Search for CP Violations in the Production and Decay of the Hyperon-Antihyperon Pairs

Abstract

This study introduces a complete joint angular distribution analysis for the process $e^{+}e^{-}\to J/\psi\to B(\to B_1\pi)\bar{B}(\to \bar{B}_1\pi)$ with polarized beams, where $B$ and $B_{1}$ are hyperons. We consider both transverse and longitudinal beam polarization and analyze $CP$ violation in the production and decay of hyperons. We present the complete Fisher information matrix for the sensitivities of the weak decay parameters $\alpha_{-},~\alpha_{+},~\phi_{\Xi}$ and $\bar{\phi}_{\Xi}$, the $P$-violating term $F_{A}$, and the EDM $d_{B}$ (derived from the $CP$-violating term $H_{T}$), under the BESIII and STCF statistics. We find that polarization enhances the sensitivity of the parameters. Specifically, longitudinal polarization provides a more significant improvement compared to transverse polarization, with the enhancement being more pronounced for single-step decays than for multistep decays. With the expected statistics from the BESIII experiment, the estimated EDM sensitivities for $\Lambda$ and $\Sigma^{+}$ are on the order of $10^{-19}~e~\rm cm$, while those for $\Xi^{-}$ and $\Xi^{0}$ are $10^{-18}~e~\rm cm$. The upcoming STCF experiment is expected to improve these estimates by $1-2$ orders of magnitude. Furthermore, $CP$ violation in hyperon decays originates from weak-phase differences among partial-wave amplitudes. Based on a refined isospin analysis, we emphasize the non-negligible contribution of $\Delta I = 3/2$ amplitudes to $CP$ violation and advocate for increased theoretical attention to this aspect in future studies..