Measurement of differential cross sections for the production of top quark pairs and of additional jets in lepton+jets events from pp collisions at $\sqrt{s} =$ 13 TeV

Differential and double-differential cross sections for the production of top quark pairs in proton-proton collisions at $\sqrt{s} =$ 13 TeV are measured as a function of kinematic variables of the top quarks and the top quark-antiquark ($\mathrm{t}\overline{\mathrm{t}}$) system. In addition, kinematic variables and multiplicities of jets associated with the $\mathrm{t}\overline{\mathrm{t}}$ production are measured. This analysis is based on data collected by the CMS experiment at the LHC in 2016 corresponding to an integrated luminosity of 35.8 fb$^{-1}$. The measurements are performed in the lepton+jets decay channels with a single muon or electron and jets in the final state. The differential cross sections are presented at the particle level, within a phase space close to the experimental acceptance, and at the parton level in the full phase space. The results are compared to several standard model predictions that use different methods and approximations. The kinematic variables of the top quarks and the $\mathrm{t}\overline{\mathrm{t}}$ system are reasonably described in general, though none predict all the measured distributions. In particular, the transverse momentum distribution of the top quarks is more steeply falling than predicted. The kinematic distributions and multiplicities of jets are adequately modeled by certain combinations of next-to-leading-order calculations and parton shower models.


Introduction
Measurements of differential production cross sections of top quark pairs (tt) provide important information for testing the standard model and searching for phenomena beyond the standard model. Precise theoretical predictions of these measurements are challenging since higher-order effects of quantum chromodynamics (QCD) and electroweak (EW) corrections [1] are important. Moreover, the generation of tt events requires a realistic modeling of the parton shower (PS). The measured kinematic properties and multiplicities of jets allow for a detailed comparison of different PS models to the data and provide insight into their tuning.
In this paper, differential and double-differential production cross sections as a function of kinematic variables of the top quarks and the tt system are reported. In addition, measurements of multiplicities and kinematic properties of jets in tt events are presented. The measurements are based on proton-proton (pp) collision data at a center-of-mass energy of 13 TeV corresponding to an integrated luminosity of 35.8 fb −1 [2]. The data were recorded by the CMS experiment at the CERN LHC in 2016. Only tt decays into the +jets ( = e, µ) final state are considered, where, after the decay of each top quark into a bottom quark and a W boson, one of the W bosons decays hadronically and the other one leptonically. Hence, the experimental signature consists of two jets coming from the hadronization of b quarks (b jets), two jets from a hadronically decaying W boson, a transverse momentum imbalance associated with the neutrino from the leptonically decaying W boson, and a single isolated muon or electron.
This measurement continues a series of differential tt production cross section measurements in pp collisions at the LHC. Previous measurements of differential cross sections at √ s = 7 TeV [3, 4] and 8 TeV [5][6][7][8][9][10][11] have been performed in various tt decay channels. First measurements at 13 TeV are available [12][13][14]. Previous studies of multiplicities and kinematic properties of jets in tt events can be found in Refs. [15][16][17]. With about 15 times more data and an improved understanding of systematic uncertainties, we provide an update and extension to the previous CMS analysis in the +jets channel at 13 TeV [18]. We measure differential cross sections defined in two ways: at the particle level and the parton level. For the particle-level measurement a proxy of the top quark is defined based on experimentally accessible quantities, such as properties of jets, which are made up of quasistable particles with a mean lifetime greater than 30 ps. These quantities are described by theoretical predictions that require modeling of the PS and hadronization, in addition to the matrix-element calculations. The kinematic requirements on these objects are chosen to closely reproduce the experimental acceptance. Muons and electrons stemming from τ lepton decays are not treated separately and can contribute to the particle-level signal. A detailed definition of particle-level objects is given in Section 3. The particle-level approach has the advantage that it reduces theoretical uncertainties in the experimental results by avoiding theory-based extrapolations from the experimentally accessible portion of the phase space to the full range, and from jets to partons.
For the parton-level measurement top quarks in the +jets decay channel are defined as signal directly before their decays into a bottom quark and a W boson. The τ+jets decay channel is not considered here as signal even in cases where the τ lepton decays into a muon or electron. No restriction on the phase space is applied for parton-level top quarks. The corrections and extrapolations used in this measurement are based on a next-to-leading-order (NLO) calculation of tt production, combined with a simulation of the PS.
For both particle-and parton-level measurements the tt system is reconstructed at the detector level with a likelihood-based approach using the top quark and W boson mass constraints to identify the corresponding top quark decay products. The differential cross sections are measured at the particle and parton levels as a function of the transverse momentum p T and the absolute rapidity |y| of the top quarks, separately for the hadronically (labeled t h ) and leptonically (labeled t ) decaying W bosons, and the p T , |y|, and invariant mass M of the tt system. In addition, the differential cross sections at the parton level are determined as a function of the lower-and higher-p T values of the top quarks in an event. Double-differential cross sections for the following combinations of variables are determined at both levels: |y(t h )| vs. p T (t h ), M(tt) vs. |y(tt)|, and p T (t h ) vs. M(tt). At particle level, the differential cross sections as a function of p T (t h ), p T (tt), and M(tt) are measured in bins of jet multiplicity. Using the four jets identified as the tt decay products and the four highest-p T additional jets, the cross sections are determined as a function of the jet p T and absolute pseudorapidity |η|, the minimal separation ∆R j t of jets from another jet in the tt system, and the separation ∆R t of jets from the closest top quark. Here ∆R = √ (∆φ) 2 + (∆η) 2 , where ∆φ and ∆η are the differences in azimuthal angle (in radians) and pseudorapidity between the directions of the two objects. Finally, we determine the gap fraction, defined as the fraction of events that do not contain jets above a given p T threshold, and the jet multiplicities for various thresholds of the jet p T . This paper is organized as follows: In Section 2, we provide a description of the signal and background simulations, followed by the definition of the particle-level top quarks in Section 3. After a short overview of the CMS detector and the particle reconstruction in Section 4, we describe the object and event selections in Section 5. Section 6 contains a detailed description of the reconstruction of the tt system. Details on the background estimation and the unfolding are presented in Sections 7 and 8. After a discussion of systematic uncertainties in Section 9, the differential cross sections as a function of observables of the top quark and the tt system are presented in Section 10. Finally, observables involving jets are discussed in Section 11. The results are summarized in Section 12.

