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

Abstract

Using a sample of $1.31\times 10^9$ $J/\psi$ events collected with the BESIII detector at the electron-positron collider BEPCII, we analyse the full $J/\psi \to$ ${\Xi }^{-}{\overline{\Xi }}^{+}$, ${\Xi }^{-}\to \Lambda {\pi }^{-}$, $\Lambda \to p{\pi }^{-}$, ${\overline{\Xi }}^{+}\to \overline{\Lambda }{\pi }^{+}$, $\overline{\Lambda }\to \overline{p}{\pi }^{+}$ decay chain. A new method, exploiting the fact that the ${\Xi }^{-}{\overline{\Xi }}^{+}$ 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 ${\Xi }^{-}\to \Lambda {\pi }^{-}$ decay (${\alpha }_{\Xi }$, ${\varphi }_{\Xi }$) as well as the ${\overline{\Xi }}^{+}\to \overline{\Lambda }{\pi }^{+}$ decay (${\overline{\alpha }}_{\Xi }$, ${\overline{\varphi }}_{\Xi }$). From the decay parameters, two independent CP tests were performed, quantified by the observables $A_{\mathrm{CP}}^{\Xi }$ and $\Delta {\varphi }_{\Xi }$. Our results, $A_{\mathrm{CP}}^{\Xi }$ = $(6.0\pm 13.4\pm 5.6)\times 10^{-3}$ and $\Delta {\varphi }_{\Xi }=(-4.8\pm 13.7\pm 2.9)\times 10^{-3}\mathrm{rad}$, are consistent with CP symmetry. Furthermore, our method enables a separation of strong and weak $\Xi \to \Lambda \pi$ 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 $({\delta }_P-{\delta }_S)=(-4.0\pm 3.3\pm 1.7)\times 10^{-2}$ rad. In addition, we provide an independent measurement of the recently debated $\Lambda$ decay parameter, ${\alpha }_{\Lambda }=0.757\pm 0.011\pm 0.008$. The $\Lambda \overline{\Lambda }$ asymmetry is measured to be $A_{\mathrm{CP}}^{\Lambda }=(-3.7\pm 11.7\pm 9.0)\times 10^{-3}$.

24 pages, 4 figures and 5 tables

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