Measurement of the B               ± production cross-section in pp collisions at $ \sqrt {s} $ = 7 TeV

<jats:title>A<jats:sc>bstract</jats:sc>           </jats:title>           <jats:p>The production of <jats:italic>B</jats:italic>             <jats:sup>±</jats:sup> mesons in proton-proton collisions at <jats:inline-formula>               <jats:tex-math>$ \sqrt {s} $</jats:tex-math>             </jats:inline-formula> = 7 TeV is studied using 35 pb<jats:sup>−1</jats:sup> of data collected by the LHCb detector. The <jats:italic>B</jats:italic>             <jats:sup>±</jats:sup> mesons are reconstructed exclusively in the <jats:italic>B</jats:italic>             <jats:sup>±</jats:sup> → <jats:italic>J/ψK</jats:italic>             <jats:sup>±</jats:sup> mode, with <jats:italic>J/ψ</jats:italic> → <jats:italic>μ</jats:italic>             <jats:sup>+</jats:sup>             <jats:italic>μ</jats:italic>             <jats:sup>−</jats:sup>. The differential production cross-section is measured as a function of the <jats:italic>B</jats:italic>             <jats:sup>±</jats:sup> transverse momentum in the fiducial region 0 <jats:italic>&lt; p</jats:italic>             <jats:sub>T</jats:sub>             <jats:italic>&lt;</jats:italic> 40 GeV<jats:italic>/</jats:italic>c and with rapidity 2<jats:italic>.</jats:italic>0 <jats:italic>&lt; y &lt;</jats:italic> 4<jats:italic>.</jats:italic>5. The total cross-section, summing up <jats:italic>B</jats:italic>             <jats:sup>+</jats:sup> and <jats:italic>B</jats:italic>             <jats:sup>−</jats:sup>, is measured to be <jats:italic>σ</jats:italic>(<jats:italic>pp</jats:italic> → <jats:italic>B</jats:italic>             <jats:sup>±</jats:sup>             <jats:italic>X,</jats:italic> 0 <jats:italic>&lt; p</jats:italic>             <jats:sub>T</jats:sub>             <jats:italic>&lt;</jats:italic> 40 GeV<jats:italic>/</jats:italic>c<jats:italic>,</jats:italic> 2<jats:italic>.</jats:italic>0 <jats:italic>&lt; y &lt;</jats:italic> 4<jats:italic>.</jats:italic>5) = 41<jats:italic>.</jats:italic>4 ± 1<jats:italic>.</jats:italic>5 (stat<jats:italic>.</jats:italic>) ± 3<jats:italic>.</jats:italic>1 (syst<jats:italic>.</jats:italic>) <jats:italic>μb</jats:italic>.</jats:p>

section_content: The study of heavy-quark production in high-energy hadronic interactions plays a critical role in testing next-to-leading order (NLO) Quantum Chromodynamics (QCD) calculations [1]. The first such measurements were made more than two decades ago by the UA1 Collaboration at the CERN S ppS collider [2, 3] operating at a center of mass energy of √ s = 0. 63 TeV, while more recent measurements have been made by the CDF and D0 Collaborations at the Fermilab Tevatron for √ s = 1. 8 and 1. 96 TeV [4? -10]. Substantial progress has been achieved in the understanding of heavy-quark production at Tevatron energies [11], but large theoretical uncertainties remain due to the dependence on the renormalization and factorization scales. Particularly important in the perturbative expansion are terms that scale as powers of ln ( √ s/m b ) at low transverse momentum p T of the b quark [12, 13], or as powers of ln (p T /m b ) when p T m b [14], where m b is the mass of the b quark. Measurements of b-hadron production at the higher energies provided by the Large Hadron Collider (LHC) represent an important new test of theoretical calculations [15, 16]. 

Recently, the LHCb Collaboration measured the production cross section for b hadrons at the LHC in the forward region using partially reconstructed decays [17]. This Letter presents the first measurement of exclusive B-meson production in pp collisions at √ s = 7 TeV. A sample of B ± → J/ψ K ± decays, with J/ψ → µ + µ -, is reconstructed in 5. 84 ± 0. 64 pb -1 of data collected by the Compact Muon Solenoid (CMS) experiment operating at the LHC. Charge conjugation is assumed in the remainder of this paper, where B + will be used to refer to both charge states. The signal yield in bins of transverse momentum p B T and rapidity y B is measured with a maximum likelihood fit to the reconstructed invariant mass M B and proper decay length ct of the B + candidates. These yields are corrected for detection efficiencies and luminosity to compute the differential production cross sections dσ/dp B T and dσ/dy B. The results are compared to theoretical predictions based on NLO QCD. 

