 0.078, µ3 ≈ 0.06056, ξ ≈ 0.07751, M ≈ 2.2872 · 1019 . The upper diagonal matrix element m2β is connected with the propability of the neutrinoless double beta decay, while absolute values of two additional diagonal matrix elements mµµ and mτ τ are most likely equal each other. However without additional input one cannot define the CP-phases δ, α, and β, so m2β estimations cannot be obtained with account of CP violating terms. In order for such estimations to be made, we consider the case of schizophrenic neutrinos [9]. In particular we will use the case when one neutrino is the Majorana neutrino, while two other neutrino are the quasi-Dirac ones. In this case, if one takes into account the relation between mµµ and mτ τ , the following equation holds: 2 tan 2θ23 sin θ13 cos δ + tan θ12 = cot θ12 sin2 θ13 . This equation gives us the possibility to determine the CP-phase δ, whereas the knowledge of the CP-phases α and β are nonessential for obtaining of m2β estimations in this case. Taking into account the data [2,3] we obtain δ ≈ 86.2◦ in NH-case and δ ≈ 83.4◦ in IH-case, as distinguished from δ = 0◦ frequently used. We can estimate the neutrino mass observables mC , mβ , m2β in eV . N H : mC ≈ 0.07473, mβ ≈ 0.0696, m2β ≈ 0.04717. IH : mC ≈ 0.07202, mβ ≈ 0.07747, m2β ≈ 0.05263. The m2β value in the IH-case does not contradict to the limit obtained previously [10]. Calculated neutrino mass values µi along with the δ, mC , mβ , m2β estimations can be used for interpretations of results of various neutrino experiments. Acknowledgments This work was supported by the RFBR under grant 11-02-00882-a. References [1] M. C. Gonzalez-Garcia, M. Maltoni, J. Salvado, JHEP 1004, 056 (2010). [2] K. Nakamura et al., (PDG), J. Phys. G 37, 075021 (2010) . [3] T. Schwetz, M. Tortola and J. W. F. Valle, arXiv:1103.0734[hep-ph]. [4] E. Komatsu et al. [ WMAP Collab.], Astrophys. J. Suppl. 192, 18 (2011). [5] E. W. Otten, C. Weinheimer, Rept. Prog. Phys. 71, 086201 (2008). [6] H.V. Klapdor-Kleingrothauset al., Nucl.Phys.Proc.Suppl.100,309(2001). [7] C. Aalseth et al., arXiv:hep-ph/0412300. [8] V. V. Khruschov, arXiv:1106.5580[hep-ph]. [9] J. Barry, R. N. Mohapatra and W. Rodejohann, arXiv:1012.1761[hep-ph]. [10] S. Pascoli and S. T. Petcov, Phys. Let. B 544, 239 (2002); ibid. 580, 280 (2004).

208 NEUTRINO-TRIGGERED ASYMMETRIC MAGNETOROTATIONAL PULSAR NATAL KICK (“CHERRY-STONE SHOOTING” MECHANISM) A. V. Kuznetsov a , N. V. Mikheev b Division of Theoretical Physics, Yaroslavl State University, 150000 Yaroslavl, Russia Abstract.The sterile neutrino mechanisms for natal neutron stars kicks are reanalyzed. It is shown that the magnetic field strengths needed for a kick were underestimated essentially. Another mechanism with standard neutrinos is discussed where the outgoing neutrino flux in a supernova explosion with a strong toroidal magnetic field generation causes the field redistribution in “upper” and “lower” hemispheres of the supernova envelope. The resulting magnetic field pressure asymmetry causes the pulsar natal kick.

There are many mechanisms for pulsar natal kick, and the one using sterile neutrinos and proposed by A. Kusenko e.a. (see [1] and the references cited therein) looks the most attractive. However, as the analysis shows [2], the effect of sterile neutrinos on the pulsar kick described in those papers was overvalued more than in order of magnitude. For the declared effect, the magnetic field strength should be much larger, not ∼ 1016 G, but ∼ 4 × 1017 G. With such strong magnetic fields, it is possible to manage with standard neutrinos. As it was shown in the papers by our group [3], neutrino-electron and neutrino-nucleon processes in a strong magnetic field, caused the appearance of a force density acting on plasma along the field direction, ( ) B dyne FB ≃ 0.6 × 1021 . (1) 1016 G cm3 If the strong toroidal magnetic field is generated in the vicinity of the supernova core (magnetorotational supernova model by G.S. Bisnovatyi-Kogan [4]), the neutrino flux, pushing the plasma, torques the toroids in different directions. Thus, three stages of a pulsar kick can be identified: i) pre-supernova core is collapsing with rotation during 0.1 sec when a strong toroidal magnetic field is generated due to the differential rotation; ii) the neutrino outburst, pushing the plasma by the tangential force along the toroidal magnetic field which is frozen in plasma, leads to a magnetic field asymmetry: the field strength is enhancing in one hemisphere and is decreesing in another one, during ∼ 1 sec; iii) the pressure difference arising in the two hemispheres, causes the kick to a core. a e-mail: b e-mail:

[email protected] [email protected]

209 According to the momentum conservation, an energetic plasma jet must be formed opposite to the pulsar velocity direction. Surely, a detailed multy-dimensional numerical simulation of the process is needed. Let us estimate in order of magnitude what to expect. A pressure difference arising in the two hemispheres can be evaluated as: ∆p ≃ (eB)2 /(8πα), where α = 1/137 is the fine-structure constant. The magnetic field pressure causes the plasma acceleration (see [2] for details): ( )2 ( ) )2 ( B R dVkick 1.4 M⊙ 4 km ≃ 4 × 10 , (2) dt sec2 1016 G 20 km M where R is the parameter that characterize the region of a strong toroidal magnetic field. In fact, the acceleration is not a constant, and an expansion of the magnetic field volume, which reduces the magnitude of the field, should be taken into account. The magnetic flux conservation provides: p V 2 = const. Within the same geometry, one obtains: ( )( )( )1/2 ( )1/2 km R B0 ∆z 1.4 M⊙ Vkick ≃ 600 , (3) sec 1016 G 20 km 5 km M where B0 is the initial field strength, ∆ z is a distance traveled by a compact remnant of the explosion. Because of large acceleration, a pulsar acquires big velocity during very short time, like in a shot. So, we may consider a kind of “Cherry-Stone Shooting” mechanism for pulsar natal kick. Acknowledgments This work was performed in the framework of realization of the Federal Target Program “Scientific and Pedagogic Personnel of the Innovation Russia” for 2009 - 2013 (State contract no. P2323) and was supported in part by the Ministry of Education and Science of the Russian Federation under the Program “Development of the Scientific Potential of the Higher Education” (project no. 2.1.1/13011), and by the Russian Foundation for Basic Research (project no. 11-02-00394-a). References [1] A. Kusenko, Phys. Rept. 481, 1 (2009). [2] A. V. Kuznetsov, N. V. Mikheev, arXiv:1110.1041 (2011). [3] A. V. Kuznetsov, N. V. Mikheev, Phys. Lett. B 394, 123 (1997); JETP 91, 748 (2000); A. A. Gvozdev, I. S. Ognev, JETP 94, 1043 (2002). [4] G. S. Bisnovatyi-Kogan, “Stellar Physics 2: Stellar Evolution and Stability”, (Nauka, Moscow, 1989; Springer, New York, 2001).

210 CONTRIBUTION TO THE NEUTRINO FORM FACTORS COMING FROM THE CHARGED HIGGS OF A TWO HIGGS DOUBLET MODEL Carlos G. Tarazona a , Rodolfo A. Diaz b , Jhon Morales c Abstract. The presence of a charged Higgs in the two Higgs doublet model induces corrections to the neutrino form factors. We calculate and analyze such contributions in the parameter space of the two Higgs doublet model type II. The characterization of the neutrino form factors could discriminate between Majorana and Dirac neutrinos

1

Introduction

Even with charge neutrality, neutrinos can participate in electromagnetic interactions via loop diagrams and like other particles, neutrinos can be described by electromagnetic form factors with vertex functions. The most general expression for Λµ (l, q) is Λµ (q)=FQ (q 2 )γµ +FM (q 2 )iσµν q ν +FE (q 2 )σµν q ν γ5 +FA (q 2 )(q 2 γµ −qµ ¬q )γ5

(1)

where: FQ (q2 ) represents the electric charge, FM (q2 ) represents the dipole magnetic moment, FE (q2 ) represents the dipole electric moment and FA (q2 ) represents the anapole moment [1], [2]. For Dirac neutrinos only FM is possible, because the other terms vanish owing to the CP invariance and hermiticity of JµEM . On the other hand, for Majorana neutrinos only FA is possible, because the other terms vanish owing to their self-conjugate nature. Therefore, the neutrino electromagnetic properties can be used to distinguish Majorana and Dirac neutrinos. We shall study the electromagnetic properties of the neutrinos in the framework of the non-supersymmetric two Higgs doublet model (2HDM) [4], [3], in which the symmetry breaking is implemented by using two identical Higgs doublets. The Higgs ( ) spectrum is extended ( )and consists of: Two Higgs CP-even scalars H 0 , h0 , one CP-odd scalar A0 and two charged Higgs bosons (H ± ). The charged Higgs bosons give additional contributions to the electromagnetic form factors of the neutrinos. 2

Radiative corrections

In SM, the neutrino electromagnetic properties arise from one loop diagrams in the form of vertex corrections and vacuum polarization [5]. In a two Higgs doublet model we should add three new types of diagrams which are analyzed for their contributions. In the extension of the SM including right-chiral neutrinos, the magnetic moment arises and the theoretical value for the magnetic mv moment is 3.2×10−19 µB ×( 1eV ) calculated by K. Fujikawa and R.Shrock [6].

211 In this work, we use a very conservative scenario in which the decoupling limit of the 2HDM is used such that the couplings of the lightest CP even Higgs is SM-like. Our preliminary results, show that in this particular scenario the contribution of new physics is up to 10% of the SM value. 3

Conclusion and perspectives

The magnitude of the magnetic moments could be modified with physics beyond the standard model, in particular for the 2HDM we evaluated the contributions coming from the insertion of the charged Higgs boson into the loops. For our preliminary results in the decoupling limit the contribution of the new physics of 2HDM is up to 10% of the SM contribution. However, a more complete analysis of the allowed free parameters should be done to see whether a sizable contribution coming from the new Physics is still possible. In particular, large values of the tan β parameter could provide enough enhancement to approach the experimental threshold. Besides the evaluation of the radiative corrections, the complete characterization of the neutrino form factors requires an analysis of the dependence on the neutrino source (stellar astrophysics, primordial nucleosynthesis etc.), from which the form factors acquires a relation with their masses in most models. For example in left-right symmetric models, they are proportional to the lepton mass. References [1] Marek Nowakowski, E. A. Paschos, J. M. Rodriguez, All electromagnetic form factors, Eur. J. Phys. 26 (2005) 545, arXiv:physics/0402058. [2] Carlo Giunti, Alexander Studenikin, Neutrino electromagnetic properties, Phys. Atom. Nucl. 72 (2009) 2089-2125, arXiv:0812.3646. [3] J. Gunion, H. Haver, G. Kane, S. Dawson. Higgs hunter´s guide, Perseus publishing. 2000 [4] R. A. D´ıaz, Ph.D. Thesis [arXiv: hep-ph/0212237]. [5] K. Bhattacharya, Palash B. Pal, Neutrinos and magnetic .elds: A Short review, Proc Indian Natm Sci Acad, 70 A, 2004 [6] K Fujikawa and R Shrock “The magnetic moment of a massive neutrino and neutrino spin rotation” Phys Rev Lett 45 (1980) 963

212 INTERFERENCE OF THE SOLAR NEUTRINOS Akmarov K.A a Engineering Physics Department, National Research University of Information Technologies, Mechanics and Optics., St. Petersburg, Russia Abstract. The report presents the results of the analysis of experiments on the observation of the angular distribution of solar neutrinos. Assumptions have been done about the nature of neutrinos and the mechanisms responsible for the angular distribution, similar to the interference pattern.

1

Introduction

Sun neutrinogramm for 500 days measured by Super-Kamiokande detector [1] shows very large deviations from the center of the Sun. It must look like a small point of 0.2 Sun diameter. Neutrinogramm is located rather symmetrically about the center. This suggests a more complex structure of the areas of energy processes inside the Sun. Investigation of processes inside the Sun is possible with the help of solar neutrinos. It is badly implemented due to insufficient knowledge of neutrino properties. The plasma parameters in the depths of the Sun are not known too. 2

Formation of magnetic structure, scattering the neutrino

The point S is the center of the Sun. Suppose, at the point O in the central part of the Sun there was a local energy release [2] (Fig. 1(a)). From the principle of the least action, the main pulse energy is distributed along the radius towards the sun’s surface in the direction of decreasing density of matter. In this case the formation of different magnetic structures is possible [3]. For example, turbulent vortex rings (TVR) (Fig.1(b),(c)). Due to the different mobility of electrons and ions - the electrons are pulled out ahead after the burst and scattered by the peripheral layers of the ring. In such a ring with the lack of electrons spinning plasma toroid of the coils with moving charges is formed. A magnetic field appears, which compresses this toroid to some equilibrium of densities of magnetic and kinetic energies. This forms a strong magnetic ring formation in the form of TVR. Its structure is not homogeneous. In the center of the toroid coils a magnetic field is maximum and fast decreases outside the toroid.(Fig.1(d)) In an inhomogeneous magnetic field on the neutrino having nonzero rest √ 3 2 mass and magnetic moment will be a influenced by a force: F = 16π Gmν e dB dr , where G = 1.03 × 10−5 (m−2 p ) the Fermi constant. This force will act to the bigger field gradients. In this case the ring may be a dispersing element and a e-mail:[email protected]

213

Figure 1: Formation of TVR. a - local excess energy release; b - emission of the plasma to the surface of the sun; c - TVR; d - vector structure of TVR. Vi - the movement of ions, B vector of the magnetic field, dB/dr - magnetic field gradients.

Figure 2: Scheme of formation of the interference pattern.

form interference system (Fig.2). In the approximation that l  ∆x and l  d we can obtain an expression for the wavelength of the neutrinos: λ = 2d tan α −

d2 l

where ∆x - the distance between the peaks of interference pattern, d the distance between the virtual source, α the angle formed by virtual sources, l distance from the virtual sources to the maximums of interference pattern.

3

Experimental part and conclusion

On the solid state neutrino telescope [4], which has a higher sensitivity (more than 106 SNU) and angular resolution, a lot of different charts had been received.

214

Figure 3: The appearance of the neutrino burst.

Figure 4: Neutrino bursts.

At the time of passage of the Sun through the ecliptic set point pulse is not great, does not differ from background values (Fig. 3(a)). At certain times there are local, short increase of the intensity of the flow (Fig. 3(b)). It was found that regularly arise of “neutrino bursts ”- time-limited neutrino fluxes of high-intensity, sometimes many times greater than the mean (Fig. 3(c), Fig. 4). This represents a significant increase in the rate of nuclear reactions in a space near the center of the sun. Hence, the energy release at this time is much higher than the average. In diagrams in Fig. 4(b) and (c) the intensity of the peaks so high that they do not fit in memory and in the process of accumulation is reset. It looks like a negative peak. Often, there are diagrams similar to the interference pattern (Fig. 5). It might be done for many years of observation. Measurements (Fig. 6) was as follows: the telescope was adjusted to a precomputed point of the ecliptic. Most often they were ecliptic pole. The recorder automatically switched on an hour or half an hour before the Sun passing this point. The distance between the interference peaks have different values.

215

Figure 5: Diagrams obtained at the time of the Sun passing ecliptic pole, on which the telescope has been pointed. a, b - passing the South Pole (at midnight); c - the north pole (at noon).

Figure 6: Scheme of measurements. 1 - solar neutrino flux, 2 - the Earth, 3 - the direction of the optical axis of the telescope in day measurements, 4 - the direction of the optical axis of the telescope at night measurements.

4

Conclusion

Having adopted the possibility of presenting neutrino in the form of wave particles we can interpret neutrinogramm obtained by Super-Kamiokande and our experimental results as a sign of interference of the solar neutrinos. The resulting numerical values indicate a lack of information about nuclear structure and physical properties of the solar neutrinos. The work confirms the existence of a nonzero neutrino rest mass. References [1] M. Koshiba. Uspekhi Fizicheskikh Nauk, v. 174, 4, p.418-426, 2004. [2] Akmarov A.A., Akmarov K.A. Abstracts “Solar and Solar-Terrestrial physics 2010”, October 3-9, 2010, St. Petersburg, p. 9. [3] Zhdanov V.M. Transport processes in multicomponent plasma. Moscow: Fizmatlit, 2009. [4] Akmarov A.A., Akmarov K.A. The method of neutrino detection. The claim on the innovation 2010135503/28(050415) on 8/24/2010.

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Astroparticle Physics and Cosmology

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219 PARTICLE DARK MATTER: DAMA/LIBRA RESULTS AND PERSPECTIVES R. Bernabei a , P. Belli, A. Di Marco, F. Montecchia b Dip. di Fisica, Univ. di Roma “Tor Vergata” and INFN sez. Roma “Tor Vergata”, I-00133 Rome, Italy F. Cappella, A. d’Angelo, A. Incicchitti, D. Prosperi c Dip. di Fisica, Univ. di Roma “La Sapienza” and INFN, sez. Roma, I-00185 Rome, Italy R. Cerulli Laboratori Nazionali del Gran Sasso, I.N.F.N., Assergi, Italy C.J. Dai, H.L. He, X.H. Ma, X.D. Sheng, R.G. Wang, Z.P. Ye d Chinese Academy, P.O. Box 918/3, Beijing 100039, China Abstract. The present DAMA/LIBRA and the former DAMA/NaI experiments (exposed masses: ≃ 250 kg and ≃ 100 kg of highly radiopure NaI(Tl) respectively) have released so far a total exposure of 1.17 ton × yr collected over 13 annual cycles. They have obtained a positive model independent result for the presence of Dark Matter particles in the galactic halo at 8.9 σ C.L.. A brief summary of the obtained results and future perspectives are mentioned.

1

Introduction

The DAMA project is an observatory for rare processes located deep underground at the Gran Sasso National Laboratory of the I.N.F.N.. It is based on the development and use of low background scintillators [1–15]. The main apparatus, DAMA/LIBRA, is investigating the presence of Dark Matter (DM) particles in the galactic halo by exploiting the model independent DM annual modulation signature. In fact, as a consequence of its annual revolution around the Sun, which is moving in the Galaxy traveling with respect to the Local Standard of Rest towards the star Vega near the constellation of Hercules, the Earth should be crossed by a larger flux of Dark Matter particles around ∼2 June (when the Earth orbital velocity is summed to the one of the solar system with respect to the Galaxy) and by a smaller one around ∼2 December (when the two velocities are subtracted). Thus, this signature has a specific origin with peculiarities not correlated with seasons. This DM annual modulation signature is very distinctive since the effect induced by DM particles must simultaneously satisfy all the following requirements: (1) the rate must contain a component modulated according to a cosine function; (2) with one year period; (3) with a phase that peaks roughly around ∼ 2nd June; (4) this modulation must be present only a e-mail:

[email protected] Sperim. Policentrico di Ingegneria Medica, Universit` a di Roma “Tor Vergata” c Deceased d also: University of Jing Gangshan, Jiangxi, China b also:Lab.

220 in a well-defined low energy range, where DM particles can induce signals; (5) it must be present only in those events where just a single detector, among all the available ones in the used set-up, actually “fires” (single-hit events), since the probability that DM particles experience multiple interactions is negligible; (6) the modulation amplitude in the region of maximal sensitivity has to be 10 TeV. b) Adding the peak from ATIC, a clear indication for the mass emerges: DM has to be a particle with mass ∼ 1 TeV that dominantly annihilates into leptons. c) Replacing the ATIC peak with the FERMI smoother spectrum and the indication for a cutoff at a few TeV from HESS shifts somewhat the best fit, but not the main features: DM has to be a particle with mass ∼ 3 TeV that mostly annihilates into leptons (τ is best). Models with M  1 TeV appear anyway to be already disfavored. For what concerns the magnitude of the annihilation cross section, the large flux above the background in the PAMELA data indicates a very large σv, of the order of 10−23 cm3 /sec or more (see fig. 2). • What are the constraints from diffuse galactic γ rays? Constraints are imposed by high energy gamma rays (generated directly from the DM annihilation process or by the ICS upscattering of the CMB and starlight photons) from the galactic center region and from satellite galaxies and by synchrotron radiation (generated by e± in the galactic center’s magnetic field). The results show that the regions of the parameter space that allow to fit the PAMELA (and ATIC or FERMI+HESS) data are disfavored by about one order of magnitude if a benchmark Einasto (or NFW) profile is assumed. Choosing a smoother profile and/or assuming that a part of the cross section is due to an astrophysical boost factor that would not be present in dwarf galaxies and the Galactic Center due to tidal disruption re-allows part of the space. ICS constraints are however more robust and more difficult to circumvent with these arguments. It is fair to say that a tension is present between the charged CR signals and the gamma ray constraints. • Which conclusions can be drawn on the DM interpretation of the data? As apparent, the data point to a Dark Matter particle that (1) features really ‘unexpected’ properties and (2) has anyway disturbing ‘internal’ tensions (with γ ray constraints). So, either the DM interpretation is not the right one, i.e. an astrophysical source will turn out to be responsible for the excesses. Or we are on the verge of a big change of paradigm in the field of DM modelling. References [1] [2] [3] [4] [5] [6]

M. Cirelli et al., Nucl.Phys.B 813 (2009) 1 [arXiv:0809.2409]. G. Bertone et al., JCAP 0903 (2009) 009 [arXiv:0811.3744]. M. Cirelli and P. Panci, Nucl. Phys. B 821 (2009) 399 [arXiv:0904.3830]. M. Cirelli et al., JCAP 0910 (2009) 009 [arXiv:0907.0719]. M. Cirelli et al., Nucl. Phys. B 840 (2010) 284, arXiv:0912.0663. M. Cirelli et al., JCAP 1103 (2011) 051 [arXiv:1012.4515].

232 RECENT RESULTS OF THE HIGH ENERGY STEREOSCOPIC SYSTEM (H.E.S.S.) Henning Gast a , for the H.E.S.S. Collaboration Max-Planck-Institut f¨ ur Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany Abstract. The High Energy Stereoscopic System (H.E.S.S.) is an array of four imaging atmospheric-Cherenkov telescopes located in Namibia and designed to detect extensive air showers initiated by γ-rays in the very-high-energy (VHE) domain, above the energy threshold of 0.1 TeV. Since it began full operation in December 2003, H.E.S.S. has shed light on a wide range of astrophysical objects, from supernova remnants, pulsar wind nebulae and binary systems, to active galactic nuclei. A systematic scan of the inner Galaxy has revealed many previously unknown sources of VHE gamma-rays. In addition, a considerable fraction of the annual observation time is devoted to fundamental physics, especially the search for the elusive dark matter.

1

Introduction

At the far end of the energy spectrum accessible to astronomical observations, imaging atmospheric Cherenkov telescopes (IACTs) are employed to detect extended air showers initiated by very-high-energy (VHE; E > 0.1 TeV) photons. With the latest generation of IACTs, the detection of VHE γ-rays has turned into a mature astronomical discipline, and more than 120 sources are currently known. Here we report on the latest results obtained with the High Energy Stereoscopic System (H.E.S.S.). H.E.S.S. covers a diverse physics program, reaching from the discovery and study of individual astrophysical objects to fundamental physics. We will follow this range here, by first looking at the latest view of the inner Galaxy at TeV energies, as unveiled by the H.E.S.S. Galactic plane survey. Then, we will highlight two recent additions to the ensemble of H.E.S.S. sources. The discovery of VHE γ-ray emission from a starburst galaxy (NGC 253) and the tentative association of a new γ-ray source with the globular cluster Terzan 5 show that new classes of VHE γ-ray emitters are still within reach of the current generation of instruments. Finally, we will report on indirect searches for dark matter and a test of Lorentz invariance. H.E.S.S. consists of four identical 12 m diameter IACTs located at an altitude of 1800 m above sea level in the Khomas Highlands of Namibia [1]. Each of the four H.E.S.S. telescopes is equipped with a camera containing 960 photomultiplier tubes and a tesselated mirror with a combined area of 107 m2. The optical design allows for a comparatively large, 5◦ field-of-view (FoV). The H.E.S.S. array has an angular resolution of ∼ 0.1◦ and an energy resolution of ∼ 15 %. a e-mail:

[email protected]

233 2

Status of the H.E.S.S. galactic plane survey

With a sizable fraction of the annual observation budget of H.E.S.S. dedicated to it, the Galactic Plane Survey undertaken by H.E.S.S. aims at performing a systematic scan of the inner Galaxy, with the main goal of discovering previously unknown emitters of VHE γ-rays. More than 60 Galactic VHE γ-ray sources are now known. The population is dominated by sources that are linked to the final stages in stellar evolution, namely pulsar wind nebulae (PWNe) and supernova remnants (SNRs). For nearly a third of the sources, however, no plausible counterpart at other wavelengths has been found yet, or the physical origin of the detected emission remains unclear. Most of the available observation time of H.E.S.S. is spent looking at predefined targets that seem promising because of their known astrophysical properties. In the H.E.S.S. Galactic Plane Survey [2], a different approach is followed. Here, the inner Galaxy is systematically scanned using observation positions with overlapping fields-of-view, with the main goal of discovering new γ-ray sources and enabling population studies of Galactic source classes as a consequence. Advanced analysis techniques for background suppression, e.g. [3–6], play a very important role in this endeavour. Over the course of its operation, H.E.S.S. has assembled an impressive dataset in the region of the inner Galaxy. In the last journal publication on the H.E.S.S. Galactic Plane Survey in January 2006 [7], the detection of 17 sources in the range ` ± 30◦ and b ± 3◦ was presented using a dataset comprising 230 h of observation time, corrected for readout dead-time. Since then, this dataset has increased dramatically; it now includes over 2300 h of data covering the longitude range from ` = 250◦ to 65◦ , and more than 60 Galactic sources have been detected as a result. The total dataset that constitutes the Galactic Plane Survey is made up of observations taken with two different strategies: Firstly, in scan mode, pointings are distributed systematically along the Galactic plane, usually in three strips in latitude (b = −1, 0, +1◦) and with spacings of ∼ 0.7◦ in longitude. Deeper, pointed observations are taken on promising source candidates, and all other observations that fall within the survey region are included in the dataset, too. For the past and ongoing observation campaigns in 2010 and 2011, the focus of the survey effort has been put on achieving a more uniform exposure in the survey core region (` = 282◦ to 60◦ ), and on deepening the exposure in the region from ` = 268◦ to 282◦ . Figure 1 shows the latest significance map obtained for the survey region. After calibration and quality selection, a multivariate analysis technique [3] based on shower and image shape parameters is used to discriminate γ-ray events from cosmic ray-induced showers. A minimum image amplitude of 160 p.e. is required. The remaining background is estimated by the ring background technique [1], with the inner and outer ring radii being increased appropriately around large sources. The significance value for each position is then calculated

234

Figure 1: Latest significance map for the H.E.S.S. Galactic Plane Survey. The pre-trials significance for a correlation radius of 0.22◦ is shown. The colour transition from blue to red corresponds to ∼ 5σ post-trials significance. The trial factor takes into account the fact that many sky positions are tested for an excess above the background, thus increasing the chance of finding a random upward fluctuation of the background. The map has been filled for regions on the sky where the sensitivity of H.E.S.S. for point sources (5σ pre-trials, and assuming the spectral shape of a power law with index 2.5) is better than 10 % Crab.

235 from the formula derived by Li and Ma [8], by summing the candidate events within a fixed and pre-defined correlation radius of 0.22◦ , suitable for extended sources, and comparing to the estimated background level at that position. 3

Discovery of VHE γ-ray emission from a starburst galaxy

Starburst galaxies are characterized by a high rate of formation of massive stars in localized regions, which explode - at the end of their life cycle — as supernovae and hence give rise to a high flux of cosmic rays, accelerated in the supernova shocks. The high cosmic ray density, combined with the intense radiation fields and high gas densities, leads to favourable conditions for the production of VHE γ-rays. At a distance of about 10 million light years, NGC 253 is a relatively nearby starburst galaxy. In deep observations of NGC 253, accumulating 119 hours of data and using advanced image analysis techniques, H.E.S.S. succeeded to establish γ-ray emission from the core of NGC 253 [9]. Comparison with the optical image of NGC 253 shows clearly that the γ-rays come from the location of the central starburst region. This is the first non-AGN extragalactic object detected in very high energy γ-rays, i.e. the first extragalactic object where γ-ray emission is powered by supernova explosions, rather than by accretion of mass onto a supermassive black hole. The observed flux level is well in the range of the theoretical estimates based on the rate of supernovae in NGC 253. Assuming hadronic γ-ray production, the cosmic ray number density above 1.3 TeV in the starburst region of NGC 253 is about three orders of magnitude larger than at the earth. About 5 % of the energy in cosmic rays is found to be converted into γ-rays. 4

VHE γ-ray emission from the direction of Terzan 5

Globular clusters (GCs) are very old stellar systems with exceptionally high densities of stars in their cores, leading to numerous stellar collisions. GCs also contain many millisecond pulsars, which is likely related to the large fraction of binary systems. GCs are predicted to emit high-energy γ-rays, generated by energetic electrons accelerated in the huge fields near millisecond pulsars [10], or in the termination shocks of electron winds flowing away from the pulsars [11]. H.E.S.S. has discovered a new VHE γ-ray source (HESS J1747-248), located in the immidiate vicinity of the Galactic globular cluster Terzan 5 [12]. The source appears extended and offset from the cluster core but overlaps significantly with Terzan 5. A random coincidence with the globular cluster is unlikely (∼ 10−4 ), but this possibility cannot be firmly excluded. With the largest population of identified millisecond pulsars, a very large core stellar density and the brightest GeV-range flux as measured by Fermi-LAT, Terzan 5 stands out

236 among Galactic globular clusters. Interpretation of the available data accommodates several possible origins for this VHE γ-ray source. 5

Indirect search for dark matter

The nature of dark matter remains one of the most intriguing mysteries in particle physics. γ-ray astronomy offers a method of searching for dark matter that is complementary to direct searches, searches at collider experiments and indirect searches using suitable cosmic-ray species as messengers. Generically, VHE γ-rays are produced from decays of π 0 particles arising in the hadronization processes following annihilations of two dark matter particles, if the mass mχ of the dark matter particle is sufficiently high. With a spatial model of the dark matter density ρ and a parametrization of the energy spectrum of γ-rays produced in the annihilation process, the VHE γ-ray flux can be derived as a function of the thermally-averaged annihilation cross section hσvi and upper limits can then be quoted for this quantity. Targets with presumably high concentrations of dark matter offer the best prospects for detection, and searches for dark matter with H.E.S.S. have recently been published for the Galactic Center Halo [13], the globular clusters NGC 6388 and M 15 [14], as well as for two dwarf galaxies [15], in addition to the search from the Sagittarius dwarf galaxy. The upper limits on hσvi at mχ = 1 TeV for these source classes, while strongly depending on the assumed model for ρ, are now in the 3 × 10−25 to 3 × 10−24 cm3 s−1 range. 6

Test of Lorentz invariance

Several models of quantum gravity (QG) predict Lorentz symmetry breaking at energy scales approaching the Planck scale (EP = 1.22 × 1019 GeV). Generically, Lorentz invariance can be tested by looking for an energy-dependence of the speed of light, v = c(1 − ξ(E/EP ))

and

v = c(1 − ζ(E/EP )2 )

(1)

for a linear and quadratic correction to the photon dispersion relation c2 p2 = E 2 , respectively. In the context of VHE γ-ray astronomy, the giant flare observed from the Active Galactic Nucleus (AGN) PKS 2155-304 on July 28th, 2006 offers a unique opportunity to look for an energy-dependence of the arrival times of the γ-ray photons, that could add up to a measurable signal over the cosmological distance to the AGN, e.g. for the linear case: Z z ξ (1 + z 0 ) dz0 ∆t p ≈ (2) ∆E EP H0 0 Ωm (1 + z 0 )3 + ΩΛ

237 where z is redshift, Ωm and ΩΛ are the usual cosmological parameters and H0 is the Hubble constant. Using the low-energy lightcurve with its characteristic five-peak structure as a temporal template and assuming no energy dependence at the source, an event-by-event likelihood was used to estimate the value of ∆t/∆E and its confidence interval, thereby considerably improving the sensitivity of an earlier analysis. No hint for a violation of Lorentz invariance was found and 95 % CL upper limits on the QG mass scales q l l MQG = MP /ξ and MQG = MP /ζ were set as MQG > 2.1 × 1018 GeV and q 10 MQG > 6.4 × 10 GeV [16]. Acknowledgments The support of the Namibian authorities and of the University of Namibia in facilitating the construction and operation of H.E.S.S. is gratefully acknowledged, as is the support by the German Ministry for Education and Research (BMBF), the Max Planck Society, the French Ministry for Research, the CNRS-IN2P3 and the Astroparticle Interdisciplinary Programme of the CNRS, the U.K. Science and Technology Facilities Council (STFC), the IPNP of the Charles University, the Polish Ministry of Science and Higher Education, the South African Department of Science and Technology and National Research Foundation, and by the University of Namibia. We appreciate the excellent work of the technical support staff in Berlin, Durham, Hamburg, Heidelberg, Palaiseau, Paris, Saclay, and in Namibia in the construction and operation of the equipment. References [1] F. Aharonian et al. (H.E.S.S. Coll.), A&A 457 (2006) 899-915 [2] H. Gast et al., for the H.E.S.S. Coll., proc. 32nd ICRC (Beijing, 2011) [3] S. Ohm et al., Astropart. Phys. 31 (2009) 383 [4] M. de Naurois and L. Rolland, Astropart. Phys. 32 (2009) 231 [5] A. Fiasson et al., Astropart. Phys. 34 (2010) 25 [6] Y. Becherini et al., Astropart. Phys. 34 (2011) 858 [7] F. Aharonian et al. (H.E.S.S. Coll.), ApJ 636 (2006) 777-797 [8] T. Li and Y. Ma, ApJ 272 (1983) 317-324 [9] F. Acero et al. (H.E.S.S. Coll.), Science 326 (2009) 1080 [10] C. Venter et al., ApJL 696 (2009) L52-L55 [11] W. Bednarek and J. Sitarek, MNRAS 377 (2007) 920-930 [12] W. Domainko, for the H.E.S.S. Coll., proc. 32nd ICRC (Beijing, 2011) [13] A. Abramowski et al. (H.E.S.S. Coll.), PRL 106 (2011) 161301 [14] A. Abramowski et al. (H.E.S.S. Coll.), Astropart. Phys. 34 (2011) 608 [15] A. Abramowski et al. (H.E.S.S. Coll.), arXiv: 1104.2548 [16] A. Abramowski et al. (H.E.S.S. Coll.), Astropart. Phys. 34 (2011) 738

238 SELECTED ISSUES IN LEPTOGENESIS Enrico Nardia INFN, Laboratori Nazionali di Frascati, C.P. 13, 100044 Frascati, Italy. Abstract.I review the leptogenesis performance in producing the cosmic baryon asymmetry, addressing in some detail its connections with the scale of the light neutrino masses. I clarify under which assumptions leptogenesis can provide an upper limit on the neutrino mass scale. Assuming these conditions hold, a dedicated numerical analysis that includes the effects of the Higgs density-asymmetry, scatterings with the top-quark and thermal corrections yields a 3σ limit mν < 0.10 eV.

1

Introduction

The baryon asymmetry of the Universe (BAU) is a clear evidence of physics beyond the standard model (SM). In fact, even if the SM has all the required ingredients [1] to produce dynamically a baryon asymmetry [2], quantitatively it fails to do so by several orders of magnitude [3]. WMAP observations of the CMB power spectrum [4] imply that the relative baryon contribution to the energy density of the Universe Ωb ≡ ρb /ρtot is: 102 Ωb h2 = 2.258+0.057 −0.056

(68% c.l.) ,

(1)

where h ≡ H0 /(100 km sec−1 Mpc−1 ) with H0 the Hubble constant. Observations of light elements abundances synthesized during Big Bang Nucleosynthesis (BBN) give a measurement of the number of baryons relative to the number of photons η ≡ nb /nγ . By using only the abundance of deuterium ref. [5] quotes: 1010 η = 5.7 ± 0.6

(95% c.l.) .

(2)

The two numbers in eq. (1) and eq. (2) are related by 1010 η = 274 Ωb h2 and measure the same quantity. However, not only are the two measurements independent, they are also extracted from two different periods in the evolution of the Universe: eq. (1) comes from physics at the epoch of recombination at T < ∼ O(1) eV, while eq. (2) is derived from the network of nuclear reactions at T < ∼ O(1) MeV. A third way to express the amount of matter-antimatter asymmetry is in terms of the baryon asymmetry normalized to the entropy density: Y∆B ≡ (nb − n ¯ b )/s. This is a useful quantity since it is conserved during the evolution of the Universe. The relation with η is simply given by the present entropy density divided by the number density of photons s0 /nγ = 7.04. In terms of Y∆B , eq. (1) and (2) give, at 95% c.l.: (WMAP)

Y∆B

= (8.79 ± 0.22) × 10−11 ,

(BBN)

Y∆B

= (8.1 ± 0.9) × 10−11 .

(3)

The good agreement between these two determinations represents a striking success of the standard big bang theory. a e-mail:

[email protected]

239 2

Leptogenesis

Leptogenesis [6, 7] is a class of scenarios in which the BAU is produced from a lepton asymmetry Y∆L generated in the decays of heavy SU (2) singlet Majorana neutrinos N . The same heavy states can also elegantly explain the suppression of the light neutrino mass scale by means of the seesaw mechanism, and thus leptogenesis provides a profound connection between baryogenesis and neutrino physics. In the basis in which the charged lepton Yukawa couplings are diagonal (λeα e¯α ℓα ) the seesaw Lagrangian can be written as: 1 ¯ic Nic − λiα N ¯i ℓα H ˜† , L = − Mi N 2

(4)

where i = 1, 2, . . . labels the heavy Majorana states, ℓα the SU (2) lepton dou˜ = iσ2 H ∗ with H the Higgs field. This simple Lagrangian contains blets, and H all the ingredients to satisfy qualitatively the three Sakharov conditions: (i) Since there is no lepton number assignment for N which would leave invariant under U (1)L both terms in eq. (4), B−L is violated. By choosing to assign L(N ) = 0 the processes induced by the λ-terms have ∆(B − L) = ±1. (ii) Complex phases in the λ couplings are responsible for CP violation in the interference between the tree-level and one-loop N ’s decay diagrams. (iii) Sufficient deviations from thermal equilibrium can occur if, when the temperature drops down to T ∼ MN , the age of the Universe tU (MN ) is of the order of the N ’s lifetime τN . 2.1

Deviations from thermal equilibrium

The third condition requires that the time scale for N -related processes should be large enough that at T ∼ MN they do not occur frequently during one expansion time. However, they should also not occur too infrequently, otherwise a population of N ’s could not be generated thermally. Does this require a special choice of the seesaw parameters? Of course! For the lightest Majorana singlet √ M12 M1 N1 we have τ1−1 = Γ1 = 16π (λλ† )11 , while t−1 U (M1 ) ≈ H1 = 1.7 g∗ mP (with g∗ = 106.75 the number of relativistic d.o.f. in the SM and mP the Planck mass). By a suitable rescaling of H1 and Γ1 we can write: m∗ ≡ 16π

v2 × H1 ≈ 10−3 eV , M12

m ˜ ≡ 16π

v2 v2 ( † ) × Γ = λλ 11 , 1 M12 M1

(5)

where v is the Higgs vev. The condition τ1 ≈ t−1 ˜ ≈ m∗ . AcU (M1 ), now reads: m tually, values of m ˜ between one and two orders of magnitude larger than m∗ are theoretically preferred, firstly because in this case equilibrium is reached, and this renders the results much less dependent on initial conditions; secondly because when m ˜ > m∗ the final value of Y∆B gets somewhat suppressed, and often

240 this suppression is necessary to reproduce the observations. The second quantity in eq. (5) should be confronted with the expression for the neutrino seesaw mass matrix mαβ = v 2 λjα Mj−1 λjβ . Although m ˜ does not correspond to any specific entry in mαβ , it is reasonable to expect that its value is grossly of the order of the neutrino masses, and it is indeed quite remarkable that values of m ˜ of the order of the solar (m⊙ ≡ (∆m2⊙ )1/2 ) or atmospheric (m⊕ ≡ (∆m2⊕ )1/2 ) mass scales would be optimal to satisfy the out of equilibrium condition. 2.2

The role of CP violation

Is there a limit on neutrino masses from leptogenesis? The fair answer to this question is ‘no’. However, it is also true that something more than the generic semi-quantitative indication discussed in the previous section can be said about the interrelation between neutrino masses and leptogenesis. The new theoretical ingredient needed for this is the requirement that the second condition (ii), that is CP violation, is also satisfied quantitatively. By computing the CP Γ −Γ ¯ asymmetry ϵα ≡ ℓαΓN ℓα for N1 decays into ℓα one obtains: 1

∑ Im ϵα = − j̸=1

{

[ 1 ]} 3 ( †) 3xj2 ( † ) 5xj2 ( † ) λjα λ∗1α λλ + xj λλ 1j + λλ j1 + . . . . 8π(λλ† )11 | 2 {z j1} | {z } | 6 {z } ̸L: D5 =(ℓϕ)2

¯ ∗ )∂ L: D6 =(ℓϕ ̸ (ℓϕ)

̸L: D7 =(ℓϕ)∂ 2 (ℓϕ)

1 Here I have written ϵα as an expansion in powers of xj = M Mj and, for each term, I have labeled the under-braces with the corresponding effective operator. If the heavy neutrinos are strongly hierarchical, M1 ≪ Mj , then only the first operator is important. This is the L-violating D5 seesaw operator responsible for neutrino masses, and for this reason its contribution to ϵ can be bound in terms of neutrino mass differences [9]: ∑ 3 M1 (D5 ) (D5 ) |ϵ |= (m3 − m1 ) , (6) ϵα ≤ α 16π v 2

with m3 (m1 ) the heaviest (lightest) neutrino mass eigenstate. A sufficiently large ϵ(D5 ) thus requires a sufficiently large M1 and this is why leptogenesis needs generically very high temperatures [9]. In the limit m1,3 ≫ m⊕ we can ∆m2

rewrite m3 − m1 ≃ 2m3⊕ ; this shows how ϵ gets suppressed as the mν scale is increased. Increasing M1 cannot compensate this indefinitely, since when 13 4 M1 > ∼ 10 GeV, λ → 1 and the O(λ ) ∆L = 2 processes start washing out strongly the lepton asymmetry. This is what yields a ‘neutrino mass limit from leptogenesis’ [10]. However, it was later clarified in [11] that contributions from the L violating operator D7 can become dominant when the hierarchy is not too strong, and spoil both the bound in eq. (6) as well as the limit on

241 neutrino masses. The operatorD6 does not violate L (i.e. ϵ(D6 )= 0) but it still contributes to the individual ϵα thus permitting, in case ϵ(D5 ) is for some reason suppressed [13] and lepton flavor equilibrating processes [14] are not too strong, a ‘purely flavored’ leptogenesis scenario [12]. Full realization of the relevance of 12 flavor effects in leptogenesis [15–17] clarified that below T < ∼ 10 GeV, eq. (6) is ineffective, since instead than ϵ the source of leptogenesis are the flavored CP asymmetries ϵα , for which no similar bound exist [16]. Finally, it was pointed out in [18] that even within the unflavored regime, and regardless the strength of N1 washouts, the lepton asymmetries produced in N2,3 decays are never completely erased. Then, given that no analogous of eq. (6) exist for ϵ2,3 , if N2,3 contribute substantially to leptogenesis, there is also no limit on the neutrino mass. Resuming, type I seesaw leptogenesis can predict an upper limit on neutrino masses only if the following three conditions are satisfied: (1) The mass hierarchy for the heavy neutrinos is sufficiently strong: M1 ≪ M2,3 . (2) Leptogenesis occurs in the unflavored regime, that is above T ∼ 1012 GeV. (3) N2,3 contributions to leptogenesis are negligible (either because ϵ2,3 are small, or because the washout parameters m ˜ 2,3 are large, or both). If any of these conditions is not realized, more parameters become important, leptogenesis looses predictivity, and the mν limit evaporates. 3

The neutrino mass limit

Obtaining information on leptogenesis from experiments is a difficult task, and it is thus important to analyze seriously any possible way through which leptogenesis scenarios could be constrained. In particular, leptogenesis can say something about the maximum allowed value for the neutrino mass scale mν . However, in order to obtain an accurate bound, several different effects must be included. Already in [19] it was remarked that the inclusion of the effects of the Higgs asymmetry would strengthen the mν bound by some 20%. Higgs effects were included in [20] in the reasonable approximation of summing up the lepton and Higgs density-asymmetries. However, when scatterings with the top-quark are included, additional factors enter, and this simple approximation does not hold any more. Here we present the results of a dedicated analysis [21] in which, besides the Higgs asymmetry, CP violating scatterings with top-quarks [22] and thermal corrections [23] are also included. Our results are shown in figure 1 as contour plots in the m ˜ 1 -M1 plane corresponding to different values of the heavier neutrino mass m3 . In the analysis (and in the plots) values related to light masses mν are renormalized at the leptogenesis scale µ ∼ 1013 GeV according to m(µ) = r × mν , where the renormalization factor r ∼ 1.3 has been estimated in [23]. The right egg-shaped curves in figure 1 are for the case when the Higgs asymmetry (yH ) is neglected, while

242

2.0

m3= 1.29 yH ¹ 0

M1 A1013 GeVE

1.8

yH = 0

m3=1.61

m3=1.30 m 3=1.62

1.6 1.4

m3=1.31

m3= 1.63

1.2 1.0 1.3

1.4

1.5

1.6

1.7

1.8

1.9

Ž m1 A10 -1 eVE Figure 1: Limits on the heaviest ν mass mν3 with (left) and without (right) Higgs effects.

the curves on the left have the Higgs effects included. Points inside the contoured areas correspond to parameters that allow to account for the observed BAU (allowing for a 3 σ uncertainty on Y∆B ). Outside the areas, a too small BAU is produced. As the heavier neutrino mass m3 is increased, the allowed area shrinks. In the yH = 0 case it disappears completely when m3 > ∼ 0.16 eV. With Higgs effects included, leptogenesis fails already when m3 > ∼ 0.13 eV. This confirms the strengthening of the bound by about 20% estimated analytically in [19]. The continuous and dashed lines correspond to two different ways of including the effects of the ∆L = 2 scatterings [21]. It is apparent that the differences are negligible. Renormalizing down to low energy the limit that can be red from figure 1, we obtain for the mass of the heavier neutrino ν3 at 3 σ: mν3 < 0.10 eV. (7) ∑ The limit in eq. (7) correspond to i mi ≃ 0.3 eV, a value that appears well in the reach of forthcoming cosmological observations. If a value larger than this is measured, we will learn that leptogenesis occurs in the flavored regime, or that there is no large hierarchy among the heavy N ’s, or that the CP asymmetries in the decays of the heavier N2,3 contribute substantially to the BAU. 4

Discussion and conclusions

In this talk I have reviewed what can be said in type-I seesaw leptogenesis about the neutrino mass scale. In the supersymmetric case, in spite of various qualitative differences [8] one obtains approximately the same quantitative results. However, the results discussed here do not hold for other leptogenesis models,

243 like the type-II and type-III seesaw, not to mention more exotic possibilities. Even in the standard case, while the generic indication of m ˜ 1 ≈ m⊙ , m⊕ is still valid, the relevant CP asymmetries might not correspond to anything like the expansion in eq. (6). This can happen, for example, when the N ’s are highly degenerate and their CP asymmetries are resonantly enhanced [24]. Moreover, supersymmetry unavoidably includes the possibility of baryogenesis via soft leptogenesis [25] or via R-genesis [26], in which case the CP asymmetries relevant for leptogenesis have a completely different origin. In both these cases, the requirement of satisfying quantitatively the second Sakharov condition (ii) does not yield additional information on the light neutrino masses. [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25]

[26]

A.D. Sakharov, JETP. Lett. 6, 24 (1967). V. Kuzmin, V. Rubakov, M. Shaposhnikov, Phys. Lett. B155, 36 (1985). M.B. Gavela et al., Nucl. Phys. B430, 382 (1994). D. Larson et al., Astrophys.J.Suppl., 192, 16 (2011). F. Iocco et al., Phys. Rept. 472, 1 (2009). M. Fukugita and T. Yanagida, Phys. Lett. B174, 45 (1986). S. Davidson, E. Nardi and Y. Nir, Phys. Rept. 466, 105 (2008). C. S. Fong et al., JCAP 1012, 013 (2010). S. Davidson and A. Ibarra, Phys. Lett. B535, 25 (2002). J. R. Ellis and M. Raidal, Nucl. Phys. B643, 229 (2002); W. Buchmuller et al., Nucl. Phys. B643, 367 (2002); ibid. B665, 445 (2003). T. Hambye et al., Nucl. Phys. B695, 169 (2004). D. A. Sierra, M. Losada and E. Nardi, Phys. Lett. B659, 328 (2008); D. A. Sierra, L. A. Mu˜ noz and E. Nardi, Phys. Rev. D80, 016007 (2009). S. Antusch et al. JHEP1001 (2010) 017. D. Aristizabal Sierra, M. Losada and E. Nardi, JCAP0912 (2009) 015. R. Barbieri et al.,Nucl. Phys. B575, 61 (2000); T. Endoh, T. Morozumi and Z. h. Xiong, Prog. Theor. Phys. 111 (2004)123. A. Abada et al., JHEP0609, 010 (2006). E. Nardi, Y. Nir, E. Roulet and J. Racker, JHEP 0601, 164 (2006). G. Engelhard et al., Phys. Rev. Lett. 99, 081802 (2007). E. Nardi, Y. Nir, J. Racker and E. Roulet, JHEP 0601, 068 (2006). S. Blanchet and P. Di Bari, Nucl. Phys. B807, 155 (2009). L. A. Mu˜ noz, E. Nardi and J. Nore˜ na, in preparation. E. Nardi, J. Racker and E. Roulet, JHEP0709, 090 (2007). G.F. Giudice et al., Nucl. Phys. B685, 89 (2004). A. Pilaftsis and T. Underwood, Nucl. Phys. B692, 303 (2004). Y. Grossman, T. Kashti, Y. Nir and E. Roulet, Phys. Rev. Lett. 91, 251801 (2003); G. D’Ambrosio, G. F. Giudice and M. Raidal, Phys. Lett. B575, 75 (2003); C. S. Fong, M. C. Gonzalez-Garcia, E. Nardi, Int.J.Mod.Phys. A26 3491 (2011). C. S. Fong, M. C. Gonzalez-Garcia, E. Nardi, JCAP 1102, 032 (2011).

244 FIVE YEARS OF PAMELA IN ORBIT Piero Spillantini a Astronomy and Physics Dept., Firenze University, Via Sansone 1, 50019 Sesto Fiorentino, Italy Abstract. In the 5 years of data taking and analysis the PAMELA observatory made important unforeseen observations on the energy spectra of protons and helim nuclei (precisely measured on a very wide energy range of more than three decades) and on the flux of positrons. Other outstanding results were also obtained in other observations of cosmic rays and on the behavior of heliosphere and magnetosphere. PAMELA observatory will continue its activity in next future with the accurate study of the energetic tail of solar phenomena. Other missions will follow (AMS-2, CALET, Gamma-400, JEM-EUSO), presently in different stage of their realization

1

Introduction

Pamela experiment [1] is the last step of the ‘Russian-Italian Mission’ (RIM) program born in 1992 between several Italian and Russian institutes and with the participation of the Royal Institute of Technology of Stockholm (Sweden) and the Siegen University (German). Previous steps of RIM program were the Si-Eye-1 and Si-eye-2 experiments on MIR space station dedicated to life science, the NINA experiment dedicated to Solar Cosmic Rays and the GILDA project dedicate to the study high energy gamma sources b . The Pamela experiment has been designed as a cosmic ray observatory at 1 AU: it is dedicated to the precise and high statistics study of CR fluxes on a three decades energy range, form a few tens MeV up to several hundred GeV region, with particular attention to the study of particles (protons and electrons) and antiparticles (antiprotons and positrons) energy spectra. The Pamela program also includes search for possible signals of dark matter annihilation, search for primordial antimatter (antihelium), search for new Matter in the Universe (Strangelets?), study of cosmic-ray propagation, solar physics and solar modulation, terrestrial magnetosphere. This program is made possible thanks to the outstanding performance of the instrument, that includes: a very precise magnetic spectrometer (tracking the particle trajectory by double side microstrip silicon tracker with an unprecedented precision of 3 micron per point on the uniform magnetic field of 4.3 kgauss of a permanent magnet [2], the very high granularity (2 × 2 × 4mm3 ) of the deep Si-W calorimeter [3], three planes of scintillator hodoscopes for triggering and ToF and charge measurements, a scintillator and a neutron counter behind the calorimeter for penetrating showers and a set of anticoincidence counters to clean the event pattern. The experiment, realized in the years from a e-mail:

[email protected] research program of Si-Eye experiments continued with the Si-Eye-3 and ALTEA experiments on ISS, that of NINA with the NINA-MITA experiments and the GILDA project originated the AGILE mission. b The

245

Proton Flux

Helium Flux

Figure 1: Proton (left panel) and helium (right panel) spectra in the range 10 GV – 1.2 TV. The shaded areas represent the estimated systematic uncertainty and the contribution due to tracker alignment. The straight (green) lines represent fits with a single power law in the rigidity range 30 GV - 240 GV. The red curves represent the fit with a rigidity dependent power law (30-240 GV) and with a single power law above 240 GV. The indexes of the fits are reported in the inserts.

1999 and 2005 c , was launched the 15 June 2006 from Baikonur cosmodrome on board of the Resurs-DK1 Russian satellite by a Soyuz rocket in an elliptical (350-610 km) quasi polar orbit (70◦ inclination). The average trigger rate of 25 Hz, coupled to a 73% live time, corresponding to 16 GB/day to be grounded, allowed to collect more than 109 events. 2

Measurement of the proton and helium fluxes

Protons and helium nuclei are the most abundant components of the cosmic radiation and the precise measurements of their fluxes allow understanding the acceleration and propagation of cosmic rays in the Galaxy. The precise measurements of the proton and helium spectra performed in the rigidity range 1 GV-1.2 TV are reported in Fig.1 [4]. The spectral shapes of these two species are different and cannot be well described by a single power law: at 230-240 GV they exhibit an abrupt spectral hardening. They challenge the current paradigm of cosmic-ray acceleration in supernova remnants followed by diffusive propagation in the Galaxy. More complex processes of acceleration and c It is worthwhile to remark that the instrument was realized directly by the scientists of the team in their laboratories, including the radiation test of the critical components and the integration of the models, with only a few subsystems procured from outside; therefore the total cost of the mission resulted only a few percent of that of similar missions and could be afforded by the supporting institutions (INFN and institutes) with marginal contributions of the space agencies.

246

Decreasing solar activity

Increasing GCR flux

Figure 2: Dependence of the proton spectrum at low energy from the solar activity.

2H/4He

3He/4He

Figure 3: Measurement of the 2H and 3He isotopic ratio.

propagation of cosmic rays are required to explain the observed spectral structures that show the drastic change of slope for both proton and helium, as well the not constant ration between their fluxes. The hardening in the spectra observed by PAMELA around 200 GV could be interpreted as an indication of different populations of cosmic ray sources. In [5], the softer spectra below 230GeV/c are ascribed to the expanding bubble left behind a supernova happened in the past in our region of the Galaxy d . At low energy the high statistics allows measuring the flux variation as a function of the time, counter-related to the solar activity (Fig.2). Important new measurements were obtained also for the light elements and the light isotopes (Fig.3) [8]. The self-standing calorimeter measurements allowed to extend the proton and He spectra beyond 10 and 3 TeV/n (Fig.4). d The suggestion it also coherent with previous measurements, albeit with a low statistical and systematic significance, of a change of the slope for nuclei (Z≥3), as well with the GCR flux measured in Antarctica during the last 5 decades [6], and not in contradiction with the GCR flux measured in meteorites in last 2.4 centuries [7].

247

PAMELA

Figure 4: The proton and helium spectra extended to higher energies by the self-standing calorimeter.

Donato et al. (ApJ 563 (2001) 172)

Ptuskin et al. (ApJ 642 (2006) 902)

Figure 5: Antiproton spectrum

3

Energy spectra of antiparticles

Another unforeseen result came from measurements of the energy spectra of antiprotons and positrons. While the results for antiprotons [9] extended to higher energy the measurements made by the balloon borne experiments of the past without showing any deviation from the secondary production of primary cosmic rays on the interstellar matter (Fig.5) the behavior of the positron flux [10] contradicts the prevision of the secondary production (Fig.6). It is a contradiction also in the sense that the different behavior of antiprotons and positrons calls for more complex scenarios than in the past, either invoking contributions from nearby sources for the positrons not effective for antiprotons, or indirect signal of dark matter decay under specific hypothe-

248

Secondary production Moskalenko & Strong 98

Figure 6: Positron spectrum compared with foreseen secondary production and previous data

Fermi Symposium, May 9 2011

Figure 7: Preliminary results on positron fraction from Fermi experiment (Fermi Symposium, May 9 2011.

sis, such as Kaluza-Klein DM ‘busted’ by ≥1000. The debate open by this ‘PAMELA anomaly’ is very wide, with hundreds of contributions from many scientist, and must wait for higher energy data promised by future experiments to be unraveled. The spectrum of the positron has recently been supported by the preliminary data of the Fermi experiment (Fig.7). Another important support to the PAMELA result for positrons is coming from the electron spectrum measurement [11], which agrees with the Fermi measurement of the e-+e+ flux, in particular taking also in account the PAMELA positron flux measurement (Fig.8).

249

Figure 8: The PAMELA e- and e+ fluxes compared with the other available measurements.

Figure 9: Time evolution of the energetic tail of the proton spectrum of the December 13th, 2006 solar event.

4

Other PAMELA results

This short review of PAMELA results obtained in the first five years of activity cannot be concluded without mentioning other important new measurements, such as the discovery of a belt of antiprotons trapped in the terrestrial magnetic field, and in the SAA in particular [12], and of the fluxes of quasi-trapped electrons and positrons [13], the time evolution of the energetic tail of spectra of protons and helium nuclei in the powerful solar event of December 13th 2006 (Fig.9) [14], and other magnetosphere and solar physics observations made with the PAMELA experiment [15].

