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 $\tan \beta \gtrsim 40$. The possibility for $CP$ violation in the scalar potential is discussed and regions of $\tan \beta –M_{H^{\pm }}$ 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 $\sim 0.6\mathrm{TeV}$ in the standard model to $\gtrsim 2.5\mathrm{TeV}$ in two-Higgs-doublet model depending on the mass of the lightest scalar.

• Received 5 September 2010

DOI:https://doi.org/10.1103/PhysRevD.82.125026