Tempered two-Higgs-doublet model

We discuss the phenomenological consequences of requiring the cancellation of quadratic divergences up to the leading two-loop order within the two-Higgs-doublet model. Taking into account existing experimental constraints, allowed regions in the parameter space, permitting the cancellation, are determined. A degeneracy between masses of scalar bosons is observed for tanβ40. The possibility for $CP$ violation in the scalar potential is discussed and regions of tanβ--M_H^± with a substantial amount of $CP$ violation are determined. In order to provide a source for dark matter in a minimal manner, a scalar gauge singlet is introduced and discussed. The model allows to ameliorate the little hierarchy problem by lifting the minimal scalar Higgs-boson mass and by suppressing the quadratic corrections to scalar masses. The cutoff originating from the naturality arguments is therefore lifted from ~0.6 TeV in the standard model to 2.5 TeV in two-Higgs-doublet model depending on the mass of the lightest scalar.