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 $D^0\to \text{ko}{M}^0$ and the Cabibbo-favored amplitude for $D^0\to \text{ok}{M}^0$, where $M^0=({\pi }^0,\eta ,{\eta }^{\prime })$: $A(D^0\to \text{ko}{M}^0)=-{\tan }^2{\theta }_{C}A(D^0\to \text{ok}{M}^0)$. 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 $D^{+}\to \text{ko}{\pi }^{+}$ and $D^{+}\to \text{ok}{\pi }^{+}$ 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.

Comments: 5 pages, 3 figures. Further references and text added