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Diphoton rate in the Inert Doublet Model with a 125 GeV Higgs boson

An improved analysis of the diphoton decay rate of the Higgs boson in the Inert Doublet Model is presented together with critical discussion of the results existing in the literature. For Higgs boson mass M_h equal 125 GeV, and taking into account the following constraints: vacuum stability, existence of the Inert vacuum, perturbative unitarity, electroweak precision tests and the LEP bounds, we found regions in the parameter space where the diphoton rate is enhanced. The resulting regions were confronted with the allowed values of the Dark Matter mass. We found that significant enhancement in the two photon decay of the Higgs boson is only possible for constrained values of scalar couplings λ_3 hH+H-, λ_{345} hHH and masses of the charged scalar and the Dark Matter particle. The enhancement above 1.3 demands the masses of H+ and H to be less than 135 GeV (and above 62.5 GeV) and -1.46<λ_3,λ_{345} <-0.24. In addition we analyzed the correlation of the diphoton and Z+photon rates.