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 Fröhlich-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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