Search for the rare decays $J/ψ\to D_s^-ρ^+$ and $J/ψ\to \overline{D}{}^0\overline{K}{}^{\ast0}$
A search for the rare decays of $J/ψ\to D_s^-ρ^+ + c.c.$ and $J/ψ\to \overline{D}{}^0\overline{K}{}^{\ast0} + c.c.$ is performed with a data sample of 225.3 million $J/ψ$ events collected with the BESIII detector. No evident signal is observed. Upper limits on the branching fractions are determined to be $\mathcal{B}(J/ψ\to D_s^-ρ^+ + c.c.) < 1.3 \times 10^{-5}$ and $\mathcal{B}(J/ψ\to \overline{D}{}^0\overline{K}{}^{\ast0} + c.c.) < 2.5 \times 10^{-6}$ at the $90\%$ confidence level.