Chiral Phase Transitions

Abstract

We show that melting the quark mass, the scalar $\sigma $ mass and the quark condensate leads uniquely to the quark-level SU(2) linear $\sigma $ model field theory. Upon thermalization, the chiral phase transition curve requires $T_c =2f^{CL}_{\pi}\approx 180 MeV$ when $\mu = 0$, while the critical chemical potential is $\mu_c =m_q\approx 325 MeV$. Transition to the superconductive phase occurs at $T^{(SC)}_c=\Delta /\pi e^{-\gamma_E}$. Coloured diquarks suggest $T_c^{(SC)}<180 MeV$.