Erratum: Comparing the Higgs sector of electroweak theory with the scalar sector of low energy QCD [Phys. Rev. D68, 013008 (2003)]

Abstract

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 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.

Isobar Rescattering Model and Light Scalar Mesons

“…(7). In contrast to |T 0 0 |, the magnitude of the rescattering factor | cos δ 0 0 e iδ 0 0 /(m 2 σB −s)| peaks at the much smaller physical value rather than the bare value of the sigma mass 14 . This is understandable since there is a trivial numerator and the denominator has the same structure as the denominator used to find the physical pole position.…”

“…This talk is mainly based on reinterpreting 14 which deals with production of longitudinal electroweak gauge bosons by the "gluon fusion" mechanism. …”

Structure of scalar mesons and the Higgs sector of strong interaction

“…For the SU (2) LσM this idea is not new (see e.g. [53]) because the Lagrangian written down in ( 50) is formulated in terms of fields rather than in terms of particles with a definite q q structure. Another approach to the prediction of masses of scalar mesons based on dynamical symmetry breaking has been described in subsection 4.1.…”

A Natural Explanation for Magnetars

“…We have also, for the first time, fixed all the coupling parameters of, L, from low energy hadronic data (see [26] for details). One of the parameters is the (treelevel) mass of the Sigma particle which is related to ππ scattering, and is estimated to be around m σ ∼ 800 MeV [27].…”