Signal and background modeling
The Monte Carlo generator POWHEG [19][20][21][22] (v2,hvq) is used to calculate the production of tt events at NLO accuracy in QCD. The renormalization µ r and factorization µ f scales are set to the transverse mass m T = √ m 2 t + p 2 T of the top quark, where a top quark mass m t = 172.5 GeV is used in all simulations. The result is combined with the PS simulations of PYTHIA8 [23,24] (v8.219) using the underlying event tune CUETP8M2T4 [25,26], and of HERWIG++ [27] (v2.7.1) using the tune EE5C [28]. In addition, MADGRAPH5 aMC@NLO [29] (v2.2.2) (MG5 aMC@NLO) is used to produce a simulation of tt events with additional partons. All processes with up to two additional partons are calculated at NLO and combined with the PYTHIA8 PS simulation using the FxFx [30] algorithm. The scales are selected as µ r = µ f = 1 2 (m T (t) + m T (t)). The default parametrization of the parton distribution functions (PDFs) used in all simulations is NNPDF30 nlo as 0118 [31]. The simulations are normalized to an inclusive tt production cross section of 832 +40 −46 pb [32]. This value is calculated with next-to-NLO (NNLO) accuracy, including the resummation of next-to-next-to-leading-logarithmic soft-gluon terms. Its uncertainty is evaluated by varying the choice of µ r and µ f and by propagating uncertainties in the PDFs.
Distributions that correspond to variations in the PDFs or the scales µ r and µ f are obtained by applying different event weights. These distributions are used for the corresponding uncertainty estimates. For additional uncertainty estimations we use POWHEG+PYTHIA8 simulations with top quark masses of 171.5 and 173.5 GeV, with initial and final PS scales varied up and down by a factor of two, with variations of the underlying event tune, and a simulation with an alternative color-reconnection model.
The main backgrounds are simulated using the same techniques. The MG5 aMC@NLO generator is used for the simulation of W boson production in association with jets, t-channel single top quark production, and Drell-Yan (DY) production in association with jets. The generator POWHEG [33] is used for the simulation of single top quark associated production with a W boson (tW), and PYTHIA8 is used for multijet production. In all cases, the PS and the hadronization are described by PYTHIA8. The W boson and DY backgrounds are normalized to their NNLO cross sections calculated with FEWZ [34] (v3.1). The t-channel single top quark production is normalized to the NLO calculation obtained from HATHOR [35] (v2.1). The production of tW is normalized to the NLO calculation [36], and the multijet simulation is normalized to the LO calculation obtained with PYTHIA8 [24].
The detector response is simulated using GEANT4 [37]. The simulations include multiple pp interactions per bunch crossing (pileup). The simulated events are weighted, depending on their number of pileup interactions, to reproduce the measured pileup distribution. Finally, the same reconstruction algorithms that are applied to the data are used for the simulated events.

Particle-level top quark definition
The definitions of particle-level objects constructed from quasi-stable simulated particles, obtained from the predictions of tt event generators before any detector simulation, are summarized below. These particle-level objects are further used to define the particle-level top quarks. Detailed studies on particle-level definitions can be found in Ref. [38].
• All simulated muons and electrons are corrected for effects of bremsstrahlung by adding the photon momenta to the momentum of the closest lepton if their separation is ∆R < 0.1. All photons are considered for the momentum correction. A corrected lepton is selected if it fulfills the isolation requirement that the p T sum of all quasi-stable particles, excluding corrected leptons and neutrinos, within ∆R = 0.4 is less than 35% of the corrected lepton p T . In addition, we require the lepton to have p T > 15 GeV and |η| < 2.4. • Simulated photons with p T > 15 GeV and |η| < 2.4 that are not used in the momentum correction of a lepton are considered if their isolation, defined analogously to the lepton isolation, is below 25%.
• All neutrinos are selected including those stemming from decays of hadrons.
• Jets are clustered by the anti-k T jet algorithm [39,40] with a distance parameter of 0.4. All quasi-stable particles with the exception of neutrinos are clustered. Jets with p T > 25 GeV and |η| < 2.4 are selected if there is no isolated lepton or photon, as defined above, within ∆R = 0.4. • b jets at the particle level are defined as those jets that contain a b hadron. As a result of the short lifetime of b hadrons, these are not quasi-stable particles and only their decay products should be considered for the jet clustering. However, to allow their association with a jet, the b hadrons are also included with their momenta scaled down to a negligible value. This preserves the information of their directions, but removes their impact on the jet clustering.
Based on the invariant masses of these objects, we construct a pair of particle-level top quarks in the +jets final state. Events with exactly one muon or electron with p T > 30 GeV and |η| < 2.4 are selected. Simulated events with an additional muon or electron with p T > 15 GeV and |η| < 2.4 are rejected. We take the sum of the four-momenta of all neutrinos as the neutrino candidate momentum p ν from the leptonically decaying top quark and find the permutation of jets that minimizes the quantity (1) where p j W1,2 are the four-momenta of two light-flavor jet candidates, considered as the decay products of the hadronically decaying W boson; p b ,h are the four-momenta of two b jet candidates; p is the four-momentum of the lepton; and m W = 80.4 GeV [41] is the mass of the W boson. All jets with p T > 25 GeV and |η| < 2.4 are considered. At least four jets are required, of which at least two must be b jets. The remaining jets with p T > 30 GeV and |η| < 2.4 are defined as additional jets.
Events with a hadronically and a leptonically decaying particle-level top quark are not required to be +jets events at the parton level, e.g., tt dilepton events with additional jets can be identified as +jets event at the particle level if one lepton fails to pass the selection. As an example, the comparison between the p T (t h ) distributions at the particle and parton levels are shown in Fig. 1 and demonstrates the direct relation between particle-level and parton-level top quarks.
To obtain an unambiguous nomenclature for the jets, we define j W1 to be the jet in the W boson decay with the higher p T . The additional jets j i are sorted by their transverse momenta where j 1 has the highest p T .  Figure 1: Comparison between the p T (t h ) distributions at the particle and parton level, extracted from the POWHEG+PYTHIA8 simulation. Left: fraction of parton-level top quarks in the same p T bin at the particle level (purity), fraction of particle-level top quarks in the same p T bin at the parton level (stability), ratio of the number of particle-to parton-level top quarks (bin efficiency), and fraction of events with a particle-level top quark pair that are not considered as signal events at the parton level (non-parton-level signal). Right: p T -bin migrations between particle and parton level. The p T range of the bins can be taken from the left panel. Each column is normalized such that the sum of its entries corresponds to the fraction of particle-level events in this bin at the parton level in the full phase space.

