Neutrino Oscillations Induced by Two-loop Radiative Mechanism

Two-loop radiative mechanism, when combined with an U(1)_{L'} symmetry generated by L_e-L_\mu-L_\tau (=L'), is shown to provide an estimate of \Delta m^2_{\odot}/\Delta m^2_{atm} $\sim$ \epsilon m_e/m_\tau, where \epsilon measures the U(1)_{L'}-breaking. Since \Delta m^2_{atm} $\sim 3.5x10^{-3} eV^2, we find that \Delta m^2_{\odot}$\sim$\epsilon x10^{-6} eV^2, which will fall into the allowed region of the LOW solution to the solar neutrino problem for \epsilon$\sim$ 0.1.