Low mass dark matter and invisible Higgs width in darkon models

The Standard Model (SM) plus a real gauge-singlet scalar field dubbed darkon (SM+D) is the simplest model possessing a weakly interacting massive particle (WIMP) dark matter candidate. In this model, the parameters are constrained from dark matter relic density and direct searches. The fact that interaction between darkon and SM particles is only mediated by a Higgs boson exchange may lead to significant modifications to the Higgs boson properties. If the dark matter mass is smaller than half of the Higgs boson mass, then a Higgs boson can decay into a pair of darkons resulting in a large invisible branching ratio. The Higgs boson will be searched for at the LHC and may well be discovered in the near future. If a Higgs boson with a small invisible decay width will be found, the SM+D model with small dark matter mass will be in trouble. We find that by extending the SM+D to a two Higgs doublet model plus a darkon (THDM+D) it is possible to have a Higgs boson with a small invisible branching ratio and at the same time the dark matter can have a low mass. We also comment on other implications of this model.