Family Symmetry and Neutrino Mixing

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Abstract
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-one \nu_{\mu} - \nu_{\tau} mixing, and order-\lambda^3 \nu_e - \nu_{\mu} and \nu_e - \nu_{\tau} 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.

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