Fermion masses from symmetry

We present a model with continuous or discrete abelian generation group G, which predicts all orders of magnitude for fermion masses and mixings correctly as a function of only one small parameter ΦS/M≅1/10. Here ΦS is the scale of G symmetry breaking and M the fundamental mass scale of the theory. No small Yukawa couplings for special choices of the scalar potential are needed. We perform a systematic computerized scan for similar models with abelian generation group and we find a few other examples. However, for a wide range of charges we find no anomaly free continuous symmetry and also none without mixed SU(3)xSU(2)xU(1),U(1)G anomalies consistent with realistic fermion masses if G is broken by one field with definite charge. We also scan a class of models with generation symmetry derived from a higher dimensional framework. (orig.)