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

Pascal Törek,René Sondenheimer,Axel Maas,M Della Morte,P Fritzsch,E Gámiz Sánchez,C Pena Ruano

doi:10.1051/epjconf/201817508002

Pascal Törek, René Sondenheimer + Show 5 more

Open Access

https://doi.org/10.1051/epjconf/201817508002

Copy DOI

Abstract

In gauge theories, the physical, experimentally observable spectrum consists only of gauge-invariant states. In the standard model the Fröhlich-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 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.

Highlights

The physical states of gauge theories are gauge invariant
We show that discrepancies between the spectrum predicted by perturbation theory and the observable physical spectrum arise
Using them as if they were physical in a perturbative description within a fixed gauge describes experimental results remarkably well [3]. This apparent contradiction is resolved by the Fröhlich-Morchio-Strocchi (FMS) mechanism [2, 4]: Under certain conditions, fulfilled by the standard model, the properties of the physical states can be mapped to the gauge-dependent states which appear in the Lagrangian

Summary

Introduction

The physical states of gauge theories are gauge invariant. In QCD confinement takes care of this, but in the electroweak sector of the standard model this is far more subtle [1, 2]: The W/ Z bosons, the Higgs, and the fermions, i.e. the elementary fields of the Lagrangian, are not gauge-invariant. Using them as if they were physical in a perturbative description within a fixed gauge describes experimental results remarkably well [3] This apparent contradiction is resolved by the Fröhlich-Morchio-Strocchi (FMS) mechanism [2, 4]: Under certain conditions, fulfilled by the standard model, the properties of the physical states can be mapped to the gauge-dependent states which appear in the Lagrangian. This mechanism has been confirmed in lattice computations for the bosonic sector [5, 6]. The theory has an additional global symmetry, a U(1) custodial symmetry acting only on the Higgs field

Gauge-variant description in a fixed gauge

Gauge-invariant spectrum

Conclusions