Measurement of the B − c meson production fraction and asymmetry in 7 and 13 TeV pp collisions

The production fraction of the B− c meson with respect to the sum of B − and B0 mesons is measured in both 7 and 13 TeV center-of-mass energy pp collisions produced by the Large Hadron Collider (LHC), using the LHCb detector. The rate, approximately 3.7 per mille, does not change with energy, but shows a transverse momentum dependence. The B− c −B+ c production asymmetry is also measured, and is consistent with zero within the determined statistical and systematic uncertainties of a few percent. Submitted to Physical Review D c © 2019 CERN for the benefit of the LHCb collaboration. CC-BY-4.0 licence. †Authors are listed at the end of this paper. ar X iv :1 91 0. 13 40 4v 1 [ he pex ] 2 9 O ct 2 01 9

The production fraction of the B − c meson with respect to the sum of B − andB 0 mesons is measured in both 7 and 13 TeV center-of-mass (c.m.) energy pp collisions produced by the Large Hadron Collider (LHC), using the LHCb detector. The rate, approximately 3.7 per mille, does not change with energy, but shows a transverse momentum dependence. The B − c − B þ c production asymmetry is also measured and is consistent with zero within the determined statistical and systematic uncertainties of a few percent. DOI: 10.1103/PhysRevD.100.112006

I. INTRODUCTION
The B − c meson is a bound state containing a b quark with ac quark. 1 It has the largest mass of any two differently flavored quarks in a mesonic ground state. Studies of its production or determination of individual decay widths require measurements of its branching fractions to exclusive final states. Since the branching fractions of some decay modes of B − andB 0 mesons are accurately known, we determine the ratio of B − c meson production relative to the sum of B − andB 0 mesons. Here we use techniques similar to those employed for the measurement ofB 0 s meson and Λ 0 b baryon fractions [1]. In that paper, use is made of the fact that the semileptonic widths of all bflavored hadrons with light and strange quarks are equal. However, both the b and c quarks can decay, rendering that concept inapplicable. Instead, we rely on theoretical predictions of the semileptonic decay branching fraction BðB − c → J=ψμ −ν Þ. Currently, only the relative production cross-section times the branching fraction of either the B − c → J=ψμ −ν or B − c → J=ψπ − modes have been measured by the CDF [2,3], LHCb [4,5], and CMS [6,7] experiments.
The B − c meson production fraction (f c ) relative to the sum ofB 0 (f d ) and B − (f u ) mesons is defined as where n cor refers to the efficiency and J=ψ; D branching fraction corrected number of signal events. The modes containing D 0 and D þ mesons are also corrected for cross-feeds withB 0 s and Λ 0 b decays. The determination of the corrected yields of the B → DXμ −ν decays follows our previous measurement strategy in Ref. [1] where the equations relating the fractions to the corrected yields, including cross-feed contributions, are given. We also correct for the 0.4% effect of doubly Cabibbo-suppressed decays and D 0 mixing. The relevant hadron branching fractions are listed in Table I. The average semileptonic branching fractions ofB 0 and B − , hB sl i ¼ ð10.70 AE 0.19Þ% is found by averaging measurements from the CLEO [8], BABAR [9], and Belle [10] experiments, detailed in Ref. [11]. Since only b → cμ −ν μ modes are detected in this analysis, a correction for the small b → uμ −ν μ rate of 1% is applied to the denominator of Eq. (1).
The dominant production mechanism for B − c mesons is gluon-gluon fusion, gg → B − c þb þ c. Nonrelativistic quantum chromodynamics is used along with fragmentation functions to predict cross-sections as functions of transverse momentum (p T ) and pseudorapidity (η). The literature is nicely summarized in Ref. [14]. We define H b to refer to B c , B 0 , and B − mesons, while H c refers to D 0 and D þ mesons.
In this analysis, η is determined by measuring the angle of the B meson with respect to the beam direction by using the positions of the primary pp interaction vertex (PV) and the B meson decay point into either J=ψμ − , D 0 μ − , or D þ μ − . The transverse momentum initially refers to the vector sum of the charmed-hadron and μ − momentum transverse to the proton beams. However, the results are reinterpreted in terms of the H b meson p T ðH b Þ by simulating and correcting the effects of the missing momenta.
The production asymmetry between B − c and B þ c mesons, which should be small, is defined as where the a raw and a det are the asymmetries in the signal yields and the efficiencies of B − c and B þ c detection, respectively. The CP asymmetry in the B − c → J=ψμ −ν decay is assumed to be zero in this analysis.
The branching fraction predictions from various models of semileptonic B − c decays are listed in Table II. For BðB − c → J=ψμ −ν Þ, they range from 1.4% to 7.5%, which is quite a large interval. Branching fractions for other modes are also listed where available. We use the Z expansion fit results from Ref. [15] and the method II results for Ref. [16]. Some restrictions on models are possible by comparing to lighter B meson decays. Since the inclusive semileptonic branching fraction for these decays, B sl , is about 10.5% and the B − c lifetime, τ B c , is 1=3 that of theB 0 , we disregard models that predict 10% or larger values for B c sl of the B − c . 2 This excludes from consideration the models of Refs. [17] and [20]. The average model prediction then is The standard deviation is 0.46%, which we use to estimate the systematic uncertainty on the model variation. Results of our measurement without using this branching fraction are also quoted.

