University of Birmingham Measurement of b hadron fractions in 13 TeV pp collisions

The production fractions of ¯ B 0 s and Λ 0 b hadrons, normalized to the sum of B − and ¯ B 0 fractions, are measured in 13 TeV pp collisions using data collected by the LHCb experiment, corresponding to an integrated luminosity of 1 . 67 fb − 1 . These ratios, averaged over the b hadron transverse momenta from 4 to 25 GeV and pseudorapidity from 2 to 5, are 0 . 122 (cid:1) 0 . 006 for ¯ B 0 s , and 0 . 259 (cid:1) 0 . 018 for Λ 0 b , where the uncertainties arise from both statistical and systematic sources. The Λ 0 b ratio depends strongly on transverse momentum, while the ¯ B 0 s ratio shows a mild dependence. Neither ratio shows variations with pseudorapidity. The measurements are made using semileptonic decays to minimize theoretical uncertainties. In addition, the ratio of D þ to D 0 mesons produced in the sum of ¯ B 0 and B − semileptonic decays is determined as 0 . 359 (cid:1) 0 . 006 (cid:1) 0 . 009 , where the uncertainties are statistical and systematic.

The production fractions ofB 0 s and Λ 0 b hadrons, normalized to the sum of B − andB 0 fractions, are measured in 13 TeV pp collisions using data collected by the LHCb experiment, corresponding to an integrated luminosity of 1.67 fb −1 . These ratios, averaged over the b hadron transverse momenta from 4 to 25 GeV and pseudorapidity from 2 to 5, are 0.122 AE 0.006 forB 0 s , and 0.259 AE 0.018 for Λ 0 b , where the uncertainties arise from both statistical and systematic sources. The Λ 0 b ratio depends strongly on transverse momentum, while theB 0 s ratio shows a mild dependence. Neither ratio shows variations with pseudorapidity. The measurements are made using semileptonic decays to minimize theoretical uncertainties. In addition, the ratio of D þ to D 0 mesons produced in the sum ofB 0 and B − semileptonic decays is determined as 0.359 AE 0.006 AE 0.009, where the uncertainties are statistical and systematic. DOI: 10.1103/PhysRevD.100.031102 Knowledge of the fragmentation fractions ofB 0 s (f s ) and Λ 0 b (f Λ 0 b ) hadrons is essential for determining absolute branching fractions (B) of decays of these hadrons at the LHC, allowing measurements, e.g., of BðB 0 s → μ þ μ − Þ [1] and the future evaluation of jV cb j from Λ 0 b → Λ þ c μ −ν μ decays [2]. 1 Once these fractions are determined, measurements of absolute branching fractions of B − andB 0 mesons performed at e þ e − colliders operating at the ϒð4SÞ resonance can be used to determine theB 0 s and Λ 0 b branching fractions [3].
In this paper we measure the ratios f s =ðf u þ f d Þ and where the denominator is the sum of B − andB 0 contributions, in the LHCb acceptance of pseudorapidity 2 < η < 5 and transverse momentum 4 < p T < 25 GeV, 2 in 13 TeV pp collisions. These ratios can depend on p T and η; therefore, we perform the analysis using two-dimensional binning.
Much of the analysis method adopted in this study is an evolution of our previous b hadron fraction measurements for 7 TeV pp collisions [4]. We use the inclusive semileptonic decays H b → H c Xμ −ν μ , where H b indicates a b hadron, H c a charm hadron, and X possible additional particles. Each of the different H c plus muon final states can originate from the decay of different b hadrons.
Semileptonic decays ofB 0 mesons usually result in a mixture of D 0 and D þ mesons, while B − mesons decay predominantly into D 0 mesons with a smaller admixture of D þ mesons. Both include a tiny component of D þ sK meson pairs. Similarly,B 0 s mesons decay predominantly into D þ s mesons, but can also decay into D 0 K þ and D þ K 0 meson pairs; this is expected if theB 0 s meson decays into an excited D þ s state that is heavy enough to decay into a DK pair. We measure this contribution using D 0 K þ Xμ −ν μ events. Finally, Λ 0 b baryons decay semileptonically mostly into Λ þ c final states, but can also decay into D 0 p and D þ n pairs. We ignore the contributions of b → u decays that comprise approximately 1% of semileptonic b hadron decays and contribute almost equally to all b hadron species. The detailed equations relating these yields to the final results are given in Ref. [4] and in the Supplemental Material [5].
