Chiral Hierarchies, Compositeness and the Renormalization Group

TL;DR

This paper investigates whether large hierarchies in models with compositeness and dynamical symmetry breaking are stable against Coleman--Weinberg instabilities, finding that they are generally not disallowed by such effects.

Contribution

The study applies perturbative two-loop renormalization group analysis to assess the stability of hierarchies in models with compositeness and symmetry breaking.

Findings

Large hierarchies are not generally disallowed by Coleman--Weinberg instabilities.

Two-loop RG methods provide a consistent framework for analyzing hierarchy stability.

Models can maintain significant hierarchies without destabilization.

Abstract

A wide class of models involve the fine--tuning of significant hierarchies between a strong--coupling ``compositeness'' scale, and a low energy dynamical symmetry breaking scale. We examine the issue of whether such hierarchies are generally endangered by Coleman--Weinberg instabilities. A careful study using perturbative two--loop renormalization group methods finds that consistent large hierarchies are not generally disallowed.