Measurement of double-differential cross sections for top quark pair production in pp collisions at \(\sqrt{s} = 8\) \(\,\text {TeV}\) and impact on parton distribution functions

The European Physical Journal C, Jul 2017

Normalized double-differential cross sections for top quark pair (\(\mathrm{t}\overline{\mathrm{t}}\)) production are measured in pp collisions at a centre-of-mass energy of 8\(\,\text {TeV}\) with the CMS experiment at the LHC. The analyzed data correspond to an integrated luminosity of 19.7\(\,\text {fb}^{-1}\). The measurement is performed in the dilepton \(\mathrm {e}^{\pm }\mu ^{\mp }\) final state. The \(\mathrm{t}\overline{\mathrm{t}}\) cross section is determined as a function of various pairs of observables characterizing the kinematics of the top quark and \(\mathrm{t}\overline{\mathrm{t}}\) system. The data are compared to calculations using perturbative quantum chromodynamics at next-to-leading and approximate next-to-next-to-leading orders. They are also compared to predictions of Monte Carlo event generators that complement fixed-order computations with parton showers, hadronization, and multiple-parton interactions. Overall agreement is observed with the predictions, which is improved when the latest global sets of proton parton distribution functions are used. The inclusion of the measured \(\mathrm{t}\overline{\mathrm{t}}\) cross sections in a fit of parametrized parton distribution functions is shown to have significant impact on the gluon distribution.

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Measurement of double-differential cross sections for top quark pair production in pp collisions at \(\sqrt{s} = 8\) \(\,\text {TeV}\) and impact on parton distribution functions

Eur. Phys. J. C Measurement of double-differential cross sections for top quark √ pair production in pp collisions at s = 8 TeV and impact on parton distribution functions CMS Collaboration 0 1 3 0 CERN , 1211 Geneva 23 , Switzerland 1 Faculty of Physics, Institute of Experimental Physics, University of Warsaw , Warsaw , Poland K. Bunkowski, A. Byszuk 2 , K. Doroba , A. Kalinowski, M. Konecki, J. Krolikowski, M. Misiura, M. Olszewski, A. Pyskir, M. Walczak 3 48: Also at Institute for Theoretical and Experimental Physics, Moscow, Russia 49: Also at Albert Einstein Center for Fundamental Physics, Bern, Switzerland 50: Also at Adiyaman University , Adiyaman , Turkey 51: Also at Istanbul Aydin University , Istanbul , Turkey 52: Also at Mersin University , Mersin , Turkey 53: Also at Cag University , Mersin , Turkey 54: Also at Piri Reis University , Istanbul , Turkey 55: Also at Gaziosmanpasa University , Tokat , Turkey 56: Also at Ozyegin University , Istanbul , Turkey 57: Also at Izmir Institute of Technology, Izmir, Turkey 58: Also at Marmara University , Istanbul , Turkey 59: Also at Kafkas University , Kars , Turkey 60: Also at Istanbul Bilgi University , Istanbul , Turkey 61: Also at Yildiz Technical University , Istanbul , Turkey 62: Also at Hacettepe University , Ankara , Turkey 63: Also at Rutherford Appleton Laboratory, Didcot, UK 64: Also at School of Physics and Astronomy, University of Southampton, Southampton, UK 65: Also at Instituto de Astrofísica de Canarias, La Laguna, Spain 66: Also at Utah Valley University , Orem , USA 67 : Also at BEYKENT UNIVERSITY, Istanbul, Turkey 68: Also at Erzincan University , Erzincan , Turkey 69: Also at Mimar Sinan University , Istanbul, Istanbul , Turkey 70: Also at Texas A&M University at Qatar, Doha, Qatar 71: Also at Kyungpook National University , Taegu , Korea Normalized double-differential cross sections for top quark pair (tt) production are measured in pp collisions at a centre-of-mass energy of 8 TeV with the CMS experiment at the LHC. The analyzed data correspond to an integrated luminosity of 19.7 fb−1. The measurement is performed in the dilepton e±μ∓ final state. The tt cross section is determined as a function of various pairs of observables characterizing the kinematics of the top quark and tt system. The data are compared to calculations using perturbative quantum chromodynamics at next-to-leading and approximate nextto-next-to-leading orders. They are also compared to predictions of Monte Carlo event generators that complement fixed-order computations with parton showers, hadronization, and multiple-parton interactions. Overall agreement is observed with the predictions, which is improved when the latest global sets of proton parton distribution functions are used. The inclusion of the measured tt cross sections in a fit of parametrized parton distribution functions is shown to have significant impact on the gluon distribution. - 1 Introduction Understanding the production and properties of the top quark, discovered in 1995 at the Fermilab Tevatron [ 1,2 ], is fundamental in testing the standard model and searching for new phenomena. A large sample of proton–proton (pp) collision events containing a top quark pair (tt) has been recorded at the CERN LHC, facilitating precise top quark measurements. In particular, precise measurements of the tt production cross section as a function of tt kinematic observables have become possible, which allow for the validation of the most-recent predictions of perturbative quantum chromodynamics (QCD). At the LHC, top quarks are predominantly produced via gluon–gluon fusion. Thus, using measurements of the production cross section in a global fit of the parton distribution functions (PDFs) can help to better determine the gluon distribution at large values of x , where x is the fraction of the proton momentum carried by a parton [ 3–5 ]. In this context, tt measurements are complementary to studies [ 6– 8 ] that exploit inclusive jet production cross sections at the LHC. Normalized differential cross sections for tt production have been measured previously in proton–antiproton collisions at the Tevatron at a centre-of-mass energy of 1.96 TeV [ 9,10 ] and in pp collisions at the LHC at √s = 7 TeV [ 11– 14 ], 8 TeV [ 14–16 ], and 13 TeV [ 17 ]. This paper presents the measurement of the normalized double-differential tt + X production cross section, where X is inclusive in the number of extra jets in the event but excludes tt +Z/W/γ production. The cross section is measured as a function of observables describing the kinematics of the top quark and tt: the transverse momentum of the top quark, pT(t), the rapidity of the top quark, y(t), the transverse momentum, pT(tt), the rapidity, y(tt), and the invariant mass, M (tt), of tt, the pseudorapidity between the top quark and antiquark, Δη(t, t), and the angle between the top quark and antiquark in the transverse plane, Δφ (t, t). In total, the double-differential tt cross section is measured as a function of six different pairs of kinematic variables. These measurements provide a sensitive test of the standard model by probing the details of the tt production dynamics. The double-differential measurement is expected to impose stronger constraints on the gluon distribution than single-differential measurements owing to the improved resolution of the momentum fractions carried by the two incoming partons. The analysis uses the data recorded at √s = 8 TeV by the CMS experiment in 2012, corresponding to an integrated luminosity of 19.7 ± 0.5 fb−1. The measurement is performed using the e±μ∓ decay mode (eμ) of tt, requiring two oppositely charged leptons and at least two jets. The analysis largely follows the procedures of the single-differential tt cross section measurement [ 15 ]. The restriction to the eμ channel provides a pure tt event sample because of the negligible contamination from Z/γ ∗ processes with same-flavour leptons in the final state. The measurements are defined at parton level and thus are corrected for the effects of hadronization and detector resolutions and inefficiencies. A regularized unfolding process is performed simultaneously in bins of the two variables in which the cross sections are measured. The normalized differential tt cross section is determined by dividing by the measured total inclusive tt production cross section, where the latter is evaluated by integrating over all bins in the two observables. The parton level results are compared to different theoretical predictions from leading-order (LO) and next-to-leading-order (NLO) Monte Carlo (MC) event generators, as well as with fixed-order NLO [ 18 ] and approximate next-to-next-to-leading-order (NNLO) [ 19 ] calculations using several different PDF sets. Parametrized PDFs are fitted to the data in a procedure that is referred to as the PDF fit. The structure of the paper is as follows: in Sect. 2 a brief description of the CMS detector is given. Details of the event simulation are provided in Sect. 3. The event selection, kinematic reconstruction, and comparisons between data and simulation are provided in Sect. 4. The two-dimensional unfolding procedure is detailed in Sect. 5; the method to determine the double-differential cross sections is presented in Sect. 6, and the assessment of the systematic uncertainties is described in Sect. 7. The results of the measurement are discussed and compared to theoretical predictions in Sect. 8. Section 9 presents the PDF fit. Finally, Sect. 10 provides a summary. 2 The CMS detector The central feature of the CMS apparatus is a superconducting solenoid of 13 m length and 6 m inner diameter, which provides an axial magnetic field of 3.8 T. Within the field volume are a silicon pixel and strip tracker, a lead tungstate crystal electromagnetic calorimeter (ECAL), and a brass and scintillator hadron calorimeter (HCAL), each composed of a barrel and two endcap sections. Extensive forward calorimetry complements the coverage provided by the barrel and endcap sections up to |η| < 5.2. Charged particle trajectories are measured by the inner tracking system, covering a range of |η| < 2.5. The ECAL and HCAL surround the tracking volume, providing high-resolution energy and direction measurements of electrons, photons, and hadronic jets up to |η| < 3. Muons are measured in gas-ionization detectors embedded in the steel flux-return yoke outside the solenoid covering the region |η| < 2.4. The detector is nearly hermetic, allowing momentum balance measurements in the plane transverse to the beam directions. A more detailed description of the CMS detector, together with a definition of the coordinate system and the relevant kinematic variables, can be found in Ref. [ 20 ]. 