  Unitarity, a powerful constraint on new physics, has not always been properly
accounted for in the context of hidden sectors. Feng, Rajaraman and Tu have
suggested that large (pb to nb) multi-photon or multi-lepton sugnals could be
generated at the LHC through the three-point functions of a
conformally-invariant hidden sector (an "unparticle" sector.) Because of the
conformal invariance, the kinematic distributions are calculable. However, the
cross-sections for many such processes grow rapidly with energy, and at some
high scale, to preserve unitarity, conformal invariance must break down.
Requiring that conformal invariance not be broken, and that no signals be
already observed at the Tevatron, we obtain a strong unitarity bound on
multi-photon events at the (10 TeV) LHC. For the model of Feng et al., even
with extremely conservative assumptions, cross-sections must be below 25 fb,
and for operator dimension near 2, well below 1 fb. In more general models,
four-photon signals could still reach cross-sections of a few pb, though bounds
below 200 fb are more typical. Our methods apply to a wide variety of other
processes and settings.
