Quark-antiquark and diquark condensates in vacuum in two-flavor four-fermion interaction models with any color number $N_c$

TL;DR

This paper investigates how the number of colors $N_c$ affects the interplay between quark-antiquark and diquark condensates in vacuum within various four-fermion interaction models, revealing phase diagram behaviors and the disappearance of diquark phases as $N_c$ increases.

Contribution

It provides a detailed analysis of $N_c$-dependence on condensate phases in different models, highlighting the conditions for coexistence and the limit where diquark phases vanish.

Findings

Phase diagrams are qualitatively consistent across models for varying $N_c$.

In 3D GN models, the coexistence phase exists only for $N_c \,\leq\ 4$.

Diquark condensate phases diminish and disappear as $N_c$ approaches infinity.

Abstract

The color number $N_c$-dependence of the interplay between quark-antiquark condensates $<\bar{q}q>$ and diquark condensates $<qq>$ in vacuum in two-flavor four-fermion interaction models is researched. The results show that the $G_S$-$H_S$ (the coupling constant of scalar $(\bar{q}q)^2$-scalar $(qq)^2$ channel) phase diagrams will be qualitatively consistent with the case of $N_c=3$ as $N_c$ varies in 4D Nambu-Jona Lasinio model and 2D Gross-Neveu (GN) model. However, in 3D GN model, the behavior of the $G_S$-$H_P$ (the coupling constant of pseudoscalar $(qq)^2$ channel) phase diagram will obviously depend on $N_c$. The known characteristic that a 3D GN model has not the coexistence phase of the condensates $<\bar{q}q>$ and $<qq>$ is proven to appear only in the case of $N_c\leq 4$. In all the models, the regions occupied by the phases containing the diquark condensates $<qq>$ in corresponding phase diagrams will gradually decrease as $N_c$ grows up and finally go to zero if $N_c \to \infty$, i.e. in this limit only the pure $<\bar{q}q>$ phase could exist.