Covariant tensor formalism for partial wave analyses of $\psi \rightarrow\Delta\bar{\Delta}$

Abstract

The covariant tensor formulae for partial wave analysis of $\psi \rightarrow\Delta\bar{\Delta}$, $\Delta \to p \pi^\pm$, $\bar{\Delta} \to \bar{p} \pi^\mp$ are derived, as well as the formulae for the decay sequence of $\psi \rightarrow N^* \bar{p}$, $N^* \to \Delta \pi^\mp$, $\Delta \to p \pi^\pm$. These formulae are practical for the experiments measuring $\psi$ decaying into $p \bar{p} \pi^+ \pi^-$ final states, such as BESIII with its recently collected huge $J/\psi$ and $\psi(2S)$ data samples.Comment: 10 page