Zee and Zee-Babu mechanisms in the minimal 331 model

We show that the minimal 3-3-1 model cannot accommodate the neutrino masses at tree level using present experimental data. Nevertheless, a modified Zee and the Zee-Babu mechanisms for generating neutrino masses at 1-loop and 2-loop, respectively, are automatically implemented in the minimal 3-3-1 model, without introducing new degrees of freedom to the model. We also present a systematic method for finding solutions to the leptonic sector masses and mixing. As a case study, we accommodate the charged and neutral leptons masses and the PMNS matrix in the 1-loop modified Zee mechanism contained in the minimal 3-3-1 model.