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

TL;DR

This study calculates pseudoscalar meson screening masses in a hot, magnetized medium using the SU(3) Nambu-Jona-Lasinio model, revealing magnetic and thermal effects and comparing with lattice QCD results.

Contribution

It introduces a magnetic field-dependent coupling in the NJL model to incorporate inverse magnetic catalysis effects on meson masses under strong magnetic fields.

Findings

Neutral screening masses split into perpendicular and parallel components.

Masses increase rapidly around the critical temperature, then stabilize.

Magnetic field enhances neutral and charged meson energies at high temperatures.

Abstract

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 $G(B)$, 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 $m_{\mathrm{scr},\perp} > m_{\mathrm{scr},\parallel}$, 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 $G(B)$ ($G$). Perpendicular ones display a non-monotonic magnetic behavior for $G$ (due to increasing $T_c^B$) when $T \lesssim 500$~MeV, but become magnetically enhanced when $T \gtrsim 500$~MeV. For $G(B)$ 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 $B=0$ the model overestimates the remaining quark interaction in this regime. At $B\neq 0$ 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.