Entanglement in joint $\Lambda \bar{\Lambda}$ decay

TL;DR

This paper analyzes the joint decay of Lambda and anti-Lambda particles in electron-positron collisions to extract electromagnetic form factors, presenting a covariant calculation and comparing it with an extended folding method.

Contribution

It introduces a covariant calculation of the joint decay process and extends the folding method to ensure correct counting of hyperon-spin states.

Findings

The covariant cross-section distribution is explicitly expressed in scalar products.

The extended folding method is shown to be equivalent and covariant.

Correct spin state counting is crucial for accurate decay analysis.

Abstract

We investigate the joint $\Lambda \bar{\Lambda}$ decay in the reaction $e^+ e^- \rightarrow \gamma \Lambda(\rightarrow p\pi^-) \bar{\Lambda}(\rightarrow \bar{p}\pi^+)$. This reaction may provide information on the electromagnetic form factors of the Lambda baryon, in the time-like region. We present a conventional diagram-based calculation where production and decay steps are coherent and summations over final-state proton and anti-proton spins are performed. The resulting cross-section distribution is explictly covariant as it is expressed in scalar products of the four-momentum vectors of the participating particles. We compare this calculation with that of the folding method which we extend and make explicitly covariant. In the folding method production and decay distributions, not amplitudes, are folded together. Of particular importance is then a correct counting of the number of possible intermediate-hyperon-spin states.