Two-mixing texture for three active neutrinos

Abstract

The conjecture that among three massive neutrinos $ν_1, ν_2, ν_3$ there is no direct mixing between $ν_1$ and $ν_3$ leads to a two-mixing texture for three active neutrinos $ν_e, ν_μ, ν_τ$. This texture, much discussed previously, is neatly consistent with the observed deficits of solar $ν_e$&#39;s and atmospheric $ν_μ$&#39;s, but (without extra mixing with at least one sterile neutrino $ν_s$) predicts no LSND effect for accelerator $ν_μ$&#39;s. In this option, the masses $m^2_1\stackrel{<}{\sim} m^2_2 << m^2_3$ are readily estimated. The characteristic feature of the two-mixing neutrino texture that {\it only the close neighbours in the hierarchy of massive neutrinos $ν_1, ν_2, ν_3$ mix significantly} may be physically meaningful. Going out from the notion of mixing matrix we construct an intrinsic occupation-number operator whose {\it eigenvalues} 0, 1, 2 {\it numerate the three generations of massive neutrinos}. Analogical constructions work also for charged leptons as well as for up and down quarks.