Narrow trans-TeV Higgs bosons and H → hh decays:: two LHC search paths for a hidden sector Higgs boson

We consider the addition of a condensing singlet scalar field to the Standard Model. Such a scenario may be motivated by any number of theoretical ideas, including the common result in string-inspired model building of singlet scalar fields charged under some hidden sector gauge symmetry. For concreteness, we specify an example model of this type, and consider the relevant constraints on Higgs physics, such as triviality, perturbative unitarity and precision electroweak analysis. We then show that there are two unique features of the phenomenology that present opportunities for discovery at the Large Hadron Collider (LHC). First, it is possible to identify and discover a narrow trans-TeV Higgs boson in this scenario-a mass scale that is well above the scale at which it is meaningful to discuss a SM Higgs boson. Second, the decays of the heavier scalar state into the lighter Higgs bosons can proceed at a high rate and may be the first discovery mode in the Higgs sector.