A detailed description of the CMS detector can be found elsewhere [18]. The main subdetectors used in this analysis are the silicon tracker and muon systems. The tracker consists of silicon pixel and strip detector modules and is immersed in a 3. 8 T magnetic field that enables the measurement of charged particle momenta over the pseudorapidity range |η| < 2. 5, where η = ln tan θ 2 and θ is the polar angle of the track relative to the counterclockwise beam direction. Muons are identified in the range |η| < 2. 4 by gas-ionization detectors embedded in the steel return yoke. The first level of the CMS trigger system consists of custom hardware processors and uses information from the calorimeters and muon system to select the most interesting events in less than 1 µs. The High Level Trigger (HLT) processor farm further decreases the event rate to less than 300 Hz before data storage. The events used in the measurement reported here were collected with a trigger requiring the presence of two muons at HLT with no explicit momentum threshold. 

Reconstruction of B + → J/ψ K + candidates begins by identifying J/ψ → µ + µ -decays. The muon candidates are required to have at least one reconstructed segment in the muon system that matches the extrapolated position of a track reconstructed in the tracker. Muons within |η| < 2. 4 that pass the trigger are selected and further required to satisfy a kinematic threshold that depends on pseudorapidity: p µ T > 3. 3 GeV for |η µ | < 1. 3; p µ > 2. 9 GeV for 1. 3 < |η µ | < 2. 2; and p µ T > 0. 8 GeV for 2. 2 < |η µ | < 2. 4. Candidate J/ψ mesons are reconstructed by combining pairs of oppositely charged muons having an invariant mass within 150 MeV of the nominal J/ψ mass [19]. If more than one muon pair in an event satisfies this selection, the one closest to the J/ψ mass is selected. 

Candidate B + mesons are reconstructed by combining a J/ψ candidate with a track having p T > 0. 9 GeV, at least four hits in the tracker (of which one must be in the pixel detector), and a track-fit χ 2 less than five times the number of degrees of freedom. A kinematic fit is performed to the dimuon-track combination, constraining the dimuon mass to equal the J/ψ mass and assuming the third track to be a kaon. The selected events must have a resulting χ 2 confidence level greater than 0. 1% and a reconstructed B + mass satisfying 4. 95 < M B < 5. 55 GeV. In events with at least one B + candidate, the average number of such candidates is approximately 1. 7. When multiple candidates exist, the one with the highest p T is retained, which results in the correct choice 95% of the time in simulated events containing a true signal decay. A total of 35 406 B + candidates pass all the selection criteria. 

The efficiencies corresponding to this selection range from a few percent for p B T ∼ 5 GeV, to approximately 40% for p B T > 24 GeV, as determined in large samples of signal events generated by PYTHIA 6. 422 [20], decayed by EVTGEN [21], and processed by a detailed simulation of the CMS detector based on GEANT4 [22]. The efficiencies for hadron-track reconstruction [23] and the vertex quality requirement are found to be consistent between data and simulation within the available precision, which is used to set the systematic uncertainty of these quantities. Correction factors for trigger and muon-reconstruction efficiencies are obtained from a large sample of inclusive J/ψ → µ + µ -decays using a technique similar to that described in [24], where one muon is identified with stringent quality requirements and the second muon is identified using information separately from the tracker or from the muon system. 

The proper decay length of each B + candidate is calculated as ct = (M B /p B T )L xy, where the transverse decay length L xy is the vector s pointing from the primary vertex [25] to the secondary vertex projected onto the B + transverse momentum:

The core resolution on ct is approximately 30 µm for correctly reconstructed signal decays. 

Backgrounds are dominated by prompt and non-prompt inclusive J/ψ production. Additional backgrounds arise from misreconstructed b-hadron decays, such as B → J/ψK * (892), that produce a broad peaking structure in the region M B < 5. 2 GeV. Contamination from muon pairs that do not originate from J/ψ decay is negligible after all selection criteria are applied. 

