Natural gauge mediation with a bino next-to-lightest supersymmetric particle at the LHC

Natural models of supersymmetry with a gravitino lightest supersymmetric particle provide distinctive signatures at the LHC. For a neutralino next-to-lightest supersymmetric particle, sparticles can decay to two high energy photons plus missing energy. We use the ATLAS diphoton search with 4.8 fb^-1 of data to place limits in both the top-squark-gluino and neutralino-chargino mass planes for this scenario. If the neutralino is heavier than 50 GeV, the lightest top squark must be heavier than 580GeV, the gluino must be heavier than 1100GeV, and charginos must be heavier than approximately 300-470GeV. This provides the first nontrivial constraints in natural gauge mediation models with a neutralino next-to-lightest supersymmetric particle decaying to photons and implies a fine-tuning of at least a few percent in such models.