The CMS detector
The central feature of the CMS detector is a superconducting solenoid of 6 m internal diameter, providing a magnetic field of 3.8 T. Within the solenoid 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. Forward calorimeters extend the η coverage provided by the barrel and endcap detectors. Muons are measured in gas-ionization detectors 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 and relevant kinematic variables, can be found in Ref. [42].
The particle-flow (PF) event algorithm [43] reconstructs and identifies each individual particle with an optimized combination of information from the various elements of the CMS detector. The energy of muons is obtained from the curvature of the corresponding track. The energy of electrons is determined from a combination of the electron momentum at the primary interaction vertex as determined by the tracker, the energy of the corresponding ECAL cluster, and the energy sum of all bremsstrahlung photons spatially compatible with originating from the electron track. The energy of photons is directly obtained from the ECAL measurement, corrected for zero-suppression effects. The energy of charged hadrons is determined from a combination of their momentum measured in the tracker and the matching ECAL and HCAL energy deposits, corrected for zero-suppression effects and for the response function of the calorimeters to hadronic showers. Finally, the energy of neutral hadrons is obtained from the corresponding corrected ECAL and HCAL energy.

Physics object reconstruction and event selection
The measurements presented in this paper depend on the reconstruction and identification of muons, electrons, jets, and missing transverse momentum associated with a neutrino. Muons and electrons are selected if they are compatible with originating from the primary vertex, which, among the reconstructed primary vertices, is the one with the largest value of summed physics-object p 2 T . The physics objects are jets, clustered using the jet finding algorithm [39,40] with the tracks assigned to the primary vertex as inputs, and the associated missing transverse momentum, taken as the negative vector sum of the p T of those jets.
Since leptons from tt decays are typically isolated, a requirement on the lepton isolation is used to reject leptons produced in decays of hadrons. The lepton isolation variables are defined as the sum of the p T of neutral hadrons, charged hadrons, and photon PF candidates within a cone of ∆R = 0.4 for muons and ∆R = 0.3 for electrons. It is required to be less than 15% (6%) of the muon (electron) p T . Event-by-event corrections are applied to maintain a pileup-independent isolation efficiency. The muon and electron reconstruction and selection efficiencies are measured in the data using tag-and-probe techniques [44][45][46]. Depending on the p T and η, their product is 75-85% for muons and 50-80% for electrons.
Jets are clustered from PF objects using the anti-k T jet algorithm with a distance parameter of 0.4 implemented in the FASTJET package [40]. Charged particles originating from a pileup interaction vertex are excluded. The total energy of the jets is corrected for energy depositions from pileup. In addition, p T -and η-dependent corrections are applied to correct for the detector response effects [47]. If an isolated lepton with p T > 15 GeV within ∆R = 0.4 around a jet exists, the jet is assumed to represent the isolated lepton and is removed from further consideration.
For the identification of b jets, the combined secondary vertex algorithm [48] is used. It provides a discriminant between b and non-b jets based on the combined information of secondary vertices and the impact parameter of tracks at the primary vertex. A jet is identified as a b jet if the associated value of the discriminant exceeds a threshold criterion with an efficiency of about 63% and a combined charm and light-flavor jet rejection probability of 97%.
The missing transverse momentum p miss T is calculated as the negative of the vectorial sum of transverse momenta of all PF candidates in the event. Jet energy corrections are also propa-gated to improve the measurement of p miss T .
Events considered for this analysis are selected by single-lepton triggers. These require p T > 24 GeV for muons and p T > 27 GeV for electrons, as well as various quality and isolation criteria.
To reduce the background contributions and optimize the tt reconstruction, additional requirements are imposed on the recorded events. Events with exactly one muon or electron with p T > 30 GeV and |η| < 2.4 are selected. No additional muons or electrons with p T > 15 GeV and |η| < 2.4 are allowed. In addition to the lepton, at least four jets with p T > 30 GeV and |η| < 2.4 are required. At least two of these jets must be identified as b jets.
We compare several kinematic distributions in the data to the simulation separately for the muon and electron channels to verify that there are no unexpected differences. The ratios of the measured to the expected event yields in the two channels agree within the uncertainty in the lepton reconstruction and selection efficiencies. In the remaining steps of the analysis, the two channels are combined by adding their distributions.

