Custodial symmetry, Georgi-Machacek model, and other scalar extensions

TL;DR

This paper explores the concept of custodial symmetry in gauge theories, clarifies its different classes, and introduces a more general scalar extension model beyond the Georgi-Machacek model with richer phenomenology.

Contribution

It critically examines custodial symmetry, identifies three classes, and proposes a new, more general scalar extension model with additional parameters.

Findings

Identifies three classes of custodial symmetry depending on couplings.

Shows Georgi-Machacek model is not the most general with CS.

Proposes a new scalar extension model with richer phenomenology.

Abstract

In an SU(2) gauge theory, if the gauge bosons turn out to be degenerate after spontaneous symmetry breaking, obviously these mass terms are invariant under a global SU(2) symmetry that is unbroken. The pure gauge terms are also invariant under this symmetry. This symmetry is called the {\em custodial symmetry} (CS). In $\rm SU(2)\times U(1)$ gauge theories, CS implies a mass relation between the $W$ and the $Z$ bosons. The Standard Model (SM), as well as various extensions of it in the scalar sector, possess such a symmetry. In this paper, we critically examine the notion of CS and show that there may be three different classes of CS, depending on the gauge couplings and self-couplings of the scalars. Among old models that preserve CS, we discuss the Two-Higgs Doublet Model and the one doublet plus two triplet model by Georgi and Machacek. We show that for two-triplet extensions, the Georgi-Machacek model is not the most general possibility with CS. Rather, we find, as the most general extension, a new model with more parameters and hence a richer phenomenology. Some of the consequences of this new model have also been discussed.