Measurement of the relative yields of the decay modes B 0 D π +, B 0 D K +, B 0 s D s π+, and determination of f s /f d for 7 TeV pp collisions

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1 LHCb-CONF April 5, 211 Measurement of the relative yields of the decay modes B D π +, B D K +, B s D s π+, and determination of f s /f d for 7 TeV pp collisions The LHCb Collaboration 1 Abstract The relative abundances of the three decay modes B D K +, B D π + and B s D s π+ produced in 7 TeV pp collisions at the LHC are determined from data taken during the 21 running period, corresponding to an integrated luminosity of 35 pb 1. From these, the relative branching ratio of B D K + with respect to B D π + is determined, resulting in B ( B D K + ) = (2.2 ±.17 stat ±.12 syst ) 1 4. The ratio of fragmentation fractions f s /f d is determined through the relative abundances of B D K + and B D π + with respect to B s D s π +, leading to f s /f d =.245 ±.17 stat ±.18 syst ±.18 theor. 1 Conference report prepared for the 211 Rencontres de Moriond QCD and High Energy Interactions, La Thuile, 2 27 March 211; contact authors: Vladimir V. Gligorov and Nicola Serra

2 1 Introduction The branching ratios of a large number of B decays have been measured to high precision at the B factories [1]. To determine any Bs branching ratio at the LHC, knowledge on the production rate of Bs mesons is needed. The production rates of b hadrons are determined by the fragmentation functions f u, f d, f s, f Λ, which describe the probability that a b quark will fragment into a B q meson (where q = u, d, s), or Λ b baryon, respectively. The measurement of the branching ratio of the rare decay Bs µ+ µ is the prime example where knowledge on f s /f d is crucial to reach the highest sensitivity in the search for New Physics [2]. The two decay channels B D K + and Bs D s π+ receive only contributions from color-allowed tree-diagram amplitudes and the ratio of branching ratios is therefore theoretically well understood, and suitable to measure the Bs and B relative production rate [3]: B(Bs Ds π + ) B(B D K + ) = τ B s V ud 2 ( ) [ ] 2 fπ F (s) 2 (m 2 π) a 1 (Ds π + ) 2 τ B V us f K F (d) (m 2 K ) a 1 (D K + ), (1) where τ B is the lifetime of the B meson, V qq is the relevant CKM element, f π,k is the decay constant for the pion or kaon and F (q 2 ) is the value of the form factor at 4-momentum transfer q. Charge conjugate decay modes are implied throughout this document. The quantity a 1 (D q h) describes the deviation from naive factorization. The ratio of the corresponding number of observed signal events is given by N Dsπ N DK = f s f d ǫ Dsπ ǫ DK B(B s D s π+ ) B(B D K + ), (2) where ǫ is the total detector efficiency. After taking into account all numerical factors 2 it follows that f s =.743 τ [ ] 1 ǫ B DK N Dsπ, (3) f d τ B s N a N F ǫ Dsπ N DK with N a a 1 (Ds π+ ) a 1 (D K + ) 2 [ ] F (s) = 1. ±.2 [5], N F (m2 π ) 2 F (d) (m 2 K ) = 1.24 ±.8 [6]. (4) The decay channel B D K + is however Cabibbo-suppressed, and suffers from a sizeable statistical uncertainty when using the 21 data set. The B D π + decay on the other hand occurs abundantly, but is theoretically less clean, since this decay receives contributions from W-exchange diagrams. As a result, the following relation is obtained [5], f s =.982 τ [ B f d τ B s 1 N a N F N E ǫ Dπ ǫ Dsπ ] N Dsπ, (5) N Dπ 2 Here the more accurate value for the kaon form factor, f K = MeV/c 2 [4], is used compared to the approximate value f K = 16 MeV/c 2 used in [3]. 1

