Branching ratios and direct CP asymmetries in $D\to PV$ decays

We study the two-body hadronic $D\to PV$ decays, where $P$ ($V$) denotes a pseudoscalar (vector) meson, in the factorization-assisted topological-amplitude approach proposed in our previous work. This approach is based on the factorization of short-distance and long-distance dynamics into Wilson coefficients and hadronic matrix elements of four-fermion operators, respectively, with the latter being parametrized in terms of several nonperturbative quantities. We further take into account the $\rho$-$\omega$ mixing effect, which improves the global fit to the branching ratios involving the $\rho^0$ and $\omega$ mesons. Combining short-distance dynamics associated with penguin operators and the hadronic parameters determined from the global fit to branching ratios, we predict direct $CP$ asymmetries. In particular, the direct $CP$ asymmetries in the $D^0\to K^0\overline{K}^{*0},~\overline{K}^0K^{*0}$, $D^+\to\pi^+\rho^0$, and $D_s^+\to K^+\omega,~K^+\phi$ decays are found to be of ${\cal O}(10^{-3})$, which can be observed at the LHCb or future Belle II experiment. We also predict the $CP$ asymmetry observables of some neutral $D$ meson decays.