QCD phase diagram in chiral imbalance with self-consistent mean field approximation

We employ a new self-consistent mean field approximation of the Nambu-Jona-Lasinio (NJL) model, which introduces a free parameter $\alpha$ ($\alpha$ reflects the weight of different interaction channels), to study the effects of the chiral chemical potential ${\mu }_5$ on QCD phase structure, especially the location of the QCD critical endpoint (CEP). We find that, at a high temperature, the critical temperature of QCD phase transition smoothly increases with ${\mu }_5$ at the beginning, and then decreases rapidly. At low temperature and high baryon density region, the increase of the chiral chemical potential will reduce the critical chemical potential of phase transition. The temperature of the CEP shows a nonmonotonic dependence on the chiral chemical potential with a long plateau around the maximum. At ${\mu }_5=0$, we found that the CEP will disappear when the $\alpha$ value is larger than 0.71 and will reappear when the ${\mu }_5$ increases. This study is important for exploring the QCD phase structure and the location of CEP in chiral imbalanced systems.

Figure 1

The phase diagram of $\alpha =0.5$. The solid lines and the dotted lines respectively represent the first-order phase transition and crossover at the corresponding ${\mu }_5$. The stars denote the CEPs. The difference in ${\mu }_5$ between each star is 50 MeV.

Figure 2

The phase diagram of $\alpha =0.8$. The solid lines and the dotted lines respectively represent the first-order phase transition and crossover at the corresponding ${\mu }_5$. The stars denote the CEPs. The difference in ${\mu }_5$ between each star is 50 MeV.

Figure 3

The phase diagram of $\alpha =0.9$. The stars denote the projection of CEPs onto $\mu -T$ plane. The solid lines and the dotted lines respectively represent the first-order phase transition and crossover at the corresponding ${\mu }_5$.

Figure 4

The critical temperature $T_c$ of phase transition changes with ${\mu }_5$ at $\mu =0$ for different $\alpha$.

Figure 5

The projection of CEPs onto ${\mu }_5-\mu$ plane for different $\alpha$.

Figure 6

The projection of CEPs onto ${\mu }_5-T$ plane for different $\alpha$.