Investigation of the $\Delta I = 1/2$ rule and test of CP violation through the measurement of decay asymmetry parameters in $\Xi^-$ decays

Using $(10087\pm44)\times 10^{6}$ $J/\psi$ events collected with the BESIIIdetector, numerous $\Xi^-$ and $\Lambda$ decay asymmetry parameters aresimultaneously determined from the process $J/\psi \to \Xi^- \bar{\Xi}^+ \to\Lambda(p\pi^-) \pi^- \bar{\Lambda}(\bar{n} \pi^0) \pi^+$ and itscharge-conjugate channel. The precisions of $\alpha_0$ for $\Lambda \to n\pi^0$and $\bar{\alpha}_0$ for $\bar{\Lambda} \to \bar{n}\pi^0$ compared to worldaverages are improved by factors of 4 and 1.7, respectively. The ratio of decayasymmetry parameters of $\Lambda \to n\pi^0$ to that of $\Lambda \to p\pi^-$,$\langle \alpha_0 \rangle/ \langle \alpha_{\Lambda -} \rangle $, is determinedto be $ 0.873 \pm 0.012^{+0.011}_{-0.010}$, where the first and the seconduncertainties are statistical and systematic, respectively. The ratio issmaller than unity more than $5\sigma$, which signifies the existence of the$\Delta I = 3/2$ transition in $\Lambda$ for the first time. Beside, we testfor CP violation in $\Xi^- \to \Lambda \pi^-$ and in $\Lambda \to n \pi^{0}$with the best precision to date.