The VVA correlator at three loops in perturbative QCD

TL;DR

This paper investigates the three-loop QCD corrections to the VVA correlator, revealing that contrary to previous beliefs, these corrections do not vanish and are related to the QCD beta-function, challenging earlier non-renormalization assumptions.

Contribution

The study provides the first explicit three-loop calculation of the VVA correlator, demonstrating that its non-renormalization does not extend beyond two loops in perturbative QCD.

Findings

Three-loop corrections are non-zero and proportional to the QCD beta-function.

The non-renormalization of the VVA correlator is not valid at three loops.

The results challenge previous assumptions about the all-order non-renormalization of the correlator.

Abstract

It is known that the correlator of one axial and two vector currents, that receives leading contributions through one-loop fermion triangle diagrams, is not modified by QCD radiative corrections at two loops. It was suggested that this non-renormalization of the VVA correlator persists in higher orders in perturbative QCD as well. To check this assertion, we compute the three-loop QCD corrections to the VAA-correlator u sing the technique of asymptotic expansions. We find that these corrections do not vanish and that they are proportional to the QCD beta-function.