Strong and weak $CP$ tests in sequential decays of polarized Σ⁰ hyperons

The J/ψ, ψ(3686) → Σ⁰ Σ̄⁰ 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 Σ⁰ hyperons for the first time by measuring the decay parameters, αΣ⁰ = -0.0017 ± 0.0021 ± 0.0018 and ᾱΣ⁰ = 0.0021 ± 0.0020 ± 0.0022. The weak-$CP$ test is performed in the subsequent decays of their daughter particles Λ and Λ̄. Also for the first time, the transverse polarizations of the Σ⁰ 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) → Σ⁰ Σ̄⁰ decays are obtained. These results are crucial to understand the decay dynamics of the charmonium states and the production mechanism of the Σ⁰-Σ̄⁰ pairs.