New physics in b -> s mu mu: FCC-hh or a muon collider?

Rare flavour-changing neutral-current transitions b -> s mu(+) mu(-) probe higher energy scales than what is directly accessible at the LHC. Therefore, the presence of new physics in such transitions, as suggested by the present-day LHCb anomalies, would have a major impact on the motivation and planning of future high-energy colliders. The two most prominent options currently debated are a proton-proton collider at 100TeV (FCC-hh) and a multi-TeV muon collider (MuC). In this work, we compare the discovery prospects at these colliders on benchmark new physics models indirectly detectable in b -> s mu(+) mu(-) decays but beyond the reach of the high-p(T) searches at the HL-LHC. We consider a comprehensive set of scenarios: semileptonic contact interactions, Z' from a gauged U(1) B-3-L-mu and U(1) L-mu-L-tau, the scalar leptoquark S-3, and the vector leptoquark U-1. We find that a 3TeV MuC has a sensitivity reach comparable to the one of the FCC-hh. However, for a heavy enough mediator, the new physics effects at a 3TeV MuC are only observed indirectly via deviations in the highest energy bin, while the FCC-hh has a greater potential for the discovery of a resonance. Finally, to completely cover the parameter space suggested by the bs mu mu anomalies, among the proposed future colliders, only a MuC of 10TeV (or higher) can meet the challenge.