Prediction of LSND effect as a ”sterile” perturbation of the bimaximal texture for three active neutrinos∗

As a contribution to the hypothesis of mixing of three active neutrinos with, at least, one sterile neutrino, we report on a simple 4× 4 texture whose 3× 3 part arises from the popular bimaximal texture for three active neutrinos νe , νμ , ντ , where c12 = 1/ √ 2 = s12, c23 = 1/ √ 2 = s23 and s13 = 0. Such a 3 × 3 bimaximal texture is perturbed through a rotation in the 14 plane, where ν4 is the extra neutrino mass state induced by the sterile neutrino νs which becomes responsible for the LSND effect. Then, with m 2 1 ≃ m2 we predict that sin 2θatm = 1 2 (1 + c14) ∼ 0.95 and sin 2θLSND = 1 2s414 ∼ 5 × 10, and in addition ∆matm = ∆m 2 32 and ∆m 2 LSND = |∆m41|, where c14 = sin 2θsol ∼ 0.9 and ∆m21 = ∆m 2 sol ∼ 10 eV if e.g. the LOW solar solution is applied. PACS numbers: 12.15.Ff , 14.60.Pq , 12.15.Hh .