3 Signal and background modelling The tt signal process is simulated using the matrix element event generator MadGraph (version 5.1.5.11) [ 21 ], together with the MadSpin [ 22 ] package for the modelling of spin correlations. The pythia6 program (version 6.426) [ 23 ] is used to model parton showering and hadronization. In the signal simulation, the mass of the top quark, mt, is fixed to 172.5 GeV. The proton structure is described by the CTEQ6L1 PDF set [ 24 ]. The same programs are used to model dependencies on the renormalization and factorization scales, μr and μf , respectively, the matching threshold between jets produced at the matrix-element level and via parton showering, and mt. The cross sections obtained in this paper are also compared to theoretical calculations obtained with the NLO event generators powheg (version 1.0 r1380) [ 25–27 ], interfaced with pythia6 or Herwig6 (version 6.520) [ 28 ] for the subsequent parton showering and hadronization, and mc@nlo (version 3.41) [ 29 ], interfaced with herwig. Both pythia6 and herwig6 include a modelling of multipleparton interactions and the underlying event. The pythia6 Z2* tune [ 30 ] is used to characterize the underlying event in both the tt and the background simulations. The herwig6 AUET2 tune [ 31 ] is used to model the underlying event in the powheg+herwig6 simulation, while the default tune is used in the mc@nlo+herwig6 simulation. The PDF sets CT10 [ 32 ] and CTEQ6M [ 24 ] are used for powheg and mc@nlo, respectively. Additional simulated event samples generated with powheg and interfaced with pythia6 or herwig6 are used to assess the systematic uncertainties related to the modelling of the hard-scattering process and hadronization, respectively, as described in Sect. 7. The production of W and Z/γ ∗ bosons with additional jets, respectively referred to as W+jets and Z/γ ∗+jets in the following, and tt + Z/W/γ backgrounds are simulated using MadGraph, while W boson plus associated single top quark production (tW) is simulated using powheg. The showering and hadronization is modelled with pythia6 for these processes. Diboson (WW, WZ, and ZZ) samples, as well as QCD multijet backgrounds, are produced with pythia6. All of the background simulations are normalized to the fixedorder theoretical predictions as described in Ref. [ 15 ]. The CMS detector response is simulated using Geant4 (version 9.4) [ 33 ]. 4 Event selection The event selection follows closely the one reported in Ref. [ 15 ]. The top quark decays almost exclusively into a W boson and a bottom quark, and only events in which the two W bosons decay into exactly one electron and one muon and corresponding neutrinos are considered. Events are triggered by requiring one electron and one muon of opposite charge, one of which is required to have pT > 17 GeV and the other pT > 8 GeV. Events are reconstructed using a particle-flow (PF) technique [ 34, 35 ], which combines signals from all subdetectors to enhance the reconstruction and identification of the individual particles observed in pp collisions. An interaction vertex [36] is required within 24 cm of the detector centre along the beam line direction, and within 2 cm of the beam line in the transverse plane. Among all such vertices, the primary vertex of an event is identified as the one with the largest value of the sum of the pT2 of the associated tracks. Charged hadrons from pileup events, i.e. those originating from additional pp interactions within the same or nearby bunch crossing, are subtracted on an event-by-event basis. Subsequently, the remaining neutral-hadron component from pileup is accounted for through jet energy corrections [ 37 ]. Electron candidates are reconstructed from a combination of the track momentum at the primary vertex, the corresponding energy deposition in the ECAL, and the energy sum of all bremsstrahlung photons associated with the track [ 38 ]. Muon candidates are reconstructed using the track information from the silicon tracker and the muon system. An event is required to contain at least two oppositely charged leptons, one electron and one muon, each with pT > 20 GeV and |η| < 2.4. Only the electron and the muon with the highest pT are considered for the analysis. The invariant mass of the selected electron and muon must be larger than 20 GeV to suppress events from decays of heavy-flavour resonances. The leptons are required to be isolated with Irel ≤ 0.15 inside a cone in ηφ space of Δ R = (Δη)2 + (Δφ)2 = 0.3 around the lepton track, where Δη and Δφ are the differences in pseudorapidity and azimuthal angle (in radians), respectively, between the directions of the lepton and any other particle. The parameter Irel is the relative isolation parameter defined as the sum of transverse energy deposits inside the cone from charged and neutral hadrons, and photons, relative to the lepton pT, corrected for pileup effects. The efficiencies of the lepton isolation were determined in Z boson data samples using the “tag-and-probe” method of Ref. [ 39 ], and are found to be well described by the simulation for both electrons and muons. The overall difference between data and simulation is estimated to be <2% for electrons, and <1% for muons. The simulation is adjusted for this by using correction factors parametrized as a function of the lepton pT and η and applied to simulated events, separately for electrons and muons. Jets are reconstructed by clustering the PF candidates using the anti-kT clustering algorithm [ 40, 41 ] with a distance parameter R = 0.5. Electrons and muons passing less-stringent selections on lepton kinematic quantities and isolation, relative to those specified above, are identified but excluded from clustering. A jet is selected if it has pT > 30 GeV and |η| < 2.4. Jets originating from the hadronization of b quarks (b jets) are identified using an algorithm [42] that provides a b tagging discriminant by combining secondary vertices and track-based lifetime information. This provides a b tagging efficiency of ≈80–85% for b jets and a mistagging efficiency of ≈10% for jets originating from gluons, as well as u, d, or s quarks, and ≈30–40% for jets originating from c quarks [ 42 ]. Events are selected if they contain at least two jets, and at least one of these jets is b-tagged. These requirements are chosen to reduce the background contribution while keeping a large fraction of the tt signal. The b tagging efficiency is adjusted in the simulation with the correction factors parametrized as a function of the jet pT and η. The missing transverse momentum vector is defined as the projection on the plane perpendicular to the beams of the negative vector sum of the momenta of all PF particles in an event [ 43 ]. Its magnitude is referred to as pmiss. To mitigate T the pileup effects on the pmiss resolution, a multivariate cor T rection is used where the measured momentum is separated into components that originate from the primary and from other interaction vertices [ 44 ]. No selection requirement on pmiss is applied. T The tt kinematic properties are determined from the four-momenta of the decay products using the same kinematic reconstruction method [ 45, 46 ] as that of the singledifferential tt measurement [15]. The six unknown quantities are the three-momenta of the two neutrinos, which are reconstructed by imposing the following six kinematic constraints: pT conservation in the event and the masses of the W bosons, top quark, and top antiquark. The top quark and antiquark are required to have a mass of 172.5 GeV. It is assumed that the pmiss in the event results from the two T neutrinos in the top quark and antiquark decay chains. To resolve the ambiguity due to multiple algebraic solutions of the equations for the neutrino momenta, the solution with the smallest invariant mass of the tt system is taken. The reconstruction is performed 100 times, each time randomly smearing the measured energies and directions of the reconstructed leptons and jets within their resolution. This smearing recovers events that yielded no solution because of measurement fluctuations. The three-momenta of the two neutrinos are determined as a weighted average over all the smeared solutions. For each solution, the weight is calculated based on the expected invariant mass spectrum of a lepton and a bottom jet as the product of two weights for the top quark and antiquark decay chains. All possible lepton– jet combinations in the event are considered. Combinations are ranked based on the presence of b-tagged jets in the assignments, i.e. a combination with both leptons assigned to b-tagged jets is preferred over those with one or no btagged jet. Among assignments with equal number of btagged jets, the one with the highest average weight is chosen. Events with no solution after smearing are discarded. The method yields an average reconstruction efficiency of ≈95%, which is determined in simulation as the fraction of selected signal events (which include only direct tt decays via the e±μ∓ channel, i.e. excluding cascade decays via τ leptons) passing the kinematic reconstruction. The overall difference in this efficiency between data and simulation is estimated to be ≈1%, and a corresponding correction factor is applied to the simulation [ 47 ]. A more detailed description of the kinematic reconstruction procedure can be found in Ref. [ 47 ]. In total, 38, 569 events are selected in the data. The signal contribution to the event sample is 79.2%, as estimated from the simulation. The remaining fraction of events is dominated by tt decays other than via the e±μ∓ channel (14.2%). Other sources of background are single top quark production (3.6%), Z/γ ∗+jets events (1.4%), associated tt +Z/W/γ production (1.1%), and a negligible (<0.5%) fraction of diboson, W+jets, and QCD multijet events. Figure 1 shows the distributions of the reconstructed top quark and tt kinematic variables. In general, the data are reasonably well described by the simulation, however some trends are visible. In particular, the simulation shows a harder pT(t) spectrum than the data, as observed in previous measurements [ 12–17 ]. The y(tt) distribution is found to be less central in the simulation than in the data, while an opposite behavior is observed in the y(t) distribution. The M (tt) and pT(tt) distributions are overall well described by the simulation. 