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

TL;DR

This paper measures decay asymmetry parameters in $\\Xi^-$ and $\\Lambda$ decays using a large dataset, providing new insights into the $\\Delta I=1/2$ rule and testing CP violation with unprecedented precision.

Contribution

It presents the first evidence of the $\\Delta I=3/2$ transition in $\\Lambda$ decays and improves the precision of asymmetry parameters, advancing understanding of weak decays and CP violation.

Findings

The ratio of decay asymmetry parameters is less than unity with over 5σ significance.

Improved measurements of $\\alpha_0$ and $\\bar{\alpha}_0$ by factors of 4 and 1.7.

First test of CP violation in these decay channels with the best precision to date.

Abstract

Using $(10087\pm44)\times 10^{6}$ $J/\psi$ events collected with the BESIII detector, numerous $\Xi^-$ and $\Lambda$ decay asymmetry parameters are simultaneously determined from the process $J/\psi \to \Xi^- \bar{\Xi}^+ \to \Lambda(p\pi^-) \pi^- \bar{\Lambda}(\bar{n} \pi^0) \pi^+$ and its charge-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 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 $\Lambda \to p\pi^-$, $\langle \alpha_0 \rangle/ \langle \alpha_{\Lambda -} \rangle $, is determined to be $ 0.873 \pm 0.012^{+0.011}_{-0.010}$, 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. Beside, we test for CP violation in $\Xi^- \to \Lambda \pi^-$ and in $\Lambda \to n \pi^{0}$ with the best precision to date.