Minimal seesaw model for atmospheric and solar neutrino oscillations

We present a minimal seesaw model based on an extension of the standard model (SM) which includes an additional U(1), with gauge charge $B-\frac{3}{2}{(L}_{\mu }{+L}_{\tau })$. The requirement of anomaly cancellation implies the existence of two right-handed singlet neutrinos, carrying this gauge charge, which have normal Dirac couplings to ${\nu }_{\mu }$ and ${\nu }_{\tau }$ but suppressed ones to ${\nu }_e.$ Assuming the U(1) symmetry breaking scale to be ${10}^{12}-{10}^{16}$ GeV, this model can naturally account for the large (small) mixing solutions to the atmospheric (solar) neutrino oscillations.