Reconstruction of the top quark-antiquark system
The reconstruction of the tt system follows closely the methods used in Ref. [18]. The goal is the correct identification of detector-level objects as parton-or particle-level top quark decay products. In the simulation, a jet or lepton at the particle level can be spatially matched to the corresponding detector-level object. If no one-to-one assignment to a corresponding detector-level object is possible for any of the objects in the particle-level tt system, the event is considered as "nonreconstructable" in the particle-level measurement. For the parton-level measurement a quark from the tt decay is assigned to the detector-level jet with the highest p T within ∆R = 0.4 around the parton. If no one-to-one correspondence at detector level is found for any of these quarks or the leptons, the event is "nonreconstructable" in the parton-level measurement. In particular, this includes events with merged topologies where at least two quarks are matched to the same jet. Based on these relations between detector level and parton or particle level, the efficiencies of the tt reconstruction are studied. A detailed discussion on the relationship between quantities at the parton or particle level and detector level is presented in Section 8.
For the reconstruction all possible permutations of assigning detector-level jets to the corresponding tt decay products are tested and a likelihood that a certain permutation is correct is evaluated. Permutations are considered only if the two jets with the highest b identification probabilities are the two b jet candidates. In each event, the permutation with the highest likelihood is selected. The likelihoods are evaluated separately for the particle-and the parton-level measurements.
For each tested permutation the neutrino four-momentum p ν is reconstructed using the algorithm of Ref. [49]. The idea is to find all possible solutions for the three components of the neutrino momentum vector using the two mass constraints (p ν + p ) 2 = m 2 W and (p ν + p + p b ) 2 = m 2 t . Each equation describes an ellipsoid in the three-dimensional momentum space of the neutrino. The intersection of these two ellipsoids is usually an ellipse. We select p ν as the point on the ellipse for which the distance D ν,min between the ellipse projection onto the transverse plane and p miss T is minimal. This algorithm leads to a unique solution for the longitudinal neutrino momentum and an improved resolution of its transverse component. For the cases where the invariant mass of the lepton and b candidate is above m t no solution can be found and the corresponding permutation is discarded. The minimum distance D ν,min is also used to identify the correct b , as described below.
The value of D ν,min from the neutrino reconstruction and the mass constraints on the hadronically decaying top quark are combined in a likelihood function λ, given by where P m is the two-dimensional probability density of the invariant masses of W bosons and top quarks that are correctly reconstructed, based on the matching criteria described above. The value of λ is maximized to select the permutation of jets. The probability density P m is calculated as a function of the invariant mass of the two jets, m 2 , tested as the W boson decay products, and the invariant mass of the three jets, m 3 , tested as the decay products of the hadronically decaying top quark. The distributions for the correct jet assignments, taken from the POWHEG+PYTHIA8 simulation and normalized to unit area, are shown in Fig. 2 (upper) for the particle-and parton-level measurements. This part of the likelihood function is sensitive to the correct reconstruction of the hadronically decaying top quark. Permutations with probabilities less than 0.1% of the maximum value of the probability density P m are rejected. This selection criterion discards less than 1% of the correctly reconstructed events. Especially in the parton-level measurement, it removes events that are incompatible with the hypothesis of a hadronically decaying top quark and reduces the background contribution. This is caused by the stringent mass constraints for a parton-level top quark, where, in contrast to the particlelevel top quark, close compatibility with the top quark and W boson masses are required.
The probability density P ν describes the distribution of D ν,min for a correctly selected b . In Fig. 2 (lower), the normalized distributions of D ν,min for b and for other jets are shown. On average, the distance D ν,min for a correctly selected b is smaller and has a smaller tail compared to the distance obtained for other jets. Permutations with values of D ν,min > 150 GeV are rejected since they are very unlikely to originate from a correct b association. This part of the likelihood function is sensitive to the correct reconstruction of the leptonically decaying top quark.
Since the likelihood function λ combines the probabilities from the reconstruction of the leptonically and hadronically decaying top quarks, it provides information on the reconstruction of the whole tt system. The performance of the reconstruction as a function of jet multiplicity is shown for several tt simulations in Fig. 3, where we use the input distributions P m and P ν from the POWHEG+PYTHIA8 simulation. The reconstruction efficiency of the algorithm is defined as the probability that the most-likely permutation, as identified through the maximization of the likelihood λ, is the correct one, given that all tt decay products are reconstructed and selected. The performance deteriorates with the increase in the number of jets, since the number of permutations increases drastically and the probability of selecting a wrong permutation increases. The differences observed between the various simulations are taken into account in the estimation of the systematic uncertainties. We observe a lower reconstruction efficiency for the particle-level measurement. This is caused by the less powerful mass constraints for a particle-level top quark. This can be seen in the mass distributions of Fig. 2 and the likelihood distributions in Fig. 4, where the simulations are normalized to the measured integrated luminosity of the data sample, and the tt simulation is divided into the following categories: correctly reconstructed tt systems (tt right reco); events where all decay products are available, but the algorithm failed to identify the correct permutation (tt wrong reco); the nonreconstructable events (tt nonreconstructable); and events that are according to the parton-or particle-level definitions not tt signal events (tt nonsignal). Only the last category is treated as tt background, while the other categories are considered as signal. The lower reconstruction efficiency of the particle-level top quark is compensated by the higher number of reconstructable events.      Pred. Data Figure 4: Distribution of the negative log-likelihood for the selected best permutation in the (left) parton-and the (right) particle-level measurements in data and simulations. Events generated with POWHEG+PYTHIA8 are used to describe the tt production. The contribution of multijet, DY, and W boson plus jets background events is extracted from the data (cf. Section 7). Combined experimental (cf. Section 9) and statistical uncertainties (hatched area) are shown for the total predicted yields. The data points are shown with statistical uncertainties. The ratios of data to the sum of the predicted yields are provided at the bottom of each panel.
In Fig. 5, the p T of the jets from the tt system, as identified by the reconstruction algorithm, and of the additional jets are presented and compared to the simulation. In Fig. 6, the distributions of p T and |y| of the reconstructed top quarks, and in Fig. 7, the distributions of p T (tt), |y(tt)|, and M(tt) for the parton-and particle-level measurements are shown. The simulations are normalized according to the measured integrated luminosity of the data. In general, good agreement is observed between the data and the simulation, although all measured p T spectra are softer than predicted by the simulation.

