Weak phases and CP-symmetry tests in sequential decays of entangled double-strange baryons

Using a sample of $1.31\times {10}^9$ $J\mathrm{/}\psi$ events collected with the BESIII detector at the electron-positron collider BEPCII, we analyse the full $J/\psi \to$ ${\mathrm{\Xi }}^{-}{\bar{\mathrm{\Xi }}}^{+}$, ${\mathrm{\Xi }}^{-}\to \mathrm{\Lambda }{\pi }^{-}$, $\mathrm{\Lambda }\to p{\pi }^{-}$, ${\bar{\mathrm{\Xi }}}^{+}\to \bar{\mathrm{\Lambda }}{\pi }^{+}$, $\bar{\mathrm{\Lambda }}\to \bar{p}{\pi }^{+}$ decay chain. A new method, exploiting the fact that the ${\mathrm{\Xi }}^{-}{\bar{\mathrm{\Xi }}}^{+}$ pair is entangled and sequentially decaying, and where the complete decay chains are reconstructed, is applied for the first time. This enables precision measurements of the decay parameters for the ${\mathrm{\Xi }}^{-}\to \mathrm{\Lambda }{\pi }^{-}$ decay (${\alpha }_{\mathrm{\Xi }}$, ${\varphi }_{\mathrm{\Xi }}$) as well as the ${\bar{\mathrm{\Xi }}}^{+}\to \bar{\mathrm{\Lambda }}{\pi }^{+}$ decay (${\bar{\alpha }}_{\mathrm{\Xi }}$, ${\bar{\varphi }}_{\mathrm{\Xi }}$). From the decay parameters, two independent CP tests were performed, quantified by the observables $A_{\mathrm{C}\mathrm{P}}^{\mathrm{\Xi }}$ and $\Delta \phi_\Xi$\mathrm{.}Ourresults,$A_{\rm CP}^{\Xi}$=$(6.0\pm13.4\pm5.6)\times10^{-3}$and$\Delta \phi_\Xi= (-4.8\pm13.7\pm2.9)\times10^{-3}~{\rm rad}$, are consistent with CP symmetry. Furthermore, our method enables a separation of strong and weak $\mathrm{\Xi }\to \mathrm{\Lambda }\pi$ decay amplitudes. This results in the first direct measurement of the weak phase difference for any baryon decay. The result is found to be $({\xi }_P-{\xi }_S)=(1.2\pm 3.4\pm 0.8)\times {10}^{-2}$ rad and is one of the most precise tests of CP symmetry for strange baryons. The strong phase difference is measured to be $(\delta_P - \delta_S) = (-4.0\pm3.3\pm1.7)\times10^{-2}$ rad. In addition, we provide an independent measurement of the recently debated $\mathrm{\Lambda }$ decay parameter, ${\alpha }_{\mathrm{\Lambda }}=0.757\pm 0.011\pm 0.008$. The $\mathrm{\Lambda }\bar{\mathrm{\Lambda }}$ asymmetry is measured to be $A_{\rm CP}^{\Lambda} = (-3.7\pm11.7\pm9.0)\times10^{-3}$.