Model-Independent Description and Large Hadron Collider Implications of Suppressed Two-Photon Decay of a Light Higgs Boson

For a Standard Model Higgs boson with mass between 115 GeV and 150 GeV, the two-photon decay mode is important for discovery at the Large Hadron Collider (LHC). We describe the interactions of a light Higgs boson in a more model-independent fashion, and consider the parameter space where there is no two-photon decay mode. We argue from generalities that analysis of the $t\bar t h$ discovery mode outside its normally thought of range of applicability is especially needed under these circumstances. We demonstrate the general conclusion with a specific example of parameters of a type I two-Higgs doublet theory, motivated by ideas in strongly coupled model building. We then specify a complete set of branching fractions and discuss the implications for the LHC