  We study the perturbative unitarity bound given by dimension six derivative
interactions consisting of Higgs doublets. These operators emerge from kinetic
terms of composite Higgs models or integrating out heavy particles that
interact with Higgs doublets. They lead to new phenomena beyond the Standard
Model. One of characteristic contributions by derivative interactions appear in
vector boson scattering processes. Longitudinal modes of massive vector bosons
can be regarded as Nambu Goldstone bosons eaten by each vector field with the
equivalence theorem. Since their effects become larger and larger as the
collision energy of vector bosons increases, vector boson scattering processes
become important in a high energy region around the TeV scale. On the other
hand, in such a high energy region, we have to take the unitarity of amplitudes
into account. We have obtained the unitarity condition in terms of the
parameter included in the effective Lagrangian for one Higgs doublet models.
Applying it to some of models, we have found that contributions of derivative
interactions are not so large enough to clearly discriminate them from the
Standard Model ones. We also study it in two Higgs doublet models. Because they
are too complex to obtain the bound in the general effective Lagrangian, we
have calculated it in explicit models. These analyses tell us highly model
dependence of the perturbative unitarity bounds.
