Search for the Higgs portal to a singlet fermionic dark matter at the LHC

We consider a simple extension of the standard model with a singlet fermionic dark matter. Its thermal relic density can be easily accommodated by a real singlet scalar messenger that mixes with the standard model Higgs boson. The model can change significantly the Higgs signals at the LHC via sizable invisible decays of two Higgs-like scalar bosons. After imposing the constraints from the electroweak precision tests, colliders and dark matter search experiments, one concludes that two or one or none of the two Higgs bosons, depending on the mass relations among two scalar bosons and the dark matter fermion and their couplings. In particular, if a standard model Higgs-like scalar boson is discovered around 120-125 GeV region at the LHC, it would be almost impossible to find the second Higgs-like boson since it is mostly a singlet scalar, whether it is heavier or lighter. This model can be further tested by direct dark matter search experiments.