Charged particle transverse momentum spectra in pp collisions at root{s}=0.9 and 7 TeV

EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN) CERN-PH-EP/2011-049 2011/09/30 CMS-QCD-10-008 Charged particle transverse momentum spectra in pp collisions at √s= 0.9 and 7 TeV The CMS Collaboration∗ Abstract The charged particle transverse momentum (pT) spectra are presented for pp collisions at √s=0.9 and 7 TeV. The data samples were collected with the CMS detector at the LHC and correspond to integrated luminosities of 231 µb−1and 2.96 pb−1, respectively. Calorimeter-based high-transverse-energy triggers are employed to enhance the statistical reach of the high-pTmeasurements. The results are compared with leading and next-to-leading order QCD and with an empirical scaling of measurements at different collision energies using the scaling variable xT≡2pT/√sover the pTrange up to 200 GeV/c. Using a combination of xTscaling and direct interpolation at fixed pT, a reference transverse momentum spectrum at √s=2.76 TeV is constructed, which can be used for studying high-pTparticle suppression in the dense QCD medium produced in heavy-ion collisions at that centre-of-mass energy. Submitted to the Journal of High Energy Physics ∗See Appendix A for the list of collaboration members arXiv:1104.3547v2 [hep-ex] 29 Sep 2011 1 1 Introduction The charged particle transverse momentum (pT) spectrum is an important observable for understanding the fundamental quantum chromodynamic (QCD) interactions involved in protonproton collisions. While the energy dependence of the bulk of particle production with pTbelow a few GeV/cis typically described either empirically or with phenomenological models, the rest of the spectrum can be well described by a convolution of parton distribution functions, the hard-scattering cross section from perturbative calculations, and fragmentation functions. Such a prescription has been generally successful over a large range of lower energy pp and p¯ p collisions [1–7]. Along with measurements of the jet production cross section and fragmentation functions, measurements of high-pTspectra provide a test of factorised perturbative QCD (pQCD) [8] at the highest collision energy to date. In addition to its relevance to the understanding of pQCD, the charged particle spectrum in pp collisions will be an important reference for measurements of high-pTparticle suppression in the dense QCD medium produced in heavy-ion collisions. At the Relativistic Heavy Ion Collider (RHIC), the sizable suppression of high-pTparticle production, compared to the spectrum expected from a superposition of a corresponding number of pp collisions, was one of the first indications of strong final-state medium effects [9–12]. A similar measurement of nuclear modification to charged particle pTspectra has been one of the first heavy-ion results at the Large Hadron Collider (LHC) [13]. The reference spectrum for the PbPb collisions at √sNN =2.76 TeV per nucleon can be constrained by interpolating between the pp spectra measured at √s= 0.9 and 7 TeV. In this paper, the phase-space-invariant differential yield E d3Nch/dp3is presented for primary charged particles with energy (E) and momentum (p), averaged over the pseudorapidity acceptance of the Compact Muon Solenoid (CMS) tracking system (|η|<2.4). The pseudorapidity is defined as –ln[tan(θ/2)], with θbeing the polar angle of the charged particle with respect to the counterclockwise beam direction. The number of primary charged particles (Nch) is defined to include decay products of particles with proper lifetimes less than 1 cm. Using the integrated luminosities calculated in Refs. [14, 15] with an estimated uncertainty of 11% and 4% at √s=0.9 and 7 TeV, respectively, the differential cross sections are constructed and compared to a scaling with the variable xT≡2pT/√s. Such a scaling has already been observed for p¯ p measurements at lower collision energies [4, 5, 16, 17]. For consistency with the CDF measurements at √s=0.63, 1.8, and 1.96 TeV, the pseudorapidity range of the xTdistributions has been restricted to |η|<1.0. Finally, using the new measurements presented in this paper, as well as previously measured pp and p¯ p cross sections, an estimate of the differential transverse momentum cross section is constructed at the interpolated energy of √s=2.76 TeV, corresponding to the nucleon-nucleon centre-of-mass energy of PbPb collisions recorded at the LHC. The paper is organised as follows: Section 2 contains a description of the CMS detector; Section 3 describes the trigger and event selection; Sections 4 and 5 detail the reconstruction and selection of primary vertices and tracks; Section 6 explains the characterisation of events based on the leading-jet transverse energy; Section 7 describes the various applied corrections and systematic uncertainties; Section 8 presents the final invariant differential yields and comparisons to data and simulation; and Section 9 discusses the interpolation procedures used to construct a reference spectrum at √s=2.76 TeV. 23 Event Selection 2 The CMS Detector A detailed description of the CMS experiment can be found in Ref. [18]. The central feature of the CMS apparatus is a superconducting solenoid of 6 m internal diameter, providing an axial magnetic field of 3.8 T. Immersed in the magnetic field are the pixel tracker, the silicon strip tracker, the lead tungstate crystal electromagnetic calorimeter (ECAL), and the brass/scintillator hadron calorimeter (HCAL). Muons are measured in gas ionisation detectors embedded in the steel return yoke. The CMS experiment uses a right-handed coordinate system, with the origin at the nominal interaction point, the xaxis pointing to the centre of the LHC ring, the yaxis pointing up perpendicular to the plane of the LHC, and the zaxis along the counterclockwise beam direction. The azimuthal angle, φ, is measured in the (x,y) plane. The tracker consists of 1440 silicon pixel and 15 148 silicon strip detector modules and measures charged particle trajectories within the nominal pseudorapidity range |η|<2.4. The pixel tracker consists of three 53.3 cm-long barrel layers and two endcap disks on each side of the barrel section. The innermost barrel layer has a radius of 4.4 cm, while for the second and