Tau polarization measurements at the LHC in supersymmetric models with a long-lived stau

Supersymmetry (SUSY) with a long-lived stau is an attractive scenario in the LHC experiments because one can directly observe stau tracks in each SUSY event, and thus precise measurements of SUSY particle masses are possible. In this scenario, we discuss the possibility to observe/measure parity violation in interactions among SUSY particles. Such a measurement will be important in determining spins and chiralities of SUSY particles. We use the last step of the cascade-decay chain: $\chi^0\to\tilde\tau\tau\to\tilde\tau(l\nu\bar\nu)$, where the polarization of the tau lepton can be determined statistically by looking at the energy distribution of the final state lepton. Comparing with the theoretical formula of the neutralino differential decay width, one can extract the size of parity violation in the interaction vertices among the stau, the tau lepton and the neutralino. We perform a Monte Carlo simulation to see if the effect is visible at the LHC experiments.