$\hat{I}{\pounds }^{+}$ and $\bar{\hat{I}}{\pounds }^{-}$ polarization in the $J/\ddot{I}ˆ$ and $\ddot{I}ˆ(3686)$ decays

Abstract

From $1310.6\times 10^6$ $J/\ddot{I}ˆ$ and $448.1\times 10^6$ $\ddot{I}ˆ(3686)$ events collected with the BESIII experiment, we report the first observation of $\hat{I}{\pounds }^{+}$ and $\bar{\hat{I}}{\pounds }^{-}$ spin polarization in $e^{+}{e}^{-}\to J/\ddot{I}ˆ(\ddot{I}ˆ(3686))\to \hat{I}{\pounds }^{+}\bar{\hat{I}}{\pounds }^{-}$ decays. The relative phases of the form factors $\hat{I}”\hat{I}¦$ have been measured to be $(-15.5\pm 0.7\pm 0.5{)}^{\circ }$ and $(21.7\pm 4.0\pm 0.8{)}^{\circ }$ with $J/\ddot{I}ˆ$ and $\ddot{I}ˆ(3686)$ data, respectively. The non-zero value of $\hat{I}”\hat{I}¦$ allows for a direct and simultaneous measurement of the decay asymmetry parameters of $\hat{I}{\pounds }^{+}\to p\ddot{I}{€}^0(\hat{I}{\pm }_0=-0.998\pm 0.037\pm 0.009)$ and $\bar{\hat{I}}{\pounds }^{-}\to \bar{p}\ddot{I}{€}^0(\bar{\hat{I}}{\pm }_0=0.990\pm 0.037\pm 0.011)$, the latter value being determined for the first time. The average decay asymmetry, $(\hat{I}{\pm }_0-\bar{\hat{I}}{\pm }_0)/2$, is calculated to be $-0.994\pm 0.004\pm 0.002$. The CP asymmetry $A_{\mathrm{CP},\hat{\mathrm{I}}\pounds }=(\hat{I}{\pm }_0+\bar{\hat{I}}{\pm }_0)/(\hat{I}{\pm }_0-\bar{\hat{I}}{\pm }_0)=-0.004\pm 0.037\pm 0.010$ is extracted for the first time, and is found to be consistent with CP conservation.