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

TL;DR

This paper analytically investigates 4d SU(2) gauge Higgs models, revealing phase transitions between Higgs and confined phases, and clarifying the role of Gribov copies in the gauge boson propagators.

Contribution

It provides an analytical semiclassical analysis of phase behavior in 4d SU(2) Higgs models, including effects of Gribov horizons, complementing lattice results.

Findings

Higgs phase with Yukawa propagators at small g and large v

Confined phase with Gribov-type propagators at large g or small v

Continuous transition between Higgs and confined regimes

Abstract

We present an analytical study of continuum 4d SU(2) gauge Higgs models with a single Higgs field with fixed length in either the fundamental or adjoint representation. We aim at analytically probing the renowned predictions of Fradkin & Shenker on the phase diagram in terms of confinement versus Higgs behaviour, obtained for the lattice version of the model. We work in the Landau version of the 't Hooft R_\xi gauges in which case we can access potential nonperturbative physics related to the existence of the Gribov copies. In the fundamental case, we clearly show that in the perturbative regime of small gauge coupling constant g and large Higgs vacuum expectation value v, there is a Higgs phase with Yukawa gauge boson propagators without Gribov effects. For a small value of the Higgs vev v and/or large g, we enter a region with Gribov type propagators that have no physical particle interpretation: the gauge bosons are as such confined. The transition between both behaviours is found to be continuous. In the adjoint case, we find evidence of a more drastic transition between the different behaviours for the propagator of the off-diagonal gauge bosons, whereas the "photon", i.e. the diagonal component of the gauge field, displays a propagator of the Gribov type. In the limit of infinite Higgs condensate, we show that a massless photon is recovered. We compare our findings with those of Fradkin & Shenker as well as with more recent numerical lattice simulations of the fundamental Higgs model. We also carefully discuss in which region of the parameter space (v,g) our approximations are trustworthy.