II. DETECTOR, TRIGGER, AND SIMULATION
The LHCb detector [35,36] 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 detector elements that are particularly relevant to this analysis are a silicon-strip vertex detector surrounding the pp interaction region that allows c and b hadrons to be identified from their characteristically long flight distance; a tracking system that provides a measurement of the momentum, p, of charged particles; two ring-imaging Cherenkov detectors that are able to discriminate between different species of charged hadrons; and a downstream system of iron interspersed with chambers is used to identify muons.
The magnetic field deflects positively and negatively charged particles in opposite directions and this can lead to detection asymmetries. Periodically reversing the magnetic field polarity throughout the data taking almost cancels the effect. The configuration with the magnetic field pointing upward (downward) bends positively (negatively) charged particles in the horizontal plane toward the center of the LHC ring. This analysis uses data collected in 2011 (7 TeV) and 2016 (13 TeV) where appropriate triggers are available. The data taking was split between magnetic field up and down configurations. In the 2011 data, 0.6 fb −1 (0.4 fb −1 ) was collected with the field pointing up (down), while in 2016 the split was 0.9 fb −1 with field up and 0.8 fb −1 with field down.
The trigger [37] consists of a hardware stage, based on information from the calorimeter and muon systems, followed by a software stage, in which all charged particles with p T > 500ð300Þ MeV are reconstructed for 2011 (2016) data.

Particle and decay
Bð%Þ Source [12] TABLE II. Branching fractions predictions (%). The B − c lifetime is taken as 0.507 ps [12]. The value for the semileptonic decays of the B − c meson, B c sl , is derived by summing the J=ψμ −ν and η c μ −ν individual predictions with the average predictions of 0.1% for ψð2SÞμ −ν , the sum of χ c0;1;2 μ −ν as 0.6%, and 0.3% for h c μ − ν. In one case, where η c μ −ν was not predicted, averages from other measurements are used. [17] 6.4 5.0 1.3 13.6 [18] 0.5 [19] 1.4 0.5 2.9 [20] 7.5 2.4 10.9 [21] 1.9 0.6 0.1 3.5 [22] 2 Separate hardware triggers are used for the J=ψμ − and H c samples. For the former, we require a μ þ μ − pair. For the latter, we require a single muon with large p T for the 7 TeV data as used in Ref. [38]. For the 13 TeV data, the single muon trigger was not available; therefore, at the hardware trigger stage, events are required to have a hadron, photon, or electron transverse energy greater than approximately 3.5 GeV in the calorimeters. The software trigger requires a two-, three-, or four-track secondary vertex with a significant displacement from any primary pp interaction vertex as described in Ref. [1]. At least, one charged particle must have p T > 1.6 GeV and be inconsistent with originating from a PV. A multivariate algorithm [39] 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. In the simulation, pp collisions are generated using PYTHIA [40] with a specific LHCb configuration [41]. Decays of unstable particles are described by EVTGEN [42], in which final-state radiation is generated using PHOTOS [43]. The interaction of the generated particles with the detector, and its response, are implemented using the GEANT4 toolkit [44], as described in Ref. [45].

