THERMODYNAMICS OF A QUARK PLASMA BEYOND THE MEAN-FIELD - A GENERALIZED BETH-UHLENBECK APPROACH

The thermodynamics of a quark plasma is studied within the two-flavour Nambu-Jona-Lasinio model. After reviewing the results which are obtained in the mean-field (Hartree) approximation, including chiral and quark number susceptibilities, we treat the contributions to the thermodynamic potential which arise to order 1/N-c, where N-c is the number of colours. These contributions involve the pi and sigma mesons and the scattering properties of quarks. We express the thermodynamic potential in terms of the bound states and scattering phase shifts of a quark-antiquark pair. This result resembles the Beth-Uhlenbeck formula for the second virial coefficient for a gas of non-relativistic particles. Our results hold also for the relativistic case and include the influence of temperature and chemical potential on the S-matrix that arises as a consequence of these dependences in the collective excitations that are formed. (C) 1994 Academic Press, Inc.