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 $L_e-L_{\mu }-L_{\tau }$ ($\equiv L^{\prime }$)-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 $\Delta m_{\odot }^2/\Delta m_{atm}^2\sim \epsilon m_e/m_{\tau }$ explains $\Delta m_{\odot }^2/\Delta m_{atm}^2\ll 1$ because of $m_e/m_{\tau }\ll 1$, where $\epsilon$ measures the breaking of the $L^{\prime }$-conservation. Together with $\Delta m_{atm}^2\approx 3\times 10^{-3}$ eV${}^2$, this estimate yields $\Delta m_{\odot }^2\sim 10^{-7}$ eV${}^2$ for $\epsilon \sim 0.1$, which corresponds to the LOW solution to the solar neutrino problem. Neutrino mass scale is given by $(16{\pi }^2{)}^{-2}{m}_e{m}_{\tau }/M$ ($M\sim$ 1 TeV), which is of order 0.01 eV.

10 pages,6 figures,Talk given at the Post Summer Institute 2000 on Neutrino Physics, August 21-24, 2000, Fuji-Yoshida, Yamanashi, Japan