# Determination of $f_s/f_d$ for 7 TeV $pp$ collisions and a measurement of the branching fraction of the decay $B^0 \to D^{-}K^{+}$

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## Abstract

The relative abundance of the three decay modes $B_d \to D^- K^+$, $B_d \to D^- \pi^+$ and $B_s \to D_s^- \pi^+$ produced in 7 TeV $pp$ collisions at the LHC is determined from data corresponding to an integrated luminosity of 35 pb$^{-1}$. The branching fraction of $B_d \to D^- K^+$ is found to be $\cal B (B_d \to D^- K^+) = (2.01 \pm 0.18^{\textrm{stat}} \pm 0.14^{\textrm{syst}})\times 10^{-4}$. The ratio of fragmentation fractions \fsfdt is determined through the relative abundance of $B_s \to D_s^- \pi^+$ to $B_d \to D^- K^+$ and $B_d \to D^-\pi^+$, leading to $f_s/f_d = 0.253 \pm 0.017 \pm 0.017 \pm 0.020$, where the uncertainties are statistical, systematic, and theoretical respectively.

## Figures and captions

 Probability, as a function of momentum, to correctly identify (full symbols) a kaon or a pion when requiring $\textrm{DLL}(K-\pi)>5$ or $\textrm{DLL}(K-\pi)<0$, respectively. The correspondent probability to wrongly identify (open symbols) a pion as a kaon, or a kaon as a pion is also shown. The data are taken from a calibration sample of $D^*\rightarrow D(K\pi)\pi$ decays; the statistical uncertainties are too small to display. Figure1.eps [8 KiB] HiDef png [166 KiB] Thumbnail [68 KiB] *.C file Mass distributions of the $B ^0 \rightarrow D ^- \pi^+\,$ , $B ^0 \rightarrow D ^- K^+\,$ , and $B ^0_s \rightarrow D ^-_s \pi^+\,$ candidates (top to bottom). The indicated components are described in the text. Figure2.eps [86 KiB] HiDef png [174 KiB] Thumbnail [70 KiB] *.C file Figure3.eps [72 KiB] HiDef png [222 KiB] Thumbnail [85 KiB] *.C file Figure4.eps [106 KiB] HiDef png [253 KiB] Thumbnail [99 KiB] *.C file Animated gif made out of all figures. PAPER-2011-006.gif Thumbnail

## Tables and captions

 Experimental systematic uncertainties for the $\cal B \left( B ^0 \rightarrow D ^- K^+\,\right)$ and the two $f_s/f_d$ measurements. Table_I.pdf [61 KiB] HiDef png [86 KiB] Thumbnail [13 KiB] tex code

Created on 16 February 2019.Citation count from INSPIRE on 16 February 2019.