Color superconductivity with self-consistent NJL-type model

TL;DR

This paper uses a self-consistent NJL-type model to analyze color superconductivity, revealing how interaction channel weighting affects phase structure, and confirming the second-order nature of the phase transition with temperature-dependent critical points.

Contribution

It introduces a detailed analysis of the phase structure of color superconductivity within a self-consistent NJL model, emphasizing the role of interaction channel weighting and phase transition characteristics.

Findings

The phase structure depends on the weighting factor between interaction channels.

Color superconductivity transition is second-order and occurs before chiral crossover.

Critical temperature matches perturbative diquark condensate predictions.

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 $\Delta\approx0.57T_c$.