3 where now the extra correction factor N E accounts for the contribution from the additional exchange diagram, N E =.966±.75. Both methods to determine f s /f d will be exploited in this paper. In addition to the measurement of f s /f d, this analysis is sensitive to the branching ratio of the suppressed mode B D K +, which is currently measured with modest precision. Given the selection efficiencies ǫ Dπ, ǫ DK, the ratio of branching ratio is given by: B(B D K + ) B(B D π + ) = N DK ǫ Dπ. (6) N Dπ ǫ DK 2 The LHCb detector and Data Sample The analysis is performed with the data set accumulated with the LHCb detector in the 21 running period, and corresponds to an integrated luminosity of 35 pb 1. Given the large bb production cross section at the LHC of about 3 µb [7], approximately 1 1 B mesons were produced in this running period. The LHCb [8] experiment is a single arm spectrometer, designed to study B decays at the LHC, covering the range 1.8 < η < 4.9 in pseudorapidity. The trigger system consists of a hardware trigger (L) which selects events with large (> 1 GeV/c) transverse momentum and energy deposits. This reduces the input rate of 4 MHz down to 1 MHz. Subsequently, the full event information is shipped to a software trigger implemented in a dedicated processor farm. In the first stage a partial event reconstruction is performed (HLT1) after which, at the second stage (HLT2), a full event reconstruction allows to reduce the rate to 2 khz. The tracking system determines the momenta of B decay products with a precision of δp/p =.35% at 5 GeV/c and δp/p =.5% at 1 GeV/c. In order to distinguish charged kaons and pions in the momentum range 2-1 GeV/c, LHCb is equipped with two Ring Imaging Cherenkov (RICH) detectors, one located upstream of, and the other downstream of, the dipole magnet. 3 Event selection The three decay modes, B D (K + π π )π +, B D (K + π π )K + and B s D s (K + K π )π +, are topologically identical and therefore can be selected using identical event selection criteria, thus minimizing efficiency differences between the modes. Reconstruction efficiencies are computed on large samples of fully simulated B D π +, B D K + and B s D s π + events. The reconstruction efficiency for kaons is a few percent lower than for pions, with the difference being larger at lower momentum. Events are selected at L by requiring an E T > 3.6 GeV hadron in the calorimeter. For this analysis, it is subsequently required offline that the calorimeter cluster which caused the L to fire is spatially compatible with one of the decay products of the B candidate. In addition, events are selected if triggered independently of the B decay. Subsequently, events are selected according to their HLT trigger decision. The HLT1 stage [9] requires a high transverse momentum (p T ) and good fit χ 2 track which is well displaced from the 2

4 primary interaction point. The HLT2 stage [1] employs a topological trigger selecting a 2, 3, or 4 track secondary vertex with a high sum of the p T of the tracks and significant displacement from the primary interaction. For the first 3pb 1, an additional two-track displaced vertex trigger was used at the HLT1 stage. The L efficiencies are equal within statistical uncertainty for all the decay modes, as expected. The HLT1 and HLT2 efficiencies show significant differences between the Bs and B modes. The HLT1 trigger selects a single high impact parameter track and hence prefers B decays into D mesons, over Bs decays into D s mesons, which have a shorter lifetime compared to D mesons. Conversely in HLT2, the topological trigger builds a vertex from the bachelor track (the final state particle coming directly from the B) and the decay products of the D and Ds mesons. Because of the shorter lifetime of the Ds meson its decay products are produced closer to the bachelor and are hence more likely to form a common vertex. When taking all trigger paths into account, an overall relative efficiency correction of 1.81 ±.24 is applied for Bs modes with respect to B modes. The two B modes have equal trigger efficiencies, as expected, and no correction factor is applied for the relative B yields. B mesons are heavy and long lived compared to most other particles produced in pp interactions at the LHC. The decays of B mesons can therefore be distinguished from background using variables such as the p T and impact parameter χ 2 of the B, the D, and of the final state particles with respect to the primary vertices in the event. The final event sample is selected using a multivariate technique which takes advantage of the correlations between the different discriminating variables [11]. The TMVA software package [12] was used to study the various multivariate methods available. The so-called gradient boosted decision tree (BDTG) is chosen as this is least sensitive to overtraining, and is shown to be robust for multiple sources of background. The performance of the multivariate selection methods, and the optimal selection criterion on the output of the BDTG, are based on a training sample for the background from data that corresponds to a luminosity of 2pb 1. The selection is trained on a sample of simulated signal B D π + decays. The selection is optimized with respect to the combinatorial background only, selected from the sidebands of the data mass distributions. In addition to impact parameters and p T, the vertex quality of the B and D, the B lifetime, and the angle between the B momentum vector and the vector joining the B production and decay vertices are used in the selection. The lifetimes of the Ds and D are approximately.5 ps and 1. ps [13] respectively. This difference implies that any cut on the D flight distance or on the distance of closest approach of the D decay products to the primary vertex (or impact parameter) will have different efficiencies for the B and Bs decay modes. For this reason the D lifetime, impact parameter, or flight distance are not used in the optimization. Particle identification information which distinguishes charged kaons from pions is also not used in the multivariate selection. The distributions of the input variables for data and simulated events show excellent agreement, justifying the use of simulated events in the training procedure. The BDTG selection performance is evaluated by computing the signal significance through S/ S + B using the Cabibbo favoured decays B D π +, but by scaling the signal 3

