CERN, 1211 Geneva 23, Switzerland Received: 21 August 2019 / Accepted: 2 December 2019 / Published online: 24 December 2019 © CERN for the beneﬁt of the ATLAS collaboration 2019 Abstract Single-and double-differential cross-section measurements are presented for the production of top-quark pairs, in the lepton + jets channel at particle and parton level. Two topologies, resolved and boosted, are considered and the results are presented as a function of several kinematic variables characterising the top and tt¯system and jet multiplicities. The study was performed using data from pp collisions at centre-of-mass energy of 13 TeV collected in 2015 and 2016 by the ATLAS detector at the CERN Large Hadron Collider (LHC), corresponding to an integrated luminosity of 36fb−1. Due to the large tt¯cross-section at the LHC, such measurements allow a detailed study of the properties of top-quark production and decay, enabling precision tests of several Monte Carlo generators and ﬁxed-order Standard Model predictions. Overall, there is good agreement between the theoretical predictions and the data. Contents 1 Introduction ..................... 1 2 ATLASdetector ................... 2 3 Dataandsimulation ................. 3 3.1

Signalsimulationsamples ........... 4 3.2 Background simulation samples ....... 4 4 Object reconstruction and event selection ..... 5 4.1

Detector-level object reconstruction ..... 5 4.2

Particle-level object deﬁnition ........ 6 4.3 Parton-level objects and full phase-space definition ..................... 7 4.4 Particle-and detector-level event selection .. 7 5 Backgrounddetermination ............. 7 6 Kinematic reconstruction of the tt¯system ..... 11 6.1

Resolvedtopology ............... 11 6.2 Boostedtopology ............... 12 7 Observables ..................... 14 8 Cross-sectionextraction .............. 16 8.1

Particle level in the ﬁducial phase-space ... 18 * e-mail: atlas.publications@cern.ch 8.2

Parton level in the full phase-space ...... 22 8.3 Unfoldingvalidation ............. 23 9 Systematicuncertainties .............. 25 9.1

Object reconstruction and calibration ..... 26 9.2

Signalmodelling ............... 28 9.3

Backgroundmodelling ............ 29 9.4 Statistical uncertainty of the Monte Carlo samples ...................... 30 9.5

Integratedluminosity ............. 30 9.6 Systematic uncertainties summary ...... 30 10 Results ....................... 30 10.1 Results at particle level in the ﬁducial phasespaces ..................... 36 10.2 Results at parton level in the full phase-space 42 11 Conclusion ..................... 65 References........................ 67 1 Introduction The detailed studies of the characteristics of top-quark pair (tt¯) production as a function of different kinematic variables that can now be performed at the Large Hadron Col-lider (LHC) provide a unique opportunity to test the Standard Model (SM) at the TeV scale. Furthermore, extensions to the SM may modify the tt¯differential cross-sections in ways that an inclusive cross-section measurement [1] is not sensitive to. In particular, such effects may distort the topquark momentum distribution, especially at higher momentum [2,3]. Therefore, a precise measurement of the tt¯differential cross-sections has the potential to enhance the sensitivity to possible effects beyond the SM, as well as to challenge theoretical predictions that now reach next-to-nextto-leading-order (NNLO) accuracy in perturbative quantum chromodynamics (pQCD) [4–6]. Moreover, the differential distributions are sensitive to the differences between Monte Carlo (MC) generators and their settings, representing a valuable input to the tuning of the MC parameters. This aspect is relevant for all the searches and measurements 123 that are limited by the accuracy of the modelling of tt¯production. The ATLAS [7–15] and CMS [16–22] Collaborations have published measurements of tt¯differential cross-sections √ at centre-of-mass energies ( s) of 7 TeV, 8 TeV and 13 TeV in pp collisions using ﬁnal states containing leptons, both in the full phase-space using parton-level variables and in ﬁducial phase-space regions using observables constructed from ﬁnal-state particles (particle-level). These results have been largely used to improve the modelling of MC