Non-renormalization of the full <VVA> correlator at two-loop order

TL;DR

This paper demonstrates through explicit two-loop QCD calculations that the <VVA> correlator remains unrenormalized beyond one loop, confirming its one-loop exactness in the massless fermion limit within the MS-bar scheme.

Contribution

The authors explicitly compute two-loop corrections to the <VVA> correlator and show they vanish, establishing its non-renormalization at this order and confirming the one-loop exactness.

Findings

Two-loop corrections to <VVA> correlator are absent.

The correlator's form is proportional to the one-loop result.

A missing amplitude at one-loop also does not appear at two-loop.

Abstract

By explicit calculation of the two-loop QCD corrections we show that for singlet axial and vector currents the full off-shell <VVA> correlation function in the limit of massless fermions is proportional to the one-loop result, when calculated in the MS-bar scheme. By the same finite renormalization which is needed to make the one-loop anomaly exact to all orders, we arrive at the conclusion that two-loop corrections are absent altogether, for the complete correlator not only its anomalous part. In accordance with the one-loop nature of the <VVA> correlator, one possible amplitude, which seems to be missing by accident at the one-loop level, also does not show up at the two-loop level.