Search for the decays $J\mathrm{/}\psi \to \gamma \rho \varphi$ and $J\mathrm{/}\psi \to \gamma \rho \omega$

Using 58 million $J\mathrm{/}\psi$ events collected with the Beijing Spectrometer (BESII) at the Beijing Electron-Positron Collider, the decays $J/\psi\to \gamma\phi\rho$and$J/\psi\to \gamma\omega\rho$ are searched for, and upper limits on their branching fractions are reported at the 90% C. L. No clear structures are observed in the $\gamma \rho$, $\gamma \varphi$, or $\rho \varphi$ mass spectra for $J\mathrm{/}\psi \to \gamma \varphi \rho$ nor in the $\gamma \rho$, $\gamma \omega$,or$\rho \omega$massspectrafor$J/\psi\to \gamma\omega\rho$.