TL;DR
This paper discusses how in Higgsed gauge theories, the Fröhlich-Morchio-Strocchi mechanism ensures gauge-invariant composite operators share the same masses as elementary particles, supported by lattice gauge theory results.
Contribution
It highlights the role of the Fröhlich-Morchio-Strocchi mechanism in relating composite operators to elementary particles in Higgsed theories, with lattice evidence for the standard-model Higgs sector.
Findings
Lattice gauge theory supports the mechanism in the SU(2) Higgs sector.
Composite operators have the same masses as elementary particles.
Preliminary results extend to 2-Higgs-doublet-model.
Abstract
In gauge theories, observable quantities have to be gauge-invariant. In general, this requires composite operators, which usually have substantially different properties, e.g. masses, than the elementary particles. Theories with a Higgs field, in which the Brout-Englert-Higgs effect is active, provide an interesting exception to this rule. Due to an intricate mechanism, the Fr\"ohlich-Morchio-Strocchi mechanism, the masses of the composite operators with the same quantum numbers, but modified internal quantum numbers, have the same masses. This mechanism is supported using lattice gauge theory for the standard-model Higgs sector, i.e. Yang-Mills-Higgs theory with gauge group SU(2) and custodial symmetry group SU(2). Furthermore, the extension to the 2-Higgs-doublet-model is briefly discussed, and some preliminary results are presented.
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