generators [23–27] and to reduce the uncertainties in the gluon parton distribution function (PDF) [28]. The results presented in this paper probe the top-quark √ kinematic properties at s =13 TeV and complement recent measurements involving leptonic ﬁnal states by ATLAS [13– 15] and CMS [19,21] by measuring single-and doubledifferential cross-sections in the selected ﬁducial phasespaces and extrapolating the results to the full phase-space at the parton level. In the SM, the top quark decays almost exclusively into a W boson and a b-quark. The signature of a tt¯decay is therefore determined by the W boson decay modes. This analysis makes use of the f+jets tt¯decay mode, also called the semileptonic channel, where one W boson decays into an electron or a muon and a neutrino, and the other Wboson decays into a quark–antiquark pair, with the two decay modes referred to as the e+jets and μ+jets channels, respectively. Events in which the Wboson decays into an electron or muon through a τ-lepton decay may also meet the selection criteria. Since the reconstruction of the top quark depends on its decay products, in the following the two top quarks are referred to as ‘hadronically (or leptonically) decaying top quarks’ (or alternatively ‘hadronic/leptonic top’ ), depending on the W boson decay mode. Two complementary topologies of the tt¯ﬁnal state in the f+jets channel are exploited, referred to as ‘resolved’ and ‘boosted’, where the decay products of the hadronically decaying top quark are either angularly well separated or collimated into a single large-radius jet reconstructed in the calorimeter, respectively. As the jet selection efﬁciency of the resolved analysis decreases with increasing top-quark trans-verse momentum, the boosted selection allows events with higher-momentum hadronically decaying top quarks to be efﬁciently selected. The differential cross-sections for tt¯production are measured as a function of a large number of variables (described in Sect. 7) including, for the ﬁrst time in this channel in ATLAS, double-differential distributions. Moreover, the amount of data and the reduced detector uncertainties compared to previous publications also allows, for the ﬁrst time, double differential measurements in the boosted topology to be made. The analysis investigates a list of variables that characterise various aspects of the tt¯system production. In particular, the variables selected are sensitive to the kinematics of the top and anti-top quarks and of the tt¯system or are sensitive to initial-and ﬁnal-state radiation effects. Furthermore, the variables are sensitive to the differences among PDFs and possible beyond the SM effects. Both normalised and absolute differential cross-sections are measured, with more emphasis given to the discussion of the normalised results. Differential cross-sections are measured as a function of different variables in the ﬁducial and full phase-spaces, since they serve different purposes: the particle-level crosssections in the ﬁducial phase-space are particularly suited to MC tuning while the parton-level cross-sections, extrapolated to the full phase-space, are the observables to be used for stringent tests of higher-order pQCD predictions and for the determination of the proton PDFs and the top-quark pole mass in pQCD analyses. 2 ATLAS detector ATLAS is a multipurpose detector [29] that provides nearly full solid angle1 coverage around the interaction point. Charged-particle trajectories with pseudorapidity |υ|< 2.5 are reconstructed in the inner detector, which comprises a silicon pixel detector, a silicon microstrip detector and a transition radiation tracker (TRT). The innermost pixel layer, the insertable B-layer [30,31], was added before the start of 13 TeV LHC operation at an average radius of 33 mm around a new, thinner beam pipe. The inner detector is embedded in a superconducting solenoid generating a 2 T axial magnetic ﬁeld, allowing precise measurements of chargedparticle momenta. The calorimeter system covers the pseudorapidity range |υ| < 4.9. Within the region |υ| < 3.2, electromagnetic calorimetry is provided by barrel and endcap high-granularity lead/liquid-argon (LAr) calorimeters, with an additional thin LAr presampler covering |υ|< 1.8, to correct for energy