Solution to the puzzle of Γ(${\mathit{D}}^0$→${\mathit{K}}^{+}$${\mathit{K}}^{\mathrm{-}}$)/Γ(${\mathit{D}}^0$→${\mathrm{\pi }}^{+}$${\mathrm{\pi }}^{\mathrm{-}}$) in a unified approach to D→πK¯,KK¯, and ππ and K→ππ decays

A nonperturbative algebraic approach, which deals with long-distance physics in earnest but also maintains a close contact with quark-line diagrams, has previously been applied to the derivation of the ‖ΔI‖=(1/2 rule in the K→2π decays. Reasonable estimates of the rates of $D^0$→πK¯ and φK${¯}^0$ decays in terms of the rate of $K_S^0$→ππ decay have also been obtained, to the approximation in which excited state contributions to the on-mass-shell intermediate states are being neglected for the moment. In this paper, we examine our unified approach to the D→πK¯, KK¯, and ππ and K→ππ decays further, now including the four-quark [QQ][Q¯Q¯] meson contribution to the on-mass-shell intermediate states. We find that the result provides us with a solution to the well-known puzzle in the observed rates of various Cabibbo-suppressed decays of the $D^0$ meson, particularly Γ(${\mathit{D}}^0$→${\mathit{K}}^{+}$ ${\mathit{K}}^{\mathrm{-}}$)/Γ(${\mathit{D}}^0$→${\mathrm{\pi }}^{+}$ ${\mathrm{\pi }}^{\mathrm{-}}$)≃3.6, which has never been solved in a systematic manner. In addition, it gives us a significantly improved prediction on Γ($D^0$→πK¯) in comparison with Γ($K_S^0$→ππ).