5 yield with a factor 1/2 to optimize for the Cabibbo suppressed modes. Approximately 2% of the events contain multiple candidates, of which the candidate with the best vertex χ 2 is retained. The selection efficiency of the BDTG requirement is 75% with respect to triggered events and is compatible for all channels. Subsequently, D (Ds ) candidates are identified by requiring the invariant mass under the Kππ (KKπ) hypothesis to fall within the selection window MeV/c2 ( MeV/c 2 ). Finally, the B D π + and Bs Ds π + subsamples consist of events that pass a particle identification criterion on the bachelor particle, based on the difference in log-likelihood for the two particle hypotheses (DLL) between the charged pions and kaons, DLL(K π) <. The B D K + subsample consists of events with DLL(K π) > 5. Events not satisfying either condition are not used in the fits. 4 Relative yield extraction Independent fits to the invariant mass distributions are used to separately extract the relative yields of the three B decay modes. The shapes of the signal and the various background distributions are described below. 4.1 Signal PDF The signal mass PDF is determined from simulated events. Because radiated photons are not reconstructed, the invariant mass distribution exhibits a low mass tail which is described by a Crystal Ball (CB) function. 3 A second CB function with a tail oriented in the opposite direction describes non-gaussian detector effects. The mean values of the CB functions are constrained to be identical and left free in the fit to the data sample. The parameters that describe the tails are fixed to the values obtained from simulation. The width of the signal peak is left free in some fits and constrained in others because of the different yields in the different decay modes; this is specified when the fit to each decay mode is described later on. 4.2 Signal decays under wrong mass hypothesis There are various specific backgrounds to be considered, in particular the crossfeed between the D and Ds channels, and the crossfeed to both samples from Λ b Λ + c π decays, where Λ + c pk π +. The Ds contamination in the D data sample is reduced by loose requirements on the particle identification, DLL(K π) < 1 and DLL(K π) >, for pions and kaons respectively. From simulations the resulting efficiency to reconstruct Bs D s π+ as background is evaluated to be 3 times smaller than that for B D π + (as signal) and 15 times smaller than for B D K + within the B and D signal mass windows. 3 The Crystal Ball line shape [14, 15] is a Gaussian distribution with a power-law tail on the negative side (below α σ of the mean). 4

