Going all the way in the search for WIMP dark matter at the muon collider through precision measurements

Dark Matter is a necessary ingredient for a complete theory of Nature, which has so far remained elusive in laboratory searches for new particles. Searches at current and future colliders are in principle a promising way to search for electroweak charged dark matter particles, but the sensitivity of experiments at the LHC and future $pp$ colliders falls short to fully probe the whole mass range allowed for electroweak charged dark matter particles, which extends in principle up to the O(0.1) PeV. In this work we examine the effect of on-shell and off-shell propagation of electroweak charged thermal dark matter particles on integrated and differential rates of several Standard Model final states at the muon collider, considering candidates from weak 2-plet at the TeV scale up to 7-plet and 9-plet in the O(0.1) PeV ballpark. For fermionic WIMPs we find that all dark matter candidates with $n\leq 5$, corresponding to a thermal mass up to 14~TeV, can be excluded at the high-energy muon collider for some center-of-mass energy at or below 14~TeV. For the $n>5$ WIMPs our results show that higher energy muon colliders offer a route to conclusively probe both scalar and fermionic WIMPs off-shell production all the way up to the perturbativity bound for WIMP dark matter at O(0.1)~PeV. Our results bring WIMPs over the whole allowed mass range in the realm of collider searches and motivate research and development for the realization of a high energy muon collider.