Precise Measurement of Matter-Antimatter Asymmetry with Entangled Hyperon Antihyperon Pairs

A search for $CP$ violation with an entangled system of ${\mathrm{\Xi }}^{-}{\bar{\mathrm{\Xi }}}^{+}$ pairs is performed, using $(10,087\pm 44)\times {10}^6$ $J\mathrm{/}\psi$ events collected with the BESIII experiment. A nine-dimensional helicity amplitude is used to fit $e^{+}{e}^{-}\to J\mathrm{/}\psi \to {\mathrm{\Xi }}^{-}{\bar{\mathrm{\Xi }}}^{+}$ and its subsequent decays. The ${\mathrm{\Xi }}^{-}$ and ${\mathrm{\Xi }}^{+}$ decay parameters are determined with higher precision compared to the best results reported so far. Furthermore, the strong phase difference, $({\delta }_P-{\delta }_S)=(0.3\pm 1.2\pm 0.2)\times {10}^{-2}\text{ rad}$, and the weak phase difference, $({\xi }_P-{\xi }_S)=(-0.2\pm 1.2\pm 0.1)\times {10}^{-2}\text{ rad}$, are directly determined. These are the most precise measurements to date. The $CP$ asymmetry observables $A_{CP}^{\mathrm{\Xi }}=(-7.8\pm 4.8\pm 0.8)\times {10}^{-3}$ and $\mathrm{\Delta }{\phi }_{CP}^{\mathrm{\Xi }}=(0.6\pm 5.1\pm 0.2)\times {10}^{-3}\text{ rad}$ are determined, which are consistent with $CP$ conservation. In addition, independent measurements of the $\mathrm{\Lambda }$ decay parameter and $CP$ asymmetry $A_{CP}^{\mathrm{\Lambda }}=(-2.9\pm 4.3\pm 0.7)\times {10}^{-3}$ are also obtained, which are in agreement with the previous measurements, but with much improved precision.