Possible LSND effect as a small perturbation of the bimaximal texture for three active neutrinos

Abstract

A particular form of mixing matrix for three active and one sterile neutrinos is proposed. Its $3\times 3 $ part describing three active neutrinos arises from the popular bimaximal mixing matrix that works satisfactorily in solar and atmospheric experiments if the LSND effect is ignored. Then, the sterile neutrino, effective in the fourth row and fourth column of the proposed mixing matrix, is responsible for the possible LSND effect by inducing one extra neutrino mass state to exist actively. The LSND effect, if it exists, turns out to reveal its {\it perturbative} nature related to small mixing of three active neutrinos with their sterile partner.