Feasibility of searching for the Cabibbo-favored $D^{\ast }$ $\to$ $\bar{K}{\pi }^{+}$, ${\bar{K}}^{\ast }{\pi }^{+}$, $\bar{K}{\rho }^{+}$ decays

The current knowledge on the $D^{\ast }$ mesons are still inadequate. Encouraged by the positive development prospects of high-luminosity and high-precision experiments, the Cabibbo-favored nonleptonic $D^{\ast }$ $\to$ $\bar{K}{\pi }^{+}$, ${\bar{K}}^{\ast }{\pi }^{+}$, $\bar{K}{\rho }^{+}$ weak decays are studied with the naive factorization approach. It is found that branching ratios of these processes can reach up to $\mathcal{O}({10}^{-10})$ or more, and can be accessible at STCF, CEPC, FCC-ee and LHCb@HL-LHC experiments in the future. It might even be possible to search for the $D^{\ast 0}$ $\to$ $K^{\ast -}{\pi }^{+}$ and $K^{-}{\rho }^{+}$ decays at the running SuperKEKB experiments.