5 Signal extraction and unfolding The number of signal events, N sig, is extracted from the data i in the i th bin of the reconstructed observables using Nisig = Nisel − Nibkg, 1 ≤ i ≤ n, (1) where n denotes the total number of bins, N sel is the number i of selected events in the i th bin, and N bkg corresponds to the i expected number of background events in this bin, except for tt final states other than the signal. The latter are dominated by events in which one or both of the intermediate W bosons decay into τ leptons with subsequent decay into an electron or muon. Since these events arise from the same tt production process as the signal, the normalisation of this background is fixed to that of the signal. The expected signal fraction is defined as the ratio of the number of selected tt signal events to the total number of selected tt events (i.e. the signal and all other tt events) in simulation. This procedure avoids the dependence on the total inclusive tt cross section used in the normalization of the simulated signal sample. The signal yields N sig, determined in each i th bin of the i reconstructed kinematic variables, may contain entries that were originally produced in other bins and have migrated because of the imperfect resolutions. This effect can be described as M sig i = m where m denotes the total number of bins in the true distribution, and M ujnf is the number of events in the j th bin of the true distribution from data. The quantity M sig is the i expected number of events at detector level in the i th bin, and Ai j is a matrix of probabilities describing the migrations from the j th bin of the true distribution to the i th bin of the detector-level distribution, including acceptance and detector efficiencies. In this analysis, the migration matrix Ai j is defined such that the true level corresponds to the full phase space (with no kinematic restrictions) for tt production at parton level. At the detector level a binning is chosen in the same kinematic ranges as at the true level, but with the total number of bins typically a few times larger. The kinematic ranges of all variables are chosen such that the fraction of events that migrate into the regions outside the measured range is very small. It was checked that the inclusion of overflow bins outside the kinematic ranges does not significantly alter the unfolded results. The migration matrix Ai j is taken from the signal simulation. The observed event counts N sig may be different from M sig owing to statistical i i fluctuations. The estimated value of M ujnf , designated as Mˆ j unf , is found using the TUnfold algorithm [ 48 ]. The unfolding of multidimensional distributions is performed by mapping the multidimensional arrays to one-dimensional arrays internally [ 48 ]. The unfolding is realized by a χ 2 minimization and includes an additional χ 2 term representing the Tikhonov regularization [ 49 ]. The regularization reduces the effect of the statistical fluctuations present in N sig on the high-frequency content of Mˆ j unf . The regulariziation strength is chosen such that the global correlation coefficient is minimal [ 50 ]. For the measurements presented here, this choice results in a small contribution from the regularization term to the total χ 2, on the order of 1%. A more detailed description of the unfolding procedure can be found in Ref. [ 47 ]. Fig. 1 Distributions of pT(t) (upper left), y(t) (upper right), pT(tt) (middle left), y(tt) (middle right), and M (tt) (lower) in selected events after the kinematic reconstruction. The experimental data with the vertical bars corresponding to their statistical uncertainties are plotted together with distributions of simulated signal and different background processes. The hatched regions correspond to the shape uncertainties in the signal and backgrounds (cf. Sect. 7). The lower panel in each plot shows the ratio of the observed data event yields to those expected in the simulation eV8000 0G7000 3 / 6000 s t n 5000 e vE4000 3000 2000 1000 1.5 0.5 taa C 1 D M e G 5 /2 104 s t n e vE 103 102 Data tt signal tt other Single t Diboson Z / γ* → ττ Z / γ* → ee/μμ a ta C 1 D M 19.7 fb-1 (8 TeV) Data tt signal tt other Single t Diboson Z / γ* → ττ Z / γ* →ee/μμ W+jets QCD multijets tt+Z/W/γ Uncertainty 400 600 800 1000 1200 1400 M(tt) [GeV] 6 Cross section determination The normalized double-differential cross sections of tt production are measured in the full tt kinematic phase space at parton level. The number of unfolded signal events Mˆ iujnf in bin i of variable x and bin j of variable y is used to define the normalized double-differential cross sections of the tt production process, 1 d2σ σ dx d y i j = σ Δxi Δy j B L 1 1 1 , (3) where σ is the total cross section, which is evaluated by integrating (d2σ/dx d y)i j over all bins. The branching fraction of tt into eμ final state is taken to be B = 2.3% [ 51 ], and L is the integrated luminosity of the data sample. The bin widths of the x and y variables are denoted by Δxi and Δy j , respectively. The bin widths are chosen based on the resolution, such that the purity and the stability of each bin is generally above 30%. For a given bin, the purity is defined as the fraction of events in the tt signal simulation that are generated and reconstructed in the same bin with respect to the total number of events reconstructed in that bin. To evaluate the stability, the number of events in the tt signal simulation that are generated and reconstructed in a given bin are divided by the total number of reconstructed events generated in the bin. 7 Systematic uncertainties The measurement is affected by systematic uncertainties that originate from detector effects and from the modelling of the processes. Each source of systematic uncertainty is assessed individually by changing in the simulation the corresponding efficiency, resolution, or scale by its uncertainty, using a prescription similar to the one followed in Ref. [ 15 ]. For each change made, the cross section determination is repeated, and the difference with respect to the nominal result in each bin is taken as the systematic uncertainty. To account for the pileup uncertainty, the value of the total pp inelastic cross section, which is used to estimate the mean number of additional pp interactions, is varied by ±5% [ 52 ]. The data-to-simulation correction factors for b tagging and mistagging efficiencies are varied within their uncertainties [ 42 ] as a function of the pT and |η| of the jet, following the procedure described in Ref. [ 15 ]. The datato-simulation correction factors for the trigger efficiency, determined relatively to the triggers based on pmiss, are varT ied within their uncertainty of 1%. The systematic uncertainty related to the kinematic reconstruction of top quarks is assessed by varying the MC correction factor by its estimated uncertainty of ±1% [ 47 ]. For the uncertainties related to the jet energy scale, the jet energy is varied in the simulation within its uncertainty [ 53 ]. The uncertainty owing to the limited knowledge of the jet energy resolution is determined by changing the latter in the simulation by ±1 standard deviation in different η regions [ 54 ]. The normalizations of the background processes are varied by 30% to account for the corresponding uncertainty. The uncertainty in the integrated luminosity of 2.6% [ 55 ] is propagated to the measured cross sections. The impact of theoretical assumptions on the measurement is determined by repeating the analysis replacing the standard MadGraph tt simulation with simulated samples in which specific parameters or assumptions are altered. The PDF systematic uncertainty is estimated by reweighting the MadGraph tt signal sample according to the uncertainties in the CT10 PDF set, evaluated at 90% confidence level (CL) [ 32 ], and then rescaled to 68% CL. To estimate the uncertainty related to the choice of the tree-level multijet scattering model used in MadGraph, the results are recalculated using an alternative prescription for interfacing NLO calculations with parton showering as implemented in powheg. For μr and μf , two samples are used with the scales being simultaneously increased or decreased by a factor of two relative to their common nominal value μr = μf = √mt2 + pT2, where the sum is over all additional final-state partons in the matrix element. The effect of additional jet production is studied by varying in MadGraph the matching threshold between jets produced at the matrix-element level and via parton showering. The uncertainty in the effect of the initialand final-state radiation on the signal efficiency is covered by the uncertainty in μr and μf , as well as in the matching threshold. The samples generated with powheg+herwig6 and powheg+pythia6 are used to estimate the uncertainty related to the choice of the showering and hadronization model. The effect due to uncertainties in mt is estimated using simulations with altered top quark masses. The cross section differences observed for an mt variation of 1 GeV around the central value of 172.5 GeV used in the simulation is quoted as the uncertainty. The total systematic uncertainty is estimated by adding all the contributions described above in quadrature, separately for positive and negative cross section variations. If a systematic uncertainty results in two cross section variations of the same sign, the largest one is taken, while the opposite variation is set to zero. 8 Results Normalized differential tt cross sections are measured as a function of pairs of variables representing the kinematics of the top quark (only the top quark is taken and not the top antiquark, thus avoiding any double counting of events), and tt system, defined in Sect. 1: [ pT(t), y(t)], [y(t), M (tt)], [y(tt), M (tt)], [Δη(t, t), M (tt)], [ pT(tt), M (tt)], and [Δφ (t, t), M (tt)]. These pairs are chosen in order to obtain representative combinations that are sensitive to different aspects of the tt production dynamics, as will be discussed in the following. In general, the systematic uncertainties are of similar size to the statistical uncertainties. The dominant systematic uncertainties are those in the signal modelling, which also are affected by the statistical uncertainties in the simulated samples that are used for the evaluation of these uncertainties. The largest experimental systematic uncertainty is the jet energy scale. The measured double-differential normalized tt cross sections are compared in Figs. 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 and 13 to theoretical predictions obtained using different MC generators and fixed-order QCD calculations. The numerical values of the measured cross sections and their uncertainties are provided in Appendix A. 8.1 Comparison to MC models In Fig. 2, the pT(t) distribution is compared in different ranges of |y(t)| to predictions from MadGraph+pythia6, powheg+pythia6, powheg+herwig6, and mc@nlo+herwig6. The data distribution is softer than that of the MC expectation over almost the entire y(t) range, except at high |y(t)| values. The disagreement level is the strongest for MadGraph+pythia6, while powheg+herwig6 describes the data best. Figures 3 and 4 illustrate the distributions of |y(t)| and |y(tt)| in different M (tt) ranges compared to the same set Fig. 2 Comparison of the measured normalized tt double-differential cross section as a function of pT(t) in different |y(t)| ranges to MC predictions calculated using MadGraph+pythia6, powheg+pythia6, powheg+herwig6, and mc@nlo+herwig6. The inner vertical bars on the data points represent the statistical uncertainties and the full bars include also the systematic uncertainties added in quadrature. In the bottom panel, the ratios of the data and other simulations to the MadGraph +pythia6 (MG+P) predictions are shown Fig. 3 Comparison of the measured normalized tt double-differential cross section as a function of |y(t)| in different M(tt) ranges to MC predictions. Details can be found in the caption of Fig. 2 10-1 -1 ]V e G [ ) t ) ( t y 2 σt( t)(dT d dp 10-3 ) 1 tt( σ 10-5 +P 1.2 G oM 1 t ito 0.8 a R -1 ]V e G [ ) 2 σtt)( ttt)(dM10-3 d ( y d ) 1 tt( σ10-4 650<M(tt)<1500 GeV Data MADGRAPH+PYTHIA6 POWHEG+PYTHIA6 POWHEG+HERWIG6 MC@NLO+HERWIG6 1 2 1 2 1 2 1 CMS -1 ]eV 10-2 340 <M(tt)<400 GeV 400<M(tt)<500GeV G [ ) t 2 σt)t( tt)(dM10-3 d t( y d 1 tt( 10-4 ) σ 500<M(tt)<650GeV 1 2 1 2 1 2 1 CMS 10-5 10-5 P + 1.2 G oM 1 t io 0.8 t a R of MC models. While the agreement between the data and MC predictions is good in the lower ranges of M (tt), the simulation starts to deviate from the data at higher M (tt), where the predictions are more central than the data for y(t) and less central for y(tt). In Fig. 5, the Δη(t, t) distribution is compared in the same M (tt) ranges to the MC predictions. For all generators there is a discrepancy between the data and simulation for the medium M (tt) bins, where the predicted Δη(t, t) values are too low. The disagreement is the strongest for MadGraph+pythia6. Figures 6 and 7 illustrate the comparison of the distributions of pT(tt) and Δφ (t, t) in the same M (tt) ranges to the MC models. For the pT(tt) distribution (Fig. 6), which is sensitive to radiation, none of the MC generators provide a good description. The largest differences are observed between the data and powheg+pythia6 for the highest values of pT(tt), where the predictions lie above the data. For the Δφ (t, t) distribution (Fig. 7), all MC models describe the data reasonably well. In order to perform a quantitative comparison of the measured cross sections to all considered MC generators, χ 2 values are calculated as follows: χ 2 = RTN −1Cov−N1−1RN −1, (4) where RN −1 is the column vector of the residuals calculated as the difference of the measured cross sections and the corFig. 