It is possible to ameliorate the Higgs vacuum stability problem by switching over to two-Higgs-doublet models (2HDM), ensuring a stable electroweak vacuum up to the Planck scale, even though the top quark mass may be on the high side. However, the simultaneous requirements of perturbative unitarity, and also compatibility with collider and flavor data, constrain the parameter space severely. We investigate the collider signals answering to the regions allowed by such constraints. In particular, the near degeneracy of the neutral heavy scalar and the pseudoscalar is a feature that is probed. The LHC allows distinguishability of these two states, together with signal significance of at least $3\sigma$, in its high-luminosity run. While $e^{+}{e}^{-}$ colliders may have rather low event rates, muon colliders, cashing in on the principle of radiative return, can probe 2HDM scenarios with (pseudo)scalar masses up to TeV or so, though with the price of losing distinction between the $CP$-even and -odd states.

• Received 6 April 2017

DOI:https://doi.org/10.1103/PhysRevD.96.035028