Measurement of the branching fractions of the decays Bs0→D ^̄ 0K^-π⁺ and B0→D ^̄0K⁺π^-

The first observation of the decay Bs0→D ^̄0K ^-π ⁺ is reported. The analysis is based on a data sample, corresponding to an integrated luminosity of 1.0 fb ^-1 of pp collisions, collected with the LHCb detector. The branching fraction relative to that of the topologically similar decay B0→D ^̄0π ⁺π ^- is measured to be B(Bs0→D ^̄0K ^-π ⁺)B(B0→D ^̄0π ⁺π ^-)=1.18±0.05(stat) ±0.12(syst). In addition, the relative branching fraction of the decay B0→D ^̄0K ⁺π ^- is measured to be B(B0→D ^̄0K ⁺π ^-)B(B0→D ^̄0π ⁺π ^-)=0.106±0.007(stat) ±0.008(syst).