The observable spectrum for GUT-like theories

TL;DR

This paper investigates the spectrum of GUT-like theories, revealing discrepancies between perturbative and non-perturbative predictions, using lattice simulations of a toy model to uncover complex features.

Contribution

It provides the first lattice-based analysis of the observable spectrum in a GUT-like theory, highlighting qualitative differences from perturbative expectations.

Findings

Rich spectrum with previously unseen features

Discrepancies between perturbative and non-perturbative spectra

Lattice simulations confirm qualitative differences

Abstract

The spectrum of nonabelian gauge theories cannot be described in terms of elementary particles, and so must be constructed from gauge-invariant composite operators, even in the presence of a Brout--Englert--Higgs effect. This leads to qualitative discrepancies in the prediction of the spectrum between perturbation theory and a full non-perturbative treatment in many theories. This is especially noticeable for GUTs. We present results corroborating this general statement using lattice simulations for a ''GUT-like'' toy theory, $\mathrm{SU}(3)$ Yang--Mills theory coupled to a Higgs field in the fundamental representation. Despite the apparent simplicity of the model, we find a rich spectrum with some previously unseen features. We also outline the next steps required to generate a large operator basis to extend this investigation to more realistic GUTs.