Background subtraction
After the event selection and tt reconstruction, we observe about 450 000 and 570 000 events at the parton and particle levels, respectively, where total background contributions of 4.5 and 6.0% from single top quark, DY, W boson, and multijet events are predicted. These backgrounds have to be estimated and subtracted from the selected data. In addition, a residual contamination from nonsignal tt events is expected and estimated from the simulation, as detailed below.
The predictions of the single top quark background are taken from simulations. Its overall contribution corresponds to about 2.7 and 3.3% of the selected data in the parton-and particlelevel measurements, respectively.
Single top quark production cross sections are calculated with a precision of a few percent [35,36]. However, these calculations do not consider the production of additional jets as required by the tt selection. Therefore, we use an overall uncertainty of 50%, which represents a conservative estimate of the PS modeling, scale, and PDF uncertainties. Even with such a conservative estimate, its impact on the precision of the final results is negligible.
After the full tt selection, the numbers of events in the simulations of multijet, DY, and W boson production are not sufficient to obtain smooth background distributions. Therefore, we extract a common distribution for these backgrounds from a control region in the data. Its selection differs from the signal selection by the requirement of having no b-tagged jet in the event. In this control region, the contribution of tt events is estimated to be about 15%, while the   Figure 5: Comparisons between data and simulation at the particle level of the reconstructed distributions of the p T of jets as identified by the tt reconstruction algorithm. The simulation of POWHEG+PYTHIA8 is used to describe the tt production. The contribution of multijet, DY, and W boson plus jets background events is extracted from the data (cf. Section 7). Combined experimental (cf. Section 9) and statistical uncertainties (hatched area) are shown for the total predicted yields. The data points are shown with statistical uncertainties. The ratios of data to the predicted yields are given at the bottom of each panel.  Pred. Data Figure 6: Comparisons of the reconstructed p T (upper) and |y| (lower) in data and simulations for the t (left) at the parton level and the t h (right) at the particle level. The simulation of POWHEG+PYTHIA8 is used to describe the tt production. The contribution of multijet, DY, and W boson plus jets background events is extracted from the data (cf. Section 7). Combined experimental (cf. Section 9) and statistical uncertainties (hatched area) are shown for the total predicted yields. The data points are shown with statistical uncertainties. The ratios of data to the predicted yields are given at the bottom of each panel.   Figure 7: Comparisons of the reconstructed distributions of p T (tt) (upper), |y(tt)| (middle), and M(tt) (lower) for the (left) parton-and the (right) particle-level measurements in data and simulation. The simulation of POWHEG+PYTHIA8 is used to describe the tt production. The contribution of multijet, DY, and W boson plus jets background events is extracted from the data (cf. Section 7). Combined experimental (cf. Section 9) and statistical uncertainties (hatched area) are shown for the total predicted yields. The data points are shown with statistical uncertainties. The ratios of data to the predicted yields are given at the bottom of each panel.
remaining fraction consists of multijet, DY, and W boson events. The background distributions are obtained after applying exactly the same tt reconstruction algorithm as in the signal region. The two b jet candidates still have the highest value of the b identification discriminant to maintain a similar number of allowed permutations of jets in the control and signal regions. To estimate the shape dependency on the selection of the control region, we vary the selection threshold of the b identification discriminant. This changes the tt signal contribution and the flavor composition. However, we find the observed shape variations to be small. In addition, we verify in the simulation that the shapes of the distributions obtained from the control region are compatible with the background distributions in the signal region. For the background subtraction the distributions extracted from the control region are normalized individually in each bin of jet multiplicity to the yield of multijet, DY, and W boson events predicted by the simulation in the signal region. In the control region, the expected and measured event yields agree within their statistical uncertainties. Taking into account the statistical uncertainty in the normalization factor and the shape differences between the signal and control regions in the simulation, we derive an overall uncertainty of 20% in this background estimation.
Special care has to be taken with the contribution of nonsignal tt events. For the parton-level measurement these are dilepton, all-jets, and τ+jets events. For the particle-level measurement all tt events for which no pair of particle-level top quarks exists are considered as nonsignal tt events. The corresponding contributions are about 11.5% for both the parton-and the particlelevel measurements. The behavior of these backgrounds depends on the tt cross section, and a subtraction according to the expected value can result in a bias of the measurement, especially if large differences between the simulation and the data are observed. However, the shapes of the distributions from data and simulation are consistent within their uncertainties, and we subtract the predicted relative fractions from the remaining event yields.

Corrections to particle and parton levels
After the subtraction of the backgrounds, an unfolding procedure is used to correct the reconstructed distributions for detector-specific effects, e.g., efficiency and resolutions, and to extrapolate either to the parton or particle level. We do not subtract the fractions of wrongly reconstructed or nonreconstructable events, since in many of these events a rather soft jet is misidentified, which has little impact on the resolution of the measured quantities. The iterative D'Agostini method [50] is used to unfold the data. The migration matrices, which relate the quantities at the parton or particle level and at detector level, and the acceptances are needed as the input. However, not only the detector simulation, but also the theoretical description of tt events affects the migration matrix. This dependence is reduced in the particle-level measurement, where no extrapolation to parton-level top quarks is needed. For the central results the migration matrices and the acceptances are taken from the POWHEG+PYTHIA8 simulation, and other simulations are used to estimate the uncertainties. The binning of the distributions is optimized based on the resolution in the simulation. The minimal bin widths are selected such that, according to the resolution, at least 50% of the events are reconstructed in the correct bin. As an example, the migration matrices for the parton-and particle-level measurements of p T (t h ) are shown in the right-hand plots of Fig. 8. For the measured parton-level distributions of any quantity we define the purity as the fraction of parton-level top quarks in the same bin at the detector level, the stability as the fraction of detector-level top quarks in the same bin at the parton level, and the bin efficiency as the ratio of the number of detector-to parton-level top quarks in the same bin. Similar parameters are defined for the particle-level distributions. The purity, stability, and bin efficiency are shown for the p T (t h ) measurements in the left-hand plots of Fig. 8. These illustrate the improved agreement between the reconstructed and the unfolded quantities, as well as the reduced extrapolation in the particle-level measurement.  Figure 8: Migration studies of the (upper) parton-and (lower) particle-level measurements of p T (t h ), extracted from the POWHEG+PYTHIA8 simulation. Left: purity, stability, and bin efficiency. Right: bin migrations between detector and parton (particle) level. The p T range of the bins can be taken from the left panels. Each column is normalized such that the sum of its entries corresponds to the percentage of reconstructed events in this bin at the parton (particle) level.
To control the level of regularization, the iterative D'Agostini method takes the number of iterations as an input parameter. The initial distributions for the D'Agostini unfolding are taken from the POWHEG+PYTHIA8 simulation. The number of iterations is chosen such that the compatibility between a model and the unfolded data at either the parton or particle level is the same as the compatibility between the folded model and the data at detector level. The compatibilities are determined by χ 2 tests at each level that are based on all the available simulations and on several modified spectra obtained by reweighting the POWHEG+PYTHIA8 distributions of p T (t), |y(t)|, p T (tt), or p T (j 1 ) before the detector simulation. The modified spectra are chosen such that the effect of the reweighting corresponds roughly to the observed differences between the data and the unmodified simulation at detector level.
We have found that the number of iterations needed to fulfill the above criterion is such that a second χ 2 test between the detector-level spectrum with its statistical uncertainty and the refolded spectrum with zero uncertainty exceeds a probability of 99.9%. The refolded spectrum is obtained by inverting the unfolding step. This consists of a multiplication with the response matrix and does not need any regularization. The algorithm needs between 4 and 56 iterations depending on the distribution. The numbers of iterations are higher for measurements with lower purities and stabilities of the migration matrices. This is the case for the measurements of p T (t ) and |y(t )|, whose resolutions are significant worse than those of p T (t h ) and |y(t h )| due to the missing neutrino information.
For the two-dimensional measurements with n bins in one quantity and m i , i = 1 . . . n bins in the other the D'Agostini unfolding can be generalized using a vector of B = ∑ n i m i entries of the form: b 1,1 , b 2,1 . . . b n,1 , . . . b 1,m 1 , b 2,m 2 . . . b n,m n , with a corresponding B × B migration matrix. The number of iterations is optimized in the same way.
In the measurements of jet kinematic properties, we do not unfold the measured spectra of each jet separately, but do correct for the effect of misidentified jets. The response matrix showing the migration among the identified jets is given in Fig. 9 for the measurements of the jet p T spectra.
Bins of jet type at detector level  Figure 9: Migration studies of the particle-level measurement of the jet p T spectra, extracted from the POWHEG+PYTHIA8 simulation. Left: purity, stability, and bin efficiency. Right: bin migrations between detector and particle level. On the axes the p T bins for each jet are shown. Each column is normalized in the way that the sum of its entries corresponds to the percentage of reconstructed events in this bin at the particle level.

