Self-consistent mean field approximation and application in three-flavor NJL model

Abstract

In this study, we apply a self-consistent mean field approximation of the three-flavor Nambu–Jona-Lasinio (NJL) model and compare it with the two-flavor NJL model. The self-consistent mean field approximation introduces a new parameter, , that cannot be fixed in advance by the mean field approach itself. Due to the lack of experimental data, the parameter, , is undetermined. Hence, it is regarded as a free parameter and its influence on the chiral phase transition of strong interaction matter is studied based on this self-consistent mean field approximation. affects numerous properties of the chiral phase transitions, such as the position of the phase transition point and the order of phase transition. Additionally, increasing will decrease the number densities of different quarks and increase the chemical potential at which the number density of the strange quark is non-zero. Finally, we observed that affects the equation of state (EOS) of the quark matter, and the sound velocity can be calculated to determine the stiffness of the EOS, which provides a good basis for studying the neutron star mass-radius relationship.