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We determine the next-to-leading order renormalization group equations forthe Two-Higgs-Doublet model with a softly broken $Z_2$ symmetry and CPconservation in the scalar potential. We use them to identify the parameterregions which are stable up to the Planck scale and find that in this case thequartic couplings of the Higgs potential cannot be larger than 1 in magnitudeand that the absolute values of the S-matrix eigenvalues cannot exceed 2.5 atthe electroweak symmetry breaking scale. Interpreting the 125 GeV resonance asthe light CP-even Higgs eigenstate, we combine stability constraints,electroweak precision and flavour observables with the latest ATLAS and CMSdata on Higgs signal strengths and heavy Higgs searches in global parameterfits to all four types of $Z_2$ symmetry. We quantify the maximal deviationsfrom the alignment limit and find that in type II and Y the mass of the heavyCP-even (CP-odd) scalar cannot be smaller than 340 GeV (360 GeV). Also, wepinpoint the physical parameter regions compatible with a stable scalarpotential up to the Planck scale. Motivated by the question how natural a Higgsmass of 125 GeV can be in the context of a Two-Higgs-Doublet model, we alsoaddress the hierarchy problem and find that the Two-Higgs-Doublet model doesnot offer a perturbative solution to it beyond 5 TeV.

Global fits of the two-loop renormalized Two-Higgs-Doublet model with soft $Z_2$ breaking