loss in material upstream of the calorimeters. Hadronic calorimetry is provided by the steel/scintillatingtile calorimeter, segmented into three barrel structures within 1 ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point in the centre of the detector. The positive x-axis is deﬁned by the direction from the interaction point to the centre of the LHC ring, with the positive y-axis pointing upwards, while the beam direction deﬁnes the z-axis. Cylindrical coordinates (r,φ) are used in the transverse plane, φ being the azimuthal angle around the z-axis. The pseudorapidity υ is deﬁned in terms of the polar angle χ by υ =−ln tan(χ/2). Rapidity is deﬁned as y=0.5ln[(E+pz)/(E−pz)]where E denotes the energy and pz is the component of the momentum along the beam direction. The angular distance /Ris deﬁned as (/y)2 +(/φ)2. 123 |υ| < 1.7, and two copper/LAr hadronic endcap calorimeters. The solid angle coverage is completed with forward cop-per/LAr and tungsten/LAr calorimeter modules optimised for electromagnetic and hadronic measurements respectively. The calorimeters are surrounded by a muon spectrometer within a magnetic ﬁeld provided by air-core toroid magnets with a bending integral of about 2.5 Tm in the barrel and up to 6 Tm in the endcaps. Three stations of precision drift tubes and cathode-strip chambers provide an accurate measurement of the muon track curvature in the region |υ|< 2.7. Resistive-plate and thin-gap chambers provide muon triggering capability up to |υ|=2.4. Data were selected from inclusive pp interactions using a two-level trigger system [32]. A hardware-based trigger uses custom-made hardware and coarser-granularity detector data to initially reduce the trigger rate to approximately 100 kHz from the original 40 MHz LHC bunch crossing rate. A software-based high-level trigger, which has access to full detector granularity, is applied to further reduce the event rate to 1 kHz. 3 Data and simulation The differential cross-sections are measured using data collected during the 2015 and 2016 LHC pp stable collisions √ at s =13 TeV with 25 ns bunch spacing and an average number of pp interactions per bunch crossing (μ)of around 23. The selected data sample, satisfying beam, detector and data-taking quality criteria, correspond to an integrated luminosity of 36.1 fb−1. The data were collected using single-muon or singleelectron triggers. For each lepton type, multiple trigger conditions were combined to maintain good efﬁciency in the full momentum range, while controlling the trigger rate. Different transverse momentum ( pT) thresholds were applied in the 2015 and 2016 data taking. In the data sample collected in 2015, the pT thresholds for the electrons were 24 GeV, 60 GeV and 120 GeV, while for muons the thresholds were 20 GeV and 50 GeV; in the data sample collected in 2016, the pT thresholds for the electrons were 26 GeV, 60 GeV and 140 GeV, while for muons the thresholds were 26 GeV and 50 GeV. Different pT thresholds were employed since tighter isolation or identiﬁcation requirements were applied to the triggers with lowest pT thresholds. The signal and background processes are modelled with various MC event generators described below and summarised in Table 1. Multiple overlaid pp collisions were simulated with the soft QCD processes of Pythia 8.186 [33] using parameter values from the A2 set of tuned parameters (tune) [34] and the MSTW2008LO [35] set of PDFs to account for the effects of additional collisions from the same and nearby bunch crossings (pile-up). Simulation sam- Table 1 Summary of MC samples used for the nominal measurement and to assess the systematic uncertainties, showing the event generator for the hard-scattering process, the order in pQCD ofthe cross-section used for normalisation, PDF choice, as well as the parton-shower generator and the corresponding tune used in the analysis Physics process Generator PDF set for hard process Parton shower Tune Cross-section normalisation tt¯signal Powheg-Box v2 NNPDF3.0NLO Pythia 8.186 A14 NNLO +NNLL tt¯PS syst. Powheg-Box v2 NNPDF3.0NLO Herwig7.0.1 H7-UE-MMHT NNLO +NNLL tt¯generator syst. Sherpa 2.2.1 NNPDF3.0NNLO Sherpa Sherpa NNLO +NNLL tt¯rad. syst. Powheg-Box v2 NNPDF3.0NLO Pythia 8.186 Var3cDown/Var3cUp NNLO +NNLL Single top: