Observation of the decays B(s)0 ? D<inf>s1</inf>(2536)^± K ^±

This paper reports the observation of the decays B(s)0 ? Ds1(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 Ds1(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, fs/fd. The significance for the Bs0 and B 0 signals is larger than 10 s. The ratio of the helicity amplitudes which governs the angular distribution of the Ds1(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.].