6 Comparison of the measured normalized tt double-differential cross section as a function of pT(tt) in different M(tt) ranges to MC predictions. Details can be found in the caption of Fig. 2 Fig. 7 Comparison of the measured normalized tt double-differential cross section as a function of Δφ (t, t) in different M(tt) ranges to MC predictions. Details can be found in the caption of Fig. 2 CMS responding predictions obtained by discarding one of the N bins, and CovN −1 is the (N −1)×(N −1) submatrix obtained from the full covariance matrix by discarding the corresponding row and column. The matrix Cov N −1 obtained in this way is invertible, while the original covariance matrix Cov is singular. This is because for normalized cross sections one loses one degree of freedom, as can be deduced from Eq. (3). The covariance matrix Cov is calculated as: Cov = Covunf + Covsyst, (5) where Covunf and Covsyst are the covariance matrices accounting for the statistical uncertainties from the unfolding, and the systematic uncertainties, respectively. The systematic covariance matrix Covsyst is calculated as: Covisyjst = C j,k Ci,k k 1 + 2 C +j,k Ci+,k + C −j,k Ci−,k where Ci,k stands for the systematic uncertainty from source k in the i th bin, which consists of one variation only, and Ci+,k and Ci−,k stand for the positive and negative variations, respectively, of the systematic uncertainty due to source k in the i th bin. The sums run over all sources of the corresponding systematic uncertainties. All systematic uncertainties are treated as additive, i.e. the relative uncertainties are used to scale the corresponding measured value in the construction of Covsyst. This treatment is consistent with the cross section normalization. The cross section measurements for different pairs of observables are statistically and systematically correlated. No attempt is made to quantify the correlations between bins from different double-differential distributions. Thus, quantitative comparisons between theoretical predictions and the data can only be made for individual distributions. The obtained χ 2 values, together with the corresponding numbers of degrees of freedom (dof), are listed in Table 1. From these values one can conclude that none of the considered MC generators is able to correctly describe all distributions. In particular, for [Δη(t, t), M (tt)] and [ pT(tt), M (tt)], the χ 2 values are relatively large for all MC generators. The best agreement with the data is provided by powheg+herwig6. 8.2 Comparison to fixed-order calculations Fixed-order theoretical calculations for fully differential cross sections in inclusive tt production are publicly available at NLO O (αs3) in the fixed-flavour number scheme [ 18 ], where αs is the strong coupling strength. The exact fully differential NNLO O (αs4) calculations for tt production have recently appeared in the literature [ 56, 57 ], but are not yet publicly available. For higher orders, the cross sections as functions of single-particle kinematic variables have been calculated at approximate NNLO O (αs4) [19] and next-tonext-to-next-to-leading-order O (αs5) [ 58 ], using methods of threshold resummation beyond the leading-logarithmic accuracy. The measured cross sections are compared with NLO QCD predictions based on several PDF sets. The predictions are calculated using the mcfm program (version 6.8) [ 59 ] and a number of the latest PDF sets, namely: ABM11 [ 60 ], CJ15 [ 61 ], CT14 [ 62 ], HERAPDF2.0 [ 63 ], JR14 [ 64 ], MMHT2014 [ 65 ], and NNPDF3.0 [ 66 ], available via the lhapdf interface (version 6.1.5) [ 67 ]. The number of active flavours is set to n f = 5 and the top quark pole mass mt = 172.5 GeV is used. The effect of using n f = 6 in the PDF evolution, i.e. treating the top quark as a massless parton above threshold (as was done, e.g. in HERAPDF2.0 [ 63 ]), has been checked and the differences were found to be <0.1% (also see the corresponding discussion in Ref. [ 66 ]). The renormalization and factorization scales are chosen to be μr = μf = √mt2 + [ pT2(t) + pT2(t)]/2, whereas αs is set to the value used for the corresponding PDF extraction. The theoretical uncertainty is estimated by varying μr and μf independently up and down by a factor of 2, subject to the additional restriction that the ratio μr /μf be between 0.5 and 2 [ 68 ] (referred to hereafter as scale uncertainties). These uncertainties are supposed to estimate the missing higher-order corrections. The PDF uncertainties are taken into account in the theoretical predictions for each PDF set. The PDF uncertainties of CJ15 [ 61 ] and CT14 [ 62 ], evaluated at 90% CL, are rescaled to the 68% CL. The uncertainties in the normalized tt cross sections originating from αs and mt are found to be negligible (<1%) compared to the current data precision and thus are not considered. For the double-differential cross section as a function of pT(t) and y(t), approximate NNLO predictions [ 19 ] are obtained using the DiffTop program [ 4, 69, 70 ]. In this calculation, the scales are set to μr = μf = √mt2 + pT2(t) and NNLO variants of the PDF sets are used. For the ABM PDFs, the recent version ABM12 [ 71 ] is used, which is available only at NNLO. Predictions using DiffTop are not available for the rest of the measured cross sections that involve tt kinematic variables. A quantitative comparison of the measured doubledifferential cross sections to the theoretical predictions is performed by evaluating the χ 2 values, as described in Sect. 8.1. The results are listed in Tables 2 and 3 for the NLO and approximate NNLO calculations, respectively. For the NLO predictions, additional χ 2 values are reported including the corresponding PDF uncertainties, i.e. Eq. (5) becomes Cov = Covunf + Covsyst + CovPDF, where CovPDF is a covariance matrix that accounts for the PDF uncertainties. Theoretical uncertainties from scale variations are not included in this χ 2 calculation. The NLO predictions with recent global PDFs using LHC data, namely MMHT2014, CT14, and NNPDF3.0, are found to describe the pT(t), y(t), and y(tt) cross sections reasonably, as illustrated by the χ 2 values. The CJ15 PDF set also provides a good description of these cross sections, although it does not include LHC data [ 61 ]. The ABM11, JR14, and HERAPDF2.0 sets yield a poorer description of the data. Large differences between the data and the nominal NLO calculations are observed for the Δη(t, t), pT(tt), and Δφ (t, t) cross sections. It is noteworthy that the scale uncertainties in the predictions, which are of comparable size or exceed the experimental uncertainties, are not taken into account in the χ 2 calculations. The pT(tt) and Δφ (t, t) normalized cross sections are represented at LO O (αs2) by delta functions, and nontrivial shapes appear at O (αs3), thus resulting in large NLO scale uncertainties [ 18 ]. Compared to the NLO predictions, the approximate NNLO predictions using NNLO PDF sets (where available) provide an improved description of the pT(t) cross sections in different |y(t)| ranges. To visualize the comparison of the measurements to the theoretical predictions, the results obtained using the NLO and approximate NNLO calculations with the CT14 PDF set are compared to the measured pT(t) cross sections in different |y(t)| ranges in Fig. 8. To further illustrate the sensitivity to PDFs, the nominal values of the NLO predictions using HERAPDF2.0 are shown as well. Similar comparisons, in -1 ] V e 1 G [ ) t) (y 10-1 t t( )d 2 σd t(pT d ) t 1 σt(10-3 10-5 4 1T 1.1 C to 1 o i ta0.9 R Fig. 9 Comparison of the measured normalized tt double-differential cross section as a function of |y(t)| in different M(tt) ranges to NLO O(αs3) predictions. Details can be found in the caption of Fig. 8. Approximate NNLO O(αs4) predictions are not available for this cross section CMS Fig. 8 Comparison of the measured normalized tt double-differential cross section as a function of pT(t) in different |y(t)| ranges to NLO O(αs3) (MNR) predictions calculated with CT14 and HERAPDF2.0, and approximate NNLO O(αs4) (DiffTop) prediction calculated with CT14. The inner vertical bars on the data points represent the statistical uncertainties and the full bars include also the systematic uncertainties added in quadrature. The light band shows the scale uncertainties (μ) for the NLO predictions using CT14, while the dark band includes also the PDF uncertainties added in quadrature (μ + PDF). The dotted line shows the NLO predictions calculated with HERAPDF2.0. The dashed line shows the approximate NNLO predictions calculated with CT14. In the bottom panel, the ratios of the data and other calculations to the NLO prediction using CT14 are shown -1 ] V e G [ ) t 2 σtt() tt()dM10-3 d ( y d ) t 1 t( σ10-4 4 1T 1.2 C to 1 o it a 0.8 R CMS regions of M (tt), for the |y(t)|, |y(tt)|, Δη(t, t), pT(tt), and Δφ (t, t) cross sections are presented in Figs. 9, 10, 11, 12 and 13. Considering the scale uncertainties in the predictions, the agreement between the measurement and predictions is reasonable for all distributions. For the pT(t), y(t), and y(tt) cross sections, the scale uncertainties in the predictions reach 4% at maximum. They increase to 8% for the Δη(t, t) cross section, and vary within 20–50% for the pT(tt) and Δφ (t, t) cross sections, where larger differences between data and predictions are observed. For the pT(t), y(t), and y(tt) cross sections, the PDF uncertainties as estimated from the CT14 PDF set are of the same size or larger than the scale uncertainties. The HERAPDF2.0 predictions are mostly outside the total CT14 uncertainty band, showing also some visible shape differences with respect to CT14. The approximate NNLO predictions provide an improved description of the pT(t) shape. The data-to-theory comparisons illustrate the power of the measured normalized cross sections as a function of [ pT(t), y(t)], [y(t), M (tt)], and [y(tt), M (tt)] to eventually distinguish between modern PDF sets. Such a study is performed on these data and described in the next section. The remaining measured normalized cross sections as a function of [Δη(t, t), M (tt)], [ pT(tt), M (tt)], and [Δφ (t, t), M (tt)] could be used for this purpose as well, once higher-order QCD calculations become publicly available to match the data precision. Moreover, since the latter distributions are more sensitive to QCD radiation, they will provide additional input in testing improvements to the perturbative calculations. 