Study of the ${\psi}(1S,2S)$ and ${\eta}_{c}(1S,2S)$ weak decays into $DM$

Inspired by the recent measurements on the $J/{\psi}(1S)$ ${\to}$ $D_{s}{\rho}$, $D_{u}K^{\ast}$ weak decays at BESIII and the potential prospects of the charmonium at the high-luminosity heavy-flavor experiments, we study ${\psi}(1S,2S)$ and ${\eta}_{c}(1S,2S)$ weak decays into final states including one charmed meson plus one light meson, considering the QCD corrections to hadronic matrix elements with the QCD factorization. It is found that the Cabibbo favored ${\psi}(1S,2S)$ ${\to}$ $D_{s}^{-}{\rho}^{+}$, $D_{s}^{-}{\pi}^{+}$, $\overline{D}_{u}^{0}\overline{K}^{{\ast}0}$ decays have branching ratios ${\gtrsim}$ $10^{-10}$, which might be accessible at the future experiments.