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We analyze the scalar sector properties of a general class oftwo-Higgs-doublet models which has a global U(1) symmetry in the quartic terms.We find constraints on the parameters of the potential from the considerationsof unitarity of scattering amplitudes, the global stability of the potentialand the $\rho$-parameter. We concentrate on the spectrum of the non-standardscalar masses in the decoupling limit which is preferred by the Higgs data atthe LHC. We exhibit charged-Higgs induced contributions to the diphoton decaywidth of the 125\,GeV Higgs boson and its correlation with the corresponding$Z\gamma$ width.

Scalar sector properties of two-Higgs-doublet models with a global U(1) symmetry