III. EVENT SELECTION, SIGNAL EFFICIENCIES AND YIELDS
A. Selection of B − c → J=ψμ −ν candidates The analysis is done separately for the light B meson modes and the B − c → J=ψμ −ν decay. In each case, the triggered events are subject to further filtering requirements. In addition, the J=ψμ − sample is subjected to a boosted decision tree (BDT), a multivariate classification method, using the TMVA toolkit [46]. This is not necessary for the D 0 or D þ modes because they have large signals and are relatively free from backgrounds [1].
For the J=ψμ −ν final state, the initial selection requires that muons that satisfy the J=ψ candidate trigger each have minimum p T > 550 MeV, have large impact parameters with the PV, form a good quality vertex, have a reasonable flight distance significance from the PV, and have a summed p T > 2 GeV. The "companion" muon that is not part of the J=ψ decay must be well identified and form a good quality vertex with the J=ψ candidate, which must be downstream of the PV.
To suppress muon tracks that are reconstructed more than once, we require a small minimum opening angle between the muons from the J=ψ decay and the companion muon momentum measured in the plane transverse to the beam line. Specifically, this opening angle must be greater than 0.8°. The invariant mass of the companion muon and the oppositely charged muon from J=ψ must differ from the known value of the J=ψ mass by more than 50 MeV [12], while the invariant mass with the same charged muon is required to be larger than 400 MeV.
Since we are dealing with an exclusive final state, we define where p ⊥ is the magnitude of the combination's momentum component transverse to the b-hadron flight direction. Figure 1 shows the distributions of m cor versus the invariant J=ψμ − mass, mðJ=ψμ − Þ, for both data and simulation. To remove background, a requirement of mðJ=ψμ − Þ > 4.5 GeV is applied, as indicated by the (red) dashed line.
Since we also measure the production asymmetry between B þ c and B − c mesons, we restrict the angular acceptance of the companion muon to make it more uniform by removing muons close to the edge of the detector, in the bending direction (x-direction), where large acceptance-induced asymmetries can occur. Thus, we require that the x-component of the momentum satisfies where p z is the muon momentum along the direction of the proton beam downstream of the PV, as is done in Refs. [47,48]. After these initial restrictions, we turn to the multivariate selection, forming the classifier denoted BDT in the following. The discriminating variables used are (a) the χ 2 of the vertex fit of the J=ψ with the μ − ; (b) the ln χ 2 IP , where χ 2 IP is defined as the χ 2 of the impact parameter with respect to the PV, of the J=ψ, μ − , and their combination; (c) the p T of the J=ψ and the μ − ; and (d) the cosine of the angle between the μ − and the J=ψ meson in the plane perpendicular to the beam direction. The training sample for signal is simulated B − c → J=ψμ −ν events and for background is inclusive b → J=ψX simulated events.
We then optimize the BDT output threshold by maximizing S= ffiffiffiffiffiffiffiffiffiffiffiffi S þ B p , where S and B are the number of the signal and background yields in the signal region defined as m cor ∈ ð4.8; 10.8Þ GeV. The sum, S þ B, is the total number of events within these limits, and S is taken from a fit to the m cor distribution. The optimal BDT output threshold results in a BDT signal efficiency of 89% with a background rejection of 63%, as determined by observing the resulting samples of input signal simulation events and background candidates.
The m cor distribution is shown in Fig. 2. It consists not We find shapes for these final states using simulation. The signal shape is a sum of a double crystal ball and a bifurcated Gaussian function. The sum of the combinatorial and misidentification backgrounds is represented by a Gaussian kernel shape [49]. For the other background modes, we use histograms directly. These shapes are fitted to the m cor distributions in Fig. 2 in order to determine the B − c → J=ψμ −ν yields. The ratio of the J=ψτ −ν yield to the J=ψμ −ν yield is fixed, after accounting for the relative detection efficiencies, from the LHCb measurement of 0.71 AE 0.17 AE 0.18, where the first uncertainty is statistical and the second systematic [50]; this convention is used throughout this paper. The other components of the fit are allowed to vary. We find 4010 AE 200 and 15170 AE 710 signal B − c → J=ψμ −ν events at 7 and 13 TeV, respectively, while the backgrounds sum to 950 and 5170 events at the same energies. These signal yields need to be corrected for the small background from candidates with a correctly reconstructed J=ψ meson that is paired with a hadron misidentified as a muon.
B. Efficiency for B − c → J=ψμ −ν Efficiencies are determined using both data [51,52] and simulation of B − c → J=ψμ −ν , with the generated events weighted to match the p T ðH b Þ, and η distributions observed in data. In addition, we weight accordingly the χ 2 IP distribution of the muon associated with the J=ψ. Weighting the simulation is important since the total efficiencies are functions of these variables. Efficiencies using data include trigger and muon identification. Efficiencies using simulation include detector acceptance, reconstruction and event selection, and removal of beam crossings with an excess number of hits in the detector.   Total efficiencies as a function of p T ðB − c Þ for different η intervals are shown in Fig. 3.

