Probing CP Violation through Vector Boson Fusion at High-Energy Muon Colliders

We investigate CP-violating effects in electroweak interactions at future high-energy muon colliders within the Standard Model Effective Field Theory (SMEFT) framework. Focusing on four dimension-six CP-odd operators -- $\mathcal{O}_{\widetilde{W}}, \mathcal{O}_{H\widetilde{W}}, \mathcal{O}_{H\widetilde{W}B}, \mathcal{O}_{H\widetilde{B}}$ -- we analyze vector boson fusion production of $W$ and Higgs bosons using CP-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 $\sqrt{s} = 3$ TeV with 2 ab$^{-1}$, the coefficient $C_{\widetilde{W}}$ can be constrained at the $\mathcal{O}(0.02)$ level, improving to $\mathcal{O}(0.008)$ at 10 TeV with 2 ab$^{-1}$, and $\mathcal{O}(0.003)$ with 10 ab$^{-1}$. These results significantly surpass current LHC and projected ILC sensitivities, demonstrating the unique potential of high-energy muon colliders to provide direct and model-independent probes of CP violation in the electroweak sector.