Dyson–Schwinger Equations of Chiral Chemical Potential

We discuss the chiral phase transition of quantum chromodynamics (QCD) with a chiral chemical potential μ₅ as an additional scale. Within the framework of Dyson–Schwinger equations, we focus particularly on the behavior of the widely accepted as well as interesting critical end point (CEP), using a separable gluon propagator and a Gaussian gluon propagator. We find that there may be no CEP₅ in the T–μ₅ plane, and the phase transition in the T–μ₅ plane might be totally crossover. Our results have apparent consistency with the Lattice QCD calculation. On the other hand, our study may also provide some useful hints to some other studies related to μ₅.