Comment on Neutrino Masses and Oscillations in an $SU(3{)}_L\times U(1{)}_N$ Model with Radiative Mechanism

Abstract

We discussed how neutrino masses and oscillations are radiatively generated in an $SU(3{)}_L$ $\times$ $U(1{)}_N$ gauge model with a symmetry based on $L_e-L_{\mu }-L_{\tau }$ ($\equiv$$L^{\prime }$). The model is characterized by lepton triplets ${\psi }^i=({\nu }^i,{\ell }^{-i},E^{-i})$, where $E^{-i}$ are negatively charged heavy leptons, an $SU(3{)}_L$ triplet Higgs scalar $\xi$ and a singlet Higgs scalar $k^{++}$. These Higgs scalars can be interpreted as a Zee's and Zee-Babu's scalar for radiative mechanisms. We demonstrated that the mass hierarchy of $\Delta m_{atm}^2$ $\gg$ $\Delta m_{\odot }^2$ arise as a consequence of the dynamical hierarchy between $L^{\prime }$-conserving one-loop effects and $L^{\prime }$-violating two-loop effects, and our model is relevant to yield quasivacuum solution for solar neutrino problem.

Comments: 6 Pages, Latex2e, RevTex macro