First observations of $\bar{B}_s^0\to D^+D^-$, $D_s^+D^-$ and $D^0\bar{D}^0$ decays

First observations and measurements of the branching fractions of the $\bar{B}_s^0\to D^+D^-$, $\bar{B}_s^0\to D_s^+D^-$ and $\bar{B}_s^0\to D^0\bar{D}^0$ decays are presented using 1.0 fb$^{-1}$ of data collected by the LHCb experiment. These branching fractions are normalized to those of $\bar{B}^0\to D^+D^-$, $B^0\to D_s^+D^-$ and $B^-\to D^0D_s^-$, respectively. An excess of events consistent with the decay $\bar{B}^0\to D^0\bar{D}^0$ is also seen, and its branching fraction is measured relative to that of $B^-\to D^0D_s^-$. Improved measurements of the branching fractions ${\cal{B}}(\bar{B}_s^0\to D_s^+D_s^-)$ and ${\cal{B}}(B^-\to D^0D_s^-)$ are reported, each relative to ${\cal{B}}(B^0\to D_s^+D^-)$. The ratios of branching fractions are {-0.2in} {center} {align*} {{\cal{B}}(\bar{B}_s^0\to D^+D^-)\over {\cal{B}}(\bar{B}^0\to D^+D^-)}&= 1.08\pm 0.20\pm0.10, {{\cal{B}}(\bar{B}_s^0\to D_s^+D^-)\over {\cal{B}}(B^0\to D_s^+D^-)}&= 0.050\pm 0.008\pm0.004, {{\cal{B}}(\bar{B}_s^0\to D^0\bar{D}^0)\over {\cal{B}}(B^-\to D^0D_s^-)}&= 0.019\pm 0.003\pm0.003, {{\cal{B}}(\bar{B}^0\to D^0\bar{D}^0)\over {\cal{B}}(B^-\to D^0D_s^-)}&= 0.0014\pm 0.0006\pm0.0002,{{\cal{B}}(\bar{B}_s^0\to D_s^+D_s^-)\over {\cal{B}}(B^0\to D_s^+D^-)}&= 0.56\pm 0.03\pm0.04, {{\cal{B}}(B^-\to D^0D_s^-)\over {\cal{B}}(B^0\to D_s^+D^-)}&= 1.22\pm 0.02\pm0.07, {align*} {center} \noindent where the uncertainties are statistical and systematic, respectively.

that obtained from direct measurements [14], or from lifetime measurements in other CP 11 eigenstates [15,16]. 12 The study of B → DD decays 1 can also provide a better theoretical understanding 13 of the processes that contribute to B meson decay. Feynman diagrams contributing to 14 the decays considered in this paper are shown in Fig The LHCb detector [22] is a single-arm forward spectrometer covering the pseudorapidity 33 range 2 < η < 5, designed for the study of particles containing b or c quarks. The detector 34 includes a high precision tracking system consisting of a silicon-strip vertex detector  trigger selection is applied to facilitate the determination of the relative trigger efficiency.

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The selection requires that either (i) at least one of the tracks from the reconstructed 59 signal decay is associated with energy depositions in the calorimeters that passed the 60 hardware trigger requirements, or (ii) the event triggered independently of the signal decay particles, e.g., on the decay products of the other b hadron in the event. Events that do not fall into either of these two categories (∼5%) are discarded.

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Signal efficiencies and specific backgrounds are studied using simulated events. structed in the following decay modes: where a single D 0 → K − π + π − π + decay in the final state is allowed, which approximately 75 doubles the total signal efficiency. A refit of signal candidates with D mass and vertex 76 constraints is performed to improve the B mass resolution.

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Due to similar kinematics of the D + → K − π + π + , D + s → K + K − π + and Λ + c → pK − π + with the Λ + c → pK − π + decay hypothesis if the proton is misidentified as a π + or K + , 88 respectively. The efficiencies of these D selections are determined using simulated signal 89 decays to model the kinematics of the decay and D * + → D 0 π + calibration data for the 90 PID efficiencies. Their values are given in Table 1.  Table 1.  Shown are the efficiencies to reconstruct and trigger on the final state, and to pass the charm cross-feed veto, the VS χ 2 and BDT selection requirements. The total selection efficiency is the product of these four values. The relative uncertainty on the selection efficiency for each decay mode due to the finite simulation samples sizes is 2%. Entries with a dash indicate that the efficiency factor is not applicable.  is identical for the tight selection, the BDT efficiency cancels in the ratio of branching 124 fractions, and is not included in Table 1.
decays, where the π + is misidentified as a K + , is observed. This contribution is removed 127 by requiring the mass difference, in the reconstructed decay is taken to be a π + . After the final selection around 2% of 129 events in the B 0 s → D + s D − s decay mode contain multiple candidates; for all other modes 130 the multiple candidate rate is below 1%. All candidates are kept for the final analysis.  The combinatorial background shape is described by an exponential function whose  The B 0 s → D − D + s decay is thus observed for the first time.

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The invariant mass spectrum for B 0 (s) → D + D − candidates is shown in Fig. 4 (left).  summarized in Table 2. The branching fractions are related to the measured yields by 13 ± 6 5152 ± 73 0.523 ± 0.016 Here, it is assumed that B − and B 0 mesons are produced in equal numbers. The relative 214 efficiencies, rel , are given in Table 2. They account for geometric acceptance, detection and 215 trigger efficiencies, and the additional VS χ 2 , BDT, and charm cross-feed veto requirements.

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The factor κ is a correction that accounts for the lower selection efficiency associated 227 with the shorter-lifetime CP -even eigenstates of the B 0 s system compared to flavor-specific 228 final states [14]. The impact on the B 0 s acceptance is estimated by convolving an exponential 229 distribution that has a 10% smaller lifetime than that in flavor-specific decays with the 230 simulated lifetime acceptance. The resulting correction is κ = 1.058 ± 0.029. In the B 0 sector, ∆Γ d /Γ d is below 1% [38], and the lifetime acceptance is well described by the 232 simulation.

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The measured ratios of branching fractions are computed to be  Table 3.  The fit model is validated using simulated experiments, and is found to be unbiased.

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To assess the uncertainty due to the imperfect knowledge of the various parameters   3% uncertainty to all the measurements. In total, the systematic uncertainties on the 301 branching fraction ratios range from 5.5% to 13.0%, as indicated in Table 3. source software packages that we depend on.