${\Sigma }^{+}$ and ${\overline{\Sigma }}^{-}$ Polarization in the $J/\psi $ and $\psi \left(3686\right)$ Decays

From $1310.6×{10}^{6}\text{}\text{}J/\psi $ and $448.1×{10}^{6}\text{}\text{}\psi \left(3686\right)$ events collected with the BESIII experiment, we report the first observation of ${\Sigma }^{+}$ and ${\overline{\Sigma }}^{-}$ spin polarization in ${e}^{+}{e}^{-}\to J/\psi \left[\psi \left(3686\right)\right]\to {\Sigma }^{+}{\overline{\Sigma }}^{-}$ decays. The relative phases of the form factors $\Delta \Phi $ have been measured to be $\left(-15.5±0.7±0.5\right)°$ and $\left(21.7±4.0±0.8\right)°$ with $J/\psi $ and $\psi \left(3686\right)$ data, respectively. The nonzero value of $\Delta \Phi $ allows for a direct and simultaneous measurement of the decay asymmetry parameters of ${\Sigma }^{+}\to p{\pi }^{0}\left({\alpha }_{0}=-0.998±0.037±0.009\right)$ and ${\overline{\Sigma }}^{-}\to \overline{p}{\pi }^{0}\left({\overline{\alpha }}_{0}=0.990±0.037±0.011\right)$, the latter value being determined for the first time. The average decay asymmetry, $\left({\alpha }_{0}-{\overline{\alpha }}_{0}\right)/2$, is calculated to be $-0.994±0.004±0.002$. The $CP$ asymmetry ${A}_{CP,\Sigma }=\left({\alpha }_{0}+{\overline{\alpha }}_{0}\right)/\left({\alpha }_{0}-{\overline{\alpha }}_{0}\right)=-0.004±0.037±0.010$ is extracted for the first time, and is found to be consistent with $CP$ conservation.