Texture dynamics for neutrinos

Abstract

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 $m_{\tau }^{exp}=1777.00_{-0.27}^{+0.30}$ MeV. Now it is applied to neutrinos. If the amplitude of neutrino oscillations ${\nu }_{\mu }\to {\nu }_{\tau }$ is $\sim 1/2$ and $|m_{{\nu }_{\tau }}^2-m_{{\nu }_{\mu }}^2|\sim (0.0003to0.01)e{V}^2$, as seems to follow from atmospheric-neutrino experiments, this ansatz predicts $m_{{\nu }_e}\ll m_{{\nu }_{\mu }}\sim (0.2to1)\times 10^{-2}$ eV and $m_{{\nu }_{\tau }}\sim (0.2to1)\times 10^{-1}eV$, and also the amplitude of neutrino oscillations ${\nu }_e\to {\nu }_{\mu }\sim 2_{-2}^{+4}\times 10^{-4}$ (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 $\hat{V}={\hat{U}}^{(\nu )†}{\hat{U}}^{(e)}$. Here, ${\hat{U}}^{(\nu )}$ by itself gives practically no oscillations ${\nu }_e\to {\nu }_{\mu }$, while it provides the large oscillations ${\nu }_{\mu }\to {\nu }_{\tau }$.

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