Prompt and non-prompt J/psi production in pp collisions at sqrt(s) = 7 TeV

The production of J/psi mesons is studied in pp collisions at sqrt(s)=7 TeV with the CMS experiment at the LHC. The measurement is based on a dimuon sample corresponding to an integrated luminosity of 314 inverse nanobarns. The J/psi differential cross section is determined, as a function of the J/psi transverse momentum, in three rapidity ranges. A fit to the decay length distribution is used to separate the prompt from the non-prompt (b hadron to J/psi) component. Integrated over J/psi transverse momentum from 6.5 to 30 GeV/c and over rapidity in the range |y|<2.4, the measured cross sections, times the dimuon decay branching fraction, are 70.9 \pm 2.1 (stat.) \pm 3.0 (syst.) \pm 7.8(luminosity) nb for prompt J/psi mesons assuming unpolarized production and 26.0 \pm 1.4 (stat.) \pm 1.6 (syst.) \pm 2.9 (luminosity) nb for J/psi mesons from b-hadron decays.


Introduction
Heavy-flavour and quarkonium production at hadron colliders provides an important test of the theory of Quantum Chromodynamics (QCD). The production of J/ψ mesons occurs in three ways: prompt J/ψ produced directly in the proton-proton collision, prompt J/ψ produced indirectly (via decay of heavier charmonium states such as χ c ), and non-prompt J/ψ from the decay of a b hadron. This paper presents the first measurement of the differential inclusive, prompt and non-prompt (b hadron) J/ψ production cross sections in pp collisions at a centreof-mass energy of 7 TeV, in the rapidity range |y| < 2.4, by the Compact Muon Solenoid (CMS) experiment.
Despite considerable progress in recent years [1][2][3], quarkonium production remains puzzling and none of the existing theoretical models satisfactorily describes the prompt J/ψ differential cross section [3][4][5] and polarization [6] measured at the Tevatron [7]. Measurements at the Large Hadron Collider (LHC) will contribute to the clarification of the quarkonium production mechanisms by providing differential cross sections in wider rapidity ranges and up to higher transverse momenta than was previously possible, and with corresponding measurements of quarkonium polarization. Cross-section results are largely dependent on the J/ψ polarization, as different polarizations cause different muon momentum spectra in the laboratory frame. Given the sizeable extent of this effect, for prompt J/ψ mesons (where the polarization is presently not well described by the theoretical models) we choose to quote final results for different polarization scenarios, instead of treating this effect as a source of systematic uncertainty.
Non-prompt J/ψ production can be directly related to b-hadron production, leading to a measurement of the b-hadron cross section in pp collisions. Past discrepancies between the Tevatron results (both from inclusive [5] and exclusive [8] measurements) and the next-to-leadingorder (NLO) QCD theoretical calculations, were recently resolved using the fixed-order nextto-leading-log (FONLL) approach and updated measurements of the b → J/ψ fragmentation and decay [9,10]. Measured cross-section values and spectra are also found to be in agreement with Monte Carlo generators following this approach, such as MC@NLO [11,12].
The paper is organized as follows. Section 2 describes the CMS detector. Section 3 presents the data collection, the event trigger and selection, the J/ψ reconstruction, and the Monte Carlo simulation. Section 4 is devoted to the evaluation of the detector acceptance and efficiencies to detect J/ψ events in CMS. In Section 5 the measurement of the J/ψ inclusive cross section is reported. In Section 6 the fraction of J/ψ events from b-hadron decays is derived, and crosssection results are presented both for prompt J/ψ production and for J/ψ production from bhadron decays. Section 7 presents comparisons between the measurements and model calculations.
Two different muon reconstruction algorithms are considered [23]. The first one provides highquality and high-purity muon reconstruction for tracks with p T 4 GeV/c in the central pseudorapidity region (|η| 1.3) and p T 1 GeV/c in the forward region; these muons are referred to as Global Muons. The second muon reconstruction algorithm achieves a better reconstruction efficiency at lower momenta; these muons are referred to as Tracker Muons. There is an overlap between these two reconstruction methods. If a muon is reconstructed by both algorithms, it is assigned to the Global Muon category alone, making the two categories exclusive. Global Muons have a higher reconstruction purity. In both cases, the track momentum is determined by the fit in the silicon tracker.
To reduce muon backgrounds, mostly from decays in flight of kaons and pions, and to ensure good quality reconstructed tracks, muon tracks are required to pass the following requirements: they must have at least 12 hits in the tracker, at least two of which are required to be in the pixel layers, a track fit with a χ 2 per degree of freedom smaller than four, and must pass within a cylinder of radius 3 cm and length 30 cm centered at the primary vertex and parallel to the beam line. If two (or more) tracks are close to each other, it is possible that the same muon segment or set of segments is associated with more than one track. In this case the best track is selected based on the matching between the extrapolated track and the segments in the muon detectors.
The momentum measurement of charged tracks in the CMS detector has systematic uncertainties due to imperfect knowledge of the magnetic field, modeling of the detector material, sub-detector misalignment, and biases in the algorithms which fit the track trajectory; these effects can shift and/or broaden the reconstructed peaks of dimuon resonances. In addition to calibrations already applied to the data [22,24,25], residual effects can be determined by studying the dependence of the reconstructed dimuon peak shapes on the muon kinematics. The transverse momentum corrected for the residual scale distortion is parametrized as where p meas T is the measured muon transverse momentum. A likelihood fit [26] was performed to the invariant mass shapes to minimize the difference between the reconstructed J/ψ mass and the world-average value [27]. The resulting values of a 1 and a 2 are (3.8 ± 1.9) · 10 −4 and (3.0 ± 0.7) · 10 −4 , respectively.

