CP asymmetries in Dto K⁰_(S,L)P and Dto K⁰_(S,L)V decays

$D$ meson decays into neutral kaons involve both Cabibbo-favored and doubly Cabibbo-suppressed amplitudes as well as final-state kaon mixing, providing abundant sources of CP violation. In this work, we analyze CP asymmetries in the $D\to K^0_{S,L}P$ and $D\to K^0_{S,L}V$ decays, where $P$ and $V$ denote pseudoscalar and vector mesons respectively. The formulas of the time-dependent and time-integrated CP asymmetries in these modes are derived, in which the $D^0-\overline D^0$ mixing effects and the $K^0_L$ modes are considered for the first time. The hadronic parameters that determine CP asymmetries are extracted by the global fit of branching fractions within the topological diagram approach. A significant result is that the tension between theoretical predictions and experimental data for the $K_S^0-K_L^0$ asymmetries in $D^0\to K_{S,L}^0\omega$ and $D^0\to K_{S,L}^0\phi$ modes is mitigated. The CP-violating effects arising from the interference between Cabibbo-favored and doubly Cabibbo-suppressed amplitudes with neutral kaon mixing could reach to $\mathcal{O}(10^{-3})$ order in the $D^+\to K^0_S\pi^+$, $D^+_s\to K^0_SK^+$, $D^0\to K^0_S\rho^0$, and $D^0\to K^0_S\phi$ modes. The difference between the CP asymmetries in the $D^+\to K^0_S\pi^+$ and $D^+_s\to K^0_SK^+$ modes is available on LHCb and Belle II in the near future.