Neutrino Oscillations Induced by Two-loop Radiative Effects

Abstract

Phenomena of neutrino oscillations are discussed on the basis of two-loop radiative neutrino mechanism. Neutrino mixings are experimentally suggested to be maximal in both atmospheric and solar neutrino oscillations. By using $L_e - L_μ- L_τ$ ($\equiv L^\prime$)-conservation, which, however, only ensures the maximal solar neutrino mixing, we find that two-loop radiative mechanism dynamically generates the maximal atmospheric neutrino mixing and that the estimate of $Δm^2_\odot/Δm^2_{atm} \simεm_e/m_τ$ explains $Δm^2_\odot/Δm^2_{atm} \ll 1$ because of $m_e/m_τ\ll 1$, where $ε$ measures the breaking of the $L^\prime$-conservation. Together with $Δm^2_{atm} \approx 3\times 10^{-3}$ eV$^2$, this estimate yields $Δm^2_\odot \sim 10^{-7}$ eV$^2$ for $ε\sim 0.1$, which corresponds to the LOW solution to the solar neutrino problem. Neutrino mass scale is given by $(16π^2)^{-2} m_em_τ/M$ ($M \sim$ 1 TeV), which is of order 0.01 eV.