6 Once the lower production fraction of Bs mesons is taken into account, this background is negligible. The crossfeed from Λ c decays is estimated in a similar way. However different approaches are used for the D and Ds decays, due to the different relative yields and PID nature of the two cases. A contamination of approximately 2% under the B D π + mass peak and below 1% under the B D K + peak was found, and therefore no explicit DLL(p π) cut is needed. Hence the Λ c background is neglected in the D fits, and a 2% systematic error is used to account for possible data-simulation differences and the residual contamination. Due to the smaller Bs D s π+ yields compared to the B D π + yields, the amount of Λ c background is no longer negligible, and therefore the Λ c background is taken into account in the fit using the PDF as obtained from simulated events. A particularly prominent peaking background in the fit for the B D K + yield is the B D π + crossfeed, with the pion misidentified as a kaon. The small π K misidentification rate is approximately compensated by the larger branching ratio, resulting in a similar number of B D K + events compared to misidentified B D π + events. The shape of the B D π + background under the B D K + signal, with one pion misidentified as a kaon, is determined from data in the following way. 1) A clean sample of B D π + is obtained by requiring the bachelor particle to be a high-purity pion, DLL(K π) <. 2) The mass distribution of this B D π + sample is constructed under the kaon mass hypothesis for the bachelor particle. 3) The efficiency of the DLL selection criterion is momentum dependent, and thus the momentum and mass distributions of the pure B D π + sample are corrected from the distortion due to the DLL cut applied in the previous step. 4) The result of the previous step is the mass distribution of the B D π + signal under the B D K + hypothesis in the absence of any particle identification cuts. The B D K + signal is now selected by requiring the bachelor particle to be a kaon, DLL(K π) > 5. The performance of this cut is evaluated as a function of momentum using a calibration sample of D decays, and is illustrated in Fig. 1. 5) This DLL selection criterion is again momentum dependent. The PDF of the misidentified B D π + events obtained in step (3) is reweighted according to the efficiency of the DLL cut applied in step (4). The mass distribution before and after reweighting is shown in Fig. 1. This PDF is used to describe the misidentified B D π + background under the B D K + signal in the final fit. 4.3 Other Background PDFs The combinatoric background consists of events with random pion and kaon particles, forming a fake D or D s decay. This type of background is distinguished by the secondary 5

7 Events / ( 8 MeV/c 2 ) LHCb Preliminary s = 7TeV -1 L int~35 pb Mass (MeV/c 2 ) Performance for DLL(K-π)> LHCb Preliminary * D D( Kπ)π Track Momentum (MeV/c) 3 Figure 1: Left: Mass shape of B D π + events with the bachelor misidentified as a kaon, for a PID cut of DLL(K π) > 5, before (blue) and after (red) reweighting. Right: Probability, as a function of momentum, to correctly identify a kaon (full black circles) and to wrongly identify a pion as a kaon (open red circles), for a PID cut of DLL(K π) > 5. vertex quality. Due to the fact that the reconstructed masses for the B and the D are non-peaking, the remaining background is studied using events with a reconstructed D mass in the region outside the D mass peak, the D mass sidebands. In addition, part of the combinatoric background originates from real, prompt, D or Ds mesons that combine with a random pion or kaon. The combinatoric background is modelled with an exponential mass shape, except in the case of B D K +, where it is described with a flat distribution. The largest background components originate from partially reconstructed B and Bs decays. The most important backgrounds in the B D π + mass distribution originate from B D π + and B D ρ + decays, where B D π + exhibits a characteristic double peak structure due to the D decay with the pion preferentially emitted in or against the flight direction of the D meson. Under the B D K + signal, the most relevant backgrounds are these same decays with a misidentified bachelor pion, in addition to the corresponding decays with a true bachelor kaon. For both the B D π + and B D K + fits, the invariant PDFs for these contributions were taken from the simulated event samples, and their normalization left free in the fit. For the backgrounds to B D K + involving a misidentified bachelor pion, the momentum reweighting procedure is performed in the manner described in Sec. 4.2 for the misidentified B D π + events. PDFs were generated from the shapes observed in the simulated events, using non-parametric functions. 4.4 Mass fit validation The free parameters in the final likelihood fits to the mass distributions are the event yields for the different event types, i.e. the combinatorial background, partially reconstructed backgrounds, misidentified contributions and the signal. In addition, in the fit for the B D π + signal, the mean value and widths of the signal shape and the exponent of 6

