Search for a vector glueball by a scan of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mfrac><mml:mrow><mml:mi>J</mml:mi></mml:mrow><mml:mrow><mml:mi>ψ</mml:mi></mml:mrow></mml:mfrac></mml:math>resonance

The cross section for ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\rho}\ensuremath{\pi}$ has been measured by the BES detector at BEPC at center-of-mass energies covering a 40 MeV interval spanning the $\frac{J}{\ensuremath{\psi}}$ resonance. The data are used to search for the vector gluonium state hypothesized by Brodsky, Lepage, and Tuan as an explanation of the $\ensuremath{\rho}\ensuremath{\pi}$ puzzle in charmonium physics. The shape of the $\ensuremath{\rho}\ensuremath{\pi}$ cross section is compatible with that of the total hadronic cross section. No distortions indicating the presence of a vector glueball are seen.