Higgs properties in a broken Inert Doublet Model

We consider a model for the Higgs sector with two scalar doublets and a broken $Z_2$ symmetry, the Stealth Doublet Model, where the $Z_2$ symmetry is manifest in the Yukawa sector but broken by the scalar potential. This model can be seen as a generalization of the Inert Doublet Model. One of the doublets is the Higgs doublet that participates in electroweak symmetry breaking and couples to fermions. The other doublet does not couple to fermions at tree level and does not acquire a vacuum expectation value. The broken $Z_2$ symmetry leads to interesting phenomenology such as mixing between the two doublets and charged and CP-odd scalars that can be light and have unusual decay channels. We present theoretical and experimental constraints on the model and consider the recent observation of a Higgs boson at the LHC. The data on the $H\to\gamma\gamma$ channel can be naturally accommodated in the model, with either the lightest or the heaviest CP-even scalar playing the role of the observed particle.