third layers the radii are 7.3 cm and 10.2 cm, respectively. The tracker is designed to provide an impact parameter resolution of about 100 µm and a transverse momentum resolution of about 0.7 % for 1 GeV/ccharged particles at normal incidence (η=0) [19]. The tracker was aligned as described in Ref. [20] using cosmic ray data prior to the LHC commissioning. The precision achieved for the positions of the detector modules with respect to particle trajectories is 3–4 µm in the barrel for the coordinate in the bending plane (φ). Two elements of the CMS detector monitoring system, the beam scintillator counters (BSC) [18, 21] and the beam pick-up timing for the experiments devices (BPTX) [18, 22], were used to trigger the detector readout. The BSCs are located at a distance of 10.86 m from the nominal interaction point (IP), one on each side, and are sensitive in the |η|range from 3.23 to 4.65. Each BSC is a set of 16 scintillator tiles. The BSC elements have a time resolution of 3 ns, an average minimum ionising particle detection efficiency of 95.7%, and are designed to provide hit and coincidence rates. The two BPTX devices, located around the beam pipe at a position of z=±175 m from the IP, are designed to provide precise information on the bunch structure and timing of the incoming beam, with better than 0.2 ns time resolution. The two steel/quartz-fibre forward calorimeters (HF), which extend the calorimetric coverage beyond the barrel and endcap detectors to the |η|region between 2.9 and 5.2, were used for further offline selection of collision events. The detailed Monte Carlo (MC) simulation of the CMS detector response is based on GEANT4 [23]. Simulated events were processed and reconstructed in the same manner as collision data. 3 Event Selection This analysis uses data samples collected from 0.9 and 7 TeV pp collisions in the first months of the 2010 LHC running, corresponding to integrated luminosities of (231 ±25)µb−1and (2.96 ±0.12)pb−1, respectively [14, 15]. This section gives a brief description of the requirements imposed to select good events for this analysis. A more detailed description of the CMS trigger selections can be found in Ref. [24]. First, a minimum bias trigger was used to select events with a signal in any of the BSC tiles, coincident with a signal from either of the two BPTX detectors, indicating the presence of at 3 least one proton bunch crossing the interaction point. From this sample, collision events were selected offline by requiring a coincidence of BPTX signals, indicating the presence of both beams. To select preferentially non-single-diffractive (NSD) events, at least one forward calorimeter (HF) tower with energy deposition E>3 GeV in each of the forward and backward hemispheres was required. Events with beam-halo muons crossing the detector were identified and rejected based on the time difference between BSC hits on either side of the interaction point. Beam-induced background events, producing anomalous numbers of low-quality tracks, were rejected by requiring that at least 25% of the charged particles reconstructed in the pixel–silicon tracking system satisfied the highPurity criterion. This criterion, described in Ref. [25], consists of numerous selections on the properties of the tracks, including the normalised χ2, the compatibility with the beamline and primary vertices, the number of hit layers, the number of ‘3D’ layers, and the number of lost layers. The selection on the fraction of highPurity tracks was only applied to events with more than 10 tracks, providing a clean separation between real pp collisions and beam backgrounds. The remaining non-collision event fraction, determined by applying the same selections to events where only a single beam was crossing the interaction point, is estimated to be less than 2 x 10−5. Events were required to have at least one primary vertex, reconstructed according to the description in the following section from triplets of pixel hits. A further requirement, namely at least one vertex found from fully reconstructed tracks (see next section for details) with number of degrees of freedom (Ndo f) greater than four, was imposed to improve the robustness against triggered events containing multiple pp collisions, i.e., “event pileup”. The loss in event selection efficiency from the fully-reconstructed-track vertex compared to the pixel vertex alone was determined entirely from data, based on a subset of early runs with negligible event pileup. The percentage of events remaining after each selection step is presented in Table 1. For a large part of the 7 TeV data collection, the minimum bias trigger paths had to be prescaled by large factors because of the increasing instantaneous luminosity of the LHC. In order to maximise the pTreach of the charged particle transverse momentum measurement at this centre-ofmass energy, two high-level trigger (HLT) paths were used that selected events with minimum uncorrected transverse jet energies (ET) of 15 and 50 GeV, based only on information from the calorimeters. While the higher threshold path was not prescaled during the 7 TeV data-taking period corresponding to the 2.96 pb−1used in this analysis, the lower threshold path had to be prescaled for a significant fraction of this sample. The 0.9 TeV data sample consists of 6.8 million minimum bias triggered events, while the 7 TeV sample is composed of 18.7 million minimum bias events, and 1.4 (5.6) million events selected with the HLT minimum-ETvalues of 15 (50) GeV. The selection efficiency for NSD events was determined based on simulated events from the PYTHIA [26] event generator (version 6.420, tune D6T [27]) that were subsequently passed through a Monte Carlo simulation of the CMS detector response. The resulting event selection efficiency as a function of the multiplicity of reconstructed charged particles is shown for 7 TeV collisions in Fig. 1a. The corresponding event selection efficiency is calculated by the same technique for the 0.9 TeV data (not shown). Based on events simulated with PHOJET [28, 29] and PYTHIA, the remaining fraction of single-diffractive (SD) events in the selected sample was estimated to be (5 ±1)% and (6 ±1)% for the 0.9 and 7 TeV data, respectively. 