We investigate the unique potential of a high-energy muon collider to probe lepton-flavor-violating signals arising from physics beyond the Standard Model (SM). Low-energy, precision searches for charged lepton flavor violation (LFV) are projected to dramatically improve their sensitivity in the coming years and could provide the first evidence of new physics. We interpret the sensitivity of these searches in terms of a set of LFV operators in the SM effective field theory. The same operators are then probed at the TeV scale via new, high-energy processes only available at a high-energy muon collider, such as πβ’π βπβ’π or the scattering of a muon of an electroweak gauge boson into LFV final states. We find that, for most operators, a muon collider could confirm signals if they are seen at future low-energy experiments, whereas for certain flavor combinations it extends the reach to scales well beyond those accessible at lower energies. We also project the sensitivity of a muon collider to lepton-flavor-violating decays of the SM Higgs boson and demonstrate improved sensitivity to β βπβ’π and β βπβ’π by an order of magnitude compared to the High-Luminosity LHC. The importance of having multiple, complementary probes is illustrated by considering both various combinations of operators and relative sizes of flavor-violating transitions between generations under various assumptions for the flavor structure of new physics.
