Flavor Violating Lepton Family U(1)$_\lambda$

Abstract

The Standard Model is extended minimally with a new flavor-violating family symmetry ${\rm U(1)}_\lambda$, which acts only on leptons including the right-handed neutrinos. The model is anomaly free with family-dependent ${\rm U(1)}_\lambda$ charges, and consistent with the observed neutrino mixing angles. It predicts charged lepton flavor-violating processes mediated by a new gauge boson. Under certain conditions, the smallness of $\theta_{13}$ of neutrino mixing can be justified in terms of the muon-to-tau mass ratio, at the same time explaining the electron-to-tau large mass hierarchy.