Neutral meson properties under an external magnetic field in nonlocal chiral quark models

TL;DR

This paper investigates how neutral meson properties, such as masses and decay constants, change under an external magnetic field using nonlocal chiral quark models, with results aligning well with lattice QCD data.

Contribution

It introduces Ritus transforms in nonlocal chiral quark models to analytically compute meson properties under magnetic fields, extending previous models.

Findings

π^0 mass behavior agrees with lattice QCD

Chiral relations remain valid under magnetic fields

Analytical expressions for meson observables derived

Abstract

We study the behavior of neutral meson properties in the presence of a static uniform external magnetic field in the context of nonlocal chiral quark models. The formalism is worked out introducing Ritus transforms of Dirac fields, which allow to obtain closed analytical expressions for $\pi^0$ and $\sigma$ meson masses and for the $\pi^0$ decay constant. Numerical results for these observables are quoted for various parameterizations. In particular, the behavior of the $\pi^0$ meson mass with the magnetic field is found to be in good agreement with lattice QCD results. It is also seen that the Goldberger-Treiman and Gell-Mann-Oakes-Renner chiral relations remain valid within these models in the presence of the external magnetic field.