Hidden sector dark matter and Higgs physics

We consider a hidden sector dark matter, where a singlet fermion is a cold dark matter and a real singlet scalar boson $S$ is a messenger between the SM and the hidden sectors. This singlet scalar will mix with the SM Higgs boson $h$, and we expect there are two Higgs-like scalar bosons $H_1$ and $H_2$. Imposing all the relevant constraints from collider search bounds on Higgs boson, DM scattering cross section on proton and thermal relic density. We find that there is a destructive interference between $H_1$ and $H_2$ contributions to the direct detection cross section of the DM. Also one of the two Higgs-like scalar bosons can easily escape the detections at the LHC, and there will be a universal reduction of the signal strength for the observed 125 GeV Higgs-like boson, which could be tested at the LHC with more data in the future.