Are there two sterile neutrinos cooscillating with $ν_e$ and $ν_μ$?

Abstract

The existence of two sterile neutrinos $ν_s$ and $ν'_s$ (blind to all Standard-Model interactions) is shown to be implied by a model of fermion "texture" that we develop since some time. They may mix nearly maximally with two of three conventional neutrinos, say $ν_e$ and $ν_μ$, thus leading to neutrino oscillations, say $ν_e \to ν_s$ and $ν_μ\to ν'_s$, with nearly maximal amplitudes. Then, they can be responsible for the observed deficits of solar $ν_e$'s and atmospheric $ν_μ$'s, respectiv% ely, but by themselves do not help to explain the LSND results for $ν_μ\to ν_e$ oscillations. On the other hand, they are consistent with the CHOOZ negative result. At the moment, the experiment cannot decide, whether the deficit of atmospheric $ν_μ$'s, confirmed by the recent \SK findings, has to be related to the oscillations $ν_μ\to ν_τ$ or $ν_μ\to ν'_s$. In the last Section of the paper, a new notion of "non-Abelian spin-1/2 fermions" is presented in the context of a composite option for fermion families.