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

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.

24 pages, 14 figures, 8 tables, font errors fixed

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• Gauge-invariant description of the Higgs resonance and its phenomenological implications
• The Higgs phase as a spin glass, and the transition between varieties of confinement
• Analytical relations for the bound state spectrum of gauge theories with a Brout-Englert-Higgs mechanism
• Dark Matter from self-dual gauge/Higgs dynamics
• Exploratory study of the off-shell properties of the weak vector bosons
• Excitations of elementary fermions in gauge Higgs theories
• Scheme dependence of asymptotically free solutions
• Gauge Invariant Description of the $SU(2)$ Higgs model: Ward identities and Renormalization
• A composite massless vector boson
• Constraining the Higgs valence contribution in the proton
• Testing the mechanism of lepton compositness
• Multiple breaking patterns in the Brout-Englert-Higgs effect beyond perturbation theory
• Exploring SU(3)-Higgs theories
• The Fröhlich-Morchio-Strocchi mechanism: A underestimated legacy
• The manifestly gauge-invariant spectrum of the Minimal Supersymmetric Standard Model