8 the combinatorial background distribution are left free. The fit models were tested with an ensemble of Monte Carlo pseudoexperiments, showing that the fit results are unbiased and that the uncertainties are estimated correctly. In addition, a cocktail formed from fully simulated events was generated, containing B D K +, B D π +, B D ρ +, B D π +, Λ b Λ + c π, and loosely preselected inclusive bb-events that contribute sizeable combinatoric and semi-leptonic backgrounds. The fits accurately reproduces the numbers of input B D K + and B D π + events, and the ratio between the two is within the statistical error of the measurement:.73 ±.7 compared to an input of Fit results The fits to the full B D π + and B D K + data samples are shown in Fig. 2. The resulting B D π + and B D K + event yields are 419 ± 75 and 253 ± 21, respectively. The number of misidentified B D π + events under the B D K + signal as obtained from the fit (131 ± 19), is in agreement with the number expected from the total number of B D π + events, multiplied by the average misidentification rate as determined from the PID calibration sample (145). The Bs D s π+ event sample is fitted in a similar manner as the B D π + sample. The widths of the double Crystall Ball are fixed to 93% and 81% of that found in the B D π +, according to simulated events. The B D π + background peaks under the signal with a similar shape to the signal, and therefore not only its shape but also its yield is constrained in the fit. This is estimated from the π K misidentification in the D decay, in a similar way as described in Section 4.2. A Gaussian constraint is used to account for the uncertainty on the yield. The Λ b Λ + c π background shape is extracted from simulated events, reweighted according to the particle identification efficiency, and the yield is allowed to float in the fit. Finally the relative size of the Bs D s ρ+ and Bs Ds π + backgrounds is constrained to the ratio of the B D ρ + and B D π + backgrounds in the B D π + fit. To account for systematic uncertainty on the Events / ( 8 MeV/c 2 ) LHCb Preliminary s = 7TeV -1 L int ~35 pb B d D * π B d Dπ Combinatorial B d Dρ Events / ( 16 MeV/c 2 ) LHCb Preliminary s = 7TeV -1 L int ~35 pb B d D * K B d DK B d Dπ Combinatorial B d Dρ Mass (MeV/c 2 ) Mass (MeV/c 2 ) Figure 2: Results of the fit to B D π + (left) and B D K + (right) candidates. The curves are as summarised in the legend and described in the text. 7

9 14 Events / ( 8 MeV/c 2 ) LHCb Preliminary s = 7TeV -1 L int ~35 pb B s D s π B d Dπ B * s D s π Combinatorial Λ b Λ c π B s D s ρ B s D s πππ Mass (MeV/c 2 ) Figure 3: Results of the fit to B s D s π+ candidates. The curves are as summarised in the legend and described in the text. fit model due to differences in the B and Bs systems (i.e. SU(3) symmetry breaking), this ratio is fixed using a Gaussian constraint with a width equal to 2% of the mean value. The Bs Ds π + event yield is 67 ± 34, and the fit result is shown in Fig Cross-checks of the fit stability The ratio of the yields in the D ± and D s ± samples has been investigated as a function of different requirements on the value of the multivariate output variable, and is shown to be stable. Also, the ratio of B D K + to B D π + event yields shows negligible variation for different values of the multivariate output variable, with respect to the statistical uncertainty. In addition, the stability of the signal yield has been verified in the following way: The exponent of the combinatorial background has been varied by four standard deviations, and the corresponding variation of the B D π + signal was found to be 1%. A systematic uncertainty of 1% is therefore assumed. The same procedure was applied to the B D K + sample to determine the associated systematic uncertainty. The widths of the two Crystal Ball functions were conservatively varied by 1% and 2%, i.e. assuming the same widths as in B D π +. A maximum variation of 3% was found in the B s D s π + signal yield which is taken as a systematic uncertainty. The exercise of extracting the efficiency-corrected ratio of the B D π + and B s D s π+ yields was also performed on event samples that were selected with selection criteria on each input variable separately, as opposed to the multivariate technique. These rectangular selection criteria have been studied extensively on simulated events [16]. These selection criteria, with the exception of the PID information, were applied without further optimization. The efficiency-corrected ratio 8

