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

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 $$U_A(1)$$ symmetry. We incorporate thermomagnetic effects in the four-quark coupling by fitting lattice results for the average of u and d quark condensates close to the pseudocritical temperature. 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.