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

Abstract

Using a sample of $1.31\times 10^9$ $J/\ddot{I}ˆ$ events collected with the BESIII detector at the electron-positron collider BEPCII, we analyse the full $J/\ddot{I}ˆ\to$ $\hat{I}{ž}^{-}\overline{\hat{I}}{ž}^{+}$, $\hat{I}{ž}^{-}\to \hat{I}›\ddot{I}{€}^{-}$, $\hat{I}›\to p\ddot{I}{€}^{-}$, $\overline{\hat{I}}{ž}^{+}\to \overline{\hat{I}}›\ddot{I}{€}^{+}$, $\overline{\hat{I}}›\to \overline{p}\ddot{I}{€}^{+}$ decay chain. A new method, exploiting the fact that the $\hat{I}{ž}^{-}\overline{\hat{I}}{ž}^{+}$ 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 $\hat{I}{ž}^{-}\to \hat{I}›\ddot{I}{€}^{-}$ decay ($\hat{I}{\pm }_{\hat{I}}ž$, $\ddot{I}{•}_{\hat{I}}ž$) as well as the $\overline{\hat{I}}{ž}^{+}\to \overline{\hat{I}}›\ddot{I}{€}^{+}$ decay ($\overline{\hat{I}}{\pm }_{\hat{I}}ž$, $\overline{\ddot{I}}{•}_{\hat{I}}ž$). From the decay parameters, two independent CP tests were performed, quantified by the observables $A_{\mathrm{CP}}^{\hat{I}}ž$ and $\hat{I}”\ddot{I}{•}_{\hat{I}}ž$. Our results, $A_{\mathrm{CP}}^{\hat{I}}ž$ = $(6.0\pm 13.4\pm 5.6)\times 10^{-3}$ and $\hat{I}”\ddot{I}{•}_{\hat{I}}ž=(-4.8\pm 13.7\pm 2.9)\times 10^{-3}\mathrm{rad}$, are consistent with CP symmetry. Furthermore, our method enables a separation of strong and weak $\hat{I}ž\to \hat{I}›\ddot{I}€$ decay amplitudes. This results in the first direct measurement of the weak phase difference for any baryon decay. The result is found to be $(\hat{I}{¾}_P-\hat{I}{¾}_S)=(1.2\pm 3.4\pm 0.8)\times 10^{-2}$ rad and is one of the most precise tests of CP symmetry for strange baryons. The strong phase difference is measured to be $(\hat{I}{´}_P-\hat{I}{´}_S)=(-4.0\pm 3.3\pm 1.7)\times 10^{-2}$ rad. In addition, we provide an independent measurement of the recently debated $\hat{I}›$ decay parameter, $\hat{I}{\pm }_{\hat{I}}›=0.757\pm 0.011\pm 0.008$. The $\hat{I}›\overline{\hat{I}}›$ asymmetry is measured to be $A_{\mathrm{CP}}^{\hat{I}}›=(-3.7\pm 11.7\pm 9.0)\times 10^{-3}$.

24 pages, 4 figures and 5 tables