QCD phase diagram at finite isospin and baryon chemical potentials with the self-consistent mean field approximation

The self-consistent mean field approximation of the two-flavor NJL model, with a free parameter \begin{document}$\alpha$\end{document} to reflect the competition between the "direct" channel and the "exchange" channel, is employed to study the QCD phase structure at finite isospin chemical potential \begin{document}$\mu_I$\end{document}, finite baryon chemical potential \begin{document}$\mu_B$\end{document} and finite temperature T, and especially to study the location of the QCD critical point. Our results show that in order to match the corresponding lattice results of isospin density and energy density, the contributions of the "exchange" channel need to be considered in the framework of the NJL model, and a weighting factor \begin{document}$\alpha=0.5$\end{document} should be taken. It is also found that for fixed isospin chemical potentials, the lower temperature of the phase transition is obtained with increasing \begin{document}$\alpha$\end{document} in the \begin{document}$T-\mu_I$\end{document} plane, and the largest difference of the phase transition temperature with different \begin{document}$\alpha$\end{document}'s appears at \begin{document}$\mu_I \sim 1.5m_{\pi}$\end{document}. At \begin{document}$\mu_I=0$\end{document} the temperature of the QCD critical end point (CEP) decreases with increasing \begin{document}$\alpha$\end{document}, while the critical baryon chemical potential increases. At high isospin chemical potential (\begin{document}$\mu_I=500$\end{document} MeV), the temperature of the QCD tricritical point (TCP) increases with increasing \begin{document}$\alpha$\end{document}, and in the low temperature regions the system will transition from the pion superfluidity phase to the normal phase as \begin{document}$\mu_B$\end{document} increases. At low density, the critical temperature of the QCD phase transition with different \begin{document}$\alpha$\end{document}'s rapidly increases with \begin{document}$\mu_I$\end{document} at the beginning, and then increases smoothly around \begin{document}$\mu_I>300$\end{document} MeV. In the high baryon density region, the increase of the isospin chemical potential will raise the critical baryon chemical potential of the phase transition.