The gravitational correction to PCAC

Abstract

A simple-minded perturbation calculation to order G (the Newtonian gravitational constant) of the two-graviton coupling to a pseudoscalar ( P) or axial ( A) current via a fermion loop gives an anomalous contribution which can be added to the Adler term in the form ∂ α A α = 2 m P + e 2 ϵ kλμv F kλ F μv /16 Π 2 + ϵ kλμv R kλϱσ R μvϱσ /768 Π 2. The anomalous terms can be interpreted as arising from an infinite-mass regulating loop.