Precision hyperon physics at J/$\psi$ and $\psi'$ factories

Abstract

A novel multidimensional method to study hyperon and antihyperon decays and to search for direct CP-violation signals 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. For the production processes the results include observation of a significant transverse polarization of the (anti)hyperons in $J/\psi$ and $\psi'$ decays and model independent spin determination of the $\Omega^-$ baryon. The helicity amplitudes describing electron--positron annihilation into $\Lambda\overline\Lambda$, $\Sigma^+\overline{\Sigma}\vphantom{\Sigma}^-$, $\Xi^-\overline{\Xi}\vphantom{\Xi}^+$ and $\Omega^-\overline{\Omega}\vphantom{\Omega}^+$ pairs at $J/\psi$ or $\psi'$ were determined as well as the angular asymmetry parameters of the main (anti)hyperon decay modes, non-leptonic two-body decays. The result for the $\Lambda\to p\pi^-$ asymmetry parameter $\alpha_\Lambda$ revises by 17% the value used for nearly 50 years in all analyses of $\Lambda$ polarization. In the sequential weak decays $\Xi^-\to\Lambda\pi^-$ and $\Omega^-\to\Lambda K^-$, additionally, the spin rotation parameter was measured. A comparison of the hyperon and antihyperon decay parameters allows for tests of direct CP-symmetry violation complementary to the $\epsilon'/\epsilon$ measurements in kaon decays. Of special importance are the new results on $e^+e^-\to J/\psi\to\Xi^-\overline{\Xi}\vphantom{\Xi}^+$, 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 for the precision of the CP-violation tests.