Custodial symmetry violation in the Georgi-Machacek model

TL;DR

This paper investigates how custodial symmetry is violated at the quantum level in the Georgi-Machacek model, constraining the model's ultraviolet scale and predicting small but potentially detectable effects on Higgs couplings and Higgs boson mass splittings.

Contribution

It quantifies custodial symmetry violation effects in the GM model from high scale to weak scale, providing constraints and predictions relevant for future collider experiments.

Findings

Ultraviolet completion scale constrained below tens to hundreds of TeV.

Custodial symmetry violation effects in Higgs couplings are small.

Potential detectability of effects at future electron-positron colliders.

Abstract

We study the effects of custodial symmetry violation in the Georgi-Machacek (GM) model. The GM model adds isospin-triplet scalars to the Standard Model in a way that preserves custodial symmetry at tree level; however, this custodial symmetry has long been known to be violated at the one-loop level by hypercharge interactions. We consider the custodial-symmetric GM model to arise at some high scale as a result of an unspecified ultraviolet completion, and quantify the custodial symmetry violation induced as the model is run down to the weak scale. The measured value of the eletroweak rho parameter (along with unitarity considerations) lets us constrain the scale of the ultraviolet completion to lie below tens to hundreds of TeV. Subject to this constraint, we quantify the size of other custodial-symmetry-violating effects at the weak scale, including custodial symmetry violation in the couplings of the 125 GeV Higgs boson to W and Z boson pairs and mixings and mass splittings among the additional Higgs bosons in the theory. We find that these effects are small enough that they are unlikely to be probed by the Large Hadron Collider, but may be detectable at a future $e^+e^-$ collider.