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Measurement of J/psi production in pp collisions at sqrt(s)=2.76 TeV

The production of J/psi mesons is studied with the LHCb detector using data from pp collisions at sqrt(s)=2.76 TeV corresponding to an integrated luminosity of 71 nb^-1. The differential cross-section for inclusive J/psi production is measured as a function of its transverse momentum pT. The cross-section in the fiducial region 0<pT<12 GeV/c and rapidity 2.0<y<4.5 is measured to be 5.6 +/- 0.1(stat) +/- 0.4 (syst) mub, with the assumption of unpolarised J/psi production. The fraction of J/psi production from b-hadron decays is measured to be (7.1 +/- 0.6 (stat) +/- 0.7 (syst)) %.


Introduction
This article presents the measurements of the differential inclusive J/ψ production crosssection as a function of the J/ψ transverse momentum, and of the fraction of J/ψ mesons coming from the decay of a b-hadron in pp collisions at a centre-of-mass energy of 2.76 TeV. The study is based on a sample corresponding to an integrated luminosity of 71 nb −1 collected in March 2011 with an average of one visible pp interaction per recorded event.
The main goal of this short run was to provide a reference for the study of Pb-Pb interactions carried out at the same centre-of-mass energy per nucleon-nucleon collision.
Studies of J/ψ production have been performed by the LHC experiments using data taken at √ s = 7 TeV [1 -4] as well as at lower energies [5]. The data at √ s = 2.76 TeV provide an extra measurement to test theoretical models of J/ψ production in hadron collisions and are also used to obtain a measurement of J/ψ production from b-hadron decays.
The LHCb detector [6] 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 (VELO) 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. Charged hadrons are identified using two ring-imaging Cherenkov detectors. Photon, electron and hadron candidates are identified by a calorimeter system consisting of scintillating-pad and preshower detectors, an electromagnetic calorimeter and a hadronic calorimeter. Muons are identified by a system which consists of five stations of alternating layers of iron and multiwire proportional chambers, with the exception of the centre of the first station, which uses triple-GEM detectors.
For the data used in this analysis, the VELO, which consists of two retractable halves surrounding the interaction region, was positioned during collisions with its sensitive area at a minimum distance of 13 mm from the beam instead of the nominal 8 mm. This was necessary to provide a larger aperture for the beam at the lower centre-of-mass energy of 2.76 TeV.
The trigger [7] 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. Only the triggers used in this analysis are described here. At the hardware trigger level, a single muon candidate with p T larger than 0.8 GeV/c is required. In the first stage of the software trigger a simplified event reconstruction is applied and one requires a µ + µ − candidate with invariant mass greater than 2.7 GeV/c 2 . In the second stage a full event reconstruction is performed and only events with a µ + µ − pair with invariant mass within 120 MeV/c 2 of the known J/ψ mass [8] are retained.

Event selection
The analysis strategy is based upon that described in Ref. [1]. Candidate J/ψ mesons are formed from pairs of opposite-sign charged particles reconstructed in the fiducial region 2 < η < 5 by the full tracking system using algorithms adapted to the VELO at its displaced position. Each particle must have p T above 0.7 GeV/c and be identified as a muon. The two muons are required to originate from a common vertex, and only candidates with a χ 2 probability of the vertex fit larger than 0.5% are kept. Events are selected in which at least one primary vertex is reconstructed from at least three VELO tracks, excluding the two signal muon tracks from the J/ψ decay. A VELO track is required to have at least three hits on a straight line in the radial strips of the detector.
The Monte Carlo samples used for this analysis are based on the Pythia 6.4 generator [9] configured with the parameters detailed in Ref. [10]. The EvtGen package [11] is used to generate hadron decays, in particular for J/ψ and b-hadrons. The interaction of the generated particles with the detector and its response are implemented using the Geant4 toolkit [12] as described in Ref. [13]. Radiative corrections to the decay J/ψ → µ + µ − are generated using the Photos package [14]. The simulated position of the VELO corresponds to that in the data.

