Semi-Direct Gauge Mediation with the 4-1 Model

We analyze a model of Semi-Direct Gauge Mediation in which the hidden sector is the 4-1 model and the messenger fields are charged under the U(1) gauge group. At tree level, the SUSY-breaking F-terms induce D-terms from which SUSY-split messenger masses arise. We calculate these masses by three complementary methods. Additionally, we compute the one-loop corrections to the masses. We consider this model both with and without a Fayet-Iliopoulos term for the hidden sector U(1). Finally, we write down a simple model of Minimal Gauge Mediation in which the only scale is dynamically generated.