t-channel Powheg-Box v1 CT10f4 Pythia 6.428 Perugia2012 NLO Single top: t-channel syst. Powheg-Box v1 CT10f4 Pythia 6.428 Perugia2012 radHi/radLo NLO Single top: s-channel Powheg-Box v1 CT10 Pythia 6.428 Perugia2012 NLO Single top: tWchannel Powheg-Box v1 CT10 Pythia 6.428 Perugia2012 NLO +NNLL Single top: tWchannel syst. Powheg-Box v1 CT10 Pythia 6.428 Perugia2012 radHi/radLo NLO +NNLL Single top: tWchannel DS Powheg-Box v1 CT10 Pythia 6.428 Perugia2012 NLO +NNLL t +X MadGraph5 NNPDF2.3LO Pythia 8.186 A14 NLO W(→fν)+jets Sherpa 2.2.1 NNPDF3.0NNLO Sherpa Sherpa NNLO Z(→ff)¯+jets Sherpa 2.2.1 NNPDF3.0NNLO Sherpa Sherpa NNLO WW, WZ, ZZ Sherpa 2.1.1 NNPDF3.0NNLO Sherpa Sherpa NLO 123 ples are reweighted so that their pile-up proﬁle matches the one observed in data. The simulated samples are always reweighted to have the same integrated luminosity of the data. The EvtGen v1.2.0 program [36] was used to simulate the decay of bottom and charm hadrons for all event generators except for Sherpa [37]. The detector response was simulated [38]in Geant 4[39]. A ‘fast simulation’ [40] (denoted by AFII in the plots throughout the paper), utilising parameterised showers in the calorimeter [40], but with full simulation of the inner detector and muon spectrometer, was used in the samples generated to estimate tt¯modelling uncertainties. The data and MC events were reconstructed with the same software algorithms. 3.1 Signal simulation samples In this section the MC generators used for the simulation of tt¯event samples are described for the nominal sample, the alternative samples used to estimate systematic uncertainties and the other samples used in the comparisons of the measured differential cross-sections [41]. The top-quark mass (mt) and width were set to 172.5 GeV and 1.32 GeV [42], respectively, in all MC event generators. For the generation of tt¯events, the Powheg-Box v2 [43–46] generator with the NNPDF30NLO PDF sets [47] in the matrix element (ME) calculations was used. Events where both top quarks decayed hadronically were not included. The parton shower, fragmentation, and the underlying events were simulated using Pythia 8.210 [33] with the NNPDF23LO PDF [48] sets and the A14 tune [49]. The hdamp parameter, which controls the pT of the ﬁrst gluon or quark emission beyond the Born conﬁguration in Powheg-Box v2, was set to 1.5 mt[24]. The main effect of this param-eter is to regulate the high-pT emission against which the tt¯system recoils. Signal tt¯events generated with those settings are referred to as the nominal signal sample. In all the following ﬁgures and tables the predictions based on this MC sample are referred to as ‘Pwg+Py8’. The uncertainties affecting the description of the hard gluon radiation are evaluated using two samples with different factorisation and renormalisation scales relative to the nominal sample, as well as a different hdamp parameter value [26]. For one sample, the factorisation and renormalisation scales were reduced by a factor of 0.5, the hdamp parameter was increased to 3mt and the Var3cUp eigentune from the A14 tune was used. In all the following ﬁgures and tables the predictions based on this MC sample are referred to as ‘Pwg+Py8 Rad. Up’. For the second sample, the factorisation and renormalisation scales were increased by a factor of 2.0 while the hdamp parameter was unchanged and the Var3cDown eigentune from the A14 tune was used. In all the following ﬁgures and tables the predictions based on this MC sample arereferredtoas‘Pwg+Py8 Rad. Down’. The effect of the simulation of the parton shower and hadronisation is studied using the Powheg-Box v2 generator with the NNPDF30NLO PDF interfaced to Herwig 7.0.1 [50,51] for the showering, using the MMHT2014lo68cl PDF set [52] and the H7-UE-MMHT tune [53]. In all the following ﬁgures and tables the predictions based on this MC sample arereferredtoas‘Pwg+H7’. The impact of the generator choice, including matrix element calculation, matching procedure, parton-shower and hadronisation model, is evaluated using events generated with Sherpa 2.2.1 [37], which models the zero and one additional-parton process at next-to-leading-order (NLO) accuracy and up to four additional partons at leading-order (LO) accuracy using the MEPS@NLO prescription [54], with