Search for the charmonium weak decays $J\mathrm{/}\psi \to D_s^{-}{\rho }^{+}+c\mathrm{.}c\mathrm{.}$ and $J\mathrm{/}\psi \to D_s^{-}{\pi }^{+}+c\mathrm{.}c\mathrm{.}$

Based on $(10087\pm 44)\times {10}^6$ $J\mathrm{/}\psi$ events recorded with the BESIII detector, we search for the rare charmonium weak decays $J\mathrm{/}\psi \to D_s^{-}{\rho }^{+}+c\mathrm{.}c\mathrm{.}$ and $J\mathrm{/}\psi \to D_s^{-}{\pi }^{+}+c\mathrm{.}c\mathrm{.}$ No signal is observed, and upper limits on the branching fractions at the $90\mathrm{\%}$ confidence level are set as $\mathcal{B}(J\mathrm{/}\psi \to D_s^{-}{\rho }^{+}+c\mathrm{.}c\mathrm{.})<8.0\times {10}^{-7}$ and $\mathcal{B}(J\mathrm{/}\psi \to D_s^{-}{\pi }^{+}+c\mathrm{.}c\mathrm{.})<4.1\times {10}^{-7}$. Our results provide the most stringent experimental constraints on these decays.