Strong and Weak CP Tests in Sequential Decays of Polarized Σ0 Hyperons

The J/ψ, ψ (3686) →Σ^0Σover ¯^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 parity-violating decay parameters of the decays Σ^0→Λγ and Σover ¯^0→Λover ¯γ, α⏢^₀=-0. 0017±0. 0021±0. 0018 and αover ¯⏢^₀=0. 0021±0. 0020±0. 0022, are measured for the first time. The strong CP symmetry is tested in the decays of the Σ^0 hyperons for the first time by measuring the asymmetry A₂₏^Σ=α⏢^₀+αover ¯⏢^₀= (0. 4±2. 9±1. 3) ×10^-3. The weak CP test is performed in the subsequent decays of their daughter particles Λ and Λover ¯. 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) →Σ^0Σover ¯^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-Σover ¯^0 pairs.