Measurement of fs /fu variation with proton-proton collision energy and B -meson kinematics

The ratio of the B 0 s and B þ fragmentation fractions f s and f u is studied with B 0 s → J= ψϕ and B þ → J= ψ K þ decays using data collected by the LHCb experiment in proton-proton collisions at 7, 8, and 13 TeV center-of-mass energies. The analysis is performed in bins of B -meson momentum, longitudinal momentum, transverse momentum, pseudorapidity, and rapidity. The fragmentation-fraction ratio f s =f u is observed to depend on the B -meson transverse momentum with a significance of 6 . 0 σ . This dependency is driven by the 13 TeV sample ( 8 . 7 σ ), while the results for the other collision energies are not significant when considered separately. Furthermore, the results show a 4 . 8 σ evidence for an increase of f s =f u as a function of collision energy.

The ratio of the B 0 s and B þ fragmentation fractions f s and f u is studied with B 0 s → J=ψϕ and B þ → J=ψK þ decays using data collected by the LHCb experiment in proton-proton collisions at 7, 8, and 13 TeV center-of-mass energies. The analysis is performed in bins of B-meson momentum, longitudinal momentum, transverse momentum, pseudorapidity, and rapidity. The fragmentation-fraction ratio f s =f u is observed to depend on the B-meson transverse momentum with a significance of 6.0σ. This dependency is driven by the 13 TeV sample (8.7σ), while the results for the other collision energies are not significant when considered separately. Furthermore, the results show a 4.8σ evidence for an increase of f s =f u as a function of collision energy. DOI: 10.1103/PhysRevLett.124.122002 The proton-proton (pp) collisions at the LHC produce copious pairs of b andb quarks, which immediately hadronize into the full spectrum of b hadrons. The knowledge of b-hadron production rates is crucial in order to measure their branching fractions.
The fragmentation fractions f u , f d , f s , and f baryon are defined as probabilities for a b quark to hadronize into a B þ , B 0 , B 0 s meson or a b baryon, respectively. (The inclusion of the charge-conjugate modes is implied throughout this Letter.) These include all possible contributions from intermediate states decaying to the mentioned hadrons via strong or electromagnetic interaction. The b-hadron fragmentation fractions were first measured in e þ e − collisions at the Z resonance by LEP experiments [1][2][3][4] and in pp collisions at ffiffi ffi s p ¼ 1.8 TeV center-of-mass energy by the CDF experiment [5]. In the absence of contradicting evidence, the fragmentation fractions determined in different collision environments were considered universal and averaged [6]. More recent measurements have shown that the hadronization fraction ratio f Λ 0 b =f d depends strongly on the p T and pseudorapidity of the produced b hadron [7][8][9]. Evidence has also been seen for a dependence on p B T of the relative B 0 s -and B 0 -meson production f s =f d [10]. In combination with changes in the produced b-quark spectra, it could lead to modified fragmentation-fraction ratios at higher pp collision energies and therefore affect the branching fraction measurements which rely on normalization.
This analysis studies the relative B 0 s -and B þ -meson production f s =f u dependence on pp collision energy and on the kinematics of the produced b hadron. Measuring the relative production is not only important for the studies of underlying QCD, f s =f u represents also an essential input and a dominant source of systematic uncertainty in B branching-fraction measurements performed in hadron colliders, e.g., B 0 s → μ þ μ − [11,12]. The analysis is performed on four independent data samples collected with the LHCb detector at three pp collision energies: at ffiffi ffi s p ¼ 7 TeV in the year 2011 (corresponding to 1 fb −1 ), 8 TeV in 2012 (2 fb −1 ), and at 13 TeV in the years 2015 (0.3 fb −1 ) and 2016 (1.1 fb −1 ). The relative production of B 0 s mesons to B þ mesons in the detector acceptance is measured in each sample with the ratio of efficiency-corrected yields of B þ → J=ψK þ and B 0 s → J=ψϕ decays where J=ψ → μ þ μ − and ϕ → K þ K − . Here N denotes the selected and reconstructed candidate yield and ϵ is the related efficiency.
The study is further extended to the relative productions as a function of B-meson kinematic variables: momentum (p B ), transverse momentum (p B T ), longitudinal momentum (p B L ), pseudorapidity (η B ), and rapidity (y B ). (The longitudinal momentum component is the momentum component along the beam direction.) Because of the large uncertainty on the B 0 s → J=ψϕ branching fraction, no attempt is made to measure the absolute f s =f u value.
