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

TL;DR

This paper investigates the chiral phase transition in QCD with a chiral chemical potential using Dyson-Schwinger equations, suggesting the possible absence of a critical end point and a crossover transition at low chemical potential.

Contribution

It provides new insights into the phase structure of QCD with chiral chemical potential, especially regarding the existence of the critical end point, using Dyson-Schwinger equations.

Findings

No evidence of a critical end point in the $T-$ plane.

Phase transition is likely a crossover when $<50$ MeV.

Results are consistent with lattice QCD calculations.

Abstract

Within the framework of Dyson-Schwinger equations (DSEs), we discuss the chiral phase transition of QCD with a chiral chemical potential $\mu_5$ 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 $T-\mu_5$ plane, and the phase transition in the $T-\mu_5$ plane might be totally crossover when $\mu<50$ MeV, which has apparent consistency with the Lattice QCD calculation. Our study may also provide some useful hints to some other studies related to $\mu_5$.