Low energy enhancement due to anomalous heavy fermions

We consider a renormalizable gauge-Higgs theory with chiral fermion content, in which gauge current anomalies are canceled between fermion multiplets with very different mass scales. We argue that this splitting of the anomaly cancelation can enchance certain low energy scattering amplitudes. In particular, we exhibit a logarithmic enhancement in the two-loop correction to the magnetic moment of massive neutrinos in a simplified SU(2)×U(1) version of the standard electroweak model. As an example of non-anomaly-related enhancements, we also exhibit a contribution to the anomalous magnetic moment of the W ${}_{}{}^{\pm }{}_{}{}^{}$.