44 Primary Vertex Table 1: Summary of event selection steps applied to the 0.9 and 7 TeV collision data sets and the percentage of events from the original minimum bias samples that remain after each step. Collision energy 0.9 TeV 7 TeV Selection Percentage passing each selection cut One BSC + one BPTX 100.0 100.0 BPTX coincidence 94.49 90.05 Beam halo rejection 94.08 89.83 HF coincidence 73.27 83.32 Beam background rejection 73.26 83.32 Valid pixel-track vertex 70.14 82.48 Quality full-track vertex 64.04 77.35 4 Primary Vertex In this analysis, two separate algorithms are employed to determine the primary vertex position. The first is a highly efficient algorithm based on pixel triplet tracks that requires a minimum of just a single track consistent with the beam-spot position. The position of the beam-spot, taken as the centre of the region where the LHC beams collide, is calculated for each LHC fill based on the average over many events of the three-dimensional fitted vertex positions [25]. The second vertex-finding algorithm, based on fully reconstructed tracks with hits also in the silicon strip tracker, is less efficient in selecting low-multiplicity events, but more robust in discriminating against event pileup. Since pileup is significant over the majority of the analysed data sample, only the fully-reconstructed-track vertex is used to construct the raw charged particle momentum spectra. The raw spectra are subsequently corrected for the fraction of events with fewer than four tracks (and the fraction of tracks in such low-multiplicity events), based on a subset of the event sample selected with the more efficient pixel-track vertex requirement during collision runs with negligible event pileup. To determine the zposition of the pixel vertex in each event, tracks consisting of three pixel hits are constructed with a minimum pTof 75 MeV/cfrom a region within a transverse distance of 0.2 cm from the beam axis. The xand ypositions of the pixel vertex are taken from the transverse position of the beam axis. Fitted tracks are selected based on the requirement that the transverse impact parameter is less than three times the quadratic sum of the transverse errors on the track impact parameter and the beam axis position. The selected tracks are then passed to an agglomerative algorithm [30], which iteratively clusters the tracks into vertexcandidates. The procedure is halted when the distance between nearest clusters, normalised by their respective position uncertainties, reaches 12. Only vertices consisting of at least two tracks are kept, except when the event contains a single reconstructed track, which occurs in 1.67% (0.99%) of the events at √s=0.9 (7) TeV. In the case of multiple vertex-candidates, only the vertex with the most associated tracks is kept. While this occurs in as many as 20% of events, the rejected vertex typically has very few associated tracks and is highly correlated in zposition to the vertex with the most associated tracks. These characteristics imply that the rejected vertices are not from event pileup, but rather from tracks in the tails of the impact parameter distribution that are not agglomerated into the primary vertex. The fully-reconstructed-track vertex algorithm begins from a set of tracks selected according to their transverse impact parameter to the beam-spot (<2 cm), number of hits (>6), and normalised χ2(<20). These tracks are passed to an adaptive vertex fitter, in which tracks are as- 5 Charged particle multiplicity 0 10 20 30 40 50 selected SD or f selected NSD ε 0.0 0.2 0.4 0.6 0.8 1.0 1.2 CMS Simulation PYTHIA 7 TeV NSD selection efficiency pixel vertex (NSD) track vertex (NSD) Selected event SD fraction pixel vertex (SD) track vertex (SD) (a) [cm] 0 PV z -15 -10 -5 0 5 10 15 [cm] 1 PV z -15 -10 -5 0 5 10 15 1 10 2 10 -1 Ldt = 10.2 nb ∫ = 7 TeVsCMS (b) Figure 1: (a) The efficiency (εselected NSD in Eq. (2)) for selecting non-single-diffractive (NSD) events as a function of the multiplicity of reconstructed charged particles in the tracker acceptance (|η|<2.4) after applying the full event selection described in the text, including a single pixeltrack vertex (filled circles) and additionally requiring a fully-reconstructed-track vertex with Ndo f >4 (open circles) as described in Section 4. Also, the remaining single-diffractive (SD) fraction (fselected SD in Eq. (2)) as a function of charged particle multiplicity for the same selections (solid and dashed lines). (b) Correlation between the zpositions, z0 PV and z1 PV, of the two vertices with the most associated tracks for measured events with more than one fullyreconstructed-track vertex satisfying the quality selections. signed a weight between 0 and 1 according to their compatibility with the common vertex [25]. Quality vertices are further required to have more than four degrees of freedom (Ndo f ), corresponding to at least four tracks with weights of approximately one. For events with multiple reconstructed vertices passing the quality selection, the correlation between the zpositions of the two vertices with the most associated tracks is shown in Fig. 1b. Other than the diagonal region without multiple vertices, expected from the algorithmic parameter of at least a 1 cm separation, the uncorrelated positions of the two vertices are indicative of random event pileup. The event pileup rate is estimated from the fraction of events with multiple reconstructed vertices, after correcting for vertices that are not found because of their proximity. The beam conditions varied over the analysed minimum bias data samples, such that the corrected fraction of pileup events is in the range (0.4–7.5)%. The uncertainty on the event pileup fraction, determined from the largest correction to the multiple-vertex fraction, is a constant factor of 0.2% and 1.2% for the 0.9 and 7 TeV data, respectively. 5 Track Selection This analysis uses tracks from the standard CMS reconstruction algorithm, which consists of multiple iterations of a combinatorial track finder based on various seeding layer patterns [31]. After each iteration, hits belonging unambiguously to tracks in the previous step are removed from consideration for subsequent steps. 