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

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.