J/ψ event selection
To select the events with J/ψ decays, muons with opposite charge are paired and their invariant mass is computed. The invariant mass of the muon pair is required to be between 2.6 and 3.5 GeV/c 2 . The two muon trajectories are fitted with a common vertex constraint, and events are retained if the fit χ 2 probability is larger than 0.1%. This analysis uses combinations of two Global Muons, two Tracker Muons, and one Global and one Tracker Muon. On average, 1.07 J/ψ combinations were found per selected dimuon event. In case of multiple combinations in the same event, the one with the purest muon content is chosen. If there are two or more dimuon candidates of the same type (Global-Global, Global-Tracker, or Tracker-Tracker) the one of highest p T is chosen.
The opposite-sign dimuon mass spectrum is shown in Fig. 1 for three different J/ψ rapidity ranges. About 27 000 J/ψ candidates have been reconstructed, of which about 19% are in the two-Global-Muon category, 54% in the Global-Tracker-Muon category, and the remaining in the two-Tracker-Muon category.

Acceptance
The acceptance reflects the finite geometrical coverage of the CMS detector and the limited kinematical reach of the muon trigger and reconstruction systems, constrained by the thickness of the material in front of the muon detectors and by the track curvature in the magnetic field.
The J/ψ acceptance A is defined as the fraction of detectable J/ψ → µ + µ − decays, as a function of the dimuon transverse momentum p T and rapidity y, where N det is the number of detectable J/ψ events in a given (p T , y) bin, expressed in terms of the dimuon variables after detector smearing, and N gen is the corresponding total number of generated J/ψ events in the Monte Carlo simulation. The parameter λ θ reflects the fact that the acceptance is computed for various polarization scenarios, as explained below. The large number of simulated events available allows the use of a much smaller bin size for determining A than what is used for the cross-section measurement.
The criteria for detecting the muons coming from the J/ψ decay is that both muons should be within the geometrical acceptance of the muon detectors and have enough momentum to reach the muon stations. The following kinematic cuts, defining the acceptance region, are chosen so as to guarantee a single-muon detection probability exceeding about 10%: To compute the acceptance, J/ψ events are generated with no cut on p T and within a rapidity region extending beyond the muon detector's coverage.
The acceptance as a function of p T and |y| is shown in the left plot of Fig. 2 for the combined prompt and non-prompt J/ψ mesons, with the prompt component decaying isotropically, corresponding to unpolarized production. The right plot of Fig. 2 displays the p T and |y| distribution of muon pairs measured with an invariant mass within ± 100 MeV/c 2 of the known J/ψ mass [27]. Systematic uncertainties on the acceptance have been investigated, as described in the following paragraphs.
• Final-state radiation. At the generator level, the dimuon momentum may differ from the J/ψ momentum, due to final-state radiation (FSR). The difference between the acceptance computed using the dimuon system or the J/ψ variables in Eq. 2 is taken as a systematic uncertainty.
• Kinematical distributions. Different spectra of the generated J/ψ might produce different acceptances. The difference between using the Pythia spectra and other theoretical calculations (mentioned in Section 7) is taken as a systematic uncertainty.
