International Workshop on Hadron Physics 2000: Topics on the Structure and Interaction of Hadronic Systems: Caraguatatuba, São Paulo, Brazil, 10-15 April 2000 9789812811653, 9812811656

Table of contents :
Effective Theories
Nucleon Models
High Energy Collisions
Decays and Low Energy Reactions
Nuclear Matter and Astrophysics
Structure Functions
Formal Developments.

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International Workshop On 1

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HADRON PHYSICS 2000 Topics on the Structure and Interaction of Hadronic Systems

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Fernando S. Navarra Manoel R. Robilotta Gastao Krein

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World Scientific

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International Workshop On

HADRON PHYSICS 2000 Topics on the Structure and Interaction of Hadronic Systems

International Workshop On

HADRON PHYSICS 2000 Topics on the Structure and Interaction of Hadronic Systems Caraguatatuba, Sao Paulo, Brazil 10-15 April 2000

Editors

Fernando S. Navarra Universidade de Sao Paulo

Manoel R. Robilotta Universidade de Sao Paulo

Gastao Krein Universidade Estadual Paulista

& World Scientific m

Singapore • New Jersey • London • Hong Kong

Published by World Scientific Publishing Co. Pte. Ltd. P O Box 128, Farrer Road, Singapore 912805 USA office: Suite IB, 1060 Main Street, River Edge, NJ 07661 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE

British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library.

VII HADRON PHYSICS 2000 Copyright © 2001 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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ISBN 981-02-4510-6

Printed in Singapore by Uto-Print

V

VII HADRON PHYSICS - 2000 Foreword The workshop VII Hadron Physics - 2000 was part of a regular sequence of workshops held since 1988, in different locations within Brazil, devoted to the study of hadron structure and hadronic reactions. The meeting took place between 10 and 15 of April 2000, by the sunny sands of the Tabatinga beach, in the town of Caraguatatuba, State of Sao Paulo. It was dedicated to Professor Erasmo Madureira Ferreira, in the year of his seventieth birthday, as a small tribute from our community to his outstanding role in fostering Hadron Physics in Brazil. Nowadays, the understanding of the effects of quarks and gluons on static properties of hadrons and their reactions requires either lattice calculations or the use of models, since one has to deal with QCD in the confining regime. The four series of lectures delivered at the workshop by Stanley Brodsky, Barry Holstein, Dmitri Kharzeev and Otto Nachtmann, provided an updated and pedagogical account of recent developments in the field of non-perturbative methods. The content of these lectures is reproduced in this book, which also includes material presented as seminars and contributed papers. The organizers and participants of the VII Hadron Physics - 2000 would like to acknowledge the sponsorship and support from several organizations. Among the Brazilian sources, we thank Conselho Nacional de Desenvolvimento Cientffico e Tecnologico (CNPq), Coordenagao para o Aperfeigoamento do Pessoal Superior (CAPES), Fundagao de Apoio a Pesquisa do Estado de Sao Paulo (FAPESP), Fundacao de Apoio a Pesquisa do Estado do Rio de Janeiro (FAPERJ), Fundagao de Apoio a Pesquisa do Estado do Rio Grande do Sul (FAPERGS) and Universidade de Sao Paulo (CCINT, Pro - Reitoria de pesquisa, Pro - Reitoria de pos - graduagao). We are also grateful for the contributions provided by International Agencies, especially the International Centre for Theoretical Physics (ICTP) and the Latin American Center for Physics (CLAF). We hope that readers may enjoy this book as we did in attending the workshop.

