Precise Measurements of the Decay Parameters and $CP$ Asymmetries with Entangled $Ξ^0-\barΞ^0$ Pairs

The $J/ψ\to Ξ^0 \barΞ^{0}$ process and subsequent decays are investigated using $(10087 \pm 44)\times 10^6$ $J/ψ$ events collected at the BESIII experiment. The decay parameters of $Ξ^0$ and $\barΞ^0$ are measured with greatly improved precision over previous measurements to be $α_Ξ = -0.3750 \pm 0.0034 \pm 0.0016$, $\barα_Ξ = 0.3790 \pm 0.0034 \pm 0.0021$, $ϕ_Ξ = 0.0051 \pm 0.0096 \pm 0.0018$~rad, $\barϕ_Ξ = -0.0053 \pm 0.0097 \pm 0.0019$~rad, where the first and the second uncertainties are statistical and systematic, respectively. From these measurements, precise $CP$ symmetry tests in $Ξ^0$ decay are performed, and $A^Ξ_{CP} = (-5.4 \pm 6.5 \pm 3.1) \times 10^{-3}$ and $Δϕ^Ξ_{CP} = (-0.1 \pm 6.9 \pm 0.9) \times 10^{-3}$~rad are consistent with $CP$ conservation. The sequential decay also enables a separation of weak and strong phase differences, which are found for the first time to be $ξ_{P}-ξ_{S} = (0.0 \pm 1.7 \pm 0.2) \times 10^{-2}$~rad and $δ_{P}-δ_{S} = (-1.3 \pm 1.7 \pm 0.4)\times 10^{-2}$~rad, respectively. In addition, we measure the $Λ$ decay parameters and test $CP$ symmetry in $Λ$ decays.