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We present a solution to the gravitino problem, which arises in the NMSSM,allowing for sparticle spectra from ordinary gravity-mediated supersymmetrybreaking with weak-scale gravitino dark matter. The coupling, which links thesinglet to the MSSM sector, enhances the tree-level Higgs mass, providing anattractive explanation why the observed Higgs boson is so heavy. The samecoupling induces very efficient pair-annihilation processes of the neutralinoNLSP. Its relic abundance can be sufficiently suppressed to satisfy the strongconstraints on late decaying relics from primordial nucleosynthesis -- even forvery long neutralino lifetimes. The striking prediction of this scenario is thedetection of a pseudoscalar Higgs boson in the search for top-top resonances atLHC-14, rendering it completely testable.

NMSSM with Gravitino Dark Matter to be tested at LHC