Chiral phase transition in hadronic matter at non-zero baryon density

Abstract

A qualitative analysis of the chiral phase transition in QCD at non--zero baryon density is performed. It is assumed that at zero baryonic density, $ρ=0$, the temperature phase transition is of the second order and quark condesate $η= \mid < 0\mid \bar{u} u\mid 0> \mid =\mid< 0 \mid \bar{d}d\mid 0 >\mid $ may be taken as order parameter of phase transition. It is demonstrated, that the proportionality of baryon masses to quark condensate in the power 1/3, $m_B \sim \mid < 0 \mid {\bar q} q \mid 0 > \mid^{1/3}$ is valid in the wide interval of quark condensate values. 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 $ρ$ the phase transition becomes of the first order at the temperature $T=T_{\mathrm{ph}}(ρ)$ for $ρ>0$. At temperatures $T_{\mathrm{cont}}(ρ) > T > T_{\mathrm{ph}}(ρ)$ there is a mixed phase consisting of the quark phase (stable) and the hadron phase (unstable). At the temperature $T = T_{\mathrm{cont}}(ρ)$ the system experiences a continuous transition to the pure chirally symmetric phase.