Probing C P violation through vector boson fusion at high-energy muon colliders

We investigate C P -violating effects in electroweak interactions at future high-energy muon colliders within the Standard Model effective field theory framework. Focusing on four dimension-six C P -odd operators— O W ˜ , O H W ˜ , O H W ˜ B , O H B ˜ —we analyze vector boson fusion production of W and Higgs bosons using C P -odd observables and their asymmetries. With detailed simulations including parton showering, hadronization, and detector effects, we derive exclusion sensitivities through a binned likelihood analysis. For example, at s = 3 TeV with 2 ab − 1 , the coefficient C W ˜ can be constrained at the O ( 0.02 ) level, improving to O ( 0.008 ) at 10 TeV with 2 ab − 1 , and O ( 0.003 ) with 10 ab − 1 . These results significantly surpass current LHC and projected International linear collider sensitivities, demonstrating the unique potential of high-energy muon colliders to provide direct and model-independent probes of C P violation in the electroweak sector.