Probing lepton flavour violation in slepton nslp decays

In this talk we discuss the prospects of probing lepton flavour violation in future experiments, in scenarios where the gravitino is the lightest supersymmetric particle. In this class of scenarios, different cosmological and theoretical considerations point to the possibility that the next-to-lightest supersymmetric particle (NLSP) is a right-handed stau. Since the NLSP can only decay gravitationally into gravitinos, their lifetimes could be very large. If this is the case, the NLSP would decay outside the detector, or could even be trapped in the walls of the detector for a long time. These features have interesting consequences for the search of lepton flavour violation, that are discussed here.