The Editors

VII

CONTENTS Foreword

Lectures The light-cone Fock expansion in Quantum Chromodynamics S. J. Brodsky Effective interactions are effective interactions B. R. Holstein

3 57

Three lectures on the Physics of RHIC D. Kharzeev

108

Nonperturbative processes in QCD O. Nachtmann

152

Seminars Hadron Physics in Brazil 2000 E. Ferreira

219

Instantons and nucleon magnetism H. Forkel

228

Time dependent calculations for the X(j)4 model F. L. Braghin

238

Hyperon-nucleon interaction in the Skyrme model G. L. Thomas

248

Symmetry nonrestoration at high temperatures M. B. Pinto and R. O. Ramos

258

On color superconductivity in external magnetic field E. V. Gorbar

268

Contributions Section I: Effective Theories Nucleon-nucleon interaction: Central potential and pion production C. M. Maekawa, J. C. Pupin and M. R. Robilotta

281

VIII

Deuteron Compton scattering in chiral perturbation theory M. Malheiro, S. R. Beane, D. R. Phillips and U. van Kolck

285

Peripheral scattering of nucleons by isoscalar targets R. Higa

289

Pion nucleon scattering: Chiral perturbation theory and unitarity corrected amplitudes /. P. Cavalcante and J. Sd Borges Filho

293

Section II: Nucleon Models On the effective potentials in the nucleon L. A. Trevisan and L. Tomio

299

Hyperfine splittings of hyperons to order 1/NC G. L, Thomas and C. L. Schat

302

An ansatz for the nucleon-nucleon interaction in the Skyrme model: conclusions /. P. Cavalcante

306

Non-leptonic decays of hyperons in the Skyrme model D. Gomez Dumm, A. J. Garcia and N. N. Scoccola

310

The fuzzy bag model revisited F. G. Pilotto, C. A. Z. Vasconcellos and H. T. Coelho

314

Some exact solutions of the Dirac equation A. S. de Castro and J. Franklin

318

Section III: High Energy Collisions QCD description of vector meson photoproduction E. Ferreira and U. Maor

325

Pair of heavy-exotic-quarks at LHC J. E. Cieza Montalvo and P. P. de Queiroz Filho

329

Exotic quark search at TeV energies Y. A. Coutinho, P. P. Queiroz Filho and M. D. Tonasse

333

Soft charm production in hadron-nucleus collisions C. E. Aguiar, T. Kodama and R. A. M. S. Nazareth

337

Diffractive physics and the forward proton detector A. Santoro, E. M. Gregores, T. L. Lungov and S. F. Novaes

341

Proton-proton elastic scattering with massive gluons W. K. Sauter and M. B. Gay Ducati

345

Squeezed fermions and back-to-back correlations P. K. Panda, T. Csorgo, Y. Hama, G. Krein and S. S. Padula

349

Contrasting continuous emission versus freeze-out via HBT S. S. Padula, F. Grassi, Y. Hama and 0. Socolowski Jr.

353

Studies of production of lambda using the dual parton model F. R. A. Simao, F. M. de Carvalho Filho and J. Solano

357

Section IV: Decays and Low Energy Reactions Effective mass effect on photonuclear particle production reactions at 0.8-1.4 GeV energy range E. C. de Oliveira, A. Dimarco, C. Barbero, E. L. Medeiros, S. B. Duarte, M. Gongalves and S. de Pina

363

Importance of A exchange in pp annihilation: Comparison between the two-pion and three-pion channels M. Betz, E. A. Veit and J. Haidenbauer

367

Four-fermion contact interactions at one-loop and the new atomic parity violation results A. Gusso

371

QCD sum rules for the A;, semileptonic decay R. S. Marques de Carvalho and M. Nielsen

375

Low and intermediate energy corrections in e — CS2 collision E. Veitenheimer, C. A. Z. Vasconcellos and S. E. Michelin

379

Estimating cr-meson couplings from D —> 37r decays C. Dib and R. Rosenfeld

383

Recoil effects in the electroproduction of the delta L. Amoreira, P. Alberto and M, Fiolhais

387

Model independence and relativistic spin effects in the nucleon W. R. B. de Araujo, E. F. Suisso, T. Frederico, M. Beyer and H. J. Weber

391

Section V: Nuclear M a t t e r and Astrophysics Naturalness in relativistic mean field theories A. R. Taurines, C. A. Z. Vasconcellos and M. Malheiro

