# Chiral susceptibility in Nambu Jona Lasinio model: a Wigner function approach

## TL;DR

This paper investigates chiral susceptibility at finite temperature within the NJL model using the Wigner function approach, considering effects of chiral chemical potential and magnetic field, revealing how these factors influence transition temperatures and quark behavior.

## Contribution

It introduces a novel application of the Wigner function approach to estimate chiral susceptibility in the NJL model under magnetic fields and chiral chemical potential.

## Key findings

- Transition temperature increases with magnetic field at fixed chiral chemical potential.
- Transition temperature decreases with chiral chemical potential at fixed magnetic field.
- Non-degeneracy in susceptibility observed for up and down quarks under strong magnetic fields.

## Abstract

We estimate here chiral susceptibility at finite temperature within the framework of the Nambu-Jona-Lasinio model (NJL) using the Wigner function approach. We also estimate it in the presence of chiral chemical potential ($\mu_5$) as well as a non vanishing magnetic field ($B$). We use medium separation regularization scheme (MSS) to calculate the chiral condensate and corresponding susceptibility. It is observed that for a fixed value of chiral chemical potential ($\mu_5$), transition temperature increases with the magnetic field. While for the fixed value of the magnetic field, transition temperature decreases with chiral chemical potential. For a strong magnetic field, we observe non degeneracy in susceptibility for up and down type quarks.