Constraining the Dark 2HDM

The Dark 2HDM (called also the Inert Doublet Model) is the version of the Two-Higgs-Doublet Model with an exact $Z_2$ symmetry. It contains the SM-like Higgs boson $h$ and dark scalars $H$,$H^+,H^-$,$A$. Only dark scalars have odd $Z_2$ parity and therefore the lightest of them can be a dark matter candidate. The comparison of such model and of the standard 2HDM with an explicit $Z_2$ symmetry is given.