Sequential decays of the triple strange process $\bar{p} p \rightarrow \bar{\Omega}^{+} \Omega^{-} \rightarrow K^{+} \bar{\Lambda} K^{-} \Lambda \rightarrow K^{+} \bar{p} \pi^{+} K^{-} p \pi^{-}$: a model-independent approach

Abstract

A model-independent irreducible tensor formalism is developed to analyse $\bar{\Omega}\Omega$ production in $\bar{p}p$ collisions and its subsequent decay via the triple-strange decay process, $\bar{\Omega}^{+} \Omega^{-} \rightarrow K^{+} \bar{\Lambda} K^{-} \Lambda \rightarrow K^{+} \bar{p} \pi^{+} K^{-} p \pi^{-}$. These processes are relevant for the upcoming experiments at PANDA. We not only provide expressions for the density matrix of the $\Omega\bar{\Omega}$ system but also for the products at each stage of the decay. The Fano statistical tensors so obtained not only completely characterize the relevant final systems but also provide expressions for joint angular distributions. Finally, we show which of the Fano statistical tensors characterizing the $\bar{\Omega}\Omega$ system can be inferred from the Fano statistical tensors characterizing the final $\bar{p}p$ system, wherein we also obtain the relation between the production cross sections for $\Omega\bar{\Omega}$ and the final $p\bar{p}$ system.