The theoretical basis for this measurement is the near equality of semileptonic widths, Γ SL , for all b hadron species [6] whose differences are predicted to precisions of about 1%. The values we use for the individual H b semileptonic branching fractions (B SL ) are listed in Table I. The H c decay modes used and their branching fractions are given in Table II. The ratio of D þ to D 0 meson production in the sum of semileptonicB 0 and B − decays, f þ =f 0 , is used to check the analysis method. This result can be related to models of the hadronic final states in B − andB 0 semileptonic decays [11].
The data sample corresponds to 1.67 fb −1 of integrated luminosity obtained with the LHCb detector in 13 TeV pp collisions during 2016. The LHCb detector [12,13] is a single-arm forward spectrometer covering the pseudorapidity range 2 < η < 5, designed for the study of particles containing b or c quarks.
The online event selection is performed by a trigger [14] which consists of a hardware stage, based on information from the calorimeter and muon systems, followed by a software stage, which applies a full event reconstruction. At the hardware trigger stage, events are required to have a muon with large p T or a hadron, photon or electron with high transverse energy in the calorimeters. For hadrons, the transverse energy threshold is 3.5 GeV. The software trigger requires a two-, three-or four-track secondary vertex with a significant displacement from any primary pp interaction vertex (PV). At least one charged particle must have p T > 1.6 GeV and be inconsistent with originating from a PV. A multivariate algorithm [15] is used for the identification of secondary vertices consistent with the decay of a b hadron.
Simulation is required to model the effects of the detector acceptance and the imposed selection requirements. Here pp collisions are generated using PYTHIA [16] with a specific LHCb configuration [17]. Decays of unstable particles are described by EVTGEN [18], in which finalstate radiation is generated using PHOTOS [19]. The interaction of the generated particles with the detector and its response are implemented using the GEANT4 toolkit [20] as described in Ref. [21].
Selection criteria are applied to muons and H c decay particles. The transverse momentum of each hadron must be greater than 0.3 GeV, and that of the muon larger than 1.3 GeV. Each track cannot point to any PV, implemented by requiring χ 2 IP > 9 with respect to any PV, where χ 2 IP is defined as the difference in the vertex-fit χ 2 of a given PV reconstructed with and without the track under consideration being included. All final-state particles are required to be positively identified using information from the Ring Imaging CHerenkov detectors particle identification (PID). Particles from H c decay candidates must have a good fit to a common vertex with χ 2 /ndof < 9, where ndof is the number of degrees of freedom. They must also be well separated from the nearest PV, with the flight distance divided by its uncertainty greater than 5.
Candidate b hadrons are formed by combining H c and muon candidates originating from a common vertex with vetoes are employed to remove backgrounds from real D þ or Λ þ c decays where the particle assignments are incorrect.
Background from prompt H c production at the PV needs to be considered. We use the natural logarithm of the H c impact parameter, IP, with respect to the PV in units of mm. Requiring lnðIP=mmÞ > −3 is found to reduce the prompt component to be below 0.1%, while preserving 97% of all signals. This restriction allows us to perform fits only to the H c candidate mass spectra to find the b hadron decay yields.
The H c candidates' mass distributions integrated over p T ðH b Þ and η are shown in Fig. 1. They consist of a prominent peak resulting from signal and a small contribution due to combinatorial background from random combinations of particles that pass the selection. They are fit with a signal component comprised of two Gaussian functions and a combinatorial background component modeled as a linear function. The total signal yields are 13 775 000, 4 282 700, 845 300, and 1 753 600, respectively.
Background contributions to the b hadron candidates include hadrons faking muons, false combinations of charm hadrons and muons from the two b hadrons in the event, as well as real muons and charm hadrons from B → DDX decays, where one of the D mesons decays into a muon. All the backgrounds are evaluated in two-dimensional η and p T intervals. The first two backgrounds are evaluated using events where the H c is combined with a muon of the wrong sign (e.g., D 0 μ þ ), forbidden in a semileptonic b hadron decay. The wrong-sign backgrounds are <1% for each H c species. The background from B → DDX decays is TABLE I. Branching fractions of semileptonic b hadron decays from direct measurements forB 0 and B − mesons, (hBi ≡ hB 0 þ B − i), and derived forB 0 s and Λ 0 b hadrons based on the equality of semileptonic widths and the lifetime ratios [3,6]. Corrections to Γ SL forB 0 s ð−1.0 AE 0.5Þ% and Λ 0 b ð3.0 AE 1.5Þ% are applied [6]. Correlations in theB 0 and B − branching fraction measurements have been taken into account. See Ref. [7] for more information.
