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It is well accepted that dealing with the Gribov ambiguity has a major impacton correlation functions in gauge-fixed Yang-Mills theories, in particular inthe low momentum regime where standard perturbation theory based on theFaddeev-Popov approach fails. Recent results, derived from functional tools(Dyson-Schwinger equations or exact RG) or the effective Gribov-Zwanzigeraction method, pointed towards e.g. gauge boson correlation functions that arenot compatible with the properties of observable degrees of freedom. Althoughsuch an observation is a welcome feature for gauge theories exhibitingconfinement, it would be a discomfort for gauge theories supplemented withHiggs fields, cfr. the experimental success of the electroweak model based on aSU(2) x U(1) gauge group. The purpose of this short note is to assure that theeffective action resolution to the Gribov ambiguity reduces to the standardFaddeev-Popov method in the perturbative regime of sufficiently smallcoupling/large Higgs condensate, thereby not compromising the physical particlespectrum 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 Higgscondensate, the more the Gribov problem resurfaces with all its consequences.We give some speculations w.r.t. the Fradkin-Shenker insights about the phasediagram.

The (IR-)relevance of the Gribov ambiguity in SU(2) x U(1) gauge theories with fundamental Higgs matter