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

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