Anomalous magnetic moment of hot quarks, inverse magnetic catalysis and reentrance of chiral symmetry broken phase

Abstract: The effect of anomalous magnetic moment of quarks on thermodynamic properties of the chiral condensate is studied, using of a two-flavor Nambu--Jona-Lasinio model at finite temperature $T$, chemical potential $\mu$, and in the presence of a uniform magnetic field $eB$. To this purpose, the Schwinger linear-in-$B$ ansatz for the quark anomalous magnetic moment in term of the nonperturbative Bohr magneton is considered. In a two-dimensional flavor space, it leads to the correction $\hat{T}_{Sch}=\hat{\kappa}\hat{Q} eB$ in the energy dispersion relation of quarks. Here, $\hat{Q}$ is the quark charge matrix. We consider three different sets for $\hat{\kappa}$, and numerically determine the dependence of the constituent quark mass on $T,\mu$ and $eB$ for fixed $\hat{\kappa}$. By exploring the complete phase portrait of this model in $T$-$\mu$, $\mu$-$eB$, and $T$-$eB$ phase spaces for various fixed $eB$, $T$, $\mu$ and $\hat{\kappa}$, we observe that inverse magnetic catalysis occurs for large enough $\hat{\kappa}$. Moreover, in the regime of weak magnetic fields, the phenomenon of reentrance of chiral symmetry broken and restored phases occurs for $T, \mu$ and $eB$ dependent $\hat{\kappa}$.