Large N Scalars: From Glueballs to Dynamical Higgs Models

TL;DR

This paper develops effective Lagrangians and counting schemes for large N strongly coupled theories, enabling systematic analysis of composite scalars like glueballs and their implications for electroweak models.

Contribution

It introduces a novel framework for applying large N counting rules to effective Lagrangians, specifically for non-Goldstone composite states such as glueballs and scalars in electroweak models.

Findings

Derived leading N corrections to electroweak parameters.

Applied the formalism to models with composite Higgs scenarios.

Provided a systematic approach to compare lattice results with effective theories.

Abstract

We construct effective Lagrangians, and corresponding counting schemes, valid to describe the dynamics of the lowest lying large N stable massive composite state emerging in strongly coupled theories. The large N counting rules can now be employed when computing quantum corrections via an effective Lagrangian description. The framework allows for systematic investigations of composite dynamics of non-Goldstone nature. Relevant examples are the lightest glueball states emerging in any Yang-Mills theory. We further apply the effective approach and associated counting scheme to composite models at the electroweak scale. To illustrate the formalism we consider the possibility that the Higgs emerges as: the lightest glueball of a new composite theory; the large N scalar meson in models of dynamical electroweak symmetry breaking; the large N pseudodilaton useful also for models of near-conformal dynamics. For each of these realisations we determine the leading N corrections to the electroweak precision parameters. The results nicely elucidate the underlying large N dynamics and can be used to confront first principle lattice results featuring composite scalars with a systematic effective approach.