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