SU(2) x U(1) Yang-Mills theories in 3d with Higgs field and Gribov ambiguity

TL;DR

This paper investigates the gauge propagator structures in a 3d SU(2) x U(1) Yang-Mills-Higgs model, incorporating nonperturbative effects and Gribov ambiguities, revealing different regimes depending on coupling constants and Higgs vev.

Contribution

It introduces a nonperturbative analysis of gauge propagators in 3d electroweak models considering Gribov ambiguities, extending understanding beyond standard perturbative results.

Findings

Standard Z and W propagators are recovered at small g and large nu.

Different propagator structures emerge depending on g, g', and nu.

Results set the stage for future phase diagram studies.

Abstract

We study the structure of the gauge propagators of a 3d version of the electroweak interaction in terms of the Higgs vacuum expectation value nu, of the non-Abelian gauge coupling g, and of the Abelian gauge coupling g', when nonperturbative effects related to the non-Abelian gauge fixing are introduced by means of an adapted path integral measure. In the perturbative regime of small non-Abelian coupling g and sufficiently large nu, the well-known standard Z and W propagators are recovered, together with a massless photon. In general, depending on the relative magnitudes of g, g' and nu, we uncover a quite different propagator structure. In a later stage of research, the results here derived can be used to study the associated phase diagram in more depth.