Stringent test of $CP$ symmetry in $Σ^+$ hyperon decays
The non-leptonic two-body weak decays $Σ^{+} \to p π^{0}$ and $\barΣ^{-} \to \bar{p} π^{0}$ are investigated, utilizing $(1.0087\pm0.0044)\times10^{10}$ $J/ψ$ events and $(2.7124\pm0.0143)\times10^{9}$ $ψ(3686)$ events collected by BESIII experiment. The precision of the weak-decay parameters for the decays $Σ^{+} \to p π^{0}$ ($α_{0}$) and $\barΣ^{-} \to \bar{p} π^{0}$ ($\barα_{0}$) is improved by a factor of three compared to the previous world average. Furthermore, the quantum-entangled $Σ^{+}\barΣ^{-}$ system enables the most precise test of $CP$ symmetry for the decay $Σ^+\to pπ^0$, through the asymmetry observable $A_{CP}=(α_{0}+\barα_{0})/(α_{0}-\barα_{0})$ that is measured to be $-0.0118\pm0.0083_{\rm stat}\pm0.0028_{\rm syst}$. Assuming $CP$ conservation, the average decay parameter is determined to be ${\left< α_{\rm 0}\right>} = (α_0-\barα_0)/2=-0.9869\pm0.0011_{\rm stat}\pm0.0016_{\rm syst}$, which is the most precise measurement of the asymmetry decay parameters in baryon sectors. The angular dependence of the ratio of the polarization of the $Σ^+$ in both $J/ψ$ and $ψ(3686)$ decays is studied for the first time.