Technicolor models with coupled systems of Schwinger-Dyson equations

Abstract

When technicolor (TC), QCD, extended technicolor (ETC) and other interactions become coupled through their different Schwinger-Dyson equations, the solution of these equations are modified compared to those of the isolated equations. The change in the self-energies is similar to that obtained in the presence of four-fermion interactions, but without their ad hoc inclusion in the theory. In this case TC and QCD self-energies decrease logarithmically with the momenta, which allows us to build models where ETC boson masses can be pushed to very high energies, and their effects will barely appear at present energies. Here we present a detailed discussion of this class of TC models. We first review the Schwinger-Dyson TC and QCD coupled equations and explain the origin of the asymptotic self-energies. We develop the basic ideas of how viable TC models may be built along this line, where ordinary lepton masses are naturally lighter than quark masses. One specific unified TC model associated with a necessary horizontal (or family) symmetry is described. The values of scalar and pseudo-Goldstone boson masses in this class of models are also discussed, as well as the value of the trilinear scalar coupling, and the consistency of the models with the experimental constraints.

Sigma-assisted low scale composite Goldstone–Higgs

“…Estimates based on Schwinger-Dyson equations, similar to the QCD ones [75], also indicate a low value for m σ [76], however the computation has been done for a Technicolor theory with f = v and cannot be extrapolated straightforwardly to our case. Gravitational dual results also indicate the lightest scalar mass is low compared to the other states [30,31].…”

Fermion mass splitting in the technicolor coupled scenario

“…the techni-neutrino mass has all the contributions shown in part b of the figure where, at leading order, the third generation couples only to the TC condensate and the first generation to the QCD condensate. The second generation results from the mixing of the different condensates intermediated by the horizontal (or GUT) bosons [48]. These points are going to be discussed at lenght in the next sections.…”

“…The ordinary fermion masses vary logarithmically with M E , and as proposed in Refs. [46,48] the fermion mass splitting is induced by a horizontal (or family) symmetry, 1 When solving the SDE for the fermion mass we have two possible solutions, one behaving as μ 3 / p 2 that is called regular or soft, and another behaving as μ( p 2 /μ 2 ) −γ called irregular or hard, where γ is proportional to bg 2 and b is the leading coefficient of the β function. This irregular or hard solution is similar to an explicit chiral symmetry breaking [57], i.e.…”

“…These attempts imply theories with a large number of technifermions or fermions in higher dimensional representations. Here we discuss a new approach consisting of models where TC and QCD are coupled through a larger theory [46][47][48], leading naturally to a theory with a light scalar boson, where the ETC (or unified theory) gauge boson masses can be pushed to very high energies and pseudo-Goldstone boson masses are enhanced. All this happens without the need of a strong increase of the number of technifermions or the introduction of larger dimensional fermionic representations.…”

“…Another point, as can be verified in Refs. [48], is that quarks are heavier than leptons due to the large number of diagrams contributing to their masses. The ETC gauge boson masses can be pushed to very high energies, where the symmetry breaking of the ETC (or GUT) model can be generated even by fundamental scalar bosons, that may appear naturally at Planck scale.…”