Angular distributions in the decayψ′→ψππ

A general analysis of the decay amplitudes for ${\psi }^{\prime }\to \psi \pi \pi$ is presented. Angular distributions are calculated for ${\psi }^{\prime }\to \psi {\pi }^{+}{\pi }^{-}\to {\mu }^{+}{\mu }^{-}{\pi }^{+}{\pi }^{-}$ in terms of partial-wave amplitudes diagonal in orbital and spin angular momentum. The determination of the partial-wave amplitudes for ${\psi }^{\prime }\to \psi \pi \pi$ may yield the difference between $s$-wave and $d$-wave $\pi -\pi$ phase shifts in the $I=0\mathrm{}$ channel if there is sufficient $\pi -\pi$ $d$-wave present to produce measurable interference. The angular distributions for decays of the form $\psi \to \mathrm{VPP}$ follow, mutatis mutandis, although $\mathrm{VP}$ interactions may prevent the determination of the $\mathrm{PP}$ phase shifts. Determination of the partial-wave amplitudes will test the validity of chiral-symmetry models for the ${\psi }^{\prime }\to \psi \pi \pi$ decay.