9 The PDF fit The double-differential normalized tt cross sections are used in a PDF fit at NLO, together with the combined HERA inclusive deep inelastic scattering (DIS) data [ 63 ] and the CMS measurement of the W± boson charge asymmetry at √s = 8 TeV [ 72 ]. The fitted PDFs are also compared to the ones obtained in the recently published CMS measurement of inclusive jet production at 8 TeV [ 8 ]. The xFitter program (formerly known as HERAFitter) [ 73 ] (version 1.2.0), an open-source QCD fit framework for PDF determination, is used. The precise HERA DIS data, obtained from the combination of individual H1 and ZEUS results, are directly sensitive to the valence and sea quark distributions and probe the gluon distribution through scaling violations. Therefore, these data form the core of all PDF fits. The CMS W± boson charge asymmetry data provide further constraints on the valence quark distributions, as discussed in Ref. [ 72 ]. The measured double-differential normalized tt cross sections are included in the fit to constrain the gluon distribution at high x values. The typical probed x values can be estimated using the LO kinematic relation x = (M (tt)/√s) exp [±y(tt)]. Therefore, the present measurement is expected to be sensitive to x values in the region 0.01 x 0.25, as estimated using the highest or lowest |y(tt)| or M (tt) bins and taking the low or high bin edge where the cross section is largest (see Table 11). 9.1 Details of the PDF fit The scale evolution of partons is calculated through DGLAP equations [ 74–80 ] at NLO, as implemented in the qcdnum program [ 81 ] (version 17.01.11). The Thorne–Roberts [ 82– 84 ] variable-flavour number scheme at NLO is used for the treatment of the heavy-quark contributions. The number of flavours is set to 5, with c and b quark mass parameters Mc = 1.47 GeV and Mb = 4.5 GeV [ 63 ]. The theoretical predictions for the W± boson charge asymmetry data are calculated at NLO [ 85 ] using the mcfm program, which is interfaced with ApplGrid (version 1.4.70) [ 86 ], as described in Ref. [ 72 ]. For the DIS and W± boson charge asymmetry data μr and μf are set to Q, which denotes the four-momentum transfer in the case of the DIS data, and the mass of the W± boson in the case of the W± boson charge asymmetry. The theoretical predictions for the tt cross sections are calculated as described in Sect. 8.2 and included in the fit using the mcfm and ApplGrid programs. The strong coupling strength is set to αs (mZ) = 0.118. The Q2 range of the HERA data is restricted to Q2 > Q2min = 3.5 GeV2 [ 63 ]. The procedure for the determination of the PDFs follows the approach of HERAPDF2.0 [ 63 ]. The parametrized PDFs are the gluon distribution x g(x ), the valence quark distributions x uv(x ) and x dv(x ), and the u- and d-type antiquark distributions xU (x ) and x D(x ). At the initial QCD evolution scale μf0 = 1.9 GeV2, the PDFs are parametrized as: 2 x g(x ) = Agx Bg (1 − x )Cg (1 + Egx 2 + Fgx 3) − Agx Bg (1 − x )Cg , (7) x uv(x ) = Auv x Buv (1 − x )Cuv (1 + Duv x + Euv x 2), x dv(x ) = Adv x Bdv (1 − x )Cdv , xU (x ) = AU x BU (1 − x )CU (1 + DU x + FU x 3), x D(x ) = AD x BD (1 − x )CD , assuming the relations xU (x ) = x u(x ) and x D(x ) = x d(x ) + x s(x ). Here, x u(x ), x d(x ), and x s(x ) are the up, down, and strange antiquark distributions, respectively. The sea quark distribution is defined as xΣ (x ) = x u(x )+x d(x )+ x s(x ). The normalization parameters Auv , Adv , and Ag are determined by the QCD sum rules. The B and B parameters determine the PDFs at small x , and the C parameters describe the shape of the distributions as x → 1. The parameter Cg is fixed to 25 [ 87 ]. Additional constraints BU = BD and AU = AD(1 − fs) are imposed to ensure the same normalization for the x u and x d distributions as x → 0. The strangeness fraction fs = x s/(x d + x s) is fixed to fs = 0.4 as in the HERAPDF2.0 analysis [ 63 ]. This value is consistent with the determination of the strangeness fraction when using the CMS measurements of W + c production [ 88 ]. The parameters in Eq. (7) are selected by first fitting with all D, E , and F parameters set to zero, and then including them independently one at a time in the fit. The improvement in the χ 2 of the fit is monitored and the procedure is stopped when no further improvement is observed. This leads to an 18-parameter fit. The χ 2 definition used for the HERA DIS data follows that of Eq. (32) in Ref. [ 63 ]. It includes an additional logarithmic term that is relevant when the estimated Fig. 10 Comparison of the measured normalized tt double-differential cross section as a function of |y(tt)| in different M(tt) ranges to NLO O(αs3) predictions. Details can be found in the caption of Fig. 8. Approximate NNLO O(αs4) predictions are not available for this cross section Fig. 11 Comparison of the measured normalized tt double-differential cross section as a function of Δη(t, t) in different M(tt) ranges to NLO O(αs3) predictions. Details can be found in the caption of Fig. 8. Approximate NNLO O(αs4) predictions are not available for this cross section 10-5 4 1T 1.2 C to 1 o ita 0.8 R -1 ]V e G [ ) t 2 σtt)( ,tt)(dM10-3 t d ( η Δ )d10-4 1 tt( σ 10-5 4 1 T 1.2 C to 1 o ita 0.8 R CMS 19.7 fb-1 (8 TeV) 650<M(tt)<1500 GeV Data O(αs3) [MNR] CT14 μ CT14 μ + PDF HERAPDF2.0 1 2 1 2 1 2 1 statistical and uncorrelated systematic uncertainties in the data are rescaled during the fit [ 89 ]. For the CMS W± boson charge asymmetry and tt data presented here a χ 2 definition without such a logarithmic term is employed. The full covariance matrix representing the statistical and uncorrelated systematic uncertainties of the data is used in the fit. The correlated systematic uncertainties are treated through nuisance parameters. For each nuisance parameter a penalty term is added to the χ 2, representing the prior knowledge of the parameter. The treatment of the experimental uncertainties for the HERA DIS and CMS W± boson charge asymmetry data follows the prescription given in Refs. [ 63 ] and [ 72 ], respectively. The treatment of the experimental uncertainties in the tt double-differential cross section measurements follows the prescription given in Sect. 8.1. The experimental systematic uncertainties owing to the PDFs are omitted in the PDF fit. The PDF uncertainties are estimated according to the general approach of HERAPDF2.0 [ 63 ] in which the fit, model, and parametrization uncertainties are taken into account. Fit uncertainties are determined using the tolerance criterion of Δχ 2 = 1. Model uncertainties arise from the variations in the values assumed for the b and c quark mass parameters of 4.25 ≤ Mb ≤ 4.75 GeV and 1.41 ≤ Mc ≤ 1.53 GeV, the strangeness fraction 0.3 ≤ fs ≤ 0.4, and the value of Q2min imposed on the HERA data. The latter is var650<M(tt)<1500 GeV Data O(αs3) [MNR] CT14 μ CT14 μ + PDF HERAPDF2.0 Fig. 13 Comparison of the measured normalized tt double-differential cross section as a function of Δφ (t, t) in different M(tt) ranges to NLO O(αs3) predictions. Details can be found in the caption of Fig. 8. Approximate NNLO O(αs4) predictions are not available for this cross section ) t t ( 2 σ d CMS 650<M(tt)<1500 GeV Data O(αs3) [MNR] CT14 μ CT14 μ + PDF HERAPDF2.0 650<M(tt)<1500 GeV Data O(αs3) [MNR] CT14 μ CT14 μ + PDF HERAPDF2.0 ied within 2.5 ≤ Q2min ≤ 5.0 GeV2, following Ref. [ 63 ]. The parametrization uncertainty is estimated by extending the functional form in Eq. (7) of all parton distributions with additional parameters D, E , and F added one at a time. Furthermore, μf20 is changed to 1.6 and 2.2 GeV2. The parametrization uncertainty is constructed as an envelope at each x value, built from the maximal differences between the PDFs resulting from the central fit and all parametrization variations. This uncertainty is valid in the x range covered by the PDF fit to the data. The total PDF uncertainty is obtained by adding the fit, model, and parametrization uncertainties in quadrature. In the following, the quoted uncertainties correspond to 68% CL. Cross section variables Fit results consistent with those from Ref. [ 72 ] are obtained using the W± boson charge asymmetry measurements. The resulting gluon, valence quark, and sea quark distributions are shown in Fig. 14 at the scale μf2 = 30, 000 GeV2 mt2 relevant for tt production. For a direct comparison, the distributions for all variants of the fit are normalized to the results from the fit using only the DIS and W± boson charge asymmetry data. The reduction of the uncertainties is further illustrated in Fig. 15. The uncertainties in the gluon distribution at x > 0.01 are significantly reduced once the tt data are included in the fit. The largest improvement comes from the [y(tt), M (tt)] cross section by which the total gluon PDF uncertainty is reduced by more than a factor of two at x 0.3. This value of x is at the edge of kinematic reach of the current tt measurement. At higher values x 0.3, the gluon distribution is not directly constrained by the data and should be considered as an extrapolation that relies on the PDF parametrization assumptions. No substantial effects on the valence quark and sea quark distributions are observed. The variation of μr and μf in the prediction of the normalized tt cross sections has been performed and the effect on the fitted PDFs is found to be well within the total uncertainty. The gluon distribution obtained from fitting the measured [y(tt), M (tt)] cross section is compared in Fig. 16 to the one obtained in a similar study using the CMS measurement of inclusive jet production at 8 TeV [ 8 ]. The two results are in agreement in the probed x range. The constraints provided by the double-differential tt measurement are competitive with those from the inclusive jet data. 9.3 Comparison to the impact of single-differential tt cross section measurements The power of the double-differential tt measurement in fitting PDFs is compared with that of the single-differential analysis, where the tt cross section is measured as a function of pT(t), y(t), y(tt), and M (tt), employing in one dimension the same procedure described in this paper. The measurements are added, one at a time, to the HERA DIS and CMS W± boson charge asymmetry data in the PDF fit. The reduction Nominal fit 57/42 44/39 219/159 440/377 69/70 221/254 219/204 Table 4 The global and partial χ 2/dof values for all variants of the PDF fit. The variant of the fit that uses the DIS and W± boson charge asymmetry data only is denoted as ‘Nominal fit’. Each