Upsilon production cross section in pp collisions at ffiffi s p 1⁄4 7 TeV

V. Khachatryan et al.* (CMS Collaboration) (Received 27 December 2010; published 15 June 2011) The ð1SÞ, ð2SÞ, and ð3SÞ production cross sections in proton-proton collisions at ffiffi s p 1⁄4 7 TeV are measured using a data sample collected with the CMS detector at the LHC, corresponding to an integrated luminosity of 3:1 0:3 pb . Integrated over the rapidity range jyj< 2, we find the product of the ð1SÞ production cross section and branching fraction to dimuons to be ðpp ! ð1SÞXÞ Bð ð1SÞ ! þ Þ 1⁄4 7:37 0:13þ0:61 0:42 0:81 nb, where the first uncertainty is statistical, the second is systematic, and the third is associated with the estimation of the integrated luminosity of the data sample. This cross section is obtained assuming unpolarized ð1SÞ production. With the assumption of fully transverse or fully longitudinal production polarization, the measured cross section changes by about 20%. We also report the measurement of the ð1SÞ, ð2SÞ, and ð3SÞ differential cross sections as a function of transverse momentum and rapidity.


I. INTRODUCTION
The hadroproduction of quarkonia is not understood. None of the existing theories successfully reproduces both the differential cross section and the polarization measurements of charmonium and bottomonium states [1]. It is expected that studying quarkonium hadroproduction at higher center-of-mass energies and over a wider rapidity range will facilitate significant improvements in our understanding. Measurements of the Ç resonances are particularly important since the theoretical calculations are more robust than for the charmonium family due to the heavy bottom quark and the absence of b-hadron feeddown. Measurements of quarkonium hadroproduction cross sections and production polarizations made at the Large Hadron Collider (LHC) will allow important tests of several alternative theoretical approaches. These include nonrelativistic QCD (NRQCD) factorization [2], where quarkonium production includes color-octet components, and calculations made in the color-singlet model including next-to-leading-order (NLO) corrections [3] which reproduce the differential cross sections measured at the Tevatron experiments [4,5] without requiring a significant color-octet contribution.
This paper presents the first measurement of the Çð1SÞ, Çð2SÞ, and Çð3SÞ production cross sections in protonproton collisions at ffiffi ffi s p ¼ 7 TeV, using data recorded by the Compact Muon Solenoid (CMS) experiment between April and September 2010. In these measurements, the signal efficiencies are determined with data. Consequently, Monte Carlo simulation is used only in the evaluation of the geometric and kinematic acceptances. The document is organized as follows. Sec. II contains a short description of the CMS detector. Sec. III presents the data collection, the trigger and offline event selections, the reconstruction of the Ç resonances, and the Monte Carlo simulation. Throughout this paper, Ç and ÇðnSÞ are used to denote the Çð1SÞ, Çð2SÞ, and Çð3SÞ resonances. The detector acceptance and the efficiency to reconstruct Ç resonances that decay to two muons in CMS are discussed in Secs. IV and V, respectively. In Sec. VI the fitting technique employed to extract the cross section is presented. The evaluation of systematic uncertainties on the measurements is described in Sec. VII. Sec. VIII presents the ÇðnSÞ cross section results and comparisons to existing measurements at lower collision energies [4,5] and to the predictions of the PYTHIA [6] event generator.

II. THE CMS DETECTOR
The central feature of the CMS apparatus is a superconducting solenoid, of 6 m inner diameter, providing a field of 3.8 T. Inside the solenoid in order of increasing distance from the interaction point are the silicon tracker, the crystal electromagnetic calorimeter, and the brass/scintillator hadron calorimeter. Muons are detected by three types of gas-ionization detectors embedded in the steel return yoke: drift tubes (DT), cathode strip chambers (CSC), and resistive plate chambers (RPC). The muon measurement covers the pseudorapidity range jj < 2:4, where ¼ À ln½tanð=2Þ and the polar angle is measured from the z-axis, which points along the counterclockwise beam direction. The silicon tracker consists of pixel detectors (three barrel layers and two forward disks on either side of the detector, comprising 66 Â 10 6 100 Â 150 m 2 pixels) followed by microstrip detectors (ten barrel layers plus three inner disks and nine forward disks on either side of the detector, with 10 Â 10 6 strips of pitch between 80 and 184 m). The detector systems are aligned and calibrated using LHC collision data and cosmic-ray muons [7]. Because of the strong magnetic field and the fine granularity of the silicon tracker, the muon transverse-momentum measurement, p T , based on information from the silicon tracker alone has a resolution of about 1% for a typical muon in this analysis. The silicon tracker provides the primary vertex position with $20 m accuracy. The two-level CMS trigger system selects events of interest for permanent storage. The first trigger level (L1), composed of custom hardware processors, uses information from the calorimeter and muon detectors to select events in less than 1 s. The high-level trigger (HLT) software algorithms, executed on a farm of commercial processors, further reduce the event rate using information from all detector subsystems. A more detailed description of the CMS detector can be found elsewhere [8].

