Tree level unitarity and finiteness of electroweak oblique corrections

We study perturbative unitarity and electroweak oblique corrections in the electroweak symmetry breaking models including an arbitrary number of neutral Higgs bosons. Requiring the perturbative unitarity of the high energy scattering amplitudes of weak gauge bosons and the neutral Higgs bosons at tree level, we obtain a set of conditions among the Higgs coupling strengths (unitarity sum rules). It is shown that the unitarity sum rules require the tree level rho parameter to be 1 if there are only neutral Higgs bosons. Moreover, we find that the one-loop finiteness of the electroweak oblique corrections is automatically guaranteed once the unitarity sum rules are imposed among the Higgs coupling strengths. Applying the unitarity sum rules, we obtain severe constraints on the mass of the second lightest neutral Higgs boson and the lightest neutral Higgs (a 125GeV Higgs) coupling strength from the results of the electroweak precision tests as well as the unitarity.