Measurement of normalized differential $\mathrm{t}\overline{\mathrm{t}}$ cross sections in the dilepton channel from pp collisions at $\sqrt{s} =$ 13 TeV

Normalized differential cross sections for top quark pair production are measured in the dilepton (e$^+$e$^-$, $\mu^+\mu^-$, and $\mu^\mp$e$^\pm$) decay channels in proton-proton collisions at a center-of-mass energy of 13 TeV. The measurements are performed with data corresponding to an integrated luminosity of 2.1 fb$^{-1}$ using the CMS detector at the LHC. The cross sections are measured differentially as a function of the kinematic properties of the leptons, jets from bottom quark hadronization, top quarks, and top quark pairs at the particle and parton levels. The results are compared to several Monte Carlo generators that implement calculations up to next-to-leading order in perturbative quantum chromodynamics interfaced with parton showering, and also to fixed-order theoretical calculations of top quark pair production up to next-to-next-to-leading order.


Introduction
The measurement of tt differential cross sections can provide a test of perturbative quantum chromodynamic (QCD) calculations and also improve the knowledge of parton distribution functions (PDFs) [1]. Previous measurements of differential cross sections for tt production have been performed in proton-proton (pp) collisions at the CERN LHC at center-of-mass energies of 7 [2, 3] and 8 TeV [4][5][6][7][8][9][10][11][12]. The dilepton (electron or muon) final state of the tt decay helps in the suppression of background events. This paper presents the first CMS measurement at √ s = 13 TeV in the dilepton decay final state and includes the same-flavor lepton channels (e + e − and µ + µ − ), using data corresponding to an integrated luminosity of 2.1 fb −1 . The statistical precision of the measurements is improved by the increased data sample from including the same-flavor lepton channels. The data were recorded by the CMS experiment at the LHC in 2015, and this measurement complements other recent measurements that have been reported in a different decay channel [13] and by a different experiment [14,15]. The tt differential cross section measurements are performed at the particle and parton levels. Particle-level measurements use final-state kinematic observables that are experimentally measurable and theoretically well defined. Corrections are limited mainly to detector effects that can be determined experimentally. The particle-level measurements are designed to have minimal model dependencies. The visible differential cross section is defined for a phase space within the acceptance of the experiment. Large extrapolations into inaccessible phase-space regions are thus avoided in particle-level differential cross section measurements. In contrast, the parton-level measurement of the top quark pair production cross sections is performed in the full phase space. This facilitates comparisons to predictions in perturbative QCD.
The normalized tt differential cross sections are measured as a function of the kinematic properties of the tt system, the top quarks and the top quark decay products, which include the jets coming from the hadronization of bottom quarks and the leptons. The particle-level measurements are performed with respect to the transverse momentum of the leptons and of the jets. The cross sections as a function of the invariant mass and rapidity of the tt system are also measured to help in understanding the PDFs. The angular difference in the transverse plane between the top and anti-top quarks is provided to compare to predictions of new physics beyond the standard model [16]. In addition, the normalized tt cross sections are measured as a function of the transverse momenta of the top quark and of the top quark pair.

The CMS detector and simulation 2.1 The CMS detector
The central feature of the CMS apparatus is a superconducting solenoid of 6 m internal diameter, providing a magnetic field of 3.8 T. The solenoid volume encases the silicon pixel and strip tracker, a lead tungstate crystal electromagnetic calorimeter, and a brass and scintillator hadron calorimeter, each composed of a barrel and two endcap sections. Forward calorimeters extend the pseudorapidity (η) coverage provided by the barrel and endcap detectors. Muons are detected in gas-ionization chambers embedded in the steel flux-return yoke outside the solenoid. A more detailed description of the CMS detector, together with a definition of the coordinate system used and the relevant kinematic variables, can be found in Ref. [17]. The particle-flow (PF) algorithm [18] is used to reconstruct objects in the event, combining information from all the CMS subdetectors. The missing transverse momentum vector ( p miss T ) is defined as the projection onto the plane perpendicular to the beam axis of the negative vector sum of the momenta of all PF candidates in an event [19]. Its magnitude is referred to as p miss T .