A. Event selection
The data sample used in this analysis was recorded by the CMS detector in pp collisions at a center-of-mass energy of 7 TeV. The sample corresponds to a total integrated luminosity of 3:1 AE 0:3 pb À1 [9]. The maximum instantaneous luminosity was 10 31 cm À2 s À1 , and event pileup was negligible. Data are included in the analysis if the silicon tracker, the muon detectors, and the trigger were performing well, and the luminosity measurement is available.
The trigger requires the detection of two muons at the hardware level, without any further selection at the HLT. The coincidence of two muon signals without an explicit p T requirement is sufficient to allow the dimuon trigger without prescaling. All three muon systems-DT, CSC, and resistive plate chambers-take part in the trigger decision.
Anomalous events arising from beam-gas interactions or beam scraping in the beam transport system near the interaction point, which produce a large number of hits in the pixel detector, are removed with offline software filters [10]. A good primary vertex is also required, as defined in Ref. [10].

B. Monte Carlo simulation
Upsilon events are simulated using PYTHIA 6.412 [6], which generates events based on the leading-order colorsinglet and octet mechanisms, with nonrelativistic QCD matrix elements tuned by comparing calculations with the CDF data [11] and applying the normalization and wavefunctions as recommended in Ref. [12]. The simulation includes the generation of b states. Final-state radiation (FSR) is implemented using PHOTOS [13,14]. The response of the CMS detector is simulated with a GEANT4-based [15] Monte Carlo (MC) program. Simulated events are processed with the same reconstruction algorithms as used for data.

C. Offline muon reconstruction
In this analysis, a muon candidate is defined as a charged track reconstructed in the silicon tracker and associated with a compatible signal in the muon detectors. Tracks are reconstructed using a Kalman filter technique which starts from hits in the pixel system and extrapolates outward to the silicon strip tracker. Further details may be found in Ref. [16].
Quality criteria are applied to tracks to reject muons from kaon and pion decays. Tracks are required to have at least 12 hits in the silicon tracker, at least one of which must be in the pixel detector, and a track-fit 2 per degree of freedom smaller than 5. In addition tracks are required to emanate from a cylinder of radius 2 mm and length 50 cm centered on the pp interaction region and parallel to the beam line. Muon candidates are required to satisfy: These kinematic criteria are chosen to ensure that the trigger and muon reconstruction efficiencies are high and not rapidly changing within the acceptance window of the analysis. The momentum measurement of charged tracks in the CMS detector is affected by systematic uncertainties caused by imperfect knowledge of the magnetic field, the amount of material, and subdetector misalignments, as well as by biases in the algorithms which fit the track trajectory. A mismeasurement of track momenta results in a shift and broadening of the reconstructed peaks of dimuon resonances. An improved understanding of the CMS magnetic field, detector alignment, and material budget is obtained from cosmic-ray muon and LHC collision data [7,17,18]. Residual effects are determined by studying the dependence of the reconstructed J=c dimuon invariantmass distribution on the muon kinematics [19]. The transverse momentum corrected for the residual scale distortion is parametrized as T is the measured muon transverse momentum, a 1 ¼ ð3:8 AE 1:9Þ Â 10 À4 , and a 2 ¼ ð3:0 AE 0:7Þ Â 10 À4 . Coefficients for terms linear in and quadratic in p 0 T and p 0 T Á are consistent with zero and are not included.

D. Ç event selection
To identify events containing an Ç decay, muon candidates with opposite charges are paired, and the invariant mass of the muon pair is required to be between 8 and 14 GeV=c 2 . The longitudinal separation between the two muons at their points of closest approach to the beam axis is required to be less than 2 cm. The two muon helices are fit with a common vertex constraint, and events are retained if the fit 2 probability is larger than 0.1%. The dimuon candidate is required to have passed the trigger selection. If multiple dimuon candidates are found in the same event, the candidate with the best vertex quality is retained; the fraction of signal candidates rejected by this requirement is about 0.2%. Finally, the rapidity, y, of the Ç candidates is required to satisfy jyj < 2 because the acceptance diminishes rapidly at larger rapidity. The rapidity is defined as EÀp k Þ, where E is the energy and p k the momentum parallel to the beam axis of the muon pair.