C. H c Xμ −ν selection criteria
Selection criteria for H b → H c Xμ −ν final states differ from those containing a J=ψ. The transverse momentum of each hadron must be greater than 0.3 GeV and that of the muon larger than 1.3 GeV. We require χ 2 IP > 9 with respect to any PV, ensuring that tracks do not originate from primary pp interactions. All final state particles are required to be positively identified using information from the RICH detectors. Particles from H c decay candidates must have a good fit to a common vertex with χ 2 =n:d:o:f: < 9, where n.d.o.f. 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 five.
Candidate b hadrons are formed by combining H c and muon candidates originating from a common vertex with χ 2 =n:d:o:f: < 9 and an H c μ − invariant mass in the range 3.0-5.0 GeV.
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 candidate mass distributions integrated over p T ðH b Þ and η are shown in Fig. 4 and 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 comprising two Gaussian functions and a combinatorial background component modeled as a linear function. The fitted yields are listed in Table III. These numbers must be corrected for hadrons that are misidentified as muons, and for semileptonic decays ofB 0 s and Λ 0 b hadrons that produce D 0 and D þ mesons.
In Table III, the column labeled "fake muons" shows the yields of wrong-sign D 0 Xμ þ and D þ Xμ þ combinations that pass the selections. These yields provide good estimates of the fake muon contributions in the signal samples, which are very small. Following the procedure in Ref. [1], we find the cross-feed corrections ofB 0 s → ðD 0 þD þ ÞXμ −ν and Λ 0 b → ðD 0 þ D þ ÞXμ −ν to be twice the measured yields forB 0 s → D 0 K þ Xμ −ν , which are 8500 AE 340 (7 TeV) and 69390 AE 1130 (13 TeV), and for Λ 0 b → D 0 pXμ −ν , which are 2330 AE 140 (7 TeV) and 33050 AE 460 (13 TeV). Relative efficiencies for detecting final states with a single extra hadron are taken into account when subtracting these yields.
D. Efficiencies for B → D 0 Xμ −ν and B → D + Xμ −ν Similar methods based on data, as implemented for the B − c decay, are used to evaluate the efficiencies for trigger and particle identification. Simulation is also used to determine the efficiencies of event selection and reconstruction of these modes. The total efficiencies for B meson decays into D 0 Xμ −ν and D þ Xμ −ν are shown in Fig. 5.

