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

The $\psi'\to J/\psi\pi^+\pi^-$ 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 $\psi'\to J/\psi\pi^+\pi^-$ decay.