Measurement of the branching fractions for the exclusive decays of B ⁰ and B⁺ to D̄^(*)D(*)K

We report the observation of 823±57 B⁰ and 970±65 B⁺ decays to doubly charmed final states D̄ ^(*)D^(*)K, where D̄^(*) and D^(*) are fully reconstructed and K is either a K ^± or a K⁰. We use a sample of 82.3 ±0.9 million B B̄ events collected between 1999 and 2002 with the BABAR detector at the PEP-II storage ring at the Stanford Linear Accelerator Center. The 22 ossible B decays to D̄^(*)D^(*)K are reconstructed exclusively and the corresponding branching fractions or limits are determined. The branching fractions of the B⁰ and of the B ⁺ to D̄^(*)D^(*)K are found to be Β(B⁰→D̄^(*)D^(*)K) = [4.3±0.3(stat)±0.6(syst)]%, Β(B⁺→D̄ ^(*)D^(*)K) = [3.5±0.3(stat)±0. 5(syst)]%.A search for decays to orbitally excited D_s states, B→D̄^(*)D_sJ ⁺(D_sJ ⁺→D^(*)0K⁺), is also performed. No statistically significant-contributions from D_s1 ⁺(2536) →D*⁰K⁺ and D_sJ ⁺(2573) →D⁰K⁺ to the D̄^(*)D ^(*)0K⁺ final state are found and we set 90% C.L. limits on their production rates.