• b-hadron fraction and polarization. The J/ψ mesons produced in b-hadron decays can, in principle, have a different acceptance with respect to the prompt ones, due to their different momentum spectra, leading to an uncertainty coming from the unknown proportion of b hadrons in the inclusive sample. This fraction has been varied in the Monte Carlo simulation by 20%, the average accuracy of the measurement performed here (presented in Section 6); the difference between the two acceptances is taken as an estimate of this uncertainty. For non-prompt J/ψ mesons the b-hadron events are generated with the J/ψ polarization as measured by the BaBar experi-• p T calibration and resolution. A difference between the muon momentum scale in data and simulated events would lead to a different acceptance. The muon transverse momenta have been calibrated as described in Section 3.3. The maximum residual bias remaining after the calibration is estimated to be 0.05%. As a conservative estimate, a bias equivalent to this residual uncertainty is applied to the simulated muon momenta. The change in the recomputed acceptance is taken as a systematic uncertainty. Similarly, a difference in the momentum resolution between data and simulated events would also give a different acceptance. The acceptance has been computed with simulated muon momenta smeared according to the resolution measured in data [26] and the difference is taken as a systematic uncertainty.
Finally, the distribution of the z position of the pp interaction point could in principle influence the acceptance. Several Monte Carlo samples of J/ψ mesons have been generated, each coming from different positions along the beam line (between −10 and +10 cm with respect to the centre of the collision region) and a negligible variation of the acceptance has been found.

Efficiency
The single-muon efficiency is computed using the Tag-and-Probe method [23,29]. The combined trigger and offline-reconstruction efficiency for a single muon is measured with a data sample collected with looser trigger requirements and is defined as where track is the tracking efficiency, id | track is the muon identification efficiency in the muon systems for a tracker-reconstructed muon, and finally trig | track+id is the probability for an offline reconstructed muon to have also fired the trigger.
The tracking efficiency is constant in the momentum range defined by the acceptance cuts, and it varies only slightly in the φ − η plane [29]. The muon identification and trigger efficiencies have a stronger p µ T and |η µ | dependence, which is mapped with a finer granularity (nine to twelve p µ T and five |η µ | bins). The efficiency to detect a given J/ψ event is thus dependent on the value of the muon-pair kinematic variables, and is given by The factor ρ represents a correction to the factorization hypothesis and is evaluated from the Monte Carlo simulation. The non-vanishing values of ρ, varying between −0.19 and 0.30, are mainly due to the relatively large bin sizes used to determine the muon efficiencies.
The efficiency for the two muon tracks to be consistent with coming from a common vertex (Section 3.4), vertex , is measured to be (98.35 ± 0.16)%, by comparing the number of two-Global-Muon combinations within ± 100 MeV/c 2 of the nominal J/ψ mass with and without the common vertex requirement. Given the precision of this estimate, the corresponding systematic uncertainty can be neglected. The following systematic uncertainties on the J/ψ efficiency are considered: • ρ factor. Any variation of the muon spectrum within each large bin may lead to a different value of ρ. By reweighting the Pythia Monte Carlo simulation, we vary the J/ψ p T spectrum to reproduce different theoretical predictions (Section 7), and take the largest variation as the systematic uncertainty on ρ.
• Muon efficiency. The statistical uncertainty on each muon efficiency is propagated using toy Monte Carlo experiments, and the r.m.s. of the newly computed J/ψ efficiencies are assigned as systematic uncertainties. The largest systematic errors are in the bins with less events or in those where the background is largest. When selecting the tag muon, the Tag-and-Probe method produces a slight bias on the kinematics of the probe muon, hence a small difference arises between the measured singlemuon efficiencies and those of an unbiased sample. This small effect is studied in the Monte Carlo simulation and corrected for. The whole correction is conservatively taken as a systematic uncertainty on the efficiencies and summed in quadrature with the statistical uncertainty.

