# First observation of the decays $\bar{B}^0_{(s)}\to D_s^+K^-\pi^+\pi^-$ and $\bar{B}^0_s\to D_{s1}(2536)^+\pi^-$

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## Abstract

The first observation of the decays $\bar{B}^0_{s}\to D_s^+K^-\pi^+\pi^-$ and $\bar{B}^0\to D_s^+K^-\pi^+\pi^-$ are reported using an integrated luminosity of 1.0 fb$^{-1}$ recorded by the LHCb experiment. The branching fractions, normalized with respect to $\bar{B}^0_{s}\to D_s^+\pi^-\pi^+\pi^-$ and $\bar{B}^0_{s}\to D_s^+K^-\pi^+\pi^-$, respectively, are measured to be {\br(\bar{B}^0_{s}\to D_s^+K^-\pi^+\pi^-)\over\br(\bar{B}^0_{s}\to D_s^+\pi^-\pi^+\pi^-)} &= (5.2\pm0.5\pm0.3)\times10^{-2}, {\br(\bar{B}^0\to D_s^+K^-\pi^+\pi^-)\over\br(\bar{B}^0_{s}\to D_s^+K^-^\pi^+\pi^-)} &= 0.54\pm0.07\pm0.07, where the first uncertainty is statistical and the second is systematic. The $\bar{B}^0_{s}\to D_s^+K^-\pi^+\pi^-$ decay is of particular interest as it can be used to measure the weak phase $\gamma$. First observation of the $\bar{B}^0_s\to D_{s1}(2536)^+\pi^-, D_{s1}^+\to D_s^+\pi^-\pi^+$ decay is also presented, and its branching fraction relative to $\bar{B}^0_{s}\to D_s^+\pi^-\pi^+\pi^-$ is found to be {\br(\bar{B}^0_s\to D_{s1}(2536)^+\pi^-, D_{s1}^+\to D_s^+\pi^-\pi^+)\over\br(\bar{B}^0_{s}\to D_s^+\pi^-\pi^+\pi^-)} &= (4.0\pm1.0\pm0.4)\times10^{-3}.

## Figures and captions

 Diagrams contributing to the $B ^0_ s ,\overline{ B }{} ^0_ s \rightarrow D ^+_ s K^-\pi^+\pi^-$ (a-c) and $\overline{ B }{} ^0 \rightarrow D ^+_ s K^-\pi^+\pi^-$ (d-f) decays, as described in the text. In (a-d), the additional ($\pi ^+ \pi ^-$) indicates that the $K ^- \pi ^+ \pi ^-$ may be produced either through an excited strange kaon resonance decay, or through fragmentation. TreeBs[..].eps [7 KiB] HiDef png [63 KiB] Thumbnail [21 KiB] *.C file TreeBs[..].eps [7 KiB] HiDef png [62 KiB] Thumbnail [20 KiB] *.C file Exchan[..].eps [10 KiB] HiDef png [82 KiB] Thumbnail [28 KiB] *.C file Exchan[..].eps [10 KiB] HiDef png [80 KiB] Thumbnail [28 KiB] *.C file Exchan[..].eps [8 KiB] HiDef png [74 KiB] Thumbnail [27 KiB] *.C file Exchan[..].eps [9 KiB] HiDef png [77 KiB] Thumbnail [29 KiB] *.C file Invariant mass distribution for $\overline{ B }{} ^0_ s \rightarrow D ^+_ s \pi^-\pi^+\pi^-$ candidates. The fitted signal probability disrtibution function (PDF) is indicated by the dashed line and the background shapes are shown as shaded regions, as described in the text. MassPl[..].eps [25 KiB] HiDef png [218 KiB] Thumbnail [83 KiB] *.C file Invariant mass distribution for $\overline{ B }{} ^0 _{(s)}\rightarrow D ^+_ s K ^- \pi ^+ \pi ^-$ candidates. The fitted signal (dashed lines) and background shapes (shaded/hatched regions) are shown, as described in the text. MassPl[..].eps [41 KiB] HiDef png [411 KiB] Thumbnail [132 KiB] *.C file Invariant mass distributions for (a) $X_d$, (b) smaller $\pi ^+ \pi ^-$ mass in $X_d$ and (c) the larger $\pi ^+ \pi ^-$ mass in $X_d$, from $\overline{ B }{} ^0_ s \rightarrow D ^+_ s \pi^-\pi^+\pi^-$ decays using sWeights. The points are the data and the solid line is the simulation. The simulated distribution is normalized to have the same yield as the data. Bs2Ds3[..].eps [16 KiB] HiDef png [159 KiB] Thumbnail [50 KiB] *.C file Invariant mass distributions for (a) $X_s$, (b) $\pi ^+ \pi ^-$ in $X_s$ and (c) the $K ^- \pi ^+$ in $X_s$, from $\overline{ B }{} ^0_ s \rightarrow D ^+_ s K^-\pi^+\pi^-$ data using sWeights. The points are data and the solid line is the simulation. The simulated distribution is normalized to have the same yield as the data. Bs2DsK[..].eps [16 KiB] HiDef png [150 KiB] Thumbnail [48 KiB] *.C file Invariant mass distributions for (a) $X_s$, (b) $\pi ^+ \pi ^-$ in $X_s$ and (c) the $K ^- \pi ^+$ in $X_s$, from $\overline{ B }{} ^0 \rightarrow D ^+_ s K^-\pi^+\pi^-$ data using sWeights. The points are data and the solid line is the simulation. The simulated distribution is normalized to have the same yield as the data. Bd2DsK[..].eps [17 KiB] HiDef png [158 KiB] Thumbnail [51 KiB] *.C file Distribution of the difference in invariant mass, $M( D ^+_ s \pi ^- \pi ^+ )-M( D ^+_ s )$, using $\overline{ B }{} ^0_ s \rightarrow D ^+_ s \pi^-\pi^+\pi^-$ candidates within 40 ${\mathrm{\,MeV\!/}c^2}$ of the known $B ^0_ s$ mass (points) and in the upper $B ^0_ s$ mass sidebands (filled histogram). The fit to the distribution is shown, as described in the text. Bs2Ds1Pi.eps [31 KiB] HiDef png [260 KiB] Thumbnail [87 KiB] *.C file Animated gif made out of all figures. PAPER-2012-033.gif Thumbnail

## Tables and captions

 Summary of event yields from data in the $D ^+_ s$ signal and sidebands regions, and the background corrected yield. The signal and sideband regions require $D ^+_ s$ candidates to have invariant mass $|M( K ^+ K ^- \pi ^+ )-m_{ D ^+_ s }|<20$ ${\mathrm{\,MeV\!/}c^2}$ and $35<|M( K ^+ K ^- \pi ^+ )-m_{ D ^+_ s }|<55$ ${\mathrm{\,MeV\!/}c^2}$ , respectively, where $m_{ D ^+_ s }$ is the $D ^+_ s$ mass [26]. Table_1.pdf [52 KiB] HiDef png [44 KiB] Thumbnail [7 KiB] tex code Selection efficiencies and correction factors for decay modes under study. The uncertainties on the selection efficiencies are statistical only, whereas the correction factors show the total uncertainty. Table_2.pdf [53 KiB] HiDef png [41 KiB] Thumbnail [7 KiB] tex code Summary of systematic uncertainties (in %) on the measurements of the ratios of branching fractions. Table_3.pdf [63 KiB] HiDef png [73 KiB] Thumbnail [11 KiB] tex code

Created on 16 February 2019.Citation count from INSPIRE on 21 February 2019.