New self-consistent mean field approximation and its application in strong interaction phase transition

We propose a novel self-consistent mean field approximation method by means of a Fierz transformation, taking the Nambu-Jona-Lasinio model as an example. This new self-consistent mean field approximation introduces a new free parameter alpha to be determined experimentally. When alpha assumes the value of 0.5, the approximation reduces to the mean field calculation commonly used in the past. Subsequently, we study the influence of the undetermined parameter alpha on the phase diagram of the two-flavor strong interaction matter. The value of alpha plays a crucial role in the strong interaction phase diagram, as it not only changes the position of the phase transition point of strong interaction matter, but also affects the order of the phase transition. For example, when alpha is greater than the critical value alpha(c) = 0.71, then the strong interaction matter phase diagram no longer has a critical end point. In addition, in the case of zero temperature and finite density, we found that when alpha > 1.044, the pseudo-critical chemical potential corresponds to similar to 4-5 times the saturation density of the nuclear matter, which agrees with the expected results from the picture of the hadrons degree of freedom. The resulting equations of state of strong interaction matter at low temperatures and high densities will have an important impact on studies concerning the mass radius relationship of neutron stars and the merging process of binary neutron stars.