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

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

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