Interference between doubly-Cabibbo-suppressed and Cabibbo-favored amplitudes in $D^0 \to K_S(π^0,η,η')$ 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 $M^0 = (π^0,η,η')$: $A(D^0 \to \ko M^0) = - \tan^2 θ_C A(D^0 \to \ok M^0)$. Here $θ_C$ is the Cabibbo angle. This relation, although previously recognized (for $M^0 = π^0$) 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 $R(D^0,M^0) \equiv [Γ(D^0 \to K_S M^0) - Γ(D^0 \to K_L M^0)/[Γ(D^0 \to K_S M^0) + Γ(D^0 \to K_L M^0)]$ each to be equal to $2 \tan^2 θ_C = 0.106$, in accord with a recent CLEO measurement $R(D^0) \equiv R(D^0,π^0) = 0.122 \pm 0.024 \pm 0.030$. 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