Exploring Supersymmetric Model with Very Light Gravitino at the LHC

The low-scale gauge mediation scenario of supersymmetry breaking predicts very light gravitino, which makes the next lightest supersymmetric particle (NLSP) quasi stable. We study the LHC phenomenology of the case that the NLSP is the stau. When the mass of the gravitino is of the order of 10eV, the decay length of stau is about 0.1--1 mm, so that it decays before reaching the first layer of the inner silicon detector. We show, however, that, with utilizing the impact parameter of tau-jets from the stau decay, it is possible to determine the mass spectrum of sparticles precisely. It is also possible to estimate the lifetime of the stau by observing distribution of the impact parameter.