Interplay between chiral and deconfinement phase transitions

By using the dressed Polyakov loop or dual chiral condensate as an equivalent order parameter of the deconfinement phase transition, we investigate the relation between the chiral and deconfinement phase transitions at finite temperature and density in the framework of three-flavor Nambu--Jona-Lasinio (NJL) model. It is found that in the chiral limit, the critical temperature for chiral phase transition coincides with that of the dressed Polyakov loop in the whole $(T,\mu)$ plane. In the case of explicit chiral symmetry breaking, it is found that the phase transitions are flavor dependent. For each flavor, the transition temperature for chiral restoration $T_c^{\chi}$ is smaller than that of the dressed Polyakov loop $T_c^{{\cal D}}$ in the low baryon density region where the transition is a crossover, and, the two critical temperatures coincide in the high baryon density region where the phase transition is of first order. Therefore, there are two critical end points, i.e, $T_{CEP}^{u,d}$ and $T_{CEP}^{s}$ at finite density. We also explain the feature of $T_c^{\chi}=T_c^{\cal D}$ in the case of 1st and 2nd order phase transitions, and $T_c^{\chi}<T_c^{\cal D}$ in the case of crossover, and expect this feature is general and can be extended to full QCD theory.