Properties of Hadrons in the Nuclear Medium

a r X i v :n u c l -t h /9702016v 1 7 F e

b 1997LBNL-39866PROPERTIES OF HADRONS IN THE NUCLEAR MEDIUM Che Ming Ko 1Cyclotron Institute and Physics Department Texas A&M University,College Station,Texas 77843,USA Volker Koch 2Nuclear Science Division Lawrence Berkeley National Laboratory,Berkeley,CA 94720,USA Guoqiang Li 3Department of Physics State University of New York at Stony Brook,Stony Brook,N.Y.11794,USA key words :Chiral symmetry,Goldstone bosons,vector mesons,baryons,hot and dense hadroni

c matter,heavy-ion collisions

2KO,KOCH&LI

Contents

1INTRODUCTION2 2GOLDSTONE BOSONS5

2.1The pion (6)

2.2Kaons (10)

2.3Etas (18)

3VECTOR MESONS18

3.1The rho meson (20)

3.2The omega meson (29)

3.3The phi meson (29)

4BARYONS31 5RESULTS FROM LATTICE QCD CALCULATIONS32 6SUMMARY35

1INTRODUCTION

The atomic nucleus provides a unique laboratory to study the long range and bulk properties of QCD.Whereas QCD is well tested in the per-turbative regime rather little is known about its properties in the long range,nonperturbative region.One of the central nonperturbative prop-erties of QCD is the spontaneous breaking chiral symmetry in the ground state resulting in a nonvanishing scalar quark condensate,<ˉq q>=0. It is believed and supported by lattice QCD calculations[1]that at temperatures around150MeV,QCD undergoes a phase transition to a chirally restored phase,characterized by the vanishing of the order parameter,the chiral condensate<ˉq q>.This is supported by results obtained within chiral perturbation theory[2,3].E?ective chiral models predict that a similar transition also takes place at?nite nuclear density.

The only way to create macroscopic,strongly interacting systems at ?nite temperature and/or density in the laboratory is by colliding heavy nuclei at high energies.Experiments carried out at various bombarding energies,ranging from1AGeV(BEVALAC,SIS)to200AGeV(SPS), have established that one can generate systems of large density but mod-erate temperatures(SIS,BEVALAC),systems of both large density and

IN-MEDIUM EFFECTS3 temperature(AGS)as well as systems of low density and high temper-atures(SPS).Therefore,a large region of the QCD phase diagram can be investigated through the variation of the bombarding energy.But in addition the atomic nucleus itself represents a system at zero tem-perature and?nite density.At nuclear density the quark condensate is estimated to be reduced by about30%[2,3,4,5]so that e?ects due to the change of the chiral order parameter may be measurable in reactions induced by a pion,proton or photon on the nucleus.

Calculations within the instanton liquid model[6]as well as results from phenomenological models for hadrons[7]suggest that the proper-ties of the light hadrons,such as masses and couplings,are controlled by chiral symmetry and its spontaneous as well as explicit breaking. Con?nement seems to play a lesser role.If this is the correct picture of the low energy excitation of QCD,hadronic properties should de-pend on the value of the chiral condensate<ˉq q>.Consequently,we should expect that the properties of hadrons change considerably in the nuclear environment,where the chiral condensate is reduced.Indeed, based on the restoration of scale invariance of QCD,Brown and Rho have argued that masses of nonstrange hadrons would scale with the quark condensate and thus decrease in the nuclear medium[8].This has since stimulated extensive theoretical and experimental studies on hadron in-medium properties.

By studying medium e?ects on hadronic properties one can directly test our understanding of those non-perturbative aspects of QCD,which are responsible for the light hadronic states.The best way to investigate the change of hadronic properties in experiment is to study the pro-duction of particles,preferably photons and dileptons,as they are not a?ected by?nal-state interactions.Furthermore,since vector mesons decay directly into dileptons,a change of their mass can be seen di-rectly in the dilepton invariant mass spectrum.In addition,as we shall discuss,the measurement of subthreshold particle production such as kaons[9]and antiprotons[10]may also reveal some rather interesting in-medium e?ects.

Of course a nucleus or a hadronic system created in relativistic heavy ion collisions are strongly interacting.Therefore,many-body excitations can carry the same quantum numbers as the hadrons under considera-tion and thus can mix with the hadronic states.In addition,in the nu-clear environment‘simple’many-body e?ects such as the Pauli principle are at work,which,as we shall discuss,lead to considerable modi?ca-tions of hadronic properties in some cases.How these e?ects are related to the partial restoration of chiral symmetry is a new and unsolved ques-

4KO,KOCH&LI tion in nuclear many-body physics.One example is the e?ective mass of a nucleon in the medium,which was introduced long time ago[11,12] to model the momentum dependence of the nuclear force,which is due to its?nite range,or to model its energy dependence,which results from higher order(2-particle-1-hole etc.)corrections to the nucleon self energy.On the other hand,in the relativistic mean-?eld description one also arrives at a reduced e?ective mass of the nucleon.Accord-ing to[13],this is due to so-called virtual pair corrections and may be related to chiral symmetry restoration as suggested by recent studies [3,14,15,16].

Another environment,which is somewhat‘cleaner’from the theorists point of view,is a system at?nite temperature and vanishing baryon chemical potential.At low temperatures such a system can be system-atically explored within the framework of chiral perturbation theory, and essentially model-independent statements about the e?ects of chi-ral restoration on hadronic masses and couplings may thus be given.In the high temperature regime eve …… 此处隐藏：21692字，全部文档内容请下载后查看。喜欢就下载吧 ……