First simultaneous measurement of ${\Xi }^{0}$ and ${\overline{\Xi }}^{0}$ asymmetry parameters in $\psi \left(3686\right)$ decay

The ${\Xi }^{0}$ asymmetry parameters are measured using entangled quantum ${\Xi }^{0}-{\overline{\Xi }}^{0}$ pairs from a sample of $\left(448.1±2.9\right)×{10}^{6}\text{}\text{}\psi \left(3686\right)$ events collected with the BESIII detector at BEPCII. The relative phase between the transition amplitudes of the ${\Xi }^{0}{\overline{\Xi }}^{0}$ helicity states is measured to be $\Delta \Phi =-0.050±\phantom{\rule{0ex}{0ex}}0.150±0.020\text{}\text{}\mathrm{rad}$, which implies that there is no obvious polarization at the current level of statistics. The decay parameters of the ${\Xi }^{0}$ hyperon $\left({\alpha }_{{\Xi }^{0}},{\alpha }_{{\overline{\Xi }}^{0}},{\varphi }_{{\Xi }^{0}},{\varphi }_{{\overline{\Xi }}^{0}}\right)$ and the angular distribution parameter $\left[{\alpha }_{\psi \left(3686\right)}\right]$ and $\Delta \Phi $ are measured simultaneously for the first time. In addition, the $CP$ asymmetry observables are determined to be ${A}_{CP}^{{\Xi }^{0}}=\left({\alpha }_{{\Xi }^{0}}+{\alpha }_{{\overline{\Xi }}^{0}}\right)/\left({\alpha }_{{\Xi }^{0}}-{\alpha }_{{\overline{\Xi }}^{0}}\right)=-0.007±0.082±0.025$ and $\Delta {\varphi }_{CP}^{{\Xi }^{0}}=\left({\varphi }_{{\Xi }^{0}}+{\varphi }_{{\overline{\Xi }}^{0}}\right)/2=-0.079±0.082±0.010\text{}\text{}\mathrm{rad}$, which are consistent with $CP$ conservation.