Properties of magnetized neutral mesons within a full RPA evaluation

TL;DR

This paper uses a full RPA approach within the NJL model to accurately evaluate meson properties in a magnetic field, aligning well with lattice and chiral perturbation theory results.

Contribution

It introduces a fully momentum-dependent RPA calculation for meson properties under magnetic fields, improving accuracy over previous approximations.

Findings

Results agree with lattice simulations.

Results align with chiral perturbation theory.

Method enhances evaluation of mesonic contributions in magnetized matter.

Abstract

We consider the two flavor Nambu--Jona-Lasinio model within the RPA framework to evaluate the masses of the $\sigma$ and $\pi^0$ mesons and the $\pi^0$ decay constant in the presence of a magnetic field at vanishing temperatures and baryonic densities. The present work extends other RPA applications by fully considering the external momenta, which enter the integrals representing the magnetized polarization tensor, so that more accurate results can be obtained in the evaluation of physical quantities containing pionic contributions. As we show, this technical improvement generates results which agree well with those produced by lattice simulations and chiral perturbation theory. Our method may also prove to be useful in future evaluations of quantities such as the shear viscosity and the equation of state of magnetized quark matter with mesonic contributions.