Generational Structure of Models with Dynamical Symmetry Breaking

TL;DR

This paper explores how models with dynamical symmetry breaking depend on the number of fermion generations, showing that for various generation counts, the models can produce realistic fermion masses and exhibit a slowly running gauge coupling.

Contribution

It investigates models with different numbers of generations, analyzing their symmetry breaking patterns and gauge coupling behaviors, extending understanding beyond the standard three-generation scenario.

Findings

Models with various N_{gen.} can produce electroweak-scale fermion masses.

The gauge coupling in these models remains large but slowly running, indicating an approximate infrared fixed point.

Multiple strongly coupled gauge symmetries can coexist and influence the symmetry breaking process.

Abstract

In models with dynamical electroweak symmetry breaking, this breaking is normally communicated to quarks and leptons by a set of vector bosons with masses generated via sequential breaking of a larger gauge symmetry. In reasonably ultraviolet-complete theories of this type, the number of stages of breaking of the larger gauge symmetry is usually equal to the observed number of quark and lepton generations, $N_{gen.}=3$. Here we investigate the general question of how the construction and properties of these models depend on $N_{gen.}$, regarded as a variable. We build and analyze models with illustrative values of $N_{gen.}$ different from 3 (namely, $N_{gen.}=1,2,4$) that exhibit the necessary sequential symmetry breaking down to a strongly coupled sector that dynamically breaks electroweak symmetry. Our results for variable $N_{gen.}$ show that one can robustly obtain, for this latter sector, a theory with a gauge coupling that is large but slowly running, controlled by an approximate infrared fixed point of the renormalization group. Owing to this, we find that for all of the values of $N_{gen.}$ considered, standard-model fermions of the highest generation have masses that can be comparable to the electroweak-symmetry breaking scale. We also study the interplay of multiple strongly coupled gauge symmetries in these models.