Updated analysis of $D\to PP,VP$, and $VV$ decays: Implications for $K_S^0-K_L^0$ asymmetries and $D^0-{\overline{D}}^0$ mixing

An updated analysis of the two-body $D\to PP,VP$, and $VV$ decays within the framework of the topological diagram approach is performed. A global fit to the Cabibbo-favored (CF) modes in the $VP$ sector gives many solutions with similarly small local minima in ${\chi }^2$. The solution degeneracy is lifted once we use them to predict for the singly-Cabibbo-suppressed modes. Topological amplitudes are extracted for the $\eta -{\eta }^{\prime }$ mixing angles $\varphi =40.4°$ and 43.5°. The $K_S^0-K_L^0$ asymmetries in $D\to K_{S,L}^{0}M$ decays denoted by $R(D,M)$ are studied. While the predicted $R(D^0,P)$ for $P={\pi }^0,\eta$ and ${\eta }^{\prime }$ agree with experiment, the calculated $R(D^{+},{\pi }^{+})$, $R(D_s^{+},K^{+})$, $R(D^0,\omega )$, and $R(D^0,\varphi )$ deviate from the data. We conjecture that the relative phase between the topological amplitudes ($C+A$) and ($T+C$) should be slightly smaller than 90° in order to explain the first two discrepancies and that additional singlet contributions due to the SU(3)-singlet nature of $\omega$ and $\varphi$ are needed to account for the last two. For doubly-Cabibbo-suppressed (DCS) $D\to VP$ decays, their topological amplitudes (double primed) cannot be all the same as the corresponding ones in the CF modes. The assumption of $E_{V,P}^{\prime \prime }=E_{V,P}$ for the $W$-exchange amplitude leads to some inconsistencies with the experiment. Through the measured relative phases between CF and DCS channels, the relations of $E_{V,P}^{\prime \prime }$ with $E_{V,P}$ are determined. Long-distance contributions to the $D^0-{\overline{D}}^0$ mixing parameter $y$ are evaluated in the exclusive approach. In particular, we focus on $D\to PP$ and $VP$ decays where $y$ can be reliably estimated. We conclude that $y_{PP}\sim (0.110\pm 0.011)\%$ and the lower bound on $y_{VP}$ is $(0.220\pm 0.071)\%$. It is thus conceivable that at least half of the mixing parameter $y$ can be accounted for by the two-body $PP$ and $VP$ modes. The main uncertainties arise from the yet-to-be-measured DCS channels and their phases relative to the CF ones.