Possible hadronic excess in ψ(2S) decay and the ρπ puzzle

We study the so-called $\rho \pi$ puzzle of $\psi \mathrm{}\left(2S\right)\mathrm{}$ decay by incorporating two inputs: the relative phase between the one-photon and the gluonic decay amplitude, and a possible hadronic excess in the inclusive nonelectromagnetic decay rate of $\psi \mathrm{}\left(2S\right).$ We look into the possibility that the hadronic excess in $\psi \mathrm{}\left(2S\right)\mathrm{}$ originates from a decay process of long-distance origin which is absent from the $J/\psi$ decay. We propose that the amplitude of this additional process happens to nearly cancel the short-distance gluonic amplitude in the exclusive decay $\psi \mathrm{}\left(2S\right)\mathrm{}\to 1^{-}{0}^{-}$ and turn the sum dominantly real in contrast to the $J/\psi$ decay. We present the general consequences of this mechanism and survey two models which might possibly explain the source of this additional amplitude.