Yukawa matrices from a spontaneously broken abelian symmetry

Abstract

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, $\mathrm{tg}\beta \sim \frac{m_t}{m_b}(sin{\theta }_c{)}^2$, where ${\theta }_c$ is the Cabibbo angle.

Comments: 16 pages, tex, no figures