Search for the rare decays $J/psi to D_s^-rho^+$ and $J/psi to overline{D}{}^0overline{K}{}^{ast0}$

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