250 5

News from future cosmic ray observations

Arriving now to the subject of our round table on ‘Frontiers of particle physics: News from high energies, neutrinos and cosmology’, for what concerns the future activity on the field of cosmic rays I wish to mention the continuation of the activity of PAMELA team (in particular in the niche of the observations on the hundred MeV/n and a few GeV/n, where the low energy threshold of the instrument, the precision of the magnetic spectrometer and the resumed activity of the Sun promises to play an important role besides the explores operating in our region of the solar system), the AMS instrument that is already active on the ISS with a set of sophisticated detectors, the CALET instrument that, in spite of its reduced dimensions promises a mess of data at very high energies in the different channels of the cosmic ray observation. Furthermore, as we are in Russia, it must be also mentioned the work in progress for complementing the physics program of the Gamma-400 experiment , foreseen in the Russian Federal Space program for the detailed study of gamma ray sources, with measurement of the chemical composition of CR at the knee (the difficult but central problem of the CR observation), and the fluxes of ions up to actinides. Finally the next decade could be the decade of the advance of the frontier of Ultra High Energy cosmic rays, either for the new very large array on ground for their observation, or the possible take-off of the Jem-Euso enterprise, in spite of the difficulties in which presently flounders. References [1] Picozza, P., Galper, A.M., Castellini, G. et al. PAMELA - A Payload for Antimatter Matter Exploration and Light-nuclei Astrophysics. Astroparticle Physics 27, pp.296-315, 2007. [2] Ricciarini, S. on behalf of PAMELA collaboration. PAMELA Silicon Tracking System: experience and operation. Nucl. Instrum. Methods Phys. Res., Sect. A, 582, pp.892-897, 2007. [3] Boezio, M., Pearce, M., Albi, M. et al. The electron-hadron separation performance of the PAMELA electromagnetic calorimeter. Astroparticle Physics 26, Issue, pp. 111-118, 2006. [4] Adriani, O., Barbarino, G. C., Bazilevskaya, G. A. et al. PAMELA Measurements of Cosmic-ray Proton and Helium Spectra. 10.1126/science.1199172 arXiv: 1103.4055v1. [5] Erlikin, A.D., Wolfendale, A.W. A New Component of Cosmic Rays? 32nd International Cosmic Ray Conference, Beijing 2011, contribution 1353. [6] Stozhkov, Y.I., Pokrevsky, P.E. and Okhlopkov, V.P., Long-term negative trend in cosmic ray flux, J.Geophys. Rev., 105, pp.9-18, 2000. [7] Taricco, C., Bhandari, N., Cane, D. et al. Galactic cosmic ray flux decline

251 and periodicities in the interplanetary space during the last 3 centuries revealed by 44Ti in meteorites, J. Geophys. Res. 111, A08102, 2006. [8] Malvezzi V. for the PAMELA Collaboration. Light Nuclei and Isotope Abundance in Cosmic Rays Measured by the Space Experiment PAMELA: Preliminary Results. Nucl. Instrum. Methods Phys. Res., Sect. A, 588, pp.250-254, 2008. [9] Adriani, O., Barbarino, G. C., Bazilevskaya, G. A. et al. PAMELA results on the cosmic-ray antiproton flux from 60 MeV to 180 GeV in kinetic energy. Phys. Rev. Lett. 105, 121101 (2010). [10] Adriani, O., Barbarino, G. C., Bazilevskaya, G. A. et al. An anomalous positron abundance in cosmic rays with energies 1.5-100 GeV. Nature 458, pp.607-609, 2009. [11] Adriani, O., Barbarino, G. C., Bazilevskaya, G. A. et al. The cosmic-ray electron flux measured by the PAMELA experiment between 1 and 625 GeV. Phys. Rev. Lett. 106, 201101 (2011). [12] Adriani, O., Barbarino, G. C., Bazilevskaya, G. A. et al. The discovery of geomagnetically trapped cosmic ray antiprotons Description. ApJ 737, L29, 2011. [13] Adriani, O., Barbarino, G. C., Bazilevskaya, G. A. et al. Measurements of quasi-trapped electron and positron fluxes with PAMELA. Journal Geophysical Research 114, A12218, 2009. [14] Adriani, O., Barbarino, G. C., Bazilevskaya, G. A. et al. Observations of the December 13 and 14, 2006, Solar Particle Events in the 80 MeV/n - 3 GeV/n range from space with PAMELA detector. Accepted for publication on Astrophysical journal, arXiv:1107.4519v1[astro-ph.SR]. [15] Casolino, M., Adriani, O., Ambriola, M. Magnetospheric and solar physics observations with the PAMELA experiment. Nucl. Instrum. Methods Phys. Res., Sect. A, 588, pp.243-246, 2008.

252 EXOTIC EFFECTS IN COSMIC RAYS AND EXPERIMENTS AT LHC L.I.Sarycheva a Skobeltsyn Institute of Nuclear Physics, Department of Physics, Lomonosov Moscow State University, 119991 Moscow, Russia Abstract. Some possible ways are considered to search in experiments at LHC for “exotic” phenomena, observed in cosmic rays. Such effects include: so called Centaurus — fluctuations in the ratio electromagnetic/hadronic component in individual collisions, the alignment in azimuthal direction of energetically distinguished objects (particles, clusters) and the unusual energy transfer into the depth of absorber. We have analysed the conditions for observation of such phenomena in experiments at Large Hadron Collider (LHC).

1

Centaurus

One of the first exotic phenomena, observed in the 80s years of the bygone age, was an event registered in a calorimeter type detector (Fig. 1). The characteristic of this event was the anomalous ratio charged/neutral secondary hadrons emerged from the collision of high energy cosmic ray particle with the carbon nucleus. According to the principle of isotopic invariance, the number of pions with the charge 0, +1, and −1 should be equal. The event registered by Japanese physicists contained only charged pions, while neutral pions were absent. This event was named Centaurus [1]. Figure 1: Illustration of Centaurus-event.

2

Alignment of energetically distinguished objects

Another exotic phenomenon observed in cosmic ray experiments is the coplanar production of high energy particles, which was called the “alignment”. The apparent alignment in the transverse plane of energetically distinguished centers (EDC) in the gamma-hadron families was observed experimentally by the PAMIR-Chacaltaya collaboration when analysing the families which satisfy ∑ the criteria Eγ ≥ 0.5 PeV and Nγ ≥ 3. These families appear in roentgenemulsion chambers placed under the carbon or lead absorber, revealing three, four, five EDCs located very close to a straight line (Fig. 2). a e-mail:

[email protected]

253 The spatial laboratory system at a small enough height h ∼ 50 m of the primary interaction. The spatial distribution of the most energetic clusters in the transverse (xy)-plane for a few generated events along with the corresponding values of λN are presented in Fig. 3 to give the reader a feeling for the topology of alignment events in the laboratory reference frame close to experimentally observed ones.

Figure 2: The fraction of events with alignment EDC, relative to the total number.

Figure 3: Samples of core distributions for PYTHIA simulated events with thr = 10 PeV and λ > 0.8. [3] EΣ 4

The alignment parameter λN , for N spots is: ∑N i̸=j̸=k cos(2ϕijk ) λN = . N (N − 1)(N − 2) Here ϕijk is the angle between two vectors (rk −rj ) and (rk −ri ) (for the central spot r = 0). This parameter characterises the location of N points along a straight line. The case of perfect alignment corresponds to λN = 1, when all points lie exactly along a straight line, while for an isotropic distribution λN < 0. 3

The unusual energy transfer into the depth of absorber

There is one more exotic phenomenon observed in cosmic ray experiments with multilayer calorimeters (Fig. 4) — the unusual energy transfer into the depth of absorber (Fig. 5). The analysis of this effect revealed other unusual properties associated with the same group of events, which allow consistent explanation assuming the production of a massive (∼ 10 GeV/c2 ), stable (τ ∼ 10−10 sec) particle — T with interaction length in the dense matter substantially larger than of regular hadrons — h [4] (Fig. 4). The correlation function W (T ) =

wT (x1 ) wT (x2 ) 1 wh (x1 ) wh (x2 ) wh (m)

254 (Fig. 6). If such particle exists it will most likely avoid observation in accelerator experiments with standard trigger criteria which typically reject long living secondaries. The results of analysis placed in Fig. 6,7.

Figure 4: Multilayer calorimeter.

h

T

Figure 6: W (T ) for E2 > 170 GeV.

4

Figure 5: Typical cascade with two ”humps” of ionization, and its different interpretation, (E2 /γc = MT ).

Figure 7: N (x). The average cascade for T events: solid, and for h events: dashed curves.

Discussion and conclusions

• The analysis of the data on Centaurus, first of all of the observation conditions in cosmic ray experiments, shows that the basic indicator of such phenomenon in experiments at LHC should be the fluctuations of individual events of ratio hadron to photon as a function of energy transfer in interaction, i.e. from −q 2 = t at any values of rapidity η and azimuthal angle φ. • The phenomenon of alignment indicates that the secondaries are produced within a certain azimuthal plane. References to the relevant publications may be found in [3]. We also analysed the conditions for observation of alignment

255 phenomenon and determine where these events should be sought for (e.g., as applied to the√CMS experiment at LHC). At energies s = 5.5÷14, assuming the generation point located h = 1000 m above the detector, the alignment would reveal itself at LHC in the forward rapidity region: rmin < ri → ηi < ηmax = ln(r0 /rmin ) ≈ 4.95,

(1)

ri < rmax → ηi > ηmin = ln(r0 /rmax ) ≈ 2.25, (2) √ where r0 = 2h/eη0 = 2hmp / s (η0 = 9.55 is the centre-of-mass rapidity in lab), ηi is the particle rapidity in the centre-of-mass, and ri is the radial coordinate of the particle in the detector (emulsion). At LHC, the strong azimuthal anisotropy of the energy flow will in this case be observed for all the events depositing the energy above certain threshold in the rapidity region (1, 2). The calculations made using Monte-Carlo generator PYTHIA [3]. • The analysis of this effect revealed other unusual properties associated with the same group of events, which allow consistent explanation assuming the production of a massive (m ∼ 10 GeV/c2 ), stable (τ ∼ 10−10 sec) T -particle with interaction length in the dense matter substantially larger than of regular hadrons (h) [4] (Fig. 6). To study this effect (τ ∼ 10−10 sec), a specialised experiment is required. Acknowledgments I am grateful to A.I.Demianov, A.K.Managadze, I.P.Lokhtin and A.M.Snigirev who participated in the work, and also to N.P.Karpinskaya and A.S.Proskuryakov who helped in preparation of this report. References [1] Japan-Brasil Collaboration: Conference Papers, Denver Conference of Cosmic-rays, 3 (1973), pp. 2210, 2219 and 2227. [2] I.P.Ivanenko, V.V.Kopenkin, A.K.Managadze, I.V.Rakobolskaya, Pisma v JETF, 1992, v. 56, No. 4, C, p. 192-196. [3] A.De Roeck, I.P.Lokhtin, A.K.Managadze, L.I.Sarycheva, A.M.Snigirev. Proceeding of 13-th International Conference on Elastic and Diffractive Scattering (Blois Workshop). Moving Forward into the LHC Era, 2009, talk of A.M.Snigirev, CERN – Geneva, edited by M.Deile, D.d’Enterria, A.De Roeck. [4] A.I.Anoshin, G.L.Bashindzhagian, L.I.Belzer, A.I.Demianov, V.S.Murzin, L.I.Sarycheva, N.B.Sinev. Pisma v JETF, 1972, v. 15(1), p. 10-13.

256 RELIC GRAVITATIONAL WAVES FROM PRIMORDIAL BLACK HOLES Alexander Dolgov a INFN, Ferrara 40100, Italy University of Ferrara, Ferrara 40100, Italy ITEP, 117218, Moscow, Russia Abstract. Emission of gravitational waves (GW) from dense clusters of primordial black holes in the early universe is considered. It is argued that during a temporarily matter dominated epoch all previously existed thermal relics (including GWs) are diluted and the universe became populated by newly formed relativistic species. GWs originating from PBH binaries may be observable at the present time by the next generation of high frequency detectors.

A search for cosmic background of gravitational waves (GW) generated in the early universe is a very important part of the GW astronomy which may potentially present a unique information about physical processes at hot and dense cosmological state which hardly could be observable otherwise. Here I will describe a new source of GW production by the interaction of the primordial black holes (PBH). My talk is based on two papers [1, 2] where the features of the presented here mechanism and its observational consequences are discussed in detail and a larger list of references is presented. It is assumed that sufficiently long lived PBHs were formed in the early universe. Their life-time and the mechanisms of production are specified below. Since PBH are nonrelativistic objects, at some stage they would dominate the cosmological energy density. At this stage all the previous thermal history of the universe would be forgotten and thermal relics diluted. In particular, GWs generated at the inflationary epoch could practically disappear. At the PBH matter dominated epoch the initial density perturbations would start rising, leading to the primordial structure formation resulting in dreation of high density clusters of PBH. In such clusters binaries of PBHs might be formed with reasonable probability. Such binaries were efficient sources of high frequency GWs which could be observed at the present time with a new generation of high frequency (GHz or higher) GW detectors. To avoid a conflict with Big Bang Nucleosynthesis (BBN) the life time of PBHs should be sufficiently short: τBH < 0.01sec < tBBN ∼ 1 s,

(1)

Here tBBN is the cosmological time of the onset of BBN. According to ref. [3, 4] the life-time of evaporating black hole with initial mass M is equal to: τBH = a e-mail:

[email protected]

10240 π M 3 , Nef f m4P l

(2)

257 where the Planck mass is mP l = 2.176 × 10−5 g and Nef f is the number of particle species with masses smaller than the black hole temperature: TBH =

m2P i . 8πM

(3)

The so called grey factor [4] is not taken into account here. Since Nef f ∼ 100 for the PBH in the considered below mass interval, the masses of PBHs is bounded from above as MBH < 2 × 108 g. According to the classical papers [5] PBHs could be formed in the early universe if the primordial density contrast at the cosmological horizon scale happened to be of order unity, δρ/ρ ∼ 1. Hence PBHs formed at cosmological time tp , would have masses: M = tp m2P l , or in other words tp = rg /2 where rg = 2M/m2P l is the gravitational radius of the black hole. Density perturbations generated at inflation with the so called flat spectrum lead to a power law mass spectrum of PBHs. However this is not the only possibility. For example a slightly modified Afleck-Dine scenario of baryogenesis leads to log-normal mass spectrum of PBH [6]: dN = C exp[(M − M0 )2 )/M12 ] , dM

(4)

and possibly to a larger cosmological mass fraction of PBH. The constant parameters M0 and M1 are strongly model dependent and may vary from a fraction of gram to billion solar masses. Let us denote the relative cosmological energy density of BHs at production as ΩBH (tp ) ≡ Ωp and take it as an unknown model dependent parameter. Normally Ωp ≪ Ωtot ≈ ΩR ≈ 1. Hence the universe was at RD stage before and after production of PBH with ( the )total cosmological energy density close to the critical one: ρ = 3m2P l / 32πt2 . It remained so till PBH started to dominate, if they lived long enough. At the radiation dominated (RD) stage the fractional contribution of nonrelativistic matter rises as ΩBH ∼ a(t) ∼ t1/2 , until ΩBH approaches unity. Equality of the energy densities of relativistic and nonrelativistic matters happens at t = teq = M/(m2P l Ω2p ). Later at t > teq PBHs started to dominate in the cosmological energy density, while relativistic matter quickly red-shifted away. The condition of PBH dominance requires τBH > teq , which in turn demands: ( )1/2 Nef f mP l M > 5.6 × 10−2 . (5) 100 Ωp Later at t > τBH PBHs disappeared due to their evaporation producing relativistic matter. The contribution of PBHs into cosmological energy density

258 vanishes, ΩBH → 0, while the total energy density remains equal to the critical one, Ωtot = 1, and the second cosmological RD stage started. At MD stage the density perturbations rise as the cosmological scale factor, ∆ ≡ δρ/ρ ∼ a(t). For sufficiently long PBH dominance stage, ∆ would reach unity. After that the non-linear regime of the perturbation evolution took place and they could grossly exceed unity, as we observe now on the example of galactics. At this process high density clusters of PBHs would be formed from which the emission of gravitational waves should be strongly amplified. The regions with high number density of PBH, nBH , would emit GW much more efficiently than in the homogeneous case by the following reasons. The emission of GW is proportional to vn2BH and, both the BH velocity in dense regions and nBH would be by several orders of magnitude larger than those in the homogeneous universe. The density perturbations would have enough time to evolve up to unity if τBH > t1 . To this end PBM mass should be bounded from below: 10−6 M > 10 g Ωp

(

3

10−4 ∆in

)3/4 (

)1/2

Nef f 100

.

(6)

After ∆ reached unity, rapid structure formation would take place resulting in high density clusters of PBHs, with ∆ ≫ 1. The size of such cluster at t = τBH can be estimated as: ( Rcl = 2teq

τBH teq

)2/3

−1/3

∆cl

,

(7)

where ∆cl = ρcl /ρcosm and ρcosm and ρcl are the average cosmological energy density and the density of BHs in the cluster. Thus: −2

0.2Ωp 3 Rcl = mP l

(

M mP l

) 73 (

100 Nef f

) 32 (

106 ∆cl

) 13 .

(8)

Such high density clusters of PBH would have mass: Mcl =

16 2 M m teq = 2 . 9 Pl Ωp

(9)

It is equal to the mass inside horizon at t = teq . The virial velocity inside the clusters would be √ v=

1

∆6 2Mb ≈ cl 2 mP l Rb 3

(

mP l Ωp M

) 23 (

Nef f 100

) 13 (10)

259 Maximum velocity in the cluster is limited by the condition of sufficiently large M to reach ∆ ≡ δρ/ρ ≥ 1 and reads: ( vmax ≈

1/6 0.01∆cl

∆in 10−4

)−1/3 ,

(11)

so with ∆cl as large as 106 the PBHs could be moderately relativistic. The density contrast ∆cl ∼ 106 is of the same order of magnitude as the density contrast of the contemporary galaxies. However, it might be much larger due to a new effect absent for galaxies. The galaxies have been formed relatively recently at the red-shift of order unity. So during the time which passed from the moment of the galaxy formation till the present time the average cosmological energy density was not noticeably changed. This is not so for the case of formation of the high density PBH clusters. From the moment of their formation to the moment of the PBH decay ρc dropped down as (t1 /τBH )2 and the density contrast rose correspondingly: ∆cl ∼ (τBH /t1 )2 .

(12)

PBHs in the high density clusters scatter on each other and in such process they emit gravitational waves analogously to photon bremsstrahlung in collisions of electrically charged particles. Such process was studied long ago in ref. [7]. According to this paper the crossection of the graviton bremsstrahlung in the collision of one heavy and one light black hole is equal to: ( ) 64M12 M22 3 4Ekin dω dσ = 5 + ln , (13) 15m6P l 2 ω ω where Ekin = M2 v 2 /2, BHs are non-relativistic, and M1 ≫ M2 . However we use this result for an order of magnitude estimate even for M1 ∼ M2 and approximate the averaged energy transfer as ∫ ωmax M 4 ωmax ⟨σω⟩ = dσω ≈ Q , (14) m6P l 0 where Q ∼ 102 − 103 is a numerical coefficient. The result would be noticeably larger if the Sommerfeld enhancement [8] is taken into account. The cosmological energy density of such GWs at the present day in log frequency interval would be: h20 ΩGW (t0 ) ≈ 0.6 × 10−21 K where K ∼ 105 , if ∆cl ∼ 1010 .

(

105 g M

)2 ,

(15)

260 The frequency of such GWs today would be: ( o

ω0 = 2.7

M mP l

)3/2

ω . 0.06mP l

(16)

If we take the maximum of frequency at emission, ω ∼ m2P l /M , the corresponding GW frequency today would be: ω0 ∼ (6 × 1012 /s) (M/mP l )1/2 , i.e. for M = 105 g, ω0 ∼ 1 keV. Note that usually the results are expressed in terms of f = ω/(2π). In high density clouds the formation of PBH binaries may be quite frequent. The mechanism of the energy loss to form a bound system is dynamical friction [9]. The binaries are known to emit gravitational radiation with the luminosity: L=

32M12 M22 (M1 + M2 ) 64 M 5 ≈ , 5 5r 5 r5 m8P l

(17)

2 where radius and orbital frequency are related as ωorb = (M1 + M2 )/(m2P l R3 ). Due to GWs emission the radius of the binary shrinks and the coalescence time is equal to

τco =

5R04 m6P l . 256M1 M2 (M1 + M2 )

(18)

During a short time interval, t < τco the binaries would be in the so called stationary regime, when the radius can be considered as constant and the frequency of the GWs is constant too, equal to twice ωorb . If t > τco the binary would be in the inspiral regime, when the radius of the orbit essentially decreases. At this regime the emission of GW is noticeably amplified. Both regimes are possible in the considered case but the stationary one is more probable, because typically τBH < τco . According to the estimates of ref. [2] the present day energy density of GWs in log interval of frequency from binaries in stationary regime is ΩGW (f ; t0 ) = 4.88 × 10−10 ϵ , (stat)

(19)

where ϵ is the fraction of binaries in the cluster. The frequency of such GWs ( )1/2 . could be as low a few Hz, f ≥ 5Hz 105 g/M There is one more source of gravitational waves from PBHs, namely gravitons originating from their evaporation. The average graviton energy from the BH evaporation is ωav = 3TBH = 3m2P l /8πM . Gravitons carry about 1% of the total evaporated energy and thus their contribution into the total cosmological energy density would be about 10−6 . However so large fraction of GW energy density may be difficult to observe

261 because of very high frequency of GWs. At smaller frequencies, ω < ωav , the energy density drops down as 10−6 (ω/ωav )4 . It is worth noting that the spectrum of such gravitons is noticeably different from the thermal one due to red-shift of the earlier evaporated gravitons. The mechanisms considered here lead to GWs with quite high frequency. The existing and near-future detectors are not sensitive to such GW but Ultimate DECIGO (2035), which will be sensitive to Ω = 10−20 at f = 1 Hz may put the limit, M > 103.6 mP l , or discover GWs created by PBHs. However, electromagnetic detectors based on resonance graviton to photon transformation are much more promising. The principle of such detector was proposed by Gertsenshtein [10] and later discussed by Braginsky and Mensky [11]. There is a renewed interest on these new detectors whose prototype has been constructed at Birmingham University [12] with sensitivity of the order hrms ∼ 10−14 Hz−1/2 at f ∼ 108 Hz. References [1] [2] [3] [4] [5]

[6] [7] [8] [9]

[10] [11]

[12]

A. D. Dolgov, P. D. Naselsky, I. D. Novikov, astro-ph/0009407. A.D. Dolgov, D. Ejlli, Phys. Rev. D84, 024028 (2011). S. W. Hawking, Phys. Rev. D13, 191 (1976). Don N. Page, Phys. Rev. D13, 198 (1976). Y. B. Zeldovich, I. D. Novikov, Astron. Zh. 43, 758 (1966); Sov. Astron. 10, 602 (1967); S. Hawking, Mon. Not. Roy. Astron. Soc. 152 , 75 (1971); B. J. Carr, S. W. Hawking, Mon. Not. Roy. Astron. Soc. 168 , 399 (1974). A. Dolgov, J. Silk, Phys. Rev. D47, 4244 (1993); A. D. Dolgov, M. Kawasaki, N. Kevlishvili, Nucl. Phys. B807, 229 (2009). B. M. Barker, S. N. Gupta, J. Kaskas, Phys. Rev. 182 , 1381 (1969). A. Sommerfeld, Annalen der Physik, 403 (1931) 257; A.D. Sakharov, Zh. Eksp. Teor. Fiz. 18 (1948) 631. J. Binney, S. Tremaine, “Galactic Dynamics”, Princeton University Press, Princeton, USA, 2008; C. Bambi, D. Spolyar, A. D. Dolgov et al., Mon. Not. Roy. Astron. Soc. 399, 1347 (2009). M.E. Gertsenshtein, Sov. Phys. JETP, 14, 84 (1961). V. B. Braginsky, M. B. Mensky, Zh. Exp. Teor. Fiz. Letters 13 585 (1971); V. B. Braginsky, M. B. Mensky, Gen. Rel. Grav. 3, 401 (1972). A. M. Cruise, Class. Quant. Grav. 17, 2325 (2000); A. M. Cruise, R. M. J. Ingley, Class. Quant. Grav. 22 S479 (2005); A. M. Cruise, R. M. J. Ingley, Class. Quant. Grav. 23 6185 (2006).

262 SINGULARITIES IN MODELS OF MODIFIED GRAVITY Elena V. Arbuzova a , Alexander D. Dolgov b Department of Higher Mathematics, University ”Dubna”, 141980 Dubna, Russia b Dipartimento di Fisica, Universit` a degli Studi di Ferrara, I-44100 Ferrara, Italy b Istituto Nazionale di Fisica Nucleare, Sezione di Ferrara, I-44100 Ferrara, Italy b Institute of Theoretical and Experimental Physics, 113259 Moscow, Russia

a

Abstract. Observational manifestations of some models of modified gravity, which have been suggested to explain the accelerated cosmological expansion, are analyzed for gravitating systems with time dependent mass density. It is shown that if the mass density rises with time, the system evolves to the singular state with infinite curvature scalar. The corresponding characteristic time is typically much shorter than the cosmological time. An addition of R2 -term into the action allows to avoid the singularity.

Contemporary astronomical data strongly indicate that at the present epoch the universe expands with acceleration. A possible way to explain this accelerated expansion is to assume that there is a new component in the cosmological energy density, the so called dark energy. A competing possibility to create cosmological acceleration is to modify gravity itself introducing additional terms into the usual action of General Relativity [1,2]. To this purpose the models with the following action were considered: ∫ √ m2P l S= (1) d4 x −g(R + F (R)) + Sm , 16π where mP l = 1.22 · 1019 GeV is the Planck mass, R is the scalar curvature, and Sm is the matter action. F (R) is an additional term, which changes gravity at large distances and is responsible for cosmological acceleration. In the pioneering papers [1] function F (R) = −µ4 /R, where µ is a small parameter with dimension of mass, was considered. However, as it was shown in ref. [3], such a choice of F (R) leads to a strong exponential instability near massive objects and the usual gravitational fields would be drastically distorted. A choice of F (R), which leads to an accelerated cosmological expansion and is devoid of the above mentioned instability and of some other problems was suggested in several papers [4–8]. In the present work [9] we examine a very interesting model of modified gravity with F (R) function suggested in ref. [5] : [( ] )−n R2 F (R) = λR0 1+ 2 −1 . (2) R0 Here λ > 0, n is a positive integer. R0 is a constant of the order of the present day average curvature of the universe, i.e. R0 ∼ 1/t2U , where tU ≈ 4 × 1017 sec is the universe age. a e-mail: b e-mail:

[email protected] [email protected]

263 Cosmology with gravitational action (2), as well as some other cosmological scenarios with modified gravity were critically analyzed in papers [2, 10–12]. In [9] we consider a different physical situation than those discussed in the above mentioned references. Namely we study behavior of astronomical objects with mass density which rises with time and show that curvature, R, reaches infinitely large value during the time interval which is very short in comparison with the cosmological time scale. A possible way to avoid singularity is to introduce R2 -term into the gravitational action, δF (R) = −R2 /6m2 , where m is a constant parameter with dimension of mass. Keeping in mind the bound on m > 10−2.5 eV from the laboratory tests of gravity [13], we find n ≥ 6. In ref. [2] a stronger bound is presented, m ≫ 105 GeV. In this case n ≥ 9. A natural value is m ∼ mP l and n ≥ 12. Thus we have shown that the impact of the considered above versions of modified gravity on the systems with time dependent mass density in the contemporary universe could be catastrophic, leading to the singularity R → ∞ during finite time in the future. This time is typically much shorter than the cosmological one. The problem can be fixed by the R2 -term if the power n is sufficiently large. [1] S. Capozziello, S. Carloni, A. Troisi, RecentRes. Dev. Astron. Astrophys. 1, 625 (2003); S.M. Carroll, V. Duvvuri, M. Trodden, M.S. Turner, Phys.Rev. D 70, 043528 (2004). [2] S.A. Appleby, R.A. Battye, A.A. Starobinsky, JCAP 1006, 005 (2010). [3] A.D. Dolgov, M.Kawasaki, Phys. Lett. B 573, 1 (2003). [4] S. Nojiri, S. Odintsov Phys. Rev. D 68, 123512 (2003). [5] A.A. Starobinsky, JETP Lett. 86, 157 (2007). [6] W.Hu, I. Sawicki, Phys. Rev. D 76, 064004 (2007). [7] A.Appleby, R. Battye, Phys. Lett. B 654, 7 (2007). [8] S. Nojiri, S. Odintsov, Phys. Lett. B 657, 238 (2007); S. Nojiri, S. Odintsov, Phys. Rev. D 77, 026007 (2008); G. Cognola, E. Elizalde, S. Nojiri, S.D. Odintsov, L. Sebastiani, S. Zerbini, Phys. Rev. D 77, 046009 (2008); G. Cognola, E. Elizalde, S.D. Odintsov, P. Tretyakov, S. Zerbini, Phys. Rev. D 79, 044001 (2009). [9] E.V. Arbuzova, A.D. Dolgov, Phys. Lett. B 700, 289 (2011). [10] S.A. Appleby, R.A. Battye, JCAP 0805, 019 (2008). [11] A. Dev, D. Jain, S. Jhingan, S. Nojiri, M. Sami, I. Thongkool, Phys. Rev. D 78, 083515 (2008); I. Thongkool, M. Sami, R. Gannouji, S. Jhingan, Phys. Rev. D 80, 043523 (2009); I. Thongkool, M. Sami, S. Rai Choudhury, Phys. Rev. D 80, 127501 (2009). [12] A.V. Frolov, Phys. Rev. Lett. 101, 061103 (2008). [13] D.J. Kapner, T.S. Cook, E.G. Adelberger, J.H. Gundlach, B.R. Heckel, C.D. Hoyle, H.E. Swanson, Phys. Rev. Lett. 98, 021101 (2007).

264 LIFE INSIDE BLACK HOLES Vyacheslav Dokuchaev a Institute for Nuclear Research of the Russian Academy of Sciences, Prospect 60-letiya Oktyabrya 7a, 117312 Moscow, Russia Abstract. It is considered the test planet and photon orbits of the third kind inside the black hole (BH), which are stable, periodic and neither come out the BH nor terminate at the central singularity. Interiors of the supermassive BHs may be inhabited by advanced civilizations living on the planets with the third kind orbits. In principle, one can get information from the interiors of BHs by observing their white hole counterparts.

1

Instructions

Orbits of the third kind were described in the works [1–5] under the assumption of the Kerr-Newman metric validity inside a black hole event horizon. The motion of a test particle (e. g. a planet) with a mass µ and electric charge ϵ in the background gravitational field of the Kerr-Newman BH with a mass M , angular momentum J = M a and electric charge e is completely defined by three integrals of motion: the total particle energy E, the azimuthal component of the angular momentum L and the Carter constant Q, related to a total angular momentum of the particle. An orbital trajectory of test planet is governed in the Boyer-Lindquist coordinates (t, r, θ, φ) by equations of motion [6, 7]: dr dλ dφ ρ2 dλ dt ρ2 dλ ρ2

√ = ± Vr ,

ρ2

√ dθ = ± Vθ , dλ

(1)

= L sin−2 θ + a(∆−1 P − E),

(2)

= a(L − aE sin2 θ) + (r2 +a2 )∆−1 P,

(3)

where λ = τ /µ, τ — is a proper time of particle and Vr

= P 2 − ∆[µ2 r2 + (L − aE)2 + Q],

Vθ P

= Q − cos θ[a (µ − E ) + L sin θ], (5) 2 2 2 2 2 2 2 2 2 = E(r +a )+ϵer−aL, ρ = r +a cos θ, ∆ = r −2r+a +e . (6) 2

2

2

2

2

(4)

−2

The radius of BH event horizon r = r+ and the radius√of BH inner horizon r = r− are both the roots of equation ∆ = 0: r± = 1 ± 1 − a2 − e2 . We use the normalized dimensionless variables and parameters: r ⇒ r/M , a ⇒ a/M , e ⇒ e/M , ϵ ⇒ ϵ/µ, E ⇒ E/µ, L ⇒ L/(M µ), Q ⇒ Q/(M 2 µ2 ). The effective potentials Vr and Vθ in (4) and (5) define the motion of particles in r- and θ-directions [7]. See in Fig. 1 the examples of the third kind nonequatorial a e-mail:

[email protected]

265

Figure 1: The nonequatorial stable periodic orbits of the planet (E = 0.568, L = 1.13, Q = 0.13) and photon orbit (b = L/E = 1.38, q = Q/E 2 = 0.03) inside the black hole (a = 0.9982, e = 0.05) in the locally nonrotating frame [7], viewed from the north pole (left frame) and from the outside (right frame).

orbits for the test planet and photon, calculated by numerical integration of equations (1)–(3). For the circular orbits of test particles with r =const, equations (4) and (5) provide the conditions: Vr (r) = 0,

Vr′ (r) ≡

dVr = 0. dr

(7)

The circular orbits would be stable if Vr′′ < 0 Inside the Reissner-Nordstr¨om the stable circular orbits exist only for charged particles. Inside the pure Kerr BH the are only nonequatorial stable spherical orbits, while there no the corresponding equatorial stable circular orbits [8]. The generic orbits of the third kind are nonequatorial and periodic with respect to the separate coordinates. Namely, (1) the r-periodicity means that the orbital radial coordinate r oscillates with a period Tr between the minimal (perigee) and maximal (apogee) values rp < r < ra . The values of rp and ra are defined by zeroes (the bounce points) of the radial potential, Vr (rp,a ) = 0. (2) The θ-periodicity means that the latitude coordinate θ oscillates with a period Tθ between the minimal and maximal values, π/2 − θmax < θ < π/2 + θmax , where θmax is maximum angle of latitude elevation relative to the equatorial plane at θ = π/2.The value of θmax is defined by zero (the bounce point) of the latitude potential Vθ (θmax ) = 0. At last, (3) the φ-periodicity means that the azimuth coordinate φ oscillates with a period Tφ between some φ0 and φ0 + 2π. These three periods are incommensurable, i. e. all ratios Tr /Tθ /Tφ are nor the rational numbers. For this reason the 3D space orbit of the particle is not closed (but still periodic with respect to the separate coordinates).

266

rp

ra r-

Figure 2: The stable periodic equatorial photon orbit (inner curve)) with the impact parameter b = L/E = 1.53 inside the BH with a = 0.75 and e = 0.6, viewed from the north pole. Orbit parameters: periods (Tr , Tφ ) = (2.7, 2.1), perigee and apogee (dashed circles) (rp , ra ) = (0.33, 0.61). The external dashed circle is the inner horizon with r− = 0.72. The blue circle is the circular planet orbit with the radius r = 0.65, energy E = 10.5 and impact parameter b = 1.54. The angular momentum of the black hole is directed to the north pole. The thicknesses of orbital curves are growing with proper time.

Acknowledgments This research was supported in part by the Russian Foundation for Basic Research grant No. 10-02-00635. References [1] [2] [3] [4] [5]

J.Biˇc´ ak, Z.Stuchl´ık, V.Balek, Bull.Astron.Inst.Czechosl. 40, 65 (1989). V.Balek, J.Biˇc´ ak, Z.Stuchl´ık, Bull.Astron.Inst.Czechosl. 40, 133 (1989). S.Grunau, V.Kagramanova, arXiv:1011.5399 [gr-qc]. M.Olivares, J.Saavedra, C.Leiva, J.R.Villanueva, arXiv:1101.0748 [gr-qc]. E.Hackmann, V.Kagramanova, J.Kunz, C.Lammerzahl, ¨ Phys.Rev. D 81, 044020 (2010). [6] B.Carter, Phys.Rev. 174, 1550 (1968). [7] J.M.Bardeen, W.H.Press, S.A.Teukiolsky, Astrophys.J. 178, 347 (1972). [8] V. I. Dokuchaev, arXiv:1103.6140 [gr-qc].

267 SUPERDENSE DARK MATTER CLUMPS FROM NONSTANDARD PERTURBATIONS Veniamin Berezinsky a INFN, Laboratori Nazionali del Gran Sasso, I67010 Assergi (AQ), Italy Vyacheslav Dokuchaev b , Yury Eroshenko c Institute for Nuclear Research of the Russian Academy of Sciences, Moscow, Russia Abstract. The formation of dark matter clumps around cosmic string loops is studied. These clumps can form before the matter-radiation equality and can have densities ≫ ρeq , where ρeq is the density at the equality. We take into account the velocity distribution of the strings, and consider two extreme regimes of DM annihilation: fast decay and continuous evaporation. We conclude that 100 GeV neutralino DM is incompatible with the range of the strings’ tension 5 × 10−10 < Gµ/c2 < 5.1 × 10−9 because the gamma-ray signal from DM annihilation exceeds the Fermi-LAT limit in this case.

The cosmic strings (linear topological defects) can be formed in cosmological phase transitions [1]. There is the possibility of the closed loops formation inside the network of curved cosmic strings. The string loop formed at the cosmological time ti has the length l ≃ αcti , where in the scaling regime α ≃ 0.1 [2]. The fundamental characteristic of the string is the mass per unit length µ ≡ Ml /l or the tension. There are several astrophysical restrictions on µ, and the strongest bound Gµ/c2 ≤ 4 × 10−9 was obtained from the pulsar timing [3]. In this report we present constraints on µ which was obtained from the dark matter (DM) particles annihilation in the dense clumps seeded by the loops at the cosmological stage of radiation dominance. The cosmic string loops produce extremely dense clumps due to their early formation. Only low velocity loops can produce the clumps. The probability of the low velocity loop formation is very small, but even tiny fraction of the formed loops may produce the dense clump population and significant annihilation signal. In the case of loops’ density perturbations the maximum density of the clump is restricted by the effect of adiabatic expansion of the already formed clump after the loop gravitational evaporation [4]. This restriction does not work in the case of the the loop’s decay before the clump virialization. In this situation the clump can reach density ρcl ≫ 140ρeq . We solve the same equation as (2.7) in [4], which describes the evolution of the clump’s radius r at the radiation-dominated epoch. The only quantity in [4] one need to modify is the Φ - value of the perturbation. In difference with [4] we allow the dependence of Φ on the time: steady decrease in the continuous evaporation approximation and step-like in the fast decay approximation. After the turnaround the clump virializes by contracting approximately twice in radius, and the resulting density increases by factor eight. a e-mail:

[email protected] [email protected] c e-mail: [email protected] b e-mail:

268 10

log

5

0

-5

-1.5

-1.0

0.0

-0.5

0.5

1.0

log Μ-8 Figure 1: The upper limits on the DM annihilation cross-section ⟨σv⟩ (in units 10−26 cm3 s−1 ) in dependence of the string parameter µ−8 = Gµ/(10−8 c2 ) are shown. The solid lines show the limits for the masses of DM particles (from up to down) mχ = 10 TeV, 1 TeV, 100 GeV and 100 GeV in the fast decay approximation. The limits were obtained from the comparison of the calculated signals and the Fermi-LAT data. The upper and lower horizontal dashed lines show the typical and minimal possible cross-section values, respectively. The dotted lines show the upper limits in the continuous evaporation approximation for the same masses.

We consider only the most dense central part of the clump inside the string volume, where the annihilation proceeds most effectively. This central region of the clump can be refereed as a clump core. The outer regions of the clump form through the secondary accretion of DM and have the density profile ρ(r) ∝ r−9/4 at the sufficiently high distance from the center of the clump. Therefore the annihilation concentrates near the clump core. We found that the argument of the adiabatic invariant conservation [4] is not applicable, if the loop decay occurs before turnaround moment (detachment from the cosmological expansion and the clump virialization). Really, in this case DM particles move not at the wide orbits around the loop but along the almost radial trajectories. The loop’s decay leads only to the change of the particles acceleration. The results of calculations for the clumps density in the two approximations are used subsequently for the calculations of the annihilation signals. We use the length distribution of cosmic strings’ loops from the simulations [5]. Strings decay but the clumps survive, therefore there is no need to cut of the clumps mass spectrum at the string evaporation scale.

269 The low mass cut-of of the clumps distribution is determined by the process of kinetic decoupling of the DM particles. In contrast to the ordinary inflationary density perturbations the diffusion and free streaming effects are not important for the minimum mass of the clumps which are seeded by the loops. The clumps under consideration have very large densities and the gammaray flux from DM annihilation inside the clumps may exceed the observational limits for some values of string parameter µ−8 = Gµ/(10−8 c2 ). Let us consider the neutralino (as the most popular DM particle-candidate). We compare the calculated signals with the Fermi-LAT diffuse extragalactic gamma-ray background Jobs (E > mπ0 /2) = 1.8 × 10−5 cm−2 s−1 sr−1 [6]. To obtain the most conservative limit we compare Jobs with the calculated signal in the anti-center direction. It gives the upper limit on the annihilation cross-section ⟨σv⟩ in dependence of µ−8 = Gµ/(10−8 c2 ). The results are shown at the figure 1. We consider the several values of the neutralino mass: mχ = 10 TeV, 1 TeV, 100 GeV and 100 GeV. For example, for the mass mχ = 100 GeV in the case of typical neutralino cross-section ⟨σv⟩ ≃ 3 × 10−26 cm3 s−1 (this value corresponds to the thermal production of DM particles) the limit excludes the range of parameters 0.05 < µ−8 < 0.51 in fast decay approximation and 0.1 < µ−8 < 1.16 in the continuous evaporation approximation. Therefore, the combined constraints on the loops parameters (µ and the distribution over lengths) and parameters of DM particles were obtained. The Fermi-LAT data are used as the upper limit. In principle the annihilation of DM in the clumps can explain the observed signal for the particular values, for example Gµ/c2 ≃ 5 × 10−10 . The necessity of the DM annihilation can arise if the ordinary astrophysical sources give too small signal in comparison with the observations. Acknowledgments We thank A. Vilenkin for useful discussion. This work was supported by the grants NSh 3517.2010.2 and RFBR 10-02-00635. References [1] A.Vilenkin, E.P.S.Shellard, “Cosmic strings and other topological defects”, (Cambridge University Press, Cambridge) 1994. [2] V.Vanchurin, K.D.Olum, A.Vilenkin, Phys.Rev. D 74, 063527 (2006). [3] R.van Haasteren et.al., [arXiv:1103.0576 [astro-ph]]. [4] E.W.Kolb, I.I.Tkachev, Phys.Rev. D 50, 769 (1994). [5] K.D.Olum, A.Vilenkin, Phys.Rev. D 74, 063516 (2006). [6] A.A.Abdo et al., Phys.Rev.Lett. 104, 101101 (2010).

270 ON THE SIMPLIFIED TREE GRAPHS IN GRAVITY A.I.Nikishov a , Lebedev Physical Institute, 119991 Moscow, Russia Abstract. Firstly, I give the reason why is wrong my previously made assumption that the volume integral over the pressure may not be zero in a system where the gravitation plays no role in holding the system together. Secondly, in the first nonlinear approximation I obtain the inner and outer Schwarzschild solutions in harmonic and isotropic coordinates in two different ways. One way is to start from standard solution and make the appropriate coordinate transformation. The other way is to use the perturbation theory with elements of Schwinger and Weinberg source approach. This latter method is applicable in general case and it is useful to study all its peculiarities on known simple example such as Schwarzschild solution. It turns out that this method is simpler then S-metrics approach (previously made by Duff) and more informative as it it shows which contribution comes from what region of space.

1

Introduction

For a statical system the metric at large distance (in comparison with its size) is determined by the ∫ integral over energy-momentum tensor. In particular we need the integral σik dV where σik is the stress tensor.This integral is equal ∫ to Pi xk df where Pi is the force acting on the surfice of the body and the integral is over the surfice, see §3 in [1]. As in our case Pi = 0, the integral is zero and pressure plays no role in generating the gravitational field at large distances This assertion correct the mistaken assumption in [2]. If the earth gravitational field can be measured with G2 − accuracy, than its changes, due to building up the pressure, leading to earthquakes, can be monitored. For this reason calculating the earth gravitational field with this accuracy is of interest. Thus simplifying the perturbation methods is essential. As a first step in this direction we reproduce the corresponding approximation of the Schwarzschild solution in isotropic coordinates by simple means. In three-graviton vertex all gravitons enter symmetrically. It can be simplified in particular cases. For two on-shell gravitons this has been done in [3]. In our case one graviton is external field graviton. Using integration by parts we can release it from being differentiated. Then it interact with Weiberg gravitational energy-momentum tensor, see §6 Ch. 7 in [4]. In static case this tensor gives (negative) gravitational energy density which is three times that of the Newtonian one [5]. Yet ,as shown in [5], for a pressure-free dust there is an over all agreement with Newtonian limit for total energy of the system. We shall see later on that the same is true for the ball of liquid. a e-mail:

[email protected]

271 2

Interior Schwarzschild solutions in harmonic and isotropic coordinates

Starting from standard solution, see Eq. (7.183) in [6], and using the substitution mG R2 (−3 + 2 ). (1) r = R(1 − ϕ(m.b.R)), ϕ(m.b.R) = 2b b we obtain in harmonic coordinates (for more details see [7]) 2 4 2 2 ⃗ = [1 − ϕ(m, b, R)]2 δαβ + m G ( 3R − 2R ) Xα Xβ . gαβ (X) 2 2 4 b b b R2

g00 = −[1 + 2ϕ(m, b, R) +

R4 m2 G2 15 3 R2 ( − )]. − b2 4 2 b2 4b4

(2)

(3)

a and b are the ball radii in standard and harmonic coordinates;a = b + mG. In isotropic coordinates in the considered approximation b and g00 remain iso the same as in harmonic one and gαβ differs from (2) by gauge transformation It is iso gαβ (m, R) = δαβ [1 +

mG r2 m2 G2 15 3R2 3R4 (3 − 2 ) + ( − + )], b b b2 4 b2 4b4

r < b. (4)

In both harmonic and isotropic systems the metric and their first derivatives are continuous across the boundary of the ball, see also [8] and [9]. In what follows we calculate gik in isotropic coordinates by perturbation method and we replace R by r. We use the notation gik = ηik + hik ,

1

2

hik =hik + hik +O(G3 ), (1) i

ηik = diag(−1, 1, 1, 1) R(1) = Ri

,

m=

4 πµa3 , 3 (2) i

R(2) = Ri

m′ =

4 πµb3 3

(2)

= η ik Rik ,

(5)

The index over a quantity indicate the power of G, the superscript in braces indicate the power of h. We use the formula, cf. §17 in [10] 2

′ hik (m , r) =

∫

d4 x′ D+ (x−x′ )θ(x′ )],

1

θik (x′ ) = 16πG(T¯ik (x′ )+ t¯ik (x′ )), (6)

1 r2 4 1 m′ G t¯ik = tik − ηik ti i hik = −2ϕδik, , ϕ(m′ , r) = (−3+ 2 ), m′ = πµb3 . (7) 2 2b b 3

As a final result we obtain (for details see [7]) 1

2

1

2

′ ′ h00 (m , r)+ h00 (m , r) =h00 (m, r)+ h00 (m, r),

(8)

272 where ((9b) agrees with (3); we remind that after (4) we replace R → r ) 2

r4 m′2 G2 21 3 r2 ( − + 4 ), 2 2 b 4 2b b 2 2 2 m G 15 3r r4 (m, r) = (− + 2 + 4 ), 2 b 4 2b 4b

′ h00 (m , r) = 2

h00 1

2

1

2

′ ′ hαβ (m , r)+ hαβ (m , r) =hαβ (m, r)+ hαβ (m, r), where ((11b) agrees with (4)) 2

3r4 m2 G2 51 6r2 ( − + ), b2 4 b2 4b4 m2 G2 15 3r2 3r4 (m, r) = δαβ 2 ( − 2 + 4 ), . b 4 b 4b

′ hαβ (m , r) = δαβ 2

hαβ 3

(9a) (9b) (10)

(11a). (11b)

Concluding remarks

One specific feature of the considered approach is that the metrics at any point is formed by the nonlinear sources in all space. In standard approach the inner and outer Schwarzschild solutions are obtained separately in each region. The gravitational energy density t00 of the Weinberg tensor tik is not the Newtonian one. There are arguments that observable t00 should be positive. In the Newtonian limit the gravitational energy of two bodies is −ma mb G/|⃗ra − ⃗rb |. This is the interaction energy of the system. On the other hand this energy is sitting on one body (on atom) as the red shift indicates, see Ch. 2 , §4 in [10]. The same energy is sitting on the other body, but it is just compensated by the gravitational energy of the whole gravitational field. So the latter must be positive, see also [5] and [11]. References [1] L.D.Landau and E.M.Lifshitz, Theory of Elasticity, [2] A.I.Nikishov, arXiv:1011.5620; 0912.5180[gr-qc]. [3] M.T. Grisaru, P.van Nieuwenhuizen, and C.C. Wu, Phys. Rev. D, .12, 397 (1975). [4] S. Weinberg, Gravitation and Cosmology, New York (1972). [5] A. Nikishov, Part. Nucl., 32. 5 (2001); gr-qc/9912034. [6] J.L.Synge, Relativity: The General theory,Amsterdam (1960). [7] A. Nikishov, arXiv:11110812 v1 [gr-qc]. [8] M.J. Duff, Phys Rev D,7, 2317 (1973) [9] N. Rosen, Ann. Phys. (N.Y.), 63, 127 (1970). [10] J. Schwinger, Particles, Sources and Fields,Vol.1, New York (1970). [11] A. Nikishov, Part. Nucl. 2006. V.37, No5, P.776.

273 LOOP QUANTUM COSMOLOGY CORRECTIONS TO FRIEDMANN’S MODEL Michael Fil’chenkov a , Yuri Laptev b Institute of Gravitation and Cosmology, Peoples’ Friendship University of Russia, 6 Miklukho-Maklay Street, 117198 Moscow, Russia Abstract. Loop quantum cosmology corrections to Wheeler-DeWitt’s equation for Friedmann’s model have been considered.

1

Introduction

Until recently quantum geometry corrections were applied immediately to classical cosmological models, despite quantum geometry first reduces to quantum geometrodynamics on larger scales and only thereafter is followed by the classical dynamics being described by Friedmann’s equations. In the present work, inverse-volume corrections are applied to the potential entering into WheelerDeWitt’s equation for a homogeneous isotropic quantum cosmological model with perfect fluids. 2

Quantum geometrodynamics

Quantum geometrodynamics was created by J. Wheeler and B. DeWitt in the sixties [1]. The main idea lies in considering the wave function ψ in 3 G ˆ = 0 called space. The wave equation reduces to a Hamiltonian constraint Hψ Wheeler-DeWitt’s equation. For homogeneous isotropic cosmological model in minisuperspace of scale factors a the latter reduces to Schr¨odinger’s type equation d2 ψ 2mpl − 2 [U (a) − E] ψ = 0. (1) da2 ¯h 3

Loop quantum gravity

In the eighties quantum geometrodynamics was generalized to quantizing space itself. This approach is called quantum geometry or loop quantum gravity. Ashtekar variables have been introduced as follows [2] ˆ a ψ = i δψ , E δAa

(2)

ˆ a is the operator connected with a triad, Aa the gauge field and Wilwhere E H son’s loops γ = Aa dγ a to which the operators γˆ acting on vacuum correspond. a e-mail: b e-mail:

[email protected] [email protected]

274 They generate a so-called spin network forming space. The geometrical quantities (volumes and areas) are operators. Their eigenvalues are quantized. For the area we obtain ∑√ 2 Sj = 8πlpl (3) ji (ji + 1), i

where i are integers, j halfintegers. Taking account of spatial discreteness in loop quantum cosmology reduces to introducing a factor for [3] ( Dj =

12 7

)6 (

)15 a a∗ √

(4)

j ln √2 . The potential and total correcting an inverse volume, where a∗ = lpl 3π 3 energies respectively take the form: [( ) ] B2 a2 mpl c2 2 B0 a4 2B4 r02 2 U (a) = k − B2 a − 2 − − , (5) 2 2lpl 3 r0 3Dj 3Dj

E=

mpl c2 6

(

r0 lpl

)2 B4 ,

(6)

where B0 , B2 , B4 are contributions of vacuum, strings and radiation respectively to the total energy density on de Sitter’s horizon r0 . Due to Dj the potential energy U (a) acquires an additional maximum for small a, playing the role of a wall removing the cosmological singularity. DJ = 1 for a ≫ a∗ , and quantum geometry transforms to quantum geometrodynamics. 4

Conclusion

The potential energy in the wave equation acquires an additional maximum on small scales affecting both the Universe’s pre-de Sitter spectrum and the penetration factor for tunnelling through a potential barrier, i.e. the Universe’s birth probability. The results obtained are of importance for an analysis of the initial cosmological perturbations stemming from space-time foam. References [1] J.A.Wheeler, “Einsteins Vision”, (Springer–Verlag, Berlin) 1968. [2] C.Rovelli, “Quantum Gravity”, (Cambridge University Press, Cambridge) 2004. [3] P.Sing, A.Toporensky, Phys.Rev. D 69, 104008 (2004).

275 CONSTRUCTION OF THE CURVATURE RADIATION PROFILES FROM PULSARS V. A. Bordovitsyn a , E. A. Nemchenko b Faculty of Physics, National Research Tomsk State University, 634050 Tomsk, Russia Abstract. The technique for construction of pulsar radiation profiles based on instantaneous angular distribution of electromagnetic radiation from jets of relativistic particles moving in the neutron star magnetosphere is suggested. This method is illustrated by calculation of the profiles of pulsar radiation based on the curvature model of pulsar emission. The considered profiles are compared with observed ones. A good agreement was found with profiles of some pulsars.

The discovery of pulsars [1] had a fundamental importance to the development of astrophysical investigations of the cosmic radio-wave radiation. The nature of pulsars radiation is continued to discuss in scientific literature (see, for example, [2, 3]). It is dealing with the fact that pulsars are open the big possibilities of application for the radiation theory of relativistic particles. In our research [3] we suggested a kinematic technique for construction of the pulsar radiation profiles based on the accurate spacial radiation indicatrix (angular distribution) of the relativistic instantaneous power of electrons radiation [4]. The idea of this method is that profile of the pulsar radiation can be found as the result of intersection of the indicatrix surface rotating together with the neutron star magnetosphere with the unmoving in space line of sight n of the observer. The indicatrix equation for an arbitrarily moving point charge, written in dimensionless form, is (see in [4]) ρ(θ, ϕ; α) =

sin ϕ2 sin α2 3

(1 − β cos θ)

+

[(β − cos θ) cos ϕ sin α + sin θ cos α] 5

(1 − β cos θ)

2

,

where β = u/c is the velocity of the radiating particles, expressed in terms of velocity of light, and α is the angle between the velocity and acceleration vectors. Since jets of the radiating electrons move together with the neutron star rotation magnetosphere, so and indicatrix of radiation will change its position relative the line of sight (see Fig.1). If Z-axis of the initial indicatrix of the pulsar coincide with the direction of its magnetic axis, but don’t coincide with the direction rotation axes of the pulsar Z0 , or its angular velocity Ω , then (in case plane of jet trajectory laying in ZZ0 -plane) required transformation will correspond to the turn of whole indicatrix around the Y-axis through angle of inclination η (or µ) numerically equal to the angle between the directions of the jet trajectory tangent line and the rotation axis of the pulsar for curvature radiation. a e-mail: b e-mail:

[email protected] katrin [email protected]

276

Figure 1: Scheme of the pulsar radiation profiles construction: a) coordinate system, b) the case of the symmetrical about an pulsar axis radiation when α =30◦ , c) construction of the symmetrical profiles of curvature radiation with the following parameters α =30◦ , η = µ =30◦ and λ =0◦ , d) construction of the asymmetrical profiles with the following parameters α =30◦ , η =30◦ and λ =30◦ .

It is shown that our theory give a good approximation of observed pulsar radiation profiles [5] and the plots presented in this work can certainly be refined by a more careful choice of parameters. Particular interest are properties of the pulsar radiation profiles provided by electron radiation with a glance of the superhigh magnetic field (see the work of O. F. Dorofeyev, V. Ch. Zhukovsky and A. B. Borisov in [4]).Given here approach can be propagated and to other sources of the relativistic radiation, for example, neutrino. The work was supported by the Federal Targeted Program “Scientific and scientific — pedagogical personnel of innovative Russia”, contract 789. References [1] A.Hewish, S.J.Bell, Nature 217, 709 (1968). [2] R.N.Manchester, J.H.Taylor, “Pulsars”, (Freeman, San Francisco), 281, 1977. [3] V.A.Bordovitsyn, V.Ya.Epp, V.G.Bulenok, in “Particle Physics at the Start of the New Millenium”, ed. by A.I.Studenikin, World Scientific Singapore, 187, 2001. [4] “Synchrotron Radiation Theory and its Development”, ed. by V.A.Bordovitsyn, World Scientific Singapore, 447, 1999. [5] A.D.Kuzmin, V.A.Izvekova et al., Astron. Astrophys. Suppl. Ser. 127, 355 (1998).

277 ON SPECTRUM AND MASS COMPOSITION OF ULTRAHIGH–ENERGY COSMIC RAYS FROM NEARBY SOURCES Olga P. Shustova a Faculty of Physics, Moscow State University, 119991 Moscow, Russia Abstract. In this paper spectra and mass composition of ultrahigh–energy cosmic rays produced by nearby active galactic nuclei are presented. The calculation results show that conflicting experimental data concerning the composition can be provided by different acceleration regimes in the sources.

