Motivated by the recent result reported from LHC on the di-photon search for
a Standard Model (SM) Higgs-like boson. We discuss the implications of this
possible signal in the framework of the Inert Higgs Doublet Model (IHDM),
taking into account previous limits from Higgs searches at LEP, the Tevatron
and the LHC as well as constraints from unitarity, vacuum stability and
electroweak precision tests. We show that the charged Higgs contributions can
interfere constructively or destructively with the W gauge bosons loops leading
to enhancement or suppression of the di-photon rate with respect to SM rate. We
show also that the invisible decay of the Higgs, if open, could affect the
total width of the SM Higgs boson and therefore suppress the di-photon rate.Comment: 15 pages, added reference