(In Ref. [13], the ratio R was converted to an absolute f s =f d value using a theoretical prediction for the ratio of the B 0 s → J=ψϕ and B 0 → J=ψK Ã0 branching fractions [14]. In this Letter, Ref. [14] is not used due to disputed theoretical uncertainties arising from factorization assumption.) In the different context of light and strange hadrons, the ALICE experiment has observed a dependence of their production ratios on the multiplicity of the event [15][16][17]. In this analysis, this dependence is not studied, owing to technical reasons; however, such behavior will be the subject of future studies.
The LHCb detector [18,19] is a single-arm forward spectrometer covering the (final-state track) pseudorapidity range 2 < η < 5, largely complementary to the other LHC experiments. The detector includes a high-precision tracking system consisting of a silicon-strip vertex detector surrounding the pp interaction region, a large-area siliconstrip detector located upstream of a dipole magnet, three stations of silicon-strip detectors, and straw drift tubes located downstream of the magnet. Particle identification is provided by two ring-imaging Cherenkov detectors, an electromagnetic and a hadronic calorimeter, and a muon system composed of alternating layers of iron and multiwire proportional chambers.
The online event selection is performed by a two-stage trigger and relies on muon candidate tracks. The first level (hardware) trigger decision is based on information from the muon systems and selects events containing at least one muon with a large p T or a pair of muons with a large product of their transverse momenta ( ffiffiffiffiffiffiffiffiffiffiffi p T p 0 T p ). The trigger thresholds vary between 1 and 2 GeV=c, depending on the data-taking conditions.
The second level (software) trigger reconstructs the full event, looks for dimuon vertices and requires them to be significantly displaced from any primary vertex (PV). At least one of the tracks must have p T > 1 GeV=c and be inconsistent with originating from any PV. Only events in which the trigger decision was based on the muon tracks from the signal candidates are kept. The muon candidates are required to pass the muon identification criteria [20]. No additional particle identification is required on the kaon candidates.
Off-line, the J=ψ candidates are reconstructed by combining two oppositely charged muon tracks originating from the same vertex. The ϕð1020Þ candidates are reconstructed from the decays to the K þ K − final state. The B þ → J=ψK þ (B 0 s → J=ψϕ) candidates are built by combining the J=ψ candidates with a K þ (ϕ) candidate. Prompt combinatorial background is suppressed by removing the events in which the J=ψ vertex fit χ 2 , B vertex impact parameter, or J=ψ vertex distance indicate that the decay vertex is either poorly reconstructed or close to the PV. No further selection is applied on the reconstructed ϕ vertex in order to minimize the differences between the two signalchannel selections. Only J=ψ (ϕ) candidates with mass within AE60 MeV=c 2 (AE10 MeV=c 2 ) of the known J=ψ (ϕ) masses [6] are kept; these ranges are several times the mass resolutions of about 16 MeV=c 2 ð3.5 MeV=c 2 Þ.
Signal track candidates with momenta p > 500 GeV=c, transverse momenta p T > 40 GeV=c, or pseudorapidity outside of the range 2 < η < 4.5 are removed. In addition, muon and B transverse momenta are asked to pass p T > 250 MeV=c and p B T > 500 MeV=c requirements, respectively. The selected sample covers the following B-meson kinematic range: 20 < p B < 700 GeV=c, 20 < p B L < 700 GeV=c, 0.5 < p B T < 40 GeV=c, 2.0 < η B < 6.5, and 2.0 < y B < 4.5. The η B region between 2.0 and 2.5 is also accessible to the ATLAS and CMS experiments and thus important for comparison and combination of the results.
Simulated signal events are used to determine the detection efficiencies, estimate the background contamination, and model the mass distributions of the selected candidates. The simulated pp collisions are generated using PYTHIA [21] with a specific LHCb configuration [22]. Hadron decays are described by EvtGen [23] with final-state radiation generated using PHOTOS [24]. The particle interactions with the detector material and the detector response are implemented using the GEANT4 toolkit [25,26]. The samples of simulated signal events are corrected for known differences between data and simulation [27] in bins of detector occupancy and kinematic variables. When considering the B 0 s over B þ distribution ratio, the consistency between data and simulation before correction corresponded to a p value of at least 14% in the kinematic variables and exceeded 90% in the detector occupancy.
The signal yields are obtained by fitting the B þand B 0 s -candidate mass distributions, mðJ=ψK þ Þ and mðJ=ψK þ K − Þ, in the AE100 MeV=c 2 range around the known mass values using independent extended unbinned maximum-likelihood fits. To improve the mass resolution, the B-candidate masses are computed with the J=ψ mass constrained to its known value [6].
