Ultralight Gravitino at the LHC

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In supersymmetric (SUSY) models with the gravitino being the lightest SUSY particle (LSP), the SUSY breaking scale (i.e., the gravitino mass) could be determined by measuring the lifetime of the next-to-lightest SUSY particle (NLSP). However, for an ultralight gravitino of mass of O(1) eV, which is favored cosmologically, the determination of the SUSY breaking scale, or the gravitino mass, is difficult because the NLSP decay length is too short to be measured directly. We propose a new determination of the gravitino mass by measuring a branching fraction of two decay modes of sleptons, and demonstrate that the gravitino mass may indeed be determined at the LHC with an accuracy of a few 10% for an integrated luminosity 10-100 fb^{-1}. I will also mention dark matter candidates for such a light gravitino LSP.