Susy Model with R-parity Violation, Longlived Charged Slepton and Quasistable Supermatter

We construct two SUSY SU (3) ⊗ SU (2) L ⊗ U (1) electroweak models with su-perweak R-parity violation. The scale of R-parity violation in one of the models is determined by the Majorana mass of neutrino and it is very small that leads to the existence of longlived (T ≥ O(10 −4)sec) lightest superparticle. If lightest superpar-ticle is righthanded charged slepton that can be realized within gaugino dominated scenario then the phenomenology of such model differs in a drastic way from the standard SUSY phenomenology, in particular, longlived charged sleptons can form bound states with ordinary matter-quasistable supermatter (SUSY analogs of mu-atoms and muonium). We discuss possible manifestations of the existence of such longlived charged particle at LEP2, TEVATRON and LHC. We also construct SU (3) ⊗ SU (2) L ⊗ SU (2) R ⊗ U (1) model with Majorana mass and superweak R-parity violation