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

We consider a spontaneously broken abelian gauge theory with a scalar-fermion coupling non-linear in the Higgs field, which reduces to a Yukawa term in the unitary gauge. We examine in this gauge the one-loop divergences in a physical process and we find they are not all of the renormalizable type. Comparison is made with the linear coupling theory, where cancellation of the non-renormalizable divergences occurs. Some years ago it was proposed [1] a class of pure left SU(N)⊗U(1) gauge theories with spontaneously broken symmetry, capable of accommodating the Weinberg-Salam model as well as some of its generalizations up to the Higgs sector. They exhibit the unfamiliar feature of using a non-linear scalarfermion coupling in the Higgs fields, which, however, reduces to a Yukawa term in the unitary gauge. It is natural to ask whether such a construction See discussions in Ref. [1].