Interference between doubly-Cabibbo-suppressed and Cabibbo-favored amplitudes in $D^0\to K_S({\pi }^0,\eta ,{\eta }^{\prime })$ decays

Abstract

A definite relative phase and amplitude exists between the doubly-Cabibbo-% suppressed amplitude for $D^0 \to \ko M^0$ and the Cabibbo-favored amplitude for $D^0 \to \ok M^0$, where $M^0=({\pi }^0,\eta ,{\eta }^{\prime })$: $A(D^0 \to \ko M^0) = - \tan^2 θ_C A(D^0 \to \ok M^0)$. Here ${\theta }_C$ is the Cabibbo angle. This relation, although previously recognized (for $M^0={\pi }^0$) as a consequence of the U-spin subgroup of SU(3), is argued to be less sensitive to corrections involving SU(3) breaking than related U-spin relations involving charged kaons or strange $D$ mesons. A corresponding relation between $D^+ \to \ko π^+$ and $D^+ \to \ok π^+$ is not predicted by U-spin. As a consequence, one expects the asymmetry parameters $R(D^0,M^0)\equiv [\Gamma (D^0\to K_S{M}^0)-\Gamma (D^0\to K_L{M}^0)/[\Gamma (D^0\to K_S{M}^0)+\Gamma (D^0\to K_L{M}^0)]$ each to be equal to $2{\tan }^2{\theta }_C=0.106$, in accord with a recent CLEO measurement $R(D^0)\equiv R(D^0,{\pi }^0)=0.122\pm 0.024\pm 0.030$. No prediction for the corresponding ratio $R(D^{+})$ is possible on the basis of U-spin.

5 pages, 3 figures. Further references and text added

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• Strong phases, asymmetries, and SU(3) symmetry breaking in D --> K pi decays
• SU(3) in D decays: From $30\%$ symmetry breaking to $10^{-4}$ precision
• Asymmetries from the interference between Cabibbo-favored and doubly-Cabibbo-suppressed D decays
• Measurements of Absolute Branching Fractions of $D^0\to K_L^0\varphi$, $K_L^0\eta$, $K_L^0\omega$, and $K_L^0{\eta }^{\prime }$
• CP violation analysis of $D^0\to M^{0}K\to M^0({\pi }^{\pm }{\ell }^{\mp }\nu )$
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