the NNPDF3.0NNLO PDF set [47]. The calculation uses its own parton-shower tune and hadronisation model. In all the following ﬁgures and tables the predictions based on this MC sample are referred to as ‘Sherpa’. All the tt¯samples described are normalised to the NNLO+NNLL in pQCD by the means of a k-factor. The cross-section used to evaluate the k-factor is ξt¯= t 832+20 −29(scale) ± 35 (PDF,οS) pb, as calculated with the Top++2.0 program to NNLO in pQCD, including soft-gluon resummation to next-to-next-to-leading-log order (NNLL) [55–61], and assuming mt = 172.5 GeV. The ﬁrst uncertainty comes from the independent variation of the factorisation and renormalisation scales, μF and μR, while the second one is associated with variations in the PDF and οS,following the PDF4LHC prescription with the MSTW2008 68% CL NNLO, CT10 NNLO and NNPDF2.3 5f FFN PDF sets, described in Refs. [48,62–64]. 3.2 Background simulation samples Several processes can produce the same ﬁnal state as the tt¯f+jets channel. The events produced by these backgrounds need to be estimated and subtracted from the data to determine the top-quark pair cross-sections. They are all estimated by using MC simulation with the exception of the background events containing a fake or non-prompt lepton, for which data-driven techniques are employed. The processes considered are W+jets, Z+jets production, diboson ﬁnal states and single top-quark production, in the t-channel, in association with a Wboson and in the s-channel. The contributions from top and tt¯produced in association with weak bosons and t¯t are also considered. The overall contribution of these tt¯processes is denoted by t+ X. For the generation of single top quarks in the tW channel and s-channel the Powheg-Box v1 [65,66] generator with the CT10 PDF [63] sets in the ME calculations was used. Electroweak t-channel single-top-quark events were gener 123 ated using the Powheg-Box v1 generator. This generator uses the four-ﬂavour scheme for the NLO ME calculations [67] together with the ﬁxed four-ﬂavour PDF set CT10f4. For these processes the parton shower, fragmentation, and the underlying event were simulated using Pythia 6.428 [68] with the CTEQ6L1 PDF [69] sets and the corresponding Perugia 2012 tune (P2012) [70]. The single-top-quark cross-sections for the tW channel were normalised using its NLO+NNLL prediction, while the t-and s-channels were normalised using their NLO predictions [71–76]. The modelling uncertainties related to the additional radiation in the generation of single top quarks in the tW-and tchannels are assessed using two alternative samples for each channel, generated with different factorisation and renormalisation scales and different P2012 tunes relative to the nominal samples. In the ﬁrst two samples, the factorisation and renormalisation scales were reduced by a factor of 0.5 and the radHi tune was used. For the second two samples, the factorisation and renormalisation scales were increased by a factor of 2.0 and the radLo tune was used. An additional sample is used to assess the uncertainty due to the method used in the subtraction of the overlap of tW production of single top quarks and production of tt¯pairs from the tW sample [77]. In the nominal sample the diagram removal method (DR) is used, while the alternative sample is generated using the diagram subtraction (DS) one. All the other settings are identical in the two samples. Events containing Wor Zbosons associated with jets were simulated using the Sherpa 2.2.1 [37] generator. Matrix elements were calculated for up to two partons at NLO and four partons at LO using the Comix [78] and OpenLoops [79] ME generators and merged with the Sherpa parton shower [80] using the ME+PS@NLO prescription [54]. The NNPDF3.0NNLO PDF set was used in conjunction with dedicated parton-shower tuning. The W/Z+jets events were normalised to the NNLO cross-sections [81,82]. Diboson processes with one of the bosons decaying hadronically and the other leptonically were simulated using the Sherpa 2.2.1 generator. They were calculated for up to one (ZZ)orzero(WW, WZ) additional partons at NLO and up to three additional partons at LO using the Comix and OpenLoops ME generators and merged with the Sherpa parton shower using the ME+PS@NLO