In this work we study the two-body hadronic charmed meson decays, including both the $PP$ and $VP$ modes. The latest experimental data are first analyzed in the diagrammatic approach. The magnitudes and strong phases of the flavor amplitudes are extracted from the Cabibbo-favored decay modes using ${\chi }^2$ minimization. The best-fitted values are then used to predict the branching fractions of the singly Cabibbo-suppressed and doubly Cabibbo-suppressed decay modes in the flavor SU(3) symmetry limit. We observe significant SU(3) breaking effects in some of the singly Cabibbo-suppressed channels. In the case of $VP$ modes, we point out that the $A_P$ and $A_V$ amplitudes cannot be completely determined based on currently available data. We conjecture that the quoted experimental results for both $D_s^{+}\to {\overline{K}}^0{K}^{*+}$ and $D_s^{+}\to {\rho }^{+}{\eta }^{\prime }$ are overestimated. We compare the sizes of color-allowed and color-suppressed tree amplitudes extracted from the diagrammatical approach with the effective parameters $a_1$ and $a_2$ defined in the factorization approach. The ratio $|a_2/a_1|$ is more or less universal among the $D\to \overline{K}\pi$, ${\overline{K}}^{*}\pi$, and $\overline{K}\rho$ modes. This feature allows us to discriminate between different solutions of topological amplitudes. For the long-standing puzzle about the ratio $\Gamma (D^0\to K^{+}{K}^{-})/\Gamma (D^0\to {\pi }^{+}{\pi }^{-})$, we argue that, in addition to the SU(3) breaking effect in the spectator amplitudes, the long-distance resonant contribution through the nearby resonance $f_0(1710)$ can naturally explain why $D^0$ decays more copiously to $K^{+}{K}^{-}$ than ${\pi }^{+}{\pi }^{-}$ through the $W$-exchange topology. This has to do with the dominance of the scalar glueball content of $f_0(1710)$ and the chiral-suppression effect in the decay of a scalar glueball into two pseudoscalar mesons. The same final-state interaction also explains the occurrence of $D^0\to K^0{\overline{K}}^0$ and its vanishing amplitude when SU(3) flavor symmetry is exact. Owing to the $G$-parity selection rule, $D_s^{+}\to {\pi }^{+}\omega$ does not receive contributions from the short-distance $W$-annihilation and resonant final-state interactions, but it can proceed through the weak decays $D_s^{+}\to {\rho }^{+}{\eta }^{{(}^{\prime })}$ followed by the final-state rescattering of ${\rho }^{+}{\eta }^{{(}^{\prime })}$ into ${\pi }^{+}\omega$ through quark exchange.

• Received 8 January 2010

DOI:https://doi.org/10.1103/PhysRevD.81.074021