Cross-section determination
The differential cross-section for J/ψ production in a p T bin is given by dσ dp where N (J/ψ → µ + µ − ) is the number of observed J/ψ → µ + µ − signal decays in the given bin, tot the J/ψ detection efficiency per p T bin (including both acceptance and trigger), L the integrated luminosity, B (J/ψ → µ + µ − ) = (5.93 ± 0.06) × 10 −2 [8] the branching fraction of the J/ψ → µ + µ − decay, and ∆p T the p T bin size. The number of signal J/ψ mesons per p T bin is determined from an extended unbinned maximum likelihood fit to the invariant mass distribution of the reconstructed J/ψ candidates in the interval 3.0 < M µµ < 3.2 GeV/c 2 , where the signal is described by a Crystal Ball function [15] and the combinatorial background by an exponential distribution. Figure 1 shows the J/ψ invariant mass distribution together with the fit results for each p T bin, where results for 7 < p T < 12 GeV/c are merged in the last bin.
There are two main sources that contribute to the inclusive J/ψ sample. Those produced at the pp collision point, either directly or from the decay of a directly produced higher mass charmonium state, are called prompt J/ψ . The second source, J/ψ from b, are those produced in the decay of a b-hadron. Their production is displaced from the pp collision point because of the relatively large b lifetime. The two sources are statistically separated using the measured J/ψ pseudo-decaytime, defined as where z J/ψ and z PV are the positions along the beam axis of the J/ψ decay vertex and of the primary vertex refitted after removing the two muon tracks from the J/ψ candidate; p z is the measured J/ψ momentum in the beam direction and M J/ψ the known J/ψ mass [8].
Given that b-hadrons are not fully reconstructed, the J/ψ momentum is used instead of the exact b-hadron momentum and the t z variable provides a good estimate of the b-hadron decaytime.
The fraction of J/ψ from b is determined from a simultaneous fit to the total pseudodecaytime t z and µ + µ − invariant mass. Due to the small number of J/ψ candidates, the fraction of J/ψ from b is computed over the full p T interval from 0 to 12 GeV/c. The signal decaytime distribution is described by a delta function at t z = 0 for the prompt J/ψ component and an exponential decay function for the J/ψ from b component. The function describing the t z distribution of the signal is therefore where θ(t z ) is the step function, f p and f b are the fractions of prompt J/ψ and J/ψ from b in the sample, and τ b the b-hadron pseudo-lifetime. In the fit, τ b is fixed to the value of 1.52 ps, as obtained from simulation. The prompt and b components of the signal function are convolved with a triple-Gaussian resolution function The parameter µ is the bias of the t z measurement, and β and β the fractions of the first two Gaussian functions. The background consists of random combinations of muons from semi-leptonic b and c decays, which tend to produce positive t z values, as well as of mis-reconstructed tracks from decays in flight of kaons and pions, which contribute both to positive and negative t z values. The background t z distribution is parameterised with an empirical function based on the shape obtained from the J/ψ mass sidebands. It is taken as the sum of a delta function and three exponential components, two for positive t z and one for negative t z . The exponential parameter, τ L , is common to the larger positive and negative lifetime exponential components. The explicit form is and is convolved with the same resolution function f res as the signal. The function used to describe the t z distribution is therefore where all parameters except τ b are freely varied. The total fit function is the sum of the products of the mass and t z fit functions for the signal and background. Figure 2 shows the distributions of the dimuon invariant mass and t z with the projections of the fit superimposed. The invariant mass resolution is 13.0 ± 0.3 MeV/c 2 . The parameter µ describing the bias of the t z resolution function is 2.3 ± 2.0 fs and the RMS of the t z resolution function is 84 fs. As a measure of the fit quality, a χ 2 is calculated using a binned event distribution. The resulting fit probability for the t z distribution is 90%. The fit gives a total yield of 3399 ± 65 J/ψ signal decays.  The fraction of signal J/ψ coming from b-hadron decays is measured to be F b = f b fp+f b = (6.7 ± 0.6)%. An absolute correction of 0.4% is applied based on simulation to take into account a bias produced by events in which b-hadron decay products, other than the muons from the J/ψ , are wrongly used to reconstruct the primary vertex. This leads to the result F b = (7.1 ± 0.6)% where the uncertainty is only statistical.
A simulated sample of inclusive, unpolarised J/ψ mesons is used to estimate the geometrical acceptance in each p T bin. The reconstruction efficiency, which combines the J/ψ meson detection, reconstruction and selection efficiencies, is also computed from simulation as a function of p T and is corrected to account for the difference observed in the tracking efficiency between data and simulation at √ s = 7 TeV. This correction is about 1%. The efficiency of the hardware trigger is determined directly from data using a large inclusive J/ψ sample at √ s = 7 TeV triggered and selected with the same requirements as those used in this analysis: the efficiency is calculated in small bins of the J/ψ transverse momentum and rapidity and weighted according to the p T and y distributions as given by the simulation at 2.76 TeV. The efficiency of the software trigger, which makes use of the VELO information, is determined from simulation since the data at √ s = 7 TeV were taken with the VELO in the closed position. The total efficiency, calculated as the product of acceptance, reconstruction and trigger efficiencies, and its components are displayed in Fig. 3 as a function of p T . A non-zero polarisation of the J/ψ at production can affect the total efficiency [1]. The results quoted in this article assume that the J/ψ mesons are produced unpolarised.

