Weak boson probes of Higgs unitarity restoration at 10 TeV parton colliders

Higgs coupling deviations, at levels accessible to the high-luminosity LHC, can imply a phenomenological no-lose theorem for the next generation of collider facilities. Correlating Higgs coupling deviations from the SM expectation in the gauge boson sector with high-scale unitarity requirements, we estimate and compare the sensitivity that can be expected at a future hadron collider (operating at 100 TeV centre-of-mass energy) and a 10 TeV muon collider. Both muon and hadron colliders offer discovery potential for mass scales up to ${\cal{O}}(6~\text{TeV})$ where unitarity violation induced by (sub)percent Higgs coupling modifications is mended. We comment on how an intermediate precision FCC-ee programme can corroborate such deviations.