The mass distributions are described with probability density functions (PDFs) consisting of signal, combinatorial background, and background due to pions or protons that are wrongly identified as kaons. The signal components are parametrized by Hypatia functions [28], which consist of hyperbolic cores and power-law tails on both sides. The values of the parameters that define the tails are determined from simulation. The combinatorial backgrounds in both models are described by exponential PDFs. The means and widths of the signal components and the slopes of the exponentials are unconstrained. The values obtained in the data are larger by 10% or less for the widths and are consistent for the means and the other shape parameters. The fits repeated with fixed tails in the signal shape give consistent yield results to the constrained fits used by default. The contribution due to misidentified B þ → J=ψπ þ decays in the mðJ=ψK þ Þ distribution is described using a kernel density estimator technique [29] applied to simulated events. Its fraction, relative to the signal contribution, is found to be in agreement with the estimated fraction of ð3.8 AE 0.1Þ%.
The dominant misidentified background in the mðJ=ψK þ K − Þ distribution arises from B 0 → J=ψK þ π − decays, where a pion is mistakenly reconstructed as a kaon. The total inclusive B 0 → J=ψK þ π − background is a combination of the resonant and nonresonant contributions in the K þ π − final state: B 0 → J=ψK Ã ð892Þ 0 and B 0 → J=ψK þ π − . The PDFs of these components are linked [30], each described by a combination of two Crystal Ball functions [31] with a common Gaussian mean and tails on opposite sides. The background component is included in the fit model with the yield fraction defined relative to the signal contribution and the Gaussian constrained to the expected value of ð4.1 AE 0.5Þ%, determined on simu- s → J=ψf 0 ð→π þ π − Þ are considered and found negligible. The fit results to the B þ → J=ψK þ and B 0 s → J=ψϕ candidates in 2012 data are shown in Fig. 1. Fits to all the samples are shown in the Supplemental Material [32].
The signal detection efficiencies include the detector acceptance, reconstruction efficiencies, and selection efficiencies. The efficiencies are computed using simulated samples unless stated otherwise. Tracking efficiency differences in data and simulation are corrected for. The corrections are applied for each final-state track separately, in bins of the track p T and η and event multiplicity [33].
Trigger efficiencies are determined on data, separately for each data sample [34]. The trigger decision in every event can be ascribed to the reconstructed signal candidate and/or the rest of the event. The trigger efficiency is measured through the overlap of the two categories [35].
The abundant B þ → J=ψK þ sample is used to build a twodimensional trigger efficiency map as a function of the p T and p L of the J=ψ candidates. The choice of variables accounts for small differences in the J=ψ kinematic distributions from B þ → J=ψK þ and B 0 s → J=ψϕ decays. The average signal trigger efficiencies are computed by weighting the map contents with the fractions of simulated events in each bin and averaging the results, separately for each signal mode. In case of the results in B-meson kinematic bins, the trigger efficiency maps are defined in bins of the considered kinematic variable and of an independent variable: p T of the J=ψ candidate for the f s =f u results as a function of η B , p B L , and y B , and the p L of the J=ψ candidate for results as a function of p B T . Identical trigger selection and near-identical reconstruction and off-line selection significantly reduce the uncertainties affecting the efficiency-corrected B 0 s → J=ψϕ and B þ → J=ψK þ yield ratio measurement. Because of the similarity of J=ψ kinematic distributions from B þ → J=ψK þ and B 0 s → J=ψϕ decays, the efficiency ratios are close to unity, being about 0.98 for acceptance and selection and 0.99 for the trigger. The systematic uncertainties associated with acceptance, reconstruction, and selection efficiency arise only from the limited size of simulated samples. The dominant systematic uncertainties arise from the track-reconstruction efficiency corrections and the fit. A systematic uncertainty of 0.4% (0.8%) is assigned, following the procedures in Ref. [36], to the extra kaon track in B 0 s → J=ψϕ decays in 2011 and 2012 (2015 and 2016) samples. For all the samples, the uncertainty is increased by an additional 1.1% due to the interactions between the hadrons and detector material [36].
The systematic uncertainty arising from the fit model is propagated to the fitted signal yields by allowing the parameters to float within Gaussian constraints with mean and width determined from the simulation. Most of the signal and misidentified background component shape parameters are constrained with the remaining (partially correlated) tail parameters fixed to the values determined from simulation. The effect of fixing or leaving the signal parameters free has a negligible effect on the yield.
The resonant and nonresonant structure of the mðJ=ψK þ K − Þ spectrum is measured in Ref. [37]. The resonant f 0 ð980Þ meson contribution, nonresonant S-wave contribution, and the interference effects are studied on simulated samples. No attempt is made to separate these contributions from the signal decays, and the uncertainty of the fitted inclusive B 0 s → J=ψϕ yield is increased by 0.8%, relative to the yield.
