Thermal pions in a magnetic background

TL;DR

This paper uses chiral perturbation theory to analyze how a magnetic field affects the thermal properties of pions, including mass splitting, decay constants, and the chiral transition temperature.

Contribution

It provides the first systematic low-temperature calculation of pion properties and chiral transition temperature in a magnetic background using chiral perturbation theory.

Findings

Magnetic field causes mass and decay constant splitting between neutral and charged pions.

The critical temperature for chiral symmetry restoration increases with magnetic field.

Results align with model calculations but differ from recent lattice results.

Abstract

We use chiral perturbation theory for SU(2) to compute the leading corrections to the thermal mass of the pions and the pion decay constant in the presence of the magnetic field in a low-temperature expansion. The magnetic field gives rise to a splitting between $M_{\pi^0}$ and $M_{\pi^{\pm}}$ as well as $F_{\pi^0}$ and $F_{\pi^{\pm}}$. We also calculate the free energy and the quark condensate to next-to- leading order. The results suggest that the critical temperature $T_c$ for the chiral transition is larger in the presence of a constant magnetic field, in agreement with most model calculations but in disagreement with recent lattice calculations.