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Texture dynamics including potential sterile neutrino

A unified form of mass matrix proposed previously for all fundamental fermions is extended to include the sterile neutrino $ν_s$, presumed to mix mainly with $ν_e$, while $ν_τ$ mixes strongly with $ν_μ$ (and both $ν_μ$ and $ν_τ$ weakly with $ν_e$ and $ν_s$). It turns out that the former mixing can be responsible for oscillations of solar neutrinos, while the latter for those of atmospheric neutrinos. It is mentioned in a footnote that $ν_s$ is one of two sterile neutrinos, possible from a viewpoint of an algebraic construction. The charged-lepton factor $U^{(e)}$ in the leptonic four-dimensional CKM matrix $V=U^{(ν) \dagger}U^{(e)}$ is determined through the small deviation of our previous prediction $m_τ=1776.80$ MeV (valid at the level of $ U^{(e)} = {\bf 1}$) from the experimental value $m_τ=1777.00^{+0.30}_{-0.27}$ MeV. Then, it gives corrections to the four-dimensional mixing of $ν_e$, $ν_μ$, $ν_τ$, $ν_s$ leading, in particular, to small $ν_e\toν_μ$, $ν_e\to ν_τ$ and $ν_μ\toν_s$ oscillations (absent at the level of $U^{(e)}= 1$). However, the LSND estimates of $\barν_μ\to \barν_e$ and $ν_μ\toν_e$ oscillations are too large to be explained by these corrections, though in the case of $ν_μ\toν_e$ they seem to be at the edge of such possible explanation.