First simultaneous measurement of $Ξ^0$ and $\barΞ^0$ asymmetry parameters in $ψ(3686)$ decay

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