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 $135 \mrm{GeV} \lesssim M_H \lesssim 155
\mrm{GeV}$.
