Axial-Current Divergences and the Reactionsγ+γ→Pions

Abstract

A symmetry argument is presented that gives a relation between the small-momentum limits of the reactions $\ensuremath{\gamma}+\ensuremath{\gamma}\ensuremath{\rightarrow}$ odd number of pions, as calculated explicitly from a single nucleon (or quark) loop in a theory with a formally conserved axial-vector current. These limits are nonvanishing as a consequence of the Adler anomalies in the divergence of the axial-vector current. It is argued that the relationship derived should be true in any chiral model. The cross section for $\ensuremath{\gamma}+\ensuremath{\gamma}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}+{\ensuremath{\pi}}^{\ensuremath{-}}+{\ensuremath{\pi}}^{0}$ is calculated in terms of the measured ${\ensuremath{\pi}}^{0}\ensuremath{\rightarrow}2\ensuremath{\gamma}$ decay rate.