397

X

Relativistic hadronic models in LDA J. B. Silva, A. Delfi.no and M. Malheiro

401

Effects of vacuum structure on neutron star P. K. Panda, R. Sahu and S. Mishra

405

The optimized delta expansion for relativistic models: Considering vacuum effects D. P. Menezes, M. B. Pinto and G. Krein The role of the MRHA in the Walecka model phenomenology S. S. Rocha, A. R. Taurines, C. A. Z. Vasconcellos and M. B. Pinto Dynamic variables to compute the energy-momentum tensor of nuclear matter E. F. Liitz and C, A. Z. Vasconcellos

409 413

417

Density-dependent coupling constants and charge symmetry breaking L. A. Barreiro

421

Variational principle for nuclear relativistic problems S. S. Avancini and G. Krein

425

Hot and flowing asymmetric nuclear matter G. F. Marranghello and C. A. Z. Vasconcellos

429

Section VI: Structure Functions The light antiquark asymmetry of the proton in a pion cloud model approach H. R, Christiansen and J. Magnin

435

Inclusive meson production in the meson cloud model F. Carvalho, F. 0. Duraes, F. S. Navarra and M. Nielsen

439

Meson cloud and SU(3) flavor breaking in parton distributions F. Carvalho, F. 0. Duraes, F. S. Navarra, M. Nielsen and F. M. Steffens

443

Asymmetries in heavy meson production from light quark fragmentation J. Dias de Deus and F. 0. Duraes Transverse momentum dependent gluon distribution functions J. Rodrigues and P. J. Mulders

447 451

XI

K* and nucleon strangeness M. Nielsen, F. S. Navarra and H. Forkel

455

Section VII: Formal Developments The composite operator (CJT) formalism in the scalar model at finite temperature G. N. J. Ananos, N. F. Svaiter Meson masses with WKB approximation and soft QCD A. E. Bernardini and C. Dobrigkeit On non-zero mass solutions in massless quantum field theory with curved momentum space B. E. J. Bodmann, S. Mittmann dos Santos and Th. A. J. Maris Light-front-quantized QCD in light-cone gauge P. P. Srivastava and S. J. Brodsky The sl(2) afnne Toda model coupled to the matter: Solitons and confinement H. Bias Quantum fluctuations around classical field configurations: The (^ + ±4>* + %4>%D model G. Flores

461 465

469 473

477

481

Gauge groups from brane-anti-brane systems at angles /. V. Vancea

485

List of Participants

489

LECTURES

3

The Light-Cone Fock Expansion in Quantum Chromodynamics STANLEY J. BRODSKY Stanford Linear Accelerator Center Stanford University, Stanford, California 94309 USA E-mail: [email protected] A fundamental question in QCD is the non-perturbative structure of hadrons at the amplitude level—not just the single-particle flavor, momentum, and helicity distributions of the quark constituents, but also the multi-quark, gluonic, and hidden-color correlations intrinsic to hadronic and nuclear wavefunctions. The light-cone Fock-state representation of QCD encodes the properties of a hadrons in terms of frame-independent wavefunctions. A number of applications are discussed, including semileptonic B decays, deeply virtual Compton scattering, and dynamical higher twist effects in inclusive reactions. A new type of jet production reaction, "self-resolving diffractive interactions" can provide direct information on the light-cone wavefunctions of hadrons in terms of their quark and gluon degrees of freedom as well as the composition of nuclei in terms of their nucleon and mesonic degrees of freedom. The relation of the intrinsic sea to the light-cone wavefunctions is discussed. The physics of light-cone wavefunctions is illustrated for the quantum fluctuations of an electron.