Systematic uncertainties
Several sources of experimental and theoretical systematic uncertainty are considered. Uncertainties in the jet and p miss T calibrations, pileup modeling, b identification and lepton selection efficiencies, and integrated luminosity fall into the first category.
The total uncertainty in the jet energy calibration is the combination of 19 different sources of uncertainty and the jet-flavor-specific uncertainties [47], where the uncertainty for b jets is evaluated separately. For each uncertainty source the energies of jets in the simulation are shifted up and down. At the same time, p miss T is recalculated accordingly to the rescaled jet energies. The recomputed backgrounds, response matrices, and acceptances are used to unfold the data. The observed differences between these and the original results are taken as an uncertainty in the unfolded event yields. The same technique is used to calculate the impact of the uncertainties in the jet energy resolution, the uncertainty in p miss T not related to the jet energy calibration, the b identification, the pileup modeling, and the lepton reconstruction and selection.
The b identification efficiency in the simulation is corrected using scale factors determined from data [51]. These have an uncertainty of about 1-3% depending on the p T of the b jet.
The effect on the measurement due to the uncertainty in the modeling of pileup in simulation is estimated by varying the average number of pileup events per bunch crossing by 4.6% [52] and reweighting the simulated events accordingly.
The trigger, reconstruction, and identification efficiencies of leptons are evaluated with tagand-probe techniques using Z boson dilepton decays [45,46]. The uncertainties in the scale factors, which are used to correct the simulation to match the data, take into account the different lepton selection efficiencies in events with high jet multiplicities as in tt events. The uncertainty in the lepton reconstruction and selection efficiencies depends on p T and η and is below 2% in the relevant phase-space region.
The relative uncertainty in the integrated luminosity measurement is 2.5% [2].
Uncertainties in the choice of µ r and µ f , the combination of the matrix-element calculation with the PS, the modeling of the PS and hadronization, the top quark mass, and the PDFs fall into the second category of uncertainties. The effects of these theoretical uncertainties are estimated either by using the event weights introduced in Section 2, or by using a tt signal simulation with varied settings. Again, the uncertainties are assessed using the recomputed backgrounds, response matrices, and acceptances to unfold the data.
The scales µ r and µ f are varied up and down by a factor of two individually and simultaneously in the same directions. Afterwards, the envelope of the observed variations is quoted as the uncertainty.
The uncertainty in the combination of the matrix-element calculation with the PS is estimated from an ≈40% variation of the h damp parameter in POWHEG, normally set to h damp = 1.58m t . This variation has been found to be compatible with the modeling of jet multiplicities in previous measurements at √ s = 8 TeV [16].
To estimate the uncertainty in the PS, several effects have been studied and are assessed individually. The scale of the initial-(ISR) and final-state (FSR) radiation is varied up and down by a factor of 2 and √ 2, respectively. These variations are motivated by the uncertainties in the PS tuning [25]. The effect of multiple parton interactions and the parametrization of color reconnection have been studied in Ref. [26] and are varied accordingly. In addition, we use a simulation with activated color reconnection of resonant decays. This enables the color reconnection of top quark decay products with other partons, which is not allowed in the default tune. The uncertainty in the b fragmentation function is taken from measurements at LEP experiments [53][54][55] and SLD [56], and the parametrization in PYTHIA8 is changed accordingly. Finally, the semileptonic branching fractions [41] of b hadrons are varied within their measured uncertainties.
The effect due to the uncertainty in the top quark mass is estimated using simulations with altered top quark masses. We quote as the uncertainty the cross section differences observed for a top quark mass variation of 1 GeV around the central value of 172.5 GeV used in the default simulation.
For the PDF uncertainty only the variation in the acceptance is taken into account, while variations due to migrations between bins can be neglected. It is calculated according to the uncertainties in the NNPDF30 nlo as 0118 [31] parametrization. In addition, the uncertainties obtained using the PDF sets derived with the strong coupling strength set at α s = 0.117 and 0.119 are considered.
As an example, the sources of systematic uncertainty in the measurements of p T (t h ), as well as the statistical and total uncertainty, are shown in Fig. 10. Among the experimental uncertainties, the dominant sources are the jet energy scale; lepton triggering, reconstruction, and identification; and the b identification. In the parton-level measurement, the FSR scale is typically an important contribution to the systematic uncertainty.
As an additional consistency test, we subtract the tt background and unfold the data using the reweighted simulations that include all the differences in the measured distributions at detector  Figure 10: Relative uncertainties due to the individual sources in the absolute (upper) and normalized (lower) measurement of p T (t h ) at the parton level (left) and particle level (right). Sources whose impact never exceeds 1% are summarized in the category "Others". The combination of the individual sources of jet energy uncertainty is labeled "Jet energy". The combined uncertainty is the sum in quadrature of the statistical and all the systematic uncertainties. level described in Section 8. The differences between these unfolded distributions and the one obtained with the unmodified simulation are small compared to the uncertainties evaluated by the variations described above.
10 Differential cross sections as functions of observables of the top quark and the tt system The cross section σ in each bin is calculated as the ratio of the unfolded signal yield and the integrated luminosity. These are further divided by the bin width or the product of the two bin widths to obtain the single-or double-differential cross section results, respectively. To allow for a precise comparison of the measured shapes with theoretical predictions, irrespective of the integrated cross section and its uncertainty, we also present normalized differential cross sections. For this purpose the absolute differential cross sections are divided by the normalizing cross sections σ norm , which are obtained for each measurement from the integration of the cross section over the measured one-or two-dimensional range. The uncertainties in the normalized distributions are evaluated using error propagation and include the correlations between uncertainties in the individual measurements and σ norm . For the statistical uncertainty the covariances are taken directly from the unfolding procedure. For each of the studied systematic uncertainties we assume a full correlation among all bins, while the various sources are assumed to be uncorrelated. The same assumptions about correlations of uncertainty sources are made for the calculation of the normalized theoretical predictions.
The measured differential cross sections are compared to the predictions of POWHEG, combined with the PS simulations of PYTHIA8 and HERWIG++, and the tt multiparton simulation of MG5 aMC@NLO+PYTHIA8 FxFx. In addition, several parton-level results are compared to calculations of tt production with NNLO QCD+NLO EW [1] accuracy, where a top quark mass of 173.3 GeV [57] is used. For the calculations of the theoretical cross sections as functions of M(tt) and rapidities the scales are set to µ r = µ f = (1/4) (m T (t) + m T (t)) and the scales for the p T calculations are selected as (1/2)m T (t) or (1/2)m T (t) depending on the variable under consideration. The PDF parametrizations LUXqed plus PDF4LHC15 nnlo 100 [58] are used for these calculations. The uncertainties consider variations of the scales µ r and µ f . The particle-level results are compared to a prediction obtained with the Monte Carlo generator SHERPA [59] (v2.2.3) in combination with OPENLOOPS [60]. The processes of tt production with up to one additional parton are calculated at NLO QCD accuracy, and those with up to four additional partons are calculated at LO. These processes are merged and matched with the Catani-Seymour PS [61] based on the SHERPA default tune. For the scales we select where the summation over partons includes the p T of all partons obtained from the fixed-order calculation. The NNPDF30 nlo as 0118 [31] PDF parametrizations are used. Uncertainties in the predictions of SHERPA are evaluated by halving and doubling the scales of renormalization, factorization, resummation, and the initial-and final-state PS. In addition, the PDF uncertainties are taken into account. For the predictions of POWHEG+PYTHIA8 we evaluate all the theoretical uncertainties described in Section 9. Although the SHERPA and the POWHEG+PYTHIA8 simulations are normalized to the NNLO tt production cross section, we use their intrinsic scale uncertainties.
The comparisons between the measurements and the theoretical predictions as a function of the top quark p T and |y| are shown in Figs. 11-12 and 13-14 for the parton and particle level, respectively. At parton level, the kinematic properties of t h and t are identical, and we measure the differential cross section as a function of the top quark p T using the higher-and lower-p T values in the tt pair, as shown in Fig. 15. The measured p T spectra of t h and t are consistently softer than predicted by all the simulations using the PYTHIA8 PS generator at both the parton and particle levels. Also the NNLO QCD+NLO EW calculation predicts a slightly harder p T spectrum than observed in the data. The POWHEG+HERWIG++ simulation describes the data well at the parton level. However, at the particle level, the p T (t h ) distribution is noticeably softer than in the data. In Figs. 16 and 17, the cross sections as a function of kinematic variables of the tt system are compared to the same theoretical predictions. In general, the predictions are in agreement with the measured distributions. The NNLO QCD+NLO EW calculation predicts a higher-average M(tt) spectrum than observed in the data. For POWHEG+HERWIG++ a similar behavior as for the p T (t h ) distributions is observed-while the parton-level distribution is well described, a softer spectrum is observed at the particle level.
The measurement of double-differential cross sections allows for the study of correlations between kinematic properties of the top quarks and provides insights into extreme regions of the phase space. The most fundamental double-differential distribution is that of the top quark properties |y(t h )| vs. p T (t h ). The absolute double-differential cross sections are shown in Figs The precision of the differential cross section measurements is limited by the systematic uncertainty, dominated by jet energy scale uncertainties on the experimental side and PS modeling and scale uncertainties on the theoretical side. As expected, the theoretical uncertainties are reduced in the particle-level measurements since they are less dependent on theory-based extrapolations.
We evaluate the level of agreement between the measured differential cross sections and the various theoretical predictions using χ 2 tests. In these tests, we take into account the full covariance matrices of the measured differential cross sections. For the POWHEG+PYTHIA8 and the SHERPA predictions we consider the theoretical uncertainties and their correlation among the bins. In addition, we perform the χ 2 tests without any uncertainties in the theoretical models. We do this since the generation of simulated events does not include any of these theoretical uncertainties; the simulated distributions of the various kinematic quantities correspond exactly to the central predictions. Therefore, it is worthwhile to compare how well the central predictions agree with the data, independent of the theoretical uncertainties. From the χ 2 values and the numbers of degrees of freedom, which correspond to the numbers of bins in the distributions, the p-values are calculated. The results are shown in Table 1 for the parton-level and in Table 3 for the particle-level absolute measurements. The corresponding χ 2 tests for the normalized distributions, for which the numbers of degrees of freedom are reduced by 1, are given in Tables 2 and 4 for the parton-and particle-level measurements, respectively.
The χ 2 tests show that the measurements are largely compatible with the POWHEG+PYTHIA8 and SHERPA predictions if the uncertainties in the simulations are taken into account. Some tension is observed between the data and the predictions of p T (t) and related distributions like p T (t h ) vs. M(tt). Comparisons of the p-values at the parton and particle level obtained for the             Table 1: Comparison between the measured absolute differential cross sections at the parton level and the predictions of POWHEG combined with PYTHIA8 (P8) or HERWIG++ (H++), the multiparton simulation MG5 aMC@NLO FxFx, and the NNLO QCD+NLO EW calculations. The compatibility with the POWHEG+PYTHIA8 prediction is also calculated including its theoretical uncertainties (with unc.), while those are not taken into account for the other comparisons. The results of the χ 2 tests are listed, together with the numbers of degrees of freedom (dof) and the corresponding p-values.

