Investigation of the $\Delta I=1/2$ Rule and Test of $CP$ Symmetry through the Measurement of Decay Asymmetry Parameters in ${\Xi }^{-}$ Decays

Using $\left(10087±44\right)×{10}^{6}\text{}\text{}J/\psi $ events collected with the BESIII detector, numerous ${\Xi }^{-}$ and $\Lambda $ decay asymmetry parameters are simultaneously determined from the process $J/\psi \to {\Xi }^{-}{\overline{\Xi }}^{+}\to \phantom{\rule{0ex}{0ex}}\Lambda \left(p{\pi }^{-}\right){\pi }^{-}\overline{\Lambda }\left(\overline{n}{\pi }^{0}\right){\pi }^{+}$ and its charge-conjugate channel. The precisions of ${\alpha }_{\Lambda 0}$ for $\Lambda \to n{\pi }^{0}$ and ${\overline{\alpha }}_{\Lambda 0}$ for $\overline{\Lambda }\to \overline{n}{\pi }^{0}$ compared to world averages are improved by factors of 4 and 1.7, respectively. The ratio of decay asymmetry parameters of $\Lambda \to n{\pi }^{0}$ to that of $\Lambda \to p{\pi }^{-}$, $⟨{\alpha }_{\Lambda 0}⟩/⟨{\alpha }_{\Lambda -}⟩$, is determined to be $0.873±0.01{2}_{-0.010}^{+0.011}$, where the first and the second uncertainties are statistical and systematic, respectively. The ratio is smaller than unity more than $5\sigma $, which signifies the existence of the $\Delta I=3/2$ transition in $\Lambda $ for the first time. Besides, we test for $CP$ symmetry in ${\Xi }^{-}\to \Lambda {\pi }^{-}$ and in $\Lambda \to n{\pi }^{0}$ with the best precision to date.