The dimuon invariant-mass spectrum in the ÇðnSÞ region for the dimuon transverse-momentum interval p T < 30 GeV=c is shown in Fig. 1 for the pseudorapidity intervals j j < 2:4 (top) and j j < 1:0 (bottom). The Çð1SÞ mass resolution is determined from the fit function described in Sec. VI. We obtain a mass resolution of 96 AE 2 MeV=c 2 when muons from the entire pseudorapidity range are included and 69 AE 2 MeV=c 2 when both muons satisfy j j < 1. The observed resolutions are in good agreement with the predictions from MC simulation.

IV. ACCEPTANCE
The Ç ! þ À acceptance of the CMS detector is defined as the product of two terms. The first is the fraction of upsilons of given p T and y where each of the two muons satisfies Eq. (1). The second is the probability that when there are only two muons in the event both can be reconstructed in the tracker without requiring the quality criteria. Both terms are evaluated by simulation and parametrized as a function of the p T and rapidity of the Ç.
The acceptance is calculated from the ratio where N Ç gen ðp T ; yÞ is the number of upsilons generated in a ðp T ; yÞ bin, while N Ç rec ðp T ; yÞ is the number reconstructed in the same ðp T ; yÞ region but now using the reconstructed, rather than generated, variables. In addition, the numerator requires that the two muons reconstructed in the silicon tracker satisfy Eq. (1).
The acceptance is evaluated with a signal MC sample in which the Ç decay to two muons is generated with the EVTGEN [20] package including the effects of final-state radiation. There are no particles in the event besides the Ç, its daughter muons, and final-state radiation. The upsilons are generated uniformly in p T and rapidity. This sample is then fully simulated and reconstructed with the CMS detector simulation software to assess the effects of multiple scattering and finite resolution of the detector. Systematic uncertainties arising from the dependence of the measurement of the cross section on the MC description of the p T spectrum and resolution are evaluated in Sec. VII. The acceptance is calculated for two-dimensional (2-D) bins of size ð1 GeV=c; 0:1Þ in the reconstructed ðp T ; yÞ of the Ç, and it is used in candidate-by-candidate yield corrections.
The 2-D acceptance map for unpolarized Çð1SÞ is shown in the top plot of Fig. 2. The acceptance varies with dimuon mass. This is shown in the bottom plot of Fig. 2, which displays the acceptance integrated over the rapidity range as a function of p T for each upsilon resonance. The transverse-momentum threshold for muon detection, especially in the forward region, is small compared PHYSICAL REVIEW D 83, 112004 (2011) to the upsilon mass. Therefore, when the Ç decays at rest, both muons are likely to reach the muon detector. When the Ç has a modest boost, the probability is greater that one muon will be below the muon detection threshold and the acceptance decreases until the Ç transverse momentum reaches about 5 GeV=c, after which the acceptance rises slowly. The production polarization of the Ç strongly influences the muon angular distributions and is expected to change as a function of p T . In order to account for this, the acceptance is calculated for five extreme polarization scenarios [21]: unpolarized and polarized longitudinally and transversely with respect to a polarization axis defined in two different reference frames. The first is the helicity frame (HX), where the polarization axis is given by the flight direction of the Ç in the center-of-mass system of the colliding beams. The second is the Collins-Soper (CS) frame [22], where the polarization axis is given as the bisection of the incoming proton directions in the Ç rest frame.

V. EFFICIENCY
We factor the total muon efficiency into three conditional terms, The tracking efficiency, " track , combines the efficiency that the accepted track of a muon from the ÇðnSÞ decay is reconstructed in the presence of additional particles in the silicon tracker, as determined with a track-embedding technique [23], and the efficiency for the track to satisfy quality criteria. The muon identification efficiency, " id , is the probability that the track in the silicon tracker is identified as a muon. The efficiency that an identified muon satisfies the trigger is denoted by " trig . The tag-and-probe (T&P) technique [23] is a data-based method used in this analysis to determine the track quality, muon identification, and muon trigger efficiencies. It utilizes dimuons from J=c decays to provide a sample of probe objects. A well-identified muon, the tag, is combined with a second object in the event, the probe, and the invariant mass is computed. The tag-probe pairs are divided into two samples, depending on whether the probe satisfies or not the criteria for the efficiency being evaluated. The two tag-probe mass distributions contain a J=c peak. The integral of the peak is the number of probes that satisfy or fail to satisfy the imposed criteria. The efficiency parameter is extracted from a simultaneous unbinned maximum-likelihood fit to both mass distributions.