Signal and background simulation
Monte Carlo (MC) techniques are used to simulate the tt signal and the background processes. We use the POWHEG (v2) [20][21][22][23] generator to model the nominal tt signal at next-to-leading order (NLO). In order to simulate tt events with additional partons, MADGRAPH5 aMC@NLO (v2.2.2) [24] (MG5 aMC@NLO) is used, which includes both leading-order (LO) and NLO matrix elements (MEs). Parton shower (PS) simulation is performed with PYTHIA8 (v8.205) [25], using the tune CUETP8M1 [26] to model the underlying event. Up to two partons in addition to the tt pair are calculated at NLO and combined with the PYTHIA8 PS simulation using the FXFX [27] algorithm, denoted as MG5 aMC@NLO+PYTHIA8 [FXFX]. Up to three partons are considered at LO and combined with the PYTHIA8 PS simulation using the MLM [28] algorithm, denoted as MG5 aMC@NLO+PYTHIA8 [MLM]. The data are also compared to predictions obtained with POWHEG samples interfaced with HERWIG++ [29] (v 2.7.1) using the tune EE5C [30]. The signal samples are simulated assuming a top quark mass of 172.5 GeV and normalized to the inclusive cross section calculated at NNLO precision with next-to-next-to-leading-logarithmic (NNLL) accuracy [31].
For the simulation of W boson production and the Drell-Yan process, the MG5 aMC@NLO generator is used, and the samples are normalized to the cross sections calculated at NNLO [32].
The t-channel single top quark production in the tW channel is simulated with the POWHEG generator based on the five-flavor scheme [33,34], and normalized to the cross sections calculated at NNLO [35]. Diboson samples (WW, WZ, and ZZ) are simulated at LO using PYTHIA8, and normalized to the cross section calculated at NNLO for the WW sample [36] and NLO for the WZ and ZZ samples [37].
The detector response to the final-state particles is simulated using GEANT4 [38,39]. Additional pp collisions in the same or nearby beam crossings (pileup) are also simulated with PYTHIA8 and superimposed on the hard-scattering events using a pileup multiplicity distribution that reflects that of the analyzed data. Simulated events are reconstructed and analyzed with the same software used to process the data.

Object and event selection
The dilepton final state of the tt decay consists of two leptons (electrons or muons), at least two jets, and p miss T from the two neutrinos. Events are selected using dilepton triggers with asymmetric p T thresholds. The low transverse momentum (p T ) threshold is 8 GeV for the muon and 12 GeV for the electron, and the high-p T threshold is 17 GeV for both muon and electron. The trigger efficiency is measured in data using triggers based on p miss The reconstructed and selected muons [41] and electrons [42] are required to have p T > 20 GeV and |η| < 2.4. Since the primary leptons that originated from top quark decays are expected to be isolated, an isolation criterion is placed on each lepton to reduce the rate of secondary leptons from non-top hadronic decays. A relative isolation parameter is used, which is calculated as the sum of the p T of charged and neutral hadrons and photons in a cone of angular radius ∆R = √ (∆φ) 2 + (∆η) 2 ) around the direction of the lepton, divided by the lepton p T , where ∆φ and ∆η are the azimuthal and pseudorapidity differences, respectively, between the directions of the lepton and the other particle. Any mismodeling of the lepton selection in the simulation is accounted for by applying corrections derived using a "tag-and-probe" technique based on control regions in data [43]. 45], with ∆R = 0.4. The momenta of jets are corrected to account for effects from pileup, as well as nonuniformity and nonlinearity of the detector. For the data, energy corrections are also applied to correct the detector response [46]. We select jets with p T > 30 GeV and |η| < 2.4 that pass identification criteria designed to reject noise in the calorimeters.
Jets from the hadronization of b quarks (b jets) are identified by the combined secondary vertex b tagging algorithm [47]. The jets are selected using a loose working point [48], corresponding to an efficiency of about 80% and a light-flavor jet rejection probability of 85%. The b tagging efficiency in the simulation is corrected to be consistent with that in data.
Events are required to have exactly two oppositely charged leptons with the invariant mass of the dilepton system M + − > 20 GeV, and two or more jets, at least one of which has to be identified as a b jet. For the same-flavor lepton channels (ee and µµ), additional selection criteria are applied to reject events from Drell-Yan production: p miss T > 40 GeV and |M + − − M Z | > 15 GeV, where M Z is the Z boson mass [49]. The selected numbers of events after the selection are listed in Table 1.

