The $\mu$-problem in theories with gauge-mediated supersymmetry breaking

We point out that the \mu-problem in theories in which supersymmetry breaking is communicated to the observable sector by gauge interactions is more severe than the one encountered in the conventional gravity-mediated scenarios. The difficulty is that once \mu is generated by a one-loop diagram, then usually \bmu is also generated at the same loop order. This leads to the problematic relation \bmu \sim \mu \Lambda, where \Lambda \sim 10--100 TeV is the effective supersymmetry-breaking scale. We present a class of theories for which this problem is naturally solved. Here, without any fine tuning among parameters, \mu is generated at one loop, while \bmu arises only at the two-loop level. This mechanism can naturally lead to an interpretation of the Higgs doublets as pseudo-Goldstone bosons of an approximate global symmetry.