Predicting the singlet vector channel in a partially Higgsed gauge theory

TL;DR

This paper investigates the singlet vector channel in a lattice SU(3) gauge theory with a fundamental Higgs, revealing a massive ground state contrary to perturbative predictions, and combines perturbation theory with the FMS mechanism to predict the spectrum.

Contribution

It introduces a non-perturbative analysis of the singlet vector channel in a partially Higgsed SU(3) gauge theory, integrating perturbation theory with the FMS mechanism.

Findings

Identifies a massive, non-degenerate ground state in the singlet vector channel.

Contradicts perturbative predictions of massless and massive states.

Shows gauge boson correlation functions are weakly coupled and tree-level-like.

Abstract

We study a toy version of a grand-unified theory on the lattice: An $SU(3)$ gauge theory, which experiences a Brout-Englert-Higgs effect due to a single Higgs field in the fundamental representation. This yields a perturbative breaking pattern $SU(3) \rightarrow SU(2)$. We investigate the singlet vector channel, finding an apparently non-degenerate and massive ground state. This is in contradistinction to the perturbative prediction of three massless and five massive vector states, even though the correlation functions of the gauge bosons exhibit a weak-coupling behavior, being almost tree-level-like. However, a combination of perturbation theory with the Fr\"ohlich-Morchio-Strocchi mechanism allows to predict the physical spectrum in this channel.