Solving the mu problem in gauge mediated supersymmetry breaking models with flavor symmetry

Abstract

We suggest a solution to the \mu problem of gauge mediated supersymmtery breaking models based on flavor symmetries. In this scenario the \mu term arises through the vacuum expectation value of a singlet scalar field which is suppressed by a flavor symmetry factor relative to the scale of dynamical SUSY breaking. The same flavor symmetry also ensures that the soft SUSY breaking parameter B\mu is not much larger than \mu^2, a necessary condition for the stability of electroweak symmetry breaking. Explicit examples where B\mu ~ \mu^2 and B\mu << \mu^2 are presented. The latter case provides a natural solution to the supersymmetric CP problem. We show that the same flavor symmetry that suppresses the \mu and the B\mu parameters can also play a role in explaining the fermion mass and mixing hierarchy puzzle.