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Large tan beta in Gauge-Mediated SUSY-Breaking Models

We explore some topics in the phenomenology of gauge-mediated SUSY-breaking scenarios having a large hierarchy of Higgs VEVs, $v_U/v_D = tanβ\gg 1$. Some motivation for this scenario is first presented. We then use a systematic, analytic expansion (including some threshold corrections) to calculate the $μ$ parameter needed for proper electroweak breaking and the radiative corrections to the B parameter, which fortuitously cancel at leading order. If B = 0 at the messenger scale then $tanβ$ is naturally large and calculable; we calculate it. We then confront this prediction with classical and quantum vacuum stability constraints arising from the Higgs-slepton potential, and indicate the preferred values of the top quark mass and messenger scale(s). The possibility of vacuum instability in a different direction yields an upper bound on the messenger mass scale complementary to the familiar bound from gravitino relic abundance. Next, we calculate the rate for $b\to sγ$ and show the possibility of large deviations (in the direction currently favored by experiment) from standard-model and small $tanβ$ predictions. Finally, we discuss the implications of these findings and their applicability to future, broader and more detailed investigations.