Polarization analysis in $e^+e^-\rightarrow J/ψ\rightarrow$ baryon-antibaryon pairs

TL;DR

This work develops a complete polarization framework for $e^{+}e^{-} \rightarrow J/\psi \rightarrow B_{1}\bar{B}_{2}$ within the helicity formalism, detailing production, decay, and baryon decays in a unified spin-density approach. It introduces a polarization-transfer matrix to map $J/\psi$ polarization to baryon final states and derives a full joint angular distribution that incorporates parity- and $CP$-violating effects in both baryon production and decays. By relating helicity amplitudes to baryon form factors and transition form factors, the paper provides explicit parametric forms and symmetry constraints for conjugate channels, enabling targeted CP studies, including the isospin-violating channel $J/\psi \rightarrow \Lambda\bar{\Sigma}^{0}$. Numerical sensitivity analyses show that beam polarization, especially at future facilities like STCF, dramatically enhances precision in extracting parity-violating and CP-violating parameters, with projected uncertainties reaching the $10^{-7}$–level for some form-factor combinations. Overall, the framework offers a comprehensive toolkit for probing parity and CP violation in baryon production and decay at $J/\psi$ threshold, facilitating precise tests of the Standard Model and potential new sources of CP violation.

Abstract

We present a comprehensive polarization analysis for the process $e^{+}e^{-} \rightarrow J/ψ\rightarrow$ baryon-antibaryon pairs~$B_{1}\bar{B}_{2}$. All possible helicity amplitudes for $e^{+}e^{-} \rightarrow J/ψ$ and $J/ψ\rightarrow B_{1} \bar{B}_{2}$ are provided, along with their transformation properties under parity and $CP$ operations. Taking full account of beam polarization, we analyze the polarization of the $J/ψ$ produced in $e^{+}e^{-}$ annihilation and show that all eight independent polarization components can be nonzero. By introducing a polarization transfer matrix, we propose a novel method to compute the polarization transfer in the decay $J/ψ\rightarrow B_{1} \bar{B}_{2}$. Considering both hadronic and radiative baryon decay models, we derive the joint angular distribution of the final-state particles. Focusing on the process $J/ψ\rightarrow Λ\barΣ^{0}$, we provide statistical uncertainty estimates for probing $CP$ violation in associated production of different baryons. This work establishes a complete framework for studying the parity and $CP$ violations present in baryon productions and decays within the helicity formalism.

Figures (5)

• Figure 1: Comparison of the laboratory frame (upper) and center-of-mass frame (lower) for positron-electron collisions.
• Figure 2: The $e^{+}e^{-}\rightarrow J/\psi$ process in c.m. frame. The coordinate systems $x_{e^{+}}$-$y_{e^{+}}$-$z_{e^{+}}$, $x_{e^{-}}$-$y_{e^{-}}$-$z_{e^{-}}$ and $x$-$y$-$z$ are the helicity frames for positron, electron, and $J/\psi$.
• Figure 3: The $J/\psi\rightarrow B_{1}\bar{B}_{2}$ process in $J/\psi$ rest frame (helicity frame). The coordinate systems $x_{B_{1}}$-$y_{B_{1}}$-$z_{B_{1}}$, $x_{\bar{B}_{2}}$-$y_{\bar{B}_{2}}$-$z_{\bar{B}_{2}}$, and $x$-$y$-$z$ represent the helicity frame for $B_{1}$, $\bar{B}_{2}$, and $J/\psi$, respectively. $\theta$ and $\phi$ denote the production angles of the $B_{1}$ baryon in the $J/\psi$ rest frame.
• Figure 4: Parity-violating effects in different hyperon production processes under unpolarized beam conditions.
• Figure 5: Predicted statistical uncertainties for the transition form factors $F_{3}$ and $F_{4}$ for the process $J/\psi\rightarrow\Lambda\bar{\Sigma}^{0}$ as a function of the degree of electron beam longitudinal polarization $P_{e}$.