A Model of Yukawa Hierarchies

Abstract

We present a model for the observed hierarchies among the Yukawa couplings of the standard model in the context of an effective low energy 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 $si{n}^2{\theta }_w=3/8$ 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 $\sim 1$ meV, and mixing of the order of ${\lambda }_c^3$ with each of the other two neutrinos.

15 pages, no figures, LaTex. Revised version, containing minor typographical corrections, as well as a substantial revision of the final three paragraphs of the text. Submitted to Physics Letters B

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