Nonextensive effects in the Nambu--Jona-Lasinio model of QCD

TL;DR

This paper introduces a nonextensive extension of the NJL model of QCD using Tsallis statistics, showing that key properties like chiral symmetry restoration and meson masses are affected by nonextensive effects.

Contribution

It develops a nonextensive version of the NJL model incorporating Tsallis statistics, providing a new phenomenological parameter to explore departures from Boltzmann-Gibbs behavior.

Findings

Temperature dependence of chiral symmetry restoration is affected by nonextensivity.

Masses of pion and sigma meson vary with the nonextensive parameter q.

Features of spinodal decomposition are sensitive to nonextensive effects.

Abstract

We present a nonextensive version of the recently discussed QCD-based Nambu - Jona-Lasinio (NJL) model of many-body field theory describing behavior of strongly interacting matter. It is based on the nonextensive generalization of the Boltzmann-Gibbs (BG) statistical mechanics used in NJL model, which was taken in the form proposed by Tsallis and characterized by a dimensionless nonextensivity parameter q (for q -> 1 one recovers the usual BG case). This is a new phenomenological parameter of the model which accounts summarily for all possible (so far unspecified) effects leading to departure from the conditions required by the usual BG approach to be fully applicable. It turns out that temperature dependencies of chiral symmetry restoration, masses of pion and sigma meson and characteristic features of spinodal decomposition are sensitive to the departures from the usual BG case.