Response functions of hot and dense matter in the Nambu-Jona-Lasino model

TL;DR

This paper analyzes the response functions of hot and dense matter in the Nambu-Jona-Lasinio model, incorporating mesonic fluctuations beyond mean-field theory to understand their effects on transport properties near the chiral transition.

Contribution

It derives response functions including mesonic fluctuations beyond mean-field approximation, revealing their impact on dynamical structure factors and transport properties.

Findings

Response functions recover quasiparticle RPA in mean-field theory.

Mesonic fluctuations introduce key diagrammatic contributions like Aslamazov-Lakin.

Fluctuations significantly affect transport properties near the chiral transition.

Abstract

We investigate the current-current correlation functions or the so-called response functions of a two-flavor Nambu-Jona-Lasino model at finite temperature and density. We study the linear response by using the functional path integral approach and introducing the conjugated gauge fields as external sources. The response functions can be obtained by expanding the generational functional in powers of the external sources. We derive the response functions parallel to two well-established approximations for the equilibrium thermodynamics: the mean-field theory and a beyond-mean-field theory taking into account the mesonic contributions. The response functions based on the mean-field theory recover the so-called quasiparticle random phase approximation. We calculate the dynamical structure factors for the density responses in various channels within the random phase approximation. We show that the dynamical structure factors in the baryon axial vector and isospin axial vector channels can be used reveal the quark mass gap and the Mott dissociation of mesons, respectively. Noting that the mesonic contributions are not taken into account in the random phase approximation, we also derive the response functions parallel to the beyond-mean-field theory. We show that the mesonic fluctuations naturally give rise to three kinds of famous diagrammatic contributions: the Aslamazov-Lakin contribution, the Self-Energy or Density-of-State contribution, and the Maki-Thompson contribution. Unlike the equilibrium case, in evaluating the fluctuation contributions, we need to treat carefully the linear terms in the external sources and the induced perturbations. These contributions from the mesonic fluctuations are expected to have significant effects on the transport properties of hot and dense matter around the chiral phase transition or crossover.