Extraction of Polarization Parameters in the $\mathrm{\bar{p} p} \rightarrow \bar{\Omega} \Omega$ Reaction

Abstract

A method to extract the polarization of $\Omega$ hyperons produced via the strong interaction is presented. Assuming they are spin 3/2 particles, the corresponding spin density matrix can be written in terms of seven non-zero polarization parameters, all retrievable from the angular distribution of the decay products. Moreover by considering the full decay chain $\Omega\rightarrow \Lambda K\rightarrow p\pi K$ the magnitude of the asymmetry parameters $\beta_\Omega$ and $\gamma_\Omega$ can be obtained. This method, applied here to the specific $\Omega$ case, can be generalized to any weakly decaying hyperon and is perfectly suited for the PANDA experiment where hyperon-antihyperon pairs will be copiously produced in proton-antiproton collisions. The aim is to take a step forward towards the understanding of the mechanism that reigns strangeness production in these processes.