Effects of the quark anomalous magnetic moment in the chiral symmetry restoration: magnetic catalysis and inverse magnetic catalysis

TL;DR

This study investigates how a constant anomalous magnetic moment of quarks influences chiral symmetry restoration, revealing that it causes a smooth crossover and affects magnetic catalysis phenomena in the SU(2) NJL model.

Contribution

It introduces the effect of quark AMM into the NJL model using the Schwinger ansatz and a novel regularization, showing its impact on magnetic catalysis and inverse magnetic catalysis behaviors.

Findings

Quark AMM leads to a smooth decrease in pseudocritical temperature with magnetic field.

Limited window for inverse magnetic catalysis observed, contrary to previous NJL predictions.

Chiral symmetry restoration remains a crossover for nonzero AMM, not a first order transition.

Abstract

In this work, we consider the effect of a constant anomalous magnetic moment (AMM) of quarks in the SU(2) Nambu--Jona-Lasinio model in the mean field approximation. To this end, we use the Schwinger {\it ansatz}, which represents a linear magnetic field term in the Lagrangian. A regularization method inspired in the vacuum magnetic regularization (VMR) is adopted to avoid ultraviolet divergences. Our results indicate a smooth decrease of the pseudocritical temperature and quark condensates for magnetic fields $B \leq 0.1$ GeV$^2$ when a sizable AMM is considered. We found only a small window for Inverse Magnetic Catalysis (IMC), in contradiction with NJL predictions made in the literature. For a low value of AMM, we observe for all ranges of magnetic fields considered that the pseudocritical temperature increases with the magnetic field, indicating only Magnetic Catalysis (MC). In our approach, for nonvanishing quark AMM, the chiral symmetry restoration happens always as a smooth crossover and never turns into a first order phase transition.