Test of $C\!P$ Symmetry in Hyperon to Neutron Decays
The quantum entangled $J/ψ\to Σ^{+}\barΣ^{-}$ pairs from $(1.0087\pm0.0044)\times10^{10}$ $J/ψ$ events taken by the BESIII detector are used to study the non-leptonic two-body weak decays $Σ^{+} \to n π^{+}$ and $\barΣ^{-} \to \bar{n} π^{-}$. The $C\!P$-odd weak decay parameters of the decays $Σ^{+} \to n π^{+}$ ($α_{+}$) and $\barΣ^{-} \to \bar{n} π^{-}$ ($\barα_{-}$) are determined to be $-0.0565\pm0.0047_{\rm stat}\pm0.0022_{\rm syst}$ and $0.0481\pm0.0031_{\rm stat}\pm0.0019_{\rm syst}$, respectively. The decay parameter $\barα_{-}$ is measured for the first time, and the accuracy of $α_{+}$ is improved by a factor of four compared to the previous results. The simultaneously determined decay parameters allow the first precision $C\!P$ symmetry test for any hyperon decay with a neutron in the final state with the measurement of $A_{C\!P}=(α_{+}+\barα_{-})/(α_{+}-\barα_{-})=-0.080\pm0.052_{\rm stat}\pm0.028_{\rm syst}$. Assuming $C\!P$ conservation, the average decay parameter is determined as $\left< α_{+}\right>=(α_{+}- \barα_{-})/2 = -0.0506\pm0.0026_{\rm stat}\pm0.0019_{\rm syst}$, while the ratios $α_{+}/α_{0}$ and $\barα_{-}/\barα_{0}$ are $-0.0490\pm0.0032_{\rm stat}\pm0.0021_{\rm syst}$ and $-0.0571\pm0.0053_{\rm stat}\pm0.0032_{\rm syst}$, where $α_{0}$ and $\barα_{0}$ are the decay parameters of the decays $Σ^{+} \to p π^{0}$ and $\barΣ^{-} \to \bar{p} π^{0}$, respectively.