Determining the mass for an ultralight gravitino at LHC

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. Recently we proposed a new determination of the gravitino mass by measuring a branching fraction of two decay modes of sleptons. In this paper, we investigate the prospects for determining the gravitino mass at LHC. For demonstration we take some explicit gauge-mediation models and show that the gravitino mass can be determined with an accuracy of a few 10% for an integrated luminosity 10-100 fb^{-1}.