Study of $J\mathrm{/}\psi$ $\to$ $D_{s,d}V$ decays with perturbative QCD approach

Inspired by the recent measurements on two-body nonleptonic $J\mathrm{/}\psi$ weak decay at BESIII, the charm-changing $J\mathrm{/}\psi$ $\to$ $D_{s,d}V$ weak decays are studied with perturbative QCD approach, where $V$ denotes $\rho$ and $K^{\ast }$ vector mesons. It is found that branching ratio for $J\mathrm{/}\psi$ $\to$ $D_s\rho$ decay can reach up to $\mathcal{O}({10}^{-9})$, which is within the potential measurement capability of the future high-luminosity experiments.