65 Track Selection η -2 -1 0 1 2 Algorithmic efficiency 0.5 0.6 0.7 0.8 0.9 1 PYTHIA 7 TeV > 0.4 GeV/c T p > 2.0 GeV/c T p CMS Simulation(a) [GeV/c] T p 1 10 2 10 tr ε ×A 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 PYTHIA 7 TeV <20 GeV T 0<E <40 GeV T 20<E <60 GeV T 40<E <80 GeV T 60<E <100 GeV T 80<E <120 GeV T 100<E <200 GeV T 180<E <400 GeV T 380<E CMS Simulation(b) Fake rate Figure 2: (a) The algorithmic tracking efficiency for two different momentum ranges as a function of η. (b) The product of geometrical acceptance (A) with tracking efficiency (εtr) (upper points) and the misidentification (‘fake’) rate (lower points) as a function of transverse momentum for tracks with |η|<1 in bins of corrected leading-jet transverse energy. In order to minimise the contribution from misidentified tracks and tracks with poor momentum resolution, a number of quality selections are applied. These include the highPurity selection mentioned in Section 3, the requirement of at least five hits on the track, the normalized χ2 per degree of freedom divided by the number of tracker layers used in the fit less than a maximum value which varies from 0.48 and 0.07 depending on ηand pT, and a relative momentum uncertainty of less than 20%. Furthermore, to reject non-primary tracks (i.e., the products of weak decays and secondary interactions with detector material), only the pixel-seeded tracking iterations are used, and selections are placed on the impact parameter of the tracks with respect to the primary vertex position. Specifically, the transverse and longitudinal impact parameters are required to be less than 0.2 cm and also less than 3 times the sum in quadrature of the uncertainties on the impact parameter and the corresponding vertex position. In the case of multiple quality reconstructed vertices in the minimum bias event samples, tracks that pass the impact parameter selections with respect to any vertex are used in the analysis. The number of events, by which the track pTdistribution is normalised, is then scaled by a factor to account for the event pileup fraction. In contrast, for the jet-triggered samples, tracks are selected based on the impact parameter with respect to the single vertex responsible for the trigger. The primary vertex of the hard-scattering process is identified as the vertex with the largest value of ∑p2 T for the associated fitted tracks. With the above-mentioned selections applied to the reconstructed tracks, the algorithmic efficiency determined from simulated PYTHIA events is greater than 85% (80%) for tracks with transverse momentum above 2.0 (0.4) GeV/caveraged over |η|<2.4 (Fig. 2a). In the same kinematic region, misidentified and non-primary tracks are each below 1%, while multiple reconstruction occurs for less than 0.01% of tracks. 7 6 Event Classification by Leading-Jet Energy All events in this analysis are classified according to the transverse energy of the most energetic reconstructed jet, defined as the leading jet. Jets are reconstructed from calorimeter deposits alone using the anti-kTalgorithm [32] with cone radius R=p(∆φ)2+ (∆η)2=0.5. The measured energy of the jet is adjusted according to corrections based on a MC description of the CMS calorimeter response with a 3–6% uncertainty on the jet energy scale [33]. The motivation for classifying events according to the leading-jet transverse energy is twofold. First, the degrading effect of the local-track density on the high-pTtracking performance (e.g., inside a jet) can be parametrised according to this variable. Based on events simulated with PYTHIA in minimum bias and QCD samples with various thresholds on the hard-scattering scale ( ˆ pT), the efficiency and misidentification rates of the selected tracks are estimated as a function of transverse momentum in bins of leading-jet transverse energy (see Fig. 2b). Second, as discussed in Section 3, calorimeter-based triggers with leading-jet transverse energy thresholds of 15 GeV (Jet15U) and 50 GeV (Jet50U) were used to extend the pTreach of the 7 TeV measurement. To avoid potential biases from the jet-trigger selection, it is desirable to operate in a region where the trigger is fully efficient. The region above which the jet trigger with an uncorrected energy threshold of 15 GeV becomes fully efficient is determined by first plotting the leading-jet ETdistribution for a sample of events selected with the prescaled minimum bias trigger and the offline selections described in Section 3. This distribution is then compared to the subset of those events which also fire the 15 GeV jet trigger as a function of corrected transverse energy. The resulting ratio is the trigger efficiency curve presented in the lower panel of Fig. 3a. The 15 GeV jet trigger achieves more than 99% efficiency at a corrected energy of ET=45 GeV. The analogous procedure is repeated on a sample of events selected by the 15 GeV jet trigger to determine that the 50 GeV jet trigger becomes fully efficient above ET=95 GeV. For the trigger efficiency study, an early subset of the data (10.2 nb−1) was used, because the minimum bias and lower-threshold jet triggers were highly prescaled in the later runs. In the upper panel of Fig. 3a, the ETdistributions from the jet-triggered sample are normalised per equivalent minimum bias event by matching their integrals in the regions where the triggers are fully efficient. For the 7 TeV analysis, events are divided into three classes based on leading-jet ET: below 60 GeV, between 60 and 120 GeV, and above 120 GeV. Since each event is uniquely assigned to one such leading-jet ETrange, the overall dNch/dpTdistribution is simply the sum of the spectra from the three ranges, each corresponding to a fully-efficient HLT selection (i.e., minimum bias, 15 GeV jet trigger, and 50 GeV jet trigger). The contributions to the spectra from the jet-triggered events are normalised per selected minimum bias event; the fraction of minimum bias events containing a leading jet with greater than either 60 or 120 GeV is calculated as shown in Fig. 3a by matching the fully-efficient regions of the leading-jet ETdistributions. The three contributions to the combined charged particle transverse momentum spectrum are shown in Fig. 3b. The lower panel of that figure compares the combined spectrum first to the minimum bias spectrum alone and then to a spectrum constructed with the addition of only the lower-threshold jet trigger. These are all in good agreement within their respective statistical uncertainties. A pT-dependent systematic uncertainty of 0–4% is attributed to the normalisation of the contributions from the triggered samples. This value is determined by changing the leading-jet ETranges that separate the three samples (e.g., to ET=40 and 100GeV), by basing the normalisation directly on the HLT prescale values, and by comparing the normalisations determined from different subsets of the full data sample. 