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

Abstract

Within the framework of Dyson-Schwinger equations , we discuss the chiral phase transition of QCD with a chiral chemical potential ${\ensuremath{\mu}}_{5}$ as an additional scale. We focus especially on the issues related to the widely accepted as well as interesting critical end point (CEP). With the help of a scalar susceptibility, we find that there might be no ${\mathrm{CEP}}_{5}$ in the $T\ensuremath{-}{\ensuremath{\mu}}_{5}$ plane, and the phase transition in the $T\ensuremath{-}{\ensuremath{\mu}}_{5}$ plane might be totally crossover when $\ensuremath{\mu}<50\text{ }\text{ }\mathrm{MeV}$, which has apparent consistency with the lattice QCD calculation. Our study may also provide some useful hints to some other studies related to ${\ensuremath{\mu}}_{5}$.