Search for B[superscript ±]→[K[superscript ∓]π[superscript ±]][subscript D]K[superscript ±] and Upper Limit on the b→u Amplitude in B[superscript ±]→DK[superscript ±]

Abstract

We search for B[superscript ±]→[K[superscript ∓]π[superscript ±]]DK[superscript ±] decays, where [K[superscript ∓]π[superscript ±]][subscript D] indicates that the K[superscript ∓]π[superscript ±] pair originates from the decay of a D[superscript 0] or D̅[superscript 0). Results are based on 120×10[superscript 6] Υ(4S)→BB̅ decays collected with the BABAR detector at SLAC. We set an upper limit on the ratio R[subscript Kπ]≡ [Γ(B[superscript +]→[K[superscript -]π[superscript +]]DK[superscript +])+Γ(B[superscript -]→[K[superscript +]π[superscript -]]DK[superscript -])]/[Γ(B[superscript +]→[K[superscript +]π[superscript -]][subscript D]K[superscript +])+Γ(B[superscript -]→[K[superscript -]π[superscript +]][subscript D]K[superscript -])]<0.026 (90% C.L.). This constrains the amplitude ratio r[subscript B]≡ |A(B[superscript -]→D̅ [superscript 0]K[superscript -])/A(B[superscript -]→D[superscript 0]K[superscript -])|<0.22 (90% C.L.), consistent with expectations. The small value of r[subscript B] favored by our analysis suggests that the determination of the Cabibbo-Kobayashi-Maskawa phase γ from B→DK will be difficult.