Observation of the decays B s 0 $$ {B}_{(s)}^0 $$ → D s1(2536)∓ K ±

Abstract This paper reports the observation of the decays B s 0 $$ {B}_{(s)}^0 $$ → 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 ¯ $$ \overline{D} $$ 0 K + K − . The D s1(2536) − meson is reconstructed in the D ¯ $$ \overline{D} $$ *(2007)0 K − decay channel and the products of branching fractions are measured to be B B s 0 → D s 1 2536 ∓ K ± × B D s 1 2536 − → D ¯ ∗ 2007 0 K − = 2.49 ± 0.11 ± 0.12 ± 0.25 ± 0.06 × 10 − 5 , B B 0 → D s 1 2536 ∓ K ± × B D s 1 2536 − → D ¯ ∗ 2007 0 K − = 0.510 ± 0.021 ± 0.036 ± 0.050 × 10 − 5 . $$ {\displaystyle \begin{array}{c}\mathcal{B}\left({B}_s^0\to {D}_{s1}{(2536)}^{\mp }{K}^{\pm}\right)\times \mathcal{B}\left({D}_{s1}{(2536)}^{-}\to {\overline{D}}^{\ast }{(2007)}^0{K}^{-}\right)\\ {}=\left(2.49\pm 0.11\pm 0.12\pm 0.25\pm 0.06\right)\times {10}^{-5},\\ {}\mathcal{B}\left({B}^0\to {D}_{s1}{(2536)}^{\mp }{K}^{\pm}\right)\times \mathcal{B}\left({D}_{s1}{(2536)}^{-}\to {\overline{D}}^{\ast }{(2007)}^0{K}^{-}\right)\\ {}=\left(0.510\pm 0.021\pm 0.036\pm 0.050\right)\times {10}^{-5}.\end{array}} $$ The first uncertainty is statistical, the second systematic, and the third arises from the uncertainty of the branching fraction of the B 0 → D ¯ $$ \overline{D} $$ 0 K + K − normalisation channel. The last uncertainty in the B s 0 $$ {B}_s^0 $$ result is due to the limited knowledge of the fragmentation fraction ratio, f s /f d . The significance for the B s 0 $$ {B}_s^0 $$ 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 ¯ $$ \overline{D} $$ *(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.