Chiral phase transition in hadronic matter: the influence of baryon density

Abstract

A qualitative analysis of the chiral phase transition in QCD with two massless quarks and non-zero baryon density is performed. It is assumed that at zero baryonic density, $\rho=0$, the temperature phase transition is of the second order and quark condesate $\eta=< 0\mid \bar{u} u\mid 0> =< 0 \mid \bar{d}d\mid 0>$ may be taken as order parameter of phase transition. The baryon masses strongly violate chiral symmetry, $m_B \sim < 0 \mid \bar{q}q\mid 0 >^{1/3}$. By supposing, that such specific dependence of baryon masses on quark condensate takes place up to phase transition point, it is shown, that at finite baryon density $\rho$ the phase transition becomes of the first order at the temperature $T=T_{\mathrm{ph}}(\rho)$ for $\rho>0$. At temperatures $T_{\mathrm{cont}}(\rho) > T > T_{\mathrm{ph}}(\rho)$ there is a mixed phase consisting of the quark phase (stable) and the hadron phase (unstable). At the temperature $T = T_{\mathrm{cont}}(\rho)$ the system experiences a continuous transition to the pure chirally symmetric phase.