1

Introduction

Quantum Chromodynamics, the non-abelian SU(Nc — 3) gauge theory of quark and gluons is the central theory of particle and nuclear physics. The range of applications of QCD to physical processes is extraordinary, ranging from the dynamics and structure of hadrons and nuclei, the properties of electroweak transitions, quark and gluon jet processes, to the properties and phases of hadronic matter at the earliest stages of the universe. At very short distances QCD is believed to unify with the electroweak interactions, and possibly even gravity, into more fundamental theories. There has been enormous progress in understanding QCD since its inception in 1973,1 particularly in the applications of the perturbative theory to inclusive and exclusive processes involving collisions at large momentum transfer. New experimental tools are continually being developed which probe the non-perturbative structure of the theory, such as hard diffractive reactions, self-resolving jet reactions, semi-exclusive reactions, deeply virtual Compton scattering, and heavy ion collisions. Nevertheless, many fundamental questions have not been resolved. These include rigorous proofs of color confinement, the behavior of the QCD coupling at small scales, the computation of the nonperturbative structure of hadrons in terms of their quark and gluon degrees of freedom, the problem of n! growth of the perturbation theory (renormalon

4

phenomena), the nature of the pomeron and reggeons, the nature of shadowing and antishadowing in nuclear collisions, the apparent conflict between QCD vacuum structure and the small size of the cosmological constant, and the problems of scale and scheme ambiguities in perturbative QCD expansion. One of the most pressing problems is to understand the QCD physics of exclusive .B-meson decays at the amplitude level, since the interpretation of the basic parameters of the electroweak theory and CP violation depend on hadronic dynamics and phase structure. The most challenging nonperturbative problem in QCD is the solution of the bound state problem; i.e., to determine the structure and spectrum of hadrons and nuclei in terms of their quark and gluon degrees of freedom. Ideally, one wants a frame-independent, quantum-mechanical description of hadrons at the amplitude level capable of encoding multi-quark, hidden-color and gluon momentum, helicity, and flavor correlations in the form of universal process-independent hadron wavefunctions. Remarkably, the light-cone Fock expansion allows just such a unifying representation. Formally, the light-cone expansion is constructed by quantizing QCD at fixed light-cone time 2 r = t + z/c and forming the invariant light-cone Hamiltonian: H%gD = P+P~ - P | where P± = P° ± Pz? The operator P~ = i£ generates light-cone time translations. The P+ and P± momentum operators are independent of the interactions. Each intermediate state consists of t2 _1_ 2

particles with light-cone energy k~ = ±k^n > 0 and positive k+. The procedure for quantizing non-Abelian gauge theory in QCD is wellknown.4'5 In brief: if one chooses light-cone gauge A+ = 0, the dependent gauge field A~ and quark field ip~ — A~?/> can be eliminated in terms of the physical transverse field A1- and A+ = A+tp fields. Here A ± = I T ^ T * are hermitian projection operators. Remarkably, no ghosts fields appear in the formalism, since only physical degrees of freedom propagate. The interaction Hamiltonian includes the usual Dirac interactions between the quarks and gluons, the threepoint and four-point gluon non-Abelian interactions plus instantaneous 5 lightcone time gluon exchange and quark exchange contributions: nint

= -0^7" +| f (? + ^r

abc

W (dtlA

a v

-

dvA\)Ah»Acv

fahcfadeAbllAdllAcvAev

5

tJ

9

2J

+

+

a7^J a (d^2

a

(1)

+ fabcid-A^A""

(2)

where

j+ a = j> V(*a) V

Srivastava and I have recently shown how one can use the Dyson-Wick formalism to construct the Feynman rules in light-cone gauge for QCD. The gauge fields satisfy both the light-cone gauge and the Lorentz condition d^A^ = 0. We have also shown that one can also effectively quantize QCD in the covariant Feynman gauge.6 The eigen-spectrum of H^c in principle gives the entire mass squared spectrum of color-singlet hadron states in QCD, together with their respective I *p) — light-cone wavefunctions. For example, the proton state satisfies: H^c Mp\ \f p ). The projection of the proton's eigensolution | \PP) on the color-singlet B = 1, Q = 1 eigenstates {|n)} of the free Hamiltonian Hj°c (g = 0) gives the light-cone Fock expansion: 7

VP;P+,P±,\

n

d2kj_idxi

= .£, . /nSU .. ./S716TT

3

n>3,Ai

16r»Wl-$>h ( a ) (£^J n

\ xi+

i xi*±. + K±ii Aj ) tyn/p\xii k±i, Aj).

