Chiral Symmetry Breaking and Pion Decay in a Magnetic Field

TL;DR

This paper investigates how a uniform magnetic field affects chiral symmetry breaking and pion decay, providing model-independent low-energy theorems and comparing theoretical approaches with lattice QCD results.

Contribution

It derives model-independent low-energy theorems for pion matrix elements in magnetic fields and applies them to compute pion decay rates.

Findings

Results are consistent with chiral perturbation theory and lattice QCD, with some tension.

Provides low-energy theorems for QCD in magnetic fields.

Calculates pion decay rates in magnetic environments.

Abstract

The pattern of chiral symmetry breaking is exploited to compute vector and axial-vector pion matrix elements in a uniform magnetic field. Our results are model independent, and thereby constitute low-energy theorems that must be obeyed by QCD in external magnetic fields. Chiral perturbation theory and lattice QCD results are compared, for which there is some tension. As an application, the matrix elements are utilized to compute pion decay rates in a magnetic field.