Tensor amplitudes for partial wave analysis of $\psi \to \mathrm{\Delta }\bar{\mathrm{\Delta }}$ within helicity frame

We have derived the tensor amplitudes for partial wave analysis of $\psi \to \mathrm{\Delta }\bar{\mathrm{\Delta }}$, $\mathrm{\Delta }\to p\pi$ within the helicity frame, as well as the amplitudes for the other decay sequences with same final states. 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 $J\mathrm{/}\psi$ and $\psi (2S)$ data samples.