The light-cone Fock wavefunctions ipn/H(xiikj_i,\i) thus interpolate between the hadron H and its quark and gluon degrees of freedom. The light-cone momentum fractions of the constituents, x, = kf/P+ with Y27=iXi = -*•' = L a and the transverse momenta k^i with Y^7=i ^J-i ^- P P e a r a s the momentum coordinates of the light-cone Fock wavefunctions. A crucial feature is the frame-independence of the light-cone wavefunctions. The Xj and k±i are relative coordinates independent of the hadron's momentum P M . The actual physical transverse momenta are p±i = XiP± + fcj_iThe Aj label the light-cone spin Sz projections of the quarks and gluons along the z direction. The physical gluon polarization vectors ep(fc, A — ±1) are specified in light-cone gauge by the conditions k • e = 0, rj • c = e+ = Q. Each light-cone Fock wavefunction satisfies conservation of the z projection of angular momentum: Jz — Y^7=i &i + 23j=i '1 • The s u m o v e r $? represents the contribution of the intrinsic spins of the n Fock state constituents. The sum over orbital angular momenta / | = — i(^jgfr — k? g|r) derives from the

6

n — 1 relative momenta. This excludes the contribution to the orbital angular momentum due to the motion of the center of mass, which is not an intrinsic property of the hadron.8 Light-cone wavefunctions are thus the frame-independent interpolating functions between hadron and quark and gluon degrees of freedom. Hadron amplitudes are computed from the convolution of the light-cone wavefunctions with irreducible quark-gluon amplitudes. For example, space-like form factors can be represented as the diagonal An = 0 overlap of light-cone wavefunctions. Time-like form factors such as semi-exclusive B decays can be expressed as the sum of diagonal An = 0 and An = 2 overlap integrals. Structure functions are simply related to the sum over absolute squares of the light-cone wavefunctions. More generally, all multi-quark and gluon correlations in the bound state are represented by the light-cone wavefunctions. Thus in principle, all of the complexity of a hadron is encoded in the light-cone Fock representation, and the light-cone Fock representation is thus a representation of the underlying quantum field theory. The LC wavefunctions ipn/H(xi>k±i, A;) are universal, process-independent, and thus control all hadronic reactions. In the case of deep inelastic scattering, one needs to evaluate the imaginary part of the virtual Compton amplitude M[j*(q)p —> ~y*(q)p]- The simplest frame choice for electroproduction is q+ = 0,(zi = Q 2 = -q\q~ = 2q-p/P+,p+ = P+,p± = 0±,p~ = M*/P+. At leading twist, soft final-state interactions of the outgoing hard quark line are power-law suppressed in light-cone gauge, so the calculation of the virtual Compton amplitude reduces to the evaluation of matrix elements of the products of free quark currents of the free quarks. The absorptive amplitude imposes conservation of light-cone energy: p~ + q~ = J27 ^h f° r t n e n—particle Fock state. In the impulse approximation, where only one quark q recoils against the scattered lepton, this condition becomes M3 +

2 g

.

( p =

^

+

^)2

+ m

'+V^

+ m

>.

(3)

If we neglect the transverse momenta k\ relative to Q2 in the Bjorken limit Q2 —> oo, Xbj = Q2/2q-p fixed, we obtain the condition xq = Xf,j\ i.e., the light-cone fraction xq = k+ /p+ of the struck quark is kinematically fixed to be equal to the Bjorken ratio. Contributions from high k\ = 0{Q2) which originate from the perturbative QCD radiative corrections to the struck quark line lead to the DGLAP evolution equations. Thus given the light-cone wavefunctions, one can compute4 all of the leading twist helicity and transversity distributions measured in polarized deep

7

inelastic lepton scattering? For example, the helicity-specific quark distributions at resolution A correspond to

,A) = £ / n ^ ^ D O * ^ < , A , ) | a n,qa

J

j=l

(4)

Xi

xl67r3«5 M - f > J ( E ^ )