Thermodynamics of a Quark Plasma Beyond the Mean Field: A Generalized Beth-Uhlenbeck Approach

Abstract

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 π and σ 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.