prescription. The CT10 PDF set was used in conjunction with dedicated partonshower tuning. The samples were normalised to the NLO cross-sections evaluated by the generator. The t¯tZ samples were simulated using Mad tW and t¯Graph5_aMC@NLO and the NNPDF23NNLO PDF set [48] for the ME. In addition to the t¯tZ samples, the tW and t¯predictions for tZ, ttt¯¯tWW and tWZ are included in the t, t¯t+ Xbackground. These processes have never been observed at the LHC, except for strong evidence for tZ [83,84], and have a cross-section signiﬁcantly smaller than for t¯ tW and t¯ tZ production, providing a subdominant contribution to the t + X background. The simulation of the tZ, t¯ tWW and ttt¯t¯samples was performed using MadGraph while the simulation of the tWZ sample was obtained with Mad-Graph5_aMC@NLO. For all the samples in the t+ Xbackground, Pythia 8.186 [33] and the PDF set NNPDF23LO with the A14 tune were used for the showering and hadronisation. 4 Object reconstruction and event selection The following sections describe the detector-and particlelevel objects used to characterise the ﬁnal-state event topology and to deﬁne the ﬁducial phase-space regions for the measurements. 4.1 Detector-level object reconstruction Primary vertices are formed from reconstructed tracks that are spatially compatible with the interaction region. The hard-scatter primary vertex is chosen to be the one with at least two associated tracks and the highest pT2, where the sum extends over all tracks with pT > 0.4 GeV matched to the vertex. Electron candidates are reconstructed by matching tracks in the inner detector to energy deposits in the EM calorimeter. They must satisfy a ‘tight’ likelihood-based identiﬁcation criterion based on shower shapes in the EM calorimeter, track quality and detection of transition radiation produced in the TRT detector [85]. The reconstructed EM clusters are required to have a transverse energy ET > 27GeV and a pseudorapidity |υ| < 2.47, excluding the transition region between the barrel and endcap calorimeters (1.37 < |υ| < 1.52). The longitudinal impact parameter z0 of the associated track is required to satisfy |/z0 sinχ| < 0.5 mm, where χ is the polar angle of the track, and the transverse impact parameter signiﬁcance |d0|/ξ(d0)< 5, where d0 is the trans-verse impact parameter and ξ(d0) is its uncertainty. The impact parameters d0 and z0 are calculated relative to the beam spot and the beam line, respectively. Isolation requirements based on calorimeter and tracking quantities are used to reduce the background from jets misidentiﬁed as prompt leptons (fake leptons) or due to semileptonic decays of heavyﬂavour hadrons (non-prompt real leptons) [86]. The isolation criteria are pT-and υ-dependent, and ensure an efﬁciency of 90% for electrons with pT of 25 GeV and 99% efﬁciency for electrons with pT of 60 GeV. The identiﬁcation, isolation and trigger efﬁciencies are measured using electrons from Z boson decays [85]. Muon candidates are identiﬁed by matching tracks in the muon spectrometer to tracks in the inner detector [87]. The track pT is determined through a global ﬁt to the hits, which 123 takes into account the energy loss in the calorimeters. Muons are required to have pT >27 GeV and |υ| <2.5. To reduce the background from muons originating from heavy-ﬂavour decays inside jets, muons are required to be isolated using track-quality and isolation criteria similar to those applied to electrons. Jets are reconstructed using the anti-kt algorithm [88] with radius parameter R = 0.4 as implemented in the Fast-Jet package [89]. Jet reconstruction in the calorimeter starts from topological clustering of individual calorimeter cell [90] signals. They are calibrated to be consistent with electromagnetic cluster shapes using corrections determined in simulation and inferred from test-beam data. Jet four-momenta are then corrected for pile-up effects using the jet-area method [91]. To reduce the number of jets originating from pile-up, an additional selection criterion based on a jet-vertex tagging (JVT) technique is applied. The jet-vertex tagging is a likelihood discriminant that combines information from several track-based variables [92] and the criterion is only applied to jets with pT <60 GeV and |υ| <2.4. The jets’ energy