Lepton flavor violation induced by neutral and doubly-charged scalars at future lepton colliders

New physics scenarios beyond the Standard Model (SM) for neutrino mass mechanism often necessitate the existence of a neutral scalar $H$ and/or doubly-charged scalar $H^{\pm \pm }$, which couple to the SM charged leptons in a flavor violating way, while evading all existing constraints. Such scalars could be effectively produced at future lepton colliders like CEPC, ILC, FCC-ee and CLIC, either on-shell or off-shell, and induce striking charged lepton flavor violating (LFV) signals. We find that a large parameter space of the scalar masses and the LFV couplings can be probed at lepton colliders, well beyond the current low-energy constraints in the lepton sector. The neutral scalar explanation of the muon $g-2$ anomaly could also be directly tested.