IV. RESULTS
A. Corrections to the p T ðH b Þ distributions due to the missing neutrino Since the production kinematics of B and B − c mesons can differ as functions of p T ðH b Þ and η, we need to measure f c =ðf u þ f d Þ as functions of these variables. The measurement of η is straightforward; however, we do not measure directly the p T ðH b Þ of the b-flavored hadron because of the missing neutrino, and in the case of the B meson possible missing extra particles. Following a procedure similar to the one used in Ref. [1], we determine a correction factor, k, that is the ratio of the average reconstructed to true p T ðH b Þ as a function of the invariant mass of the charmed hadron plus muon. The ratio distribution as a function of hadron-muon invariant mass is shown in Fig. 6. The average correction, the k-factor, is shown in the figure. For the B meson, it varies from 0.75 to unity over the interval from 3 GeV to the B mass, and for the B − c meson, it varies from 0.85 to unity over the interval from 4 GeV to the B − c mass.

B. B − c fraction results
The ratio of production fractions, f c =ðf u þ f d Þ, is shown as functions of p T ðH b Þ and η in Fig. 7. There is little dependence on η, but the decrease as a function of p T ðH b Þ is noticeable.
To describe the p T ðH b Þ dependence, we use an equation of the form where A represents the overall normalization and contains the total global systematic uncertainty; thus, A ¼ 1 AE 0.24; 3 hp T i is taken as 7.2 GeV, close to the average p T of the B − c . The slopes, p 2 , are similar in size to those measured for the B s meson fraction ratio as a function of p T [1,53]. Results of fits to the data using Eq. (5) are listed in Table IV. The average fractions in the interval 4 < p T ðH b Þ < 25 GeV are found by integrating over p T ðH b Þ. To allow for facile changes to our results due to improved theoretical predictions, we provide the results for   where the third uncertainty is due to the theoretical prediction of BðB − c → J=ψμ −ν Þ. To find f c =f u , just double these numbers.
We also measure the ratio of the B − c production fraction at 7 TeV to that at 13 TeV. Figure 8 shows the ratio as functions of p T and η. Here most of the systematic uncertainties cancel. The integrated value of the ratio of 13 and 7 TeV is measured as 1.02 AE 0.02 AE 0.04, consistent with no increase in the B − c fraction ratio as a function of c.m. energy.
The B − c fraction with respect to inclusive b-hadron production can be derived from the information in previous LHCb b-hadron fraction papers in Ref. [1,38,53] where the uncertainties contain both statistical and systematic components added in quadrature. For the measurement of the f Λ 0 b fraction at 7 TeV, the dominant systematic uncertainty is from the lack of the knowledge of BðΛ þ c → pK − π þ Þ at that time [38]; here the value and uncertainty have been recalculated according to the latest value of BðΛ þ c → pK − π þ Þ from the PDG [12]. Taking the sum of all the b-hadron fractions to be unity, and ignoring f c here because it is so small, where δ ¼ 0.25 AE 0.10 is a correction factor derived in Ref. [11] that accounts for heavier b-baryons, mainly the Ξ b . Solving for f u þ f d yields We find that where the first uncertainty is statistical, the second is systematic, and the third is from the fractions of the B 0 s and Λ 0 b given in Eq. (9). We also provide the result for f c , where the first uncertainty is statistical, the second is systematic including that from BðB − c → J=ψμ −ν Þ, and the third is from the fractions of the B 0 s and Λ 0 b given in Eq. (9).
C. The B − c − B + c production asymmetry The production asymmetries are measured in two different magnetic field configurations and then averaged. No significant asymmetry is observed in any intervals of p T ðH b Þ or η. The results are summarized in Table V.

