真空中任意色数$N_c$的双味四费米子相互作用模型中的夸克-反夸克和双夸克凝聚
Quark-antiquark and diquark condensates in vacuum in two-flavor four-fermion interaction models with any color number $N_c$
摘要：
研究了真空中双味四费米子相互作用模型中夸克-反夸克凝聚$<\bar{q}q>$和双夸克凝聚$<qq>$之间相互作用的色数$N_c$依赖性。结果表明，当$N_c$在4D Nambu-Jona Lasinio模型和2D Gross-Neveu（GN）模型中变化时，$G_S$ - $H_S$（标量$(\bar{q}q)^2$ -标量$(qq)^2$通道的耦合常数）相图与$N_c=3$的情况定性一致.然而，在三维GN模型中，$G_S$ - $H_P$（赝标$(qq)^2$通道的耦合常数）相图的行为将明显依赖于$N_c$。证明了三维GN模型不具有凝聚体$<\bar{q}q>$和$<qq>$共存相的已知特征仅出现在$N_c\leq 4$的情况下。在所有模型中，含双夸克凝聚$<qq>$的相在相应相图中所占的区域随着$N_c$的长大而逐渐减小，当$N_c \to \infty$为$N_c \to \infty$时，最终趋于零，即在此极限下只能存在纯$<\bar{q}q>$相。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
