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

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.