Properties of neutral mesons in a hot and magnetized quark matter: size-dependent effects

TL;DR

This paper studies how finite size, temperature, chemical potential, and magnetic fields influence neutral mesons in hot quark matter using the NJL model, revealing complex interdependent effects on meson properties.

Contribution

It introduces a comprehensive analysis of combined finite-size and thermomagnetic effects on meson properties within the NJL model framework.

Findings

Meson masses and decay constants are significantly affected by size, temperature, and magnetic field.

The interplay of variables leads to non-trivial modifications of chiral symmetry restoration.

Observables depend on the balance of competing effects from different parameters.

Abstract

In this work we investigate the combined finite-size and thermomagnetic effects on the properties of neutral mesons in a hot medium, in the context of the Nambu--Jona-Lasinio model. In particular, by using the mean-field approximation and the Schwinger proper time method in a toroidal topology with antiperiodic conditions, we evaluate the chiral phase transition, the constituent quark mass and meson observables like the $\pi ^0$ and $\sigma$ meson masses and pion decay constant under the change of the size, temperature, chemical potential and strength of external magnetic field. The results indicate that the observables are strongly affected by the conjoint effects of relevant variables, and the net result will depend on the balance of these competing phenomena.