The spectrum of an SU(3) gauge theory with a fundamental Higgs field

TL;DR

This paper investigates the physical spectrum of an SU(3) gauge theory with a fundamental Higgs, revealing differences from elementary and perturbative predictions, and demonstrates the effectiveness of a gauge-invariant analytic approach.

Contribution

It provides the first lattice gauge theory determination of the spectrum in this model and validates the Froehlich-Morchio-Strocchi mechanism as a reliable analytic method.

Findings

The physical spectrum differs from elementary and perturbative predictions.

The gauge-invariant approach accurately reproduces the spectrum.

Leading-order analytic calculations match lattice results reasonably well.

Abstract

In gauge theories, the physical, experimentally observable spectrum consists only of gauge-invariant states. This spectrum can be different from the elementary spectrum even at weak coupling and in the presence of the Brout-Englert-Higgs effect. We demonstrate this for an SU(3) gauge theory with a single fundamental Higgs, a toy theory for grand-unified theories. The manifestly gauge-invariant approach of lattice gauge theory is used to determine the spectrum in four different channels. It is found to be qualitatively different from the elementary one, and especially from the one predicted by standard perturbation theory. The result can be understood in terms of the Froehlich-Morchio-Strocchi mechanism. In fact, we find that analytic methods based on this mechanism, a gauge-invariant extension of perturbation theory, correctly determines the spectrum, and gives already at leading order a reasonably good quantitative description. Together with previous results this supports that this approach is the analytic method of choice for theories with a Brout-Englert-Higgs effect.