Comparing the Higgs sector of electroweak theory with the scalar sector of low energy QCD

We first review how the simple K-matrix unitarized linear SU(2) sigma model can explain the experimental data in the scalar ππ 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 the tree-level Higgs boson 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 a large bare Higgs boson mass by effectively 'integrating out' the Higgs boson 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 boson mass. One amusing point which emerges is that the characteristic factor of the W-W fusion mechanism for Higgs boson 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