  It is well accepted that dealing with the Gribov ambiguity has a major impact
on correlation functions in gauge-fixed Yang-Mills theories, in particular in
the low momentum regime where standard perturbation theory based on the
Faddeev-Popov approach fails. Recent results, derived from functional tools
(Dyson-Schwinger equations or exact RG) or the effective Gribov-Zwanziger
action method, pointed towards e.g. gauge boson correlation functions that are
not compatible with the properties of observable degrees of freedom. Although
such an observation is a welcome feature for gauge theories exhibiting
confinement, it would be a discomfort for gauge theories supplemented with
Higgs fields, cfr. the experimental success of the electroweak model based on a
SU(2) x U(1) gauge group. The purpose of this short note is to assure that the
effective action resolution to the Gribov ambiguity reduces to the standard
Faddeev-Popov method in the perturbative regime of sufficiently small
coupling/large Higgs condensate, thereby not compromising the physical particle
spectrum of massive gauge bosons and a massless photon for the SU(2) x U(1)
gauge-Higgs model. The closer the theory gets to the limit of vanishing Higgs
condensate, the more the Gribov problem resurfaces with all its consequences.
We give some speculations w.r.t. the Fradkin-Shenker insights about the phase
diagram.