The number n sig of signal decays in each p B T and y B bin is obtained using an unbinned extended maximum-likelihood fit to M B and ct. The likelihood for event j is obtained by summing the product of yield n i and probability density P i for each of the signal and background hypotheses i. Five individual components are considered: signal, B + → J/ψπ +, misreconstructed b b events that peak in M B, non-prompt J/ψ, and prompt J/ψ. The extended likelihood function is then the product of likelihoods for all events:

The probabilities P i are the probability density functions (PDFs) with shape parameters α i for M B, and β i for ct, evaluated separately for each of the i fit components. The yields n i are then determined by maximizing L with respect to the yields and a subset of the PDF parameters. 

The yield for J/ψπ + is constrained to equal the J/ψ K + yield times the ratio of branching fractions for the two decay modes [19]. 

The M B PDFs are the sum of three (two) Gaussians for the signal (J/ψπ) with parameters obtained from simulation; an exponential for both prompt and non-prompt J/ψ; and a combination of two Gaussians and an exponential for the peaking b b background. The resolution on M B for signal decays is approximately 30 MeV. The ct PDFs are a single exponential convolved with the resolution function to describe the signal, J/ψπ, and peaking background components, where the lifetime is allowed to be different for the latter; the sum of two exponentials 8. 5 convolved with the resolution function for the non-prompt J/ψ component; and the pure resolution function for the prompt J/ψ component. The resolution function is common for signal and background, and is described by the sum of two or three Gaussian functions, depending on p B T and y B. The fit proceeds in several steps so that all background shapes are obtained directly from data, except for the peaking component. This technique relies on the assumption that in the signalfree region 5. 40 < M B < 5. 55 GeV (upper sideband) there are only two contributions: prompt and non-prompt J/ψ background (ignoring the small contribution from J/ψπ). To obtain the effective lifetime of the non-prompt J/ψ background, the ct distribution is fitted for events in the inclusive B + sample defined by p B T > 5 GeV and y B < 2. 4 that lie in the M B upper sideband region, allowing the resolution function parameters to vary freely. The resolution function is then fixed and the signal B + lifetime in the inclusive sample is obtained by fitting ct and M B simultaneously. The result, cτ = 481 ± 22 µm (statistical uncertainty only), is in good agreement with the world-average value of 491 ± 9 µm [19]. With the effective lifetime for signal and nonprompt background fixed, the resolution function parameters are then determined separately in each bin of p B T and y B. Finally, with all ct resolution and background lifetime parameters fixed, the signal and background yields are fitted in each bin, together with the parameters describing the shape of the prompt and non-prompt J/ψ components in M B. 

The accuracy and robustness of the fit strategy were checked with a set of 400 pseudoexperiments where signal and background events were generated randomly from the PDFs in each bin. The fitted yields were unbiased and the uncertainties were estimated properly. The effects of correlations between M B and ct were studied by mixing together fully simulated signal and background events to produce 100 pseudoexperiments. No significant evidence of bias in the signal yield was found, and the observed deviations (a few percent) between fitted and gener-ated yields are taken as the systematic uncertainty due to potential biases in the fit method. 

Table 1 summarizes the fitted signal yield in each bin of p B T and y B, while Fig. 1 shows the fit projections for M B and ct from the inclusive sample with p B T > 5 GeV and y B < 2. 4. The total number of signal events is 912 ± 47, where the error is statistical only. 

The differential cross sections for B + production as a function of p B T and y B (averaged for positive and negative rapidities) are defined as

where n sig (p B T ) and n sig ( y B ) are the fitted signal yields in the given bin, (p B T ) and ( y B ) are the efficiencies in each bin for a B + meson produced with p B T > 5 GeV and y B < 2. 4 to pass all the selection criteria, ∆p B T is the bin size in p B T, and ∆y B = 2 ∆ y B is the bin size in y B. The total branching fraction B is the product of the individual branching fractions B(B + → J/ψ K + ) = (1. 014 ± 0. 034) × 10 -3 and B(J/ψ → µ + µ -) = (5. 93 ± 0. 06) × 10 -2 [19]. The factor of two in the denominator of Eq. 2 takes into account the choice of quoting the cross section for a single charge (taken to be B + ), while n sig includes both charge states. All efficiencies, (p B T ) or ( y B ), are calculated separately in each bin, and account for bin-to-bin migrations (a few percent) due to the resolution on the measured momentum and rapidity. 

