Revisiting the phase diagram of the three-flavor quark system in the Nambu–Jona-Lasinio model

Abstract

We propose the $2+1$ flavor chiral susceptibility criterion to identify the chiral phase transition of the $2+1$ flavor quark system and take it to determine the phase boundary and the critical end point (CEP) in the Nambu-Jona-Lasinio model. We give explicitly the phase diagram of the $2+1$ flavor quark system in terms of the temperature, quark chemical potential and strange quark mass and that in terms of the temperature, quark chemical potential, and flavor-mixing interaction strength. We locate the CEP of the $2+1$ quark system with physical masses at $({\ensuremath{\mu}}_{E},{T}_{E})=(316.2\text{ }\text{ }\mathrm{MeV},68.1\text{ }\text{ }\mathrm{MeV})$. We show that increasing the mass of the strange quark lowers the temperature and enhances the chemical potential of the CEP if the mass is not quite large, and there exists a critical flavor-mixing interaction strength $(K{\ensuremath{\Lambda}}^{5}{)}_{c}\ensuremath{\approx}6.05$ for the crossover to turn into a first order phase transition. Increasing the flavor-mixing strength beyond the critical one induces the temperature of the CEP to increase drastically and raises slightly at first and then descends the chemical potential.