Polarization analysis in $e^{+}{e}^{-}\to J/\psi \to$ baryon-antibaryon pairs

Abstract

We present a comprehensive polarization analysis for the process $e^{+}{e}^{-}\to J/\psi \to$ baryon-antibaryon pairs~$B_1{\bar{B}}_2$. All possible helicity amplitudes for $e^{+}{e}^{-}\to J/\psi$ and $J/\psi \to B_1{\bar{B}}_2$ are provided, along with their transformation properties under parity and $CP$ operations. Taking full account of beam polarization, we analyze the polarization of the $J/\psi$ 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 $J/\psi \to B_1{\bar{B}}_2$. Considering both hadronic and radiative baryon decay models, we derive the joint angular distribution of the final-state particles. Focusing on the process $J/\psi \to \Lambda {\bar{\Sigma }}^0$, 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.