# Effect of anomalous magnetic moment of quarks on the phase structure and mesonic properties in the NJL model

## TL;DR

This paper investigates how the anomalous magnetic moment of quarks influences the phase transition and mesonic properties in the NJL model under magnetic fields, revealing inverse magnetic catalysis and effects on meson masses.

## Contribution

It introduces a field-dependent regularization technique and studies the impact of quark AMM on phase structure and mesonic properties in a magnetized medium.

## Key findings

- Critical temperature decreases with magnetic field (inverse magnetic catalysis).
- Meson masses show a jump at the Mott transition, decreasing with magnetic field when AMM is considered.
- AMM significantly affects the phase diagram and mesonic behavior in hot, dense magnetic environments.

## Abstract

Employing a field dependent three-momentum cut-off regularization technique, we study the phase structure and mesonic masses using the $2$-flavour Nambu-Jona Lasinio model at finite temperature and density in presence of arbitrary external magnetic field. This approach is then applied to incorporate the effects of the anomalous magnetic moment(AMM) of quarks on constituent quark mass and thermodynamic observables as a function of temperature/baryonic density. The critical temperature for transition from chiral symmetry broken to the restored phase is observed to decrease with the external magnetic field, which can be classified as inverse magnetic catalysis, while an opposite behaviour is realized in the case of a vanishing magnetic moment, implying magnetic catalysis. These essential features are also reflected in the phase diagram. Furthermore, the properties of the low lying scalar and neutral pseudoscalar mesons are also studied in presence of a hot and dense magnetized medium including AMM of the quarks using random phase approximation. For non-zero values of magnetic field, we notice a sudden jump in the mass of the Goldstone mode at and above the Mott transition temperature which is found to decrease substantially with the increase in magnetic field when the AMM of the quarks are taken into consideration.