Difermion condensates in vacuum in 2-4D four-fermion interaction models

Details Difermion condensates in vacuum in 2-4D four-fermion interaction models Difermion condensates in vacuum in 2-4D four-fermion interaction models

2007-04-06

arxiv.org/abs/0704.0841v3

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, 4 figures, General Poster 76 (Physical sciences) at 2007 AAAS Annual Meeting, San Francisco, Feb. 14-20, 2007, minor

Scientific paper

Theoretical analysis of interplay between the condensates $<\bar{q}q>$ and $$ in vacuum is generally made by relativistic effective potentials in the mean field approximation in 2D, 3D and 4D models with two flavor and $N_c$ color massless fermions. It is found that in ground states of these models, interplay between the two condensates mainly depend on the ratio $G_S/H_S$ for 2D and 4D case or $G_S/H_P$ for 3D case, where $G_S$, $H_S$ and $H_P$ are respectively the coupling constants in a scalar $(\bar{q}q)$, a scalar $(qq)$ and a pseudoscalar $(qq)$ channel. In ground states of all the models, only pure $<\bar{q}q>$ condensates could exist if $G_S/H_S$ or $G_S/H_P$ is bigger than the critical value $2/N_c$, the ratio of the color numbers of the fermions entering into the condensates $$ and $<\bar{q}q>$. As $G_S/H_S$ or $G_S/H_P$ decreases to the region below $2/N_c$, differences of the models will manifest themselves. Depending on different models, and also on $N_c$ in 3D model, one will have or have no the coexistence phase of the two condensates, besides the pure $$ condensate phase. The $G_S-H_S$ (or $G_S-H_P$) phase diagrams in these models are given. The results also implicate a real constraint on two-flavor QCD-analogous NJL model.

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