Color superconductivity with self-consistent NJL-type model

Abstract

In this paper, the NJL-type model is used to investigate the color superconductivity. The four-fermion interactions of the NJL-type model are Fierz-transformed into two different classes, i.e., the quark-antiquark and the quark-quark interaction channels, associated with the chiral symmetry breaking and color superconductivity respectively. We conclude that the weighting factor between quark-antiquark and quark-quark interaction channels has significance on the phase structure when the mean-field approximation is employed, and the baryon number density gives a tight constraint on the weighting factor of quark-antiquark interaction channels. Besides, the susceptibilities show that the color superconducting phase transition is of the second-order and takes place before the chiral crossover transition as quark number density increases. In the end, we study the critical temperatures T c of the color superconductivity and it agrees with the perturbative result of diquark condensate ∆ ≈ 0.57T c .

Hybrid stars and QCD phase transition with a NJL-like model

“…So, the introduction of a term by hand is quite arbitrary and will make the method lose its reliability [39]. In order to overcome the arbitrariness brought by the above method, the self-consistent mean field approximation method is necessary, which can release all the interaction channels hidden in the original Lagrangian by the Fierz transformation [40]. Because the Fierz transformation is an equivalent transformation, the new Lagrangian L R = (1 − α)L + αL F used in this paper is equivalent to the original NJL model, which is another advantage of our method.…”