Tests of $CP$ symmetry in the entangled ${\mathrm{\Xi }}^0-{\bar{\mathrm{\Xi }}}^0$ Pairs

The $J\mathrm{/}\psi \to {\mathrm{\Xi }}^0{\bar{\mathrm{\Xi }}}^0$ process and subsequent decays are investigated using $(10087\pm 44)\times {10}^6$ $J\mathrm{/}\psi$ events collected at the BESIII experiment. The decay parameters of ${\mathrm{\Xi }}^0$ and ${\bar{\mathrm{\Xi }}}^0$ are measured with greatly improved precision over previous measurements to be ${\alpha }_{\mathrm{\Xi }}=-0.3750\pm 0.0034\pm 0.0016$, ${\bar{\alpha }}_{\mathrm{\Xi }}=0.3790\pm 0.0034\pm 0.0021$, ${\phi }_{\mathrm{\Xi }}=0.0051\pm 0.0096\pm 0.0018$~rad, ${\bar{\phi }}_{\mathrm{\Xi }}=-0.0053\pm 0.0097\pm 0.0019$~rad, where the first and the second uncertainties are statistical and systematic, respectively. From these measurements, precise $CP$ symmetry tests in ${\mathrm{\Xi }}^0$ decay are performed, and $A_{CP}^{\mathrm{\Xi }}=(-5.4\pm 6.5\pm 3.1)\times {10}^{-3}$ and $\mathrm{\Delta }{\phi }_{CP}^{\mathrm{\Xi }}=(-0.1\pm 6.9\pm 0.9)\times {10}^{-3}$~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 ${\xi }_P-{\xi }_S=(0.0\pm 1.7\pm 0.2)\times {10}^{-2}$~rad and ${\delta }_P-{\delta }_S=(-1.3\pm 1.7\pm 0.4)\times {10}^{-2}$~rad, respectively. In addition, we measure the $\mathrm{\Lambda }$ decay parameters and test $CP$ symmetry in $\mathrm{\Lambda }$ decays.