double-differential tt cross section is added (+) to the nominal data, one at a time. For the HERA measurements, the energy of the proton beam, Ep, is listed for each data set, with the electron energy being Ee = 27.5 GeV, CC and NC stand for charged and neutral current, respectively. The correlated χ 2 and the log-penalty χ 2 entries refer to the χ 2 contributions from the nuisance parameters and from the logarithmic term, respectively, as described in the text Data sets CMS double-differential tt HERA CC e−p, Ep = 920 GeV HERA CC e+p, Ep = 920 GeV HERA NC e−p, Ep = 920 GeV HERA NC e+p, Ep = 920 GeV HERA NC e+p, Ep = 820 GeV HERA NC e+p, Ep = 575 GeV HERA NC e+p, Ep = 460 GeV CMS W± asymmetry Correlated χ 2 Log-penalty χ 2 Total χ 2/dof Fig. 14 The gluon (upper left), sea quark (upper right), u valence quark (lower left), and d valence quark (lower right) PDFs at μf2 = 30, 000 GeV2, as obtained in all variants of the PDF fit, normalized to the results from the fit using the HERA DIS and CMS W± boson charge asymmetry measurements only. The shaded, hatched, and dotted areas represent the total uncertainty in each of the fits +[y(t), M(tt)] +[y(tt), M(tt)] 10/15 56/42 44/39 219/159 437/377 68/70 220/254 219/204 Fig. 15 Relative total uncertainties of the gluon (upper left), sea quark (upper right), u valence quark (lower left), and d valence quark (lower right) distributions at μf2 = 30, 000 GeV2, shown by shaded, hatched, and dotted areas, as obtained in all variants of the PDF fit 10-3 CMS xg(x) μ2 = 30000 GeV2 NLO f HERA + CMS W± 8 TeV HERA + CMS jets 8 TeV HERA + CMS W± 8 TeV + [y(tt), M(tt)] 8 TeV 10-2 10-1 1 x Fig. 16 The gluon distribution at μ2 f = 30, 000 GeV2, as obtained from the PDF fit to the HERA DIS data and CMS W± boson charge asymmetry measurements (shaded area), the CMS inclusive jet production cross sections (hatched area), and the W± boson charge asymmetry plus the double-differential tt cross section (dotted area). All presented PDFs are normalized to the results from the fit using the DIS and W± boson charge asymmetry measurements. The shaded, hatched, and dotted areas represent the total uncertainty in each of the fits 1 x 1 x f ) re 2 μ0f.4 , x ( Σ x / 0.2 2 ) f μ , x Σ( 0 x δ -0.2 -0.4 f ) re 2μ0f.4 , x (v d /x0.2 2) f μ , (v 0 x d x δ -0.2 -0.4 CMS xΣ(x) μ2 = 30000 GeV2 NLO f HERA + CMS W± 8 TeV + [pT(t), y(t)] 8 TeV + [y(t), M(tt)] 8 TeV + [y(tt), M(tt)] 8 TeV 10-3 CMS 10-2 10-1 xdv(x) μ2 = 30000 GeV2 NLO f HERA + CMS W± 8 TeV + [pT(t), y(t)] 8 TeV + [y(t), M(tt)] 8 TeV + [y(tt), M(tt)] 8 TeV 1 x 1 x 10-3 10-2 10-1 10-3 10-2 10-1 of the uncertainties for the resulting PDFs is illustrated in Fig. 17. Similar effects are observed from all measurements, with the largest impact coming from y(t) and y(tt). For the single-differential tt data one can extend the studies using the approximate NNLO calculations [ 4, 19, 69, 70 ]. An example, using the y(t) distribution, is presented in Appendix B. A comparison of the PDF uncertainties from the doubledifferential cross section as a function of [y(tt), M (tt)], and single-differential cross section as a function of y(tt) is presented in Fig. 18. Only the gluon distribution is shown, since no substantial impact on the other distributions is observed (see Figs. 14, 15, 17). The total gluon PDF uncertainty becomes noticeably smaller once the double-differential cross sections are included. The observed improvement makes future PDF fits at NNLO using the fully differential calculations [ 56, 57 ], once they become available, very interesting. 10 Summary A measurement of normalized double-differential tt production cross sections in pp collisions at √s = 8 TeV has been Fig. 17 The same as in Fig. 15 for the variants of the PDF fit using the single-differential tt cross sections 2μ)0ffre.4 , x ( g x /)0.2 2 μf , x (xg 0 δ -0.2 -0.4 x1 x1 2 μ)0ffre.4 , x ( Σ /x0.2 2 μ)f , x Σ( 0 x δ -0.2 -0.4 2μ)0ffre.4 , (xv d /x0.2 2μ)f , (xv 0 d x δ -0.2 -0.4 CMS xΣ(x) μf2 = 30000 GeV2 NLO HERA + CMS W± 8 TeV + pT(t) 8 TeV + M(tt) 8 TeV + y(t) 8 TeV + y(tt) 8 TeV 10-3 CMS 10-2 10-1 xdv(x) μf2 = 30000 GeV2 NLO HERA + CMS W± 8 TeV + pT(t) 8 TeV + M(tt) 8 TeV + y(t) 8 TeV + y(tt) 8 TeV x1 x1 10-3 10-2 10-1 10-3 10-2 10-1 ) fre 2μf0.4 , x ( g x /) 0.2 2 μf , x g 0 ( x δ -0.2 -0.4 CMS xg(x) μf2 = 30000 GeV2 NLO HERA + CMS W± 8 TeV + y(tt) 8 TeV + [y(tt), M(tt)] 8 TeV 10-3 10-2 10-1 1 x Fig. 18 Relative total uncertainties of the gluon distribution at μf2 = 30, 000 GeV2, shown by shaded (or hatched) bands, as obtained in the PDF fit using the DIS and W± boson charge asymmetry data only, as well as single- and double-differential tt cross sections presented. The measurement is performed in the e±μ∓ final state, using data collected with the CMS detector at the LHC, corresponding to an integrated luminosity of 19.7 fb−1. The normalized tt cross section is measured in the full phase space as a function of different pairs of kinematic variables describing the top quark or tt system. None of the tested MC models is able to correctly describe all the double-differential distributions. The data exhibit a softer transverse momentum pT(t) distribution, compared to the Monte Carlo predictions, as was reported in previous single-differential tt cross section measurements. The double-differential studies reveal a broader distribution of rapidity y(t) at high tt invariant mass M (tt) and a larger pseudorapidity separation Δη(t, t) at moderate M (tt) in data compared to simulation. The data are in reasonable agreement with next-to-leading-order predictions of quantum chromodynamics using recent sets of parton distribution functions (PDFs). The measured double-differential cross sections have been incorporated into a PDF fit, together with other data from HERA and the LHC. Including the tt data, one observes a significant reduction in the uncertainties in the gluon distribution at large values of parton momentum fraction x , in particular when using the double-differential tt cross section as a function of y(tt) and M (tt). The constraints provided by these data are competitive with those from inclusive jet data. This improvement exceeds that from using single-differential tt cross section data, thus strongly suggesting the use of the double-differential tt measurements in PDF fits. Acknowledgements We congratulate our colleagues in the CERN accelerator departments for the excellent performance of the LHC and thank the technical and administrative staffs at CERN and at other CMS institutes for their contributions to the success of the CMS effort. In addition, we gratefully acknowledge the computing centres and personnel of the Worldwide LHC Computing Grid for delivering so effectively the computing infrastructure essential to our analyses. Finally, we acknowledge the enduring support for the construction and operation of the LHC and the CMS detector provided by the following funding agencies: the Austrian Federal Ministry of Science, Research and Economy and the Austrian Science Fund; the Belgian Fonds de la Recherche Scientifique, and Fonds voor Wetenschappelijk Onderzoek; the Brazilian Funding Agencies (CNPq, CAPES, FAPERJ, and FAPESP); the Bulgarian Ministry of Education and Science; CERN; the Chinese Academy of Sciences, Ministry of Science and Technology, and National Natural Science Foundation of China; the Colombian Funding Agency (COLCIENCIAS); the Croatian Ministry of Science, Education and Sport, and the Croatian Science Foundation; the Research Promotion Foundation, Cyprus; the Secretariat for Higher Education, Science, Technology and Innovation, Ecuador; the Ministry of Education and Research, Estonian Research Council via IUT23-4 and IUT236 and European Regional Development Fund, Estonia; the Academy of Finland, Finnish Ministry of Education and Culture, and Helsinki Institute of Physics; the Institut National de Physique Nucléaire et de Physique des Particules/CNRS, and Commissariat à l’Énergie Atomique et aux Énergies Alternatives/CEA, France; the Bundesministerium für Bildung und Forschung, Deutsche Forschungsgemeinschaft, and Helmholtz-Gemeinschaft Deutscher Forschungszentren, Germany; the General Secretariat for Research and Technology, Greece; the National Scientific Research Foundation, and National Innovation Office, Hungary; the Department of Atomic Energy and the Department of Science and Technology, India; the Institute for Studies in Theoretical Physics and Mathematics, Iran; the Science Foundation, Ireland; the Istituto Nazionale di Fisica Nucleare, Italy; the Ministry of Science, ICT and Future Planning, and National Research Foundation (NRF), Republic of Korea; the Lithuanian Academy of Sciences; the Ministry of Education, and University of Malaya (Malaysia); the Mexican Funding Agencies (BUAP, CINVESTAV, CONACYT, LNS, SEP, and UASLP-FAI); the Ministry of Business, Innovation and Employment, New Zealand; the Pakistan Atomic Energy Commission; the Ministry of Science and Higher Education and the National Science Centre, Poland; the Fundação para a Ciência e a Tecnologia, Portugal; JINR, Dubna; the Ministry of Education and Science of the Russian Federation, the Federal Agency of Atomic Energy of the Russian Federation, Russian Academy of Sciences, the Russian Foundation for Basic Research and the Russian Competitiveness Program of NRNU MEPhI; the Ministry of Education, Science and Technological Development of Serbia; the Secretaría de Estado de Investigación, Desarrollo e Innovación, Programa Consolider-Ingenio 2010, Plan de Ciencia, Tecnología e Innovación 2013–2017 del Principado de Asturias and Fondo Europeo de Desarrollo Regional, Spain; the Swiss Funding Agencies (ETH Board, ETH Zurich, PSI, SNF, UniZH, Canton Zurich, and SER); the Ministry of Science and Technology, Taipei; the Thailand Center of Excellence in Physics, the Institute for the Promotion of Teaching Science and Technology of Thailand, Special Task Force for Activating Research and the National Science and Technology Development Agency of Thailand; the Scientific and Technical Research Council of Turkey, and Turkish Atomic Energy Authority; the National Academy of Sciences of Ukraine, and State Fund for Fundamental Researches, Ukraine; the Science and Technology Facilities Council, UK; the US Department of Energy, and the US National Science Foundation. Individuals have received support from the Marie-Curie programme and the European Research Council and EPLANET (European Union); the Leventis Foundation; the A. P. Sloan Foundation; the Alexander von Humboldt Foundation; the Belgian Federal Science Policy Office; the Fonds pour la Formation à la Recherche dans l’Industrie et dans l’Agriculture (FRIABelgium); the Agentschap voor Innovatie door Wetenschap en Technologie (IWT-Belgium); the Ministry of Education, Youth and Sports (MEYS) of the Czech Republic; the Council of Scientific and Industrial Research, India; the HOMING PLUS programme of the Foundation for Polish Science, cofinanced from European Union, Regional Development Fund, the Mobility Plus programme of the Ministry of Science and Higher Education, the National Science Center (Poland), contracts Harmonia 2014/14/M/ST2/00428, Opus 2014/13/B/ST2/02543, 2014/15/B/ST2/03998, and 2015/19/B/ST2/02861, Sonata-bis 2012/07/ E/ST2/01406; the National Priorities Research Program by Qatar National Research Fund; the Programa Clarín-COFUND del Principado de Asturias; the Thalis and Aristeia programmes cofinanced by EU-ESF and the Greek NSRF; the Rachadapisek Sompot Fund for Postdoctoral Fellowship, Chulalongkorn University and the Chulalongkorn Academic into Its 2nd Century Project Advancement Project (Thailand); and the Welch Foundation, contract C-1845. Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecomm ons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Funded by SCOAP3. Appendix A: Values of the normalized double-differential cross sections Tables 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21 and 22 provide the measured tt double-differential cross sections for all pairs of variables, including their correlation matrices of statistical uncertainties and detailed breakdown of systematic uncertainties. The b tagging systematic uncertainty is obtained by combining in quadrature variations of the data-to-simulation correction factors as a function of pT and |η|, performed separately for jets originating from b quarks and other partons, as presented in Sects. 4 and 7. The PDF systematic uncertainty is obtained by combining in quadrature variations corresponding to the 52 eigenvectors of the CT10 PDF set [ 32 ]. Page 20 of 45 Table 5 The measured normalized tt double-differential cross sections in different bins of y(t) and pT(t), along with their relative statistical and systematic uncertainties pT(t) (GeV) 1 d2σ (tt) σ (tt) dy(t)d pT(t) (GeV−1) +100.0 +1.8 BΔiηn(t, t).1The values are expressed as percentages. For bin indices see Table 14 Page 25 of 45 459 Eur. Phys. J. C (2017) 77:459 Table 15 The correl2ation matrix of statistical uncertainties for the normalized tt double-differential cross sections as a function of M (tt) and 3 4 5 6 7 8 9 10 11 12 a function of M (tt) and Δη(t, t). For bin indices see Table 14 Syst. source Sources and values of the relative systematic uncertainties in percent of the measured normalized tt double-differential cross sections as \ Bin 1 2 3 4 5 6 7 8 9 10 11 12 Jet energy scale Jet energy resolution Kin. reconstruction Pileup Trigger Page 26 of 45 Table 17 The measured normalized tt double-differential cross sections in different bins of M (tt) and pT(tt), along with their relative statistical and systematic uncertainties M (tt) (GeV) 340–400 400–500 500–650 650–1500 pT(tt) (GeV) 1 d2σ (tt) σ (tt) dM(tt)d pT(tt) (GeV−2) BΔiφn(t, t).1The values are expressed as percentages. For bin indices see Table 20 (2017) 77:459 459 Page 28 of 45 Eur. Phys. J. C Table 21 The correl2ation matrix of statistical uncertainties for the normalized tt double-differential cross sections as a function of M (tt) and 3 4 5 6 7 8 9 10 11 12 +2.1 −30.7 −1.2 −33.5 +6.9 −9.2 −18.5 Fig. 19 The gluon distribution (left) and its fractional total uncertainty (right) at μf2 = 30, 000 GeV2, as obtained in the PDF fit at NNLO using the DIS and W± boson charge asymmetry data only, as well as y(t) cross sections. The distributions shown in the left panel are normalized Appendix B: PDF fit of single-differential tt measurement at NNLO Approximate NNLO predictions [ 19 ] for the y(t) singledifferential cross section are obtained using the DiffTop program, which is interfaced to fastNLO [ 90 ] (version 2.1). The results are used in a PDF fit at NNLO. The procedure follows the determination of the PDFs at NLO described in Sect. 9.1. In the NNLO fit, the scales for tt production are set to μr = μf = mt, with mt = 173 GeV being the top quark pole mass. The scale evolution of partons is calculated through the DGLAP equations at NNLO. The DIS and W± boson charge asymmetry theoretical predictions are calculated at NNLO accuracy. For the W± boson charge asymmetry predictions, the NNLO corrections are obtained by using K-factors, defined as the ratios of the predictions at NNLO to the ones at NLO, both calculated with the fewz [ 91 ] program (version 3.1), using the NNLO CT10 [ 32 ] PDFs. As in Ref. [ 63 ], the charm quark mass parameter is set to Mc = 1.43 GeV for a fit at NNLO. To stabilise for the comparison, the fit of the gluon distribution at NNLO, which suffers from insufficient constraints when using the inclusive HERA DIS and W± boson charge asymmetry data alone, the Q2 range of the HERA data is further restricted to Q2 > Q2min = 7.5 GeV2. In addition, a reduced set of 15 parameters is used for the PDFs, which are parametrized at the initial scale of the QCD evolution as: x g(x ) = Ag x Bg (1 − x )Cg − Ag x Bg (1 − x )Cg , x uv (x ) = Auv x Buv (1 − x )Cuv (1 + Euv x 2), x dv (x ) = Adv x Bdv (1 − x )Cdv , xU (x ) = AU x BU (1 − x )CU (1 + EU x 2), x D(x ) = A D x BD (1 − x )CD (1 + E D x 2). (8) to the results from the fit using the DIS and W± boson charge asymmetry data only. The total uncertainty of each distribution is shown by a shaded (or hatched) band The PDF uncertainty estimation follows the NLO fit procedure described in Sect. 9.1, except for the model parameter variations of 5 ≤ Q2min ≤ 10 GeV2 and 1.37 ≤ Mc ≤ 1.49 GeV. The resulting gluon distribution at a scale of μf2 = 30, 000 GeV2 mt2 is shown in Fig. 19, together with its uncertainty band. The reduction of the total gluon PDF uncertainty is noticeable at large x , once the tt cross sections are included in the fit. This impact is smaller compared to the one observed in the 18-parameter fit at NLO (Fig. 17). Page 30 of 45 CMS Collaboration Yerevan Physics Institute, Yerevan, Armenia A. M. Sirunyan, A. Tumasyan Institut für Hochenergiephysik, Vienna, Austria W. Adam, E. Asilar, T. Bergauer, J. Brandstetter, E. Brondolin, M. Dragicevic, J. Erö, M. Flechl, M. Friedl, R. Frühwirth1, V. M. Ghete, C. Hartl, N. Hörmann, J. Hrubec, M. Jeitler1, A. König, I. Krätschmer, D. Liko, T. Matsushita, I. Mikulec, D. Rabady, N. Rad, B. Rahbaran, H. Rohringer, J. Schieck1, J. Strauss, W. Waltenberger, C.-E. Wulz1 Institute for Nuclear Problems, Minsk, Belarus O. Dvornikov, V. Makarenko, V. Mossolov, J. Suarez Gonzalez, V. Zykunov National Centre for Particle and High Energy Physics, Minsk, Belarus N. Shumeiko Vrije Universiteit Brussel, Brussel, Belgium S. Abu Zeid, F. Blekman, J. D’Hondt, N. Daci, I. De Bruyn, K. Deroover, S. Lowette, S. Moortgat, L. Moreels, A. Olbrechts, Q. Python, K. Skovpen, S. Tavernier, W. Van Doninck, P. Van Mulders, I. Van Parijs Université de Mons, Mons, Belgium N. Beliy Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, Brazil W. L. Aldá Júnior, F. L. Alves, G. A. Alves, L. Brito, C. Hensel, A. Moraes, M. E. Pol, P. Rebello Teles Universidade do Estado do Rio de Janeiro, Rio de Janeiro, Brazil E. Belchior Batista Das Chagas, W. Carvalho, J. Chinellato3, A. Custódio, E. M. Da Costa, G. G. Da Silveira4, D. De Jesus Damiao, C. De Oliveira Martins, S. Fonseca De Souza, L. M. Huertas Guativa, H. Malbouisson, D. Matos Figueiredo, C. Mora Herrera, L. Mundim, H. Nogima, W. L. Prado Da Silva, A. Santoro, A. Sznajder, E. J. Tonelli Manganote3, F. Torres Da Silva De Araujo, A. Vilela Pereira Universidade Estadual Paulistaa , Universidade Federal do ABCb, São Paulo, Brazil S. Ahujaa , C. A. Bernardesa , S. Dograa , T. R. Fernandez Perez Tomeia , E. M. Gregoresb, P. G. Mercadanteb, C. S. Moona , S. F. Novaesa , Sandra S. Padulaa , D. Romero Abadb, J. C. Ruiz Vargasa Institute for Nuclear Research and Nuclear Energy, Sofia, Bulgaria A. Aleksandrov, R. Hadjiiska, P. Iaydjiev, M. Rodozov, S. Stoykova, G. Sultanov, M. Vutova University of Sofia, Sofia, Bulgaria A. Dimitrov, I. Glushkov, L. Litov, B. Pavlov, P. Petkov Beihang University, Beijing, China W. Fang5 State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing, China Y. Ban, G. Chen, Q. Li, S. Liu, Y. Mao, S. J. Qian, D. Wang, Z. Xu Faculty of Electrical Engineering Mechanical Engineering and Naval Architecture, University of Split, Split, Croatia N. Godinovic, D. Lelas, I. Puljak, P. M. Ribeiro Cipriano, T. Sculac Faculty of Science, University of Split, Split, Croatia Z. Antunovic, M. Kovac Institute Rudjer Boskovic, Zagreb, Croatia V. Brigljevic, D. Ferencek, K. Kadija, B. Mesic, T. Susa Charles University, Prague, Czech Republic M. Finger7, M. Finger Jr.7 Universidad San Francisco de Quito, Quito, Ecuador E. Carrera Jarrin Academy of Scientific Research and Technology of the Arab Republic of Egypt, Egyptian Network of High Energy Physics, Cairo, Egypt A. Ellithi Kamel8, M. A. Mahmoud9,10, A. Radi10,11 National Institute of Chemical Physics and Biophysics, Tallinn, Estonia M. Kadastik, L. Perrini, M. Raidal, A. Tiko, C. Veelken Department of Physics, University of Helsinki, Helsinki, Finland P. Eerola, J. Pekkanen, M. Voutilainen IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette, France M. Besancon, F. Couderc, M. Dejardin, D. Denegri, B. Fabbro, J. L. Faure, C. Favaro, F. Ferri, S. Ganjour, S. Ghosh, A. Givernaud, P. Gras, G. Hamel de Monchenault, P. Jarry, I. Kucher, E. Locci, M. Machet, J. Malcles, J. Rander, A. Rosowsky, M. Titov Institut Pluridisciplinaire Hubert Curien (IPHC), Université de Strasbourg, CNRS-IN2P3, Strasbourg, France J.-L. Agram12, J. Andrea, D. Bloch, J.-M. Brom, M. Buttignol, E. C. Chabert, N. Chanon, C. Collard, E. Conte12, X. Coubez, J.-C. Fontaine12, D. Gelé, U. Goerlach, A.-C. Le Bihan, P. Van Hove Georgian Technical University, Tbilisi, Georgia A. Khvedelidze7 Tbilisi State University, Tbilisi, Georgia D. Lomidze RWTH Aachen University, I. Physikalisches Institut, Aachen, Germany C. Autermann, S. Beranek, L. Feld, M. K. Kiesel, K. Klein, M. Lipinski, M. Preuten, C. Schomakers, J. Schulz, T. Verlage RWTH Aachen University,III. Physikalisches Institut B, Aachen, Germany V. Cherepanov, G. Flügge, B. Kargoll, T. Kress, A. Künsken, J. Lingemann, T. Müller, A. Nehrkorn, A. Nowack, C. Pistone, O. Pooth, A. Stahl14 Institut für Experimentelle Kernphysik, Karlsruhe, Germany M. Akbiyik, C. Barth, S. Baur, C. Baus, J. Berger, E. Butz, R. Caspart, T. Chwalek, F. Colombo, W. De Boer, A. Dierlamm, S. Fink, B. Freund, R. Friese, M. Giffels, A. Gilbert, P. Goldenzweig, D. Haitz, F. Hartmann14, S. M. Heindl, U. Husemann, F. Kassel14, I. Katkov13, S. Kudella, H. Mildner, M. U. Mozer, Th. Müller, M. Plagge, G. Quast, K. Rabbertz, S. Röcker, F. Roscher, M. Schröder, I. Shvetsov, G. Sieber, H. J. Simonis, R. Ulrich, S. Wayand, M. Weber, T. Weiler, S. Williamson, C. Wöhrmann, R. Wolf Institute of Nuclear and Particle Physics (INPP), NCSR Demokritos, Aghia Paraskevi, Greece G. Anagnostou, G. Daskalakis, T. Geralis, V. A. Giakoumopoulou, A. Kyriakis, D. Loukas, I. Topsis-Giotis National and Kapodistrian University of Athens, Athens, Greece S. Kesisoglou, A. Panagiotou, N. Saoulidou, E. Tziaferi National Technical University of Athens, Athens, Greece K. Kousouris MTA-ELTE Lendület CMS Particle and Nuclear Physics Group, Eötvös Loránd University, Budapest, Hungary N. Filipovic, G. Pasztor Wigner Research Centre for Physics, Budapest, Hungary G. Bencze, C. Hajdu, D. Horvath18, F. Sikler, V. Veszpremi, G. Vesztergombi19, A. J. Zsigmond