  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.
