Texture dynamics for neutrinos

An ansatz for mass matrix was recently proposed for charged leptons, predicting (in its diagonal approximation) $m_{\tau }\simeq 1776.80$ 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 $\sim 1\mathrm{/}2$ and $\mathrm{\mid }{m}_{{\nu }_{\tau }}^2-m_{{\nu }_{\mu }}^2\mathrm{\mid }\sim (0.0003to0.01)e{V}^2$, 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} $eVand$m_{\nu_\tau}\sim(0.2 to 1)\times 10^{-1} eV$,andalsotheamplitudeofneutrinooscillations$\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 $MeVusedtodeterminethedeviationofthediagonalizingmatrix$\hat{U}^{(e)}$from$\hat{1}$intheleptonCabibbo-Kobayashi-Maskawamatrix$\hat{V} = \hat{U}^{(\nu) \dagger}\hat{U}^{(e)}$\mathrm{.}Here,$\hat{U}^{(\nu)}$ by itself gives practically no oscillations ${\nu }_e\to {\nu }_{\mu }$, while it provides the large oscillations ${\nu }_{\mu }\to {\nu }_{\tau }$.