On the cancellation of hard anomalies in gauge field models: a regularization independent proof

In this paper we prove Bardeen's conjecture that the anomaly of the Adler-Bardeen-Bell-Jackiw-Schwinger type in gauge models are definitely absent if they are cancelled at the first order of the perturbation expansion. Our analysis develops within the regularization independent B.P.H.Z. renormalization scheme. We discuss the possible appearance of anomalies in an enlarged class of gauge models admitting soft violations of the Slavnov-Taylor identities which prescribe the gauge transformation properties of the Green functions. By a repeated use of the Callan-Symanzik equation we conclude that the lowest non vanishing contributions to the anomalies must necessarily correspond to the first order in the perturbation expansion, hence if they are cancelled at this order the theory will be definitely anomaly free.