Supersymmetric Custodial Higgs Triplets and the Breaking of Universality

TL;DR

This paper introduces a supersymmetric extension of the Georgi-Machacek model that maintains agreement with electroweak precision data even without small triplet VEVs, and predicts observable deviations in Higgs couplings at the LHC.

Contribution

It constructs a supersymmetric model with high-scale custodial symmetry that relaxes traditional constraints, allowing larger triplet contributions and distinctive LHC signatures.

Findings

Model accommodates high-scale custodial symmetry breaking.

Predicts deviations in Higgs couplings to W and Z bosons.

Enables lighter stops with less mixing in the Higgs sector.

Abstract

Higgs triplet models are known to have difficulties obtaining agreement with electroweak precision data and in particular constraints on the $\rho$ parameter. Either a global $SU(2)_L \otimes SU(2)_R$ symmetry has to be imposed on the scalar potential at the electroweak scale, as done in the well-known Georgi-Machacek (GM) model, or the triplet vacuum expectation values must be very small. We construct a supersymmetric model that can satisfy constraints on the $\rho$ parameter, even if these two conditions are not fulfilled. We supersymmetrize the GM model by imposing the $SU(2)_L \otimes SU(2)_R$ symmetry at a scale $\mathcal M$, which we argue should be at or above the messenger scale, where supersymmetry breaking is transmitted to the observable sector. We show that scales $\mathcal M$ well above 100 TeV and sizable contributions from the triplets to electroweak symmetry breaking can be comfortably accommodated. We discuss the main phenomenological properties of the model and demonstrate that the departure from custodial symmetry at the electroweak scale, due to radiative breaking, can show up at the LHC as a deviation in the `universal' relation for the Higgs couplings to $WW$ and $ZZ$. As a by-product of supersymmetry, we also show that one can easily obtain both large tree-level \emph{and} one loop corrections to the Higgs mass. This allows for stops that can be significantly lighter and with smaller mixing than those needed in the MSSM.