The pi pi Phase Shifts from psi' to J/psi pi^+ pi^- Decays

The ${\psi }^{\mathrm{\prime }}\to J\mathrm{/}\psi {\pi }^{+}{\pi }^{-}$ decay process provides a new way to extract the $\pi \pi$ $S$ wave phase shifts up to $0.59GeV$. In this paper we derive the formulae for extracting the $\pi \pi$ $S$ wave phase shifts from the invariant mass spectrum of $\pi \pi$ in the ${\psi }^{\mathrm{\prime }}\to J\mathrm{/}\psi {\pi }^{+}{\pi }^{-}$ decay.