Strong and weak $CP$ tests in sequential decays of polarized $Σ^0$ hyperons
The $J/ψ, ψ(3686) \to Σ^0 \barΣ^{0}$ processes and subsequent decays are studied using the world's largest $J/ψ$ and $ψ(3686)$ data samples collected with the BESIII detector. The strong-$CP$ symmetry is tested in the decays of the $Σ^0$ hyperons for the first time by measuring the decay parameters, $α_{Σ^0} = -0.0017 \pm 0.0021 \pm 0.0018$ and $\barα_{Σ^0} = 0.0021 \pm 0.0020 \pm 0.0022$. The weak-$CP$ test is performed in the subsequent decays of their daughter particles $Λ$ and $\barΛ$. Also for the first time, the transverse polarizations of the $Σ^0$ hyperons in $J/ψ$ and $ψ(3686)$ decays are observed with opposite directions, and the ratios between the S-wave and D-wave contributions of the $J/ψ, ψ(3686) \to Σ^0 \barΣ^{0}$ decays are obtained. These results are crucial to understand the decay dynamics of the charmonium states and the production mechanism of the $Σ^0-\barΣ^0$ pairs.