High-scale validity of a two-Higgs doublet scenario: a study including   LHC data
  We consider the conditions for the validity of a two-Higgs doublet model at high energy scales, together with all other low- and high-energy constraints. The constraints on the parameter space at low energy, including the measured value of the Higgs mass and the signal strengths in channels are juxtaposed with the conditions of vacuum stability, perturbativity and unitarity at various scales. We find that a scenario with an exact $\mathbb{Z}_2$ symmetry in the potential cannot be valid beyond about 10 TeV without the intervention of additional physics. On the other hand, when the $\mathbb{Z}_2$ symmetry is broken, the theory can be valid even up to the Planck scale without any new physics coming in. The interesting feature we point out is that such high-scale validity is irrespective of the uncertainty in the top quark mass as well as $\alpha_{s}(M_Z)$, in contrast with the standard model with a single Higgs doublet. It is also shown that the presence of a CP-violating phase is allowed when the $\mathbb{Z}_2$ symmetry is relaxed. The allowed regions in the parameter space are presented for each case. The results are illustrated in the context of a Type-II scenario. 
Nabarun Chakrabarty, Ujjal Kumar Dey and Biswarup Mukhopadhyaya
hep-ph