Chiral phase transition at high temperature and density in the QCD-like theory

The chiral phase transition at finite temperature T and/or chemical potential μ is studied using the QCD-like theory with a variational approach. The "QCD-like theory" means the improved ladder approximation with an infrared cutoff in terms of a modified running coupling. The form of the Cornwall-Jackiw-Tomboulis effective potential is modified by the use of the Schwinger-Dyson equation for a generally nonzero current quark mass. We then calculate the effective potential at finite T and/or μ and investigate the phase structure in the chiral limit. We have a second-order phase transition at T_c=129 MeV for μ=0 and a first-order one at μ_c =422 MeV for T=0. A tricritical point in the T-μ plane is found at T=107 MeV, μ=210 MeV. The position is close to that of the random matrix model and some version of the Nambu-Jona-Lasinio model.