1

Introduction

At present the topic concerning spectrum and mass composition of ultrahigh– energy cosmic rays (UHECRs) is of great interest. The latest data collected by the High Resolution Fly’s Eye (HiRes) and Telescope Array (TA) in Utah, USA on the one hand and by the Pierre Auger Observatory (PAO) in Argentina on the other, show some differences. In fact, the HiRes team clearly locates the start point of the GZK cutoff in the UHECR spectrum [1], whereas one of two PAO fits has a smooth shape [2]. The shower maximum measurements obtained by HiRes [3] and TA [4] show the proton dominance while PAO [5] points out a transition from protons to heavy nuclei. There is also a disagreement in anisotropy of the UHECR arrival directions. One of the possible explanations of these discrepancies might be the idea that the flux of heavy nuclei at ultrahigh energies is supplied by some local active galactic nuclei (AGNs) in the southern hemisphere (see [6]). The aim of this work is focused on the assessment of acceleration regimes in UHECR sources which can explain the experimental data. 2

Model assumptions and calculation results

CR spectra and mass composition in the energy range of (0.5 − 2) × 1020 eV are calculated on the basis of the following assumptions. 1) AGNs within the radius of ≈ 40 Mpc are considered as UHECR sources. Their distances R are taken from [7]. All sources are assumed to be identical in CR intensity so the contribution to the total flux from each object differs by a factor R−2 . The spectra compared with the HiRes and PAO measurements are obtained with allowance for the field of view of each facility. 2) Maximum acceleration energies are close to 4 × 1019 eV for protons and 9.3 × 1019 Z 2/3 eV for nuclei with charge Z ≥ 2 (such values were obtained for moderate–power objects in [8, 9]). Exact values are specified to fit observations. Usually rigidity–dependent maximum energies (Emax ∼ Z) are discussed (see, for instance, [10]). In the acceleration a e-mail:

[email protected]

278 the PAO fit: E

10

19.75

= 4.2

-1 -2

= 2.2

yr

2

[eV m

0

0

E J(E) [eV km

= 4.7

He

0

M H VH

3

10

HiRes-1

10

tot

37

PAO

HiRes-2

10

p p (He)

2

24 3

E J(E)/10

38

sr

-2

s

= 5.4 at E > 10

19.75

]

= 2.8 at E < 10

-1

1

-1

sr

-1

]

the HiRes fit:

10

-1

19.6

19.8

20.0

lg(E/eV)

20.2

19.6

19.8

20.0

20.2

lg(E/eV)

Figure 1: Differential energy spectra of the nuclei groups at γ0 = 2.2 (the left panel) and 4.7 (the right panel). The flux of secondary protons generated by nuclei of the helium group is marked by p (He). The total spectrum is denoted by grey circles. The HiRes [1] and PAO [2] experimental points are also shown. The broken power-law fits obtained by HiRes (the left panel) and PAO (the right panel) are presented by a thin solid line. Another PAO fit, having a smooth shape, is indicated by a dotted line.

model accepted the dependence Z 2/3 arises due to output energy losses. 3) The particle composition at the sources resembles the space content, i.e. the most abundant stable nuclei are taken into account. 4) The partial injection spectra obey a broken power law with indices −γ0 and −(γ0 + 4) below and above Emax . Thereby the number of nuclei with mass number A and energy in the range of (E, E + dE), is proportional to Aγ0 −1 . Over a hundred isotopes appearing during the propagation of initial nuclei through the intergalactic medium are considered. They are divided into six groups depending on their mass number: the proton and helium (He) groups as well as the groups of light (L), mean (M), heavy (H) and very heavy (VH) nuclei. The calculation scheme is given in [11]. Calculations show that the break and the slope in the HiRes spectrum can be reproduced quite well by γ0 = 2.2 while the PAO events require steeper injection spectra. Figure 1 demonstrates the spectra calculated at γ0 = 2.2 and 4.7 as well as the PAO and HiRes data and fits. Here the maximum acceleration energy for protons is considered to be equal to the start point of suppression in the HiRes spectrum, ≈ 5.7×1019 eV. The energy range is extended down to 1019.5 eV to show the behavior of experimental points at lower energies. As for the UHECR mass composition, it is measured only to ≈ 5 × 1019 eV because of insufficient statistics, so here it is extrapolated to higher energies. In the

279 case of γ0 = 2.2, the calculated mass composition corresponds to a mixture of protons and nuclei of the helium group up to 7×1019 eV, which is consistent with the HiRes results, and then gradually grows heavy. In turn, the spectrum at γ0 = 4.7 is produced by heavy nuclei with average mass number of more than 34 and consequently is compatible to a large extent with the PAO data. 3

Conclusions

The calculation results obtained within the model accepted lead us to the following conclusions. 1) UHECR sources are expected to be nearby AGNs located within a few tens of Mpc. 2) The HiRes and PAO experimental data could be explained by different values of the injection index. Acknowledgments The author expresses deep gratitude to N. N. Kalmykov and A. V. Uryson for fruitful discussions and useful comments. References [1] P. Sokolsky (The HiRes Collaboration), Nucl. Phys. B Proc. Sup. 196, 67 (2009). [2] F. Salamida (The Pierre Auger Collaboration), Contributions to the 32th International Cosmic Rays Conference, August 2011, Beijing, China [arXiv:1107.4809]. [3] R. U. Abbasi et al. (The HiRes Collaboration), Phys. Rev. Lett. 104, 161101 (2010) [arXiv:0910.4184]. [4] C. C. H. Jui (The Telescope Array Collaboration) Proceedings to the Division of Particle and Fields Meeting, August 2011, Brown University, Providence, RI, USA [arXiv:1110.0133]. [5] J. Abraham et al. (The Pierre Auger Collaboration), Phys. Rev. Lett. 104, 091101 (2010) [arXiv:1002.0699]. [6] B. Schwarzschild, Physics Today May 15 (2010). [7] M.–P. Veron–Cetty, P. Veron, Astron. Astrophys. 518, A10 (2010). [8] A. V. Uryson, Astron. Lett. 27, 775 (2001). [9] A. V. Uryson, Astron. Rep. 48, 81 (2004). [10] R. Aloisio, V. Berezinsky, A. Gazizov, Astropart. Phys. 34, 620 (2011). [11] O. P. Shustova, N. N. Kalmykov, A. V. Uryson, Bull. Rus. Acad. Sci. Phys. 75, 313 (2011).

280 NONCOMMUTATIVE BRANEWORLD INFLATION 1

2

Kourosh Nozari1,2 and Siamak Akhshabi1 Department of Physics,Faculty of Basic Sciences,University of Mazandaran,P.O.Box 47416-95447, Babolsar, Iran

Research Institute for Astronomy and Astrophysics of Maragha, P.O.Box 55134-441, Maragha, Iran

Abstract. We construct a new noncommutative braneworld inflation within the smeared, coherent state picture of spacetime noncommutativity. This model realizes an inflationary, bouncing solution without recourse to any axillary scalar or vector fields in a Randall-Sundrum II setup. There is no initial singularity and the model has the potential to produce scale invariant spectrum of scalar perturbations. We study also the evolution of perturbations in this noncommutative braneworld setup and we compare our results with recent observations. PACS numbers: 02.40.Gh , 11.10.Nx, 04.50.-h,98.80.Cq

1

Introduction

Motivated by string theory and also loop quantum gravity, spacetime fuzziness can be encoded using the relation [ˆ xi , x ˆj ] = iθij where θij is a real, antisymmetric matrix, with the dimension of length squared which determines the fundamental cell discretization of spacetime manifold [1]. As a consequence of this noncommutativity, the notion of point in the spacetime manifold becomes obscure since there is a fundamental uncertainty in measuring the coordinates as ∆xi ∆xj ≥ 12 |θij |. This finite resolution of the spacetime points especially affects the cosmological dynamics in the early stages of the universe evolution. Essentially, effects of trans-Planckian physics should be observable in the cosmic microwave background radiation. For this reason, various attempts to construct noncommutative inflationary models have been done by adopting various different approaches [2]. A new approach uses the smeared, coherent state picture of noncommutativity [3]. The key idea in this model is that noncommutativity smears the initial singularity and as a result there will be an smooth transition between pre and post big bang eras via an accelerated expansion. It has been shown that noncommutativity eliminates point-like structures in the favor of smeared objects in flat spacetime [4]. The effect of smearing is mathematically implemented as a substitution rule: position Dirac-delta function √ is replaced everywhere with a Gaussian distribution of minimal width θ. In this framework, the mass density of a static, spherically symmetric, smeared, r2 ). particle-like gravitational source can be described as ρθ (r) = M 3 exp(− 4θ (2πθ) 2

The particle mass M , instead of being √ perfectly localized at a point, is diffused throughout a region of linear size θ. Based on this novel idea, in this letter we construct a noncommutative braneworld inflation on the RSII setup and we study evolution of cosmological perturbations in this framework.

281 2

The model

The Friedmann equation governing the cosmological evolution on the RS II brane is given as follows [5] ( ) ( ) 8π 4π E0 Λ4 2 + ρ+ ρ2 + 4 , (1) H = 3 3M42 3M53 a where M4 and M5 are four and five dimensional fundamental scales respectively and Λ4 is the effective cosmological constant on the brane. We suppose that the initial singularity that leads to RS II geometry afterwards, is smeared due to spacetime noncommutativity. In this respect, the energy density on the 2 ⃗ 2 ⃗ 2 brane can be decomposed as ρ = ρ0 e−|τ | /4θ e−|X| /4θ where R2 = τ 2 + |X| and τ = it is the Euclidean time. We suppose that the universe enters the RS II geometry immediately after the initial smeared singularity which is a reasonable assumption from a M-theory perspective of the cyclic universe. In ⃗ the spacetime foliation, from one hypersurface to another, the X-dependent part of ρ does not change, so it can be included into ρ0 . If we neglect the dark radiation term and also the brane cosmological [ ] constant, the Friedmann equation (1) can be rewritten as H 2 =

8π ρ 3M42

ρ 1 + 2λ . In our noncommutative

setup, this equation could be rewritten as follows [6] [ ( )2 ] 2 a˙ 8π ρ0 e−t /4θ −t2 /4θ ρ0 e 1+ = . a 3M42 2λ This equation can be solved for a(t) to obtain √ √ 8π ([ ρ0 − 2 2θ λ3/2 ] [1] 3M42 1 a (t) = H , , 4 ρ0 2 √ √ 2) 8π 1 2 3M42 [(4 ρ0 + 4 λ) θ + tρ0 ] √ 8 θ λρ0 √ √ 8π { [(8 ρ + 8 λ) θ + tρ ] 2 3M 2 t } 0 0 1 4 √ ×exp − 16 θ λ + [(4 ρ0 + 4 λ) θ + tρ0 ] √ √ 8π } { 1 [(8 ρ0 + 8 λ) θ + tρ0 ] 2 3M42 t √ ×exp − 16 θ λ √ √ 8π 3/2 ([ 3 ρ0 − 2 2θ λ ] [3] 3M42 1 ×H , , 4 ρ0 2

(2)

282

Figure 1: Evolution of the scale factor in noncommutative Randall-Sundrum II geometry. There is an inflationary era without recourse to any scalar or vector fields. The model avoids also the initial singularity.

1 8

√ √ 8π 2 2 3M 2 [(4 ρ0 + 4 λ) θ + tρ0 ] 4 √ , θ λρ0

(3)

where H shows the Hypergeometric function of the arguments. Figure 1 shows that this noncommutative model naturally gives an inflation era without consulting to any axillary inflaton field. On the other hand, due to smeared picture adopted in this noncommutative framework, there is no initial singularity in this setup. The number of e-folds in this model is given by ∫

tf

N =

Hdt ti

] [ (1 t ) 1 √ ( 1 √2t ) √ 8 f f −1 √ + √ ≃ π ρ0 πθ erf 2πθ erf λ M4 −2 3 2 θ 2 2 θ [ ] (1 t ) 1 √ ( 1 √2t √ 8 i √ + √ i λ−1 M4 −2 − π ρ0 πθ erf 2πθ erf 3 2 θ 2 2 θ

283

Figure 2: Evolution of the Hubble parameter in noncommutative Randall-Sundrum II geometry.

[ 8 1 1 t3 t5 π ρ0 t − √ 3 + √ 5 3 12 πθ 2 160 πθ 2 √ 3 √ 5) ] ( 1 1 2t 1 2t −1 + 2t − √ 3 + λ M4 −2 . √ 2 6 πθ 2 40 πθ 25 ≃

(4)

If ρ0 is suitably large, we will get sufficient amount of inflation in this scenario. Supported by various observations, a scale invariant spectrum of scalar perturbations should be generated after inflation. We define the slow-roll parameters ( )2 ( ) M42 H ′′ M42 H ′ as ϵ ≡ 4π H , η ≡ 4π H . We assume that as usual the scalar spectral index is given by the ns − 1 ≃ −6ϵ + 2η. Figure 3 shows variation of ns versus the cosmic time. As one can see from this figure, it is possible essentially to have scale invariant scalar spectrum in this model. 3

Cosmological perturbations

We now suppose that the initial singularity that leads to RS II geometry afterwards, is smeared due to spacetime noncommutativity. In this respect, we

284

Figure 3: Variation of the scalar spectral index versus the cosmic time. The spectral index approaches the Harrison-Zel’dovic spectrum at the end of inflation. The parameters used to plot this figure are the same as previous figures. The spectral index is exactly one at t = ±4.021168857 × 10−21 .

set ρ(t) = 32π12 θ2 e−t /4θ . The effective noncommutative pressure in this setup t −t2 /8θ is p = −ρ + 6θ e and the equation of state parameter will be [7] 2

ω = −1 +

2 16 2 π θ te−t /8θ . 3

(5)

Similarly, the speed of sound is p˙ −3t − 64θ2 π 2 e−t /8θ + 32θπ 2 t2 e−t = ρ˙ 3t 2

c2s =

2

/8θ

.

(6)

Now we can find the effective equation of state and speed of sound where these effective quantities are essentially related to the dark radiation energy density, ρε . We note that there are constraints from nucleosynthesis on the value of ρε ρε so that ρ ≤ 0.03 at the time of nucleosynthesis [8]. In this respect, we can neglect this contribution to find ω eff =

1 − 1 t2 e 8 θ 192 [ ] −t2 −t2 −t2 × − 192 π 2 θ2 λ + 1024 te 8θ π 4 θ3 λ − 3 e 8θ + 32 te 4θ π 2 θ

285 [ ( ( ) ) ]2 −t2 1 × θ 64 π 2 θ2 λ + e 8θ π −2 θ−2 λ−1 64 [ 2( ) ) ]−1 ( −t −t2 1 −2 −2 −1 −2 −4 −1 2 2 8θ 8θ π θ λ ×π θ λ e 64 π θ λ + e , 64

(7)

2 −t /8θ which simplifies to ω eff ≈ −1+ 32 for the high energy regime (ρ ≫ λ 3 π θ te that λ is the brane tension). Similarly, the effective speed of sound in the high energy regime will be 2 16 2 (c2s )eff ≈ π θ te−t /8θ 3 2

−3t − 64θ2 π 2 e−t

2

/8θ

+ 32θπ 2 t2 e−t

2

/8θ

. 3t Now, the equation governing on the scalar perturbation is given by [7,8] [ ] dΦ (1 + w)κ2 ρ ( ρ) + 1+ 1+ Φ dN 2H 2 λ +

(8)

[

] [ ] (1 + w)κ2 ρ 3(1 + w)a2o ρ2 2N = Co − e U (9) 4H 2 λH 2 {∫ } where U = U0 exp (3w − 1)dN , and N is the number of e-folds. We can integrate equation (9) to find Φ=

1 ρ λ κ2 C0 (1 + ω) 2 2H 2 λ + (1 + ω)(κ2 ρλ + κ2 ρ2 )

( t2 ) H 2 ρ λ a0 2 U exp (3 ω a − 3 ω a0 − a + a0 ) exp 6H 2 λ + (1 + ω)(κ2 ρλ + κ2 ρ2 ) 4θ [ ] 1 2 H 2 λ + (1 + ω)(κ2 ρ λ + κ2 ρ2 ) t2 + exp . 2 H 2λ 8θ

−6(1 + ω)

(10)

Figure 4 shows the evolution of Φ for both usual braneworld scenario and our noncommutative setup in the high energy inflation regime (ρ ≫ λ). The curvature perturbation defined in the metric-based perturbation theory δρ , which reduces to R on uniform density ( δρ = 0 ) hypersuris ξ = R + 3(ρ+p) faces. If there is no dark radiation in the background (ρε = 0), we can obtain the time evolution of the curvature perturbation explicitly as follows ) ( 2 ( ) 3t2 Ei 1, 3t 8θ 1 1 e− 8θ 1 t2 2 t2 eff ξ = − + Ei 1, − e− 4θ 2 2 2 2 96 π θ λ 48 π θ λ 3 4θ 3

286

Figure 4: Evolution of the parameter Φ which is an analog of the Bardeen metric potential as defined in (35) for both usual braneworld scenario (dashed line) and our noncommutative setup (solid line) when ρλ0 = 1010 . We assumed that no dark radiation is present in the background geometry.

( ) 1 t 1 √ λ−1 π −3 θ−3 √ − erf 768 2 θ θπ ( √ ) 1 1 2t √ −1 −1 1 √ 2θ π √ − erf 24 4 θ θπ

(11)

Where Ei(a, z) is the exponential integral defined as Ei(a, z) = z a−1 Γ(1−a, z). 4

Conclusion

In summary, by adopting the smeared coherent state picture of spacetime noncommutativity, we have generalized the RS II braneworld inflation to noncommutative spaces. This model realizes an inflationary, bouncing solution without recourse to any axillary scalar or vector fields. Due to noncommutative structure of the very spacetime which admits the existence of a fundamental length scale, there is no initial singularity in this model. By treating the scalar perturbations in this setup, we have shown that it is possible essentially to have scale invariant scalar perturbations in this framework. Finally, we have studied the dynamics of cosmological perturbations in this setup.

287 References [1] [2] [3] [4] [5] [6]

R. J. Szabo, Phys. Rept. 378 (2003) 207 R. Brandenberger and P. M. Ho, Phys. Rev. D 66 (2002) 023517. M. Rinaldi, [arXiv:0908.1949]. P. Nicolini, Int. J. Mod. Phys. A 24 (2009) 1229, [arXiv:0807.1939]. L. Randall and R. Sundrum, Phys. Rev. Lett. 83 (1999) 4690. K. Nozari and S. Akhshabi, Phys. Lett. B 683 (2010) 186-190, [arXiv:0911.4418]. [7] K. Nozari and S. Akhshabi, Submitted for publication to Phys. Lett. B, April (2010). [8] D. Langlois, R. Maartens, M. Sasaki and D. Wands, Phys. Rev. D 63 (2001) 084009.

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CP Violation and Rare Decays

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291 THE PHYSICS PROGRAMME AT SUPERB Adrian Bevan (on the behalf of the SuperB Collaboration) a Department of Physics, Queen Mary, University of London, Mile End Road, London, E1 4NS, UK Abstract. SuperB is a next generation high luminosity e+ e− collider that will be built at the Cabibbo Laboratory, Tor Vergata, in Italy. The physics goals of this experiment are to search for signs of physics beyond the Standard Model through precision studies of rare or forbidden processes. While the name suggests that B physics is the main goal, this experiment is a Super Flavour Factory, and precision measurements of Bu,d,s , D, τ , Υ, and ψ(3770) decays as well as spectroscopy and exotica searches form part of a broad physics programme. In addition to searching for new physics (NP) in the form of heavy particles, or violations of laws of physics, data from SuperB will be able to perform precision tests of the Standard Model. I will briefly review of some highlights of the SuperB physics programme.

1

Introduction

Flavour physics has been instrumental in the development of the Standard Model (SM), starting from a combination of results from hyperon decays by Cabibbo [1]. Shortly after this development Glashow, Iliopolus and Maiani [2] proposed the existence of the charm quark to satisfy the observed pattern of branching fractions in kaon decays and establish a four quark model of particle physics. The discovery of CP violation by Cronin, Christenson, Turlay and Fitch in 1964 [3] was another landmark, and in time Kobayashi and Maskawa postulated a six quark model in order to accommodate CP violation naturally within the SM [4]. These developments laid the foundations of our current theory, however we know that there are a number of features missing, including an understanding of the matter-antimatter asymmetry. SuperB is a next generation e+ e− flavour factory designed to operate primarily with a centre of mass energy of the Υ(4S), and at the charm threshold ψ(3770). The project status, accelerator and detector are discussed in the contribution to these proceedings by Francesco Forti [5]. Recent reviews of the physics programme of this project can be found in Refs. [6–8]. The rest of these proceedings discuss a number of physics highlights, and how these can be used to elucidate the structure of physics beyond the SM. 2

τ Physics

The intrinsic level of charged lepton flavour violation in the τ sector arising from neutrino oscillations is expected to occur at the level of 10−54 . Given that both quark and neutral lepton number conservation is known to be violated at a small level, it is natural to presume that there may ultimately be a e-mail:

[email protected]

292 non-conservation of charged lepton number. Indeed many scenarios of physics beyond the SM predict large (up to ∼ 10−9 ) levels of charged lepton flavour violation (LFV). These predictions are model dependent: some models favour large µ → e transitions over other possibilities. Other models prefer large τ → µ or τ → e transitions. While the quest for a discovery of LFV continues, it is clear that all three sets of transitions need to be measured or well constrained in order to understand the underlying dynamics. SuperB will be able to improve upon existing limits from the B factories by between one and two orders of magnitude. Channels such as τ → ℓγ will see a factor of ten improvement as these have irreducible SM backgrounds that one will have to contend with, while other channels such as τ ± → ℓ+ ℓ− ℓ± , which are free of SM backgrounds, will see a factor of one hundred improvement. The e− beam at SuperB will be 80% polarised, enabling one to separate contributions from SM-like LFV channels and otherwise irreducible backgrounds as one can use the polarisation of the final state τ lepton produced in collisions in order to suppress background. This works well for improving limits, or indeed searching for left handed sources of NP. One can verify if there is a right handed component to any underlying NP by comparing results with and without polarised beams. Similarly as one expects some higher theory to undergo symmetry breaking in order to manifest the low energy scenarios we are studying at facilities today, which includes the LHC reach, the different types of fundamental particle may be related to each other. There are models that predict correlated effects between charged leptons decays and processes involving quarks, and of course neutrinos. Hence in order to understand any underlying deviations in any of these sectors one needs to cross check, for example, charged LFV results with neutrino mixing, neutral meson mixing and CP violation measurements in the quark sector. A number of scenarios of physics beyond the SM are discussed in Ref. [7] in order to illustrate this point. 3

B Physics

As much of the NP search potential of SuperB concerns the use of indirect constraints on rare processes to infer the existence or otherwise of some model, one naturally has some sensitivity to the corresponding energy scale ΛN P of the NP. The correlation between measurement of the rare decays (a branching fraction or other observable) and the energy scale is non trivial. If one considers the minimal supersymmetric model (MSSM) in the mass insertion hypothesis then for example the measurement of the inclusive branching fractions of b → sγ and b → sℓℓ, along with the CP asymmetry in b → sγ can be used to constrain d the mass insertion parameter (δ23 )LR . The magnitude of this parameter can be used to infer an upper limit on ΛN P to complement the null results obtained so far from the LHC. If generic MSSM was a realistic description of nature then

293 the fact that the LHC has failed to find a low mass gluino implies that there d is a non-trivial coupling (δ23 )LR , and hence in turn SuperB should be able to observe a non-trivial deviation from the SM when studying the inclusive decays b → sγ and b → sℓℓ. The magnitude of the observed deviation will benefit the SLHC community as the inferred upper bound on the energy scale obtained will provide useful information on the integrated luminosity required to yield d positive results via direct searches. For example if one measured |(δ23 )LR | = 0.05, then the implied upper limit on ΛN P is 3.5 TeV, which is also compatible with known constraints on tan β as can be seen from Ref. [7]. Other processes can be used to constrain other mass insertion parameters. There are a number of golden rare B decay channels at SuperB, including B → ℓν, where ℓ = τ, µ, e. In the SM this decay is known up to uncertainties relating to the value of Vub and fB . The rate of these processes can be modified by the existence of charged Higgs particles predicted in a number of extensions of the SM for example two-Higgs Doublet models (2HDM) or SUSY extensions of the SM. Hence the measured rate of these decays can be used to place limits on the inferred mass of any H + particle, and such constraints are a function of tan β. Existing constraints from the B factories from inclusive b → sγ decays exclude masses below 295GeV/c2 , and the constraint from B → τ ν excludes higher masses for large tan β scenarios. With 75ab−1 of data SuperB will be able to exclude, or detect, a H + with a mass 1 − 3 TeV, for tan β between 40 and 100. This constraint results from a combination of B → τ ν (dominates at lower luminosity) and B → µν (dominates at high luminosity). Ref. [7] discusses the physics potential of a number of other interesting rare B decays. Many of the CP asymmetry observables of Bu,d decays available at SuperB are dominated by loop contributions and are sensitive to the same sources of NP that can affect many of the interesting rare decays discussed above. The golden modes to use in measuring the angle β of the unitarity triangle are B decays to charmonium (cc), η ′ or ϕ and a neutral kaon. SuperB will be able to measure the CP asymmetries in these decays with precisions of 0.002, 0.008, and 0.021, respectively using a data sample of 75ab−1 . Both tree (ccK 0 ) and penguin dominated decays can be affected by the presence of NP. To complement the Bu,d programme at SuperB, there will be a dedicated run at the Υ(5S) resonance which enables the study of a number of Bs related observables that may be affected by physics beyond the SM. These include the semi-leptonic asymmetry and branching fraction Bs → γγ. 4

Charm physics

Charm mixing has been established by the B factories and is parameterised by two small numbers: x = ∆mD /Γ and y = ∆Γ/2Γ. These are currently measured as x = (0.65+0.18 −0.19 )%, and y = (0.74 ± 0.12)% [9]. The precision with

294 which these mixing parameters can be improved upon is dominated by inputs from D0 → KS h+ h− decays, where h = π, K. At large integrated luminosities one of the limiting factors of this analysis will be the knowledge of the strong phase variation across the KS h+ h− Dalitz plot. This can be measured using 0 data collected at charm threshold, where e+ e− → ψ(3770) → D0 D transitions result in pairs of quantum correlated neutral D mesons. These correlated mesons can be used to precisely determine the required map of the strong phase difference required for charm mixing measurements. With this input from a data sample of 500fb−1 b the mixing measurements at SuperB will still be statistics limited, and one should be able to achieve precisions of 0.02% and 0.01% on x and y, respectively. The strong phase difference map measured at charm threshold will also be an important input used for the determination of the unitarity triangle angle γ for SuperB, Belle II and LHCb. It has often been said that CP violation in charm will provide a unique test of the SM. The reason for this is that one expects only very small effects in the SM, and so any large measured deviation from zero would be a clear sign of NP. Just like the Bu,d system, charm has a unitarity triangle that needs to be tested. The physics potential of SuperB in this area has recently been outlined in Ref. [10]. In the months following the Lomonosov conference an intriguing hint of CP violation in charm decays was produced by the LHCb experiment [11]. This relates to a difference in direct CP asymmetry parameters measured in D → KK and D → ππ. If this is a real effect one will have to perform the measurements outlined in [10] in order to understand the underlying physics. A number of charm rare decay analogues of the B physics programme are of interest in constraining NP and elucidating the underlying decay dynamics in charm. The complication with charm is the presence of long distance dynamics that dominate the final states. The combination of charm threshold and Υ(4S) running naturally complement each other when studying rare charm decays. 5

Precision electroweak physics

In terms of precision electroweak physics, the polarised electron beam at SuperB facilitates the measurement of sin2 θW at centre of mass energy corresponding to the Υ(4S) resonance. SuperB will be able to measure this quantity with the same precision as the LEP/SLC measurements made at the Z 0 pole. However the advantage of the SuperB measurement is the fact that the e+ e− → bb result will be free from fragmentation uncertainties that limit the interpretation of the LEP/SLC measurements. The SuperB measurements will be complementary to other low energy sin2 θW measurements from the QWeak Collaboration (JLab), and at the proposed MESA experiment (Mainz). b SuperB

is expected to accumulate twice this luminosity at charm threshold

295 6

Interplay between measurements and summary

The power of SuperB comes from the ability to study a diverse set of modes that are sensitive to different types of NP. Through the pattern of deviations from SM expectations for observables one will be able to identify viable NP scenarios and reject those that are not compatible with the data. This goes beyond the motivation of simply discovering some sign of NP and is a step toward developing a detailed understanding of NP. If no significant deviations are uncovered then this in turn can be used to constrain parameter space and reject models that are no longer viable. Given that many of the observables that SuperB will measure are not accessible directly at the LHC, these results will complement the direct and indirect searches being performed at CERN. Detailed discussions on the interplay problem can be found in Refs. [6, 7]. In summary the physics programme at SuperB is varied, and the unique features of the facility: polarised electron beams and a dedicated charm threshold run add to its strengths via versatility. The charm threshold run in particular, in addition to facilitating a number of NP searches, will provide several measurements required to control systematic uncertainties for measurements of charm mixing and the unitarity triangle angle γ. Results from SuperB will be able to play a role in elucidating any NP discovered at the LHC and indirectly probe to higher energy than the LHC will be able to directly access. References [1] N. Cabibbo, Phys. Rev. Lett. 10, 531-533 (1963). [2] S. Glashow, J. Iliopoulos, and L. Maiani, Phys. Rev. D2, 1285-1292 (1970). [3] H. Christenson et et al., Phys. Rev. Lett. 13, 138-140 (1964). [4] M. Kobayashi and T. Maskawa, Prog. Theor. Phys. 49, 652-657 (1973). [5] F. Forti, in “Particle Physics on the Eve of LHC” (These proceedings of the 15th Lomonosov Conference on Elementary Particle Physics, August 18-24 2011, Moscow, Russia), ed. by A.Studenikin. [6] B. Meadows et et al., arXiv:1109.5028. [7] B. O’Leary et et al., arXiv:1008.1541. [8] A. Bevan, arXiv:1110.3901. [9] Heavy Flavour Averaging Group (HFAG), http://www.slac.stanford. edu/ xorg/hfag/. [10] A. Bevan, G. Inguglia, and B. Meadows, arXiv:1106.5075. [11] LHCb Collaboration, LHCb-CONF-2011-023.

296 STATUS AND PROSPECTS OF SUPERKEKB COLLIDER AND BELLE II EXPERIMENT Tagir Aushev a Institute for Theoretical and Experimental Physics, 117218 Moscow, Russia Abstract. High precision measurements in the quark flavor sector are essential for searching for new physics beyond the Standard model. SuperKEKB collider and Belle II detector are designed to perform such measurements. The status and prospects of the SuperKEKB and Belle II are presented in this article.

1

Introduction

Since the end of the last century, two asymmetric-energy e+ e− B factories, the KEKB [1] collider for the Belle [2] experiment at KEK and the PEPII collider for the BaBar experiment at SLAC, have been achieving a tremendous success that lead to the confirmation of the Standard Model (SM) in the quark flavor sector. The main goal of the experiments was to measure the large mixing-induced CP violation in the B 0 system predicted by the theory of Kobayashi and Maskawa [3]. The experimental data indicated that the Kobayashi-Maskawa mechanism is indeed the dominant source of the observed CP violation in Nature. Following the experimental confirmation, M. Kobayashi and T. Maskawa were awarded the 2008 Nobel Prize for physics. In addition to the observation of the CP violation in B meson system, a numerous of other important measurements and observations have been done by both experiments, such as measurements of all Cabibbo-Kobayashi-Maskawa (CKM) matrix elements; direct CP asymmetry in B 0 → π + π − and K + π − ; the first observation of rare B decays, such as B → K (∗) ℓℓ, b → sγ and τ ν; observation of the new type of particle, such as X(3872); observation of the D0 mixing, etc. Most of the results are in a good agreement with the expectation from the SM, however some measurements show tension with the SM prediction. A significantly larger statistics is necessary to investigate whether these are first hints for effects of a new physics. To solve this task a next generation experiment, Belle II, operating on the high luminosity collider, SuperKEKB, is designed. In this article, the status and prospects of the SuperKEKB collider and Belle II detector are presented. 2

The Belle experiment

The Belle detector was operating on the KEKB asymmetric-energy e+ e− collider. From 1999 to 2010, KEKB delivered an integrated luminosity of about a e-mail:

[email protected]

297 1040 fb−1 . Most of the data were taken at the center-of-mass energy of the Υ(4S) resonance and contains about 772 million B meson pair events. The achieved peak luminosity is 2.1 × 1034 cm−2 s−1 . On June 30, 2010, the Belle experiment was stopped with the ceremonial dump of the last KEKB beam. Currently, the Belle detector is rolled out from the beam interaction point and partially disassembled. 3

Hints for a new physics

Due to the unitarity of the CKM matrix and complexity of its elements, one can build a unitarity triangle on the complex plane from the CKM matrix elements. All sides and angles of this triangle can be measured independently, and the consistency of the obtained results is an important check of the SM and a search for a new physics. Currently, most of the CKM parameters are well measured and a room for a new physics is rather small (Fig. 1 left).

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However, there are still some small discrepancies: the indirect determination of the angle ϕ1 is exhibiting a 2.7σ deviation from the current world average sin 2ϕ1 [4]. Equivalently, the B ± → τ ± ντ branching fraction and the resultant |Vub | show a deviation of 2.8σ from the one predicted by the global fit [4], where the sin 2ϕ1 value gives the most stringent constraint on the indirect measurement (Fig. 1 right). Another place where a new physics can reveal is the decay of b → s¯ ss. In the SM a time-dependent CP violation in the decay B 0 → ϕKS0 is expected, similarly to B 0 → J/ψKS0 , to be sin 2ϕ1 . However, the existence of

298 new particles in the penguin loop in the decay B 0 → ϕKS0 can deviate the observed value from the expected one [5]. The current measurement gives B→J/ψK 0

B→ϕK 0

S S ∆S ≡ sin 2ϕ1 − sin 2ϕ1 = 0.22 ± 0.17. The goal of the next experiment is to down the error of this measurement by the factor of 10. A direct CP violation was measured in B → Kπ system. Since both tree and penguin processes contribute to B 0 → K + π − and B + → K + π 0 decays, sizable ACP is expected. Moreover, ACP (B 0 → K + π − ) and ACP (B + → K + π 0 ) are expected to have approximately same magnitude and sign [6]. Oppositely, both B + → K 0 π + and B 0 → K 0 π 0 are almost pure penguin processes, hence no sizable asymmetries are expected in the SM. Consistent with no asymmetry results have been obtained experimentally for the decays B + → K 0 π + and B 0 → K 0 π 0 as it was expected from the theory. However, the measured asymmetries ACP (B 0 → K + π − ) and ACP (B + → K + π 0 ) have different magnitudes and signs, and their difference is ∆ACP = ACP (B 0 → K + π − ) − ACP (B + → K + π 0 ) = −0.147 ± 0.28, which has been established with a significance of 5.3σ. There are several theoretical models, which explain the sizable ∆ACP effect by the colour-suppressed tree and penguin processes. To exclude these effects and examine for a new physics, the isospin sum rule among four ACP values can be applied [7]:

+

−

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+

π = AK CP

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+

B(B + → K 0 π + )τB 0 B(B 0 → K + π − )τB +

0 0 0 2B(B + → K + π 0 )τB 0 K 0 π 0 2B(B → K π ) + A , CP B(B 0 → K + π − )τB + B(B 0 → K + π − )

where τB 0 (τB + ) is a B 0 (B + ) meson lifetime. This relation is illustrated on Fig. 2: the current status is shown on the left plot; its approximation to Belle II data is shown on the right plot. A violation of the sum rule would be an unambiguous evidence of a new physics. With all of B and ACP results except for ACP (B 0 → K 0 π 0 ), the sum rule predicts ACP (B 0 → K 0 π 0 ) to be −0.153±0.045, which is consistent with current measurement. The discrepancy can be revealed with higher precision measurements on the larger statistics of Belle II. 4

SuperKEKB accelerator and Belle II detector

The SuperKEKB collider is designed by upgrading the existing KEKB machine. SuperKEKB should achieve a peak luminosity about 2 × 1035 cm−2 s−1 in an initial phase until 2016 and ultimately reach 8 × 1035 cm−2 s−1 afterward. This will allow to accumulate 10 ab−1 around 2016 and 50 ab−1 around 2020. These

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0π0

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Figure 2: Illustration of the sum rule for the current experimental values (left) and the projection for SuperKEKB assuming the same central values (right).

¯ pair integrated luminosities correspond approximately to 10 and 50 billion B B events, respectively. The formula for the luminosity can be expressed as: L=

σy∗ )( I± ξ±y )( RL ) γ± ( 1+ ∗ . 2ere σx βy∗ Ry

To achieve the designed luminosity goal the “nano-beam” configuration has been chosen. To increase the luminosity by the factor of 40, the accelerator parameters in the middle term of this expression will be changed: the beam current I± to be increased by the factor of 2, and the beam size βy∗ to be reduced by the factor of 20. The Belle spectrometer will to be upgraded to Belle II detector to accommodate much higher luminosity and to work efficiently in the conditions of much higher background level. The physics goals require also the improvements in the accuracies in all sub-detector systems. To improve the vertex resolution the silicon vertex detector will be replaced with a 2-layer DEPFET pixel detector and a 4-layer silicon strip detector. The Belle drift chamber will be replaced with a new one with smaller cell size to cope with the higher occupancy. Particle identification will be provided by a Time-of-Propagation (TOP) counter in the barrel region and a proximity focusing Cherencov ring imaging counter with aerogel radiators in the forward endcap (ARICH). Electromagnetic calorimeter will be equipped with a new electronics with wave-form sampling. The first two layers (closest to the interaction region) of the barrel part and the entire endcaps of the Belle muon system in the flux return of the magnet based on resistive plate chambers will be replaced with scintillator strips.

300 5

Summary

After eleven years of the successful work the Belle experiment was stopped. The Belle detector was partially disassembled and prepared for its upgrade to Belle II. The Belle II detector is designed, all sub-systems will be upgraded or replaced with new ones with better performance and stability against higher background. The aim of the new facility is to achieve a Υ(4S) data set equiv¯ pair events) around the year 2022. In alent to 50 ab−1 (about 50 billion B B the accelerator machine upgrade scheme, the increase of the luminosity will be achieved by drastically squeezing the beam size at the interaction region. A rich physics program is aimed to search for a new physics in quark flavor sector. References [1] S. Kurokawa and E. Kikutani, Nucl. Instrum. Methods Phys. Res., Sect. A 499, 1 (2003), and other papers included in this volume. [2] A. Abashian et al. (Belle Collaboration), Nucl. Instrum. Methods Phys. Res., Sect. A 479, 117 (2002). [3] M. Kobayashi and T. Maskawa, Prog. Theor. Phys. 49, 652 (1973). [4] J. Charles et al. (CKMfitter group), Phys. Rev. D 84, 033005 (2011); [5] Y. Grossman and M. P. Worah, Phys. Lett. B 395, 241 (1997); D. London and A. Soni, Phys. Lett. B 407, 61 (1997). [6] Y. Y. Keum and A. I. Sanda, Phys. Rev. D 67, 054009 (2003); M. Beneke and M. Neubert, Nucl. Phys. B 675, 333415 (2003). [7] M. Gronau, Phys. Lett. B 627 (2005) 82.

301 RARE B-MESON DECAYS Mikolaj Misiak a Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, ul. Ho˙za 69, 00-681 Warsaw, Poland Abstract. Rare decays of the B-meson that arise due to loop-mediated FCNC transitions are known to provide important constraints on beyond-SM theories. Basic properties of several such decays are reviewed here.

1

Introduction

Flavour Changing Neutral Current (FCNC) phenomena arise at the one-loop level in the Standard Model (SM). They may receive similar loop contributions from beyond-SM particles. Many rare decays of B mesons belong to this class of processes. I will begin with discussing Bs → µ+ µ− that receives particular attention this year. Next, I will pass to other decay modes that are generated by the quark-level b → sγ and b → sl+ l− transitions. 2

Bs → µ+ µ− — the 2011 highlight

The decay of Bs to two muons has a very clean experimental signature — a sharp peak in the dimuon invariant mass. However, its branching ratio in the SM is extremely small (see Sec. 4): B(Bs → µ+ µ− )SM = (3.33 ± 0.21) × 10−9 .

(1)

It is known to be very sensitive to new physics even in models with Minimal Flavour Violation [1]. Enhancements by orders of magnitude are possible even when constraints from all the other available observables are taken into account. In July 2011, a new bound on the branching ratio was announced by the CDF Collaboration [2]: B(Bs → µ+ µ− )CDF < 40 × 10−9 at 95% C.L. Since an excess of signal events remained after cuts, their measurement(could )have also been interpreted as an observation: B(Bs → µ+ µ− )CDF = 18+11 × 10−9 . −9 An excitement about its large central value ended two weeks later at the EPS 2011 conference where the LHCb and CMS collaborations announced results of their searches. They observed no signal excess and presented upper bounds only, whose combination reads [3] B(Bs → µ+ µ− )LHC < 10.8 × 10−9 at 95% C.L.

(2)

At present (November 2011), the LHC experiments have accumulated data samples that are several times larger than those used for EPS 2011. Updates of their analyses are eagerly awaited. a e-mail:

[email protected]

302 3

The low-energy effective Lagrangian

Before continuing, let me recall the basic framework that is used for calculations of flavour-changing observables at scales much below the electroweak one. We pass from the full theory of electroweak interactions to an effective one by removing the high-energy degrees of freedom, i.e. integrating out the W -boson and all the other particles with masses of order MW or heavier. The resulting Lagrangian takes the form ∑ Leff = LQCD×QED (leptons, quarks ̸= t) + N Cn Qn , (3) n

where Qn are higher-dimensional interaction terms (operators), Cn are the corresponding coupling constants (Wilson coefficients), and N is a normalization constant. Information on electroweak-scale physics is encoded in the values of Ci (µ). Such an effective theory is a modern version of the Fermi theory for weak interactions. It is “non-renormalizable” in the traditional sense, but actually renormalizable because an infinite set of operators of arbitrarily high dimensions is included. It is also predictive, because all the Ci are calculable, and only a finite number of them is necessary at each given order in the (external momenta)/MW expansion. The main advantages of using the effective theory language are easier account for symmetries and the possibility of resumming ( )n 2 large logarithms like αs ln MW /µ2 from all orders of the perturbation series using renormalization group techniques. 4

More on Bs → l+ l− and B 0 → l+ l−

There are three dimension-six operators in Leff that matter for Bs → µ+ µ− in the SM and beyond. They read ( ) ( ) ( ) QA = ¯bγα γ5 s (¯ µγ α γ5 µ) , QS = ¯bγ5 s (¯ µµ) , QP = ¯bγ5 s (¯ µγ5 µ) . (4) 2 Setting N = Vtb∗ Vts G2F MW /π 2 in Eq. (3), one obtains

¯s → µ+ µ− ) = B(B

[ )] |N |2 MB3 s fB2 s √ 2 2( 1−r2 |rCA − uCP | + |uCS | 1−r2 , (5) 8π ΓBs

where r = 2mµ /MBs and u = MBs /(mb + ms ). The decay constant fBs parametrizes the matrix element ⟨0|¯bγ ν γ5 s|Bs (p)⟩ = ipν fBs . Only the coefficient CA matters in the SM because CS,P ∼ mµ /MW , and their effects on the 2 r.h.s. of Eq. (5) are thus suppressed by MB2 s /MW with respect to those of CA . 2 SM,LO x2 −4x 3x 2 with x = m2t /MW . At the leading order, CA = 16(x−1)2 ln x + 16(x−1) When the MS mass mt (mt ) ≃ 165(1) GeV is used in x, the O(αs ) corrections [4] enhance the branching ratio by around +2.2%, while the electroweak

303 SM corrections to CA that have been calculated in Refs. [5, 6] act in the opposite way, and suppress the branching ratio by around −1.7%. The central value in Eq. (1) has been obtained for |Vcb | = 0.04185(73) [7], τBs = 1.472(26) ps [8], and using the new result of the HPQCD Collaboration fBs = 225(4) MeV [9]. The error due to fBs is no longer dominant, but still the largest. Useful phenomenological expressions for all the Bs → l+ l− and B 0 → l+ l− branching ratios in the SM can be found in Eqs. (127)–(132) of Ref. [10].b The quoted uncertainties there should be understood to include around 3% ones due to the unknown O(αs2 ) and subleading electroweak corrections. For the Bs → l+ l− decays, the current experimental bounds are above the SM predictions by factors O(106 ), 3.3, O(105 ), for l = e, µ, τ , respectively. The corresponding numbers for B 0 → l+ l− are O(107 ), 35, O(105 ). Thus, the muonic decay of Bs is definitely the most restrictive at present. Constraints on the Two-Higgs-Doublet Model II from Fig. 3 of Ref. [11] can easily be updated to include the new upper bound on Bs → µ+ µ− (2) and ¯ → Xs γ [12]. It follows the lower bound MH ± > 295 GeV that comes from B that tan β < 50 remains allowed for the charged Higgs boson mass values that ¯ → Xs γ constraint. survive the B As far as the Minimal Supersymmetric Standard Model (MSSM) is concerned, the first analysis [13] performed after the EPS 2011 conference implies that tan β larger than 50 is hard to accommodate in the CMSSM given the current Bs → µ+ µ− bounds. Assuming SM-like measurement with ±10% accuracy, the authors find that tan β must be smaller than around 40 for stop t˜1 masses up to 2 TeV.

5

What other rare B decays are interesting?

There are two basic scenarios for flavour physics beyond the SM. The scenario “A” (Attractive or Arbitrary) is characterized by Generic Flavour Violation in interactions of new particles with the SM ones. Its properties are as follows: (i) Large deviations from the SM in the Wilson coefficients are possible. (ii) Observable new physics effects may arise despite QCD-induced theory uncertainties in many FCNC decays of the B meson, like penguin-induced exclusive hadronic decays, B → K ∗ γ, B → K (∗) l+ l− , etc. (iii) Interesting constraints can be obtained from branching ratios, angular distributions and various asymmetries. The scenario “B” (Boring or Beautiful) corresponds to quite heavy new particles and Minimal Flavour Violation. In such a case: (i) Only mild beyond-SM effects in most of the Wilson coefficients are expected. (ii) CP-asymmetries are unaffected. (iii) Precise measurements are needed. Consequently, small rates b Note different normalization conventions for the operators and their Wilson coefficients there.

304 are not welcome, i.e. b → s transitions are preferred over b → d ones. (iv) Precise theory predictions in the SM case are needed, which implies that inclusive rather than exclusive hadronic final states are preferred. (v) Suppression in the SM due to parameters other than CKM angles is a positive property of any considered observable because it increases sensitivity to new physics. (vi) Apart ¯ → Xs γ is of main interest. Other from B → l+ l− , the inclusive decay B ¯ → Xs ν ν¯ or B ¯ → Xs l+ l− undergo no chiral suppresinclusive decays like B sion in the SM but still deserve consideration. (vii) Exclusive observables (like asymmetries) may still be useful to resolve discrete ambiguities. In the following, I shall comment on several observables that remain relevant in the case “B”. 6

¯ → Xs γ B

¯ → Xs γ) with B ¯ = B ¯ 0 or B − and the lower The inclusive decay rate Γ(B cut on the photon energy E > E0 is well approximated by the corresponding perturbative partonic rate Γ(b → Xsp γ), provided E0 is neither too large, nor too small. For a conventional choice E0 = 1.6 GeV ≃ mb /3, unknown nonperturbative corrections to this approximation have been analyzed in detail in Ref. [14], and estimated to remain at around ±5% level. The goal of the ongoing perturbative calculations (see Ref. [15] for a review) is to make the O(αs2 ) uncertainties negligible with respect to the non-perturbative ones. At ¯ → Xs γ)SM = (3.15 ± 0.23) × 10−4 [12] agrees present, the SM prediction B(B ¯ → Xs γ)exp = (3.55 ± 0.24 ± 0.09)×10−4 [7] within with the world average B(B 1.2σ. This fact has been used to derive constraints on various new physics models, like the bound on MH ± that has been mentioned in Sec. 4, or effects in the recent MSSM parameter space fits [16]. 7

Processes generated by the quark-level b → sl+ l− decay

¯ → Xs γ and B(s) → l+ l− , the quark-level b → sl+ l− decay Contrary to B undergoes no chiral suppression in the SM, which makes it less sensitive to new physics. It is also more complicated due to partial screening of beyond-SM effects by J/ψ and higher c¯ c resonances in the dilepton spectrum. A very recent model-independent analysis of observables that are available in processes generated by this decay has been presented in Ref. [17]. The authors con¯ → Xs l+ l− in various regions of the dilepton invariant mass, sider inclusive B asymmetries of angular distributions in B → K ∗ l+ l− , as well as the branching ratio and CP asymmetry in the radiative mode. No significant (larger than 2σ) deviations from the SM are found. However, allowed regions in the Wilson coefficient space remain large, so there is no clear indication which scenario (“A” or “B”) is preferred.

305 8

Summary

Rare B decays provide improving constraints on beyond-SM physics, with a prominent role played by Bs → µ+ µ− this year. New results are awaited soon. Acknowledgments This work has been supported in part by the Ministry of Science and Higher Education (Poland) as research project N N202 006334 (2008-11), and by the DFG through the “Mercator” guest professorship program. References [1] G. D’Ambrosio, G. F. Giudice, G. Isidori, A. Strumia, Nucl. Phys. B 645, 155 (2002) [hep-ph/0207036]. [2] T. Aaltonen et al. (CDF Collaboration), arXiv:1107.2304. [3] CMS and LHCb Collaborations, note LHCb-CONF-2011-047, CMS PAS BPH-11-019, available at http://cdsweb.cern.ch/record/1374913/ files/BPH-11-019-pas.pdf . [4] G. Buchalla, A. J. Buras, Nucl. Phys. B 400, 225 (1993), Nucl. Phys. B 548, 309 (1999) [hep-ph/9901288]; M. Misiak, J. Urban, Phys. Lett. B 451, 161 (1999) [hep-ph/9901278]. [5] G. Buchalla, A. J. Buras, Phys. Rev. D 57, 216 (1998) [hep-ph/9707243]. [6] C. Bobeth, P. Gambino, M. Gorbahn, U. Haisch, JHEP 0404, 071 (2004) [hep-ph/0312090]; T. Huber, E. Lunghi, M. Misiak, D. Wyler, Nucl. Phys. B 740, 105 (2006) [hep-ph/0512066]. [7] D. Asner et al. (Heavy Flavor Averaging Group), arXiv:1010.1589, updates at http://www.slac.stanford.edu/xorg/hfag . [8] K. Nakamura et al. (PDG Collaboration), J. Phys. G 37, 075021 (2010). [9] C. McNeile, C. T. H. Davies, E. Follana, K. Hornbostel, G. P. Lepage (HPQCD Collaboration), arXiv:1110.4510. [10] M. Artuso et al., Eur. Phys. J. C 57, 309 (2008) [arXiv:0801.1833]. [11] H. E. Logan, U. Nierste, Nucl. Phys. B 586, 39-55 (2000) [hepph/0004139]. [12] M. Misiak et al., Phys. Rev. Lett. 98, 022002 (2007) [hep-ph/0609232]. [13] A. G. Akeroyd, F. Mahmoudi, D. M. Santos, arXiv:1108.3018. [14] M. Benzke, S. J. Lee, M. Neubert, G. Paz, JHEP 1008, 099 (2010) [arXiv:1003.5012]. [15] M. Misiak, AIP Conf. Proc. 1317, 276 (2011) [arXiv:1010.4896]. [16] O. Buchmueller et al., arXiv:1110.3568; A. Arbey, M. Battaglia, F. Mahmoudi, arXiv:1110.3726. [17] W. Altmannshofer, P. Paradisi, D. M. Straub, arXiv:1111.1257.

306 RECENT RESULTS ON RARE KAON DECAYS FROM NA48/2 AND NA62 EXPERIMENTS AT CERN SPS Andrea Bizzeti a Dipartimento di Fisica, Universit` a di Modena e Reggio Emilia, via G. Campi 213/A, 41100 Modena, Italy I.N.F.N. Sezione di Firenze, via G. Sansone 1, 50019 Sesto Fiorentino (FI), Italy Abstract. The branching fractions of K ± → π ± e+ e− and K ± → π ± µ+ µ− rare decays have been measured by the NA48/2 collaboration at CERN SPS. An improved upper limit has been set on the Lepton Number Violating decay K ± → π ∓ µ± µ± . The branching ratio RK = Γ(K ± → e± ν)/Γ(K ± → µ± ν) has been measured by the NA62 collaboration at CERN SPS with an unprecedented accuracy, allowing a precise test of lepton flavour universality. The NA62 experiment is now undergoing a major upgrade in order to measure the branching fraction of the very rare K + → π + ν ν¯ decay with a 10% precision.

1

Introduction

Rare Kaon decays provide unique opportunities to search for effects of physics beyond the Standard Model. In fact, the suppression of these decays in the SM makes them very sensitive to loop-level contributions of virtual heavy particles. NA48/2 collected several thousands of K ± → π ± e+ e− and K ± → π ± µ+ µ− decays, obtaining upper limits on CP violating charge asymmetries and on the branching fraction of the Lepton Number violating decay K ± → π ∓ µ± µ± . Lepton flavour universality has been investigated by NA62 measuring the ratio RK = Γ(K ± → e± ν)/Γ(K ± → µ± ν) with unprecedented accuracy. The branching fraction (' 10−10 ) of the ultra-rare FCNC decay K +→ π + ν ν¯ is predicted by the SM [1] with a theoretical uncertainty much smaller than present experimental accuracy. NA62 will measure this BR with a 10% precision. 2

The NA48/2 and NA62 experiments

The NA48/2 and NA62 experiments at CERN SPS collected data in 2003–2004 and in 2007–2008, respectively, using the same experimental setup and a beam line able to deliver simultaneous K + and K − beams. After momentum selection, cleaning and collimation, the beams enter the fiducial decay volume, housed in a 114 m long vacuum tank, with a negligible angular divergence and a r.m.s. transverse size below 1 cm. The beams contain between 107 and 108 particles per SPS pulse (4.8 s duration), and about 5% of them are kaons. The charged particle reconstruction is provided by a magnetic spectrometer, consisting of a dipole magnet and four drift chambers. A plastic scintillator hodoscope provides fast signals for triggering on charged particles and precise time a on

behalf of the NA48/2 and NA62 collaborations. E-mail: [email protected] .

307 measurement. The energy and position of photons and electrons are precisely measured by a liquid krypton electromagnetic calorimeter (LKr), consisting of a 27X0 almost homogeneous ionization chamber with high-granularity tower read-out. A muon detector (MUV) composed of iron absorbers and three planes of scintillator is used to identify muons. An iron-scintillator hadron calorimeter and several photon veto counters complete the experimental apparatus, a detailed description of which can be found in Ref. [2]. 3

K ± → πee, K ± → πµµ and search for Lepton Number Violation

The large NA48/2 data sample collected in 2003–2004 to measure charge asymmetries in K ± → 3π decays [3] gives the opportunity to study the K ± → π ± e+ e− and K ± → π ± µ+ µ− rare decays and to search for the Lepton Number Violating (LNV) decay K ± → π ∓ µ± µ± . Three-track vertices are reconstructed extrapolating the segments from the spectrometer, taking into account the measured residual magnetic fields and multiple scattering. For each track, the ratio E/p of the associated energy deposit in the LKr calorimeter to its momentum measured by the magnetic spectrometer is used for particle identification, as described below. 3.1

K ± → π ± e+ e−

The K ± → π ± e+ e− rate is measured relative to the more abundant K ± → 0 0 → e+ e− γ is the so-called Dalitz decay), normalization channel (where πD π ± πD whose final state contains the same charged particles as the signal events. Candidate events are required to have one π ± track (E/p < 0.85) and a pair of oppositely charged electrons (E/p > 0.95); their total momentum is required to be consistent with that of beam particles. Kinematic suppression of the main 0 ) is achieved by requiring the e+ e− invariant background channel (K ± → π ± πD 0 mass to be above the π mass: z ≡ (Mee /MK )2 > 0.08 . Finally, the π ± e+ e− invariant mass is required to be consistent with the K ± mass. A total of 7253 events has been obtained, with a 1.0% background. The branching fraction has been measured to be BR(K ± → π ± e+ e− ) = (3.11 ± 0.12) × 10−7 . The first simultaneous observation of both charged kaon decays into π ± e+ e− allows to establish an upper limit for the CP violating charge asymmetry ACP = (BR+ − BR− )/(BR+ + BR− ) : |ACP | < 2.1 × 10−2 at 90% CL. More details on this analysis can be found in [4]. 3.2

K ± → π ± µ+ µ−

The K ± → π ± µ+ µ− rate is measured relative to the abundant K ± → π ± π + π − normalization channel (denoted K3π below). The K ± → π ± µ+ µ− and K3π samples are collected concurrently using the same trigger logic.

Events

Events

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Figure 1: Invariant mass distribution of (left) π ± µ+ µ− and (right) π ∓ µ± µ± candidates: data (dots), K3π and Kπµµ simulations (filled areas). Arrows indicate the signal region.

Candidate events are required to have one π ± track (with E/p < 0.95 and no correlated hits in the MUV) and a pair of oppositely charged muons (E/p < 0.2 and associated hit(s) in the MUV); their total momentum is required to be consistent with that of beam particles. The π ± µ+ µ− invariant mass is required to be consistent with the K ± mass (see Fig. 1(left)). A total of 3120 events has been obtained, with a background of (3.3 ± 0.7)%. The branching fraction has been measured to be BR(K ± → π ± µ+ µ− ) = (9.62 ± 0.25) × 10−8 , improving the precision by a factor ∼ 3 with respect to the most precise earlier measurement. The branching ratios have been measured separately for K + and K − , allowing to establish an upper limit on the CP violating charge asymmetry ACP = (BR+ − BR− )/(BR+ + BR− ) : |ACP | < 2.9 × 10−2 at 90% CL. Γ(cos θ >0)−Γ(cos θKµ 0)+Γ(cos θKµ 0.95) due to ‘catastrophic’ bremsstrahlung in the LKr. In order to reduce the corresponding uncertainty, the muon mis-

310 identification probability Pµe has been measured as a function of momentum using dedicated samples. The numbers of selected Ke2 and Kµ2 candidates are 145 958 and 4.2817 × 107 , respectively (the latter pre-scaled at trigger level). The final result of the measurement, combined over the 40 independent samples taking into account correlations between the systematic errors, is RK = (2.488 ± 0.007stat ± 0.007syst ) × 10−5 = (2.488 ± 0.010) × 10−5 . This result is consistent with the Standard Model expectation [7] RK = (2.477±0.001)×10−5 and its precision dominates the world average. 5

The ultra-rare K + → π + ν ν ¯ decay

The primary goal of the NA62 experiment [8] is the measurement of the branching fraction of the K + → π + ν ν¯ decay with 10% precision. In order to obtain this precision, NA62 aims to collect at least 100 K + → π + ν ν¯ decays in about two years of data taking. At least 1013 K + decays are needed, assuming a ≈ 10% signal acceptance and a branching ratio of ≈ 10−10 . To keep the systematic uncertainty small, a rejection factor ≈ 10−12 is required for the main K + decay modes, as well as the possibility to measure efficiencies and rejection factors directly from data. In order to match the above requirements new detectors must replace most of the existing apparatus. The experimental setup consists of an unseparated positive beam of 75 GeV/c ±1% momentum, a ∼ 80 m long evacuated decay volume and detectors downstream to identify and measure the kaon decay products. The signature of the K + → π + ν ν¯ decay is one π + track in the final state matched to one K + track in the beam, and no other detectable particle. The beam intensity rate is about 800 MHz (only 6% of the beam particles are kaons, the others are π + and protons). The rate seen by the detectors downstream is about 10 MHz, mainly due to K + decays. Backgrounds come from all kaon decays with one track in the final state. Different techniques will be combined in order to reach the required level of rejection: kinematic rejection, precise timing, highly efficient photon and muon vetos, precise particle identification systems to distinguish π + , µ+ and e+ . The layout of the NA62 detector is sketched in Fig. 3. The main subdeˇ tectors are: a differential Cerenkov counter (CEDAR) to identify the K + in the beam; a Silicon pixel beam tracker (GTK); guard-ring counters (CHANTI) surrounding the beam tracker to veto catastrophic interactions of particles in the tracker; a downstream spectrometer made of STRAW chambers in vacuum; ˇ a RICH Cerenkov counter to distinguish pions and muons; a plastic scintillator hodoscope (CHOD); a system of photon vetos including a series of annular lead glass calorimeters (LAV) surrounding the decay and detector volume, the NA48 LKr calorimeter and a small angle calorimeter (SAC) to complete the hermetic coverage for photons emitted at very small angles (down to zero); a muon veto detector (MUV).