Signal definition
The measurements of normalized tt differential cross sections are performed at both particle and parton levels as a function of kinematic observables, defined at the generator level. The particle-level top quark is defined at the generator level using the procedure described below. This approach avoids theoretical uncertainties in the measurements due to the different calculations within each generator, and leads to results that are largely independent of the generator implementation and tuning. Top quarks are reconstructed in the simulation starting from the final-state particles with a mean lifetime greater than 30 ps at the generator level, as summarized in Table 2.
Leptons are "dressed", which means that leptons are defined using the anti-k T clustering algorithm [44,45] with ∆R = 0.1 to account for final-state radiated photons. To avoid the ambiguity of additional leptons at the generator level, the clustering is applied to electrons, muons, and photons not from hadron decays. Events with leptons associated with τ lepton decays are treated as background. Leptons are required to satisfy the same acceptance requirements as imposed on the reconstructed objects described in Section 3, i.e., p T > 20 GeV and |η| < 2.4.
The generator-level jets are clustered using the anti-k T algorithm with ∆R = 0.4. The cluster-ing is applied to all final-state particles except neutrinos and particles already included in the dressed-lepton definition. Jets are required to have p T > 30 GeV and |η| < 2.4 to be consistent with the reconstructed-object selection. To identify the bottom quark flavor of the jet, the ghost-B hadron technique [13] is used in which short-lifetime B hadrons are included in the jet clustering after scaling down their momentum to be negligible. A jet is identified as a b jet if it contains any B hadrons among its constituents. A W boson at the particle level is defined by combining a dressed lepton and a neutrino. In each event, a pair of particle-level W bosons is chosen among the possible combinations such that the sum of the absolute values of the invariant mass differences with respect to the W boson mass is minimal [49]. Similarly, a top quark at the particle level is defined by combining a particle-level W boson and a b jet. The combination of a W boson and a b jet with the minimum invariant mass difference from the correct top quark mass [49] is selected. Events are considered to be in the visible phase space if they contain a pair of particle-level top quarks, constructed from neutrinos, dressed leptons, and b jets. Simulated dilepton events that are not in the visible phase space are considered as background and combined with the non-dilepton tt decay background contribution, subsequently denoted as tt-others.
In addition, the top quark and tt system observables are defined before the top quark decays into a bottom quark and a W boson and after QCD radiation, which we refer to as the parton level. The tt system at the parton level is calculated in the generator at NLO. The normalized differential cross sections at the parton level are derived by extrapolating the measurements into the full phase space, which includes the experimentally inaccessible regions, such as at high rapidity and low transverse momentum of the leptons and jets.

Reconstruction of the tt system
The top quark reconstruction method is adopted from the recent CMS measurement of the differential tt cross section [4]. In the dilepton channel, the reconstruction of the neutrino and antineutrino is crucial in measuring the top quark kinematic observables. Using an analytical approach [50,51], the six unknown neutrino degrees of freedom are constrained by the two measured components of p miss T and the assumed invariant masses of both the W boson and top quark. The efficiency for finding a physical solution depends on the detector resolution, which is accounted for by reconstructing the tt system in both the MC simulation and data with 100 trials, using random modifications of the measured leptons and b jets within their resolution functions. The efficiency for finding a physical solution to the kinematic reconstruction is approximately 90%, as determined from simulation and data. The numbers of events remaining after reconstructing the ttbar system are listed in Table 1.
In each trial, the solution with the minimum invariant mass of the tt system is selected, and a weight is calculated based on the expected invariant mass distribution of the lepton and b jet pairs (M b ) at generator level. The lepton and b jet pairs with the maximum sum of weights are chosen for the final solution of the tt system, and the reconstructed neutrino momentum is taken from the weighted average over the trials.
The kinematic variables of the leptons, b jets, top quarks, and tt system are taken from the selected final solution. Figure 1 shows the distributions of the transverse momenta of leptons (p lep T ), jets (p jet T ), and top quarks (p t T ), and the rapidity of the top quarks (y t ). Figure 2 displays the distributions of the transverse momentum (p tt T ), rapidity (y tt ), and invariant mass (M tt ) of the tt system, and the azimuthal angle between the top quarks (∆φ tt ). In the upper panel of each figure, the data points are compared to the sum of the expected contributions obtained from MC simulated events reconstructed as the data. The lower panel shows the ratio of the data to the expectations. The measured p lep T , p jet T , and p t T distributions are softer than those predicted by the MC simulation, resulting in the negative slopes observed in the bottom panels. However, in general, there is reasonable agreement between the data and simulation within the uncertainties, which are discussed in Sec. 7.

