Prospects to study a long-lived charged next lightest supersymmetric particle at the LHC

If the scalar tau $\stau$ is the next lightest supersymmetric particle and decays into a gravitino ($\gravitino$) being the lightest supersymmetric particle, it will have generally a very long lifetime. In this paper, we investigate the possibility to study the decay of such a long lived scalar tau at the LHC. If we can add to the present LHC experiments additional detectors which are able to stop the stau particles and measure the produced decay products, the decay characteristics can be studied precisely at the LHC. We identify a maximum "stopper detector" that could be added in the CMS cavern, and estimate the sensitivity to the lifetime of the stau and to the mass of gravitino with this detector. The decay of the scalar tau may be significantly modified if the decay channel to the axino $\axino$ is open. We study the possibility to distinguish such decays from decays into gravitinos by measuring the process $\stau\to \axino (\gravitino) \tau \gamma$ using the stopper detector.