Exploring the chiral and deconfinement phase transitions in a self-consistent PNJL model

In this work, we study the chiral and deconfinement phase transitions in a two-flavor Polyakov loop extended Nambu--Jona-Lasinio (PNJL) model. And note that the self-consistent mean field approximation is employed by introducing an arbitrary parameter $\alpha$ to measure the weights of the Fierz-transformed interaction channels. By making use of this model, we systematically investigate the chiral and deconfinement phase transition lines (as well as the chiral ones in the NJL model for comparison) under different values of $\alpha$. It is found that, the increasing of $\alpha$ helps to enhance the chiral (pseudo)critical temperature at fixed chemical potential, and also to enhance the chiral (pseudo)critical chemical potential at fixed temperature. And the critical end point (CEP) vanishes when $\alpha$ becomes large enough. Besides, we find that the incorporation of Polyakov loop increases $T_{CEP}$ but does not change $\mu_{CEP}$ for small values of $\alpha$.