Color-flavor dependence of the Nambu-Jona-Lasinio model and QCD phase diagram

TL;DR

This paper investigates how the number of quark flavors and colors influences chiral symmetry breaking and the QCD phase diagram using an extended NJL model, revealing critical thresholds and phase transition behaviors.

Contribution

It introduces a color-flavor dependent coupling in the NJL model and analyzes the interplay of $N_c$ and $N_f$ on chiral symmetry and phase transitions, aligning with lattice QCD and Schwinger-Dyson results.

Findings

Chiral symmetry breaks when $N_c > 2.2$ for $N_f=2$.

Chiral symmetry restores at $N_f o 8$ for $N_c=3$.

Critical temperature and chemical potential increase with $N_c$ and decrease with $N_f$.

Abstract

We study the dynamical chiral symmetry breaking/restoration for the various numbers of light quarks flavors $N_f$ and colors $N_c$, using the Nambu-Jona-Lasinio (NJL) model of quarks, dressed with a color-flavor dependence of effective coupling. Initially, we set $N_f = 2$, and varying the number of colors $N_c$, we find that the dynamical chiral symmetry is broken when $N_c$ exceeds to its critical value $N^{c}_{c}\approx2.2$. Secondly, we take $N_c = 3$, and varying $N_f$, we observed that the dynamical chiral symmetry is restored when $N_f$ reaches to its critical value $N^{c}_{f}\approx8$. The strong interplay observed between $N_c$ and $N_f$, i.e., $N_c$ anti-screens the strong interactions by strengthening the dynamical mass and quark-antiquark condensate, while $N_f$ screens the strong interaction by suppressing both the parameters. We further sketch the quantum chromodynamics (QCD) phase diagram at finite temperature $T$ and quark chemical potential $\mu$ for various $N_c$ and $N_f$. At finite $T$ and $\mu$, we observed that the critical number of colors $N^{c}_c$ enhances while the critical number of flavors $N^{c}_f$ suppresses as $T$ and $\mu$ increases. Of course, the parameters $T$ and $\mu$ produce the screening effect. Consequently, the critical temperature $T_c$, $\mu_c$ and co-ordinates of the critical endpoint $(T^{E}_c,\mu^{E}_c)$ in the QCD phase diagram enhances as $N_c$ increases while suppresses when $N_f$ increases. Our findings agree with the Lattice QCD and Schwinger-Dyson equations predictions.