Topological terms in Composite Higgs Models

TL;DR

This paper classifies topological terms in Composite Higgs models, revealing their different phenomenological effects and how measuring these terms can probe the underlying microscopic theory.

Contribution

It provides a comprehensive classification of topological action terms in various Composite Higgs models and discusses their phenomenological implications.

Findings

Two types of topological terms identified with distinct phenomenological effects.

In the $SO(5)/SO(4)$ model, a term causes $P$ and $CP$ violation at the non-perturbative level.

The $SO(6)/SO(5)$ model includes a term analogous to the Dirac monopole with classical effects.

Abstract

We apply a recent classification of topological action terms to Composite Higgs models based on a variety of coset spaces $G/H$ and discuss their phenomenology. The topological terms, which can all be obtained by integrating (possibly only locally-defined) differential forms, come in one of two types, with substantially differing consequences for phenomenology. The first type of term (which appears in the minimal model based on $SO(5)/SO(4)$) is a field theory generalization of the Aharonov-Bohm phase in quantum mechanics. The phenomenological effects of such a term arise only at the non-perturbative level, and lead to $P$ and $CP$ violation in the Higgs sector. The second type of term (which appears in the model based on $SO(6)/SO(5)$) is a field theory generalization of the Dirac monopole in quantum mechanics and has physical effects even at the classical level. Perhaps most importantly, measuring the coefficient of such a term can allow one to probe the structure of the underlying microscopic theory. A particularly rich topological structure, with 6 distinct terms, is uncovered for the model based on $SO(6)/SO(4)$, containing 2 Higgs doublets and a singlet. Of the corresponding couplings, one is an integer and one is a phase.