Normalized differential cross sections
The normalized differential tt cross sections (1/σ)(dσ/dX) are measured as a function of several different kinematic variables X. The variables include p t T , p tt T , y t , y tt , M tt , and ∆φ tt , at both the particle and parton levels. In addition, the measurements are performed with p lep T and p jet The non-tt backgrounds are estimated from simulation and subtracted from the data. For Drell-Yan processes the normalization of the simulation is determined from the data using the "R out/in " method [52][53][54]. The non-tt backgrounds are first subtracted from the measured distributions. The data distributions are slightly lower than those from the MC simulation. The tt-others backgrounds are then removed as a proportion of the total tt contribution by applying a single correction factor k shown in Eq. (1), using Eq. (2): Here, N MC non-tt is the total estimate for the non-tt background from the MC simulation, N MC tt-sig is the total MC-predicted tt signal yield, and N MC tt-others is the total MC prediction of the remaining tt background. The tt signal yield, N data tt-sig , is then extracted from the number of data events, N data , separately in each bin of the kinematic distributions, as shown in Eq. (2).
The bin widths of the distributions are chosen to control event migration between the bins at the reconstruction and generator level due to detector resolutions. We define the purity (stability) as the number of events generated and correctly reconstructed in a certain bin, divided by the total number of events in the reconstruction-level (generator-level) bin. The bin widths are chosen to give both a purity and a stability of about 50%.
Detector resolution and reconstruction efficiency effects are corrected using an unfolding procedure. The method relies on a response matrix that maps the expected relation between the  , and y t (lower right) distributions from data (points) and from MC simulation (shaded histograms). The signal definition for particle level is considered to distinguish tt-signal and tt-others. All corrections described in the text are applied to the simulation. The last bin includes the overflow events. The uncertainties shown by the vertical bars on the data points are statistical only while the hatched band shows the combined statistical and systematic uncertainties added in quadrature. The lower panels display the ratios of the data to the MC prediction.  , and ∆φ tt (lower right) distributions from data (points) and from MC simulation (shaded histograms). The signal definition for particle level is considered to distinguish tt-signal and tt-others. All corrections described in the text are applied to the simulation. The last bin includes the overflow events. The uncertainties shown by the vertical bars on the data points are statistical only while the hatched band shows the combined statistical and systematic uncertainties added in quadrature. The lower panels display the ratios of the data to the MC prediction. true and reconstructed variables taken from the POWHEG+PYTHIA8 simulation. The D'Agostini method [55] is employed to perform the unfolding. The effective regularization strength of the iterative D'Agostini unfolding is controlled by the number of iterations. A small number of iterations can bias the measurement towards the simulated prediction, while with a large number of iterations the result converges to that of a matrix inversion. The number of iterations is optimized for each distribution, using simulation to find the minimum number of iterations that reduces the bias to a negligible level. This optimization is performed with the multiplication of the response matrix and does not require any regularization. A detailed description of the method can be found in Ref. [13].

