Non-renormalization of the full 〈VVA〉 correlator at two–loop order

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 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.