Massive Meson Fluctuation in NJL Model

TL;DR

This paper develops a self-consistent scheme for the SU(2) NJL model that includes meson fluctuations beyond mean-field, revealing the impact of finite pion mass on chiral symmetry breaking.

Contribution

It introduces a novel large $N_c$ expansion scheme with explicit quark mass inclusion and an approximate meson propagator for improved NJL model analysis.

Findings

Finite pion mass effects are visible beyond mean-field approximation.

The scheme maintains proper $N_c$ order in quark self-energy.

Unified calculation of Feynman diagrams using external momentum expansion.

Abstract

Based on the self-consistent scheme beyond mean-field approximation in the large $N_c$ expansion, including current quark mass explicitly, a general scheme of SU(2) NJL model is developed. To ensure the quark self-energy expanded in the proper order of $N_c$, an approximate internal meson propagator is deduced, which is in order of $O(1/N_c)$. In our scheme, adopting the method of external momentum expansion, all the Feynman diagrams are calculated in a unified way by only expanding the quark propagator. Our numerical results show, that different from the mean field approximation in which the explicitly chiral symmetry breaking is invisible, the effect of finite pion mass can be seen clearly when beyond mean-field approximation.