July 2006 INTERFERENCE BETWEEN DOUBLY - CABIBBO - SUPPRESSED AND CABIBBO - FAVORED AMPLITUDES IN D 0 → K S ( π 0 , η , η ′ ) DECAYS

A definite relative phase and amplitude exists between the doubly-Cabibbosuppressed amplitude for D → KM and the Cabibbo-favored amplitude forD → K0M0, whereM = (π, η, η): A(D → KM) = − tan θCA(D → K 0 M). Here θC is the Cabibbo angle. This relation, although previously recognized (for M = π) 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 → Kπ and D → K0π+ is not predicted by U-spin. As a consequence, one expects the asymmetry parameters R(D,M) ≡ [Γ(D → KSM) − Γ(D → KLM)/[Γ(D → KSM) + Γ(D → KLM)] each to be equal to 2 tan θC = 0.106, in accord with a recent CLEO measurement R(D) ≡ R(D, π) = 0.122 ± 0.024 ± 0.030. No prediction for the corresponding ratio R(D) is possible on the basis of U-spin.