Institute of Nuclear Research ATOMKI, Debrecen, Hungary N. Beni, S. Czellar, J. Karancsi20, A. Makovec, J. Molnar, Z. Szillasi Institute of Physics, University of Debrecen, Debrecen, Hungary M. Bartók19, P. Raics, Z. L. Trocsanyi, B. Ujvari Indian Institute of Science (IISc), Bengaluru, India J. R. Komaragiri National Institute of Science Education and Research, Bhubaneswar, India S. Bahinipati21, S. Bhowmik22, S. Choudhury23, P. Mal, K. Mandal, A. Nayak24, D. K. Sahoo21, N. Sahoo, S. K. Swain Indian Institute of Technology Madras, Madras, India P. K. Behera Bhabha Atomic Research Centre, Mumbai, India R. Chudasama, D. Dutta, V. Jha, V. Kumar, A. K. Mohanty14, P. K. Netrakanti, L. M. Pant, P. Shukla, A. Topkar Tata Institute of Fundamental Research-A, Mumbai, India T. Aziz, S. Dugad, G. Kole, B. Mahakud, S. Mitra, G. B. Mohanty, B. Parida, N. Sur, B. Sutar Indian Institute of Science Education and Research (IISER), Pune, India S. Chauhan, S. Dube, V. Hegde, A. Kapoor, K. Kothekar, S. Pandey, A. Rane, S. Sharma Institute for Research in Fundamental Sciences (IPM), Tehran, Iran S. Chenarani26, E. Eskandari Tadavani, S. M. Etesami26, M. Khakzad, M. Mohammadi Najafabadi, M. Naseri, S. Paktinat Mehdiabadi27, F. Rezaei Hosseinabadi, B. Safarzadeh28, M. Zeinali INFN Sezione di Baria , Università di Barib, Politecnico di Baric, Bari, Italy M. Abbresciaa ,b, C. Calabriaa ,b, C. Caputoa ,b, A. Colaleoa , D. Creanzaa ,c, L. Cristellaa ,b, N. De Filippisa ,c, M. De Palmaa ,b, L. Fiorea , G. Iasellia ,c, G. Maggia ,c, M. Maggia , G. Minielloa ,b, S. Mya ,b, S. Nuzzoa ,b, A. Pompilia ,b, G. Pugliesea ,c, R. Radognaa ,b, A. Ranieria , G. Selvaggia ,b, A. Sharmaa , L. Silvestrisa ,14, R. Vendittia ,b, P. Verwilligena INFN Sezione di Cataniaa , Università di Cataniab, Catania, Italy S. Albergoa ,b, S. Costaa ,b, A. Di Mattiaa , F. Giordanoa ,b, R. Potenzaa ,b, A. Tricomia ,b, C. Tuvea ,b INFN Sezione di Firenzea , Università di Firenzeb, Florence, Italy G. Barbaglia , V. Ciullia ,b, C. Civininia , R. D’Alessandroa ,b, E. Focardia ,b, P. Lenzia ,b, M. Meschinia , S. Paolettia , L. Russoa ,29, G. Sguazzonia , D. Stroma , L. Viliania ,b,14 INFN Laboratori Nazionali di Frascati, Frascati, Italy L. Benussi, S. Bianco, F. Fabbri, D. Piccolo, F. Primavera14 INFN Sezione di Genovaa , Università di Genovab, Genova, Italy V. Calvellia ,b, F. Ferroa , M. R. Mongea ,b, E. Robuttia , S. Tosia ,b INFN Sezione di Milano-Bicoccaa , Università di Milano-Bicoccab, Milan, Italy L. Brianzaa ,b,14, F. Brivioa ,b, V. Ciriolo, M. E. Dinardoa ,b, S. Fiorendia ,b,14, S. Gennaia , A. Ghezzia ,b, P. Govonia ,b, M. Malbertia ,b, S. Malvezzia , R. A. Manzonia ,b, D. Menascea , L. Moronia , M. Paganonia ,b, D. Pedrinia , S. Pigazzinia ,b, S. Ragazzia ,b, T. Tabarelli de Fatisa ,b INFN Sezione di Napolia , Università di Napoli ’Federico II’b, Napoli, Italy, Università della Basilicatac, Potenza, Italy, Università G. Marconid , Rome, Italy S. Buontempoa , N. Cavalloa ,c, G. De Nardo, S. Di Guidaa ,d ,14, M. Espositoa ,b, F. Fabozzia ,c, F. Fiengaa ,b, A. O. M. Iorioa ,b, G. Lanzaa , L. Listaa , S. Meolaa ,d ,14, P. Paoluccia ,14, C. Sciaccaa ,b, F. Thyssena INFN Sezione di Padovaa , Università di Padovab, Padova, Italy, Università di Trentoc, Trento, Italy P. Azzia ,14, N. Bacchettaa , L. Benatoa ,b, D. Biselloa ,b, A. Bolettia ,b, R. Carlina ,b, A. Carvalho Antunes De Oliveiraa ,b, P. Checchiaa , M. Dall’Ossoa ,b, P. De Castro Manzanoa , T. Dorigoa , U. Dossellia , U. Gasparinia ,b, F. Gonellaa , S. Lacapraraa , M. Margonia ,b, A. T. Meneguzzoa ,b, J. Pazzinia ,b, N. Pozzobona ,b, P. Ronchesea ,b, R. Rossina ,b, F. Simonettoa ,b, E. Torassaa , S. Venturaa , M. Zanettia ,b, P. Zottoa ,b INFN Sezione di Pisaa , Università di Pisab, Scuola Normale Superiore di Pisaa , Pisa, Italy K. Androsova ,29, P. Azzurria ,14, G. Bagliesia , J. Bernardinia , T. Boccalia , R. Castaldia , M. A. Cioccia ,b,29, R. Dell’Orsoa , G. Fedia , A. Giassia , M. T. Grippoa ,29, F. Ligabuea ,c, T. Lomtadzea , L. Martinia ,b, A. Messineoa ,b, F. Pallaa , A. Rizzia ,b, A. Savoy-Navarroa ,30, P. Spagnoloa , R. Tenchinia , G. Tonellia ,b, A. Venturia , P. G. Verdinia INFN Sezione di Romaa , Università di Romab, Rome, Italy L. Baronea ,b, F. Cavallaria , M. Cipriania ,b, D. Del Rea ,b,14, M. Diemoza , S. Gellia ,b, E. Longoa ,b, F. Margarolia ,b, B. Marzocchia ,b, P. Meridiania , G. Organtinia ,b, R. Paramattia ,b, F. Preiatoa ,b, S. Rahatloua ,b, C. Rovellia , F. Santanastasioa ,b INFN Sezione di Torinoa , Università di Torinob, Torino, Italy, Università del Piemonte Orientalec, Novara, Italy N. Amapanea ,b, R. Arcidiaconoa ,c,14, S. Argiroa ,b, M. Arneodoa ,c, N. Bartosika , R. Bellana ,b, C. Biinoa , N. Cartigliaa , F. Cennaa ,b, M. Costaa ,b, R. Covarellia ,b, A. Deganoa ,b, N. Demariaa , B. Kiania ,b, C. Mariottia , S. Masellia , E. Migliorea ,b, V. Monacoa ,b, E. Monteila ,b, M. Montenoa , M. M. Obertinoa ,b, L. Pachera ,b, N. Pastronea , M. Pelliccionia , G. L. Pinna Angionia ,b, F. Raveraa ,b, A. Romeroa ,b, M. Ruspaa ,c, R. Sacchia ,b, K. Shchelinaa ,b, V. Solaa , A. Solanoa ,b, A. Staianoa , P. Traczyka ,b INFN Sezione di Triestea , Università di Triesteb, Trieste, Italy S. Belfortea , M. Casarsaa , F. Cossuttia , G. Della Riccaa ,b, A. Zanettia Kyungpook National University, Taegu, Korea D. H. Kim, G. N. Kim, M. S. Kim, J. Lee, S. Lee, S. W. Lee, Y. D. Oh, S. Sekmen, D. C. Son, Y. C. Yang Chonbuk National University, Jeonju, Korea A. Lee Chonnam National University, Institute for Universe and Elementary Particles, Kwangju, Korea H. Kim Hanyang University, Seoul, Korea J. A. Brochero Cifuentes, T. J. Kim Korea University, Seoul, Korea S. Cho, S. Choi, Y. Go, D. Gyun, S. Ha, B. Hong, Y. Jo, Y. Kim, K. Lee, K. S. Lee, S. Lee, J. Lim, S. K. Park, Y. Roh Seoul National University, Seoul, Korea J. Almond, J. Kim, H. Lee, S. B. Oh, B. C. Radburn-Smith, S. H. Seo, U. K. Yang, H. D. Yoo, G. B. Yu University of Seoul, Seoul, Korea M. Choi, H. Kim, J. H. Kim, J. S. H. Lee, I. C. Park, G. Ryu, M. S. Ryu Sungkyunkwan University, Suwon, Korea Y. Choi, J. Goh, C. Hwang, J. Lee, I. Yu Vilnius University, Vilnius, Lithuania V. Dudenas, A. Juodagalvis, J. Vaitkus National Centre for Particle Physics, Universiti Malaya, Kuala Lumpur, Malaysia I. Ahmed, Z. A. Ibrahim, M. A. B. Md Ali31, F. Mohamad Idris32, W. A. T. Wan Abdullah, M. N. Yusli, Z. Zolkapli Universidad Iberoamericana, Mexico City, Mexico S. Carrillo Moreno, C. Oropeza Barrera, F. Vazquez Valencia Benemerita Universidad Autonoma de Puebla, Puebla, Mexico S. Carpinteyro, I. Pedraza, H. A. Salazar Ibarguen, C. Uribe Estrada Universidad Autónoma de San Luis Potosí, San Luis Potosí, Mexico A. Morelos Pineda University of Auckland, Auckland, New Zealand D. Krofcheck University of Canterbury, Christchurch, New Zealand P. H. Butler National Centre for Physics, Quaid-I-Azam University, Islamabad, Pakistan A. Ahmad, M. Ahmad, Q. Hassan, H. R. Hoorani, W. A. Khan, A. Saddique, M. A. Shah, M. Shoaib, M. Waqas Laboratório de Instrumentação e Física Experimental de Partículas, Lisbon, Portugal P. Bargassa, C. 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Leonidov36, A. Terkulov Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow, Russia A. Baskakov, A. Belyaev, E. Boos, V. Bunichev, M. Dubinin40, L. Dudko, A. Ershov, V. Klyukhin, N. Korneeva, I. Lokhtin, I. Miagkov, S. Obraztsov, M. Perfilov, V. Savrin, P. Volkov Novosibirsk State University (NSU), Novosibirsk, Russia V. Blinov41, Y. Skovpen41, D. Shtol41 State Research Center of Russian Federation, Institute for High Energy Physics, Protvino, Russia I. Azhgirey, I. Bayshev, S. Bitioukov, D. Elumakhov, V. Kachanov, A. Kalinin, D. Konstantinov, V. Krychkine, V. Petrov, R. Ryutin, A. Sobol, S. Troshin, N. Tyurin, A. Uzunian, A. Volkov Faculty of Physics and Vinca Institute of Nuclear Sciences, University of Belgrade, Belgrade, Serbia P. Adzic42, P. Cirkovic, D. Devetak, M. Dordevic, J. Milosevic, V. Rekovic Centro de Investigaciones Energéticas Medioambientales y Tecnológicas (CIEMAT), Madrid, Spain J. Alcaraz Maestre, M. Barrio Luna, E. Calvo, M. Cerrada, M. Chamizo Llatas, N. Colino, B. De La Cruz, A. Delgado Peris, A. Escalante Del Valle, C. Fernandez Bedoya, J. P. Fernández Ramos, J. Flix, M. C. Fouz, P. Garcia-Abia, O. Gonzalez Lopez, S. Goy Lopez, J. M. Hernandez, M. I. Josa, E. Navarro De Martino, A. Pérez-Calero Yzquierdo, J. Puerta Pelayo, A. Quintario Olmeda, I. Redondo, L. Romero, M. S. Soares Universidad Autónoma de Madrid, Madrid, Spain J. F. de Trocóniz, M. Missiroli, D. Moran Instituto de Física de Cantabria (IFCA), CSIC-Universidad de Cantabria, Santander, Spain I. J. Cabrillo, A. Calderon, E. Curras, M. Fernandez, J. Garcia-Ferrero, G. Gomez, A. Lopez Virto, J. Marco, C. Martinez Rivero, F. Matorras, J. Piedra Gomez, T. Rodrigo, A. Ruiz-Jimeno, L. Scodellaro, N. Trevisani, I. Vila, R. Vilar Cortabitarte CERN, European Organization for Nuclear Research, Geneva, Switzerland D. Abbaneo, E. Auffray, G. Auzinger, P. Baillon, A. H. Ball, D. Barney, P. Bloch, A. Bocci, C. Botta, T. Camporesi, R. Castello, M. 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Paganis, A. Psallidas, J. F. Tsai Department of Physics, Faculty of Science, Chulalongkorn University, Bangkok, Thailand B. Asavapibhop, G. Singh, N. Srimanobhas, N. Suwonjandee Physics Department Science and Art Faculty, Cukurova University, Adana, Turkey A. Adiguzel, F. Boran, S. Cerci50, S. Damarseckin, Z. S. Demiroglu, C. Dozen, I. Dumanoglu, S. Girgis, G. Gokbulut, Y. Guler, I. Hos51, E. E. Kangal52, O. Kara, U. Kiminsu, M. Oglakci, G. Onengut53, K. Ozdemir54, D. Sunar Cerci50, B. Tali50, H. Topakli55, S. Turkcapar, I. S. Zorbakir, C. Zorbilmez Physics Department, Middle East Technical University, Ankara, Turkey B. Bilin, S. Bilmis, B. Isildak56, G. Karapinar57, M. Yalvac, M. Zeyrek Bogazici University, Istanbul, Turkey E. Gülmez, M. Kaya58, O. Kaya59, E. A. Yetkin60, T. Yetkin61 Istanbul Technical University, Istanbul, Turkey A. Cakir, K. Cankocak, S. Sen62 National Scientific Center, Kharkov Institute of Physics and Technology, Kharkov, Ukraine L. Levchuk, P. Sorokin Rutherford Appleton Laboratory, Didcot, UK K. W. Bell, A. Belyaev64, C. Brew, R. M. Brown, L. Calligaris, D. Cieri, D. J. A. Cockerill, J. A. Coughlan, K. Harder, S. Harper, E. Olaiya, D. Petyt, C. H. Shepherd-Themistocleous, A. Thea, I. R. Tomalin, T. Williams Brunel University, Uxbridge, UK J. E. Cole, P. R. Hobson, A. Khan, P. Kyberd, I. D. Reid, P. Symonds, L. Teodorescu, M. Turner Baylor University, Waco, USA A. Borzou, K. Call, J. Dittmann, K. Hatakeyama, H. Liu, N. Pastika Catholic University of America, Washington, DC, USA R. Bartek, A. Dominguez The University of Alabama, Tuscaloosa, USA A. Buccilli, S. I. Cooper, C. Henderson, P. Rumerio, C. West Boston University, Boston, USA D. Arcaro, A. Avetisyan, T. Bose, D. Gastler, D. Rankin, C. Richardson, J. Rohlf, L. Sulak, D. Zou University of California, Davis, Davis, USA R. Breedon, D. Burns, M. Calderon De La Barca Sanchez, S. Chauhan, M. Chertok, J. Conway, R. Conway, P. T. Cox, R. Erbacher, C. Flores, G. Funk, M. 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