Inclusive J/ψ cross section
The measurement of the inclusive p T differential cross section is based on the equation where N corr (J/ψ) is the J/ψ yield, corrected for the J/ψ acceptance and selection efficiency, in a given transverse momentum-rapidity bin, Ldt is the integrated luminosity, ∆p T and ∆y are the sizes of the p T and rapidity bins, and BR(J/ψ → µ + µ − ) is the branching ratio of the J/ψ decay into two muons.

J/ψ yields
The corrected yield, N corr (J/ψ), is determined in two steps. First, in each rapidity and p T bin an unbinned maximum likelihood fit to the µ + µ − invariant mass distribution is performed. The resulting yield is then corrected by a factor that takes into account the average acceptance (A) and detection efficiency ( ) in the bin under consideration.
In the mass fits, the shape assumed for the signal is a Crystal Ball function [30], which takes into account the detector resolution as well as the radiative tail from bremsstrahlung. The shape of the underlying continuum is described by an exponential. Table 1 lists the J/ψ uncorrected signal yields and the corresponding statistical uncertainties from the fit, for the chosen bins.
Different functions were used to assess systematic effects coming from the fit function chosen to model the signal and the continuum shapes. For the signal, the Crystal Ball function was varied to a sum of a Crystal Ball and a Gaussian, while for the background a second-order polynomial was used. The maximum difference in the result was taken as a systematic uncertainty. The uncertainty is particularly large for the low-p T bins, where the signal purity is the smallest.
Additionally, a bias on the muon momentum scale can shift the events from one J/ψ p T bin to the adjacent ones. To estimate this systematic effect, a bias has been applied to the muon momenta equal to the residual uncertainty on the scale after the calibration, as explained in Section 3.4, and a negligible variation was found.

Inclusive J/ψ cross section results
The previously discussed systematic uncertainties affecting the inclusive J/ψ cross section are listed in Table 2. In addition, the relative error on the luminosity determination is 11%, and is Table 1: Uncorrected event yield (with its statistical error from the fit) in each p T bin, together with the average acceptance times efficiency (computed in the unpolarized production scenario).  common to all bins. Table 3 reports the values of the resulting J/ψ differential cross section, for different polarization scenarios: unpolarized, full longitudinal polarization and full transverse polarization in the Collins-Soper or the helicity frames [7]. Figure 3 shows the inclusive differential cross section d 2 σ dp T dy · BR(J/ψ → µ + µ − ) in the three rapidity ranges, showing statistical and systematic uncertainties, except the luminosity uncertainty, added in quadrature. It should be noted that the first bin in the forward rapidity region extends down to zero J/ψ p T .
The total cross section for inclusive J/ψ production, obtained by integrating over p T between 6.5 and 30 GeV/c and over rapidity between −2.4 and 2.4, in the unpolarized production hy- Table 3: Differential inclusive cross sections and average p T in the bin, for each prompt J/ψ polarization scenario considered: unpolarized (λ θ = 0), full longitudinal polarization (λ θ = −1) and full transverse polarization (λ θ = +1) in the Collins-Soper (CS) or the helicity (HX) frames [7]. For the unpolarized case, the first error is statistical and the second is systematic; for the others the total error is given.
|y| <  Figure 3: Differential inclusive J/ψ cross section as a function of p T for the three different rapidity intervals and in the unpolarized production scenario. The errors on the ordinate values are the statistical and systematic errors added in quadrature. The 11% uncertainty due to the luminosity determination is not shown and is common to all bins. pothesis, gives σ(pp → J/ψ + X) · BR(J/ψ → µ + µ − ) = 97.5 ± 1.5(stat) ± 3.4(syst) ± 10.7(luminosity) nb. (6)

