Test of $CP$ Symmetry in Hyperon to Neutron Decays

The quantum entangled $J/\psi \to {\Sigma }^{+}{\overline{\Sigma }}^{-}$ pairs from $\left(1.0087±0.0044\right)×{10}^{10}\text{}\text{}J/\psi $ events taken by the BESIII detector are used to study the nonleptonic two-body weak decays ${\Sigma }^{+}\to n{\pi }^{+}$ and ${\overline{\Sigma }}^{-}\to \overline{n}{\pi }^{-}$. The $CP$-odd weak decay parameters of the decays ${\Sigma }^{+}\to n{\pi }^{+}$ (${\alpha }_{+}$) and ${\overline{\Sigma }}^{-}\to \overline{n}{\pi }^{-}$ (${\overline{\alpha }}_{-}$) are determined to be $0.0481±0.003{1}_{\mathrm{stat}}±0.001{9}_{\mathrm{syst}}$ and $-0.0565±0.004{7}_{\mathrm{stat}}±0.002{2}_{\mathrm{syst}}$, respectively. The decay parameter ${\overline{\alpha }}_{-}$ is measured for the first time, and the accuracy of ${\alpha }_{+}$ is improved by a factor of 4 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 ${A}_{CP}=\left({\alpha }_{+}+{\overline{\alpha }}_{-}\right)/\left({\alpha }_{+}-{\overline{\alpha }}_{-}\right)=-0.080±0.05{2}_{\mathrm{stat}}±0.02{8}_{\mathrm{syst}}$. Assuming $CP$ conservation, the average decay parameter is determined as $⟨{\alpha }_{+}⟩=\left({\alpha }_{+}-{\overline{\alpha }}_{-}\right)/2=-0.0506±0.002{6}_{\mathrm{stat}}±0.001{9}_{\mathrm{syst}}$, while the ratios ${\alpha }_{+}/{\alpha }_{0}$ and ${\overline{\alpha }}_{-}/{\overline{\alpha }}_{0}$ are $-0.0490±0.003{2}_{\mathrm{stat}}±0.002{1}_{\mathrm{syst}}$ and $-0.0571±0.005{3}_{\mathrm{stat}}±0.003{2}_{\mathrm{syst}}$, where ${\alpha }_{0}$ and ${\overline{\alpha }}_{0}$ are the decay parameters of the decays ${\Sigma }^{+}\to p{\pi }^{0}$ and ${\overline{\Sigma }}^{-}\to \overline{p}{\pi }^{0}$, respectively.