A study of how the particle spectra of SU(N) gauge theories with a fundamental Higgs emerge

TL;DR

This paper analytically and numerically investigates the physical spectrum of SU(N) gauge theories with fundamental Higgs fields, revealing discrepancies with perturbative predictions and extending understanding beyond the standard model.

Contribution

It provides the first analytical determination of the physical spectrum in SU(N>2) gauge theories with fundamental Higgs fields and confirms findings with lattice simulations for N=3.

Findings

Discrepancies between perturbative and physical spectra.

Analytical spectrum determination for SU(N>2) gauge theories.

Lattice simulations confirm analytical results for N=3.

Abstract

In gauge theories, the physical, experimentally observable spectrum consists only of gauge-invariant states. In the standard model the Fr\"ohlich-Morchio-Strocchi mechanism shows that these states can be adequately mapped to the gauge-dependent elementary W, Z, Higgs, and fermions. In theories with a more general gauge group and Higgs sector, appearing in various extensions of the standard model, this has not to be the case. In this work we determine analytically the physical spectrum of $\mathrm{SU}(N>2)$ gauge theories with a Higgs field in the fundamental representation. We show that discrepancies between the spectrum predicted by perturbation theory and the observable physical spectrum arise. We confirm these analytic findings with lattice simulations for $N=3$.