Three-dimensional QCD phase diagram in the pNJL model

Based on the three-flavor Polyakov-looped Nambu$-$Jona-Lasinio (pNJL) model, we have studied the structure of the three-dimensional QCD phase diagram with respect to the temperature, the baryon chemical potential, and the isospin chemical potential, by investigating the interplay among the chiral quark condensate, the pion condensate, and the Polyakov loop. While the pNJL model leads to qualitatively similar structure of the normal quark phase, the pion superfluid phase, and the Sarma phase as well as their phase boundaries, when compared to the NJL model, the inclusion of the Polyakov loop enlarges considerably the areas of the pion superfluid phase and the Sarma phase, and leads to critical end points at higher temperatures. With the contribution of the gluon dynamics effectively included, the present study is expected to give a more reliable prediction of the three-dimensional QCD phase diagram compared to that in the NJL model.