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

Within the framework of Dyson-Schwinger equations , 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 interesting critical end point (CEP). With the help of a scalar susceptibility, we find that there might be no ${\mathrm{CEP}}_5$ in the $T-{\mu }_5$ plane, and the phase transition in the $T-{\mu }_5$ plane might be totally crossover when $\mu <50\mathrm{MeV}$, which has apparent consistency with the lattice QCD calculation. Our study may also provide some useful hints to some other studies related to ${\mu }_5$.

Figure 1

$B(0,{\tilde{\omega }}_0^2)$ as a function of $\mu$ for three different $T$.

Figure 2

${\chi }_m(T,\mu )$ as a function of $\mu$ for three different $T$.

Figure 3

The relation between ${\mu }_5$ and the corresponding $T_c[{\mu }_5]$ in the $T-\mu$ plane.

Figure 4

The relation between ${\mu }_5$ and the corresponding ${\mu }_c[{\mu }_5]$ in the $T-\mu$ plane.