Probing Lepton-Flavor-Violating Four-Lepton Operators at a Muon Collider

Abstract

We investigate charged lepton-flavour violation (LFV) induced by dimension-six four-lepton operators within the Standard Model Effective Field Theory at a proposed high-energy muon collider. We study the processes $\hat{I}{¼}^{+}\hat{I}{¼}^{-}\to e^{\pm }\ddot{I}{„}^{\mp }$, $\hat{I}{¼}^{+}\hat{I}{¼}^{-}\to e^{\pm }\hat{I}{¼}^{\mp }$, and $\hat{I}{¼}^{+}\hat{I}{¼}^{-}\to \hat{I}{¼}^{\pm }\ddot{I}{„}^{\mp }$ at $\sqrt{s}=3$, $10$, and $14$~TeV, incorporating beam polarisation and hadronic $\ddot{I}„$ reconstruction. Using an optimal-observable analysis of the angular distributions, we perform a global fit to the relevant set of four-lepton operators. Projected sensitivities reach $C/\hat{I}{›}^2\sim (0.6$-$1.6)\times 10^{-11}{\mathrm{GeV}}^{-2}$, depending on the flavour and chiral structure of the operator, exceeding current limits by up to an order of magnitude. A combined analysis of multiple centre-of-mass energies and beam polarisations significantly improves the resolution of correlations among the Wilson coefficients. These results highlight the strong sensitivity of a future multi-TeV muon collider to charged lepton flavour violating four-lepton interactions, establishing it as a powerful probe of the SMEFT parameter space.

19 pages, 8 figures, 5 Tables