The J=c resonance is utilized for T&P efficiency measurements as it provides a large-yield and statisticallyindependent dimuon sample [24]. To avoid trigger bias, events containing a tag-probe pair have been collected with triggers that do not impose requirements on the probe from the detector subsystem related to the efficiency measurement. For the track-quality efficiency measurement, the trigger requires two muons at L1 in the muon system without using the silicon tracker. For the muon identification and trigger efficiencies, the trigger requires a muon at the HLT, that is matched to the tag, paired with a silicon track of opposite sign and the invariant mass of the pair is required to be in the vicinity of the J=c mass.
The component of the tracking efficiency measured with the track-embedding technique is well described by a constant value of ð99:64 AE 0:05Þ%. The efficiency of the track-quality criteria measured by the T&P method is likewise nearly uniform and has an average value of ð98:66 AE 0:05Þ%. Tracks satisfying the quality criteria are the probes for the muon identification study. The resulting single-muon identification efficiencies as a function of p T for six j j regions are shown in Fig and Table I. The probes that satisfy the muon identification criteria are in turn the probes for the study of the trigger efficiency. The resulting trigger efficiencies for the same p T and j j regions are shown in Fig. 4 and Table II. Figs. 3 and 4 also show single-muon identification and trigger efficiencies, respectively, determined from a highstatistics MC simulation. The single-muon efficiencies determined with the T&P technique in the data are found to be consistent, over most of the kinematic range of interest, with the efficiencies obtained from the Ç MC simulation utilizing the generator-level particle information (''MC truth''). Two exceptions are the single-muon trigger efficiency for the intervals j j < 0:4 and 0:8 < j j < 1:2, where the efficiency is lower in data than in the MC simulation. Both correspond to cases where the MC simulation is known to not fully reproduce the detector properties or performance: gaps in the DT coverage (j j < 0:4) and suboptimal timing synchronization  98 (2,9) between the overlapping CSC and DT subsystems (0:8 < j j < 1:2). For all cases the data-determined efficiencies are used to obtain the central results.
The Ç efficiency is estimated from the product of singlemuon efficiencies. Differences between the single and dimuon efficiencies determined from MC truth and those measured with the T&P technique can arise from the kinematic distributions of the probes and from bin averaging. This is evaluated by comparing the single-muon and dimuon efficiencies as determined using the T&P method in J=c ! þ À MC events to the efficiencies obtained in the same events utilizing generator-level particle information. In addition, effects arising from differences in the kinematic distributions between the Ç and J=c decay muons are investigated by comparing the efficiencies determined from Ç ! þ À MC events to those from J=c ! þ À MC events. In all cases the differences in the efficiency values are not significant, and are used only as an estimate of the associated systematic uncertainties.
The Çð1SÞ, Çð2SÞ, and Çð3SÞ yields are extracted via an extended unbinned maximum-likelihood fit to the dimuon invariant-mass spectrum. The measured mass-lineshape of each Ç state is parametrized by a ''crystal ball'' (CB) function [25]; this is a Gaussian resolution function with the low side tail replaced with a power law describing FSR. The resolution, given by the Gaussian standard deviation, is a free parameter in the fit but is constrained to scale with the ratios of the resonance masses. The FSR tail is fixed to the MC shape. Since the three resonances overlap in the measured dimuon mass, we fit the three ÇðnSÞ states simultaneously. Therefore, the probability distribution function (PDF) describing the signal consists of three CB FIG. 5 (color online). Fit to the dimuon invariant-mass distribution in the specified p T regions for jyj < 2, before accounting for acceptance and efficiency. The solid line shows the result of the fit described in the text, with the dashed line representing the background component.
functions. The mass of the Çð1SÞ is a free parameter in the fit, to accommodate a possible bias in the momentum scale calibration. The number of free parameters is reduced by fixing the Çð2SÞ and Çð3SÞ mass differences, relative to the Çð1SÞ, to their world average values [26]; an additional mass-scale parameter multiplying the mass differences is found to be consistent with unity. A second-order polynomial is chosen to describe the background in the 8-14 GeV=c 2 mass-fit range.
