Schwinger-Dyson approach and its application to generate a light composite scalar

TL;DR

This paper explores the generation of a light composite scalar boson within strongly interacting theories like Technicolor, using non-perturbative Schwinger-Dyson and Bethe-Salpeter equations to analyze the conditions for such a light state.

Contribution

It applies a non-perturbative approach to identify conditions under which a light composite scalar can emerge in strongly interacting theories, differing from effective Lagrangian methods.

Findings

Light scalar mass is about one order of magnitude below the strong interaction scale.

A slowly decreasing fermionic self-energy with momentum is necessary for a light composite scalar.

The study links the formation of light scalars to specific fermionic self-energy behaviors.

Abstract

We discuss the possibility of generating a light composite scalar boson, in a scenario that we may generically call Technicolor, or in any variation of a strongly interacting theory, where by light we mean a scalar composite mass about one order of magnitude below the characteristic scale of the strong theory. Instead of most of the studies about a composite Higgs boson, which are based on effective Lagrangians, we consider this problem in the framework of non-perturbative solutions of the fermionic Schwinger-Dyson and Bethe-Salpeter equations. We study a range of mechanisms proposed during the recent years to form such light composite boson, and verify that such possibility seems to be necessarily associated to a fermionic self-energy that decreases slowly with the momentum.