Observation of the decays B(s)0 → D_s1(2536)^∓ K ^±

This paper reports the observation of the decays B(s)0 → D_s1(2536)^∓ K ^± using proton-proton collision data collected by the LHCb experiment, corresponding to an integrated luminosity of 9 fb ⁻¹. The branching fractions of these decays are measured relative to the normalisation channel B ⁰ → D¯ ⁰ K ⁺ K ⁻. The D_s1(2536) ⁻ meson is reconstructed in the D¯ ^*(2007)⁰ K ⁻ decay channel and the products of branching fractions are measured to be B(Bs0→Ds1(2536)∓K±)×B(Ds1(2536)−→D¯∗(2007)0K−)=(2.49±0.11±0.12±0.25±0.06)×10−5,B(B0→Ds1(2536)∓K±)×B(Ds1(2536)−→D¯∗(2007)0K−)=(0.510±0.021±0.036±0.050)×10−5. The first uncertainty is statistical, the second systematic, and the third arises from the uncertainty of the branching fraction of the B ⁰ → D¯ ⁰ K ⁺ K ⁻ normalisation channel. The last uncertainty in the Bs0 result is due to the limited knowledge of the fragmentation fraction ratio, f_s/f_d. The significance for the Bs0 and B ⁰ signals is larger than 10 σ. The ratio of the helicity amplitudes which governs the angular distribution of the D_s1(2536) ⁻ → D¯ ^*(2007)⁰ K ⁻ decay is determined from the data. The ratio of the S- and D-wave amplitudes is found to be 1.11 ± 0.15 ± 0.06 and the phase difference between them 0.70 ± 0.09 ± 0.04 rad, where the first uncertainty is statistical and the second systematic. [Figure not available: see fulltext.].