311

Figure 3: Schematic lateral view of the NA62 experimental setup

The design of the experimental apparatus and the R&D of the new subdetectors have been completed in 2010. The experiment is under construction and the first technical run is foreseen at the end of 2012. 6

Conclusions

The NA48/2 experiment at CERN SPS has measured the branching ratios of K ± → π ± e+ e− and K ± → π ± µ+ µ− decays with a few percent relative precision and has also improved the upper limit on the branching ratio of the lepton number violating decay K ± → π ∓ µ± µ± : BR< 1.1 × 10−9 at 90% CL. Using the same detector, the NA62 experiment has obtained the most precise measurement of the ratio RK = Γ(Ke2 )/Γ(Kµ2 ) = (2.488 ± 0.010) × 10−5 , in agreement with the Standard Model prediction. The ultra-rare K + → π + ν ν¯ decay is a unique environment where to search for new physics. The NA62 experiment aims to measure its branching ratio with a 10% accuracy. After three years of successful R&D, all subdetectors are now under construction. References [1] [2] [3] [4] [5] [6] [7] [8]

J. Brod, M. Gorbahn, E. Stamou, Phys.Rev D 83, 034030 (2011) V. Fanti et al., Nucl. Instrum. Methods A 574, 433 (2007) J.R. Batley et al., Eur. Phys. J. C 52, 875 (2007) J.R. Batley et al., Phys. Lett. B 677, 246 (2009) J.R. Batley et al., Phys. Lett. B 697, 107 (2011) C. Lazzeroni et al., Phys. Lett. B 698, 105 (2011) C. Cirigliano, I. Rosell, Phys. Rev. Lett. 99, 231801 (2007) G. Anelli et al., CERN-SPSC-2005-013/SPSC-P-326 (2005)

312 LHCB RESULTS Evgeny Gushchin a Institute for nuclear research RAS, 117312 Moscow, Russia Abstract. Experimental performance of LHCb detector with special emphasis on key measurements is presented. Also some recent results related to the search for New Physics are described.

1

Introduction

The Cabibbo-Kobayashi-Maskawa (CKM) matrix describes flavour mixing in the quark sector of the SM. The last decade was very rich with precise measurements of its elements mainly done at B-factories and Tevatron. Although modern experimental data are successfully described with the CKM mechanism, there are several tensions with observables such as BR(B→τ ν ), sin(2β), Asl and room remains for New Physics (NP), i.e. in Bd,s mixing [1]. Also indirect searches for NP in loop-mediated processes suppressed in the SM can extend the discovery potential for new heavy particles to mass range far beyond that accessible in direct searches. The core LHCb physics program as presented in [5] concentrates on the precise measurement of the CKM angle γ in B→DK tree decays and in loop-mediated charmless two-body B-decays, the measurement of Bs mixing phase ϕs , the helicity structure study in B 0 →K ∗ µµ decay, the determination of branching fraction of the rare decay Bs0 →µµ, and also studies of radiative b→sγ decays. 2

Beauty production at LHC

At the time of the conference the LHC √ was operating at a luminosity of about 2 × 1033 cm−2 · sec−1 and energy of s = 7 TeV, which are below the design values, but already larger then at Tevatron by 3 and 3.5 times correspondingly. LHCb operates at instant luminosities of 3 − 3.5 × 1033 cm−2 ·sec−1 in autoleveling mode, a value optimal for the selection and reconstruction of B-decays. √ The pp→bb production cross-section at s = 7 TeV is about 300 µb−1 [2] that is 3 times larger than at Tevatron and much larger than 1.2 nb−1 of bproduction cross-section at Y (4S) energy at B-factories. A sample of about 1012 of B-mesons can be produced in LHCb during a nominal year with all b-quark species present. For example, B + , B 0 , Bs0 , Λ0b , Bc are produced in the proportion of about 40% : 40% : 10% : 10% : 0.1%. But due to a large minimum-bias cross-section equal to 65 mb−1 in LHCb acceptance only one of about 200 pp interactions contains b-quarks. This fact leads to the requirement of a very selective trigger based on the efficient event reconstruction and particle a e-mail:

[email protected]

313 identification. It also should be mentioned that the charm production crosssection is about 20 times larger [3] then the b-quark one and therefore LHCb has a great potential for charm studies too. 3

LHCb experiment

The LHCb detector [4, 6] is a single-arm forward spectrometer designed for precise measurements of CPV and rare decays of B-mesons in p − p collisions at the LHC. To exploit the bb pair production at LHC peaked in the forward direction the LHCb acceptance covers pseudo-rapidity range of about 1.9 < η < 4.9, that allows to capture almost 40% of bb events within only about 4% of solid angle. The LHCb detector consists of a vertex locator (VELO), a tracking system with a warm magnet of 4 T·m integrated field, two RICH detectors, calorimeter and muon systems. A silicon microstrip detector called VELO surrounds the beam interaction point and provides a reconstruction of decay vertex with a precision of σx,y ≈ 13 µm and σz ≈ 63 µm for 25 decay tracks. The track momentum is measured with the precision of ∆p/p ≈ 0.35 − 0.5% in a momentum range of 2 − 100 GeV/c. Two RICH detectors allow charged kaon identification in a range of 2 − 100 GeV/c with typical efficiency of up to 90% while the fake rate from pions as kaons is kept below 10%. The calorimeter system provides transverse energy measurement and identification of photons, electrons and hadrons for the zero-level trigger. Identification of muons is done by the muon system consisting of 5 detector planes interlaid with absorbers of about 20 interaction lengths. Muon identification efficiency reaches 97% with a misidentification rate of 1 − 2% for momenta above 10 GeV/c. The excellent performance of LHCb detector was demonstrated already with the results obtained with the 2010 data. For example, the outstanding proper time resolution of about 50 fs in VELO provided world-class measurements of the B-hadron lifetimes [7]. The quality of momentum measurements resulted in the world’s best B-hadron mass measurements in various B→J/ψ(µµ)X decays [8]. It is also well illustrated by the resolution of J/ψ(µµ) mass of 12.3 MeV/c2 [9], which is much better than in other LHC detectors. 4

LHCb results

The measurement of quarkonium production cross-sections at LHC energies in forward region is crucial for the understanding of the relative contributions of Color Octet and Color Singlet models. Also the measurements of exclusive dimuon events allow the study of the other QCD predicted states, such as the pomeron and odderon. The first measurements of differential production √ cross-sections [9, 10] of J/ψ, ψ(2S), Y done by LHCb at s = 7 TeV show good general agreement at high pT between data and theory predictions in

314 particular with NLO NRQCD. However, to discriminate amongst the various models in prompt J/ψ production the additional studies of other observables such as J/ψ polarization will be necessary. The double J/ψ production can be affected by the existence of charm tetra-quark states. The σ J/ψJ/ψ cross-section measured by LHCb using the first 35.2 pb−1 of data [11] is in agreement with LO QCD calculation. The exclusive dimuon production has been measured [12] in resonant and non-resonant states through intermediate production of a J/ψ, ψ(2S) or χc state. The production of individual χc0 , χc1 , χc2 components is found to be roughly equal. LHCb has also reported results on the production of the X(3872) [13], candidate to an exotic bound state. The precise determination of the angle γ of Bd CKM Unitarity Triangle is one of major goals of the LHCb program. The comparison of its measurements in tree-level decays, such as B→DK and in loop-mediated processes, such as B 0 →π + π − can provide a sign of NP. The data sample collected by LHCb until now is too small to allow the measurement of the γ-angle, but several studies have been done for validation of this program. With the 320 pb−1 of data collected in 2011 LHCb reported the most precise single measurement of direct CPV in Bd0 →Kπ and the first evidence of CPV in Bs0 →Kπ decay [14]. Another important search for open-charm B ± →(K ∓ π ± )D K ± decay with 343 pb−1 of data has been reported by LHCb in [15]. The evidence of this mode is seen with significance of 4.0 σ. Also the measurements of the observables RADS and AADS that relate to an extraction of the weak phase γ have been obtained. With the 2 fb−1 of integrated luminosity to be collected at the end of 2012 LHCb expects to measure the angle γ with a precision of about 5° [5]. The rare decay B 0 → K ∗ µ+ µ− is considered as highly sensitive to the contribution of NP changing its helicity structure. The most prominent observable is the forward-backward asymmetry of the muon system AF B (q 2 ) varying with the invariant mass of the dimuon pair. The zero-crossing point of AF B (q 2 ) is well defined in the SM, where the leading hadronic uncertainties cancel. The present analysis is based on the 309 pb−1 of data taken during 2011 [16]. There is a good agreement observed between the SM prediction and the LHCb measurement of AF B , which is currently the most precise world’s measurement. The ability to resolve the very fast Bs0 -oscillations is critical to the measurements of CPV in Bs0 system. LHCb has reported the world’s best measurement of the oscillation frequency parameter ms = 17.63 ± 0.11(stat.) ± 0.04(syst.) ps−1 [19]. The decay Bs0 → J/ψϕ is considered as a golden mode for measurement of CPV phase in Bs0 mixing. In SM the value of the phase is well predicted to be ϕs ∼ = −2βs . Its value is estimated from global fit as 2βs ≃ 0.0363+0.0016 −0.0015 rad [20]. The measurement of the contribution of NP to the phase ϕs requires high precision. Experiments on Tevatron attained precision of measurement of 0.5 rad [21]. Using the statistics of 2011 year LHCb can reach an accuracy of 0.1 rad. With data recorded in 2010 LHCb obtained the result as a confidence region in ϕs —∆Γs plane with deviation from SM point at 1.2 σ level [22].

315 The search for the rare decay Bs0 → µ+ µ− is one of the most promising ways to test the SM. The branching ratio (BR) of this decay is computed [17] to be BR(Bs0 → µ+ µ− )=(3.2 ± 0.2)· 10−9 . The upper limit measured by LHCb using 300 pb−1 of data is BR(Bs0 → µ+ µ− ) < 1.3(1.6)· 10−8 at 90%(95)% CL [18] that is less than factor 5 from the SM prediction. 5

Conclusion

The large b-quark production rate at LHC and excellent performance of LHCb detector creates a great opportunity for precise measurements of CPV and rare decays with B-mesons. All necessary components like mass and proper time resolution, particle identification and tagging capabilities, have been proved with data taken in 2010 and 2011 runs. The results obtained with key channels of the core physics program confirm the LHCb potential for the search for NP. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22]

A. Lenz et al., Phys.Rev. D 83, 036004 (2011). The LHCb Collaboration, Phys. Let. B 694,209-216, (2010). The LHCb Collaboration, CERN-LHCb-CONF-2010-013. LHCb Technical Design Report, CERN/LHCC 2003-030, (2003). The LHCb Collaboration, arxiv:0912.4179v2 [hep-ex]. The LHCb Collaboration, JINST 3 (2008) S08005. The LHCb Collaboration, CERN-LHCb-CONF-2011-001. The LHCb Collaboration, CERN-LHCb-CONF-2011-027. The LHCb Collaboration, Eur. Phys. J. C 71, 1645, (2011). The LHCb Collaboration, CERN-LHCb-CONF-2011-026; CERN-LHCbCONF-2011-016. The LHCb Collaboration, CERN-LHCb-CONF-2011-009. The LHCb Collaboration, CERN-LHCb-CONF-2011-022. The LHCb Collaboration, CERN-LHCb-CONF-2011-021. The LHCb Collaboration, CERN-LHCb-CONF-2011-042. The LHCb Collaboration, CERN-LHCb-CONF-2011-044. The LHCb Collaboration, CERN-LHCb-CONF-2011-038. A.J. Buras, arXiv:1012.1447; A.J. Buras et al., arXiv:1007.5291. The LHCb Collaboration, CERN-LHCb-CONF-2011-037. The LHCb Collaboration, CERN-LHCb-CONF-2011-005. J. Charles et al., Eur. Phys. J. C41 ,1-131, (2005), hep-ph/0406184 The CDF Collaboration, CDF/ANAL/BOTTOM/PUBLIC/10206 (2010); The D0 Collaboration, D0 Conference note 6098-CONF (2010). The LHCb Collaboration, CERN-LHCb-CONF-2011-006.

316 SEARCH FOR THE NEW PHYSICS IN RARE HEAVY FLAVOUR DECAYS AT LHCb Daria Savrina a On behalf of the LHCb collaboration Institute of Theoretical and Experimental Physics, Moscow, Russia Skobeltsyn Institute of Nuclear Physics, Moscow State University, Moscow, Russia Abstract. Rare decays of the B-mesons may provide a good test for the Standard Model (SM). The preliminary results of such searches with 300 pb−1 of data taken by the LHCb detector [1] during the first half of 2011 are presented in the current paper.

1

Introduction

Rare B-meson decays are controlled by loop diagrams, which are promissing entry points for New Physics (NP) effects to manifest themselves. Three of the most promissing measurements, representing the rare decays: measurement of the B(s,d) → µµ decays branching fractions, studies of the Bd → K ∗ µµ decay and measurement of the photon polarization in the Bs → ϕγ decay — will be discussed in the current talk. The LHCb experiment features a forward magnetic spectrometer covering a solid angle of 15-300 mrad and pseudo-rapidity range of 1.9 < η < 4.9. All the results presented here are preliminary and were obtained with 300 pb−1 of data taken during first half of 2011. 2

B(s,d) → µµ decays

Theoretical prediction for the branching of these decays is extremely small within the SM: BR(Bs → µµ) = (3.2 ± 0.2) × 10−9 and BR(Bd → µµ) = (0.10 ± 0.01) × 10−9 [2]. Both these decays may be sensitive to the models with extended Higgs and high tan β (where β is the ratio of the Higgs vacuum spectrum expectation values), like MSSM, where the partial width of these decays goes as tan6 β. Up to spring of 2011 the upper limit on these decays from the Tevatron and the 2010 LHCb data was typically an order of magnitude above the theoretical predictions [3], leaving a large space for further studies. In July 2011 an updated result from CDF was presented claiming an oservation of Bs peak in the dimuon invariant mass [5]. In LHCb, dimuon events, selected with the extremely efficient muon trigger, first undergo a soft cut-based analysis in order to reduce the dataset size to a usable level. Further, each selected event is given a probability to be a signal or a background in the 2-dimensional space, constructed of the dimuon invariant mass and Boosted Decision Tree (BDT) responce. Then, the number of selected a e-mail:

[email protected]

317 events is converted into a branching ratio with the help of three normalization channels: B + → Jψ(→ µµ)K + , Bs0 → Jψ(→ µµ)ϕ(→ KK) and B 0 → Kπ, the results of which are avaraged together. No significant excess is observed, and the following upper limits were set up on the branching ratios of both channels [4]: BR(Bs0 → µµ) < 15 × 10−9 @95%CL BR(B 0 → µµ) < 5.2 × 10−9 @95%CL Therefore the CDF excess reported in Bs → µµ is not confirmed. 3

B 0 → K ∗ µµ

This decay can give access to NP phenomena through observation of various angular distributions, like forward-backward asymmetry (AF B ) and its zero crossing point, which could be sensitive to the SM extensions, like SUSY, leftright models and additional scalar contributions. The B 0 → K ∗ µµ events are selected with the help of the BDT. The regions of J/ψ and ψ ′ resonances are cut off in the dimuon invariant mass distribution. To take into account the selection and detector geometry influence on the angular distributions, some “acceptance” corrections are introduced for each selected event. The corrected angular distributions are fit in six bins of q 2 first to calculate FL and then, with FL value fixed, to measure the AF B .

Figure 1: The theoretical predictions [6] and measurements [7] of the FL (left) and AF B (right)

As the result of this analysis, the FL and AF B were measured in six bins in 116 GeV2 /c4 q 2 range (see Fig. 1) [8]. Both measurements show no discrepancy with the SM predictions. 4

Radiative decays

The rare radiative decays of the B-mesons like B 0 → K ∗ γ and Bs0 → ϕγ have already been observed in previous experiments [9] and their branching fractions

318

400

LHCb Preliminary

350

s=7 TeV

∫ L=340.1 pb-1

300

NKπγ = 1599 ± 58 µ Kπγ = 5275 ± 5 MeV/c2 σKπγ = 153 ± 5 MeV/c2

250 200

Events / ( 80 )

Events / ( 80 )

were measured, showing a good agreement with the SM. However, for this class of decays a special interest is attracted to the photon polarization. The events in both channels are selected with a cut-based analysis. 60

LHCb Preliminary s=7 TeV

50

∫ L=340.1 pb-1

NK+K-γ = 210 ± 21 µ

K+K-γ

= 5361 MeV/c2

σK+K-γ = 150 ± 13 MeV/c2

40 30

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20

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50 0 4500

5000

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0

5000

5500

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6000

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Figure 2: The observed peaks for the B 0 → K ∗ γ (left) and Bs0 → ϕγ (right) decays

The mass peaks for the two decays are shown in Fig. 2. The Bs0 → ϕγ signal is the largest sample so far collected. The branching fractions ratio was 0 →K ∗ γ) calculated to be BR(B BR(Bs0 →ϕγ) = 1.41 ± 0.15(stat) ± 0.07(syst) ± 0.11(fs /fd ) and, using the known value for the BR(B 0 → K ∗ γ), the branching ratio for the Bs0 → ϕγ was evaluated with relative error twice smaller than in previous Belle meausrement: BR(Bs0 → ϕγ) = (3.1 ± 0.5) × 10−5 [10]. Both these measurements are consistent with the SM prediction. References [1] A. A. Alves et al. [LHCb Collaboration], JINST 3 (2009) S08005. [2] A.J. Buras, G. Isidori and P. Paradisi, “EDMs vs CPV in Bs,d mixing in two Higgs doublet models with MFV”, arXiv:1007.5291 [hep-ph] (2010) [3] CDF Public note 9892 (2009); Phys. Lett. B693, 539 (D0 collab., 2010); Phys. Lett. B699 330 (LHCb collab., 2011) [4] [LHCb Collaboration], LHCb-CONF-2011-037 [5] CDF collaboration, arxiv 1107.2304v1 (July 2011) [6] C.Bobeth et al., arXiv:1105.0376v2 [7] PRL 102, 091803 (2009); Note 10047 (2010); PRL 103, 171801 (2009) [8] [LHCb Collaboration], LHCb-CONF-2011-038 [9] Phys. Rev. Lett., 103:211802, BaBar 2009; Phys. Rev. D, 69(11):112001, Belle Jun 2004, Phys. Rev. Lett., 100:121801, Belle 2008; Phys. Rev. Lett., 84(23):52835287, CLEO Jun 2000 [10] [LHCb Collaboration], LHCb-CONF-2011-055

319 SEARCH FOR CHARGED LEPTON FLAVOR VIOLATION Yoshitaka Kuno a Department of Physics, Osaka University, Osaka, Japan Abstract. The experimental status of searches for charged lepton flavor violation with muons is described.

1

Physics motivation of CLFV

It is known that quarks and neutrinos are mixed and therefore their flavors are not conserved in the Standard Model (SM). However, lepton flavor violation for charged leptons have not yet to be observed. In the minimal version of the SM where massless neutrinos are assumed, lepton flavor conservation is a natural consequence of the gauge invariance. Therefore, it has been considered to naively explain why charged lepton flavor violation (CLFV) in charged leptons in highly suppressed. It have been confirmed that neutrinos are massive and mixed among different neutrino flavor species, by the observation of phenomena of neutrino oscillation. Therefore, lepton flavor for neutrinos is known to be violated. However, CLFV has been yet to be observed, and a discovery of CLFV is considered to be one of the important subjects in elementary particle physics [1]. In the framework of the Standard Model (SM) with massive neutrinos and their mixing, the branching ratio of µ → eγ decay (B(µ → eγ)) can be estimated. This process is suppressed by the GIM mechanism and the estimated branching ratio is about 10−54 . Therefore, the contribution from the SM with massive neutrinos turns out to be very tiny. As a result, it can be concluded that observation of CLFV would indicate a clear signal of new physics beyond the SM with massive neutrino. CLFV is known to be sensitive to various extension of new physics beyond the SM. Among them, a well-motivated physics model is a supersymmetric (SUSY) model. In SUSY models, the slepton mixing (given by off-diagonal elements of the slepton mass matrix) would introduce CLFV. In the minimum SUSY scenario, the slepton mass matrix is assumed to be diagonal at the Planck scale. At a low energy scale, new physics phenomena such as grand-unification (GUT) or neutrino seesaw would introduce off-diagonal matrix elements such as ∆mµ˜e˜ through quantum corrections (renormalization). Therefore, the slepon mixing is sensitive to GUT (at 1016 GeV) or neutrino seesaw mechanism (at 1013−14 GeV). As a result, it can be concluded that CLFV has potential to study physics at very high energy scale. a e-mail:

[email protected]

320 2

µ− N → e− N conversion experiments

The most prominent muon CLFV processes is coherent neutrino-less conversion of a negative muon to an electron (µ− N → e− N conversion) in a muonic atom. When a negative muon is stopped in some material, it is trapped by an atom, and a muonic atom is formed. After it cascades down energy levels in the muonic atom, the muon is bound in its 1s ground state. The fate of the muon is then either decay in orbit (DIO) (µ− → e− νµ ν e ) or nuclear muon capture by a nucleus N (A, Z) of mass number A and atomic number Z, namely, µ− + N (A, Z) → νµ + N (A, Z − 1). However, in the context of lepton flavor violation in physics beyond the Standard Model, the exotic process of neutrinoless muon capture, such as µ− + N (A, Z) → e− + N (A, Z),

(1)

is also expected. This process is called µ− N → e− N conversion in a muonic atom. This process violates the conservation of lepton flavor numbers, Le and Lµ , by one unit, but the total lepton number, L, is conserved. The event signature of coherent µ− N → e− N conversion in a muonic atom is a mono-energetic single electron emitted from the conversion with an energy (Eµe ) of Eµe = mµ − Bµ − Erecoil , where mµ is the muon mass, and Bµ is the binding energy of the 1s muonic atom. Erecoil is the nuclear recoil energy which is small and can be ignored. Since Bµ varies for various nuclei, Eµe could be different. For instance, Eµe = 104.3 MeV for titanium (T i) and Eµe = 94.9 MeV for lead (P b). From an experimental point of view, µ− N → e− N conversion is a very attractive process in the following reasons: (1) First, the energy of the signal electron of about 105 MeV is far above the end-point energy of the normal muon decay spectrum (∼ 52.8 MeV). (2) Secondly, since the event signature is a mono-energetic electron, no coincidence measurement is required. The search for this process has the potential to improve sensitivity by using a high muon rate without suffering from accidental background events, which would be serious for other processes, such as µ → eγ and µ → eee decays. There are several potential sources of electron background events in the energy region around 100 MeV, which can be grouped into three categories as follows. The first group is intrinsic physics backgrounds which come from muons stopped in the muon-stopping target. The second is beam-related backgrounds which are caused by beam particles of muons and other contaminated particles in a muon beam. The third is other backgrounds which are, for instance, cosmic-ray backgrounds, and fake tracking events, and so on. The previous search for µ− N → e− N conversion was performed by the SINDRUM II collaboration at PSI. The SINDRUM II spectrometer consisted of a set of concentric cylindrical drift chambers inside a superconducting solenoid magnet of 1.2 Tesla. They set an upper limit of µ− N → e− N in Au of B(µ− + Au → e− + Au) < 7 × 10−13 .

321 Next experimental projects to search for µ− N → e− N conversion with a higher sensitivity are being pursued in the USA and Japan. To suppress background events, in particular beam-related backgrounds, the following key elements have been proposed. They are based on the ideas developed in the MELC proposal at the Moscow Meson Factory. [2] • Beam pulsing: Since muonic atoms have lifetimes of the order of 1 µsec, a pulsed beam with its width that is short compared with these lifetimes would allow one to remove prompt background events by performing measurements in a delayed time window. To eliminate prompt beam-related backgrounds, proton beam extinction is required during the measurement interval. • pion capture system with a high solenoid field: Superconducting solenoid magnets of a high magnetic field surrounds a proton target to capture pions in a large solid angle. This is called the pion capture system. It leads a dramatic increase of muon yields by several orders of magnitude. • curved solenoids for muon transport: The curved solenoids are adopted to select charges and momenta of muons as well as removing neutral particles in a beam. In a curved solenoidal magnetic field, a center of the helical trajectory of a charged particle is shifted perpendicular to the curved plane. The shift, whose amount is given as a function of momentum and its charge, makes a dispersive beam.

Production Target

Stopping Target

Figure 1: Schematic layout of the Mu2e experiment at FNAL (left) and the COMET experiment at J-PARC (right).

One proposal in the USA was the MECO experiment at BNL. [3] It was mostly based on the MELC design and aimed to search for µ− N → e− N conversion at a sensitivity of better than 10−16 . It consists of the production solenoid system, the transport solenoid system and the detector solenoid system. Unfortunately, the MECO proposal was cancelled in 2005, owing to its funding problems. In 2008 a new initiative at Fermi National Accelerator Laboratory (FNAL), which is called the Mu2e experiment, has been made to perform a MECO-type experiment. [4] The Mu2e experiment is planned to combat

322 beam-related background events with the help of a 8 GeV/c proton beam of about 25 kW in beam power from the Booster machine at FNAL. Figure 1(left) shows the proposed layout of the Mu2e experiment. The Mu2e experiment was approved at Fermilab in 2009 and is in the DOE CD-0 approval. The other experimental proposal to search for µ− N → e− N conversion, which is called COMET (COherent Muon to Electron Transition), is being prepared at the Japan Proton Accelerator Research Complex (J-PARC), Tokai, Japan. [5] The COMET uses a proton beam of 56 kW from the J-PARC main ring. The aimed sensitivity at COMET is similar to Mu2e, better than 10−16 . A schematic layout of the COMET experiment is presented in Fig. 1(right). The differences of the designs between Mu2e and COMET exist in the adoption of C-shape curved solenoid magnets for both a muon beamline and a e+ spectrometer in COMET. First of all, in Mu2e, after the first 90-degree bending, the muons of their momenta of interest are necessarily shifted back to the median plane in the second 90-degree bending with opposite bending direction (therefore a S-shape), whereas in COMET, by applying a vertical correction magnetic field, the muons of interest can be kept on the median curved plane. From this fact, any opposite bending direction is not needed and a 180-degree bending in COMET would provide larger dispersion to give a better momentum selection. Secondary, a curved solenoid spectrometer in COMET is useful to eliminate low-energy events from muon decays in orbit before going into the detector, resulting in lower single counting rates in the detectors. The COMET experiment got a stage-1 approval at J-PARC, 2009 and is working for the final stage-2 approval. In the long-term future, significant improvements to aim at an experiment with a 2 × 10−19 single-event sensitivity should be considered to make a full coverage of the SUSY parameter spaces. The sensitivity of 2 × 10−19 can be achieved only together with multi MW proton beam power, which can be provided by future proton accelerators. The other potential key requirements for the improvement are the following. 3

The MuSIC project at Osaka University

In order to demonstrate the pion capture system that would be used to increase a muon beam intensity by a factor of about 1,000 for COMET, the MuSIC project at Osaka University [7] has been initiated at Research Center of Nuclear Physics (RCNP), Osaka University. RCNP has a 400 MeV proton cyclotron of 1 µA, yielding 400 Watts. The pion capture system has been constructed and commissioned. A preliminary test has showed an efficiency of muon collection has been improved by about a factor of 1000, which is as good as expected. This is the first demonstration of the pion capture system in the world. It would be beneficial not only for the COMET experiment but also R&D of neutrino

323 factories and a muon collider. The MuSIC facility now can produce as many as 108 muons/sec with 400 Watt beam power, which is almost the same as that at PSI of 1 Mega Watts.

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4

Summary

The physics of CLFV has received glowing attention from both theorists and experimentalists. The experimental status and future experimental prospects for various CLFV processes with muons are described. These attempts would offer extraordinary opportunities for exploring new phenomena which would otherwise be directly inaccessible at future high energy colliders. References [1] Y. Kuno and Y. Okada, Rev. Mod. Phys. 73, 151 (2001) [2] R.M. Dzhilkibaev and V.M. Lobashev, Sov. J. Nucl. Phys. 49 384 (1989) [Yad. Fiz. 49 622 (1989)] [3] M. Bachman et al., MECO, BNL Proposal E940 (1997). [4] R.M. Carry et al. (Mu2e collaboration), “Proposal to Search for µ− N → e− N with a Single Event Sensitivity Below 10−16 , FNAL proposal (2008). [5] Y. Kuno et al. (COMET collaboration), “A Experimental Search for Lepton Flavor Violating µ− N → e− N Conversion at Sensitivity of 10−16 with A Slow-Extracted Bunched Proton Beam”, J-PARC Proposal, 2007 and J-PARC Conceptual Design Report, 2009. [6] Y. Kuno et al. (PRISM collaboration), “An Experimental Search for a µ− N → e− N Conversion at Sensitivity of the Order of 10−18 with a Highly Intense Muon Source: PRISM”, unpublished, J-PARC LOI, 2006. [7] Y. Kuno et al. (MuSIC collaboration), “The MuSIC Project under the Center of Excellence of Sub Atomic Physics”, unpublished, July 2010.

324 STATUS AND PERSPECTIVES OF THE KLOE-2 EXPERIMENT Maxim Martemianov a on behalf of the KLOE-2 collaboration.† Institute for Theoretical and Experimental Physics, 117218 Moscow, Russia Abstract.The KLOE experiment has acquired an integrated luminosity greater than 2.5 fb−1 at the peak of ϕ-resonance on the e+ e− DAΦNE collider in the Frascati National Laboratory (LNF). New data taking with the upgraded detector (KLOE-2) and DAΦNE should start in the end of 2011. Main modifications of the detector and new interaction region give a unique possibility to collect about 20 fb−1 in 3 years. The KLOE-2 wide scientific program which contains the experimental study of CP and CP T symmetries, quantum decoherence, γγ physics and search of the dark matter is presented and briefly discussed.

1

Introduction

In 2008 the DAΦNE ϕ−factory collider has been upgraded successfully with new electron-positron interaction region based on large crossing angle and “crab-waist” compensation induced by properly designed sextupoles. New solution allowed to increase the instantaneous luminosity up to 5×1032 cm−2 s−1 , or by a factor of three larger, than the previous performance with the same beam currents [1]. Presently DAΦNE is delivering up to 15 pb−1 /day. It gives an opportunity to start new data-taking campaign with KLOE-2 detector, an upgraded successor of KLOE. 2

Detector upgrage

KLOE is a general purpose detector consisting of a large cylindrical drift chamber with an internal radius of 25 cm and an external one of 2 m, surrounded by a lead-scintillating fibers electromagnetic calorimeter. It is entirely immersed in the axial magentic field of 0.52 T [2]. The proposed KLOE-2 strategy has two well separated periods. In a first phase (STEP-0) two new detectors, namely Low Energy Tagger (LET) and a e-mail:

[email protected] collaboration: F. Achilli, D. Babusci, D. Badoni, I. Balwierz, G. Bencivenni, C. Bini, C. Bloise, V. Bocci, F. Bossi, P. Branchini, A. Budano, S. Bulychjev, L. Caldiera Balkest˚ ahl, P. Campana, G. Capon, F. Ceradini, P. Ciambrone, C. Czerwi´ nski, E. Dan´ e, E. De Lucia, G. De Robertis, A. De Santis, G. De Zorzi, A. Di Domenico, C. Di Donato, D. Domenici, O. Erriquez, G. Fanizzi, G. Felici, S. Fiore, P. Franzini, P. Gauzzi, G. Giardina, S. Giovanella, F. Gonella, E. Graziani, F. Happacher, B. H¨ oistad, L. Iafolla, E. Iarocci, M. Jacewicz, T. Johansson, A. Kowalewska, V. Kulikov, A. Kupsc, J. Lee-Franzini, F. Loddo, G. Mandaglio, M. Martemianov, M. Martini, M. Mascolo, M. Matsyuk, R. Messi, S. Miscetti, G. Morello, D. Moricciani, P. Moskal, F. Nguyen, A. Passeri, V. Patera, I. Prado Longhi, A. Ranieri, C. F. Redmer, P. Santangelo, I. Sarra, M. Schioppa, B. Schiascia, A. Sciubba, M. Silarski, S. Stucci, C. Taccini, L. Tortora, G. Venanzoni, R. Versaci, W. Wi´slicki, M. Wolke, J. Zdebik † KLOE-2

325 High Energy Tagger (HET), are installed along the beam line to detect electrons and positrons from γγ interactions. The LET is a small crystal calorimeter detecting leptons of energy between 160 and 230 MeV and installed close to the interaction point (IP). The HET is inserted in the beam pipe at distance of 11 m from the IP and constructed to register scattered particles in the energy range from 430 to 480 MeV. In this region leptons show a clear correlation between energy and deviation from the nominal orbit. Therefore the position detector was chosen. Both taggers will be ready for data-taking for late 2011 [3]. Next phase (STEP-1) is more complex upgrade including the installation of the inner tracker (IT) and two calorimeters. The KLOE-2 physical program required a good accuracy reconstruction in the region close to the IP for corresponding physics tasks: KS decays, KS KL interference, η, η ′ and K ± decays. Moreover, the construction and installation of the IT would be extremely beneficial for the KLOE-2 project. The adopted solution is a cylindrical GEM detector. It will be installed between the beam pipe and the inner wall of drift chamber. The requirements for this detector are good spatial resolution σrϕ ∼ 200 µm, σz ∼ 400 µm and total material budget below 2% of radiation length [4]. Crystal calorimeter (CCALT) will cover the low polar angle region increasing the detector acceptance from 21◦ to 8◦ [5]. New tile calorimeter (QCALT) will be used for detection of photons coming from KL decays inside drift chamber. The STEP-1 is planned to be completed next year [6]. The expected integrated luminosity for two phases is 5 fb−1 and 20 fb−1 respectively. 3

Physics with KLOE-2

There are several physics directions which can benefit of both a larger data sample and an upgraded detector. As in the case of KLOE, collaboration suggested to continue precision studies of CP and CP T symmetries. It’s planned also to start new program described below and devoted to: (i) investigation of the hadronic states produced in γγ interactions; (ii) search of the particles from secluded dark matter sector. For a detailed discussion see Ref. [7]. 3.1

CP T symmetry and quantum mechanics tests

DAΦNE provides a special opportunity for testing quantum mechanics and CP T symmetry in the kaon sector. The quantum interference between two koans in the entangled state in the CP violating channel ϕ → KS KL → π + π − π + π − has been observed for the first time. KLOE has obtained the distribution of ∆t, the difference between two kaon decay times, using 1.5 fb−1 data sample. This distribution was described by function including a decoherence parameter ζSL (ζ0¯0 ). The final result is compatible with a prediction of quantum mechanics and CP T invariance, i.e. ζSL and ζ0¯0 are close to zero [8].

326 Besides, KLOE has obtained a very pure sample of the semileptonic decay KS → π − e+ ν and KS → π + e− ν¯ with an integrated luminosity of 0.41 fb−1 . The equality of the charged asymmetries AS and AL confirms CP T invariance. KLOE value of AS = (1.5 ± 9.6stat ± 2.9syst ) × 10−3 is in good agreement with world data of AL [9]. At KLOE-2, the larger integrated luminosity and better performance of the tracking reconstruction for decays close to the IP, can improve sufficiently above results. Therefore these measurements chosen as benchmarks for planning operating at DAΦNE collider. 3.2

γγ physics

The term “γγ physics” stands for the study of reaction e+ e− → e+ e− γ ∗ γ ∗ → e+ e− X, where X is some final state allowed by conservation laws. For quasireal photons the number of produced events can be evaluated according to: ∫ dF NeeX = Lee σγγ→X (Wγγ )dWγγ , (1) dWγγ

-1

-1

dF/dWγγ × Lee ( MeV nb )

where Lee is the integrated luminosity, Wγγ is the invariant mass of two photons, dF/dWγγ is the γγ flux function (see Fig. 1). High luminosity of the DAΦNE gives us a unique opportunity for precision investigation of lowmass hadronic systems at KLOE-2 [10]. Single pseudoscalar (X = π 0 , √s = 1.4 GeV 10 2 η and η ′ ) production is important π √s = 1.2 GeV ππ for the measurement of two-photon √s = 1.02 GeV 10 decay widths of these mesons using η ηπ for determination of the η − η ′ 1 ηf ,a mixing angle and the η ′ gluonium -1 10 content. Moreover, the transition KK form factors FXγ ∗ γ ∗ (Q2 , 0) can be -2 10 evaluated first time at low Q2 in the space-like region. Special interest is -3 10 0 500 1000 devoted to the scalar resonance at W ( MeV ) X = ππ. The nature (i.e. quark substructure) and existence of the Figure 1: γγ flux as a function of Wγγ to an integrated luminosity f0 (600) or σ, accessible at DAΦNE, corresponding of 1 fb−1 and different center-of-mass energies. are still controversial [11]. ,

0

0

γγ

3.3

Searches for dark forces

The recent astrophysical observations from independent experiments can be explained by the existence of dark matter belonging to secluded gauge sector under which the Standard Model (SM) particles are uncharged. In this case, the secluded sector is associated with light U boson with mass near 1 GeV

327 and coupled to the SM via kinetic mixing. The kinetic mixing parameter ϵ has an order 10−4 −10−2 . Other dark matter particle, the Higgs boson h′ , spontaneously breaks the secluded gauge symmetry [12]. The search of the U boson was performed for ϕ → ηU with η → π + π − π 0 decays using the data sample of 1.5 fb−1 . The decay U → e+ e− is more reliable process to search for KLOE by following reasons: (i) a wide range of U boson mass to acquire; (ii) e± can be identified by time-of-flight measurement. In order to select the η decays, it was taking into account events with two tracks of different charge and two photons giving a best match to the η mass. Also we required two other tracks assigned to e+ e− . Pions coming from the IP were rejected using time-of-flight cuts, and the e± candidates are defined by electronpositron invariant mass (Mee ). The irreducible background ϕ → ηe+ e− was extracted directly from data. Finally, it was obtained a preliminary upper limit on ϵ2 ∼ 1×10−5 in a wide Mee range. This value can be improved sufficiently until 10−6 level with an expected KLOE-2 sample of 20 fb−1 . To obtain a better precision, it’s important to include into analysis other η meson final states, such as η → γγ and η → π 0 π 0 π 0 . The h′ boson can be found in e+ e− → U h′ with U → µ+ µ− assuming h′ to be lighter than the U boson. This work is still in progress and mainly concentrated to the different aspects of background rejection [13]. Acknowledgements The author is grateful to the KLOE-2 collaboration for the kind help in the preparation of this talk and express my personal thanks to Caterina Bloise, Antonio Di Domenico, Erica De Lucia and Viacheslav Kulikov. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]

M.Zobov et al., Phys.Rev.Lett. 104, 174801 (2010). F.Bossi et al., Riv.Nuovo Cim. 31, 531 (2008). D.Babusci et al. (KLOE-2), LNF Note 10/17(P) (2010). F.Archilli et al. (KLOE-2), LNF Note 10/3(P) (2010). M.Cordelli et al., J.Phys.Conf.Ser. 293, 012010 (2011). M.Cordelli et al., Nucl.Instrum.Meth. A617, 105 (2010). G.Amelino-Camelia et al. (KLOE-2), Eur.Phys.J. C68, 619 (2010). A.Di Domenico et al. (KLOE), J.Phys.Conf.Ser. 171, 012008 (2009). F.Ambrosino et al. (KLOE), Phys.Lett. B636, 173 (2006). F.Archilli et al. (KLOE-2), LNF Note 10/14(P) (2010). F.Archilli et al. (KLOE-2), arXiv:1107.3782 (2011). L.Barz`e et al., Eur.Phys.J. C71, 1680 (2011). F.Archilli et al. (KLOE-2), arXiv:1107.2531 (2011).

328 SEARCH FOR HEAVY NEUTRINO IN RARE KAON DECAYS Artur Shaikhiev a Institute for Nuclear Research, 117312 Moscow, Russia Abstract.The neutrino Minimal Standard Model predicts the existence of heavy neutrino with mass O(1) GeV. The mass interval between pion mass and kaon mass is perfectly allowed from the cosmological and experimental points of view. Is was suggested to use E949 data to search for the K + → µ+ νH decay. The allowed heavy neutrino mass region for the analysis is from ≃ 140 MeV to ≃ 280 MeV. The expected sensitivity to BR(K + → µ+ νH ) is about 10 times more than in the previous experiments. We analyzed 5% of all E949 data. We can improve current limit on heavy neutrino existence in the heavy neutrino mass region 140– 280 MeV. The details of analysis are presented.

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Introduction

There are three types of massless neutrino, νe , νµ , ντ , in the Standard Model (SM), but the neutrino oscillations experiments [1–6] confirm that neutrino has mass and mixing. In the other words, the weak eigenstates νe , νµ , ντ are the linear superposition of the mass eigenstates ν1 , ν2 , ν3 . The SM also cannot explain baryon asymmetry of the Universe and dark matter. An extension of the SM by three singlet fermions with masses smaller than the electroweak scale without adding any new physical principles (such as supersymmetry or extra dimensions) or new energy scales (like Grand Unified scale) allows to explain simultaneously the phenomena that cannot be fit to the SM. An example of such a theory is the renormalizable extension of the SM, the νMSM (neutrino Minimal Standard Model) [7, 8]. Dark matter sterile neutrino, νH1 , is likely to have a mass in the O(10) keV region [8, 9]. The masses of νH2 and νH3 should lie in the range from ≃ 150 MeV to ≃ 100 GeV and should be degenerate (∆M2,3 ≪ M2,3 ) to generate baryon asymmetry of the Universe. These two sterile neutrinos are likely to have a masses in the O(1) GeV [8, 9]. Two strategies can be used for the experimental search of these particles. The first one is related to their production. Since they are massive, the kinematics of, for example, two body decays K ± → µ± νµ and K ± → µ± νH is not the same. So the study of kinematics of rare meson decays can constrain the strength of the coupling of heavy leptons using the following expression [10]: Γ(M + → l+ νH ) = ρΓ(M + → l+ νl )|Ul |2 ,

(1)

where M = π, K; l = e, µ; ρ is kinematical factor and lies in the range from 1 to 4 for 0 < mνH < 300 MeV. This strategy have been used in a number of experiments for the search of neutral leptons in the past [11, 12], where the spectra of electrons and muons originating in decays of pions and kaons have a e-mail:

[email protected]

329 been studied. The second strategy is to look for the decays of heavy leptons to hadrons and leptons (CERN PS191 experiment) [13]. The best constraints in the small mass region mνH < 450 MeV are coming from CERN PS191 experiment, giving roughly |Ul |2 < 10−9 in the region 250 MeV< mnuH < 450 MeV. The successful predictions of the Big Bang Nucleosynthesis (BBN) allow to establish a number of lower bounds on the couplings of neutral leptons [9] which decrease considerably the admitted window for the couplings and masses of the neutral leptons. To study the kinematics of two body decay K + → µ+ νH it was suggested to use E949 (BNL, USA) experimental data. 2

E949 experiment

The E949 experiment was aimed to measure the branching ratio of rare kaon decay K + → π + ν ν¯, which is a sensitive test of the SM and new physics effects [14]. The E949 result is [?] +1.15 BR(K + → π + ν ν¯) = (1.73−1.05 ) × 10−10 .

(2)

The E949 detector has axial symmetry in beam direction and consists of several components. Incoming 710 MeV/c kaons stop and decay in scintillating fiber target. The momentum and trajectory of the outgoing charged particles are measured in drift chamber. These particles come to rest in a Range Stack (RS) of 19 layers of plastic scintillator. The primary functions of the RS are energy and range measurements of charged particles and their identification. The detection of any activities coincident with the charged track is very important for suppressing the backgrounds for K + → π + ν ν¯ decay. Photons from Kπ2 , Kµνγ , Kµ3 and other radiative decays are detected by hermetic photons detectors with ≃ 4π solid angle coverage. 2.1

The K + → µ+ νH trigger

The experimental signature of the K + → µ+ νH decay is the same as for the K + → π + ν ν¯ decay (one single charged track with no any detector activity). That’s why we decided to use the main E949 trigger. The worst trigger requirement for heavy neutrino analysis is online pion identification. It requires a signature of π + → µ+ decay in the online stopping counter. The µ+ from the π + → µ+ νµ decay at rest has the kinetic energy of 4 MeV (equivalent range in plastic scintillator is 1 mm) and rarely goes out of the stopping counter. So pulses in the stopping counter recorded by the TDs have double-pulse structure up to ∼ 70 ns. The single-pulse events were rejected. This requirement decreases E949 trigger efficiency to the K + → µ+ νH decay in 20–50 times [15]. More detail description of the E949 experiment may be found in [16].

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The search for K + → µ+ νH is to find additional peak below Kµ2 peak. So we should well understand all background sources that can fake or cover our signal. We simulated the main background sources, Kµνγ , Kµ3 and Kπ2γ decays. After trigger requirements and some offline selection criteria the Kµ3 contribution in the total number of background events is less than 1% of the Kµνγ contribution due to two photons in the final state. The K + → π + π 0 γ decay can be ignored due to three photons in the final state and large rangemomentum pion rejection (particle identification cut). Therefore, the K + → µ+ νµ γ is the dominant background source for the search of the K + → µ+ νH decay. Acceptance for the K + → µ+ νH decay was measured using Monte-Carlo simulation and some monitor triggers. The momentum dependence of acceptance after some cuts and comparison between experimental (5% all data) and simulated muon momentum shape are shown in Fig. 1. The best muon momen-

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tum region for heavy neutrino search is between 140 MeV/c and 210 MeV/c that corresponds 140 MeV < mνH < 280 MeV. The discrepancy between experimental and simulated muon momentum shape around 210 MeV/c is due to photon veto simulation and it is under investigation. To verify our acceptance measurement we calculated Kµ2 and Kµνγ branching ratios. The Kµ2 branching ratio was measured to be 0.5302 ± 0.1478 and it is consistent with PDG value (0.6355 ± 0.0011) within the error. The Kµνγ branching ratio was measured to be (2.3 ± 0.2) × 10−3 for 155 < pµ < 205 while PDG value is equal to (1.4 ± 0.2) × 10−3 for the same muon momentum region.

331 This discrepancy is due to our photon veto acceptance measurement and we are trying to fix it. Total number of stopped kaons is 1.7 × 1012 , so knowing total acceptance for the K + → µ+ νH decay and muon momentum shape (Fig. 1) we can estimate upper limit on |Uµh |2 using expression (1). The result is shown in Fig. 2. So,

Figure 2: Current limits on |Uµh |2 depending on heavy neutrino mass from BBN (lower thin red bound) and from direct searches in the CERN PS191 experiment and rare kaon decays experiment (upper blue bounds). Thick red line is our preliminary result.

we may improve current upper limit on |Uµh |2 in the mass region 140 MeV < mνH < 250 MeV. 4

Conclusion

The νMSM model predicts the heavy neutrino existence with mass in the O(1) GeV region. To study mass region Mπ < mνH < MK it was suggested to use E949 data. We measured total acceptance curve for the K + → µ+ νH decay and estimated upper limit on |Uµh |2 based on 5% experimental data. We can improve current limit on heavy neutrino existence in the heavy neutrino mass region 140–250 MeV. References [1] [2] [3] [4] [5]

S. Fukuda et al., Phys. Rev. Lett. 81, 1562 (1998) Q.R. Ahmad et al., Phys. Rev. Lett. 89, 011301 (2002) M.H. Ahn et al., Phys. Rev. D 74, 072003 (2006) P. Adamson et al., Phys. Rev. Lett. 101, 221804 (2008) K. Eguchi et al., Phys. Rev. Lett. 90, 021802 (2003)

332 [6] M. Apollonio et al., Eur. Phys.J. C 27, 331 (2003) [7] T. Asaka, M. Shaposhnikov, Phys. Lett. B 620, 17 (2005) [8] A. Boyarsky, O. Ruchayskiy, M. Shaposhnikov, Ann.Rev.Nucl.Part.Sci. 59, 191 (2009) [9] D. Gorbunov, M. Shaposhnikov, JHEP, 0710:015, (2007) [10] R. E. Shrock, Phys. Lett. D 24, 1232 (1981) [11] T. Yamazaki et al., in Proceedings of High Energy Physics, vol.1, Leipzig, 1984, p.262. [12] M. Daum et al., Phys. Rev. Lett. 85, 1815 (2000) [13] G. Bernardi et al., Phys. Rev. Lett. B 203, 332 (1988) [14] Andrzej J. Buras, Felix Schwab, Selma Uhlig, Rev.Mod.Phys. 80, 9651007 (2008) A.D. Dolgov et al., Nucl.Phys. B 590, 562 (2000) [15] A. V. Artamonov et al., Phys.Rev.D 79, 092004 (2009) [16] B. Bhuyan et al., E949 TN-K025 (2004) [17] S. Adler et al., Phys. Rev. D. 77, 052003 (2008)

Hadron Physics

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335 ONSET OF DECONFINEMENT AND CRITICAL POINT: NEWS FROM NA49 AND NA61 AT THE CERN SPS Marek Gazdzicki a Goethe University Frankfurt, Germany and Jan Kochanowski University, Kielce, Poland Abstract. In this report a status of the NA49 evidence for the onset of deconfinement as well as the NA61 search for the critical point are briefly discussed.

NA49 and NA61/SHINE are large acceptance hadron experiments which study nucleus–nucleus collisions at the CERN SPS. In the first part of this report a status of the NA49 observation of the onset of deconfinement at the low SPS is discussed in view of new LHC and RHIC data. In the second part the NA61 search for the critical point of strongly interacting matter is briefly presented. 1

NA49: onset of deconfinement

The NA49 evidence for the onset of deconfinement [3,4] is based on the observation that numerous hadron production properties measured in central Pb+Pb collisions change their energy dependence in a common energy domain (start√ ing from sN N ≈ 7.6 GeV (≈ 30A GeV/c beam momentum)) and that these changes are consistent with the predictions for the onset of deconfinement [2]. The four representative plots with the structures referred to as horn, kink and step [4] are shown in Fig. 1. They present the experimental results available in the mid of 2011. The relation between the horn, kink and step structures and the onset of deconfinement is briefly discussed below. More detailed explanation is given in Ref. [4], where a comparison with quantitative models is also presented. The horn. The most dramatic change of the energy dependence is seen for the ratio of particle yields of kaons and pions, Fig. 1 (top-left). The steep threshold rise of the ratio characteristic for confined matter changes at high energy into a constant value at the level expected for deconfined matter. In the transition region (at low SPS energies) a sharp maximum is observed caused by the higher strangeness to entropy production ratio in confined matter than in deconfined matter. This feature is not observed for proton–proton reactions. The kink. The majority of all particles produced in high energy interactions are pions. Thus, pions carry basic information on the entropy created in the collisions. On the other hand, entropy production should depend on the form of matter present at the early stage of collisions. Deconfined matter is expected to lead to a final state with higher entropy than that created by confined matter. Consequently, the entropy increase at the onset of deconfinement results in a e-mail:

[email protected]

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Figure 1: Heating curves of strongly interacting matter: status at the mid of 2011. Hadron production properties √√ (see Ref. [4] for details) are plotted as a function of collision+ energy √ ( sN N and F ≈ sN N ) for central Pb+Pb (Au+Au) collisions: top-left – the ⟨K ⟩/⟨π + ⟩ ratio, top-right – the mean pion multiplicity per participant nucleon, bottom-left – the inverse slope parameter of the transverse mass spectra of K + mesons, bottom-right: the inverse slope parameter of the transverse mass spectra of K − mesons. The observed changes of the energy dependence for central Pb+Pb (Au+Au) collisions are related to: decrease of the mass of strangeness carriers and the ratio of strange to non-strange degrees of freedom (horn: top-left plot), increase of entropy production (kink: top-right plot), weakening of transverse expansion (step: bottom plots) at the onset of deconfinement. The new LHC and RHIC data are included in the plots. The K + /π + ratio is measured by ALICE and STAR at mid-rapidity only and thus the horn plot is shown here for the mid-rapidity data.

337 a steeper increase of the collision energy dependence of the pion yield per participating nucleon. This effect is observed for central Pb+Pb collisions as shown in Fig. 1 (top-right). √√ When passing the low SPS energies the slope of the ⟨π⟩/⟨NP ⟩ vs F ≈ sN N dependence increases by a factor of about 1.3. Within the statistical model of the early stage [2] this corresponds to an increase of the effective number of degrees of freedom by a factor of about 3. The step. The experimental results on the energy dependence of the inverse slope parameter, T , of K + and K − transverse mass spectra for central Pb+Pb (Au+Au) collisions are shown in Fig. 1 (bottom). The striking features of the data can be summarized and interpreted [8] as follows. The T parameter increases strongly with collision energy up to the low SPS energies, where the creation of confined matter at the early stage of the collisions takes place. In a pure phase increasing collision energy leads to an increase of the early stage temperature and pressure. Consequently the transverse momenta of produced hadrons, measured by the inverse slope parameter, increase with collision energy. This rise is followed by a region of approximately constant value of the T parameter in the SPS energy range, where the transition between confined and deconfined matter with the creation of mixed phases is located. The resulting softening of the equation of state, EoS, ‘suppresses’ the hydrodynamical transverse expansion and leads to the observed plateau structure in the energy dependence of the T parameter [8]. At higher energies (LHC and RHIC data), T again increases with the collision energy. The EoS at the early stage becomes again stiff and the early stage pressure increases with collision energy, resulting in a resumed increase of T . In 2011 new results on central Pb+Pb collisions at the LHC and data on central Au+Au collisions from the RHIC beam energy scan program were released. The updated plots [9] are shown in Fig. 1. The RHIC results [6] agree with the NA49 measurements at the onset energies. The LHC data [7] demonstrate that the energy dependence of hadron production properties shows rapid changes only at low SPS energies. A smooth evolution is observed between the top SPS (17.2 GeV) and the current LHC (2.76 TeV) energies. This strongly supports the interpretation of the NA49 structures as due to the onset of deconfinement. Above the onset energy only a smooth change of the quark-gluon plasma properties with increasing collision energy is expected. Consequently, in agreement with the first LHC data, one expects: • an approximate independence of the K + /π + ratio of energy above the the top SPS energy, Fig. 1 (top-left), • a linear increase of the pion yield per participant with F with the slope defined by the top SPS data, Fig. 1 (top-right),

338 • a monotonic increase of the kaon inverse slope parameter with energy above the top SPS energy, Fig. 1 (bottom). 2

NA61: critical point

The confirmation of the relevant NA49 measurements and their interpretation in terms of the onset of deconfinement by the new LHC and RHIC data strengthen the arguments for the planned NA61/SHINE measurements [5] with secondary Be and primary Ar as well as Xe beams in the SPS beam momentum range (13A-158A GeV/c). Properties of the transition region can be studied experimentally in nucleusnucleus collisions only at T , µB values which correspond to collision energies higher than the energy of the onset of deconfinement. This is because signals of the critical point can be observed provided the freeze-out point is close to it. On the other hand, by definition the critical point is located on the transition line. Furthermore, the energy density at the early stage of the collision is, of course, higher than the energy density at freeze-out. Thus, the condition that the freeze-out point is near the critical point implies that the early stage of the system is above (or on) the transition line. This in turn means that the optimal energy range for the search for the critical point lies above the energy of the onset of deconfinement. This general condition limits the search for the critical point to the collision energy range ELAB > 30A GeV. The analysis of the existing experimental data [12] indicates that the location of the freeze-out point in the phase diagram depends on the collision energy and the mass of the colliding nuclei. NA49 pilot data on collisions of medium and light mass nuclei suggest that signals of the critical point are visible in C+C and Si+Si collisions at 158A GeV [10, 11]. These results motivate a systematic search for the critical point. Similar to the study of the properties of the onset of deconfinement, a two-dimensional scan in collision energy and size of the colliding nuclei is required. This scan was already stared by NA61/SHINE and the complete set of data should be registered by the end of 2015. The basic components of the NA61 facility were inherited from NA49. Several important upgrades, in particular, the new and faster TPC read-out, the new Projectile Spectator Detector as well as the installation of He beam pipes, allow to collect data of high statistical and systematic accuracy.

339 Acknowledgments I would like to thank the organizers of the 15th Lomonosov Conference on Elementary Particle Physics in Moscow for their kind invitation to this very interesting event. This work was supported by the German Research Foundation under grant GA 1480/2-1. References [1] U. W. Heinz, M. Jacob, [nucl-th/0002042]. [2] M. Gazdzicki, M. I. Gorenstein, Acta Phys. Polon. B 30, 2705 (1999). [hep-ph/9803462]. [3] C. Alt et al. [NA49 Collaboration], Phys. Rev. C 77, 024903 (2008) [arXiv:0710.0118 [nucl-ex]]. [4] M. Gazdzicki, M. Gorenstein, P. Seyboth, Acta Phys. Polon. B 42, 307 (2011) [arXiv:1006.1765 [hep-ph]]. [5] N. Antoniou et al. [NA61/SHINE Collaboration], CERN-SPSC-2006-034. [6] L. Kumar [ for the STAR Collaboration ], [arXiv:1106.6071 [nucl-ex]], B. Mohanty [ STAR Collaboration ], [arXiv:1106.5902 [nucl-ex]]. [7] J. Schukraft et al. [ for the ALICE Collaboration ], [arXiv:1106.5620 [hep-ex]], A. Toia et al. [ for the ALICE Collaboration ], [arXiv:1107.1973 [nucl-ex]]. [8] M. I. Gorenstein, M. Gazdzicki and K. A. Bugaev, Phys. Lett. B 567, 175 (2003) [arXiv:hep-ph/0303041]. [9] A. Rustamov, indico.cern.ch/conferenceDisplay.py?confId=144745 [10] T. Anticic et al. [ NA49 and NA61/SHINE Collaborations ], PoS EPSHEP2009, 030 (2009). [arXiv:0909.0485 [hep-ex]]. [11] T. Anticic et al. [ NA49 Collaboration ], Phys. Rev. C81, 064907 (2010). [arXiv:0912.4198 [nucl-ex]]. [12] F. Becattini, J. Manninen, M. Gazdzicki, Phys. Rev. C73, 044905 (2006). [hep-ph/0511092].

340 PROTON-PROTON PHYSICS WITH ALICE Ermanno Vercellin a Dipartimento di Fisica dell’ Universit´ a di Torino and INFN Torino, Italy Abstract. The main goal of ALICE (A Large Hadron Collider Experiment) is the study of heavy-ion collisions at the CERN Large Hadron Collider (LHC). In addition to heavy systems, the ALICE physics programme also includes data taking with proton beams. This is primarily aimed at providing reference data for nucleusnucleus collisions, but at the same time allows for a number of genuine pp physics studies. An overview of the ALICE pp results is presented in this paper.

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Although its design is optimized for heavy-ion collisions, ALICE has several features that make it an important contributor to proton-proton physics at the LHC. These include particle identification (PID) over a broad momentum range, excellent determination of secondary vertexes and a very robust tracking with a low pt cutoff. Quarkonia detection is also performed down to vanishing transverse momenta over a wide rapidity range. All together, these characteristics make ALICE ideally suited to perform a comprehensive study of a broad set observables in pp collisions, with emphasis on low-pt phenomena. The main component of ALICE [1] is the central barrel, where hadrons, photons and electrons are measured in the central rapidity region. It consists of high-granularity tracking detectors, operated in a weak solenoidal magnetic field (B = 0.5 T) and of detectors devoted to particle identification. Tracking and PID are performed in the pseudorapidity interval |η| ≤0.9 with full azimuthal coverage. The central barrel also houses a system of electromagnetic calorimeters where photons, neutral mesons and jets are detected. Muons are measured in a dedicated forward spectrometer, covering the pseudorapidity region 2.5≤ η ≤4.0. The ALICE set-up is completed by a set of small detectors, located at large rapidities, devoted to event characterization and to triggering. 2

ALICE pp results

ALICE took part to √ the LHC runs with proton beams by taking data at different c.m. energies ( (s)=0.9, 2.36, 2.76 and 7 TeV). It is worth noting that the data at 2.76 TeV are of special importance in view of heavy-ion physics as this is the same c.m. energy ( per nucleon pair) of the Pb-Pb data, allowing a direct comparison of the two collision systems without energy rescaling. Most of the pp data have been collected at moderate luminosity (typically between 1029 and 1030 cm−2 s−1 ) with minimum-bias and muon triggers. These data samples have allowed to perform several physics studies, which include the a e-mail:

[email protected].

