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 $B\left(J/\psi \to {\overline{D}}^{0}{\pi }^{0}+c.c.\right)<4.7×{10}^{-7}$, $B\left(J/\psi \to {\overline{D}}^{0}\eta +c.c.\right)<6.8×{10}^{-7}$, $B\left(J/\psi \to {\overline{D}}^{0}{\rho }^{0}+c.c.\right)<5.2×{10}^{-7}$, $B\left(J/\psi \to {D}^{-}{\pi }^{+}+c.c.\right)<7.0×{10}^{-8}$, and $B\left(J/\psi \to {D}^{-}{\rho }^{+}+c.c.\right)\phantom{\rule{0ex}{0ex}}<6.0×{10}^{-7}$ at the 90% confidence level.