Custodial symmetry violation in the Georgi-Machacek model

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 electroweak ρ parameter (along with perturbative unitarity) lets us constrain the scale of the ultraviolet completion to lie below tens to hundreds of tera-electron volts (TeV) over almost all of the parameter space. 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 (LHC), but may be detectable at a future e+e- collider. We note that the upper bound on the scale of the ultraviolet completion is large enough that virtual effects from the ultraviolet completion will also be undetectable at the LHC. This means that the GM model is a valid effective theory for LHC physics.