Ratio of hadronic decay rates ofJ/ψandψ(2S)and theρπpuzzle

The so-called $\rho \pi$ puzzle of $J/\psi$ and $\psi \mathrm{}\left(2S\right)\mathrm{}$ decays is examined using the experimental data available to date. Two different approaches were taken to estimate the ratio of $J/\psi$ and $\psi \mathrm{}\left(2S\right)\mathrm{}$ hadronic decay rates. While one of the estimates could not yield the exact ratio of $\psi \mathrm{}\left(2S\right)\mathrm{}$ to $J/\psi$ inclusive hadronic decay rates, the other, based on a computation of the inclusive $\mathrm{ggg}$ decay rate for $\psi \mathrm{}\left(2S\right)(J/\psi )$ by subtracting other decay rates from the total decay rate, differs by two standard deviations from the naive prediction of perturbative QCD, even though its central value is nearly twice as large as what was naively expected. A comparison between this ratio, upon making corrections for specific exclusive two-body decay modes, and the corresponding experimental data confirms the puzzles in $J/\psi$ and $\psi \mathrm{}\left(2S\right)\mathrm{}$ decays. We find from our analysis that the exclusively reconstructed hadronic decays of the $\psi \mathrm{}\left(2S\right)\mathrm{}$ account for only a small fraction of its total decays, and a ratio exceeding the above estimate should be expected to occur for a considerable number of the remaining decay channels. We also show that the recent new results from the BES experiment provide crucial tests of various theoretical models proposed to explain the puzzle.