The cross section is affected by several sources of systematic uncertainty arising from the signal yields, efficiencies, branching fractions, and luminosity. Uncertainties of the signal yields arise from potential fit biases and imperfect knowledge of the PDF parameters (2-5%), ct resolution function (1-2%), and the effects of final-state radiation on the signal shape in M B (< 1%). Uncertainties of the trigger (2%), muon identification (1%), and tracking (1-4%) efficiencies are all determined directly from data. The contribution (1-4%) related to the B + momentum spectrum is evaluated by reweighting the shape of the p B T distribution generated with PYTHIA to match the spectrum predicted by MC@NLO 3. 4 [26]. An uncertainty of 1. 5% is assigned to the efficiency of the vertex quality requirement. The effect of tracker misalignment on the cross sections due to variations in the signal yields and efficiencies is estimated to be approximately 2% using samples simulated with a different alignment than the nominal one. The total systematic uncertainty of the cross section measurement in each bin is computed as the sum in quadrature of the individual uncertainties, and is summarized in Table 1. In addition, there are common uncertainties of 3. 5% from the branching fractions and 11% from the luminosity measurement [27]. 

The differential cross sections as functions of p B T and y B are shown in Fig. 2 and Table 1. They are compared with the predictions of MC@NLO using a b-quark mass of 4. 75 GeV, renormalization and factorization scales µ = m 2 b + p 2 T, and the CTEQ6M parton distribution functions [28]. The uncertainty on the predicted cross section is calculated by varying the renormalization and factorization scales by a factor of two, m b by ±0. 25 GeV, and by using the CTEQ6. 6 parton distribution set. For reference, the prediction of PYTHIA is also included, using a b-quark mass of 4. 8 GeV, CTEQ6L1 parton distributions [28], and the D6T tune [29] to simulate the underlying event. The total integrated cross section for p B T > 5 GeV and y B < 2. 4 is calculated as the sum over all p B T bins and is found to be 28. 1 ± 2. 4 ± 2. 0 ± 3. 1 µb, where the first uncertainty is statistical, the second is systematic (including the branching fraction uncertainty), and the last is from the luminosity measurement. This result lies between the predictions of MC@NLO, 25. 5 +8. 8 -5. 4 (scale) +2. 5 -1. 8 (mass) ± 0. 8 (PDF) µb, and PYTHIA (48. 1 µb). In summary, first measurements of the total and differential cross sections for charged B production in pp collisions at √ s = 7 TeV using the decay B ± → J/ψ K ± have been presented. The measurements cover the range y B < 2. 4 and p B T from 5 GeV to greater than 30 GeV. The result is in reasonable agreement with the predictions of MC@NLO in terms of shape and absolute normalization. T > 5 GeV and y B < 2. 4. The curves in each plot are the sum of all contributions (solid blue line); signal (dashed red); prompt J/ψ (dotted green); and the sum of non-prompt J/ψ, peaking b b, and J/ψπ + (dot-dashed brown). For better visibility of the individual contributions, the M B plot includes a requirement of ct > µm.

section_content: We wish to congratulate our colleagues in the CERN accelerator departments for the excellent performance of the LHC machine. We thank the technical and administrative staff at CERN and other CMS institutes, and acknowledge support from: FMSR (Austria) ; FNRS and FWO (Belgium) ; CNPq, CAPES, FAPERJ, and FAPESP (Brazil) ; MES (Bulgaria) ; CERN ; CAS, MoST, and NSFC (China) ; COLCIENCIAS (Colombia) ; MSES (Croatia) ; RPF (Cyprus) ; Academy of Sciences and NICPB (Estonia) ; Academy of Finland, ME, and HIP (Finland) ; CEA and CNRS/IN2P3 (France); BMBF, DFG, and HGF (Germany) ; GSRT (Greece) ; OTKA and NKTH (Hungary) ; DAE and DST (India) ; IPM (Iran) ; SFI (Ireland) ; INFN (Italy) ; NRF and WCU (Korea) ; LAS (Lithuania) ; CINVESTAV, CONACYT, SEP, and UASLP-FAI (Mexico) ; PAEC (Pakistan) ; SCSR (Poland) ; FCT (Portugal) ; JINR (Armenia, Belarus, Georgia, Ukraine, Uzbekistan) ; MST and MAE (Russia) ; MSTD (Serbia) ; MICINN and CPAN (Spain) ; Swiss Funding Agencies (Switzerland) ; NSC (Taipei) ; TUBITAK and TAEK (Turkey) ; STFC ( United Kingdom ); DOE and NSF (USA).