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 ${\alpha }_{-},{\alpha }_{+},{\varphi }_{\Xi }$ and ${\bar{\varphi }}_{\Xi }$, 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 $10^{-19}e\mathrm{cm}$, while those for ${\Xi }^{-}$ and ${\Xi }^0$ are $10^{-18}e\mathrm{cm}$. 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..

Comments: 23 pages, 8 figures, 6 tables