From Refs. [9,10] determined by simulating a mixture of these decays using their measured branching fractions [3]. The only decay mode significantly affected isB 0 The dominant component inB 0 s semileptonic decays is D þ s Xμ −ν μ , where X contains possible additional hadrons. However, theB 0 s meson also can decay into D 0 K þ or D þ K 0 instead of D þ s , so we must add this component to theB 0 s rate and subtract it from the f u þ f d fraction. Similarly, in Λ 0 b semileptonic decays we find a D 0 pX component. The selection criteria for these final states are similar to those for the D 0 Xμ −ν μ and Λ þ c Xμ −ν μ final states described above with the addition of a kaon or proton with p T > 300 MeV that has been positively identified. A veto is also applied to reject D Ãþ → π þ D 0 decays where the pion mimics a kaon or a proton.
These samples contain background, resonant and nonresonant decays. Separation of these components is achieved by using both right-sign (H c with μ − ) and wrong-sign (H c with μ þ ) candidates. In addition, the logarithm of the difference between the vertex χ 2 formed by the added hadron track and the Dμ system and the vertex χ 2 of the Dμ system, lnðΔχ 2 V Þ, provides separation between combinatorial background and nonresonant semileptonic decays. True resonant and nonresonantB 0 decays peak in the lnðΔχ 2 V Þ distribution at a value of unity while the background is smooth and rises at higher values as the added track is generally not associated with the D 0 μ − vertex. To distinguish signal from background we define mðD 0 hÞ C ≡ mðD 0 hÞ − mðD 0 Þ þ mðD 0 Þ PDG and perform two-dimensional fits to the mðD 0 hÞ C and lnðΔχ 2 V Þ distributions, where h ¼ K þ ðpÞ for right-signB 0 s (Λ 0 b ) decays. The wrong-sign shapes are used to model the backgrounds. The resonant structures are modeled with relativistic Breit-Wigner functions convoluted with Gaussians to take into account the experimental resolution, except for the narrow D s1 ð2536Þ þ which is modeled with the sum of two Gaussians with a fixed mean. The nonresonant shape for the lnðΔχ 2 V Þ distribution is taken as the same as the resonant one. Figure 2 shows the data and result of the fits forB 0 s and Λ  nonresonant events. The decay rate into D 0 p is assumed to be equal to that into D þ n using isospin conservation. All decays with an extra hadron have lower detection efficiencies than the sample without.
Efficiencies for all the samples are determined using data in two-dimensional p T and η bins. Trigger efficiencies are determined using a sample of B − → J=ψK − , with J=ψ → μ þ μ − decays where only one muon track is positively identified, in conjunction with viewing the effects of combinations of different triggers [24]. This sample is also used to determine muon identification efficiencies. Decays of J=ψ mesons to muons reconstructed using partial information from the tracking system, e.g., eliminating the vertex locator information, are also used to determine tracking efficiencies using data and to correct the simulation. Finally, the PID efficiencies are evaluated using kaons and pions from D Ãþ → π þ D 0 decays, with D 0 → K − π þ , and protons from Λ → pπ − and Λ þ c → pK − π þ decays [25]. In the measurement of b hadron fraction ratios many of the efficiencies cancel and we are left with only residual effects to which we assign systematic uncertainties.
The b hadron η and p T , p T ðH b Þ, must be known because the b fractions can depend on production kinematics. While η can be evaluated directly using the measured primary and secondary b vertices, the value of p T ðH b Þ must be determined to account for the missing neutrino plus extra particles. The correction factor k is given by the ratio of the average reconstructed to true p T ðH b Þ as a function of mðH c μ − Þ and is determined using simulation. It varies from 0.75 for mðH c μ − Þ ¼3 GeV to unity at mðH c μ − Þ ¼ mðH b Þ.
The distribution of f s =ðf u þ f d Þ as a function of p T ðH b Þ is shown in Fig. 3. We perform a linear χ 2 fit incorporating a full covariance matrix which takes into account the binby-bin correlations introduced from the kaon kinematics, and PID and tracking systematic uncertainties. The factor A in Eq. (1) incorporates the global systematic uncertainties described later, which are independent of p T ðH b Þ. The resulting function is where p T here refers to p T ðH b Þ, A ¼ 1 AE 0.043, p 1 ¼ 0.119 AE 0.001, p 2 ¼ ð−0.91 AE 0.25Þ × 10 −3 GeV −1 , and hp T i ¼ 10.1 GeV. The correlation coefficient between the fit parameters is 0.20. After integrating over p T ðH b Þ, no η dependence is observed (see the Supplemental Material [5]). We determine an average value for f s =ðf u þ f d Þ by dividing the yields ofB 0 s semileptonic decays by the sum of B 0 and B − semileptonic yields, which are all efficiencycorrected, between the limits of p T ðH b Þ of 4 and 25 GeV and η of 2 and 5, resulting in where the uncertainty contains both statistical and systematic components, with the latter being dominant, and discussed subsequently. The total relative uncertainty is 4.8%. Figure 3 also shows the Λ 0 b fraction as a function of p T ðH b Þ demonstrating a large p T dependence. The distribution in η is flat. We perform a similar fit as in theB 0 s fraction case, using where p T here refers to p T ðH b Þ, A ¼ 1 AE 0.061, p 1 ¼ ð7.93 AE 1.41Þ × 10 −2 , p 2 ¼ −1.022 AE 0.047, and p 3 ¼ −0.107 AE 0.002 GeV −1 . The correlation coefficients among the fit parameters are 0.40 (ρ 12 ), −0.95 (ρ 13 ), and −0.63 (ρ 23 ).
