Interesting radiative patterns of neutrino mass in an SU(3)_C X SU(3)_L X U(1)_X model with right-handed neutrinos

We investigate a simple model of neutrino mass based on SU(3)_C X SU(3)_L X U(1)_X gauge unification. The Yukawa coupling of the model has automatic lepton-number symmetry which is broken only by the self-couplings of the Higgs boson. At tree level, neutrino spectrum contains three Dirac fermions, one massless and two degenerate in mass. At the two loop-level, neutrinos obtain Majorana masses and correct the tree-level result which naturally gives rise to an inverted hierarchy mass pattern and interesting mixing which can fit the current data with minor fine-tuning. In another scenarios, one can pick the scales such that the loop-induced Majorana mass matrix is bigger than the Dirac one and thus reproduces the usual seesaw mechanism.