Effective Theories of Dark Mesons with Custodial Symmetry

TL;DR

This paper develops effective theories for dark mesons arising from strongly-coupled dark sectors, classifying their decay behaviors based on custodial symmetry, and matching ultraviolet models to low-energy interactions with the Standard Model.

Contribution

It constructs non-linear sigma models for dark pions, distinguishes decay classes influenced by custodial symmetry, and provides a framework for connecting UV theories to observable low-energy phenomena.

Findings

Identified two classes of dark pion decay modes: gaugephilic and gaugephobic.

Showed custodial symmetry determines the decay patterns and suppresses certain processes.

Provided a method to match UV theories onto effective low-energy descriptions.

Abstract

Dark mesons are bosonic composites of a new, strongly-coupled sector beyond the Standard Model. We consider several dark sectors with fermions that transform under the electroweak group, as arise from a variety of models including strongly-coupled theories of dark matter (e.g., stealth dark matter), bosonic technicolor (strongly-coupled indcued electroweak symmetry breaking), vector-like confinement, etc. We consider theories with two and four flavors under an $SU(N)$ strong group that acquire variously chiral, vector-like, and mixed contributions to their masses. We construct the non-linear sigma model describing the dark pions and match the ultraviolet theory onto a low energy effective theory that provides the leading interactions of the lightest dark pions with the Standard Model. We uncover two distinct classes of effective theories that are distinguishable by how the lightest dark pions decay: "Gaugephilic": where $\pi^0 \rightarrow Z h$, $\pi^\pm \rightarrow W h$ dominate once kinematically open, and "Gaugephobic": where $\pi^0 \rightarrow \bar{f} f$, $\pi^\pm \rightarrow \bar{f}' f$ dominate. Custodial $SU(2)$ plays a critical role in determining the "philic" or "phobic" nature of a model. In dark sectors that preserve custodial $SU(2)$, there is no axial anomaly, and so the decay $\pi^0 \rightarrow \gamma\gamma$ is highly suppressed. In a companion paper, we study dark pion production and decay at colliders, obtaining the constraints and sensitivity at the LHC.