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measurement of inelastic and diffractive cross sections, inclusive measurements of charged particle multiplicity [2–4] and pt distributions [5], measurements of yields and spectra of identified hadrons [7–9], quarkonia [10] and heavy flavors as well as femtoscopy [6] and event fluctuations. An overview of these results is presented in this section, with emphasys on the most recent ones. 2.1

Identified particle spectra

Thanks to the excellent performance of the ALICE PID system, detailed studies of the pt spectra and yields for identified hadrons have been performed [7–9]. As a general comment, it is interesting to note that commonly-used event generators are often unable to reproduce the experimental data; some examples are presented here. The pt distributions for π, K and protons have been measured down to very small pt by combining the information from the different PID detectors. The pt dependence of the K/π ratio at 0.9 and 7 TeV is shown in Fig. 1. The two sets of data points are very close each other, indicating a very weak dependence of the ratio on the c.m. energy. In the same figure the measured ratios are compared to the predictions of PHOJET and PYTHIA (Perugia-0 and D6T tunes), which fail in reproducing the experimental data. The same statement also holds for multi-strange hadrons. The preliminary, pt spectra measured at 7 TeV for Ω and Ξ are presented in Fig. 2; the ratio between ALICE data and the recent P2011 tune of PYTHIA is shown in the same figure. This underpredicts by about a factor of four the Ω data, while the disagreement is even larger for other PYTHIA tunes, such as Z2 or Perugia-0.

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|y|) and √ model calculations for Pb–Pb at sN N = 2.76 TeV, (see [9]).

347 The centrality dependence of the charged-particle multiplicity density at mid√ rapidity in Pb–Pb collisions at sN N = 2.76 TeV measured by ALICE [9] is √ shown on Fig.2. It is very similar to the one measured at sN N = 200 GeV at RHIC bringing another important constraint for the models as noted in [9]. Predictions by models based on initial-state gluon density saturation agree best with the ALICE measurement (Fig.2).

3

Elliptic flow of charged particles in Pb–Pb collisions at √ sN N = 2.76 TeV

The geometrical overlap region of two colliding nuclei and therefore the initial matter distribution at the given impact parameter are anisotropic (almond shaped). If the matter is interacting, this spatial asymmetry is converted via multiple collisions into an anisotropic momentum distribution. The final state hadron azimuthal distribution second coefficient is called elliptic flow [10], it is a response of the dense system to the initial conditions and therefore sensitive to the early and hot, strongly interacting phase of the collision. For this analysis the ALICE Inner Tracking System and the Time Projection Chamber (TPC) were used to reconstruct charged particle tracks. Details of determination of the plane of symmetry (participant plane), of the minimum bias trigger conditions and event selection criteria can be found in [11]. The 2- and 4-particle cumulant flow coefficients, being denoted by ν2 {2} and ν2 {4}, were also analyzed demonstrating different sensitivity to flow fluctuations and nonflow effects. The measurement is performed by ALICE in the central pseudorapidity region |η| < 0.8 and transverse momentum range 0.2 < pt < 5.0 GeV/c. The elliptic flow signal ν2 measured using the 4-particle correlation method, averaged over transverse momentum and pseudorapidity, is 0.087 ± 0.002(stat) ± 0.004(syst) in the 40-50% centrality class. The differential elliptic flow ν2 (pt ) reaches a maximum of 0.2 near pt = 3 GeV/c. Integrated elliptic flow measured by ALICE vs. collision centrality is compared to results from lower energies in Fig. 3. It increases from central to peripheral collisions and reaches a maximum value in the 50-60% and 40-50% centrality class of 0.106 ± 0.001(stat) ± 0.005(syst) and 0.087 ± 0.002(stat) ± 0.004(syst) for the 2- and 4-particle cumulant method, respectively. A continuous increase in the magnitude of integrated elliptic flow measured in the 20-30% centrality class is observed moving from RHIC to LHC energies, see Fig.4. This increase is higher than current predictions from ideal hydrodynamic models. We should also mention here the analysis of higher harmonic components (ν3 , √ ν4 , ν5 ) of anisotropic flow of charged particles in Pb–Pb collisions at sN N = 2.76 TeV which are demonstrating behavior different from that of ν2 {2} [14].

348 Thus the first measurement of the elliptic flow in the Pb–Pb collisions at the LHC confirms the presence of strongly interacting matter and the hydrodynamic behavior of the system. Analysis of the viscosity effects is in progress.

Figure 3: Elliptic flow integrated over the pt range 0.2 < pt < 5.0 GeV/c, as a function of event centrality, for the 2- and 4-particle cumulant methods measured by ALICE (see full description in [11]).

4

Figure 4: Integrated elliptic flow at 2.76 TeV in Pb–Pb 20-30% centrality class and results from lower energies [11].

Dimensions of the system formed in the collision of heavy-ions

The space-time dynamic evolution of the system formed in heavy ion collisions at the LHC is studied by ALICE using Hanbury-Brown-Twiss analysis of the two particle correlation function (HBT) [12], based on the Bose-Einstein enhancement of intensity of identical bosons emitted close by in phase space. In √ the first HBT measurement in central Pb–Pb collisions at sN N = 2.76 TeV at the LHC [13] a growing trend with energy was observed not only for the longitudinal (Rlong ) and the outward but also for the sideward pion source radius. On the Fig.5 the ALICE result (red filled dot) for a product of the three pion HBT radii at kT = 0.3 GeV/c is compared to those obtained for central gold and lead collisions at lower energies at AGS, SPS and RHIC (see in [13]). One can see that pion homogeneity volume formed in Pb–Pb collisions √ at sN N = 2.76 TeV at the LHC [13] is significantly larger than those measured at RHIC. It is also noted [13] that the decoupling time for hadrons at midrapidity, estimated within hydrodynamic scenarios, is proportional to the magnitude of Rlong of the homogeneity region (i.e.to the total duration of the longitudinal expansion). Thus the decoupling time for midrapidity pions from √ the system formed in Pb–Pb collisions at sN N = 2.76 TeV exceeds 10 fm/c, which is 40% larger than at RHIC indicating that the system lives longer as compared to lower energies.

349

Figure 5: Product of the three pion HBT radii at kT = 0.3 GeV/c. The ALICE result (red filled dot) is compared to those obtained for central gold and lead collisions at lower energies at the AGS, SPS and RHIC(see references in [13]).

5

Figure 6: Comparison of RAA in central Pb–Pb collisions at LHC to measurements √ at sN N = 200 GeV by the PHENIX and STAR experiments at RHIC ( [16]).

Particle yield suppression

Suppression of charged particle production at large pt measured in central Pb– √ Pb collisions at sN N = 2.76 TeV vs. pt is shown on Fig.6. The nuclear modification factor RAA is defined in a usual way as a ratio of the charged particle yield at the given pt in Pb–Pb to that of pp collisions, scaled by the number of binary nucleon-nucleon collisions (RAA = 1 in case of no nuclear effects). Results obtained by ALICE [16] show that a more “dramatic”behavior is observed (see Fig.6) than at lower energies at RHIC. The measured suppression of high-pt particles is stronger, which can be interpreted by a denser medium formed in central Pb–Pb collisions at the LHC. Besides high-pt charged particle suppression we can also mention the ongoing analyses of D0 and J/ψ yields. The D0 signal was selected using displaced decay vertices at central rapidity and decays in the forward muon spectrometer 2.5 < |η| < 4 in Pb–Pb colllisions in [17], the result shows a suppression of about a factor of 4-5 for pt > 5 GeV/c. The preliminary ALICE results of J/ψ √ production in Pb–Pb collisions at sN N = 2.76 TeV indicate that J/ψ is suppressed independently on centrality (by the factor ∼ 2). This last experimental result appeared quite unexpected for various theoretical approaches (including sequential melting of ψ ′ and J/ψ, coalescence and particle regeneration models) indicating that, like at RHIC, the J/ψ behavior at the LHC is still to be understood.

350 6

Conclusions and outlook

√ The medium produced in Pb–Pb collisions at sN N = 2.76 TeV at the LHC has in comparison to 200 GeV data at RHIC ∼ 3 times larger energy density, ∼ 2 times larger volume of homogenity region and ∼ 20% larger lifetime (∼ 10 fm/c). It shows the properties of an almost ideal liquid (like at RHIC). It appears to be denser than at RHIC (suppression of high- pt particles is stronger). J/ψ production is suppressed (factor ∼ 2) independently on centrality, this effect is being investigated. During the next heavy-ion run in November 2011 studies will be continued √ by ALICE at the same energy of sN N = 2.76 TeV. A reference run with p-A collisions is being considered for the end of 2012. References [1] A.M. Baldin et al. Sov.J. Nucl.Phys.18,41 (1973);A.M. Baldin, Heavy Ion Interactions at High Energies, report at AIP Conf. Proc. 26, 621 (1975) [2] J.C. Collins, M.J. Perry, Phys. Rev. Lett. 34, 1353 (1975). [3] E.Shuryak, Phys. Lett. B78, 150 (1978). [4] BNL -73847-2005 Formal Report, April 18, 2005 [5] K. Aamodt et al. (ALICE collaboration), J. Instrum. 3, S08002 (2008). [6] ALICE collaboration, J. Phys. G: Nucl. Part. Phys.32, 1295 (2006). [7] see report by E.Vercellin in the current Proceedings (2011). [8] ALICE collaboration, http://arxiv.org/abs/1011.3916, Phys. Rev. Lett., 105: 252301 (2010). [9] ALICE collaboration, http://arxiv.org/abs/1012.1657, Phys. Rev. Lett., 106, 032301 (2011). [10] S. Voloshin and Y. Zhang, Z. Phys. C 70, 665 (1996); A. M. Poskanzer and S. A. Voloshin Phys. Rev. C58, 1671 (1998) [11] ALICE collaboration, http://arxiv.org/abs/1011.3914, Phys. Rev. Lett., 105, 252302 (2010). [12] R. Hanbury Brown, R. Q. Twiss, Phil. Mag. 45, 663 (1954); R. Hanbury Brown, R. Twiss, Nature 178, 1046 (1956). [13] ALICE collaboration, http://arxiv.org/abs/1012.4035, Phys. Lett. B, 696: 328-337 (2011). [14] ALICE collaboration, http://arxiv.org/abs/1105.3865, Phys. Rev. Lett., 107: 032301 (2011). [15] ALICE collaboration, http://arxiv.org/abs/1109.2501 (2011). [16] ALICE collaboration, http://arxiv.org/abs/1012.1004, Phys. Lett. B, 696: 30-39 (2011). [17] Z. Conesa del Valle, report at PANIC, 24 - 29 July 2011, Cambridge, MA, USA; arXiv:1106.1341v1 [nucl-ex] (2011).

351 RESULTS FROM HEAVY-ION COLLISIONS WITH THE CMS DETECTOR Olga Kodolova on behalf of the CMS Collaboration a Institute of the Nuclear Physics, Moscow State University, 119991 Moscow, Russia √ Abstract. The results of the CMS experiment from PbPb collisions at sN N = 2.76 TeV are presented for an integrated luminosity of approximately 7 µb−1 . Using the excellent capabilities of the CMS detector in the wide pseudorapidity range we investigate various hard probes, bulk particle production and collective phenomena.

1

Introduction

The study of the fundamental theory of strong interaction (QCD) in extreme conditions of temperature, density and the parton momentum fraction (low-x) is the motivation for the previous, ongoing and future heavy-ion experiments. The heavy-ion program in CMS is strongly motivated by the J/ψ anomalous suppression discovered at Super Proton Synchrotron (SPS) [1] and several new phenomena observed at the Relativistic Heavy-Ion Collider (RHIC). The top list of observations at RHIC [2]- [3] includes lower hadron multiplicity than expected, the constituent quark number scaling of the elliptic flow and momentum spectra, strong interaction of high pT hadrons with the dense matter and a significant suppression of the J/ψ. According to our current understanding, the regime accessible at the LHC is characterized by the following properties - an initial state dominated by high-density (saturated) parton distribution [4]; copious production of hard probes (jets, high-pT hadrons, heavyquarks, quarkonia); large yields of the weakly interacting perturbative probes (direct photons, dileptons, Z and W± bosons) [5]. The proton-proton physics run at the LHC started in November 2009 at √ center of mass energies s = 0.9, 2.36 and 7 TeV. In November 2010 Pb √ nuclei are collided at sN N = 2.76 TeV. The run finished with an integrated luminosity 8.6 µb−1 delivered and 7.2 µb−1 . For proper normalization of heavyion measurements LHC delivered 241 nb−1 of recorded luminosity for protonproton collisions with the energy 2.76 TeV. 2

CMS detector

CMS is a general purpose detector designed to explore the physics at the TeV energy scale and can provide successful measurements both for proton-proton and nuclei-nuclei collisions at LHC energies. CMS detector has a tracker, a muon system, and calorimeters with full azimuth angle and wide pseudorapidity coverage. The tracker covers |η| < 2.5 by a e-mail:

[email protected]

352 about 76 million silicon pixels and microstrips located inside supercondacting solenoid magnet of 3.8 T and provides a precise track momentum measurements (< 2 % for 100 GeV tracks). Muon chambers are extended up to η = ±2.4. Electromagnetic (ECAL) and hadronic (HCAL) calorimeters cover |η| < 3. CMS is equipped with forward calorimeter (HF) up to η = ±5. CMS has CASTOR calorimeter in pseudorapidity range 5 < |η| < 6.7. Finally, Zero degree calorimeter is located with |η| > 8. A detailed description of CMS detectors can be found in [6]. 3

Bulk measurement in PbPb collisions

The event centrality was measured using energy deposit in the very forward calorimeter in the 5% bins of cross-section. The number of participants was calculated using Glauber model. The charged particle multiplicity per unit of rapidity at mid-rapidity is related to the entropy density in the collisions and fixes the global properties of the produced medium. CMS measures the charged particle multiplicities without magnetic field by two methods: hit counting in the pixel detector using a energy loss dE/dx cut and tracklets, i.e. tracks with pixel detectors together with a vertex constraint. Both methods gives the compatible result of 1612±55 charged particles for the 0-5% centrality bin [7]. Centrality dependence of the multiplicity per unit of pseudorapidity normalized to the number of participants is well reproduced by the saturation model [8]. Transverse energy production grows more rapidly with center-of-mass energy compared to predictions which assume logarithmic scaling [9] and mean transverse energy per particle at 2.76 TeV reaches 1.22±0.15 GeV. Unless the two lead nuclei collide head on, the overlap region will have an elliptical shape. For a liquid, this initial space anisotropy is translated into a final elliptical asymmetry in momentum space. The elliptic flow parameter, v2 is the second harmonic of the azimuthal distribution of hadrons with respect to the reaction plane. CMS measures v2 and higher harmonics using both tracker and calorimeters [10]- [11]. A moderate increase from RHIC to LHC of the integrated v2 scaled by participants eccentricity is observed. Recently, CMS observed long range near side correlation of hadrons pairs up to ∆η = 4 at ∆ϕ = 0 in high-multiplicity pp events at 7 TeV. Long range correlations were also observed in central PbPb at 2.76 TeV [12]−[13]. 4

Hard (“tomographic”) probes of dense QCD matter

Hard probes (particles with large transverse momentum and/or high mass) are of crucial importance for several reasons: (i) they originate from parton scattering with large momentum transfer Q2 and are directly coupled to the fundamental QCD degrees of freedom; (ii) their production timescale is short,

353

Figure 1: Left plot: Measurements of the nuclear modification factor RAA in central heavyion collisions at three different center-of-mass energies as a function of pT for neutral pions and charged hadrons, compared to several theoretical predictions. The error bars on the points are the statistical uncertainties, and the yellow boxes around the CMS points are the systematic uncertainties. The bands for several of the theoretical calculations represent their uncertainties. Right plot: RAA for prompt J/ψ (red squares) overlaid with the non-prompt J/ψ (orange stars) and the Υ (green diamonds), the open symbols indicate the minimum bias result. An uncertainty of 7% on the measured integrated luminosity of the pp data sample is shown as gray box as a global scale uncertainty at RAA =1.

allowing them to propagate and potentially be affected by the medium; (iii) their cross-sections can be theoretically predicted with pQCD. One of the major discoveries at the RHIC is the hadron suppression at relatively high pT hadrons, i.e. jet quenching effect. This effect is visible with the pT dependence of the nuclear modification factor, RAA , which is defined by the ratio of particle yield in heavy-ion collisions to the binary collisions scaled yield in p+p collisions. The RAA dependence on charged hadron pT measured at CMS [14] is shown in Fig. 1 for the 5% most central collisions together with RHIC measurements [17]. No nuclear modification is observed for isolated photons [15] and Z-bosons [16] measured at CMS. The suppression of the quarkonia states has been show as the dependence of the RAA ratio [19] on event centrality (Fig. 1). A comparison of the relative yields of Υ resonances has been performed in PbPb and pp collisions at the same center-of-mass energy per nucleon pair of 2.76 TeV. The double ratio of the Υ(2S) and Υ(3S) excited states to the Υ(1S) ground state in PbPb and pp collisions [19]- [20], [Υ(2S + 3S)/Υ(1S)]PbPb /[Υ(2S + 3S)/Υ(1S)]pp , is found to be 0.31 +0.19 −0.15 (stat.) ± 0.03 (syst.), for muons of pT > 4 GeV/c and |η| < 2.4. 5

Summary

The CMS experiment performed smoothly during the 2010 heavy-ion run period at LHC. CMS has obtained significant statistics of hard probes. Detailed

354 measurements of global properties of medium in PbPb and pp collisions have been performed CMS measurements are consistent with the hypothesis of the hot and dense medium: strong collective effects in the medium, no quenching of weakly and electromagnetically interacting probes, strong quenching of partons, including b-quarks and suppression of quarkonia. Acknowledgments The author wish to thank the CMS colleagues for providing the material and help in presenting the first CMS Heavy-Ion results. References [1] M.C. Abreu et al. (NA50 Coll.), Phys. Lett., B 477, 2000 (2)8. [2] A. Adare et al (PHENIX), Phys.Rev. Lett. 98, 232301 (2007); [3] I. Arsene et al (BRAHMS), Nucl. Phys. A 757, (2005) 1; B. B. Back et al (PHOBOS), Nucl. Phys. A 757, (2005) 28;J. Adams et al (STAR), Nucl. Phys. A 757, (2005) 10; K. Adcox et al (PHENIX), Nucl.Phys. A 757, (2005) 184 [4] D. Kharzeev, E. Levin and M. Nardi, Nucl.Phys. A 747 (2005) 609. [5] CMS Collaboration, CMS TDR Addendum: High-Density QCD with Heavy Ions, J. Phys. G: Nucl. Part. Phys. 34 (2007) 2307. [6] The CMS Collaboration, The CMS experiment at the CERN LHC, JINST 3:S08004, 2008. [7] CMS Collaboration, CMS-PAS-HIN-10-001, JHEP, 08, (2011) 141. [8] Albacete and Dumitru, arXiv 1011.5261v1. [9] CMS Collaboration, CMS-PAS-HIN-11-003, 2011. [10] CMS Collaboration, CMS-PAS-HIN-10-002, 2011. [11] CMS Collaboration, CMS-PAS-HIN-11-005, 2011. [12] CMS Collaboration, CMS-PAS-HIN-11-001, 2011, JHEP, 07 (2011) 076. [13] CMS Collaboration, CMS-PAS-HIN-11-006,2011. [14] CMS Collaboration, CMS-PAS-HIN-10-005, 2011. [15] CMS Collaboration, CMS-PAS-HIN-11-002, 2011. [16] CMS Collaboration, CMS-PAS-HIN-10-003, 2010, Phys.Rev.Lett, 106(2011), 212301. [17] WA98 Collaboration, Eur. Phys. J., C 23 (2002) 225; D. G. dEnterria, Phys. Lett., B 596 (2004) 32; PHENIX Collaboration, Phys. Rev. Lett., 101 (2008) 232301; STAR Collaboration, Phys. Rev. Lett., 91 (2003) 172302. [18] CMS Collaboration Phys.Rev C 84,024906 (2011). [19] CMS Collaboration, CMS-PAS-HIN-10-006, 2010. [20] CMS Collaboration, Phys. Rec. 107, 052302 (2011).

355 ELLIPTIC FLOW IN HEAVY-ION COLLISIONS WITH THE CMS DETECTOR AT THE LHC: FIRST RESULTS Sergey Petrushanko a (for the CMS collaboration) Skobeltsyn Institute of Nuclear Physics, Moscow State University, Leninskiye Gory, 119991 Moscow, Russia Abstract. We report on CMS measurements of charged hadron anisotropic az√ imuthal distributions from PbPb collisions at sN N = 2.76 TeV and their decomposition into a Fourier series up to the 6th coefficient. The results are presented as a function of transverse momentum, centrality and pseudorapidity and cover a broad kinematic range. The relation between the different harmonic coefficients and the scaling with the respective participant eccentricity are studied. These results could provide constraints on the theoretical description of the early dynamics in the hot and dense medium and its transport properties.

1

Introduction

In non-central collisions between two nuclei the beam direction and the impact parameter vector define a reaction plane for each event. A measurement of the azimuthal anisotropy of particle production with respect to the reaction plane is one of the important tools for studying the properties of the dense matter created in ultrarelativistic heavy-ion collisions [1, 2]. As it was shown before, CMS detector at the LHC [3] has a good possibility to provide a precise measurement of global event characteristics [4]. This report is dedicated to CMS measurements of charged√hadron anisotropic azimuthal distributions from PbPb at the energy in c.m.s. s = 2.76 TeV per nucleon pair. 2

Methods

The elliptic flow parameter, v2 , is defined as the second harmonic coefficient in the Fourier expansion of the particle azimuthal distribution with respect to the reaction plane: dN N0 = [1 + 2v1 cos(ϕ − ΨR ) + 2v2 cos 2(ϕ − ΨR ) + ...], dϕ 2π

(1)

where ΨR is the true reaction plane angle and N0 stands for full multiplicity. Then v2 is the average over particles of cos(2(ϕ − ΨR )). The higher-order coefficients of interest are v3 (triangular flow), v4 (quadrangular flow), v5 (pentagonal flow), and v6 (hexagonal flow). There exists a wealth of anisotropic flow measurement methods, each of which has its advantages and limitations. Here we have used the methods: based on the measurement of the reaction plane angle — event plane (EP) [5], 2- and 4-particle cumulants (2, 4) [6, 7], and the Lee-Yang zeros (LYZ) [8, 9]. a e-mail:

[email protected]

356 3

Results and discussion

The vn coefficients were measured using the high-granularity CMS tracker composed of silicon pixel and strip detectors covering the pseudorapidity range of |η| < 2.4. The analysis was performed using 2.31 million PbPb events selected with a minimum bias trigger. A Glauber model MC is used to connect the centrality classes as determined from the data with the number of nucleons participating in the collision, Npart , and the respective eccentricity of the initial nuclear overlap region, part . The main results of the analysis are as follows: • vn (pT ) at |η| < 0.8 for up to 12 centrality classes in the range 0-80%, where pT is the transverse momentum of charged particle; • v2 (η) for 12 centrality classes; • integrated vn at |η| < 0.8, and vn /part as a function of Npart . The systematic uncertainties include those common to all methods, as well as method-specific ones [10, 11]. The results of v2 (pT ) obtained by four methods at mid-rapidity are presented in Fig. 1, for 12 centrality classes. The value of v2 increases from central to peripheral collisions as expected if the anisotropy is driven by the spatial anisotropy in the initial state. The transverse momentum dependence shows a rise of v2 up to pT ∼ 3 GeV/c and then a decrease. This behavior is expected if hydrodynamic flow dominates up to pT = 2 ÷ 3 GeV/c.

Figure 1: Comparison of all four methods for determining v2 as a function of pT at |η| < 0.8 for the 12 centrality classes. The error bars show the statistical uncertainties only.

357 The four methods show differences consistent with their expected sensitivities to non-flow contributions. The method which is most affected by these is the 2-particle cumulant, because the integral and differential v2 were determined in the same η-range. For the event plane method we have applied the separation between the particles used in the event plane determination and the particles used to measure the flow. The 4th-order cumulant and the Lee-Yang zeros method are much less affected by such non-flow contributions. The pseudorapidity dependence of the anisotropy parameter is of interest because it provides constraints on the description of the system evolution in the longitudinal direction. The v2 (η) results presented in Fig. 2 cover a broad pseudorapidity range of |η| < 2.4 for the tracks with 0.3 < pT < 3.0 GeV/c. Only a weak η-dependence is observed, except in the most peripheral events, which are more affected by non-flow correlations.

Figure 2: Pseudorapidity dependence of v2 for all four methods in 12 centrality classes. The error bars show the statistical uncertainties, and boxes give the systematic uncertainties.

Figures 3 and 4 display integrated vn and the eccentricity scaled value, vn /part as a function of Npart at mid-rapidity. The v3 value is weakly dependent on Npart and remains sizable even in the most central collisions. This is in contrast to the behavior of v2 , which rapidly decreases with Npart . The higher order even harmonics, v4 and v6 , show similar trends as v2 , although this is less pronounced in the case of v6 . These measurements may be used in conjunction with hydrodynamics calculations as a test of the theoretical models of the initial eccentricities.

358

Figure 3: Integrated vn as a function of Npart for |η| < 0.8. The error bars show the statistical uncertainties, the colored bands — the systematic ones.

4

Figure 4: Integrated vn /part as a function of Npart for |η| < 0.8. The error bars show the statistical uncertainties, the colored bands — the systematic ones.

Summary

We have presented the detailed measurements of the harmonic flow coefficients √ from PbPb collisions at sN N = 2.76 TeV as a function of pT , pseudorapidity and Npart for a broad range of collision centralities, and obtained with several methods. These measurements taken together may aid in the systematic validation of different approaches to the modeling of heavy-ion collisions and lead to a reliable determination of the properties of the produced hot QCD matter. Acknowledgments I would like to thank the members of the CMS collaboration for providing the materials. Many thanks for the Organizers of 15th Lomonosov Conference on Elementary Particle Physics for possibility to present the talk. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]

J.Y.Ollitrault, Phys.Rev. D 46, 229 (1992). H.Sorge, Phys. Rev.Lett. 82, 2048 (1999). CMS Collaboration, JINST 3, S08004 (2008). D.d’Enterria et al., J.Phys. G 34, 2307 (2007). A.M.Poskanzer, S.A.Voloshin, Phys.Rev. C 58, 1671 (1998). N.Borghini, P.M.Dinh, J.Y.Ollitrault, Phys.Rev. C 64, 054901 (2001). N.Borghini, P.M.Dinh, J.Y.Ollitrault, arXiv:nucl-ex/0110016. R.S.Bhalerao, N.Borghini, J.Y.Ollitrault, Nucl.Phys. A 727, 373 (2003). N.Borghini, R.S.Bhalerao, J.Y.Ollitrault, J.Phys. G 30, S1213 (2004). CMS Collaboration, CMS PAS HIN-10-002, CERN CDS 1347788 (2011). CMS Collaboration, CMS PAS HIN-11-005, CERN CDS 1361385 (2011).

359 FORWARD JETS AND FORWARD-CENTRAL JETS AT CMS Grigory Safronov a for the CMS Collaboration Institute for Theoretical and Experimental Physics, B. Cheryomushkinskaya 25, 117218 Moscow, Russia Abstract. We report on a measurement of the inclusive production of forward jets as √ well as of associated production of forward and central jets in pp collisions at s = 7 TeV. Forward jets are reconstructed with the anti-kT (R = 0.5) algorithm in the Hadronic Forward (HF) calorimeter at pseudorapidities 3.2 < |η| < 4.7, in the transverse momentum range pT = 35 – 140 GeV/c. The single differential cross section as function of the forward and central jet transverse momentum is presented and compared to next-to-leading order perturbative QCD calculations, the PYTHIA and HERWIG parton shower event generators, as well as to the CASCADE Monte Carlo.

1

Introduction

Jet production in hadron-hadron collisions is sensitive to the underlying partonic QCD processes, to the details of parton radiation and to the parton density functions (PDF) of the colliding hadrons. Measured jet cross sections at large transverse momenta (pT ) are successfully described by perturbative QCD (pQCD) calculations based on Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equation [1–4] over several orders of magnitude when jets belong to central rapidities [5]. Calorimetric coverage of the CMS detector [6] extends to pseudorapidity |η| < 5.0 which allows to measure jet production at previously unexplored forward rapidities. Measurements with jets in forward region allow to access small values of momentum fraction of incoming parton, x, where PDFs are less constrained by DIS data. In jet √ production at large c.m. energy contribution of semihard parton interactions ( s/2 >> pT > ΛQCD ) would become significant, such interactions are described by Balitski-FadinKuraev-Lipatov (BFKL) [7–9] kinematics regime. BFKL contribution is enhanced for multijet production involving jets with large rapidity separation [10]. Measurements of simultaneous production of forward-central jets or forwardbackward jets may reveal effects beyond conventional DGLAP description. Jet clustering algorithm used by CMS is anti-kT (R=0.5) [11]. For the analyses described here it is applied to calorimetric√energy deposits. Presented measurements are performed in pp collisions at s = 7TeV c.m. energy recorded in 2010. 2

Inclusive forward jet cross section measurement

Measurement of inclusive jet production at pseudorapidities 3.2 < |η| < 4.7 is performed in the analysis at Ref. [12]. The pT range considered is 35 < pT < a e-mail:

[email protected]

360

Figure 1: Ratio of forward jet inclusive cross section measurement to predictions of various MC generators and pQCD calculations.

150. Measurement corrected for detector effects is compared with predictions obtained from MC generators PYTHIA 6.422 [13], PYTHIA 8.135 [14], HERWIG6.510.3 [15] (with underlying event modelled with Jimmy [16]), and CASCADE 2.2.04 [17]. CASCADE MC generator accounts for combined DGLAP + BFKL evolution. Also the data is compared to NLO pQCD predictions obtained either at the parton level with NLOJET++ [18] or with POWHEG package [19] matched with PYTHIA parton showers. Measurements are described within experimental and theoretical uncertainty by all MC generators and pQCD NLO calculations considered. 3

Measurement of cross section of simultaneous productions of forward and central jets

Production of forward jets was measured for the case when forward jet is accompanied by central jet in the analysis at Ref. [20]. For each event it was required that there is at least one jet with pT > 35 GeV present in each of pseudorapidity ranges of |η| < 2.8 and 3.2 < |η| < 4.7. Measured cross sections are compared with predictions from PYTHIA 6, PYTHIA 8, HERWIG 6 + Jimmy, HERWIG++ [21], CASCADE, POWHEG matched with PYTHIA and HERWIG parton showers and HEJ [22] an MC generator which also, like CASCADE, accounts for the BFKL effects in jet production in hadron collisions. While the description of forward cross-section is more successfull, description of central jet production shows substantial discrepancies for PYTHIA, POWHEG+PYTHIA and CASCADE (Fig.2). Better agreement is demonstrated for HERWIG and HEJ.

361

Figure 2: Cross section of production of central jets associated with forward jets production compared to various MC generator predictions.

Figure 3: Measurement of R = σincl /σexcl corrected for detector effects and compared to various MC generator predictions.

4

Measurement of inclusive and exclusive dijet production ratio at large rapidity intervals

A measurement of inclusive over exclusive dijet production ratio R = σincl /σexcl at large rapidity intervals is a sensitive probe for effects beyond DGLAP description [23]. For the measurement at Ref. [24] jets with pT > 35 GeV and y < 4.7, where y is jet rapidity, were used. Inclusive dijets are defined as all pairwise combinations of jets passing the selection, exclusive dijets are jet pairs from events where just two jets are found. Measurement corrected for the detector effects was compared to predictions of DGLAP-motivated MC generators PYTHIA 6, HERWIG 6 and HERWIG++. It was found that the measurement is well described by PYTHIA 6 tunes while HERWIG++ and HERWIG 6 predictions significantly overestimate the ratio R especially at large values of |∆y| (Fig.3).

362 5

Conclusions

It has been shown that variety of MC predictions for inclusive jet production in forward region are in good agreement with the data. At the same time MC description of measurements involving dijets with large rapidity separation becomes problematic. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24]

V.N.Gribov and L.N.Lipatov, Sov. J Nucl. Phys. 15 (1972). L.N.Lipatov, Sov. J Nucl. Phys. 20 (1972) 94. Yu.L.Dokshitzer, Sov. Phys. JETP 46 (1977) 641. G.Altarelli and G.Parisi, Nucl. Phys. B 126 (1977) 298. CMS collaboration, CMS PAS QCD-10-011 (2011). CMS collaboration, JINST 0803 (2008) S08004. E.A.Kuraev, L.N.Lipatov and V.S.Fadin, Sov. Phys. JETP 44 (1976) 443. E.A.Kuraev, L.N.Lipatov and V.S.Fadin, Sov. Phys. JETP 45 (1977) 199. Ya.Ya.Balitskii and L.N. Lipatov, Sov. J Nucl. Phys. 28 (1978) 822. A.H.Mueller, H.Navelet, Nucl. Phys. B 282 (1987) 727. M.Cacciari, G.P. Salam and G. Soyez, JHEP 04 (2008) 063. CMS Collaboration, CMS PAS FWD-10-003 (2011). T.Sj¨ ostrand, S.Mrenna and P.Skands, JHEP 05 (2006) 026. T.Sj¨ ostrand, S.Mrenna and P.Skands, Comput. Phys. Comm. 178 (2008) 852. G.Marchesini et al., Comput. Phys. Comm. 67 (1992) 465-508. J.M.Butterworth et al., Comput. Phys. Comm. C72 (1996) 465-508. H.Jung, S.Baranov, M.Deak et al., Eur. Phys. J. C79 (2010) 1237-1249. Z.Nagy, Phys. Rev. D68 (2003) 094002. S.Alioli, K.Hamilton, P. Nason et al., JHEP 1104 (2011) 081. CMS Collaboration, CMS PAS FWD-10-006 (2011). M.Bahr et al., Eur. Phys. J. C58 (2008) 639-707. J.R.Andersen, J.M.Smillie, JHEP 1001:039 (2010). V.T.Kim, G.B.Pivovarov, Phys. Rev. D 53 (1996) 6. CMS Collaboration, CMS PAS FWD-10-014 (2011).

363 HADRONIZATION EFFECTS IN INCLUSIVE

τ

DECAY

A.V. Nesterenko a BLTPh JINR, Dubna, 141980, Russian Federation Abstract. It is shown that the nonperturbative effects due to hadronization play a crucial role in low–energy strong interaction processes. Specifically, such effects impose a stringent constraint on the infrared behavior of the Adler function and play an essential role in the theoretical analysis of inclusive τ lepton decay.

1 Introduction This paper briefly presents the results of the studies of effects due to hadronization in the theoretical description of inclusive τ lepton decay [1–8]. In this strong interaction process the experimentally measurable quantity is [9, 10] Rτ =

Γ(τ − → hadrons− ντ ) J=0 J=1 J=0 J=1 = Rτ, V + Rτ,V + Rτ,A + Rτ,A + Rτ,S . Γ(τ − → e− ν¯e ντ )

(1)

J=1 In what follows we shall restrict ourselves to the consideration of parts Rτ, V J=1 and Rτ,A . The theoretical prediction for these quantities reads

J=1 τ,V/A

R

( ) Nc ′ = |Vud |2 SEW ∆V/A QCD +δEW , 2

∆

V/A QCD

∫ =2

Mτ2

f m2V/A

( s ) ds RV/A (s) 2 , (2) 2 Mτ Mτ

where Nc = 3 is the number of colors, |Vud | = 0.9738 ± 0.0005 is Cabibbo– ′ Kobayashi–Maskawa matrix element [11], SEW = 1.0194 ± 0.0050 and δEW = V/A 0.0010 stand for the electroweak corrections (see Refs. [12–14]), and ∆QCD denotes the QCD contribution. In Eq. (2) Mτ = 1.777 GeV is the mass of τ lepton [11], mV/A stands for the total mass of the lightest allowed hadronic decay mode of τ lepton in the corresponding channel, f (x) = (1 − x)2 (1 + 2x), and [ ] 1 1 RV/A (s) = lim ΠV/A (s+iε)−ΠV/A (s−iε) = Im lim ΠV/A (s+iε), (3) ε→0+ 2πi ε→0+ π with ΠV/A (q 2 ) being the hadronic vacuum polarization function. The superscripts “V” and “A” will only be shown when relevant hereinafter. In general, it is convenient to perform the theoretical analysis of inclusive τ lepton hadronic decay in terms of the Adler function [15] D(Q2 ) = −

d Π(−Q2 ) , d ln Q2

Q2 = −q 2 = −s.

(4)

In the framework of perturbation theory its ultraviolet behavior can be approximated by power series in the strong running coupling αs (Q2 ) [ ]j ∑ℓ (ℓ) D(Q2 ) ≃ Dpert (Q2 ) = 1 + dj αs(ℓ) (Q2 ) , Q2 → ∞, (5) j=1

a e-mail:

[email protected]

364 (1)

where at the one–loop level (i.e., for ℓ = 1) αs (Q2 ) = 4π/(β0 ln z), z = Q2 /Λ2 , β0 = 11−2nf /3, Λ denotes the QCD scale parameter, nf is the number of active flavors (nf = 2 is assumed throughout this paper), and d1 = 1/π. In what follows we shall restrict ourselves to the one–loop level (ℓ = 1). 2 Perturbative approach In this Section we shall study the massless limit, that implies that the masses of all final state particles are neglected. In this case, by making use of definitions (3) and (4), and additionally employing Cauchy theorem, the quantity ∆QCD (2) can be represented as ∫ π ( )( ) 1 D Mτ2 eiθ 1 + 2eiθ − 2ei3θ − ei4θ dθ, ∆QCD = (6) 2π −π see, e.g., papers [10, 12, 16] and references therein. In fact, the only available option within perturbative approach is to directly use in the theoretical expression1 for ∆QCD the perturbative approximation of Adler function Dpert (Q2 ) (5), which contains unphysical singularities at low energies. In this case Eq. (6) eventually takes the form (see Refs. [7, 8] for the details) ( 2) ∫ π 4 Mτ λA1 (θ) + θA2 (θ) ∆pert = 1 + λ = ln dθ, , (7) 2 2 β0 0 π(λ + θ ) Λ2 where A1 (θ) = 1+2 cos(θ)−2 cos(3θ)−cos(4θ), A2 (θ) = 2 sin(θ)−2 sin(3θ)−sin(4θ). 1.6

1.6

V

A QCD

QCD

1.2

1.2

0.8

0.8

0.4

0.4

, GeV

, GeV 0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Figure 1: Comparison of perturbative expression ∆pert (7) (solid curves) with experimental data (8). The left and right plots correspond to vector and axial–vector channels, respectively.

It is worth noting here that perturbative approach gives identical predictions V A for functions ∆V/A QCD (2) in vector and axial–vector channels (i.e., ∆pert ≡ ∆pert ). However, their experimental values are different, namely [9, 10, 17] ∆Vexp = 1.221 ± 0.057, 1

∆Aexp = 0.748 ± 0.032.

(8)

Despite of the fact, that Eq. (6) is only valid for a “true physical” Adler function Dphys (Q2 ), which possesses correct analytic properties in Q2 –variable.

365 For vector channel (the comparison of perturbative result (7) experimental ) ( with+26 ) data (8) gives Λ = 465+140 MeV (the second value, Λ = 1646 −154 −29 MeV, will not be considered herein), see Fig. 1. As for the axial–vector channel, the perturbative approach fails to describe experimental data on τ lepton decay. 3 Dispersive approach It is crucial to emphasize that the analysis presented in Sect. 2 entirely leaves out the effects due to hadronization, which play an important role in the studies of strong interaction processes at low energies. Such effects were properly accounted for in the framework of Dispersive approach to QCD, that has eventually led to the following integral representations for functions (3) and (4) (see Refs. [3, 4, 6, 7] for the details): ( )3/2 ( )∫ ∞ m2 dσ m2 R(s) = 1 − , (9) +θ 1− ρ(σ) s s σ s ∫ ∞ ( )] σ − m2 dσ 3 3u(ξ) [ ξ ρ(σ) D(Q2 ) = 1+ + ln 1 + 2ξ 1 − u(ξ) + . (10) ξ 2ξ ξ + 1 m2 σ + Q2 σ It is worth noting that Eq. (9) by construction automatically takes into account the effects due to analytic continuation of spacelike theoretical results into timelike domain and Eq. (10) embodies the nonperturbative constraints, which relevant dispersion relation imposes on the Adler √ function. In Eqs. (9) and (10) θ(x) denotes the unit step–function, u(ξ) = 1 + 1/ξ, ξ = Q2 /m2 , and ρ(σ) is the spectral density. For the latter the following expression will be employed [7]: ρ(σ) =

4 Λ2 1 + , 2 β0 ln (σ/Λ2 ) + π 2 σ

(11)

see also Refs. [1, 2, 6, 18]. In the right–hand side of Eq. (11) the first term is the one–loop perturbative contribution, whereas the second term represents intrinsically nonperturbative part of the spectral density. Within the approach on hand the quantity ∆V/A QCD (2) ultimately takes the following form: ) ∫ ∞ ( ) ( √ 5 2 3 3 σ dσ V/A ∆QCD = 1 − ζV/A 1 + 6ζV/A − ζV/A + ζV/A + H ρ(σ) 2 2 8 16 M σ mV/A τ ( ) [ ] ) √ 1 3 2 ( 1 2 −3ζV/A 1 + ζV/A − ζV/A ln 1 + 1 − ζV/A − 1 , (12) 8 32 ζV/A where ζV/A = m2V/A /Mτ2 , H(x) = g(x)θ(1 − x) + g(1)θ(x − 1) − g(ζV/A ), and g(x) = x(2 − 2x2 + x3 ), see papers [7, 8] and references therein for the details. The comparison of obtained result (12) with experimental data (8) yields nearly( identical) values of QCD scale parameter Λ (in both channels, namely, ) Λ = 412 ± 34 MeV for vector channel and Λ = 446 ± 33 MeV for axial– vector one, see Fig. 2. Additionally, both these values agree very well with perturbative estimation of QCD scale parameter described in Sect. 2.

366 1.6

1.6

V

A QCD

QCD

1.2

1.2

0.8

0.8

0.4

0.4

, GeV

, GeV 0.00

0.25

0.50

0.75

0.00

0.25

0.50

0.75

Figure 2: Comparison of expression ∆QCD (12) (solid curves) with experimental data (8). The left and right plots correspond to vector and axial–vector channels, respectively.

4 Conclusions The significance of effects due to hadronization in the theoretical description of inclusive τ lepton decay is convincingly demonstrated. The Dispersive approach to QCD has proved to be capable of describing experimental data on τ lepton hadronic decay in vector and axial–vector channels. The vicinity of values of QCD scale parameter Λ obtained in both channels testifies to the self–consistency of employed approach. References [1] A.V. Nesterenko, Phys. Rev. D 64, 116009 (2001). [2] A.V. Nesterenko and J. Papavassiliou, Phys. Rev. D 71, 016009 (2005). [3] A.V. Nesterenko and J. Papavassiliou, J. Phys. G 32, 1025 (2006). [4] A.V. Nesterenko, SLAC eConf C0706044, 25 (2008). [5] M. Baldicchi, A.V. Nesterenko, G.M. Prosperi, and C. Simolo, Phys. Rev. D 77, 034013 (2008). [6] A.V. Nesterenko, Nucl. Phys. B (Proc. Suppl.) 186, 207 (2009). [7] A.V. Nesterenko, arXiv:1106.4006 [hep-ph]. [8] A.V. Nesterenko, in preparation. [9] S. Schael et al. [ALEPH Collaboration], Phys. Rept. 421, 191 (2005). [10] M. Davier, A. Hocker, and Z. Zhang, Rev. Mod. Phys. 78, 1043 (2006). [11] K. Nakamura et al. [Particle Data Group], J. Phys. G 37, 075021 (2010). [12] E. Braaten, S. Narison, and A. Pich, Nucl. Phys. B 373, 581 (1992). [13] W.J. Marciano and A. Sirlin, Phys. Rev. Lett. 61, 1815 (1988). [14] E. Braaten and C.S. Li, Phys. Rev. D 42, 3888 (1990). [15] S.L. Adler, Phys. Rev. D 10, 3714 (1974). [16] F. Le Diberder and A. Pich, Phys. Lett. B 286, 147 (1992); 289, 165 (1992). [17] R. Barate et al. [ALEPH Collaboration], Eur. Phys. J. C 4, 409 (1998). [18] A.V. Nesterenko, Phys. Rev. D 62, 094028 (2000); Int. J. Mod. Phys. A 18, 5475 (2003); Nucl. Phys. B (Proc. Suppl.) 133, 59 (2004).

367 EXPERIMENTAL SIGNATURES OF SUPERSTRONG MAGNETIC FIELDS IN HEAVY-ION COLLISIONS

a,b

a,c

Pavel Buividovich a , Mikhail Polikarpov b , Oleg Teryaev c Institute for Theoretical and Experimental Physics, 117218 Moscow, B. Cheremushkinskaya str. 25 Joint Institute for Nuclear Research, 141980 Dubna, Joliot-Curie str. 6

Abstract.We review some experimental consequences of the presence of superstrong magnetic fields of order of the nuclear scale in noncentral heavy-ion collisions. We present lattice estimates for the strength of the Chiral Magnetic Effect (CME) for different quark flavours and argue that the dependence of the anisotropy of the distribution of emitted hadrons on their flavor content might be used as another experimental evidence of the CME.

1

Introduction

It has been realized recently that in heavy-ion collision experiments hadronic matter is affected not only by extremely high temperatures and densities, but also by superstrong magnetic fields with field strength being comparable to hadron masses. Such superstrong fields are created due to the relative motion of heavy ions themselves, since they carry large charge Z ∼ 100 [1]. Obviously, the magnetic field is perpendicular to the collision plane, which can be reconstructed in experiment from the angular distribution of produced hadrons [2]. There is no direct experimental way to measure the absolute value of the field strength, but it can be estimated in some microscopic transport model, such as the Ultrarelativistic Quantum Molecular Dynamics model (UrQMD) [3]. Probably the most notable effect which arises due to magnetic fields in heavyion collisions is the so-called Chiral Magnetic Effect. The essence of the effect is the generation of electric current along the direction of the external magnetic field in the background of topologically nontrivial gauge field configurations [1,4]. Such generation is not prohibited by P-invariance, since topological charge density is a pseudoscalar field and thus nonzero topological charge explicitly breaks parity. However, since QCD is parity-invariant, the net current or the net electric charge should vanish when averaged over multiple collision events. Nevertheless, the nontrivial effect can still be detected if one considers dispersions of electric current or electric charge [5, 6]. Experimentally, the Chiral Magnetic Effect manifests itself as the dynamical enhancement of fluctuations of the numbers of charged hadrons emitted above and below the reaction plane [2, 7–9]. a e-mail:

[email protected] [email protected] c e-mail: [email protected] b e-mail:

368 In this paper we give some estimates of the expected experimental signatures of superstrong magnetic fields, basing on the lattice data. In Section 2 we consider the Chiral Magnetic Effect and argue that its strength should decrease with increasing quark mass, which can be used to discriminate between the CME and other possible effects which might result in preferential emission of charged hadrons in the direction perpendicular to the reaction plane. 2

Chiral magnetic effect

Chiral Magnetic Effect is usually characterized by the following experimental observables, suggested first in [8]:

aab =

Nb Ne Na ∑ 1 ∑ 1 ∑ cos (ϕia + ϕjb ) , Ne e=1 Na Nb i=1 j=1

(1)

where a, b = ± denotes hadrons with positive or negative charges, respectively, Ne is the number of events used for data analysis, Na and Nb are the total multiplicities of positively/negatively charged particles produced in each event, and ϕia , ϕjb are the angles w.r.t. the reaction plane at which the hadrons with labels i and j are emitted. Summation in (1) goes over all produced hadrons. In practice, only sufficiently energetic particles are considered. The main signatures of the CME is the growth of aab with impact parameter, as well as the negativity of a++ and a−− and the positivity of a+− [2, 7– 9]. However, it has been pointed out recently that these results can also be explained by other effects, such as the influence of nuclear medium on jet formation [10] and other in-medium effects [11]. It is therefore important to think about more refined experimental tests of the CME. Our main message in this paper is that the dependence of the charge fluctuations on quark mass can be used to discriminate between the CME and other possible phenomena which contribute to the observed asymmetry of charge fluctuations. Indeed, the CME emerges due to fluctuations of quark chirality [1], which are suppressed when the quark mass is increased. The dependence of the observables (1) on the quark mass can be studied if one sums separately over charged mesons with different quark content, e.g. ¯ d¯ ud¯ and d¯ u (charged pions), u¯ s and u ¯s (charged kaons) or u ¯c, c¯u, dc, c (Dmesons). The observables aab should then decrease with the meson mass. The dependence of aab on the centrality of the collision should also become weaker. Here we give a rough estimate of this effect basing on the results of lattice simulations. Let us first note that the observables aa,b can be expressed in terms of the differences of multiplicities of charged hadrons emitted above and below the

369

Figure 1: Schematic view of the collision geometry. The fireball is the hatched region of volume V ∼ 4π (R − b/2)3 within the intersection of two heavy ions of radius R each. 3

reaction plane [1]: aab =

c ⟨ ∆a ∆ b ⟩ , ⟨ Na ⟩⟨ Nb ⟩

(2)

where a, b = ±, ∆± are the differences of the multiplicities of hadrons with positive or negative charges above or below the reaction plane, respectively. The factor c depends on the hydrodynamical evolution of hadronic matter, and is usually close to unity. For multiplicities ⟨ Na ⟩ ∼ 1000 one can also with a good precision neglect the initial charge of heavy ions Z ∼ 100, and assume that ⟨ Na ⟩ = ⟨ Nb ⟩ = Nq , where Nq is the mean multiplicity of the same-charge hadrons per event. Lattice results can be compared to experimental data by considering the quantity a++ + a−− − 2a+− , which can be expressed solely in terms of the difference ∆Q = ∆+ − ∆− of net charges of hadrons emitted above and below the reaction plane: 2

a++ + a−− − 2a+− =

2

⟨ (∆Q) ⟩ ⟨ (∆+ − ∆− ) ⟩ = , 2 Nq Nq2 2

(3)

In turn, the dispersion of the charge difference ⟨ (∆Q) ⟩ can be related to the vacuum expectation values of the squared current densities ⟨ jµ2 (x) ⟩ [5]. The contribution of each quark flavor f = u, d, s, c to the total electromagnetic current is jµf (x) = q¯f γµ q f . We do not consider here the third-generation quarks, which are extremely rarely produced in heavy-ion collisions. 2 The simplest model which allows to express ⟨ (∆Q) ⟩ in terms of ⟨ jµf 2 (x) ⟩ is the model of spherical fireball, which emits positively and negatively charged

370 hadrons from its surface with intensity proportional to ⟨ jµf 2 (x) ⟩. This leads to the following relation [5]: ( ( ) ( )2 ) 2 4πτ 2 ρ2 r2 f f a++ + a−− − 2a+− = ⟨ j∥ ⟩ + 2⟨ j⊥ ⟩ , (4) 3Nq2 f where j∥f (x) and j⊥ (x) are, respectively, the currents along the magnetic field and perpendicular to it, τ is some characteristic collision time, r is the fireball radius and ρ is some typical correlation length for electric charge density in the fireball. In our estimates, we take τ ∼ 0.3 fm (this is a typical decay time for the magnetic field in heavy-ion collisions [3]), ρ ∼ 0.2 fm, which are reasonable parameters for, say, gold-gold collisions at 60 GeV/nuclon. We also assume that the fireball is a sphere with radius r = R − b/2 within the overlapping region between the two heavy ions of radius R which collide at impact parameter b. The net multiplicity Nq and the impact parameter b as the functions of collision centrality can be found in Table 1 in [1]. For simplicity, we assume that f2 ⟨ (jµ ) ⟩ are approximately constant on the surface of the fireball. Note also, that in order to exclude the effects related to the dependence of multiplicities of strange and charmed mesons on the collision centrality, which might be different from that of light mesons, we normalize the charge of emitted hadrons by the square of the total multiplicity of all hadrons. Several technical remarks are in order. First, we assume that the matter within the fireball is in the state of thermal equilibrium, and thus the expectation values ⟨ jµf 2 ⟩ can be calculated from gauge theory in Euclidean space. We also assume that the magnetic field is uniform and nearly time-independent. Of course, these are rather rough approximations, but we are aiming here at qualitative rather than quantitative estimates. We have calculated the currents in SU (2) lattice gauge theory with background magnetic field both in the confinement phase, neglecting the contribution from the virtual quark loops (quenched approximation). A comparison with SU (3) gauge theory suggests that this is a reasonable approximation [12]. A more detailed study has shown also that in the deconfinement phase the dispersions of local current densities are practically independent of the magnetic field [5], thus we do not consider here this case. The expectation values ⟨ jµf 2 ⟩ contain also the ultraviolet divergent part, which we have removed by subtracting the corresponding expectation values at zero temperature and zero magnetic field. The masses of the valence quarks took the values mq = 50 MeV (for u and d quarks), mq = 110 MeV (for s-quark) and mq = 1 GeV (for c-quark). The lowest value of the quark mass is dictated by the numerical stability of our algorithm. Thus our calculations of ⟨ jµf 2 ⟩ at mq = 50 MeV should be considered as only the lower bound for ⟨ jµf 2 ⟩ at realistic masses of u and d quarks. On Fig. 2 we compare the quantity a++ + a−− − 2a+− calculated for the experimental data by the STAR collaboration [9] with the estimate (4) based

371

103 (a++ + a-- - 2 a+-)

10

STAR data Light mesons K-mesons D-mesons

1

0.1

0.01

0.001 0

0.1

0.2

0.3

0.4

0.5

0.6

Centrality Figure 2: Comparison of the quantity a++ + a−− − 2a+− for the experimental data by the STAR collaboration [2] with the estimates (4) based on the results of lattice simulations at different quark masses.

on the results of lattice simulations at different quark masses and different temperatures. In order to match the value of the magnetic field strength in experiment and in simulations, we take the rough estimate from Eq. (A.12) in [1]: eB ∼ (0.1b/R) GeV2 ,

(5)

where b is the impact parameter. This rough fit also agrees by the order of magnitude with the results of more sophisticated calculations of the magnetic field within the UrQMD model [3]. One can see that the best agreement with the STAR data is obtained at the smallest quark mass. The combination a++ + a−− − 2a+− quickly decreases as the quark mass is increased - approximately by a factor of 5 as the quark mass changes from 50 MeV to 110 MeV, and by a factor of almost 20 as the quark mass further increases to 1 GeV. Since all observables aab are typically of the same order, one can expect that each such observable will also decrease with the quark mass. This dependence of asymmetry of angular distributions of mesons of different flavors on their mass can be used to discriminate between the CME and other phenomena which might cause such asymmetry. 3

Conclusions

In this paper we have summarized the main experimental signatures of the Chiral Magnetic Effect, which is caused in nuclear matter by superstrong mag-

372 netic fields. This effect [1] results in preferential emission of charged hadrons in the direction perpendicular to the reaction plane. The origin of the Chiral Magnetic Effect is the fluctuations of chirality, which are suppressed as the quark mass grows. Thus this asymmetry in angular distributions of charged hadrons, characterized by the coefficients aab (1), should be strongly suppressed for strange or charmed hadrons. Lattice data also suggests that the influence of the magnetic field on the properties of hadronic matter is stronger in the confinement phase. Thus heavyion collision experiments on colliders with lower beam energy but with larger luminosity (such as FAIR in Darmstadt, Germany or NICA in Dubna, Russia) might be more advantageous for studying magnetic phenomena. Acknowledgments The authors are grateful to M. N. Chernodub, A. S. Gorsky, V.I. Shevchenko, M. Stephanov and A. V. Zayakin for interesting and useful discussions. We are also deeply indebted to D. E. Kharzeev for very valuable and enlightening remarks on the present work. This work was partly supported by Grants RFBR 09-02-00338-a, RFBR 11-02-01227-a, Grant for the leading scientific schools No. NSh-6260.2010.2 and by the Federal Special-Purpose Programme ’Personnel’ of the Russian Ministry of Science and Education. P.B. was partially supported by personal grants from the “Dynasty” foundation and from the FAIR-Russia Research Center (FRRC). The calculations were partially done on the MVS 100K at Moscow Joint Supercomputer Center. References [1] D. E. Kharzeev, L. D. McLerran, and H. J. Warringa. The effects of topological charge change in heavy ion collisions: Event by event P and CP violation. Nucl. Phys. A, 803:227, 2008. [2] B.I. Abelevet al. [STAR Collaboration]. Azimuthal charged-particle correlations and possible local strong parity violation. Phys. Rev. Lett., 103:251601, 2009. [3] V. Skokov, A. Illarionov, and V. Toneev. Estimate of the magnetic field strength in heavy-ion collisions. Int. J. Mod. Phys. A, 24:5925, 2009. [4] K. Fukushima, D. E. Kharzeev, and H. J. Warringa. The chiral magnetic effect. Phys. Rev. D, 78:074033, 2008. [5] P. V. Buividovich, M. N. Chernodub, E. V. Luschevskaya, and M. I. Polikarpov. Numerical evidence of chiral magnetic effect in lattice gauge theory. Phys. Rev. D, 80:054503, 2009. [6] V. Orlovsky and V. Shevchenko. Towards a quantum theory of chiral magnetic effect. Phys. Rev. D, 82:094032, 2010.

373 [7] I. V. Selyuzhenkov [STAR Collaboration]. Global polarization and parity violation study in Au + Au collisions. Rom. Rep. Phys., 58:049, 2006. [8] S. A. Voloshin. Parity violation in hot QCD: how to detect it. Phys. Rev. C, 70:057901, 2004. [9] S. A. Voloshin for the STAR Collaboration. Probe for the strong parity violation effects at RHIC with three-particle correlations. Proceedings of Quark Matter 2008, 2008. [10] H. Petersen, T. Renk, and S. A. Bass. Medium-modified jets and initial state fluctuations as sources of charge correlations measured at RHIC. Phys. Rev. C, 83:014916, 2011. [11] G.-L. Ma and B. Zhang. Effects of final state interactions on charge separation in relativistic heavy ion collisions. Phys. Lett. B, 700:39, 2011. [12] V.V. Braguta, P.V. Buividovich, T. Kalaydzhyan, S.V. Kuznetsov, and M.I. Polikarpov. The Chiral Magnetic Effect and chiral symmetry breaking in SU(3) quenched lattice gauge theory. PoS, LAT2010:190, 2010.

