Search for the rare decaysJ/ψ→Ds−ρ+andJ/ψ→D¯0K¯*0

A search for the rare decays of $J/\ensuremath{\psi}\ensuremath{\rightarrow}{D}_{s}^{\ensuremath{-}}{\ensuremath{\rho}}^{+}+\mathrm{c}.\mathrm{c}.$ and $J/\ensuremath{\psi}\ensuremath{\rightarrow}{\overline{D}}^{0}{\overline{K}}^{*0}+\mathrm{c}.\mathrm{c}.$ is performed with a data sample of 225.3-million $J/\ensuremath{\psi}$ events collected with the Beijing Spectrometer III detector. No evident signal is observed. Upper limits on the branching fractions are determined to be $\mathcal{B}(J/\ensuremath{\psi}\ensuremath{\rightarrow}{D}_{s}^{\ensuremath{-}}{\ensuremath{\rho}}^{+}+\mathrm{c}.\mathrm{c}.)l1.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ and $\mathcal{B}(J/\ensuremath{\psi}\ensuremath{\rightarrow}{\overline{D}}^{0}{\overline{K}}^{*0}+\mathrm{c}.\mathrm{c}.)l2.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ at the 90% confidence level.