ψ(2S)→π+π−J/ψdecay distributions

Using a sample of 3.8 M $\psi \mathrm{}\left(2S\right)\mathrm{}$ events accumulated with the BES detector, the process $\psi \mathrm{}\left(2S\right)\mathrm{}\to {\pi }^{+}{\pi }^{-}J/\psi$ is studied. The angular distributions are compared with the general decay amplitude analysis of Cahn. We find that the dipion system requires some D wave amplitude, as well as S wave. On the other hand, the $J/\psi -\left({\pi }^{+}{\pi }^{-}\right)$ relative angular momentum is consistent with being pure S wave. The decay distributions have been fit to heavy quarkonium models, including the Novikov-Shifman model. This model, which is written in terms of the parameter $\kappa ,$ predicts that D wave pions should be present. We determine $\kappa =0.183\mathrm{}\pm 0.002\pm 0.003$ based on the joint $m_{\pi \pi }-\cos {\theta }_{\pi }^{*}$ distribution. The fraction of D wave amplitude as a function of $m_{\pi \pi }$ is found to decrease with increasing $m_{\pi \pi },$ in agreement with the model. We have also fit the Mannel-Yan model, which is another model that allows D wave pions.