Exploring $U_A(1)$ symmetry restoration in a magnetic field by meson screening masses in the NJL model

Abstract

We investigate the effective axial $U_A(1)$ symmetry restoration at finite temperature in an external magnetic field using meson screening masses, as well as meson susceptibilities, in a $(2+1)$-flavor Nambu-Jona-Lasinio (NJL) model. To incorporate inverse magnetic catalysis, we employ a magnetic-field-dependent four-quark coupling constrained by the lattice QCD chiral pseudo-critical temperature, with the 't Hooft coupling fixed. In the lattice-improved NJL model, the longitudinal screening mass difference between the $U_A(1)$ partners $δ^0$ and $π^0$ and their normalized meson susceptibility difference exhibit axial magnetic catalysis at low temperatures and axial inverse magnetic catalysis near the chiral crossover, whereas the transverse screening mass difference increases with $eB$ at all temperatures. Despite these different responses, the axial pseudo-critical temperatures extracted from the thermal inflection points of these three alternative order parameters decrease with $eB$, implying that a decreasing pseudo-critical temperature can coexist with an increasing transverse screening mass difference at fixed temperature.