Lepton Flavor Violation and Local Lepton Number

Abstract

We investigate the predictions for lepton number violating processes within the minimal theory of neutrino masses based on the spontaneous breaking of local lepton number. In this framework, the symmetry is broken at the low scale, leading to the existence of a viable dark matter candidate. The new fermions required for anomaly cancellation mediate lepton number violating processes at the one-loop level. We present a detailed calculation of the most relevant processes, including $\mu \to e \gamma$, $\mu \to 3 e$, and $\mu \to e$ conversion in nuclei. The regions of parameter space excluded by current experimental bounds are identified, and we emphasize the interplay between collider observables and charged lepton flavor violating signatures as a key test of this minimal theory of neutrino masses.