Deciding on the anomalous magnetic moment of quarks in a framework of nonlocal NJL model

TL;DR

This paper investigates the anomalous magnetic moment of quarks within a nonlocal NJL model, comparing different forms of AMM dependence on temperature and magnetic field to lattice data, and analyzing the phase diagram.

Contribution

It introduces a nonlocal NJL model approach to determine the most suitable form of quark AMM dependence on meanfield and external conditions, aligning with lattice results.

Findings

Second form of AMM proportional to square of meanfield fits lattice data best.

The model reproduces the lattice QCD phase diagram reasonably well.

Constant AMM assumption is less accurate than dynamic forms.

Abstract

Anomalous magnetic moment (AMM) of quarks in presence of an external magnetic field has been explored using a nonlocal Nambu\textemdash Jona-Lasinio (NJL) model. Various strengths of AMM differing in orders of magnitude are used in the literature. We explore them in our nonlocal framework to decide on their strength. We checked the validity of using constant AMM of quarks and investigate two different temperature and magnetic field dependent forms. The forms are taken as the AMM being proportional to the i) meanfield and the ii) square of the meanfield. On comparison with the lattice data for both the condensate averages and differences, it turns out that the second choice is the most suitable one, in such an effective model scenario. In the process, we also keep track of the phase diagram in the $T-eB$ plane arising from our model calculation. The outcome is reasonable as far as the lattice QCD result is concerned.