Measurements of multiplicities and kinematic properties of jets
In the following, we discuss the measurements involving the multiplicities and kinematic properties of jets in tt events. These are performed at the particle level only. In the POWHEG simulations, all jets beyond one additional jet are described by the PS simulation and, hence, their description is subject to PS tuning. In the SHERPA simulation, the production of up to one additional jet is calculated at NLO accuracy, and up to four jets at LO. However, these LO calculations are very sensitive to the choice of the scales. Since in the MG5 aMC@NLO+PYTHIA8 FxFx simulation up to two additional jets are calculated at NLO, it is expected to be more accurate at high jet multiplicities.
The absolute and normalized differential cross sections as a function of p T (t h ), M(tt), and p T (tt) for different numbers of additional jets are shown in Figs. 30-35. These distributions are helpful to estimate the tt background contribution in searches for physics beyond the standard model that are looking for signatures with high jet multiplicities. The observation that the p T (t) distribution is softer in data than in the simulations is mainly true for events with zero or one additional jet.
We also measure the properties of the individual jets in tt events. The absolute and normalized differential cross sections as a function of the p T of jets in the tt system and of the four leading additional jets are shown in Figs. 36 and 37, respectively. The trend of a softer p T spectrum of the top quark is also visible for all jets of the tt system. From these p T distributions we calculate the jet multiplicities with minimum p T thresholds of 30, 50, 75, and 100 GeV shown in Fig. 38, and gap fractions [16,17]. The gap fraction f n (p T ) is the fraction of unfolded events that contain less than n additional jets above the given p T threshold. It is shown for n = 1 and 2 in Fig. 39. In the calculations of jet multiplicities and gap fractions, we take into account the small fraction of jets above the displayed p T ranges. The uncertainties are obtained by error propagation using the full covariance matrices. The jet multiplicities and gap fractions are reasonably described by most of the simulations. However, the central predictions of SHERPA and POWHEG+HERWIG++ show noticeable deviations in the gap fraction.
In Figs. 40-45, the absolute and normalized distributions of |η|, ∆R j t , and ∆R t are shown for the jets in the tt system and the additional jets. The differential cross section as a function of |η| is well described by most of the simulations, while POWHEG+HERWIG++ overestimates the radiation of additional jets close to the jets in the tt system. In the predictions, such collinear radiation is mainly described by the PS model. Since the parton-level prediction is not affected by the simulation of the final-state PS, this overestimation of radiation may explain the discrepancies between the parton-and particle-level predictions of POWHEG+HERWIG++ in the p T (t h ) and M(tt) distributions.            Table 5: Comparison between the absolute measurements involving multiplicities and kinematic properties of jets and the predictions of POWHEG combined with PYTHIA8 (P8) or HER-WIG++ (H++) and the multiparton simulations of MG5 aMC@NLO FxFx and SHERPA. The compatibilities with the POWHEG+PYTHIA8 and the SHERPA predictions are also calculated including their theoretical uncertainties (with unc.), while those are not taken into account for the other comparisons. The results of the χ 2 tests are listed, together with the numbers of degrees of freedom (dof) and the corresponding p-values. The rows labeled as "Additional jets" refer to the measurement of the cross section as a function of jet multiplicities for up to five additional jets with p T > 30 GeV (Fig. 38 Table 6: Comparison between the normalized measurements involving multiplicities and kinematic properties of jets and the predictions of POWHEG combined with PYTHIA8 (P8) or HER-WIG++ (H++) and the multiparton simulations of MG5 aMC@NLO FxFx and SHERPA. The compatibilities with the POWHEG+PYTHIA8 and the SHERPA predictions are also calculated including their theoretical uncertainties (with unc.), while those are not taken into account for the other comparisons. The results of the χ 2 tests are listed, together with the numbers of degrees of freedom (dof) and the corresponding p-values. The rows labeled as "Additional jets" refer to the measurement of the cross section as a function of jet multiplicities for up to five additional jets with p T > 30 GeV (Fig. 38 upper row).
Distribution  All cross section values, together with their statistical and systematic uncertainties, are listed in Appendices A and B for the parton-and particle-level measurements, respectively. In addition, the corresponding normalized cross sections are provided in Appendices C and D.