The average value for f Λ 0 b =ðf u þ f d Þ is determined using the same method as in theB 0 s case. The result is where the dominant uncertainty is systematic, and the statistical uncertainty is included. The overall uncertainty is 6.9%. As a systematic check of the analysis method, and a useful measurement to test the knowledge of known semileptonic branching fractions and extrapolations used to saturate the unknown portion of the inclusive hadron spectrum, we measure the ratio of the D 0 Xμ −ν μ to D þ Xμ −ν μ corrected yields f þ =f 0 . We subtract the small contributions fromB 0 s and Λ 0 b decays, and a very small contribution from B → D þ sK μ − X decays has been taken into account [26], as in all the fractions measured above.
Assuming f u equals f d , Ref. [11] estimates the fraction of D þ μ with respect to D 0 μ modes in the sum of B − andB 0 decays as 0.387 AE 0.012 AE 0.026. The first uncertainty comes from the uncertainties on known measurements. The second uncertainty comes from the different extrapolations from excited D mesons used to saturate the remaining portion of the inclusive rate.
The f þ =f 0 ratio must be independent of η and p T . To derive an overall value for f þ =f 0 , the p T ðH b Þ distribution is fit to a constant. Only the PID and tracking systematic uncertainties on the second pion in the D þ decay need be considered. Performing a χ 2 fit using the full covariance matrix we find f þ =f 0 ¼ 0.359 AE 0.006 AE 0.009, where the first uncertainty is from bin-by-bin statistical and systematic uncertainties, including correlations, and the second is systematic. The χ 2 =ndof is 0.63, in agreement with a flat spectrum. The measurement is consistent with the prediction and places some constraints on the D ÃÃ content of semileptonic B decays [11].
The dominant global systematic uncertainties are listed in Table III   modeling of excited charm states for the f s =ðf u þ f d Þ determination and the weighting required for the f Λ 0 b =ðf u þ f d Þ ratio, due to differences between the simulated and measured p T spectra. Background uncertainties arise from DDX final states with uncertain branching fractions. Cross-feed uncertainties come from errors on efficiency estimates and the assumed D Ã to D mixtures. Other smaller uncertainties depend on p T ðH b Þ and include tracking 0.2%-1.8%, particle identification 0.4%-3.0%, trigger 0.3%-3.9% and k-factor 0.2%-1.8%.
In conclusion, we measure the ratios ofB 0 s and Λ 0 b production to the sum of B − andB 0 to be p T ðH b Þ dependent [see Eqs. (1) and (2)]. The averages in the ranges 4 < p T ðH b Þ < 25 GeV and 2 < η < 5 are f s =ðf u þ f d Þ ¼ 0.122 AE 0.006 and f Λ 0 b =ðf u þ f d Þ ¼ 0.259 AE 0.018, respectively. Using 7 TeV data, LHCb determined f s =ðf u þf d Þ¼0.1295AE0.0075 with a p T ðH b Þ slope larger than, but consistent with, these 13 TeV results [27]; no dependence on η was observed. For the Λ 0 b baryon, the fraction ratio is consistent with the 7 TeV measurements after taking into account the different p T ðH b Þ ranges used [4,28,29]. We observe no rapidity dependence over a similar p T ðH b Þ range as in Ref. [29].
These results are crucial for determining absolute branching fractions ofB 0 s and Λ 0 b hadron decays in LHC experiments. We also determine the ratio of D 0 to D þ mesons produced in the sum ofB 0 and B − semileptonic decays as f þ =f 0 ¼ 0.359 AE 0.006 AE 0.009.
We express our gratitude to our colleagues in the CERN accelerator departments for the excellent performance of the LHC. We thank the technical and administrative staff at the LHCb institutes. We acknowledge support from CERN and from the national agencies: CAPES, CNPq, FAPERJ and FINEP (