Measurement of Decay Parameters for $\Xi^{-} \to \Lambda \pi^{-}$ Decay

Based on 1.35 million polarized $\Xi^{-}$ events, we measure the parameter $\phi_{\Xi}$ to be $-1.61^{\circ} \pm 2.66^{\circ} \pm 0.37^{\circ}$ for $\Xi^{-} \to \Lambda \pi^{-}$ decay. New results for the parameters $\beta_{\Xi}$ and $\gamma_{\Xi}$ are also presented. Assuming that the CP-violating phase-shift difference is negligible, we deduce the strong phase-shift difference between the P-wave and S-wave amplitudes of the $\Lambda\pi$ final state to be $3.17^{\circ} \pm 5.28^{\circ} \pm 0.73^{\circ}$. This strong phase-shift difference reduces the theoretical uncertainty in estimating the level of CP violation in $\Xi$-hyperon decay.