14 9 Interpolation to 2.76 TeV T x -4 10 -3 10 -2 10 -1 10 ] 3 c -2 [mb GeV 3 /dpσ 3 Ed 4.9 /GeV)s( 5 10 7 10 9 10 11 10 13 10 15 10 17 10 19 10 21 10 |<1.0)η) + X (| - +h + 0.5(h→) p pp( ) -1 CMS 7 TeV (2.96 pb ) -1 bµCMS 0.9 TeV (231 CDF 1.96 TeV CDF 1.8 TeV CDF 0.63 TeV Global power-law fit (a) T x -4 10 -3 10 -2 10 -1 10 Data/NLO 0.5 1.0 1.5 = 0.9 TeVs = 1.96 TeVs = 7 TeVs T x 0.01 0.02 0.03 0.04 0.05 0.06 0.07 / Fit 3 /dpσ 3 Ed 4.9 /GeV)s( 0.5 1 1.5 2 2.5 3 3.5 = 2.76 TeVs (GeV/c) for T p 10 20 30 40 50 60 70 80 90 (b) ) + fit -1 CMS 7 TeV (2.96 pb ) + fit -1 bµCMS 0.9 TeV (231 CDF 1.96 TeV + fit interpolations T 2.76 TeV x (corrected by NLO ratios) T x 0.01 0.02 0.03 0.04 0.05 0.06 0.07 NLO ratio 1.0 1.2 1.4 1.6 1.8 = 2.75 TeV)s = 0.9, 1.96, 7 TeV / s ( 3 /dpσ 3 Ed 4.9 )s Ratio of ( = 0.9 TeVs = 1.96 TeVs = 7 TeVs Figure 6: (a) Upper panel: inclusive charged particle invariant differential cross sections, scaled by √s4.9, for |η|<1.0 as a function of the scaling parameter xT. The result is the average of the positive and negative charged particles. Lower panel: ratios of differential cross sections measured at 0.9, 1.96, and 7 TeV to those predicted by NLO calculations for factorisation scales ranging from 0.5–2.0 pT. (b) Upper panel: ratios of the scaled differential cross sections to the global power-law xTfit described in the text (coloured markers) and fits to these ratios (similarly coloured thin lines). The expected ratio for √s=2.76 TeV after applying NLO-based corrections to each of the three measurements as described in the text (solid blue lines). The uncertainty from the NLO parameters is represented by the shaded band. The upper axis translates xTto pTfor √s=2.76 TeV. Lower panel: ratios of the NLO-calculated cross sections at three different energies, scaled by √s4.9, to the cross section calculated at √s=2.75 TeV. The width of the bands represents the variation of the factorisation scale by a factor of two. the interpolated cross section has an additional component to account for possible correlations in the luminosity uncertainty between the three measurements. This term, taken as equal to the smallest individual uncertainty (4%), is added in quadrature. The direct interpolation of cross sections at a fixed value of pTis done using CDF measurements at √s=0.63, 1.8 and 1.96 TeV [4, 5, 17], the new CMS measurements at √s=0.9 and 7 TeV, as well as an earlier result at √s=2.36 TeV [24]. The latter measurement is converted to a differential cross section assuming the total inelastic cross section of 60.52 mb from PYTHIA. At each energy, an empirical fit to the pTdistribution is first constructed to provide a continuous estimation independent of different binning. Then, in arbitrarily small pTbins, these empirical fits are evaluated and the evolution of the cross section with √sis parametrised by a secondorder polynomial. Two examples of these fits are shown in Fig. 7a for pT=3 and 9 GeV/c. The uncertainty on the value of the fit evaluated at √s=2.76 TeV is taken from the covariance matrix of the fit terms, with an additional 4% added in quadrature to account conservatively for any correlation in the luminosity uncertainty between the different measurements. 15 To arrive at a single interpolated spectrum over the full pTrange, a linear combination of the two techniques is used with weights that vary linearly across the overlap range from pT=5 GeV/c(only direct interpolation at fixed pT) to pT=20 GeV/c(only xTscaling with NLO-based residual correction). In the pTrange where the two techniques overlap, the different methods agree to within their respective systematic uncertainties. (The fixed-pTinterpolation value is typically around 8% lower than the xTinterpolation.) The resulting predicted 2.76 TeV differential cross section is shown in the upper panel of Fig. 7b, and its ratio with respect to various PYTHIA tunes at that centre-of-mass energy in the lower panel. The uncertainty on the predicted cross section, shown by the grey band in the lower panel, is the weighted sum (where applicable) of the uncertainties derived from the two methods described in the preceding paragraphs. Also shown in the lower panel of Fig. 7b is the ratio of the predicted 2.76 TeV cross section to that found by simply scaling the CMS measured 7 TeV result by the expected 2.75 TeV to 7 TeV ratio from NLO calculations [42]. The interpolation used in the recent ALICE publication [13] is a few percent lower than the result quoted in this paper, but consistent within the respective systematic uncertainties. The behavior of the various generators compared to the interpolated 2.76 TeV cross section is broadly similar to the 0.9 TeV invariant yields presented in Fig. 7b. The ProQ20 tune agrees most closely (within 15%) with the interpolated cross section above 2 GeV/c. Future analysis of a recently recorded 2.76 TeV pp collision sample will provide verification of this result and a reduction in the systematic uncertainties. 