Analytical relations for the bound state spectrum of gauge theories with a Brout-Englert-Higgs mechanism

TL;DR

This paper uses the Fr"ohlich-Morchio-Strocchi method to analyze the bound state spectrum in gauge theories with a Higgs mechanism, providing a gauge-invariant framework and new constraints for beyond-standard-model theories.

Contribution

It applies a gauge-invariant approach to bound states in Higgsed gauge theories, offering insights into their spectrum and implications for grand unified theories.

Findings

Relates gauge-invariant bound states to unbroken gauge group objects

Provides a gauge-invariant formulation without spontaneous symmetry breaking terminology

Suggests new constraints on theories beyond the standard model

Abstract

We apply the method proposed by Fr\"ohlich, Morchio, and Strocchi to analyze the bound state spectrum of various gauge theories with a Brout-Englert-Higgs mechanism. These serve as building blocks for theories beyond the standard model but also stress the exceptional role of the standard model weak group. We will show how the Fr\"ohlich-Morchio-Strocchi mechanism relates gauge-invariant bound state operators to invariant objects of the remaining unbroken gauge group after gauge fixing. In particular, this provides a strict gauge-invariant formulation of the latter in terms of the original gauge symmetry without using the terminology of spontaneous gauge symmetry breaking. We also demonstrate that the Fr\"ohlich-Morchio-Strocchi approach allows us to put new constraints on theories beyond the standard model by pure field-theoretical considerations. Particularly the conventional construction of grand unified theories has to be rethought.