Non anomalous U(1)_H gauge model of flavor

Abstract

A non anomalous horizontal $U(1{)}_H$ gauge symmetry can be responsible for the fermion mass hierarchies of the minimal supersymmetric standard model. Imposing the consistency conditions for the absence of gauge anomalies yields the following results: i) unification of leptons and down-type quarks Yukawa couplings is allowed at most for two generations. ii) The $\mu$ term is necessarily somewhat below the supersymmetry breaking scale. iii) The determinant of the quark mass matrix vanishes, and there is no strong $CP$ problem. iv) The superpotential has accidental $B$ and $L$ symmetries. The prediction $m_{\mathrm{up}}=0$ allows for an unambiguous test of the model at low energy.

Comments: 5 pages, RevTex. Title changed, minor modifications. Final version to appear in Phys. Rev. D