Multiple breaking patterns in the Brout-Englert-Higgs effect beyond perturbation theory

TL;DR

This paper investigates multiple symmetry-breaking patterns in gauge theories beyond perturbation theory, revealing that only one pattern persists under certain conditions through a gauge-invariant lattice approach.

Contribution

It introduces a gauge-invariant lattice framework to analyze multiple breaking patterns in an SU(3) gauge theory with an adjoint scalar, showing that only one pattern is physically realized.

Findings

Only one symmetry-breaking pattern remains at fixed parameters.

The quantum effective potential results from complex interplay of various factors.

Gauge-invariant methods are essential for understanding non-perturbative symmetry breaking.

Abstract

In many BSM theories, especially GUTs, introducing a Brout-Englert-Higgs effect allows for multiple breaking patterns of the gauge symmetry. The possibility to select a particular pattern is usually decisive for the phenomenological viability of a theory. Beyond perturbation theory it is necessary to replace the Brout-Englert-Higgs effect by a manifestly gauge-invariant description. We study the simplest case with multiple breaking patterns, an $\textrm{SU}(3)$ Yang-Mills theory coupled to a single scalar `Higgs' field in the adjoint representation, on the lattice. We find that only one pattern remains at fixed parameters and gauge-fixing strategy, and that the associated quantum effective potential emerges from a non-trivial interplay of many aspects.