A nonconventionalU(1)e?μgauge model is proposed to explain the observed neutrino masses and the unexpected anomalous magnetic moments of the electron and muon (leptong?2), where for suppressing the neutrino coupling toZ′gauge boson, only the right-handed electron and muon in the standard model carry theU(1)e?μcharge. Although the light lepton masses are suppressed when the gauge symmetry is spontaneously broken, they can be generated through the Yukawa couplings to newly introduced particles, such as vector-like lepton doublets and singlets, and scalar singlets. It is found that the same Yukawa couplings combined with the new scalar couplings to the Higgs can induce the radiative lepton-flavor violation processes?′→?γand leptong?2, where the leptong?2is proportional tom?. When Majorana fermions and a scalar singlet are further added into the model, the active neutrinos can obtain masses via the radiative seesaw mechanism. When the bounds from themeandmμand the neutrino data are satisfied, we find that the electrong?2can reach an order of?10?12, and the muong?2can be an order of10?9. In addition, when theμ→eγdecay is suppressed, the resulting branching ratio forτ→eγcan be ofO(10?8), and that forτ→μγcan be as large as the current upper limit.
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