General Aspects of Tree Level Gauge Mediation

Tree level gauge mediation (TGM) may be considered as the simplest way to communicate supersymmetry breaking: through the tree level renormalizable exchange of heavy gauge messengers. We study its general structure, in particular the general form of tree level sfermion masses and of one loop, but enhanced, gaugino masses. This allows us to set up general guidelines for model building and to identify the hypotheses underlying the phenomenological predictions. In the context of models based on the "minimal" gauge group SO(10), we show that only two "pure" embeddings of the MSSM fields are possible using $d< 120$ representations, each of them leading to specific predictions for the ratios of family universal sfermion masses at the GUT scale, $m^2_{\bar{5}} = 2 m^2_{10}$ or $m^2_{\bar{5}} = (3/4) m^2_{10}$ (in SU(5) notation). These ratios are determined by group factors and are peculiar enough to make this scheme testable at the LHC. We also discuss three possible approaches to the $\mu$-problem, one of them distinctive of TGM.