A model of Yukawa hierarchies

We present a model for the observed hierarchies among the Yukawa couplings of the standard model in the context of an effective low enegy theory with an anomalous U(1) symmetry. This symmetry, a generic feature of superstring compactification, is a remnant of the Green-Schwarz anomaly cancellation mechanism. The gauge group is that of the standard model, augmented by X, the anomalous U(1), and two family-dependent phase symmetries Y(1) and Y(2). The correct hierarchies are reproduced only when sin2θw = 38 at the cut-off. To cancel anomalies, right-handed neutrinos and other standard model singlets must be introduced. Independently of the charges of the right-handed neutrinos, this model produces the same neutrino mixing matrix and an inverted hierarchy of neutrino masses. The heaviest is the electron neutrino with a mass ∼ 1 meV, and mixing of the order of λc3 with each of the other two neutrinos.