Even at weak coupling the physical, observable spectrum of gauge theories with a Brout-Englert-Higgs effect can deviate from the elementary one of perturbation theory. This can be analytically described and treated using the Fröhlich-Morchio-Strocchi mechanism. We confirm this by lattice simulation for an SU(3) gauge theory with a fundamental scalar, a toy model for grand unification. We also show that this has experimentally observable consequence, e.g., in scattering cross-sections of lepton collisions in this toy model.

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We discuss a variant of density of states (DoS) techniques for lattice field theories, the so-called "functional fit approach" (FFA). The DoS FFA is based on a density of states ρ(x) which is parameterized on small intervals of the argument x of ρ(x). On these intervals restricted Monte Carlo simulations with an additional Boltzmann factor exp(λ x) allow to determine ρ(x) very precisely by obtaining its parameters from fitting the Monte Carlo data to a known function of λ .We describe the method in detail and show its applicability in four different systems, three of which have a complex action problem: The SU(3) spin model with a chemical potential, U(1) lattice gauge theory, the Z 3 spin model with chemical potential, and 2-dimensional U(1) lattice gauge theory with a topological term. In all cases we compare to reference calculations, which partly were done in a dual formulation where the complex action problem is absent. In all four cases we find a very encouraging performance of the DoS FFA.