Thermomagnetic effects on light pseudoscalar meson masses within the SU(3) Nambu-Jona-Lasinio model

We calculate the screening masses of pseudoscalar mesons in a hot and strongly magnetized medium within the framework of the SU(3) Nambu-Jona-Lasinio model, using a magnetic field-independent regularization scheme. Inverse magnetic catalysis (IMC) is implemented through the use of a magnetic field-dependent coupling GoBTHORN, fitted to reproduce lattice quantum chromodynamics (QCD) results for the pseudocritical chiral transition temperature T-c(B). For the external homogeneous magnetic field considered, neutral screening masses separate in two types: perpendicular and parallel to the direction of the field, while for charged mesons only parallel energies can be defined for each Landau level. We obtain m(scr,perpendicular to) > m(scr,||), as expected from causality. Thermally, all screening energies are almost constant until some critical temperature, whose behavior is correlated with T-c(B). They rapidly increase around this value, keeping a steady enhancement afterward due to thermal excitation. Magnetically, neutral parallel masses are enhanced (suppressed) at high temperatures when considering GoBTHORN (G). Perpendicular ones display a non-monotonic magnetic behavior for G (due to increasing T-c(B)) when T less than or similar to 500 MeV, but become magnetically enhanced when T greater than or similar to 500 MeV. For GoBTHORN they always increase with B. Charged parallel energies are always magnetically enhanced, for both couplings. In the high-temperature limit, we show that both neutral and charged screening energies converge to 2 pi T. At B 1/4 0 the model overestimates the remaining quark interaction in this regime. At B not equal 0 we find that, when IMC is accounted for, the interaction is suppressed as B increases, a fact that appears to be at odds with currently available lattice QCD results.