Neutrino anomalies and quasi Dirac neutrinos

We discuss the possibility of describing solar, atmospheric and LSND results with four neutrinos forming two quasidegenerate pairs. The simplest versions of this $2+2$ scheme with either ${\nu }_e$ or ${\nu }_{\mu }$ mixing exclusively with sterile neutrino are disfavored by the SNO and atmospheric neutrino results, respectively. A generalized scheme with sterile state participating in both the solar and atmospheric oscillations is still allowed. We show that the complex pattern of mixing needed for this purpose follows from a simple $L_e{+L}_{\mu }-L_{\tau }-L_s$ symmetry. The specific form of the $L_e{+L}_{\mu }-L_{\tau }-L_s$ symmetric mass matrix is determined from experimental results. Two theoretical schemes which lead to this form and a proper breaking of $L_e{+L}_{\mu }-L_{\tau }-L_s$ symmetry are discussed.