Long-Lived Unstable Superparticles at the LHC

In various models of supersymmetry (SUSY), the lightest superparticle in the minimal SUSY standard model sector, which we call MSSM-LSP, becomes unstable. Then, we may observe the decay of the MSSM-LSP in the detector at the LHC experiment. We show that the discovery of such a decay process (and the determination of the lifetime of the MSSM-LSP) may be possible at the LHC even if the decay length of the MSSM-LSP is much longer than the size of the detector; sizable number of the MSSM-LSPs decay inside the detector if the lifetime is shorter than 0.01-1 millisec. We also discuss the implications of the study of the MSSM-LSP decay for several well-motivated SUSY models.