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We show that the minimal 3-3-1 model cannot accommodate the neutrino massesat tree level using present experimental data. Nevertheless, a modified Zee andthe Zee-Babu mechanisms for generating neutrino masses at 1-loop and 2-loop,respectively, are automatically implemented in the minimal 3-3-1 model, withoutintroducing new degrees of freedom to the model. We also present a systematicmethod for finding solutions to the leptonic sector masses and mixing. As acase study, we accommodate the charged and neutral leptons masses and the PMNSmatrix in the 1-loop modified Zee mechanism contained in the minimal 3-3-1model.

Zee and Zee-Babu mechanisms in the minimal 331 model