A study of late decaying charged particles at future colliders

In models where the gravitino is the lightest supersymmetric particle (LSP), the next-to-lightest supersymmetric particle (NLSP) is long-lived. We consider an important charged NLSP candidate, the scalar tau $\tilde{\tau}$. Slow charged NLSPs may be produced at future colliders and they may be stopped in a massive stopper which simultaneously serves as a detector for the NLSP and its decay products. We found the number of events at a 1 kton to O(10) kton detector could be significant enough to study the NLSP decays with lifetime shorter than $10^{10}$ sec at the LHC. The performance of existing 1 kton detectors may be good enough to do such studies at the LHC, if they can be placed close to the ATLAS/CMS detectors. At a future $e^- e^-$ collider, scalar electrons $\tilde{e}^-$s are copiously produced. Slow NLSPs may be produced from the $\tilde{e}^-$ decay. The number of stopped NLSPs at a future linear collider could be large enough to study rare decay modes of the NLSP.