Chiral Perturbation Theory Analysis of the Quark Condensate in a Magnetic Field

TL;DR

This paper uses two-loop chiral perturbation theory to analyze how an external magnetic field affects the quark condensate at finite and zero temperature, providing detailed theoretical results.

Contribution

It offers the first complete two-loop calculations of the quark condensate in a magnetic field, including finite temperature effects and weak field expansions.

Findings

Derived two-loop results for the quark condensate in magnetic fields.

Analyzed the impact of magnetic fields on pion interactions at finite temperature.

Provided the complete vacuum energy density and condensate at zero temperature.

Abstract

We present two-loop results for the quark condensate in an external magnetic field within chiral perturbation theory using coordinate space techniques. At finite temperature, we explore the impact of the magnetic field on the pion-pion interaction in the quark condensate for arbitrary pion masses and derive the correct weak magnetic field expansion in the chiral limit. At zero temperature, we provide the complete two-loop representation for the vacuum energy density and the quark condensate.