Gauge mediation with sequestered supersymmetry breaking

Gauge mediation models have two drawbacks, that is, the so-called μ problem and a lack of predictability of the gravitino dark matter abundance. We show that conformal sequestering in the supersymmetry breaking sector offers attractive solutions to both problems. The correct mass scale of the μ and Bμ terms is generated by taking the gravitino mass of O(100)GeV. This opens up a possibility that a neutralino, instead of gravitino, is the lightest supersymmetric particle and a candidate for dark matter, even in the gauge mediation. Surprisingly, a large anomalous dimension of the supersymmetry breaking field can naturally realize the small stau and neutralino mass difference required for the coannihilation to work yielding the right abundance of the neutralino dark matter.