Lepton Flavor Violation with Displaced Vertices

If light new physics with lepton-flavor-violating couplings exists, the prime discovery channel might not be $\mathrm{\ell }\to {\mathrm{\ell }}^{\mathrm{\prime }}\gamma$ but rather $\ell\to\ell’ X$,wherethenewboson$X$ could be an axion, majoron, familon or Z’ gauge boson. The most conservative bound then comes from $\mathrm{\ell }\to {\mathrm{\ell }}^{\mathrm{\prime }}+\mathrm{i}\mathrm{n}\mathrm{v}$, but if the on-shell $X$ can decay back into leptons or photons, displaced-vertex searches could give much better limits. We show that only a narrow region in parameter space allows for displaced vertices in muon decays, $\mu \to eX,X\to \gamma \gamma ,ee$, whereas tauon decays can have much more interesting signatures.