Chiral Symmetry Breaking and Pion Decay in a Magnetic Field

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, 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.

Comments: 16 pages, 7 figures, improved manuscript: contains further comparisons with lattice QCD and the Nambu-Jona-Lasinio model