Measurement of the B± production cross-section in pp collisions at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \sqrt {s} $\end{document} = 7 TeV

The production of B± mesons in proton-proton collisions at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \sqrt {s} $\end{document} = 7 TeV is studied using 35 pb−1 of data collected by the LHCb detector. The B± mesons are reconstructed exclusively in the B± → J/ψK± mode, with J/ψ → μ+μ−. The differential production cross-section is measured as a function of the B± transverse momentum in the fiducial region 0 < pT< 40 GeV/c and with rapidity 2.0 < y < 4.5. The total cross-section, summing up B+ and B−, is measured to be σ(pp → B±X, 0 < pT< 40 GeV/c, 2.0 < y < 4.5) = 41.4 ± 1.5 (stat.) ± 3.1 (syst.) μb.


Introduction
The study of the bb production cross-section is a powerful test of perturbative quantum chromodynamics (pQCD) calculations.These are available at next-to-leading order (NLO) [1] and with the fixed-order plus next-to-leading logarithms (FONLL) [2,3] approximations.In the NLO and FONLL calculations, the theoretical predictions have large uncertainties arising from the choice of the renormalisation and factorisation scales and the b-quark mass [4].Accurate measurements provide tests of the validity of the different production models.Recently, the LHCb collaboration measured the b b production crosssection in hadron collisions using J/ψ from b decays [5] and b → DµX decays [6].The two most recent measurements of the B ± production cross-section in hadron collisions have been performed by the CDF collaboration in the range p T > 6 GeV/c and |y| < 1 [7], where p T is the transverse momentum and y is rapidity, and by the CMS collaboration in the range p T > 5 GeV/c and |y| < 2.4 [8].This paper presents a measurement of the B ± production cross-section in pp collisions at a centre-of-mass energy of √ s = 7 TeV using 34.6 ± 1.2 pb −1 of data collected by the LHCb detector in 2010.The B ± mesons are reconstructed exclusively in the B ± → J/ψ K ± mode, with J/ψ → µ + µ − .Both the total production cross-section and the differential cross-section, dσ/dp T , as a function of the B ± transverse momentum for 0 < p T < 40 GeV/c and 2.0 < y < 4.5, are measured.
The LHCb detector [9] 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 includes a high precision tracking system consisting of a silicon-strip vertex detector surrounding the pp interaction region, a large-area silicon-strip detector located upstream of a dipole magnet with a bending power of about 4 Tm, and three stations of silicon-strip detectors and straw drift-tubes placed downstream.The combined tracking system has a momentum resolution ∆p/p that varies from 0.4% at 5 GeV/c to 0.6% at 100 GeV/c, and an impact parameter resolution of 20 µm for tracks with high transverse momentum.Charged hadrons are identified using two ring-imaging Cherenkov detectors.

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Photon, electron and hadron candidates are identified by a calorimeter system consisting of scintillating-pad and pre-shower detectors, an electromagnetic calorimeter and a hadronic calorimeter.Muons are identified by a muon system composed of alternating layers of iron and multiwire proportional chambers.
The LHCb detector uses a two-level trigger system, the first level (L0) is hardware based, and the second level is software based high level trigger (HLT).Here only the triggers used in this analysis are described.At the L0 either a single muon candidate with p T larger than 1.4 GeV/c or a pair of muon candidates, one with p T larger than 0.56 GeV/c and the other with p T larger than 0.48 GeV/c, is required.Events passing these requirements are read out and sent to an event filter farm for further selection.In the first stage of the HLT, events satisfying one of the following three selections are kept: the first one confirms the single-muon candidates from L0 and applies a harder p T selection at 1.8 GeV/c; the second one confirms the single-muon from L0 and looks for another muon in the event, and the third one confirms the dimuon candidates from L0.Both the second and third selections require the dimuon invariant mass to be greater than 2.5 GeV/c 2 .The second stage of the HLT selects events that pass any selections of previous stage and contain two muon candidates with an invariant mass within 120 MeV/c 2 of the known J/ψ mass.To reject high-multiplicity events with a large number of pp interactions, a set of global event cuts (GEC) is applied on the hit multiplicities of sub-detectors.

Event selection
Candidates for J/ψ → µ + µ − decay are formed from pairs of particles with opposite charge.Both particles are required to have a good track fit quality (χ 2 /ndf < 4, where ndf represents the number of degrees of freedom in the fit), a transverse momentum p T > 0.7 GeV/c and to be identified as a muon.In addition, the muon pair is required to originate from a common vertex (χ 2 /ndf < 9).The mass of the reconstructed J/ψ is required to be in the range 3.04 − 3.14 GeV/c 2 .
The bachelor kaon candidates used to form B ± → J/ψ K ± candidates are required to have p T larger than 0.5 GeV/c and to have a good track fit quality (χ 2 /ndf < 4).No particle identification is used in the selection of the kaon.A vertex fit is performed that constrains the three daughter particles to originate from a common point and the mass of the muon pair to match the nominal J/ψ mass.It is required that χ 2 /ndf < 9 for this fit.To further reduce the combinatorial background due to particles produced in the primary pp interaction, only candidates with a decay time larger than 0.3 ps are accepted.Finally, the fiducial requirement 0 < p T < 40 GeV/c and 2.0 < y < 4.5 is applied to the B ± candidates.