Luminosity determination
To determine the integrated luminosity, an effective interaction rate is continuously measured during data taking and an absolute calibration is performed with a dedicated van der Meer (VDM) scan [16]. The strategy is similar to that developed for the √ s = 7 TeV running [17].
The VDM method exploits the ability to move the beams in both transverse coordinates with high precision and thus to scan the colliding beams with respect to each other. The limiting systematic uncertainty affecting the VDM measurement arises from the knowledge of the number of protons in the colliding bunch pairs. These are measured with two types of beam current transformers installed in the LHC [18]. The DCCT (DC Current Transformer) measures the total beam current, and is thus used to constrain the total number of particles. The uncertainty associated with the DCCT calibration is 2.7% [19]. The other transformer, the FBCT (Fast Beam Current Transformer) is used to measure the relative charges of the individual bunches. The uncertainty in its offset and linearity contributes a 0.9% uncertainty to the overall luminosity [19]. A small fraction of protons in the LHC may be captured outside the nominally filled bunch slots. This contribution, which needs to be subtracted from the DCCT measurement, is estimated to be 2.5% from the number of beam-gas events in nominally empty bunch crossings. Due to the small number of such events and uncertainties in the trigger efficiency, the subtraction introduces a cross-section uncertainty of 0.4%. The uncertainty in the length-scale calibration, which affects the beam separation values, contributes 1% to the systematic uncertainty in the luminosity. Finally, a 2.1% uncertainty is assigned to account for a non-reproducibility of the VDM results observed when performing similar luminosity calibration measurements  [17]. The integrated luminosity for the runs considered in this analysis is measured to be 70.6 ± 2.7 nb −1 . A summary of the contributions to the overall luminosity uncertainty is provided in Table 1. The uncertainties are uncorrelated and therefore added in quadrature.

