The $\mu$-Problem in Theories with Gauge-Mediated Supersymmetry Breaking

Abstract

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 $\text{bmu}$ is also generated at the same loop order. This leads to the problematic relation $\text{bmu}\sim \mu \Lambda$, 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 $\text{bmu}$ 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.

Comments: 18 pages, 2 figures