Off-diagonal structure of the neutrino mass matrix in the seesaw mechanism and electron-muon-tau lepton universality

By a simple extension of the standard model in which $\left(e-\mu -\tau \right)$ universality is not conserved, we present a scenario within the framework of the seesaw mechanism in which the neutrino mass matrix is strictly off diagonal in the flavor basis. We show that a version of this scenario can accommodate the small angle Mikheyev-Smirnov-Wolfenstein (MSW) solution of the solar neutrino problem and ${\nu }_{\mu }-{\nu }_e$ oscillations claimed by the LSND Collaboration. Another version accommodates atmospheric ${\nu }_{\mu }-{\nu }_{\tau }$ oscillations and the large angle solution in solar neutrino experiments.