Summary
Measurements of the absolute and normalized differential and double-differential cross sections for tt production in proton-proton collisions at √ s = 13 TeV have been presented. The data correspond to an integrated luminosity of 35.8 fb −1 recorded by the CMS experiment. The tt production cross section is measured in the +jets channels at the parton and particle levels as a function of the transverse momentum p T and absolute rapidity |y| of the top quarks and p T , |y|, and invariant mass of the tt system. In addition, at the particle level detailed studies of multiplicities and kinematic properties of the jets in tt events are performed. The dominant sources of uncertainty are the jet energy scale uncertainties on the experimental side and parton shower modeling on the theoretical side.
The results are compared to several standard model predictions that use different methods and approximations for their calculations. The simulations of POWHEG+PYTHIA8 and SHERPA, for which theoretical uncertainties are considered, describe most of the studied kinematic distributions of the top quark and the tt system reasonably well. The largest deviation is the measurement of a softer p T spectrum of the top quarks compared to all the predictions. This has also been observed in other measurements [5-10, 13, 14, 18]. Most of the kinematic distributions and multiplicities of additional jets are modeled reasonably well by POWHEG+PYTHIA8, however, this description of additional jets relies on the phenomenological model of the parton shower with tuned parameters. With the selected settings SHERPA fails to describe most of these distributions. Comparisons of the measurements to the central values of all tested models, ignoring their theoretical uncertainties, result in low p-values for many distributions related to the p T of the top quarks or the tt system, and for the kinematic distributions and multiplicities of additional jets.

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 centers 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 [2] CMS Collaboration, "CMS Luminosity measurement for the 2016 data taking period", CMS Physics Analysis Summary CMS-PAS-LUM-17-001, 2017.

A Tables of parton-level cross sections.
The measured differential cross sections at the parton level as a function of all the measured variables are listed in Tables 7-16. The results are shown together with their statistical and systematic uncertainties. Table 7: Differential cross section at the parton level as a function of p T (t high ). The values are shown together with their statistical and systematic uncertainties.

B Tables of particle-level cross sections.
The measured differential cross sections at the particle level as a function of all the measured variables are listed in Tables 17-34. The results are shown together with their statistical and systematic uncertainties. Table 17: Differential cross section at the particle level as a function of p T (t h ). The values are shown together with their statistical and systematic uncertainties. 116.5 ± 0.9 ± 6.7 500-800 0.81 ± 0.03 ± 0.11  Table 19: Differential cross section at the particle level as a function of p T (t ). The values are shown together with their statistical and systematic uncertainties.  33.9 ± 0.5 ± 2.0 - Table 21: Differential cross section at the particle level as a function of p T (tt). The values are shown together with their statistical and systematic uncertainties.

C Tables of normalized parton-level cross sections.
The measured normalized differential cross sections at the parton level as a function of all the measured variables are listed in Tables 35-44. The results are shown together with their statistical and systematic uncertainties. Table 35: Differential cross section at the parton level as a function of p T (t high ) normalized to the cross section σ norm in the measured range. The values are shown together with their statistical and systematic uncertainties.