The fit to the dimuon invariant-mass spectrum, before accounting for acceptance and efficiencies, is shown in Fig. 1 for the Ç transverse-momentum interval p T < 30 GeV=c, and for the 15 p T intervals used for the Çð1SÞ differential cross-section measurement in Fig. 5. The observed ÇðnSÞ signal yields are reported in Table III. The width of the p T intervals chosen for each resonance reflects the corresponding available signal statistics. In all cases the quoted uncertainty is statistical. As shown in Table III, for each resonance the sum of the yields in each p T interval is consistent with the yield determined from a fit to the entire p T range. Given the significant and p T dependencies of the efficiencies and acceptances of the muons from ÇðnSÞ decays, we correct for them on a candidate-by-candidate basis before performing the mass fit to obtain N corrected ÇðnSÞ in Eq. (4). Specifically: an Ç candidate reconstructed with p T and y from muons with p 1;2 T and 1;2 is corrected with a weight TABLE III. The uncorrected Ç signal yield, fit quality (normalized 2 , obtained by comparing the fit PDF and the binned data; the number of degrees of freedom is 112), and average weight hwi in p T intervals for jyj < 2. The mean of the p T distribution in each interval is also given. w w acc Á w track Á w id Á w trig Á w misc ; where the factors are: (i) acceptance, w acc ¼ 1=A Ç ðp T ; yÞ; (ii) tracking, w track ¼ 1=½" track ðp 1 T ; 1 Þ Á " track ðp 2 T ; 2 Þ; (iii) identification, w id ¼ 1=½" id ðp 1 T ; 1 Þ Á " id ðp 2 T ; 2 Þ; (iv) trigger, w trig ¼ 1=½" trig ðp 1 T ; 1 Þ Á " trig ðp 2 T ; 2 Þ; and (v) additional selection criteria, w misc , including the efficiency of the vertex selection criteria. The acceptance depends on the resonance mass; the Çð3SÞ gives rise to higher-momenta muons which results in a roughly 10% larger acceptance for the Çð3SÞ than for the Çð1SÞ. Consequently, the corrected yield for each of the ÇðnSÞ resonances is obtained from a fit in which the corresponding ÇðnSÞ acceptance is employed. Figure 6 shows the fit to an example mass distribution before (top plot) and after (bottom plot) event weighting. As can be seen, the weighting procedure scales the mass distribution without introducing large distortions to the lineshape of either the signal or background distributions.
We determine the ÇðnSÞ differential cross section separately for each polarization scenario. The results are summarized in Table IV. We also divide the data into two ranges of rapidity, jyj < 1 and 1 < jyj < 2, and repeat the TABLE IV. The product of the ÇðnSÞ production cross sections, , and the dimuon branching fraction, B, measured in p T bins for jyj < 2, with the assumption of unpolarized production. The statistical uncertainty (stat.), the sum of the systematic uncertainties in quadrature ðAE syst: Þ, and the total uncertainty (Á; including stat., P syst: , and luminosity terms) are quoted as relative uncertainties in percent. Values in parentheses denote the negative part of the asymmetric uncertainty. The fractional change in percent of the cross section is shown for four polarization scenarios: fully-longitudinal (L) and fully-transverse (T) in the helicity (HX) and Collins-Soper (CS) frames.

VII. SYSTEMATIC UNCERTAINTIES
Systematic uncertainties are described in this section, together with the methods used in their determination. We give a representative value for each uncertainty in parentheses. V. The product of the ÇðnSÞ production cross sections, , and the dimuon branching fraction, B, measured in p T bins for jyj < 1 and 1 < jyj < 2, with the assumption of unpolarized production. The statistical uncertainty (stat.), the sum of the systematic uncertainties in quadrature ðAE syst: Þ, and the total uncertainty (Á; including stat., P syst: , and luminosity terms) are quoted as relative uncertainties in percent. Values in parentheses denote the negative part of the asymmetric uncertainty. The fractional change in percent of the cross section is shown for four polarization scenarios: fully-longitudinal (L) and fully-transverse (T) in the helicity (HX) and Collins-Soper (CS) frames. We determine the cross section using acceptance maps corresponding to five different polarization scenarios, expected to represent extreme cases. The values of the cross section obtained vary by about 20%. The variations depend on p T thus affecting the shapes of the p T spectrum.

