Higgs potential and hidden light Higgs scenario in two Higgs doublet models

In two Higgs doublet models, there exists an interesting possibility, the hidden light Higgs scenario, that the discovered SM-like Higgs boson is the heavier CP-even Higgs boson H0 and the lighter CP-even h0 has not been observed yet in any experiment. We study the current status of this scenario in Types I, II, X, and Y, through the scans of the parameters with all relevant theoretical and experimental constraints. We employ not only the most up-to-date Higgs signal strength measurements with the feed-down effects, but also all the available LHC exclusion limits from heavy Higgs searches. Adjusting the heavier H0 to the 125 GeV state while hiding the lighter h0 from the LEP Higgs search prohibits the extreme decoupling limit: there exist upper bounds on the masses of the pseudoscalar A0 and the charged Higgs H± below about 600 GeV. In addition, the Z2 symmetry is shown to be a good approximate symmetry since the soft Z2 symmetry breaking parameter m122 should be less than about (45GeV)2. Most interestingly, a few parameters in the Higgs potential and the related Higgs triple and quartic couplings are shown to be meaningfully constrained by the current data. The double Higgs-strahlung process at an e+e- collider is also studied.