Polarization observables in the $e^+ e^- \rightarrow \bar{\Lambda} \Lambda$ reaction

TL;DR

This paper calculates polarization observables for electron-positron annihilation into hyperon pairs, providing a method to determine hyperon electromagnetic form factors without direct spin measurements, and discusses discrepancies with previous results.

Contribution

It introduces a comprehensive framework for extracting hyperon electromagnetic form factors from polarization and decay distributions in $e^+ e^- ightarrow ar{ ext{hyperon}} ext{hyperon}$ reactions, including resolving conflicts with prior data.

Findings

Complete polarization and decay distributions derived for hyperon production.

Method to determine electromagnetic form factors without hyperon spin measurements.

Identification of conflicts with previously published tensor-polarization results.

Abstract

Cross-section, vector-polarization, and tensor-polarization distributions are calculated for the reactions $e^+ e^- \rightarrow \bar{p}p$ and $e^+ e^- \rightarrow \bar{\Lambda} \Lambda$. Each reaction requires six characteristic functions that are bilinear in the, possibly complex, electromagnetic form factors, denoted $G_E(P^2)$ and $G_M(P^2)$, of $p$ and $\Lambda$. For the hyperon reaction also the joint-decay distributions of $\Lambda$ and $\bar{\Lambda}$ are calculated. Their knowledge allow a complete determination of the hyperon electromagnetic form factors, without measuring hyperon spins. We explain how this is done in practice. For some tensor-polarization components our results are in conflict with previously repeatedly published distributions.