  A perturbatively renormalized Abelian Higgs-Kibble model with a chirally
coupled fermion is considered. The Slavnov identity is fulfilled to all orders
of perturbation theory, which is crucial for renormalizability in models with
vector bosons. BRS invariance, i.e. the validity of the identity, forces the
chiral anomaly to be cancelled by Wess-Zumino counterterms. This procedure
preserves the renormalizability in the one-loop approximation but it violates
the Froissart bounds for partial wave amplitudes above some energy and destroys
renormalizability from the second order in h bar onwards due to the
counterterms. (The paper has 3 figs. in postscript which are not included; send
request to the author's e-mailbox with subject: figures . The author is willing
to mail hard copies of the paper.)
