Chiral phase transition within effective models with constituent quarks

Abstract

We study the chiral phase transition at nonzero temperature T and baryon chemical potential ${\ensuremath{\mu}}_{B}$ within the framework of the linear sigma model and the Nambu--Jona-Lasinio (NJL) model. For small bare quark masses we find in both models a smooth crossover transition for nonzero T and ${\ensuremath{\mu}}_{B}=0$ and a first order transition for $T=0$ and nonzero ${\ensuremath{\mu}}_{B}.$ We calculate explicitly the first order phase transition line and spinodal lines in the $(T,{\ensuremath{\mu}}_{B})$ plane. As expected they all end at a critical point. We find that, in the linear sigma model, the sigma mass goes to zero at the critical point. This is in contrast to the NJL model, where the sigma mass, as defined in the random phase approximation, does not vanish. We also compute the adiabatic lines in the $(T,{\ensuremath{\mu}}_{B})$ plane. Within the models studied here, the critical point does not serve as a ``focusing'' point in the adiabatic expansion.