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

Using $(10087\pm 44)\times {10}^{6}J/\psi$ events collected with the BESIII detector, numerous ${\mathrm{\Xi }}^{-}$ and $\mathrm{\Lambda }$ decay asymmetry parameters are simultaneously determined from the process $J/\psi \to {\mathrm{\Xi }}^{-}{\overline{\mathrm{\Xi }}}^{+}\to \mathrm{\Lambda }(p{\pi }^{-}){\pi }^{-}\overline{\mathrm{\Lambda }}(\overline{n}{\pi }^0){\pi }^{+}$ and its charge-conjugate channel. The precisions of ${\alpha }_{\mathrm{\Lambda }0}$ for $\mathrm{\Lambda }\to n{\pi }^0$ and ${\overline{\alpha }}_{\mathrm{\Lambda }0}$ for $\overline{\mathrm{\Lambda }}\to \overline{n}{\pi }^0$ compared to world averages are improved by factors of 4 and 1.7, respectively. The ratio of decay asymmetry parameters of $\mathrm{\Lambda }\to n{\pi }^0$ to that of $\mathrm{\Lambda }\to p{\pi }^{-}$, $⟨{\alpha }_{\mathrm{\Lambda }0}⟩/⟨{\alpha }_{\mathrm{\Lambda }-}⟩$, is determined to be $0.873\pm 0.012_{-0.010}^{+0.011}$, 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 $\mathrm{\Delta }I=3/2$ transition in $\mathrm{\Lambda }$ for the first time. Besides, we test for $CP$ symmetry in ${\mathrm{\Xi }}^{-}\to \mathrm{\Lambda }{\pi }^{-}$ and in $\mathrm{\Lambda }\to n{\pi }^0$ with the best precision to date.

Figure 1

Distribution of antineutron missing mass. The data are shown as black data points with error bars. The blue solid curve represents the total fit result, and the red dashed line denotes the signal shape. The dotted lines in green, light blue, and magenta denote the combinatorial, resonant, and nonresonant background contributions, respectively. The red arrows indicate the signal region.

Figure 2

The ratios of helicity angular distributions for different nucleons in the final states, $R(\cos {\theta }_p,\cos {\theta }_{\overline{p}})$ and $R(\cos {\theta }_n,\cos {\theta }_{\overline{n}})$ (top) as well as $R(\cos {\theta }_n,\cos {\theta }_p)$ and $R(\cos {\theta }_{\overline{n}},\cos {\theta }_{\overline{p}})$ (bottom) versus $\cos \theta$. The dots with errors are determined by independent fits for each $\cos \theta$ bin of the corresponding nucleons. The solid curves in red with $1\sigma$ (red) and $3\sigma$ (pink) statistical uncertainty bands show the results of the simultaneous fit. The dashed curves in black show the $CP$-conserving and no $\mathrm{\Delta }I=3/2$ transition expectations.