Search for a stable alignment limit in two-Higgs-doublet models

We study the conditions required to make the two-Higgs-doublet-model (2HDM) scalar potential stable up to the Planck scale. The lightest CP-even scalar is assumed to have been found at the LHC and the alignment limit is imposed in view of the LHC Higgs data. We find that ensuring stability up to scales 1010GeV necessitates the introduction of a soft breaking parameter in the theory. Even then, some interesting correlations between the nonstandard masses and the soft breaking parameter need to be satisfied. Consequently, a 2HDM becomes completely determined by only two nonstandard parameters, namely, tanβ and a mass parameter, m0, with tanβ3. These observations make a 2HDM, in the stable alignment limit, more predictive than ever.