Two-body hadronic charmed meson decays

Abstract

We study in this work 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 (CF) decay modes using ${\chi }^2$ minimization. The best-fitted values are then used to predict the branching fractions of the singly-Cabibbo-suppressed (SCS) and doubly-Cabibbo-suppressed decay modes in the flavor SU(3) symmetry limit. We observe significant SU(3) breaking effects in some of SCS 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 $D_s^{+}\to {\bar{K}}^0{K}^{\ast +}$ 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 $D\to \bar{K}\pi$, ${\bar{K}}^{\ast }\pi$ and $\bar{K}\rho$ 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.

32 pages, 5 figures. An alternative method for error bar extraction is used; last columns of Tables~I to VI, and all entries in Tables~VII, VIII and X are modified. To appear in PRD.

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