and direction are calibrated using an energy-and υdependent simulation-based calibration scheme with in situ corrections based on data [93], and are accepted if they have pT >25 GeV and |υ| <2.5. To identify jets containing b-hadrons, a multivariate discriminant (MV2c10) [94,95] is used, combining information about the secondary vertices, impact parameters and the reconstruction of the full b-hadron decay chain [96]. Jets are considered as b-tagged if the value of the multivariate analysis (MVA) discriminant is larger than a certain threshold. The thresholds are chosen to provide a 70% b-jet tagging efﬁciency in an inclusive tt¯sample, corresponding to rejection factors for charm quark and light-ﬂavour parton initiated jets of 12 and 381, respectively. Large-R jets are reconstructed using the reclustering approach [97]: the anti-kt algorithm, with radius parameter R = 1, is applied directly to the calibrated small-R(R = 0.4) jets, deﬁned in the previous paragraph. Applying this technique, the small-R jet calibrations and uncertainties can be directly propagated in the dense environment of the reclustered jet, without additional corrections or systematic uncertainties [98]. The reclustered jets rely mainly on the technique and cuts applied to remove the pile-up contribution in the calibration of the small-Rjets. However, a trimming technique [99] is applied to the reclustered jet to remove soft small-R jets that could originate entirely from pile-up. The trimming procedure removes all the small-R jets with fraction of pT smaller than 5% of the reclustered jet pT [100,101]. Only reclustered jets with pT >350 GeV and |υ| <2.0 are considered in the analysis. The reclustered jets are considered b-tagged if at least one of the constituent small-R jets is btagged. To top-tag the reclustered jets the jet mass is required to be 120

tribution from these processes is approximately 1.4% and 2.1%, corresponding to approximately 12% and 15% of the total background estimate in the resolved and boosted topologies, respectively. Dilepton top-quark pair events (including decays into τ leptons) can satisfy the event selection and are considered in the analysis as signal at both the detector and particle levels. Table4 Event yields after the resolved and boosted selections. Events that satisfy both the resolved and boosted selections are removed from the resolved selection. The cut on the kinematic ﬁt likelihood has not been applied. The signal model, denoted tt¯in the table, was generated using Powheg+Pythia8, normalised to NNLO calculations. The uncertainties include the combined statistical and systematic uncertainties, excluding the systematic uncertainties related to the modelling of the tt¯system, as described in Sect. 9 Process Yield Resolved Boosted t¯t 1 120 000 ± 90 000 44 700 ± 1900 Single top 54 000 +10000 −11000 2000 ± 900 Multijet 34 000 ± 16 000 1000 ± 400 W+jets 34 000 ± 20 000 3200 ± 1500 Z+jets 12 000 ± 6000 380 ± 210 t+ X 3800 ± 500 440 ± 60 Diboson 1680 +220 −190 194 +19 −21 Total prediction 1 260 000 ± 100 000 52 000 ± 2900 Data 1 252 692 47 600 Data/Prediction 0.99 ± 0.08 0.92 ± 0.05 They contribute to the tt¯yield with a fraction of approximately 13% (8% after applying the cut on the likelihood of the kinematic ﬁt described in Sect. 6.1) in the resolved topol

ogy and 6% in the boosted topology. In the full phase-space analysis at parton level, events where both top quarks decay leptonically are considered as background and a correction factor is applied to the detector-level spectra to account for this background. In the ﬁducial phase-space analysis at particle level, all the tt¯semileptonic events that could pass the ﬁducial selection described in Sect. 4.4 are considered as signal. For this reason, the leptonic top-quark decays into τ -leptons are considered as signal only if the τ -lepton decays leptonically. Cases where both top quarks decay into a τ -lepton, which in turn decays into a quark–antiquark pair, are accounted for in the multijet background. The full phase-space analysis at parton level includes all semileptonic decays of the tt¯system, consequently the τ -leptons from the leptonically decaying W bosons are considered as signal, regardless of the τ -lepton decay mode. As the individual e+jets and