HX-T (%) HX-L (%) CS-T (%) CS-L (%)
The statistical uncertainties on the acceptance and efficiencies-single-muon trigger and muon ID, quality criteria, tracking and vertex quality-give rise to systematic uncertainties for the cross-section measurement. We vary the dimuon event weights in the fit coherently by AE1ðstat:Þ. The muon identification and trigger efficiencies are varied coherently when estimating the associated systematic uncertainties (8%).
The selection criteria requiring the muons to be consistent with emanating from the same primary vertex are fully efficient. This has been confirmed in data and simulation. The selection of one candidate per event using the largest vertex probability also has an efficiency consistent with unity. We assign an uncertainty (0.2%) from the frequency of occurrence of signal candidates in the data that are rejected by the largest vertex probability requirement but pass all the remaining selection criteria. The muon charge misassignment is estimated to be less than 0.01% [27] and contributes a negligible uncertainty.
Final-state radiation is incorporated into the simulation using the PHOTOS algorithm. To estimate the systematic uncertainty associated with this procedure, the acceptance is calculated without FSR and 20% of the difference is taken as the uncertainty based on a study in Ref. [14] (0.8%).
The definition of acceptance used in this analysis requires that the muons from the Ç decay produce reconstructible tracks. The kinematic selection is applied to the reconstructed p T and values of these tracks. Uncertainties on the measurement of track parameters also affect the acceptance as a systematic uncertainty. The dominant uncertainty is associated with the measurement of the track transverse momentum. The acceptance is sensitive to biases in track momentum and to differences in resolution between the simulated and measured distributions. The magnitude of these effects is quantified by comparing measurements of resonance mass and width between simulation and data [19]. To determine the effect on the Ç acceptance, we introduce a track p T bias of 0.2%, chosen to be 4 times the maximum momentum scale residual bias after calibration (0.3%). We also vary the transverse-momentum resolution by AE10%, corresponding to the uncertainty in the resolution measurement using J=c , and recalculate the acceptance map (0.1%).
Imperfect knowledge of the production p T spectrum of the Ç resonances at ffiffi ffi s p ¼ 7 TeV contributes a systematic uncertainty. The Ç MC sample used for the acceptance calculation, Eq. (2), was generated flat in p T , whereas the p T spectrum in the data peaks at a few GeV=c, and behaves as a power law above 5 GeV=c. To study the effect of this difference, we have reweighted the sample in p T to more closely describe the expected distribution in data based on a fit to the spectrum obtained from PYTHIA (1%).
The distribution of the z position of the pp interaction point influences the acceptance. We have produced MC samples of ÇðnSÞ at different positions along the beam line, between À10 and þ10 cm with respect to the center of the nominal collision region (1%).
High-statistics MC simulations are performed to compare T&P single-muon and dimuon efficiencies to the actual MC values for both the Ç and J=c , see Figs. 3 and 4. The differences and their associated uncertainties are taken as a source of systematic uncertainty. The contributions are: possible bias in the T&P technique (0.1%), differences in the J=c and Ç kinematics (1%), and the possible misestimation of the double-muon Ç efficiency as the product of the single-muon efficiencies (1.6%).
