Chiral symmetry breaking and pion decay in a magnetic field

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, lattice QCD, and Nambu–Jona-Lasinio results are compared. While there is some tension between chiral perturbation theory and lattice QCD, the tension between low-energy QCD and the Nambu–Jona-Lasinio model is more acute. As an application, the matrix elements are utilized to compute pion decay rates in a magnetic field.