A minimal three generation seesaw scenario for LSND

We show that in the minimal three generation seesaw models for neutrinos, the presence of leptonic $(L_e+L_{\mu}-L_{\tau})\times S_2$ symmetry leads to one of the right handed neutrinos remaining massless. This state can then be identified with the sterile neutrino required for a simultaneous understanding of solar, atmospheric and LSND observations. We present a gauge model where the presence of higher dimensional operators originating from Planck scale physics lead to a realistic 2+2 mixed scenario that fits all oscillation data. The model predicts a range for the mixing angle $U_{e3}$ and an effective mass for neutrinos emitted in tritium decay, which can be used to test this model.