Fundamental Tests of P and CP Symmetries Using Octet Baryons at the J/ψ Threshold

We investigate tests of the parity P and the combined parity and charge-conjugate CP symmetries from differential angular distributions of J/ψ decaying into the lowest-lying baryon pairs at BESIII and the next-generation super tau-charm facilities (STCFs). Large corrections from Z and W exchange induced parity violating effects are found for J/ψ decays with large logarithms resummed up to O(αₛ). The parity-violating asymmetries on the production and the decay sides of J/ψ are both found to be of O(10⁻⁴), thus barely observable with the 10 billion J/ψ events currently collected at BESIII. Nevertheless, these asymmetries utilizing the current BESIII data already permit a determination of the weak mixing angle with an absolute uncertainty δ sw²≈0.08, corresponding to the first determination of sw² at the J/ψ threshold. While limited by statistics currently, STCFs are estimated to improve this precision by a factor of ~\,20 to δ sw²≈0.004 within one year based on luminosity rescaling. We also obtain the 95% confidence level upper bounds on the electric dipole moments of the octet baryons, which are of O(10⁻¹⁸)\,e\,cm for BESIII and O(10⁻¹⁹)\,e\,cm for STCFs. These bounds are improved by two to three orders of magnitude in comparison with the only existing one on Λ from Fermilab. The method discussed in this work also paves a way for a first and direct measurement of the Ξ and Σ electric dipole moments.