Axial-Current Divergences and the Reactionsγ+γ→Pions

A symmetry argument is presented that gives a relation between the small-momentum limits of the reactions $\gamma +\gamma \to$ 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 $\gamma +\gamma \to {\pi }^{+}+{\pi }^{-}+{\pi }^0$ is calculated in terms of the measured ${\pi }^0\to 2\gamma$ decay rate.