Fraction of J/ψ from b-hadron decays
The measurement of the fraction of J/ψ yield coming from b-hadron decays relies on the discrimination of the J/ψ mesons produced away from the pp collision vertex, determined by the distance between the dimuon vertex and the primary vertex in the plane orthogonal to the beam line.
The primary vertices in the event are found by performing a common fit to tracks for which the points of closest approach to the beam axis are clustered in z, excluding the two muons forming the J/ψ candidate and using adaptive weights to avoid biases from displaced secondary vertices. Given the presence of pile-up, the primary vertex in the event is not unique. According to Monte Carlo simulation studies, the best assignment of the primary vertex is achieved by selecting the one closest in the z coordinate to the dimuon vertex.

Separating prompt and non-prompt J/ψ
As an estimate of the b-hadron proper decay length, the quantity J/ψ = L xy · m J/ψ /p T is computed for each J/ψ candidate, where m J/ψ is the J/ψ mass [27] and L xy is the most probable transverse decay length in the laboratory frame [31,32]. L xy is defined as where x is the vector joining the vertex of the two muons and the primary vertex of the event, in the transverse plane, u is the unit vector of the J/ψ p T , and σ is the sum of the primary and secondary vertex covariance matrices.
To determine the fraction f B of J/ψ mesons from b-hadron decays in the data, we perform an unbinned maximum-likelihood fit in each p T and rapidity bin. The dimuon mass spectrum and the J/ψ distribution are simultaneously fit by a log-likelihood function, where N is the total number of events and m µµ is the invariant mass of the muon pair. The where: • f Sig is the fraction of events attributed to J/ψ sources coming from both prompt and non-prompt components; • M Sig (m µµ ) and M Bkg (m µµ ) are functional forms describing the invariant dimuon mass distributions for the signal and background, respectively, as detailed in Section 5.1; • F Sig ( J/ψ ) and F Bkg ( J/ψ ) are functional forms describing the J/ψ distribution for the signal and background, respectively.
The signal part is given by a sum of prompt and non-prompt components, where f B is the fraction of J/ψ from b-hadron decays, and F p ( J/ψ ) and F B ( J/ψ ) are the J/ψ distributions for prompt and non-prompt J/ψ, respectively.
As J/ψ should be zero in an ideal detector for prompt events, F p ( J/ψ ) is described simply by a resolution function. The core of the resolution function is taken to be a double-Gaussian and its parameters are allowed to float in the nominal fit. Since J/ψ depends on the position of the primary vertex, an additional Gaussian component is added, to take into account possible wrong assignments of the primary vertex; its parameters are fixed from the Monte Carlo simulation.
The J/ψ shape of the non-prompt component in Eq. 10 is given by convolving the same resolution function with the true J/ψ distribution of the J/ψ from long-lived b hadrons, as given by the Monte Carlo simulation.
For the background J/ψ distribution F Bkg ( J/ψ ), the functional form employed by CDF [5] is used: where R(x) is the resolution model mentioned above, f i (i = {+, −, sym}) are the fractions of the three long-lived components with mean decay lengths λ i , and θ(x) is the step function. The effective parameters λ i are previously determined with a fit to the J/ψ distribution in the sidebands of the dimuon invariant mass distribution, defined as the regions 2.6-2.9 and 3.3-3.5 GeV/c 2 .
The parameter f B (b fraction) is determined in the same rapidity regions as used to present the inclusive production cross section but some p T bins are grouped, since more events per bin are needed to determine all fit parameters. Figure 4 shows the projection of the likelihood fits in two sample bins. The full results are reported in Table 4, where f B has been corrected by the prompt/non-prompt acceptances, as discussed in Section 4. The fitting procedure has been tested in five sample bins using toy experiments, which establish reasonable goodness-of-fit and exclude the possibility of biases in the f B determination.  Figure 4: Projection in the J/ψ dimension of the two-dimensional likelihood fit (in mass and J/ψ ) in the bins 2 < p T < 4.5 GeV/c, 1.2 < |y| < 1.6 (left) and 6.5 < p T < 10 GeV/c, 1.6 < |y| < 2.4 (right), with their pull distributions (bottom). Figure 5 shows the measured b fraction. It increases strongly with p T . At low p T , essentially all J/ψ mesons are promptly produced, whereas at p T ∼ 12 GeV/c around one third come from   beauty decays. This pattern does not show a significant change with rapidity (within the current uncertainties) over the window covered by the CMS detector. The CMS results are compared to the higher-precision data of CDF [5], obtained in proton-antiproton collisions at √ s = 1.96 TeV. It is interesting to note that the increase with p T of the b fraction is very similar between the two experiments, the CMS points being only slightly higher, despite the different collision energies.  Figure 5: Fraction of the J/ψ production cross section originating from b-hadron decays, as a function of the J/ψ p T , as measured by CMS in three rapidity bins and by CDF, at a lower collision energy.

