Ja n 19 97 Double Phase Transition Model and the problem of entropy and baryon number conservation

We continue to develop further the bag-type Double Phase Transition Model (DPTM) for transformation of Quark-Gluon Plasma (QGP) to normal hadronic matter (H-phase). The model is based on the assumed existence of an intermediate Q phase composed by massive constituent quarks and pions (as Goldstone bosons) 5, 6. In the present paper 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 17, 18 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 µ; 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 µ − 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.