Precision hyperon physics at J/ψ and ψ' factories

A novel multidimensional method to study hyperon and antihyperon decays and to search for a direct CP-violation signal is presented. The method uses spin polarization and entanglement of baryon-antibaryon pairs produced in electron-positron annihilation at the J/psi and psi' resonances. The method was applied in a series of proof-of-concept analyses at BESIII. The helicity amplitudes describing electron-positron annihilation into Lambda(Lambda) over bar, Sigma(+)(Sigma) over bar (-), Xi(-)Xi(+) and Omega(-)(Omega) over bar (+) pairs at J/psi and psi' were determined. A significant transverse polarization of the (anti)hyperons in J/psi and psi' decays was observed and spin of the Omega(-) baryon was determined in a model independent way using the reaction properties. The asymmetry parameters of the main (anti)hyperon decay modes, the non-leptonic two-body decays, were precisely measured. The result for the asymmetry parameter alpha(Lambda) in Lambda -> p pi(-) revises by 17% the value used for nearly 50 years in all analyses of Lambda polarization. Additionally, in the sequential weak decays Xi(-) -> Lambda pi(-) and Omega(-) -> Lambda K- the spin rotation parameter was measured. A comparison of the hyperon and antihyperon decay parameters allows for tests of direct CP-symmetry violation, that are complementary to the epsilon'/epsilon measurement in kaon decays. Of special importance are the new results on e+e- -> J/psi -> Xi(-)Xi(+), where the final-state interaction and weak-phase difference are disentangled. Prospects of future measurements at Super Charm-Tau Factories are discussed with the emphasis on the impact of the longitudinal polarization of the electron beams on the precision of the CP-violation tests.