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

We investigate tests of the parity P and the combined parity and charge-conjugate CP symmetries from differential angular distributions of J/ 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/ decays with large logarithms resummed up to O (ₛ). The parity-violating asymmetries on the production and the decay sides of J/ are both found to be of O (10^-4), thus barely observable with the 10 billion J/ 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 sw²0. 08, corresponding to the first determination of sw² at the J/ threshold. While limited by statistics currently, STCFs are estimated to improve this precision by a factor of \, 20 to sw²0. 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 from Fermilab. The method discussed in this work also paves a way for a first and direct measurement of the and electric dipole moments.