Monte Carlo trials of the fitter demonstrate that it is consistent with providing an unbiased estimate of the yield TABLE VI. The product of the Çð1SÞ production cross section, , and the dimuon branching fraction, B, measured in rapidity bins and integrated over the p T range p Ç T < 30 GeV=c, with the assumption of unpolarized production. The statistical uncertainty (stat.), the sum of the systematic uncertainties in quadrature ðAE syst: Þ, and the total uncertainty (Á; including stat., P syst: , and luminosity terms) are quoted as relative uncertainties in percent. Values in parentheses denote the negative part of the asymmetric uncertainty. The fractional change in percent of the cross section is shown for four polarization scenarios: fully-longitudinal (L) and fully-transverse (T) in the helicity (HX) and Collins-Soper (CS) (7) 16 (14) þ18 À23 þ20 À24 of each resonance, its mass, and the mass resolution (1%). A systematic variation may arise from differences between the dimuon invariant-mass distribution in the data and in the PDFs chosen for the signal and background components in the fit. We consider the following variations in the signal PDF. As the CB parameters which describe the radiative tail of each resonance are fixed from MC simulation in the nominal fit to the data, we vary the CB parameters by 3 times their uncertainties (3%). We also remove the resonance mass difference constraint in the p T integrated fit (0.6%). We vary the background PDF by replacing the polynomial by a linear function, while restricting the fit to the mass range 8-12 GeV=c 2 (3% when fitting the full p T and y ranges, varying with differential interval). The determination of the integrated luminosity normalization is made with an uncertainty of 11% [9]. The relative systematic uncertainties from each source are summarized TABLE VII. Relative values of the systematic uncertainties on the ÇðnSÞ production cross sections times the dimuon branching fraction, in p T intervals for jyj < 2, assuming unpolarized production, in percent. The abbreviations used indicate the various systematic uncertainty sources: the statistical uncertainty in the estimation of the acceptance (A) and the trigger and muon identification efficiencies (" trig;id ); imperfect knowledge of the momentum scale (S p ), the production p T spectrum (A p T ), the efficiency of the vertex-quality criterion (A vtx ), and the modeling of FSR (A FSR ); the use of the T&P method (T&P); the bias from using the J=c to determine single-muon efficiencies rather than the Ç (" J=c ;Ç ); the background PDF (BG); the signal PDF, the fitter, the tracking efficiency, and effects arising from the efficiency binning (add). Values in parentheses denote the negative part of the asymmetric uncertainty. The luminosity uncertainty of 11% is not included in the table. in Table VII for the full rapidity range, for two rapidity ranges in Table VIII, and for five rapidity ranges in Table IX. The largest sources of systematic uncertainty arise from the statistical precision of the efficiency measurements from data and from the luminosity normalization, with the latter dominating.

VIII. RESULTS AND DISCUSSION
The analysis of the collision data acquired by the CMS experiment at ffiffi ffi s p ¼ 7 TeV, corresponding to an integrated luminosity of 3:1 AE 0:3 pb À1 , yields a measurement of the ÇðnSÞ integrated production cross sections for the range jyj < 2: VIII. Relative values of the systematic uncertainties on the ÇðnSÞ production cross sections times the dimuon branching fraction, in p T intervals for jyj < 1 and 1 < jyj < 2, assuming unpolarized production, in percent. The abbreviations used indicate the various systematic uncertainty sources: the statistical uncertainty in the estimation of the acceptance (A) and the trigger and muon identification efficiencies (" trig;id ); imperfect knowledge of the momentum scale (S p ), the production p T spectrum (A p T ), the efficiency of the vertex-quality criterion (A vtx ), and the modeling of FSR (A FSR ); the use of the T&P method (T&P); the bias from using the J=c to determine single-muon efficiencies rather than the Ç (" J=c ;Ç ); the background PDF (BG); the signal PDF, the fitter, the tracking efficiency, and effects arising from the efficiency binning (add). Values in parentheses denote the negative part of the asymmetric uncertainty. The luminosity uncertainty of 11% is not included in the table.  Relative values of the systematic uncertainties on the Çð1SÞ production cross section times the dimuon branching fraction, in rapidity intervals for p T < 30 GeV=c, assuming unpolarized production, in percent. The abbreviations used indicate the various systematic uncertainty sources: the statistical uncertainty in the estimation of the acceptance (A) and the trigger and muon identification efficiencies (" trig;id ); imperfect knowledge of the momentum scale (S p ), the production p T spectrum (A p T ), the efficiency of the vertex-quality criterion (A vtx ), and the modeling of FSR (A FSR ); the use of the T&P method (T&P); the bias from using the J=c to determine single-muon efficiencies rather than the Ç (" J=c ;Ç ); the background PDF (BG); the signal PDF, the fitter, the tracking efficiency, and effects arising from the efficiency binning (add). Values in parentheses denote the negative part of the asymmetric uncertainty. The luminosity uncertainty of 11% is not included in the table. TABLE X. The ratios of ÇðnSÞ cross sections for different Ç p T ranges in the unpolarized scenario. The first uncertainty is statistical and the second is systematic. The ratios are independent of the luminosity normalization and its uncertainty. . Differential cross sections of the ÇðnSÞ as a function of p T in the rapidity range jyj < 2, and comparison to the PYTHIA predictions normalized to the measured p T -integrated cross sections; Çð1SÞ (left), Çð2SÞ (middle), and Çð3SÞ (right). The theory prediction is shown in the form of a continuous spectrum (curve) and integrated in the same p T bins as employed in the measurement (horizontal lines). The PYTHIA curve is used to calculate the abscissa of the data points [28]. The uncertainties on the points represent the sum of the statistical and systematic uncertainties added in quadrature, excluding the uncertainty on the integrated luminosity (11%).
