Effect of the chiral chemical potential on the position of the critical endpoint

Abstract

The effect of chiral imbalance on the QCD phase structure is studied in a framework of Dyson--Schwinger equations. It is found that the chiral phase transition is always a crossover in the $T\ensuremath{-}{\ensuremath{\mu}}_{5}$ plane when $\ensuremath{\mu}$ is 0 MeV or small values. The trail of the critical endpoints (CEPs) along with the variation of the chiral chemical potential is given. We find that the effect of ${\ensuremath{\mu}}_{5}$ is somewhat different from the existing chiral model calculations; namely, the CEP first moves roughly along the phase boundary of $T\ensuremath{-}\ensuremath{\mu}$ plane in a smaller $\ensuremath{\mu}$ direction, as in the chiral model calculations, but turns in the opposite direction to move away from the small chemical potential region, which has never been observed before. In addition, we also discuss the possibility of whether the study at finite temperature and chiral chemical potential can provide some useful information for the detection of the CEP at finite temperature and baryon chemical potential, since the former can be calculated in lattice QCD without the sign problem.