# Technicolor models with coupled systems of Schwinger-Dyson equations

## TL;DR

This paper explores coupled Schwinger-Dyson equations in Technicolor models, showing how their solutions differ from isolated cases, enabling high ETC boson masses and natural mass hierarchies, with detailed model analysis and experimental considerations.

## Contribution

It introduces a framework for coupled Schwinger-Dyson equations in Technicolor models, providing a novel approach to naturally generate fermion mass hierarchies and high-scale ETC bosons.

## Key findings

- Self-energies decrease logarithmically with momentum
- Models can push ETC boson masses to very high energies
- Lepton masses naturally lighter than quark masses

## 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 in comparison with the ones of the isolated equations. The change in the self-energies is similar to the one obtained in the presence of four-fermion interactions, but without their \textsl{ad hoc} inclusion in the theory. In this case TC and QCD self-energies decrease logarithmically with the momenta, what allow 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, explaining 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 appear 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.