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 $\gtrsim 10^{10}\mathrm{GeV}$ 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, $\tan \beta$ and a mass parameter, $m_0$, with $\tan \beta \gtrsim 3$. These observations make a 2HDM, in the stable alignment limit, more predictive than ever.

• Received 16 April 2015

DOI:https://doi.org/10.1103/PhysRevD.91.095024