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

TL;DR

The paper proposes a SMEFT-based study of CP violation in the electroweak sector at multi-TeV muon colliders using vector-boson fusion processes. It introduces CP-odd observables constructed from final-state kinematics, employs full detector-level simulations, and derives 95% CL limits on CP-odd dimension-six Wilson coefficients by a binned, two-bin likelihood in the observable $\epsilon$. The results show that at $\sqrt{s}=3$ TeV with $\mathcal{L}=2$ ab$^{-1}$, $C_{\widetilde{W}}/\Lambda^2$ can be constrained to $\mathcal{O}(0.02)$, improving to $\mathcal{O}(0.003)$ at $\sqrt{s}=10$ TeV with $\mathcal{L}=10$ ab$^{-1}$; $C_{H\widetilde{W}B}$, $C_{H\widetilde{W}}$, and $C_{H\widetilde{B}}$ receive complementary bounds. Compared with current LHC/ILC limits and EDM constraints, the high-energy muon collider provides substantially stronger, direct, model-independent probes of CP violation in the electroweak sector, highlighting its unique capability to disentangle multiple CP-odd operators via VBF kinematics.

Abstract

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.

Figures (2)

• Figure 1: Representative Feynman diagrams for W-boson (left) and Higgs-boson (right) production via vector boson fusion (VBF). The red dots mark the vertices induced by CP-odd operators.
• Figure 2: Normalized distributions of the CP-odd observable $\epsilon$ for (a) $\mu^+\mu^-\!\to \mu^\mp \nu W^\pm$ and (b) $\mu^+\mu^-\!\to \mu^+\mu^-h$. The SM expectation is symmetric, while CP-odd operators induce clear asymmetries.