10 Summary In this paper, measurements of the phase-space-invariant differential yield E d3Nch/dp3at √s = 0.9 and 7 TeV have been presented for primary charged particles, averaged over the pseudorapidity acceptance of the CMS tracking system (|η|<2.4). The results have been shown to be in reasonable agreement with the previously published CMS measurements at √s= 0.9 and 7 TeV [24, 34] and, except for the surplus of tracks at very low transverse momentum, with PYTHIA leading-order pQCD. The 7 TeV data are most consistent with PYTHIA8, which agrees at the 10% level over the full pTrange of the measurement. In contrast, the 0.9 TeV data are considerably better described by the ProQ20 tune. Additionally, the consistency of the 0.9 and 7 TeV spectra has been demonstrated with an empirical xTscaling that unifies the differential cross sections from a wide range of collision energies onto a common curve. Furthermore, within the theoretical uncertainties of the NLO calculations, the residual breaking of xTscaling above pT≈8 GeV/cis consistent between the measured cross sections and the NLO calculations. This result has removed a large uncertainty from an important ingredient of existing and future PbPb measurements, namely the pp reference spectrum corresponding to the energy of the 2010 PbPb run: 2.76 TeV per nucleon. By employing a combination of techniques to interpolate between the results presented here at √s=0.9 and 7 TeV, including information from existing CDF measurements at √s=0.63, 1.8, and 1.96 TeV, a pp reference at √s=2.76 TeV has been constructed over a large range of transverse momentum (pT= 1–100 GeV/c) with systematic uncertainties of less than 13%. Acknowledgements We wish to congratulate our colleagues in the CERN accelerator departments for the excellent performance of the LHC machine. We thank the technical and administrative staff at CERN and other CMS institutes, and acknowledge support from: FMSR (Austria); FNRS and FWO (Belgium); CNPq, CAPES, FAPERJ, and FAPESP (Brazil); MES (Bulgaria); CERN; CAS, MoST, and 16 10 Summary [TeV]s 1 10 ] 3 c -2 [mb GeV 3 /dpσ 3 Ed -2 10 -1 10 (a) = 3 GeV/c T p |<1.0)η) + X (| - +h + 0.5(h→) p pp( ) -1 CMS 7 TeV (2.96 pb CDF 1.96 TeV ) -1 bµCMS 2.36 TeV (0.2 CDF 1.8 TeV ) -1 bµCMS 0.9 TeV (231 CDF 0.63 TeV [TeV]s 1 10 3 ] x 10 3 c -2 [mb GeV 3 /dpσ 3 Ed -5 10 -4 10 = 9 GeV/c T p = 2.76 TeV interpolated values scaling interp. T x [GeV/c] T p 1 10 2 10 ] 3 c -2 [mb GeV 3 /dpσ 3 Ed -14 10 -12 10 -10 10 -8 10 -6 10 -4 10 -2 10 1 2 10 |<1.0η = 2.76 TeV, |s CMS Interpolation PYTHIA D6T PYTHIA Perugia0 PYTHIA ProQ20 PYTHIA 8 NLO rescaled CMS 7 TeV (F. Arleo et al.) = 64 mb) mb σALICE (scaled by (b) [GeV/c] T p 1 10 2 10 Interp. / Others 0.6 0.8 1.0 1.2 1.4 1.6 Figure 7: (a) Interpolations between measured charged particle differential cross sections at different √sfor the two example values of pT=3 and 9 GeV/c. Second-order polynomial fits to the measured data are shown by the solid lines. The open squares show the resulting interpolated cross sections for √s=2.76 TeV. The open circle on the lower panel represents the corresponding estimate from the xT-scaling approach in the overlap region where both can be estimated. (b) Upper panel: the predicted 2.76 TeV charged particle differential transverse momentum cross section, based on the combined direct pTinterpolation and NLO-corrected xT-scaling techniques described in the text. Lower panel: ratios of combined interpolation to predictions from several PYTHIA tunes, an NLO-based rescaling approach [42], and the ALICE interpolation used in Ref. [13]. NSFC (China); COLCIENCIAS (Colombia); MSES (Croatia); RPF (Cyprus); Academy of Sciences and NICPB (Estonia); Academy of Finland, MEC, and HIP (Finland); CEA and CNRS/IN2P3 (France); BMBF, DFG, and HGF (Germany); GSRT (Greece); OTKA and NKTH (Hungary); DAE and DST (India); IPM (Iran); SFI (Ireland); INFN (Italy); NRF and WCU (Korea); LAS (Lithuania); CINVESTAV, CONACYT, SEP, and UASLP-FAI (Mexico); PAEC (Pakistan); SCSR (Poland); FCT (Portugal); JINR (Armenia, Belarus, Georgia, Ukraine, Uzbekistan); MST and MAE (Russia); MSTD (Serbia); MICINN and CPAN (Spain); Swiss Funding Agencies (Switzerland); NSC (Taipei); TUBITAK and TAEK (Turkey); STFC (United Kingdom); DOE and NSF (USA). Individuals have received support from the Marie-Curie programme and the European Research Council (European Union); the Leventis Foundation; the A. P. 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Litov, M. Mateev, B. Pavlov, P. Petkov Institute of High Energy Physics, Beijing, China J.G. Bian, G.M. Chen, H.S. Chen, C.H. Jiang, D. Liang, S. Liang, X. Meng, J. Tao, J. Wang, J. Wang, X. Wang, Z. Wang, H. Xiao, M. Xu, J. Zang, Z. Zhang State Key Lab. of Nucl. Phys. and Tech., Peking University, Beijing, China Y. Ban, S. Guo, Y. Guo, W. Li, Y. Mao, S.J. Qian, H. Teng, L. Zhang, B. Zhu, W. Zou Universidad de Los Andes, Bogota, Colombia A. Cabrera, B. Gomez Moreno, A.A. Ocampo Rios, A.F. Osorio Oliveros, J.C. Sanabria Technical University of Split, Split, Croatia N. Godinovic, D. Lelas, K. Lelas, R. Plestina3, D. Polic, I. Puljak University of Split, Split, Croatia Z. Antunovic, M. Dzelalija Institute Rudjer Boskovic, Zagreb, Croatia V. Brigljevic, S. Duric, K. Kadija, S. Morovic University of Cyprus, Nicosia, Cyprus A. Attikis, M. Galanti, J. Mousa, C. Nicolaou, F. Ptochos, P.A. Razis Charles University, Prague, Czech Republic M. Finger, M. Finger Jr. Academy of Scientific Research and Technology of the Arab Republic of Egypt, Egyptian Network of High Energy Physics, Cairo, Egypt Y. Assran4, S. Khalil5, M.A. Mahmoud6 National Institute of Chemical Physics and Biophysics, Tallinn, Estonia A. Hektor, M. Kadastik, M. M¨ untel, M. Raidal, L. Rebane Department of Physics, University of Helsinki, Helsinki, Finland V. Azzolini, P. Eerola, G. Fedi Helsinki Institute of Physics, Helsinki, Finland S. Czellar, J. H¨ ark¨ onen, A. Heikkinen, V. Karim¨ aki, R. Kinnunen, M.J. Kortelainen, T. Lamp´ en, K. Lassila-Perini, S. Lehti, T. Lind´ en, P. Luukka, T. M¨ aenp¨ a¨ a, E. Tuominen, J. Tuominiemi, E. Tuovinen, D. Ungaro, L. Wendland Lappeenranta University of Technology, Lappeenranta, Finland K. Banzuzi, A. Korpela, T. Tuuva Laboratoire d’Annecy-le-Vieux de Physique des Particules, IN2P3-CNRS, Annecy-le-Vieux, France D. Sillou DSM/IRFU, CEA/Saclay, Gif-sur-Yvette, France M. Besancon, S. Choudhury, M. Dejardin, D. Denegri, B. Fabbro, J.L. Faure, F. Ferri, S. Ganjour, F.X. Gentit, A. Givernaud, P. Gras, G. Hamel de Monchenault, P. Jarry, E. Locci, J. Malcles, M. Marionneau, L. Millischer, J. Rander, A. Rosowsky, I. Shreyber, M. Titov, P. Verrecchia 23 Laboratoire Leprince-Ringuet, Ecole Polytechnique, IN2P3-CNRS, Palaiseau, France S. Baffioni, F. Beaudette, L. Benhabib, L. Bianchini, M. Bluj7, C. Broutin, P. Busson, C. Charlot, T. Dahms, L. Dobrzynski, S. Elgammal, R. Granier de Cassagnac, M. Haguenauer, P. Min´ e, C. Mironov, C. Ochando, P. Paganini, D. Sabes, R. Salerno, Y. Sirois, C. Thiebaux, B. Wyslouch8, A. Zabi Institut Pluridisciplinaire Hubert Curien, Universit´e de Strasbourg, Universit´e de Haute Alsace Mulhouse, CNRS/IN2P3, Strasbourg, France J.