  We study scenarios where Dark Matter is a weakly interacting particle (WIMP)
embedded in an ElectroWeak multiplet. In particular, we consider real SU(2)
representations with zero hypercharge, that automatically avoid direct
detection constraints from tree-level Z-exchange. We compute for the first time
all the calculable thermal masses for scalar and fermionic WIMPs, including
Sommerfeld enhancement and bound states formation at leading order in gauge
boson exchange and emission. WIMP masses of few hundred TeV are shown to be
compatible both with s-wave unitarity of the annihilation cross-section, and
perturbativity. We also provide theory uncertainties on the masses for all
multiplets, which are shown to be significant for large SU(2) multiplets. We
then outline a strategy to probe these scenarios at future experiments.
Electroweak 3-plets and 5-plets have masses up to about 16 TeV and can
efficiently be probed at a high energy muon collider. We study various
experimental signatures, such as single and double gauge boson emission with
missing energy, and disappearing tracks, and determine the collider energy and
luminosity required to probe the thermal Dark Matter masses. Larger multiplets
are out of reach of any realistic future collider, but can be tested in future
gamma ray telescopes and possibly in large-exposure liquid Xenon experiments.
