The gravitational correction to PCAC

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