Test of $CP$ Symmetry in Hyperon to Neutron Decays

Abstract

The quantum entangled $J/\ddot{I}ˆ\to \hat{I}{\pounds }^{+}\bar{\hat{I}}{\pounds }^{-}$ pairs from $(1.0087\pm 0.0044)\times 10^{10}$ $J/\ddot{I}ˆ$ events taken by the BESIII detector are used to study the non-leptonic two-body weak decays $\hat{I}{\pounds }^{+}\to n\ddot{I}{€}^{+}$ and $\bar{\hat{I}}{\pounds }^{-}\to \bar{n}\ddot{I}{€}^{-}$. The $CP$-odd weak decay parameters of the decays $\hat{I}{\pounds }^{+}\to n\ddot{I}{€}^{+}$ ($\hat{I}{\pm }_{+}$) and $\bar{\hat{I}}{\pounds }^{-}\to \bar{n}\ddot{I}{€}^{-}$ ($\bar{\hat{I}}{\pm }_{-}$) are determined to be $-0.0565\pm 0.0047_{\mathrm{stat}}\pm 0.0022_{\mathrm{syst}}$ and $0.0481\pm 0.0031_{\mathrm{stat}}\pm 0.0019_{\mathrm{syst}}$, respectively. The decay parameter $\bar{\hat{I}}{\pm }_{-}$ is measured for the first time, and the accuracy of $\hat{I}{\pm }_{+}$ is improved by a factor of four compared to the previous results. The simultaneously determined decay parameters allow the first precision $CP$ symmetry test for any hyperon decay with a neutron in the final state with the measurement of $A_{CP}=(\hat{I}{\pm }_{+}+\bar{\hat{I}}{\pm }_{-})/(\hat{I}{\pm }_{+}-\bar{\hat{I}}{\pm }_{-})=-0.080\pm 0.052_{\mathrm{stat}}\pm 0.028_{\mathrm{syst}}$. Assuming $CP$ conservation, the average decay parameter is determined as $⟨\hat{I}{\pm }_{+}⟩=(\hat{I}{\pm }_{+}-\bar{\hat{I}}{\pm }_{-})/2=-0.0506\pm 0.0026_{\mathrm{stat}}\pm 0.0019_{\mathrm{syst}}$, while the ratios $\hat{I}{\pm }_{+}/\hat{I}{\pm }_0$ and $\bar{\hat{I}}{\pm }_{-}/\bar{\hat{I}}{\pm }_0$ are $-0.0490\pm 0.0032_{\mathrm{stat}}\pm 0.0021_{\mathrm{syst}}$ and $-0.0571\pm 0.0053_{\mathrm{stat}}\pm 0.0032_{\mathrm{syst}}$, where $\hat{I}{\pm }_0$ and $\bar{\hat{I}}{\pm }_0$ are the decay parameters of the decays $\hat{I}{\pounds }^{+}\to p\ddot{I}{€}^0$ and $\bar{\hat{I}}{\pounds }^{-}\to \bar{p}\ddot{I}{€}^0$, respectively.