Observation of the decays $B_{(s)}^0\to D_{s1}(2536{)}^{\mp }{K}^{\pm }$

Abstract

This paper reports the observation of the decays $B_{(s)}^0\to D_{s1}(2536{)}^{\mp }{K}^{\pm }$ using proton-proton collision data collected by the LHCb experiment, corresponding to an integrated luminosity of $9{\mathrm{fb}}^{-1}$. The branching fractions of these decays are measured relative to the normalisation channel $B^0\to {\overline{D}}^0{K}^{+}{K}^{-}$. The $D_{s1}(2536{)}^{-}$ meson is reconstructed in the ${\overline{D}}^{\ast }(2007{)}^0{K}^{-}$ decay channel and the products of branching fractions are measured to be $$\mathcal{B}(B_s^0\to D_{s1}(2536{)}^{\mp }{K}^{\pm })\times \mathcal{B}(D_{s1}(2536{)}^{-}\to {\overline{D}}^{\ast }(2007{)}^0{K}^{-})=(2.49\pm 0.11\pm 0.12\pm 0.25\pm 0.06)\times 10^{-5},$$ $$\mathcal{B}(B^0\to D_{s1}(2536{)}^{\mp }{K}^{\pm })\times \mathcal{B}(D_{s1}(2536{)}^{-}\to {\overline{D}}^{\ast }(2007{)}^0{K}^{-})=(0.510\pm 0.021\pm 0.036\pm 0.050)\times 10^{-5}.$$ The first uncertainty is statistical, the second systematic, and the third arises from the uncertainty of the branching fraction of the $B^0\to {\overline{D}}^0{K}^{+}{K}^{-}$ normalisation channel. The last uncertainty in the $B_s^0$ result is due to the limited knowledge of the fragmentation fraction ratio, $f_s/f_d$. The significance for the $B_s^0$ and $B^0$ signals is larger than $10\ddot{I}ƒ$. The ratio of the helicity amplitudes which governs the angular distribution of the $D_{s1}(2536{)}^{-}\to {\overline{D}}^{\ast }(2007{)}^0{K}^{-}$ decay is determined from the data. The ratio of the $S$- and $D$-wave amplitudes is found to be $1.11\pm 0.15\pm 0.06$ and its phase $0.70\pm 0.09\pm 0.04$ rad, where the first uncertainty is statistical and the second systematic.

All figures and tables, along with machine-readable versions and any supplementary material and additional information, are available at https://cern.ch/lhcbproject/Publications/p/LHCb-PAPER-2023-014.html (LHCb public pages)