  In gauge theories, the physical, experimentally observable spectrum consists
only of gauge-invariant states. In the standard model the
Fr\"ohlich-Morchio-Strocchi mechanism shows that these states can be adequately
mapped to the gauge-dependent elementary W, Z, Higgs, and fermions. In theories
with a more general gauge group and Higgs sector, appearing in various
extensions of the standard model, this has not to be the case. In this work we
determine analytically the physical spectrum of $\mathrm{SU}(N>2)$ gauge
theories with a Higgs field in the fundamental representation. We show that
discrepancies between the spectrum predicted by perturbation theory and the
observable physical spectrum arise. We confirm these analytic findings with
lattice simulations for $N=3$.
