Zee Model with Flavor Dependent Global $U(1)$ Symmetry

We study a simple extension of the Zee model, in which a discrete $Z_2$ symmetry imposed in the original model is replaced by a global $U(1)$ symmetry retaining the same particle content. Due to the $U(1)$ symmetry with flavor dependent charge assignments, the lepton sector has an additional source of flavor violating Yukawa interactions with a controllable structure, while the quark sector does not at tree level. We show that current neutrino oscillation data can be explained under constraints from lepton flavor violating decays of charged leptons in a successful charge assignment of the $U(1)$ symmetry. In such scenario, we find a characteristic pattern of lepton flavor violating decays of additional Higgs bosons, which can be a smoking gun signature at collider experiments.