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

TL;DR

This work develops a complete joint angular distribution framework for $e^{+}e^{-}\to J/\psi\to B(\to B_1\pi)\bar{B}(\to \bar{B}_1\pi)$ with polarized beams to probe CP violation in hyperon production and decay. By formulating production and decay density matrices and linking CP-violating terms $H_T$ and $F_A$ to the hyperon EDM $d_B$, the authors construct a Fisher information matrix to quantify statistical sensitivities of weak decay parameters and CP observables under BESIII and STCF statistics. The study shows that beam polarization, especially longitudinal, significantly enhances sensitivity, with EDM reach of $|d_B| \sim 10^{-19}-10^{-18}$ $e\,\mathrm{cm}$ at BESIII and improvements of $1$–$2$ orders of magnitude at STCF, while $A_{CP}$ and $B_{CP}$ attain sensitivities at the $10^{-3}$ to $10^{-4}$ level. A key theoretical insight is the explicit incorporation of $\Delta I=3/2$ amplitudes in hyperon decays, which in the $\Lambda$ system may yield two viable solutions for the weak-phase structure, separable by the decay angle $\phi_{\Lambda}$, offering a clear experimental discriminator and guiding future STCF design for new physics searches.

Abstract

This study introduces a complete joint angular distribution analysis for the process $e^{+}e^{-}\to J/ψ\to B(\to B_1π)\bar{B}(\to \bar{B}_1π)$ 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 $α_{-},~α_{+},~φ_Ξ$ and $\barφ_Ξ$, 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 multi-step decays. With the expected statistics from the BESIII experiment, the estimated EDM sensitivities for $Λ$ and $Σ^{+}$ are on the order of $10^{-19}~e~\rm cm$, while those for $Ξ^{-}$ and $Ξ^{0}$ are $10^{-18}~e~\rm cm$. Furthermore, the STCF experiment is expected to improve these estimates by $1\sim2$ orders of magnitude.

Figures (8)

• Figure 1: Transformations of a spin-$s$ particle under P and T operators, along with the particle's electric dipole moment $(\vec{d})$, and the external magnetic $(\vec{B})$ and electric $(\vec{E})$ fields. A permanent electric dipole moment $\vec{d}$ of a fundamental particle is proportional to its angular momentun $\vec{J}$. It shows that the invariance of the particle dipole moment under P and T transformations is maintained only when $\vec{d}=0$.
• Figure 2: Helicity rest frames for electron and positron beams and that for the $J/\psi$ meson in the c.m. frame.
• Figure 3: Helicity angles in single-step decays, such as $J/\psi\to B(\to B_{1}\pi)\bar{B}(\to\bar{B}_{1}\pi)$ decays, where $B$ represents a $\Lambda$ or $\Sigma^{+}$ hyperon.
• Figure 4: Helicity angles in two-step decays, such as $J/\psi\to B(\to B_1\pi)\bar{B}(\to\bar{B}_1\pi)$ decays, where $B$ represents a $\Xi^{0}$ or $\Xi^{-}$ hyperon.
• Figure 5: Sensitivities of decay parameters (a) $~\alpha_{-}$, (b) $~\alpha_{+}$, (c) the parity-violating term $|F_{A}|$, and (d) the electric dipole moment $|d_{\Lambda}|$ to beam polarization variations in $J/\psi\to\Lambda(\to p\pi^{-})\bar{\Lambda}(\to \bar{p}\pi^{+})$ decays.