Search forψ(3770)→ρπat the BESII detector at the Beijing Electron-Positron Collider

Non-$D\overline{D}$ decay $\ensuremath{\psi}(3770)\ensuremath{\rightarrow}\ensuremath{\rho}\ensuremath{\pi}$ is searched for using a data sample of $(17.3\ifmmode\pm\else\textpm\fi{}0.5)\text{ }\text{ }\mathrm{p}{\mathrm{b}}^{\ensuremath{-}1}$ taken at the center-of-mass energy of 3.773 GeV by the BESII detector at the BEPC. No $\ensuremath{\rho}\ensuremath{\pi}$ signal is observed, and the upper limit of the cross section is measured to be $\ensuremath{\sigma}({e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\rho}\ensuremath{\pi})l6.0\text{ }\text{ }\mathrm{pb}$ at 90% C. L. Considering the interference between the continuum amplitude and the $\ensuremath{\psi}(3770)$ resonance amplitude, the branching fraction of $\ensuremath{\psi}(3770)$ decays to $\ensuremath{\rho}\ensuremath{\pi}$ is determined to be $\mathcal{B}(\ensuremath{\psi}(3770)\ensuremath{\rightarrow}\ensuremath{\rho}\ensuremath{\pi})\ensuremath{\in}(6.0\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6},2.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3})$ at 90% C. L. This is in agreement with the prediction of the $S$- and $D$-wave mixing scheme of the charmonium states for solving the ``$\ensuremath{\rho}\ensuremath{\pi}$ puzzle'' between $J/\ensuremath{\psi}$ and $\ensuremath{\psi}(2S)$ decays.