Yukawa matrices from a spontaneously broken abelian symmetry

We classify all the phenomenologically viable fermion mass matrices coming from a spontaneously broken abelian symmetry U(1)_X, with one and two additional chiral fields of opposite charges X = ±1. We find that the non-trivial Kähler metric can fill zeroes of the fermion mass matrices up to phenomenologically interesting values. A general anomaly analysis shows that for one additional chiral field the only way to achieve anomaly cancellation is by use of the Green-Schwarz mechanism. For two additional fields with X = ±1 and negative charge differences in the lepton sector the anomalies can however be directly put to zero. This case gives a unique prediction for the ratio of the two Higgs scalars of MSSM, tgβ∼ m_t m_b(sinθ_c)², where θ_c is the Cabibbo angle.