Cancellation of the Chiral Anomaly in a Model with Spontaneous Symmetry Breaking

TL;DR

This paper investigates how the chiral anomaly can be canceled in a spontaneously broken Abelian Higgs-Kibble model, highlighting issues with renormalizability and unitarity at higher orders due to counterterm procedures.

Contribution

It demonstrates the cancellation of the chiral anomaly via Wess-Zumino counterterms in a spontaneously broken gauge model and discusses the resulting renormalizability challenges.

Findings

Anomaly cancellation preserves one-loop renormalizability.

Counterterms violate Froissart bounds at higher orders.

Renormalizability is compromised beyond one-loop due to anomaly cancellation methods.

Abstract

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.)