10 Table 1: Correction factors for the relative branching ratio and f s /f d measurements. Efficiency Ratio ǫ(d π + ) ǫ(d K + ) ǫ(d K + ) ǫ(d s π + ) ǫ(d π + ) ǫ(d s π + ) K /π tracking eff ± ± ±.3 PID cuts ± ± ±.5 Bach. K P < 1 GeV/c 1.7 ± ±.1 N/A Trigger eff. N/A.925 ± ±.2 Overall correction factor ± ± ±.25 using the rectangular selection was found to be 5.54 ±.35, which is in excellent agreement with the efficiency-corrected ratio of 5.64 ±.33 as obtained using the BDTG selection. 6 Results 6.1 Relative branching ratio measurement The relative branching ratios are obtained by correcting the fitted event yields by the corresponding efficiency factors. The efficiency correction factors applied to the relative branching ratio measurements are listed in Table 1. All correction factors are multiplicative with respect to the ratio of the suppressed mode to the favoured mode. An important source of systematic error is the knowledge of the PID efficiency as a function of momentum, which is needed to obtain the mass shape of the B D π + decays under the kaon hypothesis for the bachelor track. This enters in two ways: firstly as an uncertainty on the correction factors, and secondly as part of the Fit model systematic uncertainty, since the fit shape for the misidentified backgrounds relies on correct knowledge of the PID efficiency as a function of momentum. Other systematics are due to the limited simulated event samples (affecting the relative selection efficiencies), and the assumption that the Λ b Λ + c π and B s D s π+ backgrounds are negligable in the B D π + fit. The uncertainty on the tracking efficiency refers to the different reconstruction efficiency for pions and kaons. The overall systematics budget is listed in Table 2. The efficiency correction factors are applied to the raw yield ratio computed from the fit results of Section 4.5, with the result: B (B D K + ) B (B D π + ) =.752 ±.64 ±.26, (7) where the first error is statistical, and the second is systematic. Using the PDG world 9

11 Table 2: Relative systematic uncertainties for the relative branching ratio measurements. Source Size for B Specific BG 2% PID calibration 1.5% Fit model 1.4% Tracking efficiency K /π 2% Total 3.5% average of the branching ratio of B D π + [1], this results in a value of B ( B D K + ) = (2.2 ±.17 ±.12) 1 4, (8) where the first error is statistical, and the second (including the 4.9% uncertainty on B(B D π + )) is systematic. 6.2 Measurement of f s /f d The efficiency correction factors applied to the relative branching ratio measurements are listed in Table 1, separately for f s /f d as extracted using B D K + or B D π + decays. All correction factors are multiplicative with respect to the ratio of the B mode to the Bs mode. In addition to the systematic uncertainties considered in the relative branching ratio measurement of the B decays, a systematic error also arises from the modelling of the trigger in simulated B and Bs events. The correction for the relative tracking efficiency is higher for Ds π + /D π + due to the lower momentum of the kaon in the D decay compared to the bachelor kaon. The overall systematics budget is listed in Table 3. The theoretically cleaner extraction of f s /f d is performed using the decays B D K + and Bs D s π+. The relevant formula is given in Eq. 3. The current world average for the Bs-to-B lifetime ratio is used [17] τ B s τ B =.973 ±.15, and the combined factor accounting for the non-factorizable corrections and form factors is given by [3] N a N F = 1.24 ±.8. Using B(D + K π + π + ) = (9.14 ±.2)% [18] and B(D + s K K + π + ) = (5.5 ±.27)%, the value of f s /f d is found to be f s f d =.242 ±.24 stat ±.18 syst ±.16 theor, (9) where the first error is the statistical uncertainty, the second the systematic uncertainty, and the third the theoretical uncertainty dominated by the uncertainty on the form factor 1

12 Table 3: Systematic uncertainties for the f s /f d measurements. Source Using D s π+ /D K + Using D s π+ /D π + Specific BG vetos in B fit 2% 2% PID calibration 1.5% 1.5% B fit model 1% 1% Bs fit model 3% 3% Tracking efficiency K /π 1.5% 3.5% Trigger simulation 2% 2% B(D s ± KKπ) 5% 5% B(D ± Kππ) 2% 2% τ Bs τ Bd 1.5% 1.5% Total 7.3% 8.% ratio. The statistical uncertainty in the determination of f s /f d is dominated by the yield of the B D K + mode. It is also possible to extract f s /f d from the modes B D π + and B s D s π +, an additional uncertainty from the W-exchange diagrams [5], N E =.966 ±.75 is compensated by a smaller statistical uncertainty, f s f d =.249 ±.13 stat ±.2 syst ±.25 theor. (1) The two values for f s /f d can be combined into a single value, by taking all correlated uncertainties into account, namely the uncertainties on the B s D s π+ yield, all systematic uncertainties listed in Table 3 (except the tracking efficiency difference between charged kaons and pions), the uncertainties on the ratio of form factors, and the ratio of non-factorizable effects. The averaged value of f s /f d is f s f d =.245 ±.17 stat ±.18 syst ±.18 theor. (11) All contributions to the uncertainty are assumed to be Gaussian distributed. These values of f s /f d are in good agreement with the values determined at LEP and at the Tevatron [17]. 7 Conclusions With 35 pb 1 of data collected using the LHCb detector during the 21 LHC running at a centre-of-mass energy of 7 TeV, the branching ratio of the Cabbibo-suppressed charmed B decay mode B D K + has been measured with a significantly better precision than the current world average. B ( B D K + ) = (2.2 ±.17 ±.12) 1 4, 11

