Light composite Higgs boson from the normalized Bethe-Salpeter equation

Abstract

Scalar composite boson masses have been computed in QCD and technicolor theories with the help of the homogeneous Bethe-Salpeter equation, resulting in a scalar mass that is twice the dynamically generated fermion or technifermion mass (m dyn ). We show that in the case of walking (or quasiconformal) technicolor theories, where the m dyn behavior with the momenta may be quite different from the one predicted by the standard operator product expansion, this result is incomplete and we must consider the effect of the normalization condition of the Bethe-Salpeter equation to determine the scalar masses. We compute the composite Higgs boson mass for several groups with technifermions in the fundamental and higher dimensional representations and comment about the experimental constraints on these theories, which indicate that models based on walking theories with fermions in the fundamental representation may, within the limitations of our approach, have masses quite near the actual direct exclusion limit.

The Higgs boson mass in minimal Technicolor models

“…It is also possible to obtain information on the spectrum of TC theories simply looking at the gap equations and their possible solutions, this is the simplest approach and is the point of view to be followed here using some of the results of Ref. [5]. Of course, all these attempts involve a reasonable uncertainty typical of non-perturbative theories, but the full set of results may be able to corner the main characteristics of the broken TC theory, i.e.…”

“…This possibility was investigated and confirmed by us through the use of an effective potential for composite operators [4] and through a calculation involving the Bethe-Salpeter equation (BSE) for the scalar state [5]. The BSE approach is a straightforward one, and our purpose in this work is to complement the studies of dynamical symmetry breaking of Refs.…”

“…We apply the results of Ref. [5] to compute the Higgs boson masses in the case of the Minimal and Ultraminimal TC models.…”

“…The BSE approach is a straightforward one, and our purpose in this work is to complement the studies of dynamical symmetry breaking of Refs. [4,5] in the case of the Minimal and Ultraminimal TC models. We apply the results of Ref.…”

“…Recently a Minimal and an Ultraminimal Technicolor models were proposed where the presence of TC fermions in other representations than the fundamental one led to viable models without conflict with the known value for the measured S parameter. In this work we apply the results of [5] to compute the masses of the Higgs boson in the case of the Minimal and Ultraminimal Technicolor models. …”