Nambu--Jona-Lasinio $SU(3)$ model constrained by lattice QCD: thermomagnetic effects in the magnetization

TL;DR

This paper employs a three-flavor Nambu--Jona-Lasinio model with thermomagnetic effects to study strange quark matter under strong magnetic fields, successfully reproducing lattice QCD results on magnetization and magnetic catalysis phenomena.

Contribution

It introduces a flavor SU(3) NJL model with thermomagnetic effects and a novel vacuum magnetic regularization scheme to accurately match lattice QCD magnetization data.

Findings

Reproduces lattice QCD results for magnetization.

Predicts magnetic catalysis and inverse magnetic catalysis.

Shows quark matter is paramagnetic.

Abstract

We use a three-flavor Nambu--Jona-Lasinio model to study the thermodynamics of strange quark matter under a strong magnetic field. The model Lagrangian features flavor SU(3) four-quark interactions and six-quark interactions that break the UA(1) symmetry. We incorporate thermomagnetic effects in the four-quark coupling. The model predicts magnetic catalysis at low temperatures and inverse magnetic catalysis at temperatures close to the pseudocritical temperature of the QCD transition, in agreement with lattice QCD results. We compute the pressure at the mean field level and obtain the magnetization of quark matter. We adopt the recently proposed vacuum magnetic regularization (VMR) scheme, in that divergent quark mass independent contributions are not subtracted, thereby avoiding unphysical results for the magnetization. We devote special attention to the renormalized magnetization, a projected quantity that allows for direct comparisons with lattice QCD simulations. Our results are in very good agreement with lattice data indicating a paramagnetic behavior for quark matter.