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 $X=\pm 1.$ 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 $X=\pm 1$ 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, ${\rm tg} β\sim { m_t \over m_b} (sin θ_c)^ 2$, where $θ_c$ is the Cabibbo angle.

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