Search for $J/\psi$ weak decays containing a $D$ meson

Using a sample of about 10 billion $J/\psi$ events with the BESIII detector, we search for the weak decays of $J/\psi \to {\overline{D}}^0{\pi }^0+c.c.$, $J/\psi \to {\overline{D}}^0\eta +c.c.$, $J/\psi \to {\overline{D}}^0{\rho }^0+c.c.$, $J/\psi \to D^{-}{\pi }^{+}+c.c.$, and $J/\psi \to D^{-}{\rho }^{+}+c.c.$. Since no significant signal is observed, we set the upper limits of the branching fractions of these decays to be $B(J/\psi \to {\overline{D}}^0{\pi }^0+c.c.)<4.7\times {10}^{-7}$, $B(J/\psi \to {\overline{D}}^0\eta +c.c.)<6.8\times {10}^{-7}$, $B(J/\psi \to {\overline{D}}^0{\rho }^0+c.c.)<5.2\times {10}^{-7}$, $B(J/\psi \to D^{-}{\pi }^{+}+c.c.)<7.0\times {10}^{-8}$, and $B(J/\psi \to D^{-}{\rho }^{+}+c.c.)<6.0\times {10}^{-7}$ at the 90% confidence level.