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

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.