The chiral phase transition with a chiral chemical potential in the framework of Dyson-Schwinger equations

Within the framework of Dyson-Schwinger equations (DSEs), we discuss the chiral phase transition of QCD with a chiral chemical potential $μ_5$ as an additional scale. We focus especially on the issues related to the widely accepted as well as interested critical end point (CEP). With the help of a scalar susceptibility, we find that there might be no CEP$_5$ in the $T-μ_5$ plane, and the phase transition in the $T-μ_5$ plane might be totally crossover when $μ<50$ MeV, which has apparent consistency with the Lattice QCD calculation. Our study may also provide some useful hints to some other studies related to $μ_5$.