Polarization observables in $e^+e^-$ annihilation to a baryon-antibaryon pair

TL;DR

This paper develops a formalism using helicity methods to analyze polarization observables in electron-positron annihilation producing baryon-antibaryon pairs, enabling detailed angular distribution studies and spin tests.

Contribution

It introduces modular expressions for spin density matrices of various baryon pair spins, facilitating analysis of decay chains and spin assignments in high-energy collider data.

Findings

Derived spin density matrices for different baryon pair spins.

Provided modular formulas for decay chain analysis.

Demonstrated application to $ ext{e}^+ ext{e}^- o ext{J}/ ext{ψ}$ decays.

Abstract

Using the helicity formalism of Jacob and Wick we derive spin density matrices of baryon antibaryon pairs produced in $e^+e^-$ annihilation. We consider the production of pairs with spins $1/2+\overline{1/2}$, $1/2+\overline{3/2}$ (+c.c.) and $3/2+\overline{3/2}$. We provide modular expressions to include chains of weak hadronic two-body decays of the produced hyperons. The expressions are suitable for the analysis of high statistics data from $J/\psi$ and $\psi(2S)$ decays at $e^+e^-$ colliders, by fits to the fully differential angular distributions of the measured particles. We illustrate the method by examples, such as the inclusive measurement of the $e^+e^-\to\psi(2S)\to\Omega^-\bar\Omega^+$ process where one decay chain $\Omega^-\to\Lambda K^-$ followed by $\Lambda\to p\pi^-$ is considered. Finally we show that the inclusive angular distributions can be used to test spin assignment of the produced baryons.