Phase diagrams in the three-flavor Nambu--Jona-Lasinio model with the Polyakov loop

We present extensive studies on hot and dense quark matter with two light and one heavy flavors in the Nambu--Jona-Lasinio model with the Polyakov loop (so-called PNJL model). First we discuss prescription dependence in choosing the Polyakov loop effective potential and propose a simple and rather sensible ansatz. We look over quantitative comparison to the lattice measurement to confirm that the model captures thermodynamic properties correctly. We then analyze the phase structure with changing the temperature, quark chemical potential, quark masses, and coupling constants. We particularly investigate how the effective U_A(1) restoration and the induced vector-channel interaction at finite density would affect the QCD critical point.