Non-renormalizability of a SSB gauge theory induced by a non-linear fermion-Higgs coupling of canonical dimension 4

TL;DR

This paper demonstrates that an abelian gauge theory with a non-linear fermion-Higgs coupling of canonical dimension 4 is non-renormalizable at one loop, contrasting it with the renormalizable case of a conventional coupling.

Contribution

It reveals the non-renormalizability of a specific SSB gauge theory with non-linear Higgs coupling, despite its apparent renormalizability in the unitary gauge.

Findings

One-loop divergences indicate non-renormalizability.

Comparison shows conventional coupling leads to divergence cancellation.

Non-linear coupling prevents divergence cancellation.

Abstract

We consider an abelian gauge theory with spontaneously broken symmetry containing a scalar-fermion coupling which is non-linear in the Higgs field. Although in the unitary gauge it reduces to a pure Yukawa term, suggesting that the theory is renormalizable, the one loop divergence structure in this gauge in the fermion-fermion elastic scattering amplitude shows this is not so. Comparison is made with the theory with a conventional coupling, for which cancellation of the non-renormalizable divergences occurs.