Texture dynamics for neutrinos

Abstract

An ansatz for mass matrix was recently proposed for charged leptons, predicting (in its diagonal approximation) $m_\tau\simeq1776.80$ MeV from the experimental values of $m_e$ and $m_\mu$, in agreement with $m_\tau^{exp}= 1777.00^{+0.30}_{-0.27}$ MeV. Now it is applied to neutrinos. If the amplitude of neutrino oscillations $\nu_\mu\to\nu_\tau$ is $\sim 1/2$ and $|m^2_{\nu_\tau}-m^2_{\nu_\mu}|\sim(0.0003 to 0.01) eV^2$, as seems to follow from atmospheric-neutrino experiments, this ansatz predicts $m_{\nu_e}\ll m_{\nu_\mu}\sim(0.2 to 1)\times 10^{-2} $ eV and $m_{\nu_\tau}\sim(0.2 to 1)\times 10^{-1} eV$, and also the amplitude of neutrino oscillations $\nu_e \to \nu_\mu \sim 2^{+4}_{-2}\times 10^{-4}$ (in the vacuum). Such a very small amplitude for $\nu_e \to \nu_\mu $ is implied by the value of $ m_\tau^{exp} - 1776.80 $ MeV used to determine the deviation of the diagonalizing matrix $\hat{U}^{(e)}$ from $\hat{1}$ in the lepton Cabibbo-Kobayashi- Maskawa matrix $\hat{V} = \hat{U}^{(\nu) \dagger}\hat{U}^{(e)}$. Here, $\hat{U}^{(\nu)}$ by itself gives practically no oscillations $\nu_e \to\nu_\mu$, while it provides the large oscillations $\nu_\mu \to\nu_\tau$.