Quark-Antiquark and Diquark Condensates in Vacuum in a 2D Two-Flavor Gross-Neveu Model

TL;DR

This paper investigates the conditions under which quark-antiquark and diquark condensates form in the vacuum of a 2D two-flavor Gross-Neveu model, revealing their dependence on coupling ratios and contrasting with 4D NJL model behavior.

Contribution

It provides a detailed analysis of condensate coexistence and dominance in a 2D model, highlighting differences from the 4D NJL model regarding diquark condensate formation.

Findings

Pure quark-antiquark condensates occur when G_S/H_S > 2/3.

Coexistence of both condensates happens when 0 < G_S/H_S < 2/3.

Pure diquark condensates only appear at G_S/H_S=0.

Abstract

The analysis based on the renormalized effective potential indicates that, similar to in the 4D two-flavor Nambu-Jona-Lasinio (NJL) model, in a 2D two-flavor Gross-Neveu model, the interplay between the quark-antiquark and the diquark condensates in vacuum also depends on $G_S/H_S$, the ratio of the coupling constants in scalar quark-antiquark and scalar diquark channel. Only the pure quark-antiquark condensates exist if $G_S/H_S>2/3$ which is just the ratio of the color numbers of the quarks participating in the diquark and quark-antiquark condensates. The two condensates will coexist if $0<G_S/H_S<2/3$. However, different from the 4D NJL model, the pure diquark condensates arise only at $G_S/H_S=0$ and are not in a possibly finite region of $G_S/H_S$ below 2/3.