Higgs searches and singlet scalar dark matter: Combined constraints from XENON 100 and the LHC

XENON100 and the LHC are two of the most promising machines to test the physics beyond the Standard Model. In the meantime, indirect hints push us to believe that the dark matter and Higgs boson could be the two next fundamental particles to be discovered. Whereas ATLAS and CMS have just released their new limits on the Higgs searches, XENON100 obtained very recently strong constraints on DM-proton elastic scattering. In this work, we show that when we combined WMAP and the most recent results of XENON100, the invisible width of the Higgs to scalar dark matter is negligible($\lesssim 10%$), except in a small region with very light dark matter ($\lesssim 10$ GeV) not yet excluded by XENON100 or around 60 GeV where the ratio can reach 50% to 60%. The new results released by the Higgs searches of ATLAS and CMS set very strong limits on the elastic scattering cross section, even restricting it to the region $8 \times 10^{-46} \mrm{cm^2} \lesssim \sigma_{S-p}^{SI}\lesssim 2 \times 10^{-45} \mrm{cm^{2}}$ in the hypothesis $135 \mrm{GeV} \lesssim M_H \lesssim 155 \mrm{GeV}$.