Systematic uncertainties affecting the b-fraction result
Several sources of systematic uncertainty have been addressed and are described in the following lines.
• Residual misalignments in the tracker. The effect of uncertainties in the measured misalignment of the tracker modules is estimated by reconstructing the data several times using different sets of alignment constants. These sets reflect the uncertainty in the constants and, in particular, explore possible deformations of the tracker which are poorly constrained by the data [22]. The largest difference between the results with the nominal set of constants and with these sets is taken as a systematic uncertainty.
• b-hadron lifetime model. In an alternative approach, J/ψ is described by a convolution of an exponential decay with a Gaussian function, which describes the smearing due to the relative motion of the J/ψ with respect to the parent b hadron. The difference between the nominal Monte Carlo template model and this alternative is taken as a systematic uncertainty.
• Primary vertex estimation. In an alternative approach, the beam spot as calculated on a run-by-run basis is chosen as the primary vertex in calculating J/ψ , and the fit is repeated. The difference is taken as a systematic uncertainty.
• Background. The background is fitted using only the sidebands and the result is used as input to the fit in the signal region. The effect of a ± 100 MeV/c 2 variation in the sideband boundaries is taken as a systematic uncertainty.
• J/ψ resolution model. The nominal (triple-Gaussian) fit model for the decay length resolution is compared to a model using two Gaussians only, fixing the "additional" Gaussian to be zero. The difference is taken as a systematic uncertainty.
• Different prompt and non-prompt efficiencies. The Monte Carlo simulation predicts small differences between the prompt and non-prompt J/ψ efficiencies. These are taken into account and the relative difference assumed as a systematic uncertainty.
A summary of all systematic effects and their importance is given in Table 5.

Prompt and non-prompt J/ψ production cross sections
The prompt J/ψ cross section and the cross section from b-hadron decays, together with their statistical and systematic uncertainties, are given in Tables 6 and 7, respectively, for the different polarization scenarios considered in Section 5.
The total cross section for prompt J/ψ production times BR(J/ψ → µ + µ − ), for the unpolarized Table 6: Differential prompt J/ψ cross sections for each polarization scenario considered: unpolarized (λ θ = 0), full longitudinal polarization (λ θ = −1) and full transverse polarization (λ θ = +1) in the Collins-Soper (CS) or the Helicity (HX) frames [7]. For the unpolarized case, the first error is statistical and the second is systematic; for the others the total error is given. production scenario, has been obtained by integrating the differential cross section over p T between 6.5 and 30 GeV/c and over rapidity between −2.4 and 2.4, BR(J/ψ → µ + µ − ) · σ(pp → prompt J/ψ) = 70.9 ± 2.1 ± 3.0 ± 7.8 nb , (12) where the three uncertainties are statistical, systematic and due to the measurement of the integrated luminosity, respectively. Similarly, the cross section of non-prompt J/ψ mesons from b-hadron decays, times BR(J/ψ → µ + µ − ), is The sum of these two cross sections differs slightly from the inclusive value, which was determined assuming a b fraction taken from Monte Carlo expectations.

