  Past lattice simulations tentatively suggested that the spectrum of
observable particles in BSM theories is qualitatively different than
perturbatively expected. The discrepancy can be traced back to nontrivial
field-theoretical effects arising from the requirement of gauge invariance. A
perturbative but gauge-invariant approach working directly with bound states
(as proposed by Fr\"ohlich, Morchio and Strocchi) could provide a solution, by
allowing composite-state effects to be treated within a perturbative framework.
We consider a toy GUT-like theory -- SU(3) Yang-Mills coupled to a scalar
`Higgs' in the fundamental representation -- and expand on previous work by
providing the most comprehensive spectroscopy to date, including all channels
up to spin 2. Our results strongly support the general conclusion that the
elementary spectrum is not an adequate proxy for the low-energy spectrum of a
GUT, and also suggest a possible analytical approach to BSM model-building via
the Fr\"ohlich-Morchio-Strocchi approach.