Cross-section determination
The differential production cross-section is measured as JHEP04(2012)093 where N B ± (p T ) is the number of reconstructed B ± → J/ψ K ± signal events in a given p T bin, L is the integrated luminosity, tot (p T ) is the total efficiency, including geometrical acceptance, reconstruction, selection and trigger effects, B(B ± → J/ψ K ± ) and B(J/ψ → µ + µ − ) are the branching fractions of the reconstructed decay chain [10], and ∆p T is the p T bin width.
Considering that the efficiencies depend on p T and y, we calculate the event yield in bins of these variables using an extended unbinned maximum likelihood fit to the invariant mass distribution of the reconstructed B ± candidates in the interval 5.15 < M B ± < 5.55 GeV/c 2 .We assume that the signal and background shapes only depend on p T .Three components are included in the fit procedure: a Crystal Ball function [11] to model the signal, an exponential function to model the combinatorial background and a double-Crystal Ball function1 to model the Cabibbo suppressed decay B ± → J/ψ π ± .The shape of the latter component is found to fit well the distribution of simulated events.The ratio of the number of B ± → J/ψ π ± candidates to that of the signal is fixed to B(B ± → J/ψ π ± )/B(B ± → J/ψ K ± ) from ref. [10].The invariant mass distribution of the selected B ± → J/ψ K ± candidates and the fit result for one bin (5.0 < p T < 5.5 GeV/c) are shown in figure 1.The fit returns a mass resolution of 9.14 ± 0.49 MeV/c 2 , and a mean of 5279.05 ± 0.56 MeV/c 2 , where the uncertainties are statistical only.Summing over all p T bins, the total number of signal events is about 9100.
The geometrical acceptance and the reconstruction and selection efficiencies are determined using simulated signal events.The simulation is based on Pythia 6.4 generator [12] with parameters configured for LHCb [13].The EvtGen package [14] is used to describe

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the decays of the B ± and J/ψ .QED radiative corrections are modelled using Photos [15].The Geant4 [16] simulation package is used to trace the decay products through the detector.Since we select events passing trigger selections that depend on J/ψ properties only, the trigger efficiency is obtained from a trigger-unbiased data sample of J/ψ events that would still be triggered if the J/ψ candidate were removed.The efficiency of GEC is determined from data to be (92.6 ± 0.3)%, and assumed to be independent of the B ± p T and y.The total trigger efficiency is then the product of the J/ψ trigger efficiency and the GEC efficiency.The luminosity is measured using Van der Meer scans and a beam-gas imaging method [17].The knowledge of the absolute luminosity scale is used to calibrate the number of tracks in the vertex detector, which is found to be stable throughout the data-taking period and can therefore be used to monitor the instantaneous luminosity of the entire data sample.The integrated luminosity of the data sample used in this analysis is determined to be 34.6 pb −1 .
The measurement is affected by the systematic uncertainty on the determination of signal yields, efficiencies, branching fractions and luminosity.
The uncertainty on the determination of the signal yields mainly arises from the description of final state radiation in the signal fit.The fitted signal yield is corrected by 3.0%, which is estimated by comparing the fitted and generated signal yields in the Monte Carlo simulation, and an uncertainty of 1.5% is assigned.The uncertainties from the effects of the Cabibbo-suppressed background, multiple candidates and mass fit range are found to be negligible.
The uncertainties on the efficiencies arise from trigger (0.5 − 6.0% depending on the bin), tracking (3.9 − 4.4% depending on the bin), muon identification (2.5%) [5] and the vertex fit quality cut (1.0%).The trigger systematic uncertainty has been evaluated by measuring the trigger efficiency in the simulation using a trigger-unbiased data sample of simulated J/ψ events.The tracking uncertainty includes two components: the first one is the differences in track reconstruction efficiency between data and simulation, estimated with a tag and probe method [18] using J/ψ → µ + µ − events; the second is due to the 2% uncertainty on the hadronic interaction length of the detector used in the simulation.The uncertainties from the effects of GEC, J/ψ mass window cut and inter-bin cross-feed are found to be negligible.The uncertainty due to the choice of p T binning is estimated to be smaller than 2.0%.
The absolute luminosity scale is measured with a 3.5% uncertainty [17], dominated by the beam current uncertainty.

Results and conclusion
The measured B ± differential production cross-section in bins of p T for 2.0 < y < 4.5 is given in table 1.This result is compared with a FONLL prediction [2,3] in figure 2. A hadronisation fraction fb →B + of (40.1 ± 1.3)% [10]  Table 1.Differential B ± production cross-section in bins of p T for 2.0 < y < 4.5.The first and second quoted uncertainties are statistical and systematic, respectively.
the b-quark mass, renormalisation and factorisation scales, and CTEQ 6.6 [19] Parton Density Functions (PDF), and is dominated by the uncertainty of the renormalisation and factorisation scales.Good agreement is observed between data and the FONLL prediction.

Figure 1 .
Figure1.Invariant mass distribution of the selected B ± → J/ψ K ± candidates for one bin (5.0 < p T < 5.5 GeV/c).The result of the fit to the model described in the text is superimposed.

Figure 2 .
Figure 2. Differential production cross-section as a function of the B ± transverse momentum.The left plot shows the full p T range, the right plot shows a zoom of the p T range of 0 − 12 GeV/c.The histogram (left) and the open circles with error bars (right) are the measurements.The red dashed lines in both plots are the upper and lower uncertainty limits of the FONLL computation.A hadronisation fraction fb →B + of (40.1 ± 1.3)% [10] is assumed to fix the overall scale.The uncertainty of the FONLL computation includes the uncertainties of the b-quark mass, renormalisation and factorisation scales, and CTEQ 6.6 PDF.