The fit models are validated using the fitted PDFs to generate and fit a large number of simulated pseudoexperiments according to the observed candidate yields. The pseudoexperiments are generated for the fits on the full samples as well as for the fits in bins of p B T and η B . The mass fits in the p B T and η B bins do not show a significant bias and no additional systematic uncertainty is included. The pseudoexperiments for the full samples show a small yield estimator bias, the largest of which is 20% of the statistical uncertainty. The uncertainties on these yields are therefore increased by the same amount to account for this.
The validity of the mass models over the B-meson phase space is verified by comparing the fitted fractions and the model parameters across the samples and bins. The B þ → J=ψK þ fit is performed with the B þ → J=ψπ þ background shape determined independently in high-and low-p B T regions of the simulated decays. The variation in the observed yield is negligible. The background shapes in regions of η B are very similar. The misidentified B 0 → J=ψK þ π − background PDF variation in p B T or η B regions is studied with simulation. The distributions show no evidence for significant variation and no additional uncertainty is assigned to the fits in bins due to the assumption of the same fit model.
The ratios (R) and their detailed uncertainty composition are shown in Table I. The ratios are fitted as a function of the pp collision energy with a two-parameter function: a þ k s ffiffi ffi s p , as shown in Fig. 2. The statistical significance of the f s =f u dependence on collision energy is estimated by comparing this fit with that under the null hypothesis k s ¼ 0. The χ 2 difference between the two cases is used as a test statistic and its p value is determined from the χ 2 distribution with one degree of freedom [38]. The two-sided significance of the two-parameter fit (a ¼ 0.1159 AE 0.0032, k s ¼ ð1.27 AE 0.27Þ × 10 −3 TeV −1 , correlation ρ ¼ −0.76) is 4.8σ with respect to the hypothesis of no energy dependence. The fit accounts for the correlations between the samples due to the common tracking and fit uncertainties as described in Ref. [32].
The measured double ratios for different collision energies are with the correlation coefficient ρ ¼ 0.33 between the two and the correlated uncertainties accounted for.
In each sample, the efficiency-corrected signal yield ratios are measured in bins of the B-meson kinematic variables v ∈ fp B ; p B T ; p B L ; η B ; y B g and averaged. On the vertical scale of Fig. 3, the averaged signal-yield ratios are scaled, assuming f u ¼ f d , to match the average f s =f d s → J=ψϕ and B þ → J=ψK þ yield ratios (R) and uncertainties (σ tot ), including the statistical uncertainty (σ stat ) and the fully correlated and uncorrelated systematic uncertainties among the samples (σ uncor syst , σ cor syst ). Individual contributions from tracking efficiency (σ track syst ), acceptance, reconstruction, and selection efficiency (σ sel syst ) and fit model (σ fit syst ) are shown separately. Correlations stem from the common tracking and fit model uncertainties.  39,40] at the corresponding variable distribution means; this is for illustrative purpose alone. On the horizontal scale, each data point is set to the mean value determined from simulation. The statistical significance of the f s =f u dependence is estimated by fitting the R distributions with a function A v expðk v vÞ under two hypotheses: one where no variation is allowed and the slope parameter k v is fixed to zero and one with k v left free.
The relative B 0 s and B þ production is observed to depend on the p B T with a significance of 6σ and the fitted slope parameter is k p B T ¼ −ð1.93 AE 0.46Þ × 10 −3 GeV −1 c. The strongest variation is measured for the 13 TeV samples: 8.7σ, k p B T ¼ −ð4.40 AE 0.67Þ × 10 −3 GeV −1 c, while it is not significant (2.1σ and 1.5σ) for the 7 and 8 TeV results obtained separately; see the Supplemental Material [32] for further details. The variation in p B T is further studied in three subregions of p B L (½20; 75; 125; 700 GeV=c) and a clear dependence is seen in all the regions. The results for p B T , p B L , and η B are shown in Fig. 3. No evidence is found for significant f s =f u variation in p B , p B L , η B , or y B . For the numerical results in all the studied variables and additional figures, see the Supplemental Material [32].
In conclusion, the B 0 s and B þ fragmentation-fraction ratio f s =f u is studied at 7, 8, and 13 TeV pp collision energies and in different B-meson kinematic regions. A 4.8σ evidence is seen for a f s =f u dependence on the collision energy and f s =f u is observed to depend on the B-meson transverse momentum. The observed p B T dependence is compatible with the recent LHCb result on semileptonic modes [9]. No evidence of f s =f u variation is seen in B-meson momentum, longitudinal momentum, rapidity, or pseudorapidity.
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,