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Introducing arbitrary number of neutral Higgs bosons in the electroweaksymmetry breaking sector, we derive a set of conditions among Higgs couplingswhich need to be satisfied to maintain the unitarity of the high energyscattering amplitudes of weak gauge bosons at the tree level (unitarity sumrules). It is shown that the unitarity sum rules require the tree level $\rho$parameter to be 1, without explicitly invoking the custodial symmetryarguments. The one-loop finiteness of the electroweak oblique corrections isautomatically guaranteed once these unitarity sum rules are imposed among Higgscouplings. Severe constraints on the lightest Higgs coupling (125GeV Higgscoupling) and the mass of the second lightest Higgs boson are obtained from theunitarity and the results of the electroweak precision tests (oblique parametermeasurements). These results are compared with the effective theory of thelight Higgs boson, and we find simple relationships between the mass of thesecond lightest Higgs boson in our framework and the ultraviolet cutoff in theeffective theory framework.

Does unitarity imply finiteness of electroweak oblique corrections at one-loop? - constraining extra neutral Higgs bosons -