Family Symmetry and Neutrino Mixing

The observed quark hierarchies suggest a simple family symmetry. Generalized to leptons through grand-unified quantum numbers, it produces a neutrino mixing matrix with order-1 ν_μ-ν_τ mixing, and order- λ³ ν_e-ν_μ and ν_e-ν_τ mixings. The intrafamily hierarchy and observed neutrino mass differences together require this symmetry to be anomalous, suggesting through the Green-Schwarz mechanism a string or M-theory origin for the symmetry.