Improving the Fine Tuning in Models of Low Energy Gauge Mediated Supersymmetry Breaking

The fine tuning in models of low energy gauge mediated supersymmetry breaking required to obtain the correct $Z$ mass is quantified. To alleviate the fine tuning problem, a model with split $(5+\bar{5})$ messenger fields is presented. This model has additional triplets in the low energy theory which get a mass of $O(500)$ GeV from a coupling to a singlet. The improvement in fine tuning is quantified and the spectrum in this model is discussed. The same model with the above singlet coupled to the Higgs doublets to generate the $\mu$ term is also discussed. A Grand Unified version of the model is constructed and a known doublet-triplet splitting mechanism is used to split the messenger $(5+\bar{5})$'s. A complete model is presented and some phenomenological constraints are discussed.