Double Phase Transition Model and the problem of entropy and baryon number conservation

Abstract

The problem of entropy S and baryon number N_B conservation in phase transitions from deconfined phases (QGP and Q) to hadronic matter H is considered. It is shown that standard construction of both first order phase transitions, H-Q as well as Q-QGP implies a discontinuous structure of entropy per baryon S/N_B when crossing phase boundary; this results in impossibility of equilibrium transition from QGP to hadron gas. We follow the way suggested recently by H. Satz et al. for the same problem concerning direct transition H-QGP. They proposed a modification of bag pressure parameter B_{QGP} by making it dependent on system temperature T and baryon chemical potential mu; this modification has been demonstrated to be sufficient to provide S/N_B conservation. Here we show that within DPTM such a modification turns out to be necessary and sufficient for bag pressure B_Q in the Q phase only. The DPTM modified in such a way is shown to satisfy equilibrium Gibbs criteria for phase transitions. Location of phase boundaries in $\mu -T$ plane has been demonstrated to be changed but slightly; the modification tells mainly on baryon number density within Q phase. Two alternative descriptions of nucleon-nucleon interaction - the Hard Core Model and the Mean Field Approximation - have been tested; the results for both cases appeared to be similar. All the results are shown to be stable against rather broad variations of model parameters.