Low-Energy Theorem forγ→3π

Abstract

A low-energy theorem relating $\gamma \to 3\pi$ to ${\pi }^0\to 2\gamma$ is derived by using anomalous Ward identities and by using Schwinger's proper-time technique. We discuss the theoretical significance of this low-energy theorem. In particular, the theorem is meaningful only if the partially conserved axial-vector current anomaly is in fact responsible for the decay ${\pi }^0\to 2\gamma$.