The nNJL model with a fractional Lorentzian regulator in the real time formalism

TL;DR

This paper investigates the finite temperature and chemical potential effects in a nonlocal Nambu-Jona-Lasinio model using a fractional Lorentzian regulator within the real time formalism, analyzing phase transitions and propagator poles.

Contribution

It introduces a complex-plane definition of the regulator in the real time formalism and studies the resulting phase transition behavior in the nNJL model.

Findings

Identifies the temperature for chiral symmetry restoration.

Finds a second order phase transition at lower chemical potentials.

Transitions to a first order phase transition at higher chemical potentials.

Abstract

In this article we study the finite temperature and chemical potential effects in a nonlocal Nambu-Jona-Lasinio (nNJL) model in the real time formalism. We make the usual Wick rotation to get from imaginary to real time formalism. In doing so, we need to define our regulator in the complex plane q^2. This deffinition will be crucial in our later analysis. We study the poles in the propagator of this model and conclude that only some of them are of interst to us. Once we have a well defined model in real time formalism, we look at the chiral condensate to find the temperature at which chiral symmetry restoration will occur. We find a second order phase transition that turns to a first order one for high enough values of the chemical potential.