The last Complex WIMPs standing
  We continue the study of weakly interacting massive particles (WIMP) started
in [arXiv:2107.09688], focusing on a single complex electroweak $n$-plet with
non-zero hypercharge added to the Standard Model. The minimal splitting between
the Dark Matter and its electroweak neutral partner required to circumvent
direct detection constraints allows only multiplets with hypercharge smaller or
equal to 1. We compute for the first time all the calculable WIMP masses up to
the largest multiplet allowed by perturbative unitarity. For the minimal
allowed splitting, most of these multiplets can be fully probed at future
large-exposure direct detection experiments, with the notable exception of the
doublet with hypercharge 1/2. We show how a future muon collider can fully
explore the parameter space of the complex doublet combining missing mass,
displaced track and long-lived track searches. In the same spirit, we study how
a future muon collider can probe the parameter space of complex WIMPs in
regions where the direct detection cross section drops below the neutrino
floor. Finally, we comment on how precision observables can provide additional
constraints on complex WIMPs.