13 Additionally, two measurements of the f s /f d production fraction are performed under different theoretical assumptions, from the relative yields of the B modes B D K + and B D π + with respect to B s D s π+. The measured values of f s /f d are in good agreement with each other and lead to the combined measurement References f s f d =.245 ±.17 stat ±.18 syst ±.18 theor. [1] Particle Data Group Collaboration, C. Amsler et. al., Review of particle physics, Phys. Lett. B667 (28) 1. [2] LHCb Collaboration, R. Aaij et. al., Search for the Rare Decays B s µµ and B d µµ, Submitted to Phys. Lett. B (211) [TT arxiv: ]. [3] R. Fleischer, N. Serra, and N. Tuning, New Strategy for B s Branching Ratio Measurements and the Search for New Physics in B s µ + µ, Phys. Rev. D82 (21) 3438, [TT arxiv: ]. [4] J. L. Rosner and S. Stone, Leptonic Decays of Charged Pseudoscalar Mesons, TT arxiv: [5] R. Fleischer, N. Serra, and N. Tuning, Tests of Factorization and SU(3) Relations in B Decays into Heavy-Light Final States, Phys. Rev. D83 (211) 1417, [TT arxiv: ]. [6] P. Blasi, P. Colangelo, G. Nardulli, and N. Paver, Phenomenology of B s decays, Phys. Rev. D49 (1994) , [TT hep-ph/93729]. [7] LHCb Collaboration, R. Aaij et. al., Measurement of σ(pp b bx) at s=7 TeV in the forward region, Phys. Lett. B694 (21) , [TT arxiv: ]. [8] A. A. Alves Jr. et al., The LHCb Detector at the LHC, JINST 3 (28) S85. [9] V. V. Gligorov, A single track HLT1 trigger, Tech. Rep. LHCb-PUB-211-3, CERN, Geneva, Jan, 211. [1] M. Williams et. al., The HLT2 Topological Lines, Tech. Rep. LHCb-PUB-211-2, CERN, Geneva, Jan, 211. [11] S. Easo, Selection of B s D s K+ and B s D s π+ decay modes in LHCb using Multivariate Methods. LHCb-PUB-21-9, 21. [12] A. Hoecker et. al., TMVA: Toolkit for multivariate data analysis, PoS ACAT (27) 4, [TT physics/7339]. 12

14 [13] K. Nakamura et. al., Review of Particle Physics, J. Phys. G 37 (21), no [14] J. Gaiser, Charmonium spectroscopy from radiative decays of the J/ψ and ψ, Ph.D. thesis, Appendix F. SLAC-R-255, [15] T. Skwarnicki, A study of the radiative cascade transitions between the Υ and Υ resonances, Ph.D. thesis, Appendix E. DESY F , [16] V. V. Gligorov, Reconstruction of the decay modes B d D± d π, B s D s π +, and B s D ± s K at LHCb. LHCb-PUB-29-3, 29. [17] Heavy Flavor Averaging Group Collaboration, D. Asner et. al., Averages of b-hadron, c-hadron and tau-lepton Properties [18] CLEO Collaboration, S. Dobbs et. al., Measurement of Absolute Hadronic Branching Fractions of D Mesons and e + e D D Cross Section at the ψ(377), Phys. Rev. D76 (27) 1121, [TT arxiv: ]. 13