Systematic uncertainties
The different contributions to the systematic uncertainty affecting the cross-section measurement are summarised in Table 2. Correction factors estimated directly from data to take into account residual differences between simulation and data are also detailed.
The influence of the choice of the fit function used to describe the shape of the dimuon mass distribution is estimated by fitting the J/ψ invariant mass distribution with the sum of two Crystal Ball functions. The relative difference of 2.2% in the number of signal events is taken as systematic uncertainty.
A fraction of J/ψ events have a lower mass because of the radiative tail. Based on Monte Carlo studies, 5% of the J/ψ signal is estimated to be outside the analysis mass window (M µµ < 3.0 GeV/c 2 ) and not counted as signal. The fitted signal yields are therefore corrected, and an uncertainty of 1% is assigned to the cross-section measurement based on a comparison between the radiative tail observed in data and simulation.
To cross-check and assign a systematic uncertainty to the Monte Carlo determination of the muon identification efficiency, the single track muon identification efficiency is measured on data using a tag-and-probe method. This method reconstructs J/ψ candidates in which one muon is identified by the muon system ("tag") and the other one ("probe") is identified by selecting a track with a minimum-ionising energy deposition in the calorimeters. The absolute muon identification efficiency is then evaluated on the probe muon, as a function of the muon momentum and found to be larger than 95%. The ratio of the muon identification efficiency measured in data to that obtained in the simulation is convolved with the momentum distribution of muons from J/ψ to obtain an efficiency correction. This factor is found to be 1.024 ± 0.011 and is consistent with being constant over the full J/ψ transverse momentum and rapidity range; the error on the correction factor is included as a systematic uncertainty.
Studies at √ s = 7 TeV have shown that the Monte Carlo simulation reproduces the determination from data of the efficiency to reconstruct the two muon tracks from the J/ψ decay within 0.8% to 1.1%, depending on the J/ψ transverse momentum. This difference is taken as a systematic uncertainty. An additional uncertainty of 1% per track is assigned to cover differences in the efficiency of the track χ 2 /ndf cut between data and simulation. Similarly, for the selection based on the J/ψ vertex χ 2 probability, a difference below 0.3% is measured between the cut efficiency computed in data and simulation, which is assigned as systematic uncertainty. To take into account the model dependence of the simulation in the efficiency calculation, the main parameters of the Pythia 6.4 generator related to prompt J/ψ production were varied. These parameters define the minimum p T cut-offs for regularising the cross-section. A 4.5% effect on the total efficiency was observed. Applied only to J/ψ from b fraction t z fit 10.0 Applied only to σ(pp → bbX) The hardware trigger efficiency is determined using a sample of events at √ s = 7 TeV that would still be triggered if the J/ψ candidate were removed. The software trigger efficiency is obtained from the simulation. Its uncertainty is evaluated by comparing true and measured trigger efficiency using a trigger-unbiased sample of simulated J/ψ events.
Uncertainties related to the t z fit procedure are taken into account by varying the slope of the exponential function of the J/ψ from b component by its uncertainty in the simulation (2%). The resulting 10% variation of the number of J/ψ from b is used as a systematic uncertainty that affects the measurement of F b . The influence of the background parametrisation was studied by varying the number of exponential functions in Eq. (5) and found to be negligible. Furthermore, an uncertainty of 8.6% on the average branching fraction of b decays to a final state containing a J/ψ meson contributes to the uncertainty on the extrapolation to the total bb cross-section. Table 3: Differential cross-section dσ/dp T at √ s = 2.76 TeV for inclusive J/ψ production in bins of p T . The rapidity range covered is 2.0 < y < 4.5. The first uncertainty is statistical and the second is systematic.

Results
The measured differential cross-section for inclusive J/ψ production as a function of p T , after all corrections and assuming no polarisation, is given in Table 3 and displayed in Fig. 4. The integrated inclusive cross-section for J/ψ production in the defined fiducial region is σ (J/ψ , p T < 12 GeV/c, 2.0 < y < 4.5) = 5.6 ± 0.1 ± 0.4 µb.
The first uncertainty is statistical and the second systematic. Studies indicate that this result could change by up to 20% assuming fully longitudinal or fully transverse J/ψ polarisation [1]. The fraction of J/ψ from b is measured to be F b = (7.1 ± 0.6 ± 0.7)% in the same acceptance range, p T < 12 GeV/c and 2.0 < y < 4.5. From the above results, one can deduce σ (J/ψ from b, p T < 12 GeV/c, 2.0 < y < 4.5) = 400 ± 35 ± 49 nb, in good agreement with the theoretical prediction of 370 +170 −110 nb, based on NLO calculations described in Ref. [20]. In addition, the total bb production cross-section is computed as where the factor α 4π = 6.3 is an extrapolation factor of the cross-section from the measured to the full kinematic region. This factor is obtained using the simulation software described previously. The inclusive b → J/ψ X branching fraction is B(b → J/ψ X) = (1.16 ± 0.10)% [8]. The resulting total bb cross-section is σ(pp → bbX) = 110 ± 9 ± 16 µb. No systematic uncertainty has been included for the extrapolation factor α 4π estimated from the simulation. The value of the extrapolation factor given by NLO calculations is 6.1 [20].

Conclusions
The differential cross-section for inclusive J/ψ production is measured as a function of the J/ψ transverse momentum in the forward region, 2.0 < y < 4.5. The analysis is based on a data sample corresponding to an integrated luminosity of 71 nb −1 collected by the LHCb experiment at the Large Hadron Collider at a centre-of-mass energy of √ s = 2.76 TeV. The results obtained are in good agreement with earlier measurements of the inclusive J/ψ production cross-section in pp collisions at the same centre-of-mass energy, performed by ALICE in the region 2.5 < y < 4.0 [21]. A first measurement of the production of J/ψ from b-hadron decays at 2.76 TeV is also obtained.