374 OBSERVATION OF CORRELATIONS OF THE DOUBLE ϕ-MESON SYSTEM IN THE SELEX EXPERIMENT Grigory Nigmatkulov a , Dmitry Romanov b on behalf of the SELEX collaboration Faculty of Experimental and Theoretical Physics, National Research Nuclear University “MEPhI”, 115409 Moscow, Russia Abstract. We report preliminary results of the study of the double ϕ-meson system and the study of massive hadron states decaying via double ϕ-meson channel obtained in the SELEX experiment.

1

Introduction

One of the most efficient methods of studying space and time characteristics of the emission source is HBT correlations. HBT interferometry originates from two particle wave function properties. In spite of the fact that HBT correlations have a long history of studying it was done for the long-living particles only. The ϕ(1020) of the vector meson nonet is a thoroughly studied s¯ s state. The study of the double ϕ-meson system is a favorable place to look for hadronic production of glueballs [1] and exotic meson states having C = +1. The ϕϕ system has been studied in exclusive π − p [2] and inclusive π − Be [3], pp [4] and p¯p [5] induced interactions. A partial wave analysis (PWA) of the exclusive data revealed the presence of the interfering J P C = 2++ resonances, the f2 (2010), f2 (2300) and f2 (2340), originally called gT states [6]. The inclusive data show the evidence for two structures with parameters compatible with those measured for the gT states but a PWA was not possible. The main drawback of all these experiments is a limited experimental statistics. 2

Experimental apparatus and data selection

2.1

The SELEX experiment

The Fermilab experiment SELEX (E781) is SEgmented LargE XF baryon spectrometer - a fixed target (C, Cu) experiment with Σ− , p and π − beams with 600 GeV mean energy. It is designed to perform high statistics studies of production mechanisms and decay physics of charmed and charmed-strange baryons and require a good charge particle identification and high precision decay vertex reconstruction to look for the different decay modes. For these purpose there were vertex detector placed immediately behind the composite target, two analysis magnets with 800 MeV/c pt -kick each in-between surrounded by multi-ware proportional and drift chambers which provide particle tracking and a RICH detector which provide charged particle identification in a wide momentum range. A detailed description can be found in [7, 8]. a e-mail: b e-mail:

[email protected] [email protected]

375 2.2

The data selection and processing

dN2/dM1dM2

(a) 1000

500

1.08

0 1.06

M(

K

+

1.04

K) 1 [G e

1.08 1.06

1.02

V/

c2 ]

1.04 1.02

1 0.98 0.98

1

2

V/c + ) [Ge K 2 M(K -

]

dN/dM [entries/((20 MeV/c2)/channel)]

In this paper we report results of the analysis of events produced on the Σ− beam. ϕ0 (1020) mesons were identified by ϕ → K + K − decays in inclusive reaction Σ− + C(Cu) → ϕ0 + ϕ0 + X. The data sample presented here was reconstructed by the SELEX Off-line Analysis Program, further processing was done using VBK software package [9]. The reconstruction of ϕ mesons required that each event had at least two positively and two negatively charged particles which had the momentum in the range from 40 to 180 GeV/c for providing a good identification of kaons in the RICH detector. We select

250

(b)

200

150

100

50

0 2

2.2

2.4

2.6

2.8

3

3.2

3.4

3.6

3.8

M(φφ) [GeV/c2]

Figure 1: (a) Scatter plot of the invariant masses M (K + K − )1 vs M (K + K − )2 . (b) Invariant mass of the ϕϕ system obtained on the Σ− beam

only tracks measured in VX, M2 and identified in RICH detector as kaons. For particle identification, we calculated likelihoods for different particle hypotheses [10] using the information from the tracking system. If the event had more than two positively or two negatively charged kaons we select pairs with the minimal χ2 . Figure 1(a) is a scatter plot of the invariant mass of one K + K − pair plotted against the mass of the second K + K − pair. Clear bands corresponding to the single ϕ production seen in the Fig. 1(a) and with a very strong enhancement for ϕϕ production.

3

Results

We required the invariant mass of each K + K − pair to be within ±4 MeV/c2 range from the nominal ϕ meson mass value. After the processing of all experimental data (∼ 109 trigger events) 3455 ϕ meson pairs were selected. The invariant mass distribution is shown on the figure 1(b). We see the enhancement about 2.3 GeV/c2 which can be either f2 (2300) or f2 (2340) mesons or both of them, but the limited statistics prevent us from calculate their parameters.

376 4

Conclusion

We introduce the preliminary result of the reconstruction and selection of the double ϕ meson system in the SELEX experiment. ϕ mesons were reconstructed by decaying to charged kaons. Pairs of oppositely charged kaons which satisfy all requirements were selected. Total selected sample contains 3455 ϕϕ pairs. In the Fig. 1(b) shown the invariant mass spectra of the ϕϕ system and seen the enhancement about 2.3 GeV/c2 which can be a signal of the decaying massive hadron states such as f2 (2300) or f2 (2340). This result is in agreement with the measurements from MPS [2, 6] and OMEGA [3]. Statistic sufficient Monte-Carlo data which is in progress would help to produce a background substraction and would allow to study HBT correlations of ϕϕ pairs. Acknowledgments We thank the SELEX collaboration members for useful and stimulating discussions and ITEP for provided computing power for data analysis and simulations. This work was supported by RFBR grant No. 11-02-01302-a. References [1] G.Bali et al., Phys.Lett. B 309, 378 (1993); J.Sexton, A.Vacarino and D. Weingarten, Phys.Rev.Lett. 75, 4563 (1995). [2] A.Etkin et al., Phys.Rev. D 12, 2007 (1982). [3] P.Booth et al., Nucl.Phys. B 273, 677 (1986). [4] T.Davenport et al., Phys.Rev. D 33, 2519 (1986). [5] C.Evangelista et al., Phys.Rev. D 57, 5370 (1998). [6] S.Lindenbaum, Phys.Lett B 131, 221 (1983); A.Etkin et al., Phys.Lett. B 165, 217 (1985); A.Etkin et al., Phys.Lett. B 201, 568 (1988). [7] J.Russ et al., in 29th International Conference on High Energy Physics (Proceedings of the 29th International Conference on High Energy Physics, vol. II, 1998, Vancouver, Canada) ed. by A.Astbury, World Scientific Singapore, 1998 (Preprint hep-ex/9812031). [8] J.Engelfried et al., Nucl.Instrum. and Meth. A 409, 53 (1999) (Preprint hep-ex/9811001, FERMILAB-Pub-98/299-E). [9] G.Nigmatkulov and A.Savchenko, Bull. of the RAS: Physics 75 480 (2011). [10] U.M¨ uller et al., Nucl.Instr. and Meth. A 343, 279 (1994).

New Developments in Quantum Field Theory

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379 THE “SPIN-CHARGE-FAMILY-THEORY”, WHICH OFFERS THE MECHANISM FOR GENERATING FAMILIES, PREDICTS THE FOURTH FAMILY AND EXPLAINS THE ORIGIN OF THE DARK MATTER Norma Susana Mankoˇc Borˇstnik a Faculty of Mathematics and Physics, University of Ljubljana, 1000 Ljubljana, Slovenia Abstract. The theory unifying the spin, the charges and the families predicts the number of families, explains the origin of charges and family members, of gauge fields and of scalar fields. It explains the contribution of the scalar fields to the breaks of symmetries and correspondingly to properties of fermions and gauge fields. It predicts the fourth family which might be observed at the LHC and explains the dark matter as clusters of the stable fifth family members. Massive scalar dynamical fields, with all the charges in the adjoint representations, manifest effectively at low energies as the Higgs and Yukawa coupling and will show up deviations at least when searching for them.

1

Introduction

A theory making a next step beyond the standard model and being able to propose relevant experiments must explain at least: i. The origin of families and consequently the number of families. ii. The origin of the Higgs and Yukawa couplings. iii. The origin of the dark matter. The theory unifying the spin, charges and families, to be called the spincharge-family-theory, is offering the answers to these and hopefully also to several other open questions. It predicts the number of families, explains the origin of charges and family members, of gauge fields and of scalar fields. There are several dynamical scalar gauge fields with nonzero vacuum expectation values and with all the charges in the adjoint representations of all the groups manifesting at low energies effectively as Higgs and Yukawa couplings. Searching for these scalar fields will manifests that they are several. Predicting that there are two stable families the theory is offering the explanation for the dark matter. 2

Short presentation of the spin-charge-family-theory

A simple starting Lagrange density [1,2] for spinors in d > (1 + 3), which carry two kinds of spin – the Dirac one (described by γ a , S ab = 4i (γ a γ b − γ b γ a )) and the additional one (described by γ˜ a , with the same Clifford algebra properties as γ a and anti commuting with γ a , S˜ab = 4i (˜ γ a γ˜ b − γ˜ b γ˜ a ), there exists no third kind of the spin) – no charges, and interact with only the gravitational field a e-mail:

[email protected]

380 through the vielbeins and the two kinds of the spin connection fields, the gauge fields of S ab and S˜ab , 1 (E ψ¯ γ a p0a ψ) + h.c. , 2 1 1 1 = f α a p0α + {pα , Ef α a }− , p0α = pα − S ab ωabα − S˜ab ω ˜ abα , 2E 2 2

Lf = p0a

(1)

manifests (after particular breaks of the starting symmetry) in d = (1 + 3) two groups of four massless families. The gravitational gauge fields are assumed to appear in the action ∫ ∫ d ˜ S= d x E Lf + dd x E (α R + α ˜ R) (2) through the vielbeins (f α a , f α a eb α = δab ) and the spin connection fields of two kinds (ωabc = f α c ωabα and ω ˜ abc = f α c ω ˜ abα ) as R = 12 f α[a f βb] (ωabα,β − ˜ = 1 f α[a f βb] (˜ ωabα,β − ω ˜ caα ω ˜ c bβ ) , with f α[a f βb] = f αa f βb − ωcaα ω c bβ ) , R 2 αb βa f f . These gauge fields manifest in d = (1 + 3) as the gauge fields of the observed charges and as the scalar fields which contribute to the two successive breaks (from SO(1, 3) × SU (2)I × SU (2)II × U (1)II × SU (3) into SO(1, 3) × SU (2)I ×U (1)I ×SU (3) and further to SO(1, 3)×U (1)×SU (3)), and determine, together with the gauge fields, the low energy properties of fermions and bosons. In this talk a short overview of properties of the two kinds of the scalar dynamical fields – one (the gauge fields of S ab ) distinguishing only among the members (α , α ∈ (u , d , ν , e)) of a family, the other (the gauge fields of S˜ab ) only among the families – is made and the influence of scalar fields on properties of the mass matrices of twice (decoupled) four families and on the gauge fields presented. The reader is kindly asked to read for more information the ref. [4] and the references cited there. To see that the action of Eq. (1) manifests after the breaks of symmetries [2, 4, 5] all the known gauge fields, with the mass matrices included, let us rewrite formally the action for a Weyl spinor of (Eq.(1)) as follows ∑ ¯ n (pn − Lf = ψγ g A τ Ai AAi n )ψ +{

∑

A,i

¯ s p0s ψ} ψγ

s=7,8

+the rest, (3) ∑ where n = 0, 1, 2, 3 and τ Ai = a,b cAi ab S ab , {τ Ai , τ Bj }− = iδ AB f Aijk τ Ak . Index A enumerates all possible spinor charges and g A is the coupling constant to a particular gauge vector field AAi n . Before the electroweak break stays A = 1 for the weak charge, A = 2 for the hyper charge and A = 3 for the

381 colour charge. The first row of Eq.(3) manifests the dynamical the ∑ part,¯ while s second row manifests the mass term. In the mass term ( s=7,8 ψγ p0s ψ), in which the summation runs only over s = 7, 8, the operators γ s transform quantum numbers of the right handed members into those of the left handed partners. To the mass matrix two kinds of spin connection fields contribute 1 ˜ abσ , and we p0s = f σ s p0σ + 2E {pσ , Ef σ s }− , p0σ = pσ − 12 S ab ωabσ − 12 S˜ab ω ∑ Ai Ai ab Ai Bj AB Aijk Ak ˜ have correspondingly τ˜ = a,b c ab S , {˜ τ , τ˜ }− = iδ f τ˜ . The scalar fields which originate in S˜ab and couple to only the upper four families are responsible with their nonzero vacuum expectation values for mass matrices of the upper four families on the tree level. The lower four families stay massless up to the electroweak break, when the scalar fields which are orthogonal to the ones which determine mass matrices of the upper four families, gain nonzero vacuum expectation values. To the mass matrices of the lower four families also the scalar fields originating in ωabs contribute. While the mass matrices of different members of a family are on the tree level strongly correlated (u has the same off diagonal matrix elements as ν and d has the same off diagonal matrix elements as e ), the so far evaluated one loop corrections [3] give a real hope that the loop corrections to all orders take care of the great differences in the properties of the family members for the lower four families. b The influence of the loop corrections on the upper four families is expected to be much smaller than on the lower four families, since the scalar fields originating in the “Dirac kind” of the spin connection fields (ωss′ s” c ), which distinguish among the family members (not among families d ), gain nonzero vacuum expectation values at the electroweak break, while the upper four families gain masses at for several orders of magnitude higher scale e . The upper group of four families (Σ = II) do not couple to the lower one (Σ = I). Correspondingly the mass matrices of each family member (α ∈ b For neutrinos a Majorana like term appears, which might be to high extent responsible for the smallness of masses of the so far observed three families. c The scalar fields originating in the “Dirac kind” of spin γ s manifest after the elec′ troweak break in terms presented in the last line of Eq. (7) as e Q As + g 1 cos θ1 Q′ ZsQ + ′ g 2 cos θ2 Y ′ AY s . d The gauge scalar fields of τ ˜Ai , which distinguish among families, are presented in Eq. (7) ˜ ˜′ ˜ ⃗˜ ⃗˜NR g ˜2 ˜Y˜ ′ + √ ˜2+ + τ˜2− A ˜2− )]+ τ 2+ A A + g˜Y Y˜ ′ A (˜ in the second and the third line as {[˜ g NR N R

˜

s

s

2

s

s

˜′ ˜ ′ ˜ ′ ˜Q ⃗˜ A ⃗˜NL + g˜Q g ˜1 ˜1− ˜1+ Q As + √ N (˜ ˜1− A τ 1+ A L s s )]]}. The term within the parentheses s +τ 2 [ ] couples to the upper four families, while the term within the parentheses [[ ]] couples to the lower four families. e Together with the upper four families also the vector gauge fields, which are the super⃗ 2 and A4 , gain masses when SU (2)II × U (1)II symmetry breaks into U (1)I . position of A m m

˜ [[˜ g NL

382 (u , d , ν , e)) demonstrate twice four by four diagonal matrices ( α II ) M 0 Mα = , 0 MαI

(4)

α II,I where M α II,I have on the tree level (M(o) ) the structure



M(o)

 −a1 b 0 c  b −a2 c 0  . =  0 c a1 b  c 0 b a2

(5)

Accordingly there are two stable families of quarks and leptons. The first one (u1 , d1 , ν1 , e1 ) and the fifth family one (u5 , d5 , ν5 , e5 ). All the fifth family members are expected to have quite comparable masses due to the fact that the main dependence on the family members quantum number appears at the electroweak break, as explained above. It follows accordingly that the lightest baryon is very likely the neutron (n5 ) f . 3

Mass matrices on tree and beyond tree level

After the electroweak break the Lagrange density for spinors (Eq. (1)) is equal to Lf = ψ¯ (γ m p0m − M )ψ , g1 Q′ 1− 1+ + √ (τ 1+ Wm p0m = pm − {e Q Am + g 1 cos θ1 Q′ Zm ) + τ 1− Wm 2 ′ g2 2− 2− (6) + g 2 cos θ2 Y ′ AYm + √ (τ 2+ A2+ Am ) , m +τ 2 with the mass term ψ¯ M ψ = ψ¯ γ s p0s ψ , ˜R N

g˜2 2+ ˜2+ ˜′ ˜′ + g˜Y Y˜ ′ A˜Ys + √ (˜ τ As + τ˜2− A˜2− s ) 2 g˜1 1+ ˜1+ ˜ ′ ˜ ′ ˜Q ˜′ + g˜Q Q As + √ (˜ τ As + τ˜1− A˜1− s ) 2

˜ ⃗˜ ⃗˜ p0s = ps − {˜ g NR N R As ˜

N ˜ ⃗˜ ⃗˜ L + g˜NL N L As

′

′

+ e Q As + g 1 cos θ1 Q′ ZsQ + g 2 cos θ2 Y ′ AYs } , s ∈ {7, 8} .

(7)

We have before the two SU (2) × U (1) breaks two times (Σ ∈ (II, I)) four α massless vectors ψΣ(L,R) for each member of a family α. Let i, i ∈ (1, 2, 3, 4), f Properties

of the fifth family members are under consideration [3].

383 denotes one of the four family members of each of the two groups of massless families α α α α α ψΣ(L,R) = (ψΣ (8) 1 , ψΣ 2 , ψΣ 3 , ψΣ 4 )(L,R) . Let Ψα Σ(L,R) be the final massive four vectors for each of the two groups of families, with all loop corrections included, α α α ψΣ (L,R) = VΣ ΨΣ (L,R) ,

VΣα = VΣα(o) VΣα(1) · · · VΣα(k) · · · .

(9)

Then we have for the mass term of Eq. (6) α 0 αΣ α α 0 α† αΣ α < ψΣ |ψΣ VΣ |Ψα L |γ M R >=< ΨΣ L |γ VΣ M ΣR > .

(10)

Rough analyses (without loop corrections included) of the properties for the lower group of four families [2,5] and for the fifth family members [6] were done by taking into account the so far observed properties of family members g and the dark matter observations and can be found in the cited references. The fourth family members were predicted to be possibly observed at the LHC or at somewhat higher energies. The analyses with the loop corrections taken into account are in preparations [3] manifesting so far their strong dependence on family member quantum number. This gives correspondently a real hope that the loop correction will change the tree level mass matrices (which have the off diagonal matrix elements of u equal to those of ν and equivalently for d and e) in agreement with the observations. 4

Dark matter candidates

The spin-charge-family-theory predicts a stable fifth family, with masses above the fourth family masses, let us say > 10 TeV, and pretty much below 1013 GeV, which is a possible scale of the first of the two SU (2) × U (1) breaks. We followed [6] the history of the stable fifth family members in the expanding universe from the time when they start to decouple from the cosmic plasma, through the freezing out procedure and the colour phase transition, up to the today’s matter, showing that the fifth family members, the (colourless) baryons and anti-baryons and neutrinos and anti-neutrinos are very likely the dark matter constituents. Neutrinos and antineutrinos are expected to annihilate during the electroweak phase transition to the density which is in agreement with cosmological observations of the dark matter density. The estimations need to be followed by more accurate calculations and several assumptions made need to be clarify. g The calculations of the lower four families properties were done under the assumption that loop corrections change the off diagonal matrix elements while keeping approximately the mass matrices symmetry of Eq. (5).

384 We calculated the present number density of baryons and anti-baryons of the fifth family members (nc5 (T0 )) as a function of the fifth family members mass. Taking into account the estimation inaccuracy the interval for the fifth family masses followed 10 TeV < m5 c2 < 4 · 102 TeV.

(11)

We used the Bohr-like model to estimate the cross section for the fifth family neutrons. The interval for π(rc5 )2 is: 10−8 fm2 < σc5 < 10−6 fm2 . One can see that the cross section of the fifth family “nuclear force” is at least 10−6 × smaller than the cross section of the first family nuclear force. This explains why is the dark matter so inert. We studied [6] also properties of the fifth family baryons and anti-baryons and neutrinos and anti-neutrinos in direct measurements done so far. My prediction is, after several discussions with the members of most of the groups performing direct measurements, that if DAMA/LIBRA measures our fifth family clusters other direct measurements will confirm their results. 5

Comments on standard model and extensions of it as seen from spin-charge-family-theory

Let us try to understand the standard model as an effective approach of the spin-charge-family-theory. The main “extension” of the proposed theory is in offering the mechanism for generating families, and in the unification of all the internal degrees of freedom. h Mass matrices of fermions of the lower four families are in the spin-chargefamily-theory, according to Eq.(7), determined by the scalar fields through the operator ˜

N 78 ′ 1⃗ 1 ˜ ⃗˜ ⃗˜ L ˆ I∓ =(∓) {˜ ˜∓ + eQAQ + g Q′ Q′ Z Q + g Y ′ Y ′ AY∓′ }, (12) Φ g NL N ˜1⃗τ˜ A L A∓ + g ∓ ∓ 78

78

with (∓)= 12 (γ 7 ∓γ 8 ). One can easily check (see ref. [1,4]) that the operator (−) transforms the weak and the hyper charge of the right handed uR and νR (−) 78

into those of the left handed ones, while (+) does the same for the dR and eR . All the scalar bosons as also all the vector bosons of Eq. (12) have all the charges 78

in the adjoint representations of the charge groups. The operator (∓) obviously does what in the standard model the Higgs by “dressing” the right handed quarks and leptons with the appropriate charges does. The part of the operator h The inclusion of the right handed neutrino as a regular family member, which is a necessary part of the spin-charge-family-theory, is a very small extension of the standard model.

385 ˜L N

1

′

1⃗ ˜ ⃗˜ ⃗˜ ˜∓ +e Q AQ +g Q′ Q′ Z Q +g Y ′ Y ′ AY∓′ }, of Eq. (12), that is {˜ g NL N g 1 ⃗τ˜ A L A∓ +˜ ∓ ∓ takes care of the mass matrices on the tree level, and together with the vector massive fields also beyond the tree level. The spin-charge-family-theory evidently manifests that the scalar fields are new interactions, as the Yukawa couplings already do. 78

If replacing the operator (∓) with the vacuum expectation value of an “effective Higgs” ΦvI ∓ , which is a weak doublet of appropriate hyper charge like it is a Higgs of the standard model (see the ref. [4]) and taking into account g1 1+ 1 Q 1 ′ Q′ that p0m = pm − √ [τ 1+ Am + τ 1− A1− m ] + g sin θ1 Q Am + g cos θ1 Q Am , 2 (Eq. (6)) one finds that 1 2 ˆ I )† (p m Φ ˆ I ) = { (g ) A1+ A1− m (p0m Φ ∓ 0 ∓ m 2 1 ′ g vI Q′ m +( )2 AQ }T r(ΦvI† mA ∓ Φ∓ ). 2 cos θ1

(13)

2

v vI Assuming, like in the standard model, that T r(ΦvI† ∓ Φ∓ ) = 2 we extract from the masses of gauge bosons one information about the vacuum expectation values of the scalar fields, their coupling constants and their masses. We see that the standard model Higgs and Yukawa couplings are in the spin-charge-family-theory represented by a bunch of scalar fields, which only effectively manifest as the Higgs and the Yukawa couplings, but are expected to show up at the LHC as a bunch of scalar fields. Let me at the end comment on models [9], which extend the standard model by assuming that the observed families manifest the SU (3) flavour group and that the scalar fields are in the “bi-fundamental” representations of the SU (3) flavour group. From the point of view of the spin-charge-family-theory with the scalar fields in the adjoint representations with respect to all the groups the “bi-fundamental” representations of the SU (3) flavour group look quite artificial. It is not easy to connect the spin-charge-family-theory scalar fields to scalar fields in the “bi-fundamental” representations of the SU (n) group.

6

Concluding remarks

The spin-charge-family-theory [1,2,4,5] is offering the way beyond the standard model by proposing the mechanism for generating families and consequently predicting their number at low energies and the mass matrices for each of the family member. It explains the appearance of charges as well. It predicts the fourth family to be possibly measured at the LHC or at some what higher energies and the fifth family which is, since it is decoupled in the mixing matrices from the lower four families and it is correspondingly stable, the candidate to form the dark matter [6].

386 In the proposed theory there are two kinds of scalar fields, interacting with fermions through the Dirac spin and through the second kind of the Clifford operators (anti commuting with the Dirac ones). The Dirac one distinguishes among the family members, the second one among the families. Beyond the tree level these two kinds of scalar fields and the vector massive fields start to contribute coherently, leading hopefully to the measured properties of the so far observed three families of fermions and to the observed weak gauge fields. At low energies these scalar dynamical fields manifest effectively, although they all have the charges in the adjoint representations of all the groups, as the standard model Higgs and Yukawa couplings together. The differences will show up at least when searching for these scalar fields. It is obvious from the point of view of the spin-charge-family-theory that the scalar fields represent a new kind of interactions, what the standard model Yukawas already manifest. The proposed theory predicts that there is no supersymmetric partners of the observed fermions or bosons, at least not below the unification scale of the three known interactions. References [1] N.S. Mankoˇc Borˇstnik, Phys. Lett. B 292, 25 (1992), J. Math. Phys. 34 3731 (1993), Int. J. Theor. Phys. 40 315 (2001), Modern Phys. Lett. A 10, 587 (1995), hep-ph/0711.4681 p.94, arXiv:0912.4532, p.119, hep-ph/0711.4681, p. 94-113, arXiv:0912.4532, p.119-135, arxiv.org/abs/1005.2288. [2] A. Borˇstnik, N.S. Mankoˇc Borˇstnik, hep-ph/0401043, hep-ph/0401055, hep-ph/0301029, Phys. Rev. D 74, 073013 (2006), hep-ph/0512062. [3] A. Hern´andez-Galeana, N.S. Mankoˇc Borˇstnik, in preparation, arXiv:1012.0224, p.166-176. [4] N.S. Mankoˇc Borˇstnik, arXiv:.org/abs/1011.5765. [5] G. Bregar, M. Breskvar, D. Lukman, N.S. Mankoˇc Borˇstnik, New J. of Phys. 10 093002 (2008). [6] G. Bregar, N.S. Mankoˇc Borˇstnik, Phys. Rev. D 80, 083534 (2009), G. Bregar, R.F. Lang, N.S. Mankoˇc Borˇstnik, arXiv:1012.0224, p. 161-165. [7] N.S. Mankoˇc Borˇstnik, H.B. Nielsen, arXiv:1001.4679v5. [8] R. Bernabei et al., Int.J. Mod. Phys. D13 (2004) 2127-2160; Z. Ahmed et al., Phys. Rev. Lett. 102 (2009) 011301, arXiv:0802.3530; M. Fich and S. Tremaine, Ann. Rev. Astron. Astrophys. 29 (1991), 420; Z. Ahmed et al., Phys. Rev. Lett. 102 (2009) 011301, arXiv:0802.3530; E. Aprile et al., Phys. Rev. Lett. 105 (2010) 131302, arXiv:1005.0380. [9] R.S. Chivukula and H. Georgi, Phys. Lett. B 188 (1987) 99, G. DAmbrosio, G. Giudice, G. Isidori, and A. Strumia, Nucl. Phys. B645 (2002) 155187, arXiv:hep-ph/0207036, R. Alonso, M.B. Gavela, L. Merlo, S. Rigolin, arXiv: 1103.2915v1[hep-ph].

387 A NEW LOOK AT SOME GENERAL PUZZLES OF UNIVERSE Plamen Fiziev a , Dmitrii Shirkov BLTP, JINR, Dubna, 141980 Moscow Region, Russia Abstract. In this talk we outline novel ideas to reveal some general mysteries of the Universe: alternatives to/for the Higgs mechanism, quantum gravity, what was before the Big Bang, CPT properties of elementary particles, baryon – antibaryon asymmetry, etc. by applying new Physics on manifolds with variable topological dimension and reduction of space dimensions.

1

Introduction

The idea of reducing the number of topological dimensions of the physical space at small distances (proposed recently [1]) was implemented in our previous papers [2, 3] for the (2 + 1)-dim space-times which comprise the 2-dim static axial spaces with an arbitrary shape function ρ(z) ≥ 0 . This was done to develop general methods and get insight into possible features of physics in such a specific variable geometry, including dimensional reduction (DR). Dimensional reduction of the physical space in GR can be regarded as unrealized and as yet untapped consequence of Einstein’s equations (EEqs) themselves which takes place around singular points of their solutions. The oldest indication for this phenomenon can be found in the well known 1921 Kasner solution of EEqs [4]: For a 3-dim space-cube, approaching the singularity there are possible two types of Kasner’s evolution: 1. “Pancake evolution”: one of the dimensions tends to zero and the cube becomes 2-dimensional square. 2. “Cigar evolution”: two of the dimensions tends to zero and the cube becomes 1-dimensional line. This demonstrates a clear trend toward dimensional reduction, but a continuation after the singular point was never considered. We analyze time dependent axial geometry of the 2-dim space. The {t, z}dependence of the shape function ρ(t, z) ≥ 0 is obtained by solving the EEqs in (2 + 1)-dim space-time. We refer to these specific space-times as to the (2 + 1)dim axial universes (AxU). The EEqs fix quite firmly the axial geometry under consideration, but there still remains a variety of dynamically admissible spacetime manifolds, including some of the previously studied static ones. In any (2 + 1)-dim GR universe the local degrees of freedom, which may be related with gravitational waves, are freezed and we have no freely moving excitations of the gravitational field. While this feature makes the theory simple, it does not quite make it trivial. It simplifies drastically the analysis of the dynamics described by the EEqs in the (2 + 1)-dim universes. For AxUs the axial symmetry yields an additional simplification of the physical problem and ensures the existence of nontrivial fundamental group. It turns even possible to find the general solution of the EEqs for different matter contents of the a e-mail:

[email protected], [email protected]

388 (2 + 1)-dim AxUs and to study the novel physical phenomena related with the variable topological dimension in them. This is our main subject. 2

The (2 + 1)-dim time dependent axial universes (1,3)

Consider auxiliary Minkowski (3+1)-dim space-time Ex0 x1 x2 x3 with the interval dσ 2 = (dx0 )2 − (dx1 )2 − (dx2 )2 − (dx3 )2 . We introduce axial universe (AxU) as a hypersurface defined by the equations: { 0 x = t, x1 = ρ(t, z) cos ϕ, (1,2) Mtϕz : (1) x3 = z, x2 = ρ(t, z) sin ϕ, assuming t ∈ (−∞, ∞), z ∈ (−∞, ∞), and ϕ ∈ [0, 2π]. This pseudo-Riemannian (1) (1) (1,2) (1) (1) (2+1)-dim manifold has a structure Mtϕz = Rt ⊗Rz ⊗Sϕ , with Sϕ being (2)

(1)

(1)

a circle. Clearly, the space Mϕz = Rz ⊗ Sϕ is a 2-dim rotational surface with time-dependent variable shape function ρ(t, z) ≥ 0 . Thus, for the AxU ( ) ( ) 2 ds2 = 1 − ρ˙ 2 dt2 − 2ρρ ˙ ′ dtdz − 1 + ρ′ dz 2 − ρ2 dϕ2 ; (2) ρ˙ = ∂t ρ(t, z), ρ′ = ∂z ρ(t, z). ( ) We restrict the lapse function 1 − ρ˙ 2 > 0 to preserve the relativistic causality and the physical meaning of the time variable t. The AxUs (2) is not static but stationary. It describes non-rotating universe, yielding solutions of EEqs, interesting for study of the dimensional reduction. At the points where ρ(t, z) = 0 the dimension of the 2-dim axial space reduces. We call these points the dimensional reduction points (DRPs). In general, they move along the z-axis: z drp = z drp (t). There exist two type of DRPs: 1. Isolated: in a small enough vicinity there are no other DRPs, for example, the vertex of a cone, without extension (“>•”), or the vertex of a two-sided cone ( “>••−”). 3

The Einstein equations for the time dependent (2 + 1)-dim AxU

After some algebra the nontrivial EEqs in the presence of matter read ρ¨ = −ρg2 T zz ,

ρ′′ = −ρg2 T tt ,

ρ˙ ′ = ρg2 T tz .

( ( )2 )/ 2 2 .ϕ − ρ¨ρ′′ − ρ˙ ′ g = Tϕ. , g = 1 − ρ˙ 2 + ρ′ > 0

(3) (4)

.z .ϕ ≡ 0 and restrict the motion of The other EEqs lead to Tt..ϕ = Tz. = Tϕ.t . = Tϕ. the matter in the specific universes with metric (2).

389 The Eq. (4) yields the constraint T ϕϕ = g2 (T tt T zz − T tz T zt ), or ( )2 det T = det ||T ij || = T ϕϕ /g ≥ 0.

(5)

The full dynamics of the universe is defined adding the equation ∇i Tji = 0. 4

The solutions to the Einstein equations for the AxU

4.1

The vacuum solutions to the Einstein equations (3) are

1. ρ(t, z) = v0 (t − t0 ) + ρ0 , where ρ0 ≥ 0 is a constant, v0 is the constant velocity of the expansion of the 1-dim filament all points of which are non-isolated DRP on the surface of the cylinder of the radius ρ(t); 2. ρ(t, z) = (z − z0 ) tan α, where α is the constant angle at the vertex of a static cone. The short notation σ = tan α is used further. The static isolated DRP is the point z = z0 = const; 3. ρ(t, z) = v0 (t − t0 ) + σ(z − z0 ), v0 ̸= 0 is the velocity of a moving 2-dim cone with the vertex angle α ∈ (0, π/2). Here an isolated running DRP z drp (t) = z0 − v(t − t0 )/σ moves with constant velocity v0 /σ . In the three vacuum cases we have DRP of the solutions, related to a reduction of the topological dimension from (2 + 1) to (1 + 1), or even to (1 + 0). 4.2

The solutions with a positive Λ term

For positive lambda term Λ = 1/R2 > 0, one has the only solution in the AxU: √ ρ(t, z) = R2 − (z − z0 )2 – a 2-dim static sphere of constant radius R. This solution is briefly discussed in [2]. It has two isolated static DRPs: z = z0 ± R which are not singular. 4.3

The solutions for the (2 + 1)-dim axial universe filled with dust

In (2 + 1)-dim AxU filled with dust: T ij = µ(t, z)ui (t, z)uj (t, z). As a result, from Eq. (5) one obtains T ϕϕ ≡ 0 and the problem reduces 2 to the well-known homogeneous Monge-Amp`ere equation ρ¨ρ′′ − (ρ˙ ′ ) = 0. Its implicit general solution contains two arbitrary functions a(v) and b(v): ρ = tv + a(v)z + b(v),

t + a,v (v)z + b,v = 0,

where the comma denotes the corresponding partial differentiation.

(6)

390 In the case a,vv (v)z + b,vv ≡ 0 the Monge-Amp`ere equation has a solution ρ(t, z) = v0 t + ρ0 (z),

|v0 | < 1, v0 = const,

(7)

ρ0 (z) ≥ 0 being an arbitrary time-independent shape function. The general solution of the Cauchy problem for arbitrary initial data ρ0 (z) ≥ 0 and ρ˙ 0 (z) is ρ(t, z) = ρ0 (ζ) + (z − ζ)ρ0,z (ζ) − tρ˙ 0 (ζ),

(8)

where ζ is defined by the equation tρ˙ 0,z (ζ) = (z − ζ)ρ0,zz (ζ) ⇒ ζ = ζ(t, z). From gij ui uj = 1 assuming v˙ = ρ¨ ̸= 0, one obtains the dynamics of matter: ut (t, z) µ(t, z) where η(v) = 5

a,v 1 , uz (t, z) = , uϕ (t, z) = 0, η(v) η(v) )2 ( η(v) ≥ 0, ⇒ ρ¨ ≤ 0, = −¨ ρ 1 − v 2 + a2 = −

(9) (10)

√ (1 − v 2 )(a,v )2 + v(a2 ),v − a2 − 1.

Summary and outlook

Our main results are: 1. A special kind of the (2 + 1)-dim toy models of time dependent universes with axial space (“axial universes” (AxU)) are introduced and considered in detail. It is shown that these models allow the study of topological-dimension reduction phenomena defined by the zeros of the shape function. 2. The shape function ρ(t, z) solves the Einstein equations (EEqs) for various energy-momentum tensors of matter. The exact solutions for the vacuum AxUs, AxUs filled with Λ term, as well as the exact general solution of the EEqs for the AxUs filled with dust are found. It is shown that some of the previously considered static AxUs are solutions to the EEqs. 3. The dynamics of the dimensional reduction points in the time dependent AxUs is studied. It is found that these points can emerge and disappear. 4. The spreading of test particles in variable geometry, including reduction of topological dimension can be studied obtaining exact solutions for test particles described by the Klein-Gordon eq. in different time-dependent AxUs in terms of various special functions. These results allow us to express a hope for possible further development: • The time dependent AxUs with variable space-time geometry could give one a simple basis for commenting the real situation concerning the C, P, and also T properties of the particles. • The considered models of time-dependent AxUs inspire an intriguing idea: to treat the very Big Bang as a transition from the pre-Big-Bang-Universe

391 with a lower topological dimension (d = 1, or d = 2): (or as a sequence of such transitions), to the present-day space with d = 3. For this purpose a generalization of the model, described in [5] is needed. • It is important to stress that as well as in the Kaluza-Klein models, in our design of dimensional reduction the numerical-field-degrees-of-freedom of the theory are preserved during the transition from one to another space-time dimension. The only thing that changes is the grouping of these field-degreesof-freedom in different multiplets, because of the different symmetry groups in the tangent foliations of the parts with different dimension of the space-time manifold. Acknowledgments The research has been partially supported by the Bulgarian National Scientific Fund under contracts DO-1-872, DO-1-895, DO-02-136, by the Sofia University Scientific Fund, contract 185/26.04.2010 as well as by the Russian Presidential grant, Scientific School–3810.2010.2 and by RFBR grant 11-01-00182, References [1] D.V. Shirkov, (2010) Coupling running through the Looking-Glass of dimensional Reduction, Particles and Nuclei (PEPAN), Letters, 7, No 6(162); arXiv:1004.1510. [2] D.V. Shirkov, P.P. Fiziev, Amusing properties of Klein-Gordon solutions on manifolds with variable geometry, talk given at the International Workshop “Bogoliubov Readings”, Sept. 22-25, JINR, Dubna, 2010. See the URL address: http://tcpa.uni-sofia.bg/index.php?n=7 . [3] P. P. Fiziev, D. V. Shirkov, Solutions of the Klein-Gordon equation on manifolds with variable geometry, including dimensional reduction, Teoreticheskaya i Matematicheskaya Fizika, 167(2), 323-336 (2011) - in Russian; Theor. and Math. Physics, 167(2): 680-691 (2011) - in English. arXiv:1009.5309v2. [4] L. D. Landau, L.D., E. M. Lifshitz, The Classical Theory of Fields (Course of Theor. Physics, Vol. 2) (revised 4th English ed.). N.Y.: Pergamon Press (1975), Chapter 14. [5] P. P. Fiziev, Partially Compact (1 + d)-dim Riemannian Space-Times which Admit Dimensional Reduction to Any Lower Space Dimension and the Klein-Gordon Equation, arXiv:1012.3520 [math-ph]. [6] P. P. Fiziev, D. V. Shirkov, A new look at some general puzzles of Universe, talk presentation: http://tcpa.uni-sofia.bg/index.php?n=7

392 VACUUM ENERGY DECAY a ´ Enrique Alvarez , Roberto Vidal b Instituto de F´ısica Te´ orica UAM/CSIC and Departamento de F´ısica Te´ orica Universidad Aut´ onoma de Madrid, E-28049–Madrid, Spain

Abstract. The problem of the vacuum energy decay is studied through the analysis of the vacuum survival amplitude A(z, z ′ ). Transition amplitudes are computed for finite time-span, Z ≡ z ′ − z, and their late time behavior is discussed up to first order in the coupling constant, λ.

1

Introduction

It has been claimed [1] that the free energy corresponding to an interacting theory in de Sitter space has got an imaginary part that can be interpreted as some sort of instability. Some general arguments can be advanced supporting that this result is to be found at two-loop or higher orders [2]. Namely, the optical theorem relates the computation of this imaginary part to a simpler tree level calculation: the vacuum decay into identical particles. It is true, however, that all our intuition is based upon flat space examples, with the ensuing asymptotic regions, and S-matrix elements that can be computed through LSZ techniques. Outside this framework it is not even known how to define a particle to be decayed into, nor the interacting vacuum |vac⟩ in the absence of a well-defined energetic argument. A related issue is the study of the time dependence of transition amplitudes. The linear dependence in time is one of the key aspects of Fermi’s golden rule. The fact that is problematic in curved space, where there is no naturally preferred coordinate system in general, has been remarked in [3]. We have attempted to calculate some well defined overlaps between states that differ by a finite time transformation in a certain coordinate frame. We have adopted a formalism based on the functional Schr¨odinger picture [4] applied in curved space-times. We are able to recover some basic results in Minkowski space-time, and also to examine the (conformal) time dependence of transition amplitudes in de Sitter space. For further details we refer the reader to the complete work [5]. 2

Survival amplitudes

A survival amplitude is an overlap of an state in two different times: A(t, tf ) = ⟨ψ(ti )|ψ(tf )⟩ a e-mail: b e-mail:

[email protected] [email protected]

(1)

393 The unitary evolution guarantees that the quantity Γ(tf , ti ) = −

2 |A(tf , ti )| tf − ti

(2)

is positive, and in case it is independent of T = tf −ti in the asymptotic regime, could be rightfully interpreted as the decay width of the state. We assume that the path-integral representation of the survival amplitude is valid even in a curved background: ∫ A(tf , ti ) = ⟨out tf |in ti ⟩ = [Dφf ][Dφi ] Ψ∗tf [φf ]Ψti [φi ] K[J][φf tf , φi ti ] (3) where [Dφ] is the integration measure defined in the space of field configurations at fixed “time”, the functionals Ψ are the wavefunctionals of the initial and final states, and K is the field transition amplitude or Feynman kernel: ∫ φf ∫ tf K[J][φf tf , φi ti ] ≡ ⟨φf tf |φi ti ⟩ = Dϕ ei ti L (4) J

φi

where an external source J is included for computational purposes. This technique can be illustrated with a flat space example. The vacuum survival amplitude for a free field in Minkowski space-time can be rederived directly from the path-integral representation. The functional representation for the vacuum reads: ∫ 1 (5) ⟨φ|0⟩ = N e− 2 φωφ √ where ω(⃗x, ⃗y ) is the Fourier transform of the energy ωk = k 2 + m2 . The amplitude can be separated in three pieces [6]: the contribution from the external sources J, the integration of the wavefunctionals weighed by the exponential of the classical action, and the determinant of the quantum fluctuations. When J = 0, the regularization of the two latter contributions yields: A(tf , ti ) = exp [−iVn−1 E0 T + . . .]

(6)

where Vn−1 is the spatial volume, E0 a constant and we omit subleading contributions independent of time. 3

Vacuum amplitude in de Sitter space

In a conformal space-time, we can shift all the dependence on the background towards the potential by redefining the field variables: ϕ→a

n−2 2

ϕ

(7)

394

m(z)2

Order (0, 0)

Order (1, 0)

λ(z)

λ(z) m(z)2

Order (0, 1)

Order (1, 1)

Figure 1: The first few diagrams that contribute to the vacuum energy.

where a is the scale factor. In the case of de Sitter in the Poincare patch, a(z) = 1/z. The survival amplitude can be computed perturbatively in this effective interaction V (z) (made up of time-dependent mass m(z) and interaction coupling λ(z)) through the diagrams showed in Fig. 1. The calculation is similar to the one for Minkowski with a (finite time) propagator modified by the boundary terms coming from (7). Putting everything together the (loosely called) vacuum decay width that we obtain exhibits the following behavior: Z→∞

Γ(Z) −→

A ReI00 (Z) + λBZ n−5 ImI01 (Z) Z

(8)

where A and B are constants and I00 and I01 are certain integrals that can be computed in the limit mlzi → ∞: ( ) ( ) iΓ 2 − n2 Γ n−1 2 √ I00 (Z) → − 2 π I01 (Z) → Cn (Z)Z

1−n 2

(9)

where Cn is a pure oscillatory function of Z. The asymptotic behavior of the n−9 decay width in this limit is then proportional to Z 2 . Acknowledgments E.A. tanks Alexander Studenikin for the kind invitation to this interesting and successful conference. This work has been partially supported by the European

395 Commission (HPRN-CT-200-00148) as well as by FPA2009-09017 (DGI del MCyT, Spain) and S2009ESP-1473 (CA Madrid). R.V. is supported by a MEC grant, AP2006-01876. References [1] A. M. Polyakov, “De Sitter Space and Eternity”, Nucl. Phys. B 797 (2008) 199 [arXiv:0709.2899 [hep-th]]. A. M. Polyakov, “Decay of Vacuum Energy,” arXiv:0912.5503 [hep-th]. [2] E. Alvarez and R. Vidal, “Eternity and the cosmological constant,” JHEP 0910 (2009) 045 [arXiv:0907.2375 [hep-th]]. “Comments on the vacuum energy decay,” JCAP 1011 (2010) 043 , [arXiv:1004.4867 [hep-th]]. [3] J. Bros, H. Epstein and U. Moschella, “Particle decays and stability on the de Sitter universe,” arXiv:0812.3513 [hep-th]. J. Bros, H. Epstein and U. Moschella, “Lifetime of a massive particle in a de Sitter universe,” JCAP 0802 (2008) 003 [arXiv:hep-th/0612184]. [4] R. Jackiw, “Analysis On Infinite Dimensional Manifolds: Schrodinger Representation For Quantized Fields,” In *Jackiw, R.: Diverse topics in theoretical and mathematical physics* 383-445.. [5] E. Alvarez, R. Vidal, “Finite Time Vacuum Survival Amplitude and Vacuum Energy Decay”, [arXiv:1107.3134 [hep-th]]. [6] B. Sakita, “Quantum theory of many-variable systems and fields”, (World Scientific, 1985)

396 PROBLEMS IN THEORY OF THE CASIMIR EFFECT Vladimir M. Mostepanenkoa Noncommercial Partnership “Scientific Instruments”, Tverskaya Street 11, Moscow, 103905, Russia Abstract. The Casimir effect manifests itself as a force acting between two uncharged macrobodies in vacuum. It originates from the existence of zero-point and thermal fluctuations of the electromagnetic field. During the last few years the Lifshitz theory describing the Casimir force between bodies made of real materials faces contradictions with basic principles of thermodynamics and with the experimental data. We review basic theoretical and experimental problems arising in this connection.

1

Introduction

The Casimir effect in its simplest form [1] is the attraction of a pair of neutral, parallel ideal metal plates resulting from the modification of the electromagnetic vacuum by the boundaries. It is a purely quantum effect caused by the existence of zero-point oscillations. The Casimir energy and force per unit area of the plates (i.e., the Casimir pressure) are given by E(a) = −

π2 , 720a3

P (a) = −

∂E(a) π2 =− , ∂a 240a4

(1)

where a is the separation between the plates. The Casimir force is closely connected with the so-called dispersion forces acting between two polarizable particles, between a particle and a macroscopic body and between two macrobodies. The dispersion forces (which are also called the van der Waals forces [2]) are caused by electromagnetic fluctuations. The Casimir force between two ideal metal plates is in fact an extension of the van der Waals force to relatively large separations between metallic bodies, where relativistic effects come into play and specific material properties become of no importance. A unified theory of the van der Waals and Casimir forces between real materials was created by Lifshitz [3]. In this theory material bodies at any nonzero temperature are considered and their properties are described by means of the frequency-dependent dielectric permittivity. During more than half a centure passed after the creation of the Lifshitz theory it was used in hundreds of papers. Presently this theory is gaining in importance in connection with numerous experiments on measuring the Casimir force [4–7] and prospective applications of the Casimir effect in nanotechnology [7]. Here we discuss the outstanding problems that were found in the Lifshitz theory during the last 10 years. It was proved [4, 7, 8] that for the Drude metals with perfect crystal lattices the Lifshitz theory violates the third law a [email protected]

397 of thermodynamics (the Nernst heat theorem). The same violation holds for dielectric materials with taken into account dc conductivity. With respect to the experiment, the predictions of the Lifshitz theory for both the Drude metals and dielectrics with included dc conductivity were found to be excluded by the measurement data at high confidence level. Below we consider these results in more detail and discuss possible ways on how to solve the problems. Here and below we use units with ¯h = c = 1. 2

Two parallel ideal metal planes at nonzero temperature

Using the thermal quantum field theory in Matsubara formulation the Casimir results (1) were generalized [7, 9] for the case of ideal metal planes in thermal equilibrium with environment at some constant temperature T . In this case the role of energy E is played by the free energy ∞ ∫ √ 2 2 kB T ∑ ′ ∞ k⊥ dk⊥ ln(1 − e−2a k⊥ +ξl ), F(a, T ) = (2) π 0 l=0

where kB is the Boltzmann constant, k⊥ is the magnitude of the wave vector projection on the metal planes, ξl = 2πkB T l with l = 0, 1, . . . are the Matsubara frequencies, and the prime near the summation sign means that the term with l = 0 is multiplied by 1/2. Then the Casimir pressure at nonzero temperature is given by √ ∞ ∫ k 2 + ξl2 ∂F(a, T ) 2kB T ∑ ′ ∞ P (a, T ) = − =− k⊥ dk⊥ √ ⊥ . (3) 2 2 ∂a π 0 e2a k⊥ +ξl − 1 l=0 As we will see below, at nonzero temperature one more physical quantity, the Casimir entropy, plays important role. For two ideal metal planes it takes the form S(a, T ) = −

∞ ∂F(a, T ) 1 kB ∑ 2 ξl ln(1 − e−2aξl ), = − F(a, T ) + ∂T T π

(4)

l=1

where F(a, T ) is defined in (2). The behaviors of Eqs. (2)–(4) at low and high temperatures provide important information on the contribution of thermal effects to the Casimir force. Thus, at low temperature T ≪ Teff ≡ 1/(2akB ) from Eq. (2) one obtains [7] [ ( )3 ( )4 ] 45ζ(3) T T π2 1+ − , (5) F(a, T ) = − 720a3 π3 Teff Teff where ζ(z) is the Riemann zeta function. As can be seen from Eq. (5), at room temperature the thermal corrections to the Casimir result (1) are very

398 small (note that at a typical separation a = 1 µm the effective temperature Teff ≈ 1145 K). In a similar way, from Eqs. (3) and (4) in the limit of low temperature one arrives at [ ( )4 ] T π2 1 1+ (6) P (a, T ) = − 240a4 3 Teff for the thermal Casimir pressure and ( )2 [ ] 3ζ(3)kB T 4π 3 T S(a, T ) = 1 − 8πa2 Teff 135ζ(3) Teff

(7)

for the Casimir entropy. From Eq. (6) one can see that the thermal correction to the Casimir pressure at T = 0 in Eq. (1) is very small. From Eq. (6) one can see that S(a, T ) → 0 when T → 0, i.e., the third law of thermodynamics (the Nernst heat theorem) for the Casimir entropy is satisfied as it should be. In the limit of high temperature T ≫ Teff it holds [7] F(a, T ) = −

kB T ζ(3), 8πa2

P (a, T ) = −

kB T ζ(3), 4πa3

S(a, T ) =

kB ζ(3). 8πa2

(8)

From Eq. (8) it follows that at high T the Casimir effect is in fact entirely thermal. Note that the results (8) are determined by the zero Matsubara frequency contribution alone, whereas the contributions of all Matsubara frequencies with l ≥ 1 are exponentially small. 3

The Lifshitz theory

The Lifshitz theory [3] starts from the standard electrodynamic continuity boundary conditions for the electric field, magnetic induction and electric displacement on the boundary planes of two semispaces separated with a gap of width a (instead of the ideal-metal boundary conditions used by Casimir). The material of semispaces is characterized by the frequency-dependent dielectric permittivity ε(ω). In the framework of the Lifshitz theory the Casimir free energy per unit area is given by [3, 7] ∞ ∫ { [ ] kB T ∑ ′ ∞ 2 F(a, T ) = k⊥ dk⊥ ln 1 − rTM (iξl , k⊥ )e−2aql 2π 0 l=0 [ ]} 2 + ln 1 − rTE (iξl , k⊥ )e−2aql . (9) 2 Here, ql2 = k⊥ + ξl2 and the reflection coefficients for the two independent polarizations of the electromagnetic field (transverse magnetic and transverse electric) are defined as

rTM (iξl , k⊥ ) =

εl ql − kl , εl ql + kl

rTE (iξl , k⊥ ) =

ql − kl , ql + kl

(10)

399 where 2 kl2 = k⊥ + εl ξl2 ,

εl = ε(iξl ).

(11)

Then the Casimir pressure and entropy are obtained from Eq. (9) by negative differentiations with respect to a and T , respectively. The dielectric permittivity of metals is conventionally presented using the Drude model ωp2 , (12) εD (ω) = εc (ω) − ω[ω + iγ(T )] where ωp is the plasma frequency, γ(T ) is the relaxation parameter and the permittivity of bound core electrons is expressed in an oscillator form εc (ω) = 1 +

K ∑ j=1

gj . ωj2 − ω 2 − iγj ω

(13)

Here, K is the number of oscillators, ωj are the oscillator frequencies, gj are the oscillator strengths, and γj are the damping parameters. The dielectric permittivity of dielectric is given by εd (ω) = εc (ω) + i

4πσ0 (T ) , ω

(14)

where σ0 (T ) is the static dc conductivity. The remarkable fact is that the Lifshitz theory with dielectric permittivities (12) and (14) violates the Nernst theorem leading to S(0) < 0 for metals with perfect crystal lattices and S(0) > 0 for dielectrics, respectively [7, 8, 10]. To bring the Lifshitz theory in agreement with thermodynamics one should omit the relaxation parameter γ(T ) in Eq. (12) and the dc conductivity σ0 (T ) in Eq. (14). Keeping in mind that the correct dielectric response at low frequencies is inverse proportional to ω, this presents a serious theoretical problem. 4

Comparison of the Lifshitz theory with experimental data

The Casimir pressure between two Au plates was determined dynamically from the measured gradient of the Casimir force between an Au sphere and an Au plate [4, 7, 11, 12]. It was shown that the data exclude the Lifshitz theory with εD in Eq. (12) at a 99.9% confidence level if γ ̸= 0. The same data are consistent with the Lifshitz theory if γ = 0. The difference in the Casimir forces between an Au sphere and Si plate was measured in the presence and in the absence of a laser light on the plate [4, 7, 13, 14]. In the presence of light Si was in the metallic state and in the absence of light in the dielectric state. It was shown that the data exclude the Lifshitz theory with εd in Eq. (14) at a 95% confidence level if σ0 ̸= 0. The same data are consistent with the Lifshitz theory if σ = 0.

400 The Casimir-Polder force between 87 Rb atoms and dielectric SiO2 plate was measured [4,7,15]. Again the measurement data were found [16] to exclude the Lifshitz theory with εd at a 70% confidence level if σ ̸= 0 and to be consistent with the data if σ0 = 0 [15]. The Casimir force between an Au sphere and a metallic indium tin oxide (ITO) plate was measured [17] before and after the plate was UV-treated. Presumably, the UV treatment caused the phase transition of the ITO from metallic to dielectric state. The data for the UV-treated sample were found to exclude the Lifshitz theory with εd in Eq. (14) at a 95% confidence level if σ0 ̸= 0 and to be consistent with the data if σ0 = 0 [17]. Thus, experiments exclude the Lifshitz theory in all the cases when it violates the Nernst heat theorem. 5

Conclusions and discussion

From the foregoing one can conclude that the Lifshitz theory in combination with two conventional models of dielectric permittivity used to describe metallic and dielectric materials contradicts to the third law of thermodynamics. Furthermore, computational results obtained using the Lifshitz theory and these models of dielectric permittivity are excluded at a high confidence level by the measurement data of several experiments performed by different experimental groups. Many attempts were undertaken during 12 years in order to solve these problems, but with no satisfactory results. At the present the opinion was proposed [18] that the problems in the theory of the Casimir effect cannot be solved without serious changes in basic concepts of quantum statistical physics regarding interaction of quantum fluctuations with matter. Acknowledgments This work was partially supported by DOE Grant No. DEF010204ER46131 and by the DFG Grant BO 1112/20-1. References [1] H.B.G.Casimir, Proc. K. Ned. Akad. Wet. B 51, 793 (1948). [2] V.A.Parsegian, Van der Waals Forces: A Handbook for Biologists, Chemists, Engineers, and Physicists (Cambridge University Press, Cambridge) 2005. [3] E.M.Lifshitz, Zh. Eksp. Teor. Fiz. 29, 94 (1956) [Sov. Phys. JETP 2, 73 (1956)]. [4] G. L. Klimchitskaya, U. Mohideen, V. M. Mostepanenko, Rev. Mod. Phys. 81, 1827 (2009).

401 [5] G. L. Klimchitskaya, U. Mohideen, V. M. Mostepanenko, Int. J. Mod. Phys. B 25, 171 (2011). [6] A.W.Rodriguez, F.Capasso and S.G.Johnson, Nature Photon. 5, 211 (2011). [7] M. Bordag, G. L. Klimchitskaya, U. Mohideen, V. M. Mostepanenko, Advances in the Casimir Effect (Oxford University Press, Oxford) 2009. [8] V.B.Bezerra, G.L.Klimchitskaya, V.M.Mostepanenko, C.Romero, Phys. Rev. A 69, 022119 (2004). [9] L.S.Brown, G.J.Maclay, Phys. Rev. 184, 1272 (1969). [10] B.Geyer, G.L.Klimchitskaya, V.M.Mostepanenko, Phys. Rev. D 72, 085009 (2005). [11] R.S.Decca, D.L´opez, E.Fischbach, G.L.Klimchitskaya, D.E.Krause, V.M.Mostepanenko, Phys. Rev. D 75, 077101 (2007). [12] R.S.Decca, D.L´opez, E.Fischbach, G.L.Klimchitskaya, D.E.Krause, V.M.Mostepanenko, Eur. Phys. J. C 51, 963 (2007). [13] F.Chen, G.L.Klimchitskaya, V.M.Mostepanenko, U.Mohideen, Optics Express 15, 4823 (2007). [14] F.Chen, G.L.Klimchitskaya, V.M.Mostepanenko, U.Mohideen, Phys. Rev. B 76, 035338 (2007). [15] J.M.Obrecht, R.J.Wild, M.Antezza, L.P.Pitaevskii, S.Stringari, E.A.Cornell, Phys. Rev. Lett. 98, 063201 (2007). [16] G.L.Klimchitskaya, V.M.Mostepanenko, J. Phys. A 41, 312002 (2008). [17] C.-C.Chang, A.A.Banishev, G.L.Klimchitskaya, V.M.Mostepanenko, U.Mohideen, Phys. Rev. Lett. 107, 090403 (2011). [18] G.L.Klimchitskaya, V.M.Mostepanenko, Int. J. Mod. Phys. A 25, 2302 (2010).

402 CONSTRAINTS ON LIGHT ELEMENTARY PARTICLES AND EXTRA DIMENSIONAL PHYSICS FROM THE CASIMIR EFFECT Galina L. Klimchitskayaa Department of Physics, North-West Technical University, Millionnaya Street 5, St.Petersburg, 191065, Russia Abstract. Many extensions of the standard model predict the existence of Yukawatype corrections to Newtonian gravity in the interaction range below one millimeter. The strongest constraints on these corrections at separations from one nanometer to one micrometer follow from measurements of the Casimir force. We report new constraints on light elementary particles and extra dimensional unification schemes obtained from the Casimir effect during the last two years.

