Random matrix model for chiral and color-flavor locking condensates

TL;DR

This paper models the phase diagram of quark matter using a random matrix approach, revealing the conditions for chiral symmetry breaking and color-flavor locking phases at various densities and quark mass configurations.

Contribution

It introduces a random matrix model with independent order parameters for chiral and diquark condensates, analyzing phase transitions and flavor effects at finite temperature and chemical potential.

Findings

CFL phase appears at high chemical potential

Finite quark masses shift the CFL transition to higher densities

Two-flavor superconducting phase emerges at medium densities

Abstract

We study the phase diagram of a chiral random matrix model with three quark flavors at finite temperature and chemical potential, taking the chiral and diquark condensates as independent order parameters. Fixing the ratio of the coupling strengths in the quark-antiquark and quark-quark channels applying the Fierz transformation, we find that the color-flavor locked (CFL) phase is realized at large chemical potential, while the ordinary chirally-broken phase appears in the region with small chemical potential. We investigate responses of the phases by changing small quark masses in the cases with three equal-mass flavors and with 2+1 flavors. In the case with three equal-mass flavors, we find that the finite masses make the CFL phase transition line move to the higher density region. In the case with 2+1 flavors, we find the two-flavor color superconducting phase at the medium density region as a result of the finite asymmetry between the flavors, as well as the CFL phase at higher density region.