Interference between doubly-Cabibbo-suppressed and Cabibbo-favored amplitudes in $D^0 \to K_S(\pi^0,\eta,\eta')$ 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 $M^0 = (\pi^0,\eta,\eta')$: $A(D^0 \to \ko M^0) = - \tan^2 \theta_C A(D^0 \to \ok M^0)$. 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 $D^+ \to \ko \pi^+$ and $D^+ \to \ok \pi^+$ 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.