Charged pseudoscalar and vector meson masses under strong magnetic fields in an extended NJL model

TL;DR

This paper investigates the effects of strong magnetic fields on charged meson masses using an extended NJL model, incorporating Schwinger phases and meson field expansions, and compares results with lattice QCD data.

Contribution

It introduces an improved NJL model calculation that accounts for Schwinger phases and meson field expansions in magnetic fields, providing more accurate meson mass spectra.

Findings

ρ+ meson spectrum disfavors magnetic-field-induced condensate

π+ and ρ+ meson masses are computed under magnetic fields

Model predictions align with lattice QCD results

Abstract

The mass spectrum of $\pi^+$ and $\rho^+$ mesons in the presence of a static uniform magnetic field $\vec B$ is studied within a two-flavor NJL-like model. We improve previous calculations taking into account the effect of Schwinger phases carried by quark propagators, and using an expansion of meson fields in terms of the solutions of the corresponding equations of motion for nonzero $B$. It is shown that the meson polarization functions are diagonal in this basis. Our numerical results for the $\rho^+$ meson spectrum are found to disfavor the existence of a meson condensate induced by the magnetic field. In the case of the $\pi^+$ meson, $\pi$ - $\rho$ mixing effects are analyzed for the meson lowest energy state. The predictions of the model are compared with available lattice QCD results.