production. Assumptions of fully-transverse or fullylongitudinal polarizations change the measured cross section values by about 20%. The differential ÇðnSÞ cross sections as a function of p T for the rapidity intervals jyj < 1, 1 < jyj < 2, and jyj < 2 are shown in Fig. 7. The p T dependence of the cross section in the two exclusive rapidity intervals is the same within the uncertainties. The Çð1SÞ differential cross sections as a function of rapidity and integrated in p T are shown in the left plot of Fig. 8. The cross section shows a slight decline towards jyj ¼ 2, consistent with the expectation from PYTHIA. The ratios of ÇðnSÞ differential cross sections as a function of p T are reported in Table X and shown in the right plot of Fig. 8. The uncertainty associated with the luminosity determination cancels in the computation of the ratios. Both ratios increase with p T . In Fig. 9 the differential cross sections for the Çð1SÞ, Çð2SÞ, and Çð3SÞ are compared to PYTHIA. The normalized p T -spectrum prediction from PYTHIA is consistent with the measurements, while the integrated cross section is overestimated by about a factor of 2. We have not included parameter uncertainties in the PYTHIA calculation. We do not compare our measurements to other models as no published predictions exist at ffiffi ffi s p ¼ 7 TeV for Ç production.
The ÇðnSÞ integrated cross sections are expected to increase with ffiffi ffi s p . As the gluon-gluon amplitude is expected to dominate production of Ç resonances at both the LHC and the Tevatron, we compare, in Table XI, our measurement of the Çð1SÞ integrated cross section in the central rapidity region jyj < 1 to previous measurements [4,5] performed in p " p collisions. Previous measurements were performed in the range p T < 20 GeV=c, and jyj < 0:4 for CDF and jyj < 1:8 for DØ. Under the assumption that the cross section is uniform in rapidity for the measurement range of each experiment, the cross section we measure at ffiffi ffi s p ¼ 7 TeV is about 3 times larger than the cross section measured at the Tevatron. Although our measurement extends to higher p T than the Tevatron measurements, the fraction of the cross section satisfying p T > 20 GeV=c is less than 1% and so can be neglected for this comparison. We compare the normalized differential cross sections in p T at the Tevatron to our measurements in Fig. 10.

IX. SUMMARY
The study of the ÇðnSÞ resonances provides important information on the process of hadroproduction of heavy quarks. In this paper we have presented the first measurement of the ÇðnSÞ differential production cross section for proton-proton collisions at ffiffi ffi s p ¼ 7 TeV. Integrated over the range p T < 30 GeV=c and jyj < 2, we find the product of the Çð1SÞ production cross section and dimuon branching fraction to be ðpp ! Çð1SÞXÞ Á BðÇð1SÞ ! þ À Þ ¼ 7:37 AE 0:13 þ0:61 À0:42 AE 0:81 nb, where the first uncertainty is statistical, the second is systematic, and the third is associated with the estimation of the integrated luminosity of the data sample. Under the assumption that the cross section is uniform in rapidity for the measurement range of each experiment, the cross section we measure at ffiffi ffi s p ¼ 7 TeV is about 3 times larger than the cross section measured at the Tevatron. The Çð2SÞ and Çð3SÞ integrated cross sections and the Çð1SÞ, Çð2SÞ, and Çð3SÞ differential cross sections in transverse-momentum in two regions of rapidity have also been determined. The differential cross FIG. 10 (color online). Comparison of the CMS differential ÇðnSÞ cross sections as a function of p T , normalized by TOT ¼ P ðd=dp T ÞÁp T , to previous measurements; Çð1SÞ (left), Çð2SÞ (middle), and Çð3SÞ (right). section measurements have been compared to previous measurements and PYTHIA. Finally, the cross section ratios of the three ÇðnSÞ have been measured.
The dominant sources of systematic uncertainty on the cross-section measurement arise from the tag-and-probe determination of the efficiencies and from the integrated luminosity normalization. Both will be reduced with additional data. Assuming fully-transverse or fully-longitudinal production polarization instead of unpolarized ÇðnSÞ production changes the cross-section measurements by about 20%. With a larger accumulated data sample, it will become possible to perform a simultaneous measurement of the polarization and the cross section. This work provides new experimental results which will serve as input to ongoing theoretical investigations of the correct description of bottomonium production.

ACKNOWLEDGMENTS
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.