-L. Agram9, J. Andrea, D. Bloch, D. Bodin, J.-M. Brom, M. Cardaci, E.C. Chabert, C. Collard, E. Conte9, F. Drouhin9, C. Ferro, J.-C. Fontaine9, D. Gel´ e, U. Goerlach, S. Greder, P. Juillot, M. Karim9, A.-C. Le Bihan, Y. Mikami, P. Van Hove Centre de Calcul de l’Institut National de Physique Nucleaire et de Physique des Particules (IN2P3), Villeurbanne, France F. Fassi, D. Mercier Universit´e de Lyon, Universit´e Claude Bernard Lyon 1, CNRS-IN2P3, Institut de Physique Nucl´eaire de Lyon, Villeurbanne, France C. Baty, S. Beauceron, N. Beaupere, M. Bedjidian, O. Bondu, G. Boudoul, D. Boumediene, H. Brun, J. Chasserat, R. Chierici, D. Contardo, P. Depasse, H. El Mamouni, J. Fay, S. Gascon, B. Ille, T. Kurca, T. Le Grand, M. Lethuillier, L. Mirabito, S. Perries, V. Sordini, S. Tosi, Y. Tschudi, P. Verdier Institute of High Energy Physics and Informatization, Tbilisi State University, Tbilisi, Georgia D. Lomidze RWTH Aachen University, I. Physikalisches Institut, Aachen, Germany G. Anagnostou, M. Edelhoff, L. Feld, N. Heracleous, O. Hindrichs, R. Jussen, K. Klein, J. Merz, N. Mohr, A. Ostapchuk, A. Perieanu, F. Raupach, J. Sammet, S. Schael, D. Sprenger, H. Weber, M. Weber, B. Wittmer RWTH Aachen University, III. 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Shi, W. Sun, W.D. Teo, J. Thom, J. Thompson, J. Vaughan, Y. Weng, L. Winstrom, P. Wittich Fairfield University, Fairfield, USA A. Biselli, G. Cirino, D. Winn Fermi National Accelerator Laboratory, Batavia, USA S. Abdullin, M. Albrow, J. Anderson, G. Apollinari, M. Atac, J.A. Bakken, S. Banerjee, L.A.T. Bauerdick, A. Beretvas, J. Berryhill, P.C. Bhat, I. Bloch, F. Borcherding, K. Burkett, J.N. Butler, V. Chetluru, H.W.K. Cheung, F. Chlebana, S. Cihangir, W. Cooper, D.P. Eartly, V.D. Elvira, S. Esen, I. Fisk, J. Freeman, Y. Gao, E. Gottschalk, D. Green, K. Gunthoti, 31 O. Gutsche, J. Hanlon, R.M. Harris, J. Hirschauer, B. Hooberman, H. Jensen, M. Johnson, U. Joshi, R. Khatiwada, B. Klima, K. Kousouris, S. Kunori, S. Kwan, C. Leonidopoulos, P. Limon, D. Lincoln, R. Lipton, J. Lykken, K. Maeshima, J.M. Marraffino, D. Mason, P. McBride, T. Miao, K. Mishra, S. Mrenna, Y. Musienko45, C. Newman-Holmes, V. O’Dell, R. Pordes, O. Prokofyev, N. Saoulidou, E. Sexton-Kennedy, S. Sharma, W.J. Spalding, L. Spiegel, P. Tan, L. Taylor, S. Tkaczyk, L. Uplegger, E.W. Vaandering, R. Vidal, J. Whitmore, W. Wu, F. Yang, F. Yumiceva, J.C. Yun University of Florida, Gainesville, USA D. Acosta, P. Avery, D. Bourilkov, M. Chen, M. De Gruttola, G.P. Di Giovanni, D. Dobur, A. Drozdetskiy, R.D. Field, M. Fisher, Y. Fu, I.K. Furic, J. Gartner, B. Kim, J. Konigsberg, A. Korytov, A. Kropivnitskaya, T. Kypreos, K. Matchev, G. Mitselmakher, L. Muniz, C. Prescott, R. Remington, M. Schmitt, B. Scurlock, P. Sellers, N. Skhirtladze, M. Snowball, D. Wang, J. Yelton, M. Zakaria Florida International University, Miami, USA C. Ceron, V. Gaultney, L. Kramer, L.M. Lebolo, S. Linn, P. Markowitz, G. Martinez, D. Mesa, J.L. Rodriguez Florida State University, Tallahassee, USA T. Adams, A. Askew, J. Bochenek, J. Chen, B. Diamond, S.V. Gleyzer, J. Haas, S. Hagopian, V. Hagopian, M. Jenkins, K.F. Johnson, H. Prosper, L. Quertenmont, S. Sekmen, V. Veeraraghavan Florida Institute of Technology, Melbourne, USA M.M. Baarmand, B. Dorney, S. Guragain, M. Hohlmann, H. Kalakhety, R. Ralich, I. Vodopiyanov University of Illinois at Chicago (UIC), Chicago, USA M.R. Adams, I.M. Anghel, L. Apanasevich, Y. Bai, V.E. Bazterra, R.R. Betts, J. Callner, R. Cavanaugh, C. Dragoiu, L. Gauthier, C.E. Gerber, S. Hamdan, D.J. Hofman, S. Khalatyan, G.J. Kunde46, F. Lacroix, M. Malek, C. O’Brien, C. Silvestre, A. Smoron, D. Strom, N. Varelas The University of Iowa, Iowa City, USA U. Akgun, E.A. Albayrak, B. Bilki, W. Clarida, F. Duru, C.K. Lae, E. McCliment, J.-P. Merlo, H. Mermerkaya47, A. Mestvirishvili, A. Moeller, J. Nachtman, C.R. Newsom, E. Norbeck, J. Olson, Y. Onel, F. Ozok, S. Sen, J. Wetzel, T. Yetkin, K. Yi Johns Hopkins University, Baltimore, USA B.A. Barnett, B. Blumenfeld, A. Bonato, C. Eskew, D. Fehling, G. Giurgiu, A.V. Gritsan, Z.J. Guo, G. Hu, P. Maksimovic, S. Rappoccio, M. Swartz, N.V. Tran, A. Whitbeck The University of Kansas, Lawrence, USA P. Baringer, A. Bean, G. Benelli, O. Grachov, R.P. Kenny Iii, M. Murray, D. Noonan, S. Sanders, J.S. Wood, V. Zhukova Kansas State University, Manhattan, USA A.f. Barfuss, T. Bolton, I. Chakaberia, A. Ivanov, S. Khalil, M. Makouski, Y. Maravin, S. Shrestha, I. Svintradze, Z. Wan Lawrence Livermore National Laboratory, Livermore, USA J. Gronberg, D. Lange, D. Wright University of Maryland, College Park, USA A. Baden, M. Boutemeur, S.C. Eno, D. Ferencek, J.A. Gomez, N.J. Hadley, R.G. Kellogg, M. Kirn, 32 A The CMS Collaboration Y. Lu, A.C. Mignerey, K. Rossato, P. Rumerio, F. Santanastasio, A. Skuja, J. Temple, M.B. Tonjes, S.C. Tonwar, E. Twedt Massachusetts Institute of Technology, Cambridge, USA B. Alver, G. Bauer, J. Bendavid, W. Busza, E. Butz, I.A. Cali, M. Chan, V. Dutta, P. Everaerts, G. Gomez Ceballos, M. Goncharov, K.A. Hahn, P. Harris, Y. Kim, M. Klute, Y.-J. Lee, W. Li, C. Loizides, P.D. Luckey, T. Ma, S. Nahn, C. Paus, D. Ralph, C. Roland, G. Roland, M. Rudolph, G.S.F. Stephans, F. St¨ ockli, K. Sumorok, K. Sung, E.A. Wenger, S. Xie, M. Yang, Y. Yilmaz, A.S. Yoon, M. Zanetti University of Minnesota, Minneapolis, USA S.I. Cooper, P. Cushman, B. Dahmes, A. De Benedetti, P.R. Dudero, G. Franzoni, J. Haupt, K. Klapoetke, Y. Kubota, J. Mans, V. Rekovic, R. Rusack, M. Sasseville, A. Singovsky University of Mississippi, University, USA L.M. Cremaldi, R. Godang, R. Kroeger, L. Perera, R. Rahmat, D.A. Sanders, D. Summers University of Nebraska-Lincoln, Lincoln, USA K. Bloom, S. Bose, J. Butt, D.R. Claes, A. Dominguez, M. Eads, J. Keller, T. Kelly, I. Kravchenko, J. Lazo-Flores, H. Malbouisson, S. Malik, G.R. Snow State University of New York at Buffalo, Buffalo, USA U. Baur, A. Godshalk, I. Iashvili, S. Jain, A. Kharchilava, A. Kumar, S.P. Shipkowski, K. Smith Northeastern University, Boston, USA G. Alverson, E. Barberis, D. Baumgartel, O. Boeriu, M. Chasco, S. Reucroft, J. Swain, D. Trocino, D. Wood, J. Zhang Northwestern University, Evanston, USA