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

The J/psi,psi(3686) -> Sigma(0)(Sigma) over bar (0) processes and subsequent decays are studied using the world's largest J/psi and psi(3686) data samples collected with the BESIII detector. The parity-violating decay parameters of the decays Sigma(0) -> Lambda gamma and (Sigma) over bar (0) ->(Lambda) over bar gamma, alpha(Sigma 0) = -0.0017 +/- 0.0021 +/- 0.0018 and (alpha) over bar (Sigma 0) = 0.0021 +/- 0.0020 +/- 0.0022, are measured for the first time. The strong CP symmetry is tested in the decays of the S0 hyperons for the first time by measuring the asymmetry A(CP)(Sigma) = alpha(Sigma 0) + (alpha) over bar (Sigma 0) =(0.4 +/- 2.9 +/- 1.3) x 10(-3). The weak CP test is performed in the subsequent decays of their daughter particles Lambda and (Lambda) over bar. Also for the first time, the transverse polarizations of the Sigma(0) hyperons in J/psi and psi(3686) -> decays are observed with opposite directions, and the ratios between the S-wave and D-wave contributions of the J/psi, psi(3686) -> Sigma(0)(Sigma) over bar (0) decays are obtained. These results are crucial to understand the decay dynamics of the charmonium states and the production mechanism of the Sigma(0) - (Sigma) over bar (0) pairs.