$K_{S}^{0}-K_{L}^{0}$ asymmetries in $D$-meson decays

The $K_{S}^{0}-K_{L}^{0}$ asymmetries in the $D$ meson decays, induced by the interference between the Cabibbo-favored and the doubly Cabibbo-suppressed amplitudes, can help to understand the dynamics of charm decays. All possible processes of two-body non-leptonic $D$ decays into one neutral kaon and another pseudoscalar or vector meson are considered. We study the $K_{S}^{0}-K_{L}^{0}$ asymmetries and the branching fractions of corresponding processes in the factorization-assisted topological-amplitude approach in which significant flavor $SU(3)$ symmetry breaking effects are included. The branching fractions of $K_{L}^{0}$ modes are predicted. It is first found that the $K_{S}^{0}-K_{L}^{0}$ asymmetries in the $D^0$-meson decays are shifted by the $D^0-\overline D^0$ mixing parameter $y_{D}\simeq0.006$, to be $0.113\pm0.001$ for all the relevant $D^{0}$ decay modes. Our results on $K_{S}^{0}-K_{L}^{0}$ asymmetries are consistent with the current data and could be tested by experiments in the future.