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We present an analytical study of continuum 4d SU(2) gauge Higgs models witha single Higgs field with fixed length in either the fundamental or adjointrepresentation. We aim at analytically probing the renowned predictions ofFradkin & Shenker on the phase diagram in terms of confinement versus Higgsbehaviour, obtained for the lattice version of the model. We work in the Landauversion of the 't Hooft R_\xi gauges in which case we can access potentialnonperturbative physics related to the existence of the Gribov copies. In thefundamental case, we clearly show that in the perturbative regime of smallgauge coupling constant g and large Higgs vacuum expectation value v, there isa Higgs phase with Yukawa gauge boson propagators without Gribov effects. For asmall value of the Higgs vev v and/or large g, we enter a region with Gribovtype propagators that have no physical particle interpretation: the gaugebosons are as such confined. The transition between both behaviours is found tobe continuous. In the adjoint case, we find evidence of a more drastictransition between the different behaviours for the propagator of theoff-diagonal gauge bosons, whereas the "photon", i.e. the diagonal component ofthe gauge field, displays a propagator of the Gribov type. In the limit ofinfinite Higgs condensate, we show that a massless photon is recovered. Wecompare our findings with those of Fradkin & Shenker as well as with morerecent numerical lattice simulations of the fundamental Higgs model. We alsocarefully discuss in which region of the parameter space (v,g) ourapproximations are trustworthy.

Semiclassical analysis of the phases of 4d SU(2) Higgs gauge systems with cutoff at the Gribov horizon