Probing extended Higgs sectors by the synergy between direct searches at the LHC and precision tests at future lepton colliders

We discuss a possibility that the parameter space of the two Higgs doublet model is significantly narrowed down by considering the synergy between direct searches for additional Higgs bosons at the LHC and its luminosity upgraded operation and precision measurements of the Higgs boson properties at future electron-positron colliders such as the International Linear Collider. We show that, in the case where the coupling constants of the discovered Higgs boson are slightly different from the predicted values in the standard model, most of the parameter space is explored by the direct searches of extra Higgs bosons, in particular for the decays of the extra Higgs bosons into the discovered Higgs boson, and also by the theoretical arguments such as perturbative unitarity and vacuum stability. This can be done because there appears an upper limit on the mass of the extra Higgs bosons as long as the deviation exists in the Higgs boson coupling. We also show that in the alignment limit where all the Higgs boson couplings take the standard model like values most of the parameter space cannot be excluded because most of the Higgs to Higgs decays are suppressed and also there is no upper limit on the masses from the theoretical arguments.