Gauge Unification, Yukawa Hierarchy and the $\mu$ Problem

Abstract

The hierarchy in the Yukawa couplings may be the result of a gauged horizontal $U(1{)}_H$ symmetry. If the mixed anomalies of the Standard Model gauge group with $U(1{)}_H$ are cancelled by a Green-Schwarz mechanism, a relation between the gauge couplings, the Yukawa couplings and the $\mu$-term arises. Assuming that at a high energy scale $g_3^2=g_2^2=\frac{5}{3}{g}_1^2$ and $(m_e{m}_{\mu }{m}_{\tau })/(m_d{m}_s{m}_b)\sim \lambda$ (where $\lambda$ is of the order of the Cabibbo angle), the $U(1{)}_H$ symmetry solves the $\mu$-problem with $\mu \sim \lambda m_{3/2}$.

Comments: 7 pages, harvmac