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

We study the conditions required to make the 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 {\em alignment limit} is imposed in view of the LHC Higgs data. We find that ensuring stability up to scales $\gtrsim {10}^{10}$~GeV 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, $\text{tb}$ and a mass parameter, $m_0$, with $\text{tb}\gtrsim 3$. These observations make a 2HDM, in the {\em stable alignment limit}, more predictive than ever.