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 νs, presumed to mix mainly with νe, while ντ mixes strongly with νμ (and both νμ and ντ weakly with νe and νs). 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 νs 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 Cabibbo—Kobayashi—Maskawa matrix V = U (ν) †U (e) is determined through the small deviation of our previous prediction mτ = 1776.80 MeV (valid at the level of U (e) = 1) from the experimental valuemτ = 1777.00 +0.30 −0.27 MeV. Then, it gives corrections to the four–dimensional mixing of νe, νμ, ντ , νs leading, in particular, to small νe → νμ, νe → ντ and νμ → νs oscillations (absent at the level of U (e) = 1). However, the LSND estimates of ν̄μ → ν̄e and νμ → νe oscillations are too large to be explained by these corrections, though in the case of νμ → νe they seem to be at the edge of such possible explanation. PACS numbers: 12.15.Ff , 12.90.+b March 1998 Work supported in part by the Polish KBN–Grant 2–B302–143–06.