Based on a sample of $144\times {10}^6$ polarized ${\Xi }^{-}\to \Lambda {\pi }^{-},\Lambda \to p{\pi }^{-}$ decays collected by the HyperCP experiment (E871) at Fermilab, we report a new measurement of the ${\Xi }^{-}$ decay-parameter angle ${\phi }_{\Xi }=(-2.39\pm 0.64\pm 0.64)°$ from which we deduce the decay parameters ${\beta }_{\Xi }=-0.037\pm 0.011\pm 0.010$ and ${\gamma }_{\Xi }=0.888\pm 0.0004\pm 0.006$. Assuming that the $CP$-violating phase difference between $s$ and $p$ waves is negligible, the strong phase-shift difference, ${\delta }_p-{\delta }_s$, for $\Lambda \pi$ scattering is determined to be $(4.6\pm 1.4\pm 1.2)°$.

• Received 13 February 2004

DOI:https://doi.org/10.1103/PhysRevLett.93.011802