Neutral pion mass in the linear sigma model coupled to quarks at arbitrary magnetic field

TL;DR

This study investigates how an external magnetic field influences the neutral pion mass within the linear sigma model coupled to quarks, revealing nonmonotonic behavior and aligning with weak-field results.

Contribution

It extends the linear sigma model to arbitrary magnetic fields, providing new insights into pion mass behavior beyond weak-field approximations.

Findings

Neutral pion mass exhibits nonmonotonic dependence on magnetic field strength.

Results agree with existing weak-field approximations.

Provides a framework for studying meson properties in strong magnetic fields.

Abstract

We calculate the neutral pion mass in the presence of an external magnetic field of arbitrary strength in the framework of the linear sigma model coupled to quarks at zero temperature. We find nonmonotonic behavior of the pion mass as a function of magnetic field. We are also able to reproduce existing results for the weak-field approximation.