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Light Higgsino in Heavy Gravitino Scenario with Successful Electroweak Symmetry Breaking

We consider, in the context of the minimal supersymmetric standard model, the case where the gravitino weighs 10^6 GeV or more, which is preferred by various cosmological difficulties associated with unstable gravitinos. Despite the large Higgs mixing parameter B together with the little hierarchy to other soft supersymmetry breaking masses, a light higgsino with an electroweak scale mass leads to successful electroweak symmetry breaking, at the price of fine-tuning the higgsino mixing mu parameter. Furthermore the light higgsinos produced at the decays of gravitinos can constitute the dark matter of the universe. The heavy squark mass spectrum of O(10^4) GeV can increase the Higgs boson mass to about 125 GeV or higher.