A. Anastassov, A. Kubik, N. Odell, R.A. Ofierzynski, B. Pollack, A. Pozdnyakov, M. Schmitt, S. Stoynev, M. Velasco, S. Won University of Notre Dame, Notre Dame, USA L. Antonelli, D. Berry, M. Hildreth, C. Jessop, D.J. Karmgard, J. Kolb, T. Kolberg, K. Lannon, W. Luo, S. Lynch, N. Marinelli, D.M. Morse, T. Pearson, R. Ruchti, J. Slaunwhite, N. Valls, M. Wayne, J. Ziegler The Ohio State University, Columbus, USA B. Bylsma, L.S. Durkin, J. Gu, C. Hill, P. Killewald, K. Kotov, T.Y. Ling, M. Rodenburg, G. Williams Princeton University, Princeton, USA N. Adam, E. Berry, P. Elmer, D. Gerbaudo, V. Halyo, P. Hebda, A. Hunt, J. Jones, E. Laird, D. Lopes Pegna, D. Marlow, T. Medvedeva, M. Mooney, J. Olsen, P. Pirou´ e, X. Quan, H. Saka, D. Stickland, C. Tully, J.S. Werner, A. Zuranski University of Puerto Rico, Mayaguez, USA J.G. Acosta, X.T. Huang, A. Lopez, H. Mendez, S. Oliveros, J.E. Ramirez Vargas, A. Zatserklyaniy Purdue University, West Lafayette, USA E. Alagoz, V.E. Barnes, G. Bolla, L. Borrello, D. Bortoletto, A. Everett, A.F. Garfinkel, L. Gutay, Z. Hu, M. Jones, O. Koybasi, M. Kress, A.T. Laasanen, N. Leonardo, C. Liu, V. Maroussov, P. Merkel, D.H. Miller, N. Neumeister, I. Shipsey, D. Silvers, A. Svyatkovskiy, H.D. Yoo, J. Zablocki, Y. Zheng 33 Purdue University Calumet, Hammond, USA P. Jindal, N. Parashar Rice University, Houston, USA C. Boulahouache, V. Cuplov, K.M. Ecklund, F.J.M. Geurts, B.P. Padley, R. Redjimi, J. Roberts, J. Zabel University of Rochester, Rochester, USA B. Betchart, A. Bodek, Y.S. Chung, R. Covarelli, P. de Barbaro, R. Demina, Y. Eshaq, H. Flacher, A. Garcia-Bellido, P. Goldenzweig, Y. Gotra, J. Han, A. Harel, D.C. Miner, D. Orbaker, G. Petrillo, D. Vishnevskiy, M. Zielinski The Rockefeller University, New York, USA A. Bhatti, R. Ciesielski, L. Demortier, K. Goulianos, G. Lungu, S. Malik, C. Mesropian, M. Yan Rutgers, the State University of New Jersey, Piscataway, USA O. Atramentov, A. Barker, D. Duggan, Y. Gershtein, R. Gray, E. Halkiadakis, D. Hidas, D. Hits, A. Lath, S. Panwalkar, R. Patel, A. Richards, K. Rose, S. Schnetzer, S. Somalwar, R. Stone, S. Thomas University of Tennessee, Knoxville, USA G. Cerizza, M. Hollingsworth, S. Spanier, Z.C. Yang, A. York Texas A&M University, College Station, USA R. Eusebi, J. Gilmore, A. Gurrola, T. Kamon, V. Khotilovich, R. Montalvo, I. Osipenkov, Y. Pakhotin, J. Pivarski, A. Safonov, S. Sengupta, A. Tatarinov, D. Toback, M. Weinberger Texas Tech University, Lubbock, USA N. Akchurin, C. Bardak, J. Damgov, C. Jeong, K. Kovitanggoon, S.W. Lee, P. Mane, Y. Roh, A. Sill, I. Volobouev, R. Wigmans, E. Yazgan Vanderbilt University, Nashville, USA E. Appelt, E. Brownson, D. Engh, C. Florez, W. Gabella, M. Issah, W. Johns, P. Kurt, C. Maguire, A. Melo, P. Sheldon, B. Snook, S. Tuo, J. Velkovska University of Virginia, Charlottesville, USA M.W. Arenton, M. Balazs, S. Boutle, B. Cox, B. Francis, R. Hirosky, A. Ledovskoy, C. Lin, C. Neu, R. Yohay Wayne State University, Detroit, USA S. Gollapinni, R. Harr, P.E. Karchin, P. Lamichhane, M. Mattson, C. Milst` ene, A. Sakharov University of Wisconsin, Madison, USA M. Anderson, M. Bachtis, J.N. Bellinger, D. Carlsmith, S. Dasu, J. Efron, K. Flood, L. Gray, K.S. Grogg, M. Grothe, R. Hall-Wilton, M. Herndon, P. Klabbers, J. Klukas, A. Lanaro, C. Lazaridis, J. Leonard, R. Loveless, A. Mohapatra, F. Palmonari, D. Reeder, I. Ross, A. Savin, W.H. Smith, J. Swanson, M. Weinberg †: Deceased 1: Also at CERN, European Organization for Nuclear Research, Geneva, Switzerland 2: Also at Universidade Federal do ABC, Santo Andre, Brazil 3: Also at Laboratoire Leprince-Ringuet, Ecole Polytechnique, IN2P3-CNRS, Palaiseau, France 4: Also at Suez Canal University, Suez, Egypt 5: Also at British University, Cairo, Egypt 6: Also at Fayoum University, El-Fayoum, Egypt 34 A The CMS Collaboration 7: Also at Soltan Institute for Nuclear Studies, Warsaw, Poland 8: Also at Massachusetts Institute of Technology, Cambridge, USA 9: Also at Universit´ e de Haute-Alsace, Mulhouse, France 10: Also at Brandenburg University of Technology, Cottbus, Germany 11: Also at Moscow State University, Moscow, Russia 12: Also at Institute of Nuclear Research ATOMKI, Debrecen, Hungary 13: Also at E¨ otv¨ os Lor´ and University, Budapest, Hungary 14: Also at Tata Institute of Fundamental Research - HECR, Mumbai, India 15: Also at University of Visva-Bharati, Santiniketan, India 16: Also at Sharif University of Technology, Tehran, Iran 17: Also at Shiraz University, Shiraz, Iran 18: Also at Isfahan University of Technology, Isfahan, Iran 19: Also at Facolt` a Ingegneria Universit` a di Roma ”La Sapienza”, Roma, Italy 20: Also at Universit` a della Basilicata, Potenza, Italy 21: Also at Laboratori Nazionali di Legnaro dell’ INFN, Legnaro, Italy 22: Also at Universit` a degli studi di Siena, Siena, Italy 23: Also at California Institute of Technology, Pasadena, USA 24: Also at Faculty of Physics of University of Belgrade, Belgrade, Serbia 25: Also at University of California, Los Angeles, Los Angeles, USA 26: Also at University of Florida, Gainesville, USA 27: Also at Universit´ e de Gen` eve, Geneva, Switzerland 28: Also at Scuola Normale e Sezione dell’ INFN, Pisa, Italy 29: Also at University of Athens, Athens, Greece 30: Also at The University of Kansas, Lawrence, USA 31: Also at Institute for Theoretical and Experimental Physics, Moscow, Russia 32: Also at Paul Scherrer Institut, Villigen, Switzerland 33: Also at University of Belgrade, Faculty of Physics and Vinca Institute of Nuclear Sciences, Belgrade, Serbia 34: Also at Gaziosmanpasa University, Tokat, Turkey 35: Also at Adiyaman University, Adiyaman, Turkey 36: Also at Mersin University, Mersin, Turkey 37: Also at Izmir Institute of Technology, Izmir, Turkey 38: Also at Kafkas University, Kars, Turkey 39: Also at Suleyman Demirel University, Isparta, Turkey 40: Also at Ege University, Izmir, Turkey 41: Also at Rutherford Appleton Laboratory, Didcot, United Kingdom 42: Also at School of Physics and Astronomy, University of Southampton, Southampton, United Kingdom 43: Also at INFN Sezione di Perugia; Universit` a di Perugia, Perugia, Italy 44: Also at Utah Valley University, Orem, USA 45: Also at Institute for Nuclear Research, Moscow, Russia 46: Also at Los Alamos National Laboratory, Los Alamos, USA 47: Also at Erzincan University, Erzincan, Turkey