Nonperturbative Evaluation of the Anomalies in Low-Energy Theorems

Abstract

It is shown that the anomalous constant $S$ associated with the soft ${\pi }^0\to 2\gamma$ decay amplitude is determined by a product of high-energy electroproduction and annihilation cross sections. A similar result holds for the coupling of the trace of the stress-energy tensor to photons. Wilson's theory of broken scale invariance is assumed. We observe that the Fritzsch-Gell-Mann algebra of bilocal operators uniquely specifies disconnected contributions, and, in particular, implies $S=\frac{1}{6}$, the quark field-theoretic value.