Two-body hadronic charmed meson decays

Abstract

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 ${\ensuremath{\chi}}^{2}$ 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 ${D}_{s}^{+}\ensuremath{\rightarrow}{\overline{K}}^{0}{K}^{*+}$ and ${D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\rho}}^{+}{\ensuremath{\eta}}^{\ensuremath{'}}$ 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 $D\ensuremath{\rightarrow}\overline{K}\ensuremath{\pi}$, ${\overline{K}}^{*}\ensuremath{\pi}$, and $\overline{K}\ensuremath{\rho}$ modes. This feature allows us to discriminate between different solutions of topological amplitudes. For the long-standing puzzle about the ratio $\ensuremath{\Gamma}({D}^{0}\ensuremath{\rightarrow}{K}^{+}{K}^{\ensuremath{-}})/\ensuremath{\Gamma}({D}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}})$, 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 ${K}^{+}{K}^{\ensuremath{-}}$ than ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ 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 ${D}^{0}\ensuremath{\rightarrow}{K}^{0}{\overline{K}}^{0}$ and its vanishing amplitude when SU(3) flavor symmetry is exact. Owing to the $G$-parity selection rule, ${D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}\ensuremath{\omega}$ does not receive contributions from the short-distance $W$-annihilation and resonant final-state interactions, but it can proceed through the weak decays ${D}_{s}^{+}\ensuremath{\rightarrow}{\ensuremath{\rho}}^{+}{\ensuremath{\eta}}^{{(}^{\ensuremath{'}})}$ followed by the final-state rescattering of ${\ensuremath{\rho}}^{+}{\ensuremath{\eta}}^{{(}^{\ensuremath{'}})}$ into ${\ensuremath{\pi}}^{+}\ensuremath{\omega}$ through quark exchange.