Comparison with theoretical calculations
The prompt J/ψ differential production cross sections, in the rapidity ranges considered in the analysis, as summarized in Table 6, were compared with calculations made with the Pythia [16] and CASCADE [33,34] event generators, as well as with the Color Evaporation Model (CEM) [35][36][37][38][39]. These calculations include the contributions to the prompt J/ψ yield due to feed-down decays from heavier charmonium states (χ c and ψ(2S)) and can, therefore, be directly compared to the measured data points, as shown in Fig. 6. In contrast, it is not possible to compare our measurement with the predictions of models such as the Color-Singlet Model (including higher-order corrections) [40][41][42][43] or the LO NRQCD model (which includes singlet and octet components) [44,45], because they are only available for the direct J/ψ production component, while the measurements include a significant contribution from feed-down decays, of the order Table 7: Differential non-prompt J/ψ cross section times the J/ψ branching ratio to dimuons, assuming the polarization measured by the BaBar experiment [28] at the Υ(4S). The first uncertainty is statistical and the second is systematic.  [46,47]. At forward rapidity and low p T the calculations underestimate the measured yield.
The non-prompt J/ψ differential production cross sections, as summarized in Table 7, have been compared with calculations made with the Pythia and CASCADE Monte Carlo generators, and in the FONLL framework [10]. The measured results are presented in Fig. 7 and show a good agreement with the calculations.

Conclusions
We have presented the first measurement of the J/ψ production cross section in pp collisions at √ s = 7 TeV, based on 314 nb −1 of integrated luminosity collected by the CMS experiment during the first months of LHC operation. The p T differential J/ψ production cross section, in the dimuon decay channel, has been measured in three rapidity ranges, starting at zero p T for 1.6 < |y| < 2.4, at 2 GeV/c for 1.2 < |y| < 1.6, and at 6.5 GeV/c for |y| < 1.2. The measured total cross section for prompt J/ψ production in the unpolarized scenario, in the dimuon decay channel, is σ(pp → J/ψ + X) · BR(J/ψ → µ + µ − ) = 70.9 ± 2.1(stat) ± 3.0(syst) ± 7.8(luminosity) nb , for transverse momenta between 6.5 and 30 GeV/c and in the rapidity range |y| < 2.4. Aside from the luminosity contribution, the systematic uncertainty is dominated by the statistical precision of the muon efficiency determination from data. The measured total cross section times BR(J/ψ → µ + µ − ) for J/ψ production due to b-hadron  Figure 6: Differential prompt J/ψ production cross section, as a function of p T for the three different rapidity intervals. The data points are compared with three different models, using the PYTHIA curve to calculate the abscissa where they are plotted [48]. decays, for 6.5 < p T < 30 GeV/c and |y| < 2.4, is σ(pp → bX → J/ψX) · BR(J/ψ → µ + µ − ) = 26.0 ± 1.4 (stat) ± 1.6 (syst) ± 2.9 (luminosity) nb .
The differential prompt and non-prompt measurements have been compared with theoretical calculations. A reasonable agreement is found between data and theory for the non-prompt case while the measured prompt J/ψ cross section exceeds the expectations at forward rapidity and low p T .  Figure 7: Differential non-prompt J/ψ production cross section, as a function of p T for the three different rapidity intervals. The data points are compared with three different models, using the PYTHIA curve to calculate the abscissa where they are plotted [48]. UK; the US Department of Energy, and the US National Science Foundation. Individuals have received support from the Marie-Curie IEF program (European Union); the Leventis Foundation; the A. P. Sloan Foundation; the Alexander von Humboldt Foundation; the Associazione per lo Sviluppo Scientifico e Tecnologico del Piemonte (Italy); the Belgian Federal Science Policy Office; the Fonds pour la Formationà la Recherche dans l'índustrie et dans l'Ágriculture (FRIA-Belgium); and the Agentschap voor Innovatie door Wetenschap en Technologie (IWT-Belgium).