Production of long-lived staus in the Drell-Yan process

We investigate the phenomenology of the gravitino dark matter scenario with a stau as the next-to-lightest supersymmetric particle at the LHC. For a wide range of gravitino masses the lighter stau is stable on the scale of a detector and gives rise to a prominent signature as a "slow muon". The direct stau production via the Drell-Yan process is always present and independent of the mass spectrum of the other superparticles, thus providing a lower bound for the discovery potential of this scenario. Performing a careful analysis with particular emphasis on the criteria for observing stau pairs and for distinguishing them from the background, we find that the 14 TeV run of the LHC has a promising potential for finding long-lived staus from Drell-Yan production up to very large stau masses.