Muon Anomalous Magnetic Moment and Lepton Flavor Violation

A non-universal interaction, which involves only the third family leptons induces lepton flavor violating couplings and contributes to the anomalous magnetic moment of muon. In this paper, we study the effects of non-universal interaction on muon (g-2) and rare decay $\tau \to \mu \gamma$ by using an effective lagrangian technique, and as an example considering a phenomenological $Z^\prime$ model where $Z^\prime$ couples only to the third family lepton. We find that the deviation from the theory can be explained and the induced $\tau \to \mu \gamma$ rate is very close to the current experimental limit, in model with $Z^\prime$ its mass has to be lighter than 2.6 TeV.