Can one of three righthanded neutrinos be light enough to produce a small LSND effect?

Abstract

It is shown on the ground of a simple 6\times 6 neutrino mixing model that one of three conventional sterile (righthanded) neutrinos, if light enough, may be consistently used for explaining a {\it small} LSND effect. Then, it is still considerably heavier than the three active (lefhanded) neutrinos, so that a kind of {\it soft} seesaw mechanism can work. The usual condition that the Majorana lefthanded component of the overall 6\times 6 neutrino mass matrix ought to vanish, {\it implies} the smallness of active-neutrino masses versus sterile-neutrino masses, when three mixing angles between both sorts of neutrinos are small. In the presented model, the mass spectrum of active neutrinos comes out roughly degenerate, lying in the range (5 - 7.5)\times 10^{-2} eV, {\it if} there is a {\it small} LSND effect with the amplitude of the order 10^{-3} and with the mass-squared splitting \sim 1 eV^2.