The gravitational correction to PCAC

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 ∂_αA_α = 2mP + e²ϵ_kλμvF_kλF_μv/16Π² + ϵ_kλμvR_kλϱσR_μvϱσ/768Π². The anomalous terms can be interpreted as arising from an infinite-mass regulating loop.