Gaussian effective potential for the standard model SU(2)xU(1) electroweak theory

TL;DR

This paper derives the Gaussian Effective Potential for the electroweak SU(2)xU(1) theory, demonstrating its gauge invariance and applicability as a non-perturbative tool consistent with experimental data, including predictions about the Higgs boson.

Contribution

It extends the GEP method to the full non-Abelian electroweak theory, establishing its gauge invariance and relevance for non-perturbative analysis of the standard model.

Findings

GEP is gauge invariant in the Abelian case

GEP remains a genuine variational tool in non-Abelian gauge theories

Predicts a light Higgs boson in the strong coupling regime

Abstract

The Gaussian Effective Potential (GEP) is derived for the non-Abelian SU(2)xU(1) gauge theory of electroweak interactions. First the problem of gauge invariance is addressed in the Abelian U(1) theory, where an optimized GEP is shown to be gauge invariant. The method is then extended to the full non-Abelian gauge theory where, at variance with naive derivations, the GEP is proven to be a genuine variational tool in any gauge. The role of ghosts is discussed and the unitarity gauge is shown to be the only choice which allows calculability without insertion of further approximations. The GEP for the standard model is derived and its predictions are compared to the known phenomenology, thus showing that the GEP provides an alternative non-perturbative description of the known experimental data. By a consistent renormalization of masses the full non-Abelian calculation confirms the existence of a light Higgs boson in the non-perturbative strong coupling regime of the Higgs sector.