V. SYSTEMATIC UNCERTAINTIES
Systematic uncertainties are separated into two categories: "global," which applies across the phase space, and "local," which is calculated in each two-dimensional p T ðH b Þ − η bin. These uncertainties are listed in Table VI. First, let us consider the B − c → J=ψμ −ν decay. The uncertainty due to the signal shape used to fit the m cor distribution is determined by changing the baseline signal  shape, the sum of a double sided crystal ball function and a bifurcated Gaussian, to a kernel estimation. To find the shape of the combinatorial and misidentification backgrounds, we use simulated inclusive samples of b → J=ψX events not including B − c decays. A total of 500 samples are generated and different fits to the samples are performed to determine the possible uncertainty. This procedure is also used for the a prod measurement. We call contributions to the J=ψμ − mass spectrum "feed-down" contributions, occurring from other B − c decay channels including J=ψτν, ψð2SÞμ −ν , and χ c μ −ν . The systematic uncertainty results from the uncertainties in their branching fractions. Different decay models for B − c → J=ψμ −ν decays can change the m cor shape. We use the model of Ebert et al. [18] for our baseline prediction. Then we also use the model by Kiselev [29] to find the efficiencies and take half the difference as the systematic uncertainty. We also estimate the uncertainty due to the sensitivity to various selection requirements and simulation statistics. The muon identification efficiencies are determined from data using inclusive samples of J=ψ decay where one of the muon candidates is not identified. The trigger efficiency is determined by using three independent samples of events, those that trigger on a J=ψ, those that triggered on something else in the event, and those that trigger on both the J=ψ and something else. These samples are then used to compute the trigger efficiencies in two-dimensional p T ðH b Þ and η bins.
Next, we turn to the B → DXμν modes. The efficiencies and their uncertainties for identifying pions and kaons are determined by using almost background free samples of D Ãþ → π þ D 0 , D 0 → K − π þ decays. The trigger and muon identification efficiencies, and their uncertainties, are obtained in the same manner as for the B − c → J=ψμ −ν mode. There are small systematic uncertainties related to efficiency estimates and the assumed D Ã to D mixtures, as well as simulation statistics. Global systematic uncertainties include the hadron branching fractions listed in Table I, cross-feed corrections arising fromB 0 s and Λ 0 b decays into DXμ −ν events, and a global hadron plus photon multiplicity requirement. The latter is evaluated with data.

VI. CONCLUSIONS
In 7 and 13 TeV pp collisions the product of BðB − c → J=ψμ −ν Þ with the relative fraction of B − c mesons with respect to the sum of B 0 and B þ mesons in the ranges 2.5 < η < 4.5 and 4 < p T ðH b Þ, < 25 GeV is found to be TABLE VI. Summary of the relative systematic uncertainties for f c =ðf u þ f d Þð%Þ and the absolute production asymmetries a prod ð%Þ. For local uncertainties, the ranges correspond to the minimum and maximum uncertainties evaluated in the p T ðH b Þ and η ranges.  We derive the product of f c · BðB − c → J=ψμ −ν Þ at the two energies as where the first uncertainties are statistical, the second systematic, and the third due to the theoretical prediction of BðB − c → J=ψμ −ν Þ. There is a small dependence on the transverse momentum of the B þ c meson, but no dependence on its pseudorapidity is observed. We also report where the first uncertainty is statistical, the second is systematic including that from BðB − c → J=ψμ −ν Þ, and the third is from the fractions of the B 0 s and Λ 0 b given in Eq. (9). The ratio of fractions, 1.02 AE 0.02 AE 0.04, for 13 TeV=7 TeV is consistent with no increase in the B − c fraction. Furthermore, using the assumption of no CP violation in the B − c → J=ψμ −ν decay, we find that the average asymmetry in B − c − B þ c production is consistent with zero. The measurements are ð−2.5 AE 2.1 AE 0.5Þ% and ð−0.5 AE 1.1 AE 0.4Þ% at c.m. energies of 7 and 13 TeV, respectively.

Global uncertainties
These results are useful to extract absolute branching fractions for B − c measurements, albeit with a relatively large uncertainty. They also challenge QCD calculations to predict the measured B − c fractions and explain the consistency between the fractions measured at 7 and 13 TeV [14,54].

ACKNOWLEDGMENTS
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,