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.