During the last few decades the possible existence of Yukawa-type corrections to Newtonian gravitational law has attracted considerable attention [1]. For two point-like particles with masses m1 and m2 spaced at a separation r apart, such corrections are conventionally presented in the form [1, 2] VYu (r) = −

αGm1 m2 −r/λ e . r

(1)

Here, G is the gravitational constant, α and λ are the strength and the interaction range of the Yukawa interaction, respectively. Corrections (1) can be caused by the exchange of light elementary particles between pairs of atoms belonging to two macrobodies [1, 3] (in this case λ is the Compton wavelength of a respective particle). Such corrections are also generated in multidimensional compactification schemes, where extra dimensions are compactified at relatively low energy of the order 1 TeV [4, 5]. Constraints on the parameters of Yukawa-type potential (1), α and λ, were traditionally obtained from the E¨otvos- and Cavendish-type experiments (see Refs. [2, 6, 7] for a review). At short interaction range (below a few micrometers), gravitational experiments do not lead to competitive constraints because the gravitational force becomes too weak. Here, the hypothetical interactions should be considered on a background of the van der Waals and Casimir forces, which originate from zero-point and thermal fluctuations of the electromagnetic field. The possibility of obtaining constraints on the Yukawa- and power-type corrections to Newton’s gravity from the measurements of the Casimir force was predicted in Refs. [8, 9], respectively (see also Ref. [3] for a review of all constraints from the old measurements of the van der Waals and Casimir forces). The energy of Yukawa interaction between two homogeneous macrobodies can be calculated as Z Z e−|r 1 −r 2 |/λ EYu (a) = −Gαρ1 ρ2 dr 1 dr 2 , (2) |r 1 − r 2 | V1 V2 a e-mail:

[email protected]

403 ½¼



35

30

25

20

15 -8.5

-8

-7.5 ½¼ 

-7 

Figure 1: The strongest constraints on Yukawa-type corrections to Newton’s gravitational law obtained at a 95% confidence level from measurements of the lateral Casimir force between corrugated surfaces (the solid line), measurements of the normal Casimir force by means of an atomic force microscope (the long-dashed line) and measurements of the Casimir pressure by means of a micromachined oscillator (the short-dashed line). The allowed values in the (λ, α)-plane lie beneath the lines.

where V1,2 and ρ1,2 are the volumes of the bodies and densities of their materials, respectively, and a is the separation between the bodies. Then one can calculate the Yukawa force between these bodies as F Yu (a) = −∂EYu (a)/∂a. Usually the Casimir force between two macrobodies FC (a) or its gradient FC0 ≡ ∂FC (a)/∂a are measured (see Ref. [10] for a review of recent measurements). Then the constraints on the parameters of Yukawa-type interaction (1) can be obtained from the respective inequalities [2, 11, 12] ∂EYu (a) ≤ ΞF 0 (a), |F Yu (a)| ≤ ΞFC (a) or (3) C ∂a where ΞFC (a) [or ΞFC0 (a))] is the confidence interval for differences between theory and experiment found at a chosen confidence level (95% in Refs. [11,12]). The best constraints on the Yukawa-type corrections to Newtonian gravity obtained at a 95% confidence level from measurements of the Casimir force are presented in Fig. 1. The allowed values of λ and α in this figure lie beneath each line. The solid line shows constraints obtained [13] from measurements of the lateral Casimir force [14, 15]. They are up to 5 orders of magnitude stronger than the previously known constraints obtained [11, 16] from measurements of the normal Casimir force using an atomic force microscope [17, 18]. The short-dashed line demonstrates constraints obtained from measurements of the Casimir pressure by means of the micromachined oscillator [11]. The prospects of further strengthening of constraints on Yukawa-type interactions are discussed in Refs. [13, 20] where several new experimental configurations are analyzed.

404 Acknowledgments This work was partially supported by DOE Grant No. DEF010204ER46131 and by DFG Grant BO 1112/20-1. References [1] E.Fischbach, C.L.Talmadge, The Search for Non-Newtonian Gravity (Springer, New York) 1999. [2] M.Bordag, G.L.Klimchitskaya, U.Mohideen, V.M.Mostepanenko, Advances in the Casimir Effect (Oxford University Press, Oxford) 2009. [3] V.M.Mostepanenko, I.Yu.Sokolov, Phys. Rev. D 47, 2882 (1993). [4] E.G.Floratos, G.K.Leontaris, Phys. Lett. B 465, 95 (1999). [5] A.Kehagias, K.Sfetsos, Phys. Lett. B 472, 39 (2000). [6] E.G.Adelberger, B.R.Heckel, C.W.Stubbs, W.F.Rodgers, Annu. Rev. Nucl. Part. Sci. 41, 269 (1991). [7] E.G.Adelberger, B.R.Heckel, C.W.Stubbs, W.F.Rodgers, Annu. Rev. Nucl. Part. Sci. 53, 77 (2003). [8] V.A.Kuzmin, I.I.Tkachev, M.E.Shaposhnikov, Pis’ma Zh. Eksp. Teor. Fiz. 36, 49 (1982) [JETP Lett. 36, 59 (1982)]. [9] V.M.Mostepanenko, I.Yu.Sokolov, Phys. Lett. A 125, 405 (1987). [10] G.L.Klimchitskaya, U.Mohideen, V.M.Mostepanenko, Rev. Mod. Phys. 81, 1827 (2009). [11] R.S.Decca, D.L´ opez, E.Fischbach, G.L.Klimchitskaya, D.E.Krause, V.M.Mostepanenko, Eur. Phys. J. C 51, 963 (2007). [12] E.Fischbach, G.L.Klimchitskaya, D.E.Krause, V.M.Mostepanenko, Eur. Phys. J. C 68, 223 (2010). [13] V.B.Bezerra, G.L.Klimchitskaya, V.M.Mostepanenko, C.Romero, Phys. Rev. D 81, 055003 (2010). [14] H.-C.Chiu, G.L.Klimchitskaya, V.N.Marachevsky, V.M.Mostepanenko, U.Mohideen, Phys. Rev. B 80, 121402(R) (2009). [15] H.-C.Chiu, G.L.Klimchitskaya, V.N.Marachevsky, V.M.Mostepanenko, U.Mohideen, Phys. Rev. B 81, 115417 (2010). [16] G.L.Klimchitskaya, U.Mohideen, V.M.Mostepanenko, J. Phys. A 40, F339 (2007). [17] B.W.Harris, F.Chen, U.Mohideen, Phys. Rev. A 62, 052109 (2000). [18] F.Chen, G.L.Klimchitskaya, U.Mohideen, V.M.Mostepanenko, Phys. Rev. A 69, 022117 (2004). [19] V.B.Bezerra, G.L.Klimchitskaya, V.M.Mostepanenko, C.Romero, Phys. Rev. D 83, 075004 (2011). [20] G.L.Klimchitskaya, C.Romero, Phys. Rev. D 82, 115005 (2010).

405 SPHERICAL CASIMIR EFFECT WITHIN D = 3 + 1 MAXWELL–CHERN–SIMONS ELECTRODYNAMICS Oleg Kharlanov a and Vladimir Zhukovsky b Faculty of Physics, Moscow State University, 119991 Moscow, Russia Abstract. We calculate the Casimir tension on the conducting sphere within electrodynamics with the Lorentz-violating interaction with the axial vector condensate ηµ .

The Maxwell–Chern–Simons electrodynamics is well known within the context of (2 + 1)-dimensional models [1]; in particular, it describes graphene, as well as other effectively two-dimensional structures. The (3 + 1)-dimensional analogue of this theory also arises within the models involving the axion field, which were recently shown to provide the possibility of dynamical Lorentz violation [2]. After the Lorentz violation, the Lagrangian of the photon sector of such a model reads [3] 1 L = − Fµν F µν + η µ Aν F˜µν , 4

1 F˜µν = µναβ F αβ , 2

(1)

and contains the interaction of photons with the homogeneous axial vector background (condensate) η µ . We consider the Casimir effect [4] in the spatially isotropic case η µ = (η, 0), using the dyadic Green’s function formalism [5]: Z 0 Γij (x, x ; ω) = i dt hEi (x, t)Ej (x0 , 0)i0 eiωt . (2) The above function satisfies the equations, which come from the field equations for the electric field E(x) and the boundary conditions on the conductor, (∇2 + ω 2 − 2η∇)Γ(x, x0 ; ω) = (1∇2 − ∇ ⊗ ∇ − 2η∇)δ 3 (x − x0 ), 0

(3)

0

x, x ∈ V ;

(4)

0

0

(5)

∇ · Γ(x, x ; ω) = 0, n × Γ(x, x ; ω) = 0,

x ∈ ∂V, x ∈ V,

where ∂V is the conducting boundary of spherical domain V , n is the unit normal on this boundary, and we use the matrix notation: (i )jk = ijk , (∇ ⊗ ∇)jk = ∂j ∂k . Scalar (dot) and cross products in the second and the third equations are understood over the first index of Γij . Recently we have shown [6] that the solution of the above system of equations can be presented in the form i ω 2 X h (λ) B (x, x0 ) − e(λ) (x, x0 ) , (6) Γ(x, x0 ) = δ 3 (x − x0 ) + 2¯ ω λ=±1

e a e-mail: b e-mail:

(λ)

0

(x, x ) = (Kλ 1 +

[email protected] [email protected]

Kλ−1 ∇

⊗ ∇ + λ∇)ϕ(x, x0 ; Kλ ),

(7)

406 p ¯ , and the scalar function ϕ is an arbitrary where ω ¯ = ω 2 + η 2 , Kλ = −λη + ω solution of the Helmholtz equation (∇2 +K 2 )ϕ(x, x0 ; K) = δ 3 (x−x0 ). The matrix functions B (λ) determine the electromagnetic field by its given tangential components on ∂V and satisfy the homogeneous wave equations: (∇2 + ω 2 − 2η∇)B (λ) (x, x0 ; ω) = 0, ∇ · B (λ) = 0, x, x0 ∈ V ; n × B (λ) = n × e(λ) , x ∈ ∂V, x0 ∈ V.

(8) (9)

In the case of the conducting sphere of radius R, the spherical symmetry favors the expansion of the desired Green’s function (2) over the vector spherical p harmonics X jm (er ) = (x × ∇)Yjm (er )/ j(j + 1), er ≡ x/r, r ≡ |x|: B (λ) (x, x0 ) =

Xn (λ)j (λ)j BE (r, r0 )Ξjm (er , e0r ) + rot(BME Ξjm ) j,m

←− ←− o (λ)j (λ)j + (BEM Ξjm )rot0 + rot(BM Ξjm )rot0 ,

(10)

where Ξjm (er , e0r ) = X jm (er ) ⊗ X ∗jm (e0r ). The non-triviality of the second and the third terms in brackets is typical for the η 6= 0 case and indicates the spatial parity violation. The expression for the Casimir tension on the sphere is derived from the partially symmetrized electromagnetic stress tensor and has the form

f =−

+∞ Z ∞ n X j(j + 1)  j dω (2j + 1) ω 2 − BM (r, r0 ) 2 R j=1

i 16π 2

−∞ 0 j (r, r0 ) o r =r=R+0 1 ∂ BE . ω2 ∂r∂r0 r 0 =r=R−0 2

+

(11)

Within the theory under consideration, it is impossible to find the symmetric and gauge invariant stress tensor due to the Lorentz violation. However, one can demonstrate that the desired normal-normal component of the partially symmetrized tensor is gauge invariant after the integration over the sphere. The result of this integration is shown in the above expression. The EM - and M E-components of the Green’s function expansion are parityodd and vanish after the integration over the sphere. The two remaining spherical components of the Green’s function, which are present in (11), can be

407 (λ)j

expressed in terms of the functions BE,M (r, r0 ), (λ)j

BE (r, r0 ) = −i

X

j λ0 Kλ Kλ0 Gλλ 0 Cλ0 [Kλ jj (Kλ R), −λξR jj (Kλ R)],

(12)

λ0 =±1 (λ)j

BM (r, r0 ) = i

X

j −1 Kλ Gλλ 0 Cλ0 [−λjj (Kλ R), Kλ ξR jj (Kλ R)],

(13)

λ0 =±1

βK−λ0 jj (K−λ0 R) − λ0 αξR jj (K−λ0 R) , (14) K+ jj (K+ R)ξR jj (K− R) + K− jj (K− R)ξR jj (K+ R) p j 0 where Gλλ π/2xJj+1/2 (x) are the spherical 0 ≡ j(Kλ0 r)jj (Kλ r ), jj (x) = Bessel functions, and ξR ≡ 1 + R∂/∂R. The analogous expressions apply to the exterior of the sphere r, r0 > R. Substitution of the above solutions into (11) leads to the desired expression for the Casimir tension, which, being numerically analyzed, reveals the presence of a quadratic correction in the pseudovector condensate η. Cλ0 [α, β] =

Acknowledgments The authors are grateful to A. V. Borisov and A. E. Lobanov for the discussion of the results obtained. References [1] S.-S. Chern and J. Simons, Ann. Math. II 99, 48 (1974). [2] A. A. Andrianov, R. Soldati, and L. Sorbo, Phys. Rev. D 59, 025002 (1998). [3] D. Colladay and V. A. Kosteleck´ y, Phys. Rev. D 58, 116002 (1998). [4] H. B. G. Casimir, Proc. K. Ned. Akad. Wet. 51, 793 (1948). [5] K. A. Milton, “The Casimir Effect: Physical Manifestation of Zero-Point Energy” (World Scientific, New York), 2001. [6] V. Ch. Zhukovsky and O. G. Kharlanov, in “Proceedings of the Lomonosov Readings Scientific Conference, section of Physics, 16–25 April, 2010” (Faculty of Physics, MSU, Moscow), 112, 2010 [in Russian].

408 GENERAL RELATIVITY AND WEYL GEOMETRY: TOWARDS A NEW INVARIANCE PRINCIPLE Carlos Romero a , J. B. Fonseca-Neto b Departamento de Fisica, Universidade Federal da Paraiba, Caixa Postal 5008, 58051-970 , J. Pessoa, Pb, Brazil Abstract. Our aim in this talk is to show that one can formulate general relativity using the language of a non-Riemannian geometry, namely, the one known as Weyl integrable geometry. In this formulation, general relativity appears as a theory in which the gravitational field is described simultaneously by two geometrical fields: the metric tensor and the Weyl scalar field, the latter being an essential part of the geometry, manifesting its presence in almost all geometrical phenomena, such as curvature, geodesic motion, and so on. In this new geometrical setting, general relativity exhibits a new kind of invariance, namely, the invariance under Weyl transformations. We are then led to a scenario in which the gravitational field is not associated only with the metric tensor, but with the combination of both the metric and the geometrical scalar field

1

Introduction

It is a very well known fact that the principle of general covariance has played a major role in leading Einstein to the formulation of the theory of general relativity (GR). A rather different kind of invariance that has been considered in some branches of physics is invariance under conformal transformations. These represent changes in the units of length and time that differ from point to point in the space-time manifold. Conformal transformations were first introduced in physics by H. Weyl in his attempt to formulate a unified theory of gravitation and electromagnetism [1]. It turns out that Einstein’s theory of gravity in its original formulation is not invariant neither under conformal transformations nor under Weyl transformations. One of our aims in this talk is to show that one can formulate general relativity using the language of a non-Riemannian geometry, namely, the one known as Weyl integrable geometry. In this formulation, general relativity appears as a theory in which the gravitational field is described simultaneously by two geometrical fields: the metric tensor and the Weyl scalar field [2]. As we shall see, in this new geometrical setting general relativity exhibits a new kind of invariance, namely, the invariance under Weyl transformations. 2

Weyl geometry

The geometry conceived by Weyl consists of a generalization of Riemannian. Instead of postulating that the covariant derivative of the metric tensor g is zero, we assume the more general condition ∇α gµν = σα gµν

(1)

409 where { ∂ } σα denotes the components with respect to a local coordinate basis of a one-form field σ defined on M . This, in fact, represents a gener∂xα alization of the Riemannian condition of compatibility between the connection ∇ and g, namely, the requirement that the length of a vector remain unaltered by parallel transport. If σ = dϕ, where ϕ is a scalar field, then we have what is called an integrable Weyl geometry. The set (M, g, ϕ) consisting of a differentiable manifold M endowed with a metric g and a Weyl scalar field ϕ is usually referred to as a Weyl frame. It is interesting to note that the Weyl condition (1) remains unchanged when we go to another Weyl frame (M, g, ϕ) by performing the following simultaneous transformations in g and ϕ: g = ef g

(2)

ϕ=ϕ+f

(3)

where f is a scalar function defined on M . Condition (1) is sufficient to determine the Weyl connetion ∇ in terms of the metric g and the Weyl one-form field σ. Indeed, a straightforward calculation shows that 1 αβ α Γα (4) [gβµ σν + gβν σµ − gµν σβ ] µν = {µν } − g 2 1 αβ where {α [gβµ,ν + gβν,µ − gµν,β ] represents the Christoffel symbols, µν } = 2 g i.e., the components of the Levi-Civita connection.

3

General relativity and a new kind of invariance

The fact that geodesics are invariant under (2) and (3) and that Riemannian geometry is a particular case of Weyl geometry seems to suggest that general relativity may be formulated in a more general geometrical setting, namely, one in which the form of the field equations is also invariant under Weyl transformations. We shall now show that this is indeed possible, and we shall proceed through the following steps. First, we shall assume that the space-time manifold which represents the arena of physical phenomena may be described by a Weyl integrable geometry, which means that now gravity will be described by two geometric entities: a metric and a scalar field. The second step is to set up an action S invariant under Weyl transformations. We shall require that S be chosen such that there exists a unique frame in which it reduces to the Einstein-Hilbert action. The third step consists of extending Einstein’s geodesic postulate to arbitrary frames, such that in the Riemann frame it should describe the motion of test particles and light exactly in the same way as predicted by general relativity. Finally, the fourth step is to define proper time in an arbitrary frame. This definition should be invariant under Weyl transformations and coincide with the definition of GR’s proper time in the

410 Riemann frame. It turns out then that the simplest action that can be built under these conditions is ∫ { } √ S = d4 x −ge−ϕ R + 2Λe−ϕ + κe−ϕ Lm , (5) where R denotes the scalar curvature defined in terms of the Weyl connection, Λ is the cosmological constant, Lm stands for the Lagrangian of the matter fields and κ is the Einstein‘s constant. In n-dimensions we would have ∫ } { √ n Sn = dn x −ge(1− 2 )ϕ R + 2Λe−ϕ + κe−ϕ Lm . (6) In order to see that the above action is, in fact, invariant with respect to Weyl transformations, we just need to recall that under (2) and (3) we have √ µ n √ g µν = e−f g µν , −g = e 2 f −g, R ναβ = Rµναβ , Rµν = Rµν , R = g αβ Rαβ = e−f g αβ Rαβ = e−f R. It will be assumed that Lm generally depends on ϕ, gµν and the matter fields, its form being obtained from the special theory of relativity through the prescription ηµν → e−ϕ gµν and ∂µ → ∇µ , where ∇µ denotes the covariant derivative with respect to the affine connection. As it can be easily seen, these rules also ensure the invariance under Weyl transformations of part of the action that is responsible for the coupling of matter with the gravitational field, and, at the same time, reduce to the principle of minimal coupling adopted in general relativity when we set ϕ = 0, that is, in the Riemann frame. We now turn our attention to the motion of test particles and light rays. Here, our task is to extend GR’s geodesic postulate in such a way that it is invariant under Weyl transformations. The extension is straightforward and may be stated as follows: if we represent parametrically a timelike curve as xµ = xµ (λ), then this curve will correspond to the world line of a particle free from all non-gravitational forces, passing through the events xµ (a) and xµ (b), if and only if it extremizes the functional ∫

b

∆τ =

−ϕ 2

e a

( )1 dxµ dxν 2 gµν dλ, dλ dλ

(7)

which is obtained from the special relativistic expression of proper time by using the prescription ηµν → e−ϕ gµν . Clearly, the right-hand side of this equation is invariant under Weyl transformations and reduces to the known expression of the propertime in general relativity in the Riemann frame. We take ∆τ , as given above, as the extension of GR’s clock hypothesis, i.e., the assumption that ∆τ measures the proper time measured by a clock attached to the particle, to an arbitrary Weyl frame, Therefore, the extension of the geodesic postulate by requiring that the functional (7) be an extremum is equivalent to postulating that the particle motion

411 must follow affine geodesics defined by the Weyl connection Γµαβ . Since both the connection components Γµαβ and the proper time τ are invariant when we switch from one Weyl frame to the other, the affine geodesic equations are manifestly covariant under Weyl transformations. Because the path of light rays are null curves, one cannot use the proper time as a parameter to describe them. In fact, light rays are supposed to follow null affine geodesics, which cannot be defined in terms of the functional (7), but, instead, they must be characterized by their behaviour with respect to parallel transport. We shall extend this postulate by simply assuming that light rays follow Weyl null affine geodesics. Finally, one sees that the causal structure of space-time remains unchanged in all Weyl frames. This seems to complete our program of formulating general relativity in a geometrical setting that exhibits a new kind of invariance, namely, that with respect to Weyl transformations. Acknowledgments C. Romero would like to thank Prof. Alexander Studenikin and the Organizing Committee for hospitality. References [1] H. Weyl, Sitzungesber Deutsch. Akad. Wiss. Berli 465 (1918); H. Weyl, “Space, Time, Matter” (Dover, New York ) 1952. [2] C. Romero, J. B. Fonseca-Neto, M. L. Pucheu, Int. J. Mod. Phys. A 26, 3721 (2011). C. Romero, J. B. Fonseca-Neto, M. L. Pucheu, Found. Phys. 41 (2011).

412 DERIVATION OF THE NSVZ BETA-FUNCTION IN N=1 SQED REGULARIZED BY HIGHER DERIVATIVES BY SUMMATION OF DIAGRAMS Konstantin Stepanyantza Faculty of Physics, Moscow State University, 119991 Moscow, Russia Abstract. We briefly describe the derivation of the exact NSVZ β-function in the N = 1 supersymmetric electrodynamics (SQED), regularized by higher derivatives.

1

Higher derivative regularization

The higher covariant derivative regularization was proposed in [1]. This regularization can be applied to calculation of quantum corrections in supersymmetric theories [2]. It does not break the supersymmetry and, unlike the dimensional reduction, is consistent. The action of the massless N = 1 SQED, regularized by higher derivatives, in terms of superfields is written as 1 S = 2 Re 4e

∫ 4

2

ab

d x d θ Wa C R

( ∂2 ) Λ2

1 Wb + 4

∫

( ) d4 x d4 θ ϕ∗ e2V ϕ + ϕe∗ e−2V ϕe ,

(1) where R(0) = 1 and R(∞) = ∞. For example, it is possible to choose R = 1 + ∂ 2n /Λ2n . Then all Feynman diagrams beyond the one-loop approximation become finite. The remaining one-loop diagrams are regularized by inserting the Pauli–Villars determinants [3] into the generating functional. Masses MI of the Pauli–Villars fields should be proportional to the parameter Λ. 2

The exact β-function

In order to find the β-function we calculate ) d ( −1 β(α0 ) dα−1 . d (α0 , Λ/p) − α0−1 =− 0 = d ln Λ d ln Λ α02 p=0

(2)

The function d−1 is extracted from the two-point Green function of the gauge superfield by the substitution V → θ¯a θ¯a θb θb ≡ θ4 . For N = 1 SQED this Green function is given by [4]

(2)

∆ΓV = a e-mail:

⟨

( )2 ⟩ − 2i Tr(V J0 ∗) − 2iTr(V J0 ∗ V J0 ∗) − 2iTr(V 2 J0 ∗) + . . . , (3)

[email protected]

413 ˜ where dots denotes contribution of ϕ-loops and the Pauli-Villars fields, ¯ 2 D2 /16∂ 2 ) ∗ ≡ 1/(1 − (e2V − 1)D

(4)

encode sequences of vertexes and propagators on the matter line, and J0 = ¯ 2 D2 /16∂ 2 is the effective vertex. After some algebraic transformations [4] e2V D the first term in Eq. (3) gives the contribution ) )2 ⟩ d ⟨( ( Tr − 2θc θc θ¯d [θ¯d , ln(∗)] + iθ¯c (γ ν )c d θd [yν∗ , ln(∗)] + . . . . (5) d ln Λ Similarly, the second term in Eq. (3) gives −2i

⟨ [ [ ]]⟩ d Tr θ4 yµ∗ , (y µ )∗ , ln(∗) + . . . − terms with a δ-function. (6) d ln Λ The third term in Eq. (3) vanishes. From expressions (5) and (6) we see that in all orders the β-function is given by integrals of double total derivatives. This is in agreement with the results of explicit calculations [5, 6]. Summing all terms with δ-function [4] we obtain the exact NSVZ β-function [7] i

β(α) =

) α2 ( 1 − γ(α) . π

(7)

Acknowledgments This work was supported by Russian Foundation for Basic Research grants No 11-01-00296-a. References [1] A. A. Slavnov, Nucl. Phys., B 31, 301 (1971); Theor. Math. Phys. 13, 1064 (1972). [2] V. K. Krivoshchekov, Theor. Math. Phys. 36, 745 (1978); P. West, Nucl. Phys. B 268, 113 (1986). [3] L. D. Faddeev, A. A. Slavnov, “Gauge fields, introduction to quantum theory”, (Benjamin Reading), 1990. [4] K. V. Stepanyantz Nucl. Phys. B 852, 71 (2011). [5] A. A. Soloshenko, and K. V. Stepanyantz, Theor. Math. Phys. 140, 1264 (2004). [6] A. Smilga, A. Vainshtein, Nucl. Phys. B 704, 445 (2005). [7] V. Novikov, M. Shifman, A. Vainshtein, and V. Zakharov, Nucl. Phys. B 229, 381 (1983); Phys. Lett. B 166, 329 (1985); A. I. Vainshtein, V. I. Zakharov, and M. A. Shifman, JETP Lett. 42, 224 (1985).

414 POST–EXPONENTIAL DECAY OF UNSTABLE PARTICLES: POSSIBLE EFFECTS IN PARTICLE PHYSICS AND ASTROPHYSICS K. Urbanowskia , J.Piskorskib University of Zielona G´ ora, Institute of Physics, ul. Prof. Z. Szafrana 4a, 65–516 Zielona G´ ora, Poland Abstract. Properties of the decay law at long times t are studied. Analyzing the transition time region between exponential and non-exponential form of the survival amplitude it is found that the instantaneous energy of unstable particle can take very large values, much larger than the energy of this state for t from the exponential time region. Basing on the results obtained for a model considered, it is hypothesized that this purely quantum mechanical effect can have astrophysical consequences, eg. this effect may be responsible for causing unstable particles to emit electromagnetic–, X– or γ–rays at some time intervals from the transition time regions.

1

Introduction

One of quantities characterizing unstable states |ϕ⟩, |ϕα ⟩ ∈ H (where H is the Hilbert space of states of the considered system) is their decay law. The decay law, Pϕ (t) of an unstable state |ϕ⟩ decaying in vacuum is defined as follows Pϕ (t) = |a(t)|2 ,

(1)

where a(t) is the probability amplitude of finding the system at the time t in the initial state |ϕ⟩ prepared at time t0 = 0, a(t) = ⟨ϕ|ϕ(t)⟩ and |ϕ(t)⟩ is the solution of the Schr¨ odinger equation for the initial condition |ϕ(0)⟩ = |ϕ⟩. From basic principles of quantum theory it is known that the amplitude a(t), and thus the decay law Pϕ (t) of the unstable state |ϕ⟩, are completely determined by the density of the energy distribution ω(E) for the system in this state [1, 2] ∫ i a(t) = ω(E) e− h¯ E t dE. (2) Spec.(H)

where ω(E) ≥ 0 and a(0) = 1. Note that in fact the amplitude a(t) contains information about the decay law Pϕ (t) of the state |ϕ⟩, that is about the decay rate γϕ0 (or lifetime τϕ = γh¯0 ) of ϕ

this state, as well as the energy Eϕ0 of the system in this state. This information can be extracted from a(t) using the so–called ”effective Hamiltonian”, hϕ , which is defined for the one–dimensional subspace of states H|| spanned by the normalized vector |ϕ⟩ as follows [3], def

hϕ = i¯h a e–mail: b e–mail:

∂a(t) 1 . ∂t a(t)

[email protected] [email protected]

(3)

415 Hence the instantaneous energy and the instantaneous decay rate of the system in the state |ϕ⟩ equal [4, 5], Eϕ ≡ Eϕ (t) = ℜ (hϕ (t)),

γϕ ≡ γϕ (t) = − 2 ℑ (hϕ (t)),

(4)

where ℜ (z) and ℑ (z) denote the real and imaginary parts of z, respectively. 2

The model

Let us assume that Spec.(H) = [0, ∞), and let us choose ω(E) as follows ω(E) =

γϕ0 N Θ(E) , γ0 2π (E − Eϕ0 )2 + ( 2ϕ )2

(5)

where N is a normalization constant and Θ(E) = {1 for E ≥ 0, and 0 for E < 0}. The substitution of this ω(E) into (2) leads to the analytical expression for a(t) as the sum of the exponential function and the integral exponential functions [1, 4, 5] and in general one has a(t) ≡ aexp (t) + anon (t),

(6)

γ0

where aexp (t) = N exp [− h¯i (Eϕ0 − i 2ϕ )t] and anon (t) = a(t) − aexp (t). Numerical calculations were performed for times t ∼ tas (for times from the transition time region), where tas ≫ τϕ denotes the time t at which con2 tributions to a(t) t→∞ from the exponential component and from the non– exponential component proportional to t12 are comparable, that is (see (6)), |aexp (t)|2 ≃ |anon (t)|2

(7)

for t → ∞. Some results of the calculations are presented in Fig. 1.

Figure 1: Instantaneous energy Eϕ (t) in the transition time region. The case

0 Eϕ

γ0

ϕ

= 10.

416 3

Concluding remarks

All the above results were obtained for particles being in their rest coordinate system. The question is what effects can be observed when the unstable particle is moving with a relativistic velocity in relation to an external observer. The obvious assumption is that the energy of the moving particle (the kinetic energy W ϕ ) ϕ is conserved, W1ϕ = W2ϕ , (8) where W1ϕ ≡ m0ϕ c2 γ1 , γ1 = γ(t1 ), and it is assumed that t1 ∼ τϕ′ and t1 ≪ t′as , (τϕ′ = γ1 τϕ ), W2ϕ = m0ϕ (t2 ) c2 γ(t2 ), γ(t2 ) = γ2 , t2 ∼ t′as , t′as = γ(t) tas , and E0

γ = γ(t) = (1 − (v ϕ (t)/c2 )2 )−1/2 . There is m0ϕ = cϕ2 , and m0ϕ (t2 ) = Thus W1ϕ ≡ Eϕ0 γ1 , and W2ϕ = Eϕ (t2 ) γ(t2 ).

Eϕ (t2 ) c2 .

(9)

The consequences of (8) and (9): Eϕ0 γ1 = Eϕ (t2 )γ(t2 ), or γ1 = κ(t2 )γ(t2 ), where κ(t2 ) =

(10)

Eϕ (t2 ) = κ2 . Eϕ0 v ϕ −v ϕ

So, if κ2 ̸= 1 then γ2 ̸= γ1 which means that v2ϕ ̸= v1ϕ and thus a ¯ = t22 −t11 ̸= 0 (¯ a is the average acceleration). Now using an expression for the energy dW ϕ emitted in the unit of time dt′ by a moving charged relativistic particle ϕ, 2

dW ϕ 1 q 2 v˙ϕ 6 = γ , dt′ 6πϵ0 c2

(11)

(where q is the electric charge, ϵ0 – permittivity for free space) one infers that the moving charged unstable particle ϕ has to emit electromagnetic radiation at the transition time region. The same concerns neutral unstable particles with non–zero magnetic moment. Such relativistic particles are produced, e.g. in some astrophysical processes. For ultra–relativistic muons, e.g. for W1µ ≃ 1018 [eV], it is found within the model considered that for some time intervals from µ 12 the transition time region dW [eV/s]. dt′ can reach values (0, 11 ÷ 172) × 10 References [1] [2] [3] [4] [5]

K. Urbanowski and J. Piskorski, arXiv: 0908.2219, 1007.1742. S. Krylov, V. A. Fock, Zh. Eksp. Teor. Fiz. 17, 93 (1947). K. Urbanowski, Phys. Rev. A 50, 2847 (1994). K. Urbanowski, Cent. Eur. J. Phys. 7, 696 (2009). K. Urbanowski, Eur. Phys. J. D 54, 25 (2009).

417 MORE ON NONCOMMUTATIVE MAGNETIC MOMENT AND LEPTON SIZE Tiago Adorno a , Dmitry Gitman b Instituto de F´ısica, Universidade de S˜ ao Paulo, Brazil, Anatoly Shabad c P.N. Lebedev Physics Institute, Moscow, Russia, Abstract. Upper bounds on elementary length are discussed resulting from the magnetic moment inherent [1] to a charged particle in noncommutative electrodynamics

1

Introduction

In the recent works by D. Vassilevich and the present authors [1] we formulated classical field equations in U (1)∗ -theory (noncommutative electrodynamics) that – at least within the first order in the noncommutativity (NC) parameter θ – restrain the gauge invariance in spite of the presence of external current. Let the latter be just a static electric charge distributed inside a sphere of a finite radius a with the uniform charge density 3 Ze → ρ (− x)= , 4π a3

r < a,

→ r = |− x|.

(1)

→ Outside the sphere there is no charge: ρ (− x ) = 0, if r > a. It was found that the above finite-size static total charge Ze, where e is the elementary charge, produces not only the electrostatic field, but also behaves itself as a magnetic dipole with the magnetic field given in the remote region r >> a by the following vector-potential [ ] − → − → M × x 2e → − → → − − A = , M = θ (Ze)2 , (2) r3 5a → − where M was called the noncommutative magnetic moment of the charged − → particle. Here the three spacial components of the vector θ are defined as i ijk jk θ ≡ (1/2)ε θ , i, j, k = 1, 2, 3 in terms of the antisymmetric NC tensor θµν that fixes the commutation relations between the operator-valued coordinate components [X µ , X ν ] = iθµν , and only the space-space NC, i.e. the special case of θ0ν = 0 in a certain Lorentz frame, was considered. The extension a of the charge in (2) should be kept nonzero in the spirit of the noncommutative theory that does with their size smaller √ not admit objects − → than the elementary length l = θ, where θ = | θ |. For a point charge a a e-mail:

[email protected] [email protected] c e-mail: [email protected] b e-mail:

418 magnetic solution also exists [2], although in this case it is not a magnetic dipole one. It is more important that that solution is too singular in the point r = 0, where the charge is located, and hence it cannot be given a mathematical sense in terms of the distribution theory in a conventional way. If we understand the radius a in (2) as the size of an electrically charged elementary particle (Z = 1), we can speculate on what the contribution of NC − → into its magnetic moment M may be. Certainly, this is expected to be very small, because of the extreme smallness of the NC√parameter θ. It is primarily supposed [3] that the corresponding length l = θ should be of the Planck scale of l ∼ 10−33 cm (or ΛPl ∼ 4 × 1019 Gev in energy units). The reason is that at so small distances unification of gravity with quantum mechanics requires quantization of space-time. Although the Planck scale is well off any experimental reach, the everlasting problem is to estimate the upper limits on θ basing on the existing and advancing experimental preciseness. In [1] it was discussed what new restrictions on the extent of NC may follow from the newly established fact that a charged elementary particle is a carrier of the magnetic moment (2) in a noncommutative theory, irrespective of its orbital moment or spin. In the present article we shall further elaborate this matter addressing the charged leptons e and µ as the “smallest” – and hence providing the maximum contribution of (2) – particles, to leave alone quarks – also small, but whose magnetic moment is beyond measurements. 2

2.1

Upper bounds for elementary length from noncommutative magnetic moment Limitations based on high-energy scattering estimates of lepton sizes

In high-energy electron-positron collisions leptons manifest themselves as structureless particles (see e.g. [4] for an early discussion of this point), described by a fundamental, not composite field. No deviation from this rule has been up to now reported. Taking the LEP scale of 200 Gev as an upper limit, to which this statement may be thought of as checked, we must accept that a possible structureness of these leptons is below the length (call it divisibility length) r0 = 10−3 Fm. In our further consideration we identify the charge extension a with the divisibility length, because it is hard to imagine a region occupied by a charge that extends above this length, but cannot be divided into parts. (If it could, either the resulting charge would acquire a continuous value, smaller than e, which contradicts basic assumptions, or the resulting charge would occupy a smaller space and we are left again with smaller a, down to the divisibility length.) Bearing in mind that, for electron, the existing local theory perfectly explains the value of its magnetic moment Me , we expect that the NC might only contribute into the experimental and theoretical uncertainty δMe existing

419 in measuring and calculating this quantity. A recent direct measurement of the anomalous magnetic moment of electron, using the magnetic resonance spectroscopy of an individual electron in the Penning trap [5], gives the result [6] ( ) Me − 1 = 0.00115965218073 ± 28 × 10−14 , (3) µ MRS where µ = e/2m is the Bohr magneton. On the other hand, a new report [7] appeared on an independent experimental determination of the same magnetic moment with a matching accuracy, obtained with the use of a measurement of the ratio h/mRb between the Planck constant and the mass of the 87 Rb atom. The result is ( ) Me − 1 = 0.00115965218113 ± 84 × 10−14 . (4) µ Rb Authors of [7] fit the value of the fine structure constant α in such a way as to make (4) coincide with the theoretical prediction for the electron anomalous magnetic moment (this fit leads to the so far most precise value α−1 = 137.035999037(91)). For this reason the value (4) is referred to as “theoretical”. (Certainly, the roles of (4) and (3) might be reversed.) The theoretical, (4), and experimental, (3), values of the electron magnetic moment do not contradict each other, demonstrating the hitherto best confirmation of QED. The discrepancy between them δMe ∼ 10−12 (5) µ lies within the accuracy of measurements and calculations. We demand that a possible contribution of the noncommutative magnetic moment in (2) should not exceed it: δMe 4m α = e2 , (6) > α|θ| , µ 5a With the high-energy restriction on the size a < r0 accepted above, Eq. (6) −3 implies θ < δM Fm, we get from here the restriction µ (r0 /4mα). As√r0 ∼ 10 on the elementary length l = θ < 7 × 10−6 Fm = (28 T ev)−1 . 2.2

Ultimate estimate

Once there is no evidence for any electron extension it is worth admitting√that it may be only restricted by the elementary length. Then, using a = l = θ in (6), we obtain the ultimate bound of l < 6.6 × 10−8 Fm = (3 × 103 T ev)−1 . 2.3

Muons

Two analogous (weaker) estimates for the elementary length, inferred from the data on magnetic moment of muon [8], may be found in [1]. Contrary to the

420 estimates basing on the electron data, which are expected to become stronger as the experimental and theoretical precision grows, these will not be improved until the known discrepancy between the theory and experiment for the muon magnetic moment is overcome by an extension beyond the Standard Model. 3

Upper bounds based on compositeness estimates of lepton sizes

There are [4] much stronger restrictions on the lepton sizes than those following from the high-energy collision experiments. These extend to the energy scale far exceeding the accelerator means. The point is that if one imagines a lepton as a bound state of much heavier particles so that the binding energy compensates the most part of their masses to make the resulting state light, the Bohr radius R of the composite state – to be treated as its size – is much smaller than the Compton length of the lepton λC . According to the Drell-Hearn-Gerasimov sum rule (see [4] for the references) the deviation of the anomalous magnetic moment (M/µ−1) from its QED value , which is the measure of compositeness, is proportional to the ratio R/λC . Based on the experimental data on magnetic moments of the known composite particles – proton and triton – plotted against their measured sizes, a conjecture was formulated by Dehmelt [5] that the proportionality coefficient should be of the order of unity. Then, R = λC δM/µ. Referring to Eqs. (3, 4) and using (5) we may update his 1988 result for the electron of R < 4 × 10−8 Fm to R < 4 × 10−10 Fm. This is two orders of magnitude smaller than our ultimate estimate of 6.6 × 10−8 Fm for the elementary length in Subsection 2.2. (The use √of the assertion R = λC δM/µ together with (6) results in the condition l < 5/8α(δM/µ)λC = 9.25R, weaker than the already accepted condition that the elementary length should be smaller than any size, including the composite electron radius R.) So, Dehmelt’s conjecture provides a stronger bound on the elementary length, than the noncommutative magnetic moment. This means that no more than 10−2 part of the measured difference (6) may be at the most attributed to noncommutative contribution. Supported by FAPESP, CNPq and by RFBR under the Project 11-02-00685a. References [1] T. C. Adorno, D. M. Gitman, A. E. Shabad, D. V. Vassilevich, Phys.Rev. D 84, 065031 (2011); ibid 84, 065003 (2011). [2] A. Stern, Phys.Rev.Lett. 100, 061601 (2008). [3] S. Doplicher, K. Fredenhagen and J. E. Roberts, Phys.Lett. B 331, 39 (1994); Commun.Math.Phys. 172, 187 (1995). [4] S.J. Brodsky and S.D. Drell, Phys.Rev. D 22, 2236 (1980). [5] H. Dehmelt, Physica Scripta, T22, 102 (1988)

421 [6] D. Hanneke, S. Fogwell, G. Gabrielse, Phys.Rev.Lett. 100, 120801 (2008). [7] R. Bouchendira, P. Clad´e, S. Guellati-Kh´elifa, F. Nez, F. Biraben, Phys.Rev.Lett. 106, 080801 (2011); M. Cadoret, E. de Mirand´es, P. Clad´e, S. Guellati-Kh´elifa, F. Nez, F. Biraben, Comptes Rendus Physique, 12, iss. 4, p. 379-386 (2011). [8] P.J. Mohr, B.N. Taylor and D.B. Newell, Rev.Mod.Phys. 80, 633 (2008).

422 ANALYTICAL ACCOUNT FOR THE CONSTANT MAGNETIC FIELD EFFECT ON THE UNDULATOR RADIATION SPECTRUM K.V. Zhukovsky a Faculty of Physics, Moscow State University, Leninskie Gory, Moscow, 119991, Russia Abstract. The effect of the constant magnetic field on the planar undulator radiation (UR) is studied. We employ generalized special functions to investigate the UR intensity and spectrum, calculate critical strength of the constant field, affecting the electron motion in undulators. The influence of the Earth magnetism on several real undulators’ emission and spectrum is investigated.

Theoretical studies of electron emission in magnetic fields [1], SR and UR [2], [3] in the last 50 years determined progress in accelerators and free electron lasers (FEL) technique. Nowadays FEL work on high frequencies and require high quality radiation from undulators. Modern undulators frequently work with complex, multiple magnetic fields and many periods to obtain given emission characteristics. Distortions of the periodic magnetic field in such undulators effect their operation. We account for homogeneous and inhomogeneous distortions in undulators using modified special functions to obtain analytical expressions for the effect of a non periodic constant magnetic field: √ ⃗ = B0 (ρ, κ + sin(kλ z), 0) , kλ = (2π/λu ) , Bd = B0 κ1 , κ1 = κ2 + ρ2 , (1) B where κ and ρ — factors, relating the components of the constant magnetic field Bd to the oscillating amplitudeB0 . The electron trajectory in such undulator becomes complicated; Bd significantly modifies differential electron emission in the far zone [3], giving rise to additional constant terms in the exponential phase and modifying oscillating terms. The shape of the spectral line is determined now by the modified Airy function S(α, β, ε), instead of the sinc(α) function in the common expression for the undulator brightness [3]: ∫1 S (α, β, ε) ≡

ei(α τ +ε τ

2

+β τ 3 )

dτ ,

S (α, β) = S (α, β, 0) .

(2)

0

Variables β and ε shift the maximum of the oscillating function S(α, β, ε) respectively to sinc α function. The on-axis UR spectrum consists of peaks with frequencies ( ) 2nγ 2 ω0 2 k √ ωn |ψ=0 = nωR = κ1 (πN ) , , n = 0, 1, 2, ..., ϑ = H 2 3 γ (1 + k 2 /2) + (γϑH ) (3) a e-mail:

[email protected]

423 where n is the harmonic number, N is the number of the undulator periods, ϑH is the bending angle due to the constant magnetic field component. Note from (3) that its effect is accumulated along the undulator length, depending on N and the well known common formula for the resonance frequencies ωR0 of a planar undulator is applicable also in a weak constant magnetic field, provided the absolute value of this field is below κ ˜ B0 : √

) ω ωR → ωR0 νn = 2πN n −1 . ωn (4) The intensity of the on-axis UR in a weak constant magnetic field reads as follows: 1 κ1 0.5×10−4 distortions of the spectral line become significant and for κ1 > 0.7×10−4 — unacceptable. Since this is the order of the strength of the magnetic field of the Earth, careful screening is absolutely necessary to cut off any other source of magnetic distortion and compensation coils may be needed. The UR spectrum is less subjected to distortions in undulators with N ∼ 100.

424

I 1 0.5 0

0.5

1

(κ2+ρ2)1/2×10-4

1.5 2 2.5

12 6 3 0 ?n -3 -6 -12

Figure 1: Spectral line of the main harmonic of the undulator with N = 200 periods in relative units vs. the constant field parameter κ1 and the detuning parameter νn .

References [1] A.A. Sokolov, D.V. Gal’tsov, V.Ch. Zhukovsky, Zh. Tekhn. Fiz. 43, 682 (1973). [2] I.M. Ternov, V.V. Mikhailin, V.R. Khalilov, “Synchrotron Radiation and its Applications”, (Harwood Academic), 1985. [3] V.A Bordovitsyn ed. “Synchrotron Radiation theory and its development” (World Scientific Publishing, Singapore), 1999.

425 NUMERICAL INVESTIGATION OF LATTICE WEINBERG SALAM MODEL M.A.Zubkov a ITEP, B.Cheremushkinskaya 25, Moscow, 117259, Russia Abstract. Lattice Weinberg - Salam model without fermions for the value of the 1 Weinberg angle θW ∼ 30o , and bare fine structure constant around α ∼ 150 is investigated numerically. We consider the value of the scalar self coupling corresponding to bare Higgs mass around 150 GeV. We investigate phenomena existing in the vicinity of the phase transition between the physical Higgs phase and the unphysical symmetric phase of the lattice model. This is the region of the phase diagram, where the continuum physics is to be approached. We find the indications that at the energies above 1 TeV nonperturbative phenomena become important in the Weinberg - Salam model.

The investigation of finite temperature Electroweak phase transition [1] requires nonperturbative methods. The phase diagram of the lattice WeinbergSalam model at zero temperature also contains the phase transition. It is expected, that the continuum physics is approached in some vicinity of this transition. Basing on an analogy with the case of finite temperature Electroweak phase transition we suggest the hypothesis that the nonperturbative effects may become important close to the phase transition of the zero temperature model, i.e. at high enough energies (above about 1 TeV). This justifies the use of lattice methods in investigation of this model. We indeed obtain some results that support the mentioned hypothesis. Here we report these results. In our investigation we restrict ourselves by the following bare values of 1 couplings: fine structure constant α ∼ 150 , the Weinberg angle θW = π/6, the Higgs boson mass MH ∼ 150 GeV. From the previous analysis [2] we know that the renormalized values of α and MH do not deviate essentially from their bare values. We consider the model without fermions. We exclude the first order phase transition because we do not observe any sign of a two - state signal. Also we find the indications that the second order phase transition is present. The ultraviolet cutoff is increased when the phase transition is approached. We consider three different effective constraint potentials. For their definition see [2]. The three mentioned above effective potentials give three different definitions of the scalar field condensate (as the value of ϕ, where the potential V (ϕ) has its minimum). In Fig. 1 we represent these three condensates as functions of the cutoff. Also we calculate the percolation of the Nambu monopoles and the Z - strings. We observe the condensation of Nambu monopoles and Z - strings for Λ > 1 TeV and the deviation of the calculated values of the scalar field condensates from the expected value 2MZ /gZ ∼ 273 GeV for the values of Λ around 1 TeV. We consider these results as indications that nonperturbative effects become a e-mail:

[email protected]

426

Figure 1: The scalar field condensate (in GeV) as a function of the cutoff for λ = 0.0025, β = 12. Circles correspond to the UZ potential, lattice 163 × 32. Squares correspond to the UZ potential, lattice 83 × 16. Crosses correspond to the UDZ potential, lattice 163 × 32. Stars correspond to the UDZ potential, lattice 83 ×16. Triangles correspond to the ultraviolet potential, lattice 163 × 32. Diamonds correspond to the ultraviolet potential, lattice 83 × 16.

important in lattice Weinberg - Salam model for the value of the cutoff above about 1 TeV. This work was partly supported by RFBR grant 09-02-00338, 11-02-01227, by Grant for Leading Scientific Schools 679.2008.2. The numerical simulations have been performed using the facilities of Moscow Joint Supercomputer Center, the supercomputer center of Moscow University, and the supercomputer center of Kurchatov Institute. References [1] K. Rummukainen, M. Tsypin, K. Kajantie, M. Laine, and M. Shaposhnikov, Nucl. Phys. B 532, 283 (1998); Yasumichi Aoki, Phys. Rev. D 56, 3860 (1997); N. Tetradis, Nucl. Phys. B 488, 92 (1997); B. Bunk, Ernst-Michael Ilgenfritz, J. Kripfganz, and A. Schiller (BI-TP92-46), Nucl. Phys. B 403, 453 (1993); [2] M.A. Zubkov. Phys.Lett.B684:141-146,2010, arXiv:0909.4106 M.A. Zubkov, proceedings of QUARKS2010, arXiv:1007.4885 M.A. Zubkov, Phys.Rev.D82:093010,2010 M.I.Polikarpov, M.A.Zubkov, Phys. Lett. B 700 (2011) pp. 336-342

427 CHIRAL DENSITY WAVES IN 2D NAMBU-JONA-LASINIO MODEL D.Ebert1 a , N.V.Gubina2 b , K.G.Klimenko3 c S.G.Kurbanov 2 d , V.Ch.Zhukovsky 2 e 1 Institute of Physics, Humboldt-University Berlin, 12489 Berlin, Germany 2 Faculty of Physics, Moscow State University,119991 Moscow, Russia 3 IHEP and university ”Dubna”, 142281, Protvino, Moscow region, Russia Abstract. We investigate the phase portrait of the (1+1)-dimensional massless two-flavored NJL2 model containing a quark number chemical potential µ and an isospin chemical potential µI in the limit of a large number of colors Nc → ∞.

1

The model

This investigation is motivated by the experiments on heavy-ion collision and studying the matter inside compact stars which sign the isotopical asymmetry of the matter. One of the most interesting is a phase with spatially inhomogeneous chiral condensate [1] taking the form of a chiral density wave (CDW). The Lagragian for massless SUL (2) × SUR (2) symmetric N JL2 model with two chemical potentials reads [ ] ] µI G[ L = q¯ γ ρ i∂ρ + µγ 0 + τ3 γ 0 q + (¯ qq)2 + (¯ qiγ 5⃗τ q)2 , (1) 2 Nc where γ 0 = σ2 , γ 1 = iσ1 , γ 5 = γ 0 γ 1 = σ3 , the quark field q(x) ≡ qiα (x) is a flavor doublet with Pauli matrices τk (k = 1, 2, 3) and color Nc -plet (α = 1, ..., Nc ), G is a dimensionless coupling constant. We introduce new bosonic fields σ(x) = −2 NGc (¯ q q); πa (x) = −2 NGc (¯ q iγ 5 τa q). Their ground state expectation values are taken to be equal: ⟨σ(x)⟩ = M cos(2bx), ⟨π3 (x)⟩ = M sin(2bx), ⟨π1 (x)⟩ = ∆, ⟨π2 (x)⟩ = 0. In the limit Nc → ∞ thermodynamic potential Ω is defined as follows: ∫ 1 d2 xΩ(M, b, ∆) = − Seff {σ(x), πa (x)} σ(x)=⟨σ(x)⟩,πa (x)=⟨πa (x)⟩ . Nc Here we modified energy cutoff regularization scheme from [2] and obtain: ∫ Λ−˜ν ∫ 2 2 1 Λ+˜ν − + e reg (M, b, ∆) = M + ∆ − 1 dp1 E∆ Ω dp1 E∆ − 4G π 0 π 0 ∫ ∞ } dp1 { + + − − − (µ − E∆ )θ(µ − E∆ ) + (µ − E∆ )θ(µ − E∆ ) , (2) π 0 a e-mail:

[email protected] [email protected] c e-mail: [email protected] d e-mail: [email protected] e e-mail: [email protected] b e-mail:

428 µ/M0 1.2

L CDW1

1

CDW2

0.8

µ = µα s

α 0.6

PC

0.4

PC

0.2

–0.2

0

0.2

0.4

0.6

0.8

1

ν M0

1.2

Figure 1: The (ν, µ) phase portrait of the model at T = 0 when a spatial CDW inhomogeneity is taken into account. In the CDW1 (CDW2 ) phase b > 0 (b < 0). On the curve L b = 0 T /M0 0.6

0.5

SYMMETRIC PHASE

0.4

0.3

PC

0.2

0.1

CDW1 0

0.2

0.4

0.6

µc M0

0.8

CDW2 1

b−1 0 (ν) M0

1.2

1.4

µ M0

Figure 2: The (µ, T ) phase portrait at each fixed ν, where να = 0.6M0 < ν. (In symmetric phase M = 0, b = 0, ∆ = 0) ± ± where E∆ = E∆ (b + ν), ν˜ = (b + ν). At Fig.1 one can see that for µ > µα ≈ 0.68M0 at arbitrary values of ν we have spatially inhomogeneous condensates. This is contrary to the case of continuous UL (1)×UR (1) chiral symmetry, where the CDW phase appears at arbitrary nonzero values of µ (see. [3], [4]). The influence of T ̸= 0 on the formation of the CDW phases is following: { [ ] ∫∞ 2 + + − +∆2 −β(E∆ −µ) 1 ΩT (M, b, ∆) = M 4G − −∞ dp 2π E∆ + E∆ + T ln 1 + e [ ] [ ] [ ]} + − − +T ln 1 + e−β(E∆ +µ) + T ln 1 + e−β(E∆ −µ) + T ln 1 + e−β(E∆ +µ) , ± where β = 1/T and E∆ . Numerical investigation are shown at Fig.2.

References [1] C.f.Mu, L.y.He, Y.x.Liu, Phys.Rev. D 82, 056006 (2010). [2] I.E.Frolov, K.G.Klimenko, V.Ch.Zhukovsky, Phys.Rev. D 82, 076002 (2010). Moscow Univ. Phys. Bull. 65, 539 (2010). [3] K.Ohwa, Phys.Rev. D 65, 085040 (2002). [4] V.Schon, M.Thies, Phys.Rev. D 62, 096002 (2000).

429 FINITE SIZE EFFECTS IN THE GROSS–NEVEU MODEL WITH ISOSPIN AND BARYONIC CHEMICAL POTENTIALS Tamaz Khunjua a , Vladimir Zhukovsky b Faculty of Physics, Moscow State University,119991 Moscow, Russia Dietmar Ebert c Institute of Physics, Humboldt-University Berlin, 12489 Berlin, Germany Konstantin Klimenko d IHEP and University “Dubna” (Protvino branch), 142281, Protvino, Moscow Region, Russia Abstract. The properties of the two-flavored massless Gross-Neveu model in the (1+1)-dimensional R1 × S 1 spacetime with compactified space coordinate are investigated in the presence of isospin and quark number chemical potentials µI , µ. The consideration is performed in the large Nc limit, where Nc is the number of colored quarks. It is shown that at L = ∞ (L is the length of the circumference S 1 ) the pion condensation (PC) phase with zero quark number density is realized at arbitrary nonzero µI and for rather small values of µ. However, at arbitrary finite values of L the phase portrait of the model contains the PC phase with nonzero quark number density. Hence, finite sizes of the system can serve as a factor promoting the appearance of the PC phase in quark matter with nonzero baryon densities. In contrast, the phase with chiral symmetry breaking may exist only at rather large values of L.