Systematic uncertainties
Several sources of systematic uncertainties are studied. The normalized differential cross sections are remeasured with respect to each source of systematic uncertainty individually, and the differences from the nominal values in each bin are taken as the corresponding systematic uncertainty. The overall systematic uncertainties are then obtained as the quadratic sum of the individual components.
The pileup distribution used in the simulation is varied by shifting the assumed total inelastic pp cross section by ±5%, in order to determine the associated systematic uncertainty. The systematic uncertainties in the lepton trigger, identification, and isolation efficiencies are determined by varying the measured scale factors by their total uncertainties. Uncertainties coming from the jet in the jet energy scale (JES) and jet energy resolution (JER) are determined on a per-jet basis by shifting the energies of the jets [56] within their measured energy scale and resolution uncertainties. The b tagging uncertainty is estimated by varying its efficiency uncertainty.
The uncertainty in the non-tt background normalization is estimated using a 15-30% variation in the background yields, which is based on a previous CMS measurement of the tt cross section [40]. The uncertainty in the shape of the tt-others contribution is obtained by reweighting the p T distribution of the top quark for the tt-others events to match the data and comparing with the unweighted contribution. For the theoretical uncertainties, we investigate the effect of the choice of PDFs, factorization and renormalization scales (µ F and µ R ), variation of the top quark mass, top quark p T , and hadronization and generator modeling.
The PDF uncertainty is estimated using the uncertainties in the NNPDF30 NLO as 0118 set with the strong coupling strength α s = 0.118 [57]. We measure 100 individual uncertainties and take the root-mean-square as the PDF uncertainty, following the PDF4LHC recommendation [58]. In addition, we consider the PDF sets with α s = 0.117 and 0.119. The MC generator modeling uncertainties are estimated by taking the difference between the results based on the POWHEG and MG5 aMC@NLO generators.
The uncertainty from the choice of µ F and µ R is estimated by varying the scales by a factor of two up and down in POWHEG independently for the ME and PS steps. For the ME calculation, all possible combinations are considered independently, excluding the most extreme cases of (µ F , µ R ) = (0.5, 2) and (2, 0.5) [59,60]. The scale uncertainty in the PS modeling is assessed using dedicated MC samples with the scales varied up and down together. The uncertainties in the factorization and renormalization scales in the ME and PS calculations are taken as the envelope of the differences with respect to the nominal parameter choice.
We evaluate the top quark mass uncertainty by taking the maximum deviation between the nominal MC sample with a top quark mass of 172.5 GeV and samples with masses of 171.5 and 173.5 GeV. The tt signal cross sections are not corrected for the mismodeling of the top quark p T distribution in simulation. Instead, a systematic uncertainty from this mismodeling is obtained by comparing the nominal results to the results obtained from a response matrix using tt-signal in which the top quark p T distribution is reweighted to match the data. The uncertainty from hadronization and PS modeling is estimated by comparing the results obtained from POWHEG samples interfaced with PYTHIA8 and with HERWIG++. Table 3 lists typical values for the statistical and systematic uncertainties in the measured normalized tt differential cross sections. The table gives the uncertainty sources and corresponding range of the median uncertainty of each distribution, at both the particle and parton levels. The hadronization is the dominant systematic uncertainty source for p t T (4.9% at particle and 7.1% at parton level) and M tt (5.9% at particle and 7.4% at parton level), and the MC generator modeling is dominant for y t (2.3% at particle and 2.2% at parton level), p tt T (6.1% at particle and 3.9% at parton level), y tt (1.2% at particle and 1.6% at parton level), and ∆φ tt (9.2% at particle and 7.3% at parton level). In general, the MC generator modeling and hadronization are the dominant systematic uncertainty sources for both the particle-and parton-level measurements. Table 3: Statistical and systematic uncertainties in the normalized tt differential cross sections at particle and parton levels. The uncertainty sources and the corresponding range of the median uncertainty of each distribution are shown in percent.

Results
The normalized differential tt cross sections are measured by subtracting the background contribution, correcting for detector effects and acceptance, and dividing the resultant number of tt signal events by the total inclusive tt cross section. Figs. 3 and 4 show the normalized differential tt cross sections as a function of p lep T , p jet T , p t T , y t , p tt T , y tt , M tt , and ∆φ tt at the particle level in the visible phase space. Parton-level results are also independently extrapolated to the full phase space using the POWHEG+PYTHIA8 tt simulation. Figures 5 and 6 show the normalized differential tt cross sections as a function of p t T , y t , p tt T , y tt , M tt , and ∆φ tt at parton level in the full phase space. The measured data are compared to different standard model predictions from POWHEG+PYTHIA8, MG5 aMC@NLO+PYTHIA8[FXFX], MG5 aMC@NLO+PYTHIA8[MLM], and POWHEG+HERWIG++ in the figures. The values of the measured normalized differential tt cross sections at the parton and particle levels with their statistical and systematic uncertainties are listed in Appendices A and B.
The compatibility between the measurements and the predictions is quantified by means of a χ 2 test performed with the full covariance matrix from the unfolding procedure, including the systematic uncertainties. Tables 4 and 5 report the values obtained for the χ 2 with the numbers of degrees of freedom (dof) and the corresponding p-values [61]. The lepton, jet, and top quark p T spectra in data tend to be softer than the MC predictions for the high-p T region. A similar trend was also observed at √ s = 8 TeV by both the ATLAS and CMS experiments [4, 5]. The POWHEG+PYTHIA8 generator better describes the p tt T , y t , and y tt distributions at the particle and parton levels, while POWHEG+HERWIG++ is found to be in good agreement for the p t T at the parton and particle levels. In general, measurements are found to be in fair agreement with predictions within the uncertainties.
The parton-level results are also compared to the following perturbative QCD calculations: • An approximate NNLO calculation based on QCD threshold expansions beyond the leading-logarithmic approximation using the CT14nnlo PDF set [62].
• An approximate next-to-NNLO (N 3 LO) calculation performed with the resummation of soft-gluon contributions in the double-differential cross section at NNLL accuracy in momentum space using the MMHT2014 PDF set [63,64].
• An improved NNLL QCD calculation (NLO+NNLL') [65] with simultaneous resummation of soft and small-mass logarithms to NNLL accuracy, matched with both the standard soft-gluon resummation at NNLL accuracy and the fixed-order calculation at NLO accuracy, using the MTSW2008nnlo PDF set.
The measurements and the perturbative QCD predictions are shown in Figs. 7 and 8. Table 6 gives the χ 2 /dof and the corresponding p-values for the agreement between the measurements and QCD calculations. The normalized differential tt cross sections as a function of the y t , y tt , and p tt T are found to be in good agreement with the different predictions considered. We observe some tension between the data and the NNLO predictions for other variables such as the p t T and M tt .

