# Measurement of the branching fractions of the decays $B_s^0 \rightarrow D_s^\mp K^\pm$ and $B_s^0 \rightarrow D_s^- \pi^+$

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## Abstract

The decay mode $\B^{0}_{s} \to D^{\mp}_{s} K^{\pm}$ allows for one of the theoretically cleanest measurements of the CKM angle $\gamma$ through the study of time-dependent $CP$ violation. This paper reports a measurement of its branching fraction relative to the Cabibbo-favoured mode $\B^{0}_{s} \to D^{-}_{s} \pi^{+}$ based on a data sample of 0.37 fb$^{-1}$ proton-proton collisions at $\sqrt{s} = 7$ TeV collected in 2011 with the LHCb detector. In addition, the ratio of $\mathrm{B}$ meson production fractions $f_s/f_d$, determined from semileptonic decays, together with the known branching fraction of the control channel $B^{0} \to D^{-} \pi^{+}$, is used to perform an absolute measurement of the branching fractions: $B (\B^0_s \to D^-_s \pi^+) \;= (2.95 \pm 0.05 \pm 0.17^{\,+\,0.18}_{\,-\,0.22}) \times 10^{-3}$, $B (\B^0_s \to D^\mp_s K^\pm) = (1.90 \pm 0.12 \pm 0.13^{\,+\,0.12}_{\,-\,0.14}) \times 10^{-4}\,$, where the first uncertainty is statistical, the second the experimental systematic uncertainty, and the third the uncertainty due to $f_s/f_d$.

## Figures and captions

 Mass distribution of the $B ^0 \!\rightarrow D ^- \pi ^+$ candidates (top) and $B ^0_s \!\rightarrow D ^-_s \pi ^+$ candidates (bottom). The stacked background shapes follow the same top-to-bottom order in the legend and the plot. For illustration purposes the plot includes events from both magnet polarities, but they are fitted separately as described in the text. Figure1.pdf [47 KiB] HiDef png [184 KiB] Thumbnail [71 KiB] *.C file Figure2.pdf [32 KiB] HiDef png [203 KiB] Thumbnail [77 KiB] *.C file Mass distribution of the $B ^0_s \!\rightarrow D_s^\mp K^\pm$ candidates. The stacked background shapes follow the same top-to-bottom order in the legend and the plot. For illustration purposes the plot includes events from both magnet polarities, but they are fitted separately as described in the text. Figure3.pdf [26 KiB] HiDef png [272 KiB] Thumbnail [101 KiB] *.C file Animated gif made out of all figures. PAPER-2011-022.gif Thumbnail

## Tables and captions

 PID efficiency and misidentification probabilities, separated according to the up (U) and down (D) magnet polarities. The first two lines refer to the bachelor track selection, the third line is the $D ^-$ efficiency and the fourth the $D ^-_s$ efficiency. Probabilities are obtained from the efficiencies in the $D ^{*+}$ calibration sample, binned in momentum and $p_{\rm T}$. Only bachelor tracks with momentum below 100 GeV$/c$ are considered. The uncertainties shown are the statistical uncertainties due to the finite number of signal events in the PID calibration samples. Table_1.pdf [46 KiB] HiDef png [52 KiB] Thumbnail [9 KiB] tex code Results of the mass fits to the $B ^0 \!\rightarrow D ^- \pi ^+$ , $B ^0_s \!\rightarrow D ^-_s \pi ^+$ , and $B ^0_s \!\rightarrow D_s^\mp K^\pm$ candidates separated according to the up (U) and down (D) magnet polarities. In the $B ^0_s \!\rightarrow D_s^\mp K^\pm$ case, the number quoted for $B ^0_s \!\rightarrow D ^-_s \pi ^+$ also includes a small number of $B ^0 \!\rightarrow D ^- \pi ^+$ events which have the same mass shape (20 events from the expected misidentification). See Table 3 for the constrained values used in the $B ^0_s \!\rightarrow D_s^\mp K^\pm$ decay fit for the partially reconstructed backgrounds and the $B ^0 \!\rightarrow D ^- K ^+$ decay channel. Table_2.pdf [76 KiB] HiDef png [57 KiB] Thumbnail [10 KiB] tex code Gaussian constraints on the yields of partially reconstructed and misidentified backgrounds applied in the $B ^0_s \!\rightarrow D_s^\mp K^\pm$ fit, separated according to the up (U) and down (D) magnet polarities. Table_3.pdf [53 KiB] HiDef png [111 KiB] Thumbnail [19 KiB] tex code Relative systematic uncertainities on the branching fraction ratios. Table_4.pdf [60 KiB] HiDef png [52 KiB] Thumbnail [9 KiB] tex code

Created on 19 April 2019.Citation count from INSPIRE on 24 April 2019.