The $μ$-Problem in Theories with Gauge-Mediated Supersymmetry Breaking

Abstract

We point out that the $μ$-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 $μ$ is generated by a one-loop diagram, then usually $\bmu$ is also generated at the same loop order. This leads to the problematic relation $\bmu \sim μΛ$, where $Λ\sim$ 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, $μ$ 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.