Neutral pion mass in warm magnetized medium within Linear Sigma Model coupled to Quarks $\left(\text{LSM}_q\right)$ framework

TL;DR

This paper investigates how the neutral pion mass varies with magnetic field strength and temperature using the Linear Sigma Model coupled to Quarks, revealing a decrease in mass with magnetic field and an increase with temperature.

Contribution

It provides a detailed calculation of neutral pion mass in a magnetic field at finite temperature within the LSMq framework, including meson self-coupling effects.

Findings

Pion mass decreases as magnetic field increases.

Pion mass increases with rising temperature.

The study offers insights into meson behavior in magnetized hot media.

Abstract

We study the neutral pion mass in the presence of an external arbitrary magnetic field in the framework of the linear sigma model coupled to quark (LSMq) at finite temperature. In doing so, we have calculated the pion self-energy, constructed the dispersion equation via re-summation, and solved the dispersion relation at zero three momentum limit. In calculating the pion mass, we have included meson self-coupling's thermal and magnetic contribution and approximate chiral order parameter $v_0$. We report that the $\pi^0$ mass decreases with the magnetic field and increases with temperature.