Our present work is devoted to the consideration of the charged pion condensation phenomenon under influence of finite size effects. The problem was partially solved in [1]. Since in this paper quark chemical potential µ was taken to be zero, we reasonably get a conclusion that the problem deserves a further investigation [2], this time with both nonzero chemical potentials, µ ̸= 0, µI ̸= 0. We consider a (1+1)-dimensional GN model to mimic a phase structure of real dense quark matter with two quark flavors which can appear in heavy-ion collisions. Its Lagrangian has the form: [ ] ] µI G [ − Lq,q = q γ ν i∂ν + µγ 0 + τ3 γ 0 q + (qq)2 + (qiγ 5 → τ q)2 , (1) 2 Nc where each quark field q(x) ≡ qiα (x) is a flavor doublet (i = 1, 2 or i = u, d) and color Nc -plet (α = 1, . . . , Nc ). Moreover, it is a two-component Dirac spinor. τk (k = 1, 2, 3) are Pauli matrices; the quark number chemical potential µ in (1) is responsible for the nonzero baryonic density of quark matter, whereas the isospin chemical potential µI is taken into account in order to study properties of quark matter at nonzero isospin densities. a e-mail:

[email protected] [email protected] c e-mail: [email protected] d e-mail: [email protected] b e-mail:

430 If µI = 0, the Lagrangian (1) has not only SU (Nc ) symmetry, but is also invariant under transformations from the chiral SUL (2) × SUR (2) group. However, if µI ̸= 0, the latter symmetry is reduced to UI3 (1)×UAI3 (1), where UI3 (1) is the isospin subgroup and UAI3 (1) is the axial isospin subgroup. Quarks are transformed under these subgroups as q → exp(iατ3 )q and q → exp(iαγ 5 τ3 )q, respectively. The linearized version of Lagrangian (1), which contains composite bosonic fields σ(x) and πa (x)(a = 1, 2, 3), has the following form: [ ] µI Nc Lσ,π = q γ ν i∂ν + µγ 0 + τ3 γ 0 − σ − iγ 5 πa τa q − [σσ + πa πa ] . (2) 2 4G where bosonic fields are: σ(x) = −2 NGc (qq); πa (x) = −2 NGc (qiγ 5 τa q). Starting from (2), one can define the thermodynamic potential (TDP) of the model in the mean-field approximation: ∫ σ 2 + πa2 d2 p µI ΩµµI (σ, πa ) = +iTrsf ln(γp+µγ 0 + τ3 γ 0 −σ−iγ 5 πa τa ). (3) 4G (2π)2 2 To simplify the task, let us note that the TDP (3) depend effectively only on two combinations (π12 + π22 ) and (π32 + σ 2 ) of the bosonic fields, which are invariants with respect to the UI3 (1)×UAI3 (1) group. In this case, without loss of generality, one can put π2 = π3 = 0, and study the thermodynamic potential (3) TDP as a function of only two variables, M ≡ σ and ∆ ≡ π1 . Then we put our (1+1)-dimensional system with Lagrangian (1) into a restricted space region of the form 0 ≤ x ≤ L. It means that we can consider the model (1) in spacetime of the topology R1 × S 1 and with quantum fields satisfying some boundary conditions of the form q(t, x + L) = q(t, x). So after all calculations one can obtain the following expression for the TDP in restricted space: √ ∞ 1 ∑ { + 4π 2 n2 − ΩLµµI (M, ∆) = VL (ρ) − EL∆n + EL∆n − 2 ρ2 + L n=−∞ L2 } + + − − + (µ − EL∆n )θ(µ − EL∆n ) + (µ − EL∆n )θ(µ − EL∆n ) , (4) √ where ρ = M 2 + ∆2 , v( )2 u √ u 4π 2 n2 t ± 2 EL∆n = M + ±ν + ∆2 (5) L2 and

( ( ) ) M0 L 2ρ ln +γ − 4π L ] ∞ [√ ∑ 4 ρ2 L2 − 2 4π 2 n2 + L2 ρ2 − 2nπ − , L n=1 4nπ

ρ2 VL (ρ) − VL (0) = − π

(6)

431 μ

μ

3

λ = 0.1

2

10

λ=1

Symmetric phase

Symmetric phase 5

PCd 1

II

PCd

PC 0

1

PC 2

3

ν

0

ν 1

2

3

4

5

6

7

where γ = 0.577... is the Euler constant. The TDP (4) is already renormalized. The detailed derivation of (6) and renormalization technique is presented in [1]. For further discussion, we need also the expression for the quark number density nqL in the R1 × S 1 spacetime, which can be easily obtained from the TDP, ∂ΩLµµI nqL ≡ − ∂µ . Moreover, in what follows it will be convenient to use the µI π M ∆ dimensionless quantities: λ = LM ,µ ˜ = Mµ0 , ν˜ = Mν0 ≡ 2M ,m = M ,δ = M . 0 0 0 0 Since we are going to study the phase diagram of the initial GN model, the ∂ΩµµI (m,δ) ∂ΩµµI (m,δ) system of gaps equation is needed: = 0; = 0. The ∂m ∂δ coordinates m and δ of the global minimum point (GMP) of the TDP provide us two order parameters (gaps), which are proportional to the ground state expectation values < qq > and < qiγ 5 τ1 q >, respectively. The results of numerical investigations of the TDP (4) global minimum point (GMP) are presented in left and right figures, where the phase portraits of the model are depicted at λ = 0.1 and λ = 1. There, in the symmetric phase the global minimum of the TDP lies at the UI3 (1) × UAI3 (1) symmetric point (m = 0, δ = 0). The phase II corresponds to UI3 (1) symmetric GMP of the form (m ̸= 0, δ = 0). In this phase quarks are massive and quark number density nqL is nonzero. In contrast to the case λ = 0 (L = ∞) (was considered in [3]), we see that at λ ̸= 0 the phase II occupies a compact region in the phase diagram and vanishes at all at λ > λp ≈ 0.16. Moreover, one can see two pion condensation phases, PC and PCd. The main difference between these pion condensation phases is the following. In PC phase the quark number density nqL is equal to zero, whereas in PCd phase this quantity is nonzero. References [1] D. Ebert, K.G. Klimenko, A.V. Tyukov and V.C. Zhukovsky, Phys. Rev. D 78, 045008 (2008). [2] D. Ebert, T.G. Khunjua, K.G. Klimenko and V.C. Zhukovsky, arxiv:1106.2928v1 [hep-ph]. [3] V. C. Zhukovsky, K. G. Klimenko and T. G. Khunjua, Moscow Univ. Phys. Bull. 65, 21 (2010).

432 PROBING LORENTZ VIOLATION Petr Satunin a Institute for Nuclear Research of the Russian Academy of Sciences, 60th October Anniversary Prospect, 7a, 117312 Moscow, Russia Abstract. We consider Lorentz-violating modification of QED. Considering constraints from accelerator and astroparticle experiments we argue that there exist allowed regions in the parameter space with large absolute values of violation parameters compatible with predictions of quantum gravity models.

1

Introduction and theoretical setup

We consider Lorentz-violating modification of QED with quartic terms added to dispersion relation and different speed of light constant for photons and electrons (the same for left-handed and right-handed). We assume gauge, rotational and CPT symmetries are valid. Dispersion relations are: γ:

4

k02 = k 2 + α Mk 2 ,

(1)

Pl

e± :

4

p20 = (1 + ξ)p2 + m2 + β Mp 2 .

(2)

Pl

We look for possible large violation: |α|, |β| ≫ 1, consistent with healthy quantum gravity theories [1]. Photon time of flight observations [2], the absence of anomalous synchrotron at LEP collider [3] and in astrophysical accelerators [4] make bounds: |α| < 3.6 × 1016 , 2

|ξ| < 7.5 × 10−15 ,

−3 × 1011 < β < 5 × 1011 .

(3)

Reactions

Lorentz Invariance Violation can change kinematics of particle reactions. Photon decay γ → e+ e− . This reaction is kinematically forbidden in LI case. In LIV case it occurs rapidly above some threshold. From energymomentum conservation we obtain threshold equation: If inequality β M2 m2 MP2 l ≥ ξ P2 l + 4 . (4) 4 k k4 is valid, then photon decay occurs. Photon splitting γ → 3γ. In LIV case this reaction have no threshold — it occurs always if α > 0. This reaction is strongly suppressed if photon decay γ 7→ e+ e− occurs. Otherwise, the width of photon splitting is α−

Γ (γ → 3γ) ≃ 0.3 × 10−15

(

α5 Eγ19 E2

E4

m8 MP10l 1 + ξ mγ2 + β m2 Mγ 2

Pl

a e-mail:

[email protected]

)4 .

(5)

433 Photon splitting effectively occurs if its mean free path is less than distance to the source. Pair production γγb → e+ e− . This reaction suppresses the photon flux with energy more than threshold from distant sources. Threshold of pair production on CMB is kth ∼ 400 TeV, and mean free path of more energetic photons is a few Mpc. The flux of more energetic photons is suppressed by pair production on radio background. Possible LIV can shift this threshold. Pair production occurs if the next inequality is valid: α− 3

kb MP2 l β M2 m2 MP2 l > ξ P2 l − 4 +4 . 3 4 k k k4

(6)

Results and discussion

The novel bound on LV came from observations 50 TeV photons from the Crab Nebula: α < 1011 . Extra bounds we may obtain from GZK photon observations (previous discussion by [5]). The intersection of areas in parametric space α−

β − 1018 ξ < −2.3 × 10−7 4

and

( )4 α < 10−10 1 + 4ξ · 1026 + 4β · 108 5

seems to be excluded by observations now. Finally, large areas of huge (up to 1011 ) LIV parameters on parametric plane are not exluded now. If photon splitting occurs, a lot of photons with energy 1016 − 1018 eV will appear. Detection of the photon flux compatible with the predictions of the GZK process will exclude most of the remaining part of LIV parameters. Acknowledgments Author thanks G.Rubtsov and S.Sibiryakov for helpful discussions. This work was supported by Dynasty foundation. References [1] [2] [3] [4] [5]

P.Horava, Phys.Rev. D 79, 084008 (2009). A.Abramowski et.al., Astropart.Phys. 34, 738 (2011). B.Altschul, Phys.Rev. D 80, 091901 (2009). B.Altschul, Phys.Rev. D 74, 083003 (2006). M.Galaverni and G.Sigl, Phys.Rev. D 78, 063003 (2008).

434 CLASSICAL SPIN LIGHT THEORY Vladislav Bagrov a , Vladimir Bordovitsyn b , Olga Konstantinova c Faculty of Physics, National Research Tomsk State University, 36 Lenin avenue, 634050, Tomsk, Russia Abstract. The purpose of this report is, firstly, the systematic exposition of a classical approach to describing the precession of the spin relativistic particles and its correspondence with the quantum mechanical calculations for the different initial conditions, secondly, the comparison of classical and quantum radiation theory of relativistic neutrons and, finally, the classical description and the evaluation of radiative self-polarization effect of neutrons.

1

Introduction

The spin magnetic moment µ of a relativistic particles moving in a magnetic field is a source of the electromagnetic radiation. This radiation called spin light shows up at high energies and very strong magnetic fields. Here the spin light identification problem is considered for a relativistic neutron, which is a source of pure spin light radiation. Initially, it will be shown that for identical initial conditions in spin orientation the classical and quantum theories of spin precession is completely adequate to one another. After this, the classical theory on the example of the spin precession of a neutron moving in a uniform magnetic field is constructed, and found that all the characteristics of the radiation (total power, angular distribution, linear and circular polarization) are exactly the formulas that were obtained in the quantum theory of radiation of the neutron by I.M. Ternov, V.G. Bagrov, A.M. Khapaev [1]. 2

Classical radiation theory of neutrons

The classical theory of neutron spin light was built by V.A. Bordovitsyn et al [2]. Here we give a comparison of this theory with the quantum theory of radiation of the neutron [1]. At the heart of the classical theory of radiation is the field tensor ν] ¨ [µλ ˜ µν = −|µ|c Π r˜λ r˜ ∼ 1 . H (˜ rρ υ ρ )3 r˜

(1)

Here Πµν is a dimensionless spin tensor, r˜µ = (˜ r, ⃗r) is the light-like vector drawn from the world point of neutron to the observer at time t˜, the dot denotes the derivative with respect to the proper time τ . a e-mail:

[email protected] [email protected] c e-mail: [email protected] b e-mail:

435 Applying the standard mathematical formalism of the relativistic theory of radiation [2], we can find the average for the period of precession of the radiation power, and show that all the characteristics of the radiation (angular distribution, linear and angular polarization, frequency radiation) are totally in accordance with the theory of Ternov-Bagrov-Khapaev. 3

Radiative self-polarization of neutrons

This effect was first discovered for relativistic electrons in the quantum theory of synchrotron radiation, and later confirmed experimentally (see, for example, [3]). In the case of neutron spin-light radiation self-polarization time in quantum theory is determined by the reciprocal of the total probability of radiation [4]. To get the same effect in the classical theory, it should be considered as the spin precession time-dependent process that leads to the minimum potential energy, when the neutron spin is oriented against the direction of the ⃗ = (0, 0, H). The solutions of the equation of radiative selfmagnetic field H ⃗ = β(sin α, 0, cos α) if in the initial polarization for a neutron with the velocity β moment it was unpolarized leads to the time of radiative self-polarization [5] T =

3 c3 ¯h4 1 . 64 |µ|5 H 3 γ 2 (1 − β 2 cos2 α)3/2

(2)

However, as shown by calculation, for the neutron to compared with the electron this effect is small and becomes noticeable only at high magnetic fields and at very high energies. 4

Conclusion

Thus we have shown that classical and quantum theories of the spin light and radiative self-polarization of the neutron fully adequate to each other. The work was partially supported by the Federal Targeted Program “Scientific and scientific — pedagogical personnel of innovative Russia”, contract No 02.740.11.0238; No P789. References [1] I. M. Ternov, V. G. Bagrov, A. M. Khapaev, JETF 21, 613 (1965). [2] V. A. Bordovitsyn, in “Synchrotron Radiation Theory and it’s Development. In Memory of Ternov”, ed. by V. A. Bordovitsyn, (World Scientific, Singapore) 1999. [3] A. A. Sokolov, I. M. Ternov, “Radiation from Relativistic Electrons”, (AIP, New York) 1986. [4] V. L. Lyuboshits, Yad. Fiz. 4, 2693 (1966). [5] I. M. Ternov, V. A. Bordovitsyn, S. V. Sorokin Izv. VUZov Fiz. 8, 122 (1983).

436 “STERILE” NEUTRINOS AND EXTENDED GAUGE FORMALISM Valery Koryukin a Faculty of Physics and Mathematics, Mari State University, 424001 Yoshkar-Ola, Russia Abstract. In the early eighties of the twentieth century it was offered the extended gauge formalism, which allowed to construct the renormalized model of electroweak interactions without scalar fields. We offer to consider that the Universe is filled by right neutrinos and left antineutrinos with the sufficiently high Fermi energy which generates not only the symmetry violation in weak interactions but and allows consider the offered formalism as the maximum plausible one.

Extending the idea of Dirac on the presence of the electron sea, we assume in the late 1970s, that the minimal gauge formalism can be constructed only on the base of particles with nonzero spins and fields with nonzero vacuum averages. In consequence of this the extended derivatives of spinor fields and the strengths of gauge must have the non-standard form which is generated by the spontaneous breaking of symmetry of the physical system. As a result it was produced the propagator [1] ( )−1 Dij (p) = pm pm − m2 [−gij + ] (pi pj −Ci Cj ) (pk pk −q◦ m2 )+(1−q◦ ) pk Ck (pi Cj +Ci pj ) (1 − q◦ ) (pl p −q m2 )2 +(1−q )2 (pl C )2 l

◦

◦

l

(we shall use the system of units h/(2π) = c = 1, where h is the Planck constant and c is the velocity of light) of a vector boson with a non-zero rest mass (pk is the 4-momentum, and m is the mass of the vector boson). Notice that owing to the vacuum polarization (Ci ̸= 0) the propagator of a vector boson has the rather cumbersome view, which is simplified and which receives the familiar form only in the Feynman calibration (q◦ = 1). This propagator allows to construct the renormalizable quantum theory of weak interactions (Dij (p) → 0, by p → ∞), not attracting hypothetical scalar fields (the search of Higgs scalar bosons, forecasted in the standard model of electroweak interactions, is unsuccessful one for quite more quarter of a century). As is known the background neutrinos play the slight role in the Universe standard model in the consequence of their assumed low density. The given assumption is unable be verified in the direct experiments by the inelastic scattering having the enough high energy thresholds of reactions. This allows to consider alternative models and in the first place with the use of “sterile” neutrinos and “sterile” antineutrinos (neutrinos and antineutrinos having the opposite polarization to observable neutrinos and antineutrinos by an inelastic scattering). As a result the assumed high density of “sterile” neutrinos by the a e-mail:

[email protected]

437 enough low density of “normal” neutrinos (that causes to the observable spatial parity breakdown of weak interactions) may be explained by the spontaneous breaking of symmetry. The given state of physical systems is characterized by the low temperature T◦ ∼ 10−13 GeV. This low temperature may be estimated by the temperature of the cosmic microwave background. In the experiments on the propagation of spin waves in the gases [2] the main role were allotted for a polarization of them. For it were used both magnetic fields and the laser pumping. This role performs transverse virtual photons in the Coulomb interaction in my opinion at the same time as longitudinal virtual photons afford the “right” dependence on space coordinates [3]. By making of the gravitational interaction the neutrino pumping can stand duty as an analog of the laser pumping and the main role for the “right” space dependence can be play quanta of longitudinal oscillations. Taking into account the above we shall assume that the energy of the gravitational interaction must depend on numbers of particles and quasi-particles participating in this interaction. By this the energy dependence on space coordinates is defined by the average number of quasi-particles (bosons), which are exchanged two interacting real particles. As a result we shall have (n is the boson number, x > 0): / ∞ ∞ ∑ ∑ A −nx V = −A ne e−nx = − x , (1) e −1 n=0 n=0 ∫ where in the general case A = ρ1 σν ρν σν ρ2 dV1 dV2 (ρ1 and ρ2 are the particle densities of the macroscopic bodies, ρν is the density of the Universe background neutrinos, σν is the cross-section for scattering of background neutrinos on macroscopic body particles). By this approach it might be worthwhile to go over to the Lobachevsky — Chernikov potential [4] for the gravitational interaction of macroscopic bodies. By this we note, that GN ∼ σν (GN is the gravitational constant). Let in the formula (1) for macroscopic distances x = 2ρν σν r, then it is possible the Lobachevsky constant L to give the physical interpretation as the mean free path 1/(σν ρν ). So, we renounced to consider, that the Universe vacuum is the sterile one. It allows using a potential in the form (1) for arbitrary interactions at “amply large distances”. References [1] V. M. Koryukin, arXiv.0801.0694 physics.gen-ph (physics.hep-ph). [2] E. P. Bashkin, Pisma ZhETF, 33, 11 (1981). [3] R. P. Feynman, “The Theory of Fundamental Processes”, (California Insti-tute of Technology W. A. Benjamin, Inc., New York), 1961. [4] V. M. Koryukin, Abstructs of International Conference on Modern Problems of Gravitation, Cosmology and Relativistic Astrophysics (PFUR, Moscow, RUSSIA, 27 June 3 July, 2010), PFUR, Moscow, 59, 2010.

438 DIRAC ALGORITHM AND ELEMENTARY PARTICLE PHYSICS Oleg Kosmachev a Joint Institute for Nuclear Research, 141980 Dubna Moscow region, Russia Abstract. The Dirac algorithm is a totality of necessary and sufficient conditions for formulation of the wave equations for all lepton sector. All equations were obtained under rigorous restrictions by adopted suppositions. Generality and accuracy of the developed method allow to put question on its extension for hadron sector.

1

Introduction

The Dirac algorithm is a totality of necessary and sufficient conditions for formulation of the wave equations for all lepton sector. All equations were obtained under rigorous restrictions by adopted suppositions. Algorithm was ascertained on the base of exhaustive analysis of Dirac equation [1]. The five initial suppositions are following: the equations must be invariant and covariant under homogeneous Lorentz transformations taken into account all four connected components; the equations must be formulated on the base of irreducible representations of the groups determining every lepton equation; conservation of four-vector of probability current must be fulfilled and fourth component of the current must be positively defined; the lepton spin is supposed equal to 1/2; every lepton equation must be reduced to Klein-Gordon equation. 2

Lepton sector

We obtained full and closed set of groups for formulation wave equations both stable and unstable leptons [2], [3]. The completeness and the closure mean that in the frame of accepted suppositions there is no possibility to obtain additional equations and for formulation every of them it is sufficient four conjugate components of Lorentz group (i.e. subgroups dγ , fγ , bγ , cγ ). Evident and important corollary of the fulfilled construction is presence of its own composition in every case. It allows by definition to speak on its own set of quantum numbers in every case [4]. The structural compositions of the stable leptons are following: the Dirac equation — Dγ (II){ dγ , bγ , fγ }; the equation for a doublet of massive neutrinos — Dγ (I) { dγ , cγ , fγ }; the equation for a quartet of massless neutrinos — Dγ (III) { dγ , bγ , cγ , fγ }; the equation for a massless T -singlet — Dγ (IV ){ bγ }; the equation for a massless (P T )-singlet — Dγ (V ){ cγ }; a e-mail:

[email protected]

439 Here Dγ (II) is the group of Dirac equation [1], Dγ (I) is the group of Majorana equation [5]. The Dγ (III) is group of equation derived by Pauli [6]. Equations Dγ (IV ) and Dγ (V ) one can connect with truly neutral massless neutrino [7]. Unstable lepton groups (∆1 , ∆2 , ∆3 ) were obtained by means of extension of stable lepton groups with the help of additional (fifth) generator. All they contain stable lepton groups as substructures. Namely: ∆1 {Dγ (II), Dγ (III), Dγ (IV )}; ∆3 {Dγ (II), Dγ (I), Dγ (III)}; ∆2 {Dγ (I), Dγ (III), Dγ (V )}. One can show that first two groups are connected with equations for charged particles (µ-,τ -leptons) and third one with massive unstable neutrino. 3

Conclusion and summary

All results in lepton sector are opening new possibilities for description of the structures with different characteristics including those ones which can not be really observable particles such as hadron constituents (partons, quarks). There are no principle prohibitions for generalization of the proposed method on the hadron sector in a such manner that they internal structures were formed on the base of Lorentz-invariant structures Structural complexity growing in this connection will be determine the symmetries which we relate now with unitary one. In a such approach the leptons and hadrons would be described on the unit relativistic base. In this case unnatural situation is excluded when lepton sector completely missed out from the unitary symmetries. The reason may be that division of the hadrons into parts (quark for instance) is larger than it is permissible for lepton descriptions. From this point of view a peculiar interest is a study of τ -lepton because of 60% cases between them are connected with hadron birth. It is clear that realization of such programm will be mean bridging between strong and electroweak interactions on the base of relativity and invariants known as structural constituents. References [1] [2] [3] [4]

P.Dirac, Proc.Roy. Soc. A vol.117,610 (1928). A.Gusev, O.Kosmachev, Phys. Part. Nucl. Lett. T.5, N2, 26 (2008). O.Kosmachev, Phys. Part. Nucl. 2010. T.7, N2, 149 (2010). H.Weyl, The theory of groups and quantum mechanics,(Nauka, Moscow), 16 1986. [5] E.Majorana, Il Nuovo Cimento v.14, 171 (1937). [6] W.Pauli, The general principles of wave mechanics, (GITTL, Moscow) 254 1947. [7] O.Kosmachev, A.Gusev,Vestnik RUDN. Ser.Matem.Inform. Fiz. N2, 91 (2008). (in russian)

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Problems of Intelligentsia

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443 THE INTELLIGENTSIA: GUARDIAN OF NATIONAL CULTURE by John Kuhn Bleimaier a 15 Witherspoon Street, Princeton, New Jersey 08542 USA

The term the intelligentsia was coined in 19th Century Russia. However, the phenomenon of the existence of an intellectual elite within society is of long standing. As far back as the Greek and Roman classical periods there is reason to believe in the presence of a cadre of individuals in the community who devoted their time and energy to abstract contemplation. The intelligentsia is a group of persons who seek to accumulate knowledge and attain wisdom. In ancient times there was a single intelligentsia centered first at Athens and later at Rome. From the Middle Ages down to the period of the Renaissance there appears to have been a single western intelligentsia, although the members of this far flung grouping were to be found from the Italian city states to the Scots highlands, from France to the Germanies. The members of the Renaissance intelligentsia were, by and large, aware of one anothers existence. In some instances they maintained written communication with each other notwithstanding separation by substantial physical distance. The language of the intellectual dialogue within Christendom at that time was Latin. The presence of a universal language for serious, scholarly intercourse rendered this intelligentsia remote and exclusive from the perspective of the masses, yet it was a unified entity. Beyond the bounds of medieval Catholic Europe, perhaps there were separate, independent intellectual groupings in Byzantium, the Islamic world and the Far East. Their existence lies beyond the purview of this discussion. It was the Reformation that shattered the intellectual monolith in European society. The division of the western church into Roman Catholic and Protestant camps forever rent asunder the unity of this community of analytical and creative individuals. Latin lost its position of primacy in discussions between intellectuals. Martin Luthers translation of the Bible into German transformed the language of intellectual inquiry from Latin to the vernacular. As learned individuals came to carry on their communication in their diverse native tongues the intelligentsia took on a national, as opposed to a cosmopolitan character. Inevitably the intelligentsia came to reflect national culture. The period between the Congress of Vienna in 1815 and the revolutionary year1848 witnessed the blooming of national consciousness in the western world. Perhaps it was the decades long march of foreign armies across the continent during the Napoleonic Wars, which awakened an awareness of national and cultural diversity. The cause of national self determination was taken up by educated people in post-Congress of Vienna Europe. A sense of nationalism or patriotism began to stir in the breasts of European peoples. This nationalism was often alloyed with a spirit of egalitarianism, first spread by the armies of France in the aftermath of the French Revolution. These patriotic phenomena further evolved in the context of a peaceful and prosperous Europe where a middle class began to emerge. This new bourgeoisie a B.A.; Master of International Affairs; Juris Doctor; member of the New York, New Jersey and US Supreme Court bars; Fellow of Mathey College, Princeton University

444 possessed the economic stability, liberal education and leisure time requisite for intellectual pursuits. They swelled the ranks of the national intelligentsias. It is quite natural that these middle class thinkers chafed at monarchal privilege and the vestiges of noble advantage. The upshot of the evolution of a bourgeois national intelligentsia was the outbreak of revolt in the fateful year of 1848. The intellectual revolutionists of 1848 sought to create republican nation states. Most notably in the multiple principalities which constituted pre-unification Germany there was a strong movement for national and cultural unification coupled with liberal reform. The polyglot, multinational Habsburg Empire was shaken to the core in 1848 by the notion of the nation state, possessed of a single language and culture. The component groups of the Austro-Hungarian Empire including Hungarians, Slovaks and Czechs rose up under the leadership of their respective intelligentsias. In Italy the intelligentsia also rose up for national unity and democratic reform. For various reasons the revolutions of 1848 were largely unsuccessful in toppling the multinational and culturally diverse monarchies which controlled the European continent. However, in France, 1848 saw the end of the Bourbon restoration and the ascendance of Napoleon III in Paris. This is significant because of the Bonapartist espousal of the nationality principle as the basis of Frances continental policy. Ironically, while France pursued a nationality based policy between 1848 and 1871, the French language had attained an international status as a medium for cultural dialogue as a result of the contemporary preeminence of French arts and literature. In eastern Europe the mid 19th Century witnessed the development of two divergent movements within the national intelligentsia. Pan Slavism militated for joining the various Slavic peoples in a single sovereign unit. This was the de facto official ideology of the Russian Empire until its collapse in 1917. On the other hand there were centrifugal forces in play in the Slavic community. Particularly in Poland, but also later in Little Russia (Ukraine) national intelligentsias came to work for the establishment of independent nation states and the dismemberment of the tsarist empire. Both Pan Slavism and the struggle for Polish independence represent two distinct facets of the same nationalist orientation of the Eastern European intelligentsia. It was in the realm of the arts, literature and music that the 19th Century intelligentsia distinguished itself as guardian of the national traditions. The novel reached full maturity as a literary genre during this period and proved to be an invaluable vehicle for conveying the message of preserving national culture. Full-length works of fiction were widely read and the oft times nationalist political message of the author was reflected in the prose. Similarly, in poetry a national heroic tradition was promulgated. In the plastic arts the genre painters seized upon the subject matter of historic struggle to inspire broad canvasses, which traveled from exhibition to exhibition, lighting the spark of patriotism. Monumental sculptures placed prominently in the metropolis tugged at the heartstrings of the populous. Thus creative intellectuals began to take their patriotic, unifying message to the people. It was also during this period that young members of the intelligentsia began to fan out into the countryside in order to collect national folklore and to set down the texts of folk epics, heretofore exclusively the sphere of oral tradition. The codification of folk literature resulted in local dialect being written down

445 for the first time. Particularly in Little Russia, the collection of traditional lore resulted in the first exemplars of text written in the Ukrainian language. With the creation of a written language the engendering of a sense of distinct national identity could not be far behind. The intelligentsias field trip to the village resulted in a cultural two way street. The young intellectuals became enamored of their local heritage, while the peasants became infected with a national consciousness. During the age of romanticism music also served its part in enshrining the national culture. Composers began to integrate folk musical themes in their large-scale compositions. Opera particularly served as the medium for dramatizing the battle for national identity and patriotic self-determination. All the emotions inspired and manipulated by music came to be harnessed in the service of preserving and consolidating national culture. Thus the concept of the nation state and the ideologies associated with nationalism in Europe were the products of the intelligentsia. Quite logically the peasant, anchored to his land and his agricultural toil, has little time or motivation to contemplate the idea of nationhood. It is the intellectual, exposed to a wider world and possessed of the incentive to contemplate his national roots, who recognizes the existence of a distinct national culture. The intelligentsia identifies the characteristics, which constitute the nation, and then nurtures them, molding the past, present and future. In the light of wars and enmities it is natural to inquire as to the actual benefits of nationhood. Is not the history of inter group struggle justification for questioning the utility of nationalism? Indeed the question must be asked, but the considered answer is that love of nation is not the basis of conflict. An objective analysis of history reveals that dynastic rivalries, economic ambitions of industrialists and ideological divergence between different oligarchies are the causes of ruinous wars. The affection for ones family, neighbors and countrymen militates against international conflict. The intelligentsia is not liable for having created a monster of destruction. It is rather to be praised for having enshrined the diversity of cultures that immeasurably enriches human life on this planet. The efforts undertaken by the Polish intelligentsia during the 19th Century represent a classical example of the contribution of intellectuals to the nation building process. The partition of Poland between the Prussian, Russian and Habsburg dynasties in the 18th Century spelled the end of Polish sovereignty. Nevertheless, the Polish intelligentsia consistently harbored a desire to resurrect the Polish state. The Polish rising of 1863 was decisively suppressed by the Russian Empire in part because the Polish peasantry did not support the rebellion. In fact the Polish peasants actually cooperated with the troops of the Russian tsar in putting down the revolt because they were under the impression that the Polish nobility wished to break away from Russia in order to reintroduce the institution of serfdom. After a series of rebellions failed to attain their goal, influential elements of the Polish intelligentsia pursued a different path. The Organic Work movement in the territories which had constituted Poland prior to the partition entailed conscious effort on the part of educated Poles to preserve their distinct language and culture. This movement was particularly important in Russian and Prussian Poland where the imperial governments made significant efforts to integrate the Poles into the respective Russian and German cultures. The Organic Work movement set for itself a particular goal

446 of instilling a sense of national consciousness in the peasantry. Ultimately the efforts undertaken by the proponents of Organic Work were crowned with success. Jan Paderewski, the Polish intellectual and composer, played a significant role in the diplomacy and planning, which led to the establishment of a new Polish state after the First World War. The 14 Points which represented the war objectives of the United States upon its entry into World War I, put emphasis on the concept of national self-determination. At the Versailles Peace Conference at the conclusion of hostilities in 1919, the national aspirations of various peoples, as articulated by their respective intelligentsias, were at the core of redrawing the map of Europe. While the American president Woodrow Wilsons diplomatic ineptitude resulted in the creation of an unjust and fragile situation after the signing of the peace treaty, the concept of national self-determination has been entrenched in western consciousness since 1920. The injustices embodied in the peace treaty which concluded the First World War led inevitably to the second global conflagration which came upon its heals in 1939. A careful analysis of the cultural and intellectual activity during the interwar period reveals that the various national intelligentsias were hard at work advancing the distinct agendas of their national constituencies. However, at the same time there was a separate internationalist movement present in virtually all countries, which set as its goal the unification of the various peoples under a single world government. This one-world perspective was almost exclusively alloyed with one or another socialist ideology. The tragedy of the Second World War is that it was in reality a European Civil War. In virtually all the combatant states, and even in neutral countries, there were left wing right wing, nationalist and internationalist elements, which battled against one another. The League of British Fascists and the German Karl Liebknecht brigade for example demonstrate that on either side of the battle lines drawn in the Second World War were vocal opposition groups radically opposed to the policies of their respective countries. Illustrating the horrific irony of history nationalists fought nationalists and internationalists battled internationalists in counterproductive mortal combat. Yet despite all the bitterness and bloodshed of World War II the notion of the nation state and the concept of patriotism have shown their resiliency. The intelligentsias, notwithstanding their recognition of the futility of fratricidal conflict, yet cling to their affection for their national cultures. As natural as the family is the sense of nationhood. In postwar society opposition to communism and other forms of totalitarian governance has coalesced around the national intelligentsias. Indeed, the failure of Marxism is largely the result of the fact that intellectuals have felt first allegiance to their neighbors, their fellow countrymen and their coreligionists. An abstract materialist ideology has no chance in competition with the emotional tug of la patrie. Furthermore, the communist international has often seemed to be nothing more than a thinly disguised attempt by one wellorganized oligarchy to attain primacy over other, earlier oligarchic forms of dominion. Patriotic national intelligentsias ultimately brought down the Soviet juggernaut. Yugoslavia and Czechoslovakia were disassembled by their component intelligentsias more rapidly than they had been created by overzealous internationalist bureaucrats. Woodrow Wilsons disastrous, bumbling dissonance is

447 slowly being overcome by a white noise of peace and reconciliation. The patriots of the various intelligentsias are at liberty to work for the commonweal. By struggling for the optimized good of each nation we lessen the likelihood of conflict between nations. The intelligentsia thus functions as the guardian of national culture, the guardian of all national cultures. During the postwar epoch, even that first of all international organizations, the Roman Catholic Church, has embraced the nationality principle. A half millennium after Martin Luther published the Bible in the German vernacular, the Roman church has begun to intone the mass in the various languages of its congregants, instead of in Latin. Under a Polish nationalist Pontiff, Rome has undertaken a conscious campaign to canonize saints for all the worlds distinct national groups. At the beginning of the 21st Century the most powerful force inspiring the national consciousness of the intelligentsia is perhaps the monstrous prospect of globalization. Under the guise of economic rationalization, a cadre of international financial manipulators has determined to impoverish the working men and women of the erstwhile industrial world while simultaneously enslaving the populations of developing nations in industrial peonage, while polluting the planet with abandon. The common threat of a globalized oligarchy is enough to drive all the disparate national intelligentsias into productive collaboration in the interests of joint survival. Last but not least, we are gathered at the Moscow Conference on the Intelligentsia in order to make yet another mighty effort to safeguard the survival of our various national cultures. Yes, in Moscow, once the capital of an immense, anti-national, cosmopolite cabal, there gather every two years a gallant company of intellectuals dedicated to addressing our common problems. We invariably do so from the unique perspectives provided by our individual cultural heritages. In so doing we guarantee mutual survival, prosperity and progress of our nations and of mankind as a whole.

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449 Programme of the 15th Lomonosov Conference on Elementary Particle Physics and the 9th International Meeting on Problems of Intelligentsia 18 August, Thursday 09.00 – 09.15 Opening (Conference Hall) A.Studenikin, Chairman of Organizing Committee (MSU & JINR) V.Belokurov, Vice Rector of Moscow State University A.Slavnov, Head of Department of Theoretical Physics, Faculty of Physics of MSU M.Itkis, Acting Director of Joint Institute for Nuclear Research 09.15 – 13.25 MORNING SESSION (Conference Hall) Chairman: Mikhail Itkis 09.15 P.Jenni (CERN) Roadmap for Discoveries at the LHC, History and Prospects (30 min) 09.45 M.Titov (CEA Saclay, IRFU/SPP) Higgs Searches at Tevatron (25 min) 10.10 A.Cheplakov (JINR) ATLAS status and latest results (20 min) 10.30 V.Gavrilov (ITEP) New results from CMS (20 min) 10.50 – 11.20 Tea break Chairman: Victor Savrin 11.20 A.Soffer (Tel Aviv Univ.) Recent results from BaBar (25 min) 11.45 A.Bevan (Queen Mary Univ. of London) The SuperB project (25 min) 12.10 A.Litvinenko (JINR) The NICA/MPD project at JINR (25 min) 12.35 S.Levonian (DESY) Recent results from HERA (25 min) 13.00 A.Slavnov (MIRAN & MSU) Electroweak interactions without Gribov ambiguities (25 min) 13.25 – 15.00 Lunch 15.00 – 18.30 AFTERNOON SESSION (Conference Hall) Chairman: Yuri Kudenko 15.00 A.Ereditato (Univ. of Bern) Tau appearance with the OPERA experiment (25 min) 15.25 V.Gavrin (INR, Moscow) Opportunities of SAGE with artificial neutrino source for investigation of active-sterile transitions (25 min) 15.50 A.Guglielmi (INFN, Padova) ICARUS: present and future (25 min) 16.15 P.Fiziev, D.Shirkov (JINR) A new look at some general puzzles of Universe (25 min) 16.40 – 17.00 Tea break Chairman: Belen Gavela 17.00 M.Cirelli (CERN) Dark Matter Indirect (and Direct) Detection phenomenology: a status assessment (25 min) 17.25 A.Cherepashchuk (Sternberg Astr. Inst., MSU) Black holes in X-rays binary systems (25 min) 17.50 F.Simkovic (JINR & Bratislava) Matrix Elements for Double Beta Decay (20 min) 18.10 E.Akhmedov (Max-Planck-Inst., Heidelberg & Kurchatov Ins.) Neutrino oscillations in quantum mechanics and quantum field theory (20 min) 19.00 – 23.30 SPECIAL SESSION (40 0) Reception banquet will be held on board of a ship that will stream along the river across the central part of Moscow; the conference buses to the ship will depart from the entrance to the Faculty of Physics at 18.50

450 19 August, Friday 09.00 – 13.35 MORNING SESSION (Conference Hall) Chairman: Alberto Guglielmi 09.00 A.Izmaylov (INR, Moscow) New oscillation results from the T2K experiment (25 min) 09.25 M.Ieva (IFAE, Barcelona) T2K non-oscillation physics with near detectors (25 min) 09.50 C.White (Illinois Inst. of Techn.) Theta_13 and the Daya Bay Reactor Neutrino Experiment (25 min) 10.15 W.Huelsnitz (Los Alamos Nat. Lab.) Recent Results and Implications from MiniBooNE (25 min) 10.40 L.Bornschein (Karlsruhe Inst. of Techn.) Tritium-beta-decay Experiments - The direct way to the absolute neutrino mass (25 min) 11.05 – 11.35 Tea break Chairman: Alexander Barabash 11.35 N.Barros (Tech. Univ. Dresden) Final results from SNO and prospects for future SNO+ experiment (25 min) 12.00 E.Litvinovich (Kurchatov Inst.) Solar neutrino studies with Borexino (25 min) 12.25 Y.Obayashi (Kamioka Observatory) Recent results from Super-Kamiokande (20 min) 12.45 Y.Obayashi (Kamioka Observatory) Next generation water Cherenkov detector Hyper-K (20 min) 13.05 O.Ryazhskaya (INR RAS) Search for neutrino flux from collapsing stars (25 min) 13.30 – 15.00 Lunch 15.00 – 19.10 AFTERNOON SESSION (Conference Hall) Chairman: Antonio Ereditato 15.00 E.Strahler (VUB-ELEM, Brussels) Latest Results from the IceCube Neutrino Telescope (25 min) 15.25 M.Anghinolfi (INFN, Genoa) The Antares underwater neutrino telescope (25 min) 15.50 E.Shirokov (MSU) The KM3Net project (15 min) 16.05 A.Kozlov (Tokyo Univ.) Towards the KamLAND-Zen experiment (25 min) 16.30 A.Barabash (ITEP) The Majorana double beta decay experiment: present status (20 min) 16.50 A.Studenikin (MSU) New constraints on neutrino magnetic moment (10 min) 17.00 – 17.30 Tea break Chairman: Anatoly Shabad 17.30 S.Sukhotin (Kurchatov Inst.) Status of the DoubleChooz experiment (20 min) 17.50 S.T. Lin (Inst. of Phys., Academia Sinica, Taipei) Low energy neutrino and dark matter physics with sub-keV germanium detector (20 min) 18.10 K.Fomenko (LNGS - INFN & JINR) Study of rare processes with the Borexino detector (20 min) 18.30 A.Lokhov (MSU) Spin light of neutrino in plasma (10 min) 18.40 C.Tarazona, R.Diaz Sanchez, J.Morales (National Univ. of Colombia) Contribution of the form factors of neutrinos from the burden of a Higgs doublet model with two Higgs (10 min) 18.50 A.Borisov (MSU), B.Kerimov (late), P.Sizin (Moscow St. Mining Univ.) Neutrino emission from a strongly magnetized degenerate electron gas: the Compton mechanism via a neutrino magnetic moment (10 min)

451 19.00 A.Kuznetsov (Yaroslavl St. Univ.) Neutrino-triggered asymmetric magnetorotational pulsar natal kick (“cherry-stone shooting” mechanism) (10 min) 19.30 – 22.30 Sight-seeing bus excursion in Moscow 20 August, Saturday 09.00 – 13.35 MORNING SESSION (Conference Hall) Chairman: Marco Cirelli 09.00 E.Nardi (LNF – INFN) Selected issues in Leptogenesis (25 min) 09.25 D.Gorbunov (INR RAS) Sterile neutrinos and cosmology (25 min) 09.50 H.Gast (Max-Planck-Inst., Heidelberg) Recent results of the High Energy Stereoscopic System (H.E.S.S.) (25 min) 10.15 S.Germani (INFN-Perugia) Fermi Large Area Telescope science highlights (20 min) 10.35 R.Bernabei (Univ. of Rome Tor Vergata) Particle dark matter (25 min) 11.00 – 11.30 Tea break Chairman: Marco Cirelli 11.30 A.Dolgov (INFN-Ferrara & ITEP) Relic gravitational waves from primordial black holes (25 min) 11.55 E.Alvarez (Univ. of Madrid) Vacuum energy decay (20 min) 12.15 V.Dokuchaev (INR RAS) Life inside black holes (15 min) 12.30 V.Berezinsky (LNGS-INFN), V.Dokuchaev, Yu.Eroshenko (INR RAS) Superdense dark matter clumps from nonstandard perturbations (15 min) 12.45 M.Savina (JINR) Search for Microscopic Black Hole signatures in the CMS Experiment (15 min) 13.00 Y.Kuno (Osaka Univ.) Search for Charged Lepton Flavor Violation (25 min) 13.25 K.Nozari (Univ. of Mazandaran) Noncommutative Braneworld Inflation (10 min) 13.35 – 15.00

Lunch

15.00 – 18.30 AFTERNOON SESSION (Conference Hall) Chairman: Alexander Dolgov 15.00 M.Vasiliev (Lebedev Phys.Inst.) Higher-spin interactions (20 min) 15.20 A.Nikishev (Lebedev Phys.Inst.) On the simplified tree graphs in gravity (15 min) 15.35 M.Fil'chenkov (Peop. Friend. Univ. of Rus.) Loop quantum cosmology corrections to Friedmann's model (10 min) 15.45 Yu.Dumin (IZMIRAN, Moscow) Perturbation of a planetary orbit by the dark energy (10 min) 15.55 E.Arbuzova (Univ. "Dubna") Singularities in some models of modified gravity (10 min) 16.05 A.Nesterenko (JINR) Hadronization effects in inclusive tau decay (15 min) 16.20 G.Nigmatkulov (Nat. Res. Nucl. Univ. "MEPhI") Observation of correlations of the double phi-meson system in the SELEX experiment (15 min) 16.35 P.Satunin (MSU & INR) Probes of Lorenz violation (10 min) 16.45 – 17.10 Tea break Chairman: Alexander Nesterenko 17.10 K.Stepanyants (MSU) Derivation of the NSVZ beta-function in N=1 SQED regularized by higher derivatives by summation of diagrams (10 min) 17.20 Ye.Zenkevich (MSU & INR) Conbstraint on holographic technicolour (10 min)

452 17.30 K.Zhukovsky (MSU) Undulator radiation in periodic magnetic fields with constant component (10 min) 17.40 V.Braguta (IHEP, Protvino) Thermal Abelian monopoles as selfdual dyons (10 min) 17.50 A.Panin (INR) Dark Matter and Baryon asymmetry of the Universe from scalaron decay (10 min) 18.00 O.Kharlanov, V.Zhukovsky (MSU) Spherical Casimir effect within D=3+1 Maxwell-Chern-Simons Electrodynamics (10 min) 18.10 N.Gubina (MSU) Chiral density waves in (1+1) Gross-Neveu model (10 min) 18.20 T.Khunjua (MSU) Finite size effect in the Gross-Neveu model with isospin and barionic chemical potentials (10 min) 21 August, Sunday 9.00 – 19.00

Bus excursion to Sergiev Posad 22 August, Monday

09.00 – 13.45 MORNING SESSION (Conference Hall) Chairman: Enrique Alvarez 09.00 S.Klimenko (Univ.of Florida, on behalf of LIGO and Virgo) From Initial to Advanced LIGO and Virgo: results, challenges and prospects (25 min) 09.25 A.Starobinsky (Landau Inst. Theor. Phys.) Primordial and present dark energy in f(R) gravity (25 min) 09.50 A.Zakharov (ITEP) Constraints on a Randall-Sundrum II braneworld metric of the black hole at the Galactic Center (20 min) 10.10 C.Romero Filho (Univ. Federal da Paraiba) General Relativity and Weyl Geometry: towards a new Invariance Principle (20 min) 10.30 N.Mankoc (Univ. of Ljubliana) The ''spin-charge-family-theory'', which offers the mechanism for generating families, predicts the fourth family, explains the origin of the dark matter, and offers answers to other open questions (25 min) 10.55 B.Gavela (UAM, Madrid) The Scalar Potential of Minimal Flavour Violation (25 min) 11.20 – 11.40 Tea break Chairman: Yury Kudenko 11.40 Z.Djurcic (Argonne Nat.Lab.) NOvA Experiment (20 min) 12.00 Z.Djurcic (Argonne Nat.Lab.) DAEdALUS Experiment (20 min) 12.20 F.Pupilli (L'Aquila Univ. and INFN) Search for ντ interactions with the nuclear emulsions of the OPERA experiment (20 min) 12.40 R.Rescigno (Salerno Univ.) The Electronic Detectors of the hybrid OPERA Neutrino Experiment (20 min) 13.00 C.Solans Sanchez (Univ. of Valencia) Higgs searches at ATLAS (20 min) 13.20 T.Kobayashi (KEK) Future accelerator based neutrino experiments (25 min) 13.45 – 15.00

Lunch

15.00 – 19.05 AFTERNOON SESSION (Conference Hall) Chairman: Ermanno Vercellin 15.00 A.Cakir (DESY) Searches for Supersymmetry with the CMS Experiment (25 min) 15.25 V.Bednyakov (JINR) Anomalously interacting extra bosons and first results of their search at LHC (20 min)

453 15.45 D.Tlisov (INR) Search for a heavy neutrino and right-handed W of the left-right symmetric model with CMS detector (15 min) 16.00 M.Tokarev (JINR) Jets at Tevatron and LHC (20 min) 16.20 G.Safronov (ITEP) Forward jets and forward-central jets at CMS (20 min) 16.40 A.-K.Sanchez (ETH Zurich) Measurements of forward energy flow with CMS (15 min) 16.55 – 17.20 Tea break Chairman: Piero Spillantini 17.20 O.Kodolova (SINP MSU) Results from Heavy Ion Collisons in CMS (20 min) 17.40 S.Petrushanko (SINP MSU) Elliptic flow in heavy-ion collisions with the CMS detector at the LHC: first results (20 min) 18.00 A.Proskuryakov (SINP MSU) Diffraction at CMS (20 min) 18.20 L.Sarycheva (SINP MSU) Exotic Effects in Cosmic Rays and Experiments at LHC (15 min) 18.35 I.Shakiryanova (INR RAS) Supernova neutrino type identification with adding NaCl in LVD (10 min) 18.45 S.Aleshin, O.Kharlanov, A.Lobanov (MSU) Recalculation of the Day-Night Flavor Asymmetry for Solar Neutrinos (10 min) 18.55 V.Khruschov (Kurchatov Inst.) Phenomenological relations for neutrino mixing angles and masses (10 min) 23 August, Tuesday 09.00 – 13.35 MORNING SESSION (Conference Hall) Chairman: Mikhail Tokarev 09.00 M.Misiak (Univ. of Warsaw) Rare B meson decays – theory (25 min) 09.25 E.Gushchin (INR RAS) LHCb results (20 min) 09.45 V.Balagura (CERN and ITEP) Electroweak and QCD measurements at LHCb (20 min) 10.05 P.Chang (National Taiwan Univ.) Recent Results from Belle (20 min) 10.25 T.Aushev (ITEP) Status and Prospects of SuperKEKB/Belle II (25 min) 10.50 M.Gazdzicki (Frankfurt & Kielce Univ.) Onset of deconfinement and critical point: news form NA49 and NA61 at the CERN SPS (25 min) 11.15 – 11.35 Tea break Chairman: Mikolaj Misiak 11.35 A.Bizzeti (INFN-Florence) Recent results from NA48 and NA62 (30 min) 12.05 A.Shaikhiev (INR RAS) Search for heavy neutrino in rare kaon decays (15 min) 12.20 P.Krokovny (Bundek Inst. of Nuclear Physics) Search for New Physics in CP violating measurements at LHCb (15 min) 12.35 D.Savrina (SINP MSU) Search for New Physics in rare heavy flavour decays at LHCb (15 min) 12.50 M.Martemyanov (ITEP) Status and perspectives of the KLOE-2 experiment (20 min) 13.10 M.Primavera (INFN-Lecce) SUSY searches at ATLAS (25 min) 13.35 – 15.00

Lunch

15.00 – 18.50 AFTERNOON SESSION (Conference Hall) Chairman: Andrea Bizzeti 15.00 M.Venturi (Univ. of Freiburg) Boson and Diboson production at ATLAS (25 min) 15.25 A.Khanov (Oklahoma State Univ.) Top physics with ATLAS (20 min) 15.45 J.Frost (Cambridge Univ.) Exotics searches at ATLAS (20 min)

454 16.05 S.Ferrag (Univ. of Glasgow) Soft QCD studies with ATLAS (20 min) 16.25 M.Delmastro (CERN) Photon and diphoton production at ATLAS (20 min) 16.45 D.Tsybychev (Stony Brook Univ.) Jets and W/Z+jets results from ATLAS (20 min) 17.05 – 17.30 Tea break Chairman: Altan Cakir 17.30 D.Costanzo (Univ. of Sheffield) Monte Carlo tuning using ATLAS data (20 min) 17.50 R.Yoosoofmiya (Univ. of Pittsburgh) A search for WR and heavy neutrinos in the dileptons+jets channel in ATLAS experiment (20 min) 18.10 S.Sivoklokov (SINP MSU) Heavy Flavour production at ATLAS (LHC) (20 min) 18.30 G.Kukartsev (Brown University) QCD Studies at CMS (20 min) 24 August, Wednesday 09.00 – 13.30 MORNING SESSION (Conference Hall) Chairman: Alexander Khanov 09.00 A.Alton (Univ. of Michigan) Electroweak + QCD physics with TEVATRON (25 min) 09.25 S.De Cecco (LPNHE, Paris) B physics with TEVATRON (25 min) 09.50 F.Rizatdinova (Oklahoma State Univ.) Top physics at the TEVATRON (20 min) 10.10 G.Borisov (Lancaster Univ.) Updated measurement of dimuon charge asymmetry (15 min) 10.25 G.Feofilov (St.Petersburg State Univ.) Recent ALICE results from heavy-ion collisions at the LHC (25 min) 10.50 E.Vercellin (Univ.of Turin & INFN) Proton-proton physics with the ALICE experiment at the LHC (25 min) 11.15 – 11.35 Tea break Chairman: Warren Huelsnitz 11.35 V.Mostepanenko (Noncommercial Partnership "Scientific Instruments") Problems in the theory of the Casimir effect (25 min) 12.00 G.Klimchitskaya (North-West Tech. Univ.) Constraints on light elementary particles and extra dimensional physics from the Casimir effect (15 min) 12.15 V.Belokurov, E.Shavgulidze (MSU) Quantum field theory on loop space (20 min) 12.35 M.Polikarpov (ITEP) Conductivity and superconductivity of the vacuum of Lattice Gluodynamics at Strong Magnetic Fields (20 min) 12.55 M.Zubkov (ITEP) Investigation of Lattice Weinberg - Salam model (10 min) 13.05 K.Urbanowski (Univ. of Zielona Gora) Post-exponential decay of unstable particles: possible effects in particle physics and astrophysics (10 min) 13.15 T.Adorno (Univ. São Paolo), D.Gitman (Univ. Fed. do ABC, Brazil), A.Shabad (Lebedev Phys. Inst.), D.Vassilevich (St.Petersburg State Univ.) Noncommutative magnetic moment of charged particles (15 min) 13.30 – 15.00

Lunch ROUND TABLE DISCUSSION "Frontiers of particle physics: news from high energies, neutrinos and cosmology"

Chairman: Takashi Kobayashi 15.00 P.Spillantini (Univ. of Florence) Main results from the PAMELA space experiment after 5 years in flight (25 min)

455 15.25 M.Lindner (Max-Planck-Inst., Heidelberg) Opportunities, challenges and potential surprises in neutrino physics (25 min) 15.50 M.Mezzetto (INFN-Padova) Recent results in neutrino physics (25 min) 16.15 F.Forti (INFN-Pisa) SuperB Status Report (20 min) 16.35 A.Gritsan (Johns Hopkins Univ.) Searches for the Higgs boson with the CMS Experiment (25 min) 17.00 Discussion 17.05 – 17.30 Tea break NINTH INTERNATIONAL MEETING ON PROBLEMS OF INTELLIGENTSIA: "The Intelligentsia: Custodial of Civilization"

17.30 – 18.30 Conference Hall Chairman: Alexander Studenikin 17.30. J.Bleimaier (Princeton) The Intelligentsia: Guardian of National Culture 18.00 Discussion and conclusion Closing of the 15th Lomonosov Conference on Elementary Particle Physics and the 9th International Meeting on Problems of Intelligentsia SPECIAL SESSION (40 0)

POSTER SESSION K.Akmarov (NRU ITMO, St.Petersburg) Solar neutrino interference N.Gromov (KSC RAS, Syktyvkar) Contraction of lepton sector of electroweak model and neutrino О.Konstantinova (Tomsk St. Univ.) Classical spin light theory V.Koryukin (Mari State Univ.) "Sterile" neutrinos and the extended gauge formalism О.Kosmachev (JINR) Dirac algorithm and elementary particle physics Е.Nemchenko (Tomsk State Univ.) Construction of magnetopolar and curvature radiation profiles from pulsars O.Shustova (MSU) On the spectrum of ultrahigh-energy cosmic rays from expected sources

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List of participants of the 15th Lomonosov Conference on Elementary Particle Physics and the 9th International Meeting on Problems of Intelligentsia

Agafonova Natalia Akmarov Konstantin Aleshin Sergey Alton Andrew Alvarez Enrique Anghinolfi Marco Arbuzova Elena Balagura Vladislav Barabash Alexander Barros Nuno Bernabei Rita Bevan Adrian Bizzeti Andrea Bleimaier John Bordovitsyn Vladimir Borisov Anatoly Borisov Gennady Bornschein Lutz Braguta Victor Burinskii Alexander Cakir Altan Chang Paoti Cheplakov Alexander Cirelli Marco Costanzo Davide De Cecco Sandro Delmastro Marco Diaz Sanchez Rodolfo Djurcic Zelimir Dumin Yurii Ereditato Antonio Feofilov Grigory Ferrag Samir Fil'chenkov Michael Fiziev Plamen Fomenko Kirill Forti Francesco

INR RAS NRU ITMO, St.Petersburg MSU Univ. of Michigan UAM, Madrid INFN Univ. "Dubna" CERN and ITEP ITEP Tech. Univ. Dresden Univ. of Rome Tor Vergata Univ. of London INFN Princeton Tomsk State Univ. MSU Lancaster Univ. Karlsruhe Inst. of Techn. IHEP IBRAE RAS DESY National Taiwan Univ. JINR CERN Univ. of Sheffield LPNHE, Paris CERN National Univ. of Colombia Argonne Nat.Lab. IZMIRAN, Moscow Univ. of Bern St.Petersburg State Univ. Univ. of Glasgow Peop. Friend. Univ. of Rus. JINR, Dubna LNGS - INFN & JINR INFN

[email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected]

458 Frost James Gast Henning Gavela Belen Gavrilov Vladimir Gazdzicki Marek Germani Stefano Gomez Tarazona Carlos Gorbunov Dmitry Gritsan Andrei Gromov Nikolay Gubina Nadezda Guglielmi Alberto Gushchin Evgeny Huelsnitz Warren Ieva Michela Izmaylov Alexander Jenni Peter Khanov Alexander Kharlanov Oleg Khruschov Viacheslav Khunjua Tamaz Klimchitskaya Galina Klimenko Sergey Kobayashi Takashi Kodolova Olga Konstantinova Olga Koryukin Valery Kosmachev Oleg Kozlov Alexandre Krokovny Pavel Kudenko Yury Kukartsev Gennadiy Kuno Yoshitaka Kuznetsov Alexander Levonian Sergey Lindner Manfred Litvinenko Anatoly

Univ. of Cambridge Max-Planck-Inst., Heidelberg UAM, Madrid ITEP Frankfurt & Kielce Univ. INFN National Univ. of Colombia INR RAS Johns Hopkins Univ. KSC RAS, Syktyvkar MSU INFN INR RAS Los Alamos Nat. Lab. IFAE, Barcelona INR RAS CERN Oklahoma State Univ. MSU Kurchatov Inst. MSU North-West Tech. Univ. Univ. of Florida KEK SINP MSU Tomsk State Univ. Mari State Univ. JINR Tokyo Univ. Bundek Inst. of Nuclear Physics INR RAS Brown Univ. Osaka Univ. Yaroslavl St. Univ. DESY Max-Planck-Inst., Heidelberg JINR

[email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] Galina.Klimchitskaya@ itp.uni-leipzig.de [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected]

459 Litvinovich Evgeny Lobanov Andrey Borstnik Norma Susana Mankoc Martemyanov Maxim Mezzetto Mauro Misiak Mikolaj Mostepanenko Vladimir Nardi Enrico Natoli Paolo Nemchenko Ekaterina Nesterenko Alexander Nigmatkulov Grigory Nozari Kourosh Obayashi Yoshihisa Panin Alexander Petrushanko Sergey Polikarpov Mikhail Primavera Margherita Proskuryakov Alexandr Pupilli Fabio Rescigno Regina Rizatdinova Flera Roganova Tatiana Romero Filho Carlos Ryazhskaya Olga Safronov Grigory Sanchez Ann-Karin Sarycheva Ludmila Satunin Petr Savina Maria Savrina Daria Shabad Anatoly Shaikhiev Artur Shakiryanova Irina Shin-Ted Lin Shirokov Evgheny

Kurchatov Inst. MSU Univ. of Ljubliana

[email protected] [email protected] [email protected]

ITEP INFN Univ. of Warsaw Noncommercial Partnership "Scientific Instruments" LNF – INFN Univ. of Ferrara Tomsk State Univ. JINR Nat. Res. Nucl. Univ. "MEPhI" Univ. of Mazandaran Univ. of Tokyo INR RAS SINP MSU ITEP INFN SINP MSU

[email protected] [email protected] [email protected] Vladimir.Mostepanenko@ itp.uni-leipzig.de

INFN - LNGS INFN Oklahoma State Univ. SINP MSU Univ. Federal da Paraiba INR RAS ITEP ETH Zurich SINP MSU MSU & INR JINR SINP MSU & ITEP Lebedev Phys. Inst. INR RAS INR RAS Inst. of Phys., Academia Sinica, Taipei MSU

[email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected]

460 Shustova Olga Sivoklokov Sergey Sizin Pavel Soffer Abner Solans Sanchez Carlos Spillantini Piero Stepanyantz Konstantin Strahler Erik Sukhotin Sergey Titov Maxim Tokarev Mikhail Tsybychev Dmitri

MSU SINP MSU Moscow St. Mining Univ. Tel Aviv Univ. Univ. of Valencia Univ. of Florence MSU

[email protected] [email protected] [email protected] [email protected] [email protected] [email protected] [email protected]

VUB-ELEM, Brussels Kurchatov Inst. CEA Saclay, IRFU/SPP JINR Stony Brook University

Urbanowski Krzysztof

Univ. of Zielona Gora

Venturi Manuela

Univ. of Freiburg

Vercellin Ermanno White Christopher Yoosoofmiya Reza Zakharov Alexander Zenkevich Yegor Zhukovsky Konstantin Zubkov Mikhail

Univ.of Turin & INFN Illinois Inst. of Techn. Univ. of Pittsburgh ITEP MSU & INR MSU ITEP

[email protected] [email protected] [email protected] [email protected] Dmitri.Tsybychev@stonybrook. edu [email protected] ra.pl [email protected] [email protected] whitec@iit. [email protected] [email protected] [email protected] [email protected] [email protected]