Color superconductivity in the Nambu Jona-Lasinio model complemented by a Polyakov loop

TL;DR

This paper investigates color superconductivity using the PNJL model with a $$-dependent Polyakov loop potential, analyzing phase transitions and identifying a new sSC phase in the density plane.

Contribution

It provides analytical formulations for various phases in the PNJL model, including normal, 2-flavor, and color-flavor-locked phases, with detailed phase transition analysis.

Findings

First order phase transitions at low T for chiral symmetry restoration, deconfinement, and phase change.

Identification of an sSC phase in the quark and strange quark density plane.

Analytical equations established for all studied phases and conditions.

Abstract

The color superconductivity was studied with an adaptation of the Nambu and Jona-Lasinio model (NJL). This one was coupled to a Polyakov loop, to form the PNJL model. A $\mu$-dependent Polyakov loop potential was considered. An objective of the presented works was to describe the analytical calculations required to establish the equations to be solved, in all of the treated cases. They concerned the normal quark phase, the 2-flavor color-superconducting and the color-flavor-locked phases, in an SU(3)f X SU(3)c description. The calculations were performed according to the temperature T, the chemical potentials $\mu_{f}$ or according to the densities $\rho_{f}$, with or without the isospin symmetry. Among the obtained results, it was found that at low T, the restoration of the chiral symmetry, the deconfinement transition and the transition between the normal quark and 2-flavor color-superconducting phases occur via first order phase transitions at the same chemical potential. Moreover, an sSC phase was identified in the $\rho_{q}$, $\rho_{s}$ plane.