Two viable large scalar multiplet models with a Z2 symmetry

We study models in which the Higgs sector is extended by a single scalar electroweak multiplet Z with isospin T=5/2 (sextet) or 7/2 (octet) and the same hypercharge as the Standard Model Higgs doublet, in which Z is odd under a global Z2 symmetry. This Z2 symmetry keeps the lightest (neutral) member of Z stable and has interesting implications for phenomenology. We determine the constraints on these models from precision electroweak measurements and Higgs boson decays to two photons. We compute the thermal relic density of the stable member of Z and show that, for masses below 1 TeV, it can make up at most 1% of the dark matter in the universe. We also show that current dark matter direct detection experiments do not constrain the models, but future ton-scale experiments will probe their parameter space.