  We first review how the simple K-matrix unitarized linear SU(2) sigma model
can explain the experimental data in the scalar pi pi scattering channel of QCD
up to about 800 MeV. Since it is just a scaled version of the minimal
electroweak Higgs sector, which is often treated with the same unitarization
method, we interpret the result as support for this approach in the electroweak
model with scaled values of tree level Higgs mass up to at least about 2 TeV.
We further note that the relevant QCD effective Lagrangian which fits the data
to still higher energies using the same method involves another scalar
resonance. This suggests that the method should also be applicable to
corresponding beyond minimal electroweak models. Nevertheless we note that even
with one resonance, the minimal K matrix unitarized model behaves smoothly for
large bare Higgs mass by effectively "integrating out" the Higgs while
preserving unitarity. With added confidence in this simple approach we make a
survey of the Higgs sector for the full range of bare Higgs mass. One amusing
point which emerges is that the characteristic factor of the W-W fusion
mechanism for Higgs production peaks at the bare mass of the Higgs boson, while
the characteristic factor for the gluon fusion mechanism peaks near the
generally lower physical mass.
