Chiral perturbation theory in a magnetic background - finite-temperature effects

TL;DR

This paper analyzes how a constant magnetic field affects chiral perturbation theory at finite temperature, revealing modifications in pion properties and suggesting an increased critical temperature for chiral symmetry restoration.

Contribution

It provides leading and next-to-leading order calculations of pion masses, decay constants, free energy, and quark condensate in a magnetic background, highlighting the magnetic field's impact on chiral transition temperature.

Findings

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

Pion decay constants and quark condensate decrease more slowly with temperature under magnetic field.

Critical temperature for chiral transition increases with magnetic field, aligning with some models but conflicting with recent lattice results.

Abstract

We consider chiral perturbation theory for SU(2) at finite temperature $T$ in a constant magnetic background $B$. We compute the thermal mass of the pions and the pion decay constant to leading order in chiral perturbation theory in the presence of the magnetic field. The magnetic field gives rise to a splitting between $M_{\pi^0}$ and $M_{\pi^{\pm}}$ as well as between $F_{\pi^0}$ and $F_{\pi^{\pm}}$. We also calculate the free energy and the quark condensate to next-to-leading order in chiral perturbation theory. Both the pion decay constants and the quark condensate are decreasing slower as a function of temperature as compared to the case with vanishing magnetic field. The latter result suggests that the critical temperature $T_c$ for the chiral transition is larger in the presence of a constant magnetic field. The increase of $T_c$ as a function of $B$ is in agreement with most model calculations but in disagreement with recent lattice calculations.