Gauge Unification, Yukawa Hierarchy and the $μ$ 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 $μ$-term arises. Assuming that at a high energy scale $g_3^2=g_2^2={5\over3}g_1^2$ and $(m_e m_μm_τ)/(m_d m_s m_b)\sim λ$ (where $λ$ is of the order of the Cabibbo angle), the $U(1)_H$ symmetry solves the $μ$-problem with $μ\simλm_{3/2}$.