Vacuum structure of the $\mathbb{Z}_2$ symmetric Georgi-Machacek model

TL;DR

This paper analyzes the vacuum structure of a $ ext{Z}_2$ symmetric Georgi-Machacek model, identifying conditions for stable minima in phases relevant for dark matter and electroweak symmetry.

Contribution

It provides a detailed analysis of the vacuum phases of the $ ext{Z}_2$ symmetric Georgi-Machacek model, including conditions for the stability of the custodial and dark matter phases.

Findings

Conditions for absolute minima in custodial and dark matter phases.

Identification of phases leading to charge breaking or incorrect electroweak symmetry.

Viability of a dark matter candidate within the model.

Abstract

We discuss the vacuum structure of a version of the Georgi-Machecek model with an exact $\mathbb{Z}_2$ symmetry acting on the triplet fields. Besides the usual custodial-symmetric model, with $\rho=1$ at tree-level, a model with a dark matter candidate is also viable. The other phases of the model lead to electric charge breaking, a wrong pattern of electroweak symmetry breaking or to $\rho \neq 1$ at tree-level. We derive conditions to have an absolute minimum in each of the two viable phases, the custodial and the dark matter phases.