Texture dynamics for neutrinos

Abstract

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