Summary
The normalized differential cross sections for top quark pair production have been presented by the CMS experiment in the dilepton decay channel in pp collisions at √ s = 13 TeV with data corresponding to an integrated luminosity of 2.1 fb −1 . The differential cross sections are measured as a function of several kinematic variables at particle level in a visible phase space corresponding to the detector acceptance and at parton level in the full phase space. The measurements are compared to the predictions from Monte Carlo simulations and calculations in perturbative quantum chromodynamics. In general, the measurements are in fairly good agreement with predictions. We confirm that the top quark p T spectrum in data is softer than the Monte Carlo predictions at both particle and parton levels, as reported by the ATLAS and CMS experiments. The present results are in agreement with the earlier ATLAS and CMS measurements. We also find that the measurements are in better agreement with calculations within       quantum chromodynamics up to next-to-next-to-leading-order accuracy at the parton level compared to previous next-to-leading-order predictions.  Figure 7: Normalized differential tt cross sections as a function of top quark p T (left) and top quark rapidity (right), measured at the parton level in the full phase space and combining the distributions for top quarks and antiquarks. The vertical bars on the data points indicate the total (combined statistical and systematic) uncertainties, while the hatched band shows the statistical uncertainty. The measurements are compared to different perturbative QCD calculations of an approximate NNLO [62], an approximate next-to-NNLO (N 3 LO) [63], an improved NLO+NNLL (NLO+NNLL') [65], and a full NNLO [66]. The lower panel gives the ratio of the theoretical predictions to the data. , and M tt (lower) for the top quarks or antiquarks, measured at parton level in the full phase space. The vertical bars on the data points indicate the total (combined statistical and systematic) uncertainties, while the hatched band shows the statistical uncertainty. The measurements are compared to different perturbative QCD calculations of an improved NLO+NNLL (NLO+NNLL') [65] and a full NNLO [66]. The lower panel gives the ratio of the theoretical predictions to the data.

Acknowledgments
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 [4] CMS Collaboration, "Measurement of the differential cross section for top quark pair production in pp collisions at √ s = 8 TeV", Eur. Phys. J. C 75 (2015) 542, doi:10.1140/epjc/s10052-015-3709-x, arXiv:1505.04480.
[16] S. Choi and H. S. Lee, "Azimuthal decorrelation in tt production at hadron colliders", Phys.   [54] CMS Collaboration, "Measurement of the tt production cross section in the dilepton channel in pp collisions at √ s = 7 TeV", JHEP 11 (2012) 067, doi:10.1007/JHEP11(2012)067, arXiv:1208.2671. A Tables of differential tt cross sections at the particle level Table 7: Normalized differential tt cross sections with statistical and systematic uncertainties at the particle level as a function of p lep T . The factor given in the last column applies to the values of the normalized cross section and the statistical and systematic uncertainties in that row.   Table 9: Normalized differential tt cross sections with statistical and systematic uncertainties at the particle level as a function of p t T . The factor given in the last column applies to the values of the normalized cross section and the statistical and systematic uncertainties in that row.
(1/σ)(dσ/dp t T ) stat syst factor [0, 65] 4.14 0.12 0.13 ×10 −3 [65,125] 5  10: Normalized differential tt cross sections with statistical and systematic uncertainties at the particle level as a function of y t . The factor given in the last column applies to the values of the normalized cross section and the statistical and systematic uncertainties in that row.   12: Normalized differential tt cross sections with statistical and systematic uncertainties at the particle level as a function of y tt . The factor given in the last column applies to the values of the normalized cross section and the statistical and systematic uncertainties in that row.    B Tables of differential cross section at the parton level   Table 15: Normalized differential tt cross sections with statistical and systematic uncertainties at the parton level as a function of p t T . The factor given in the last column applies to the values of the normalized cross section and the statistical and systematic uncertainties in that row. p t T [GeV] (1/σ)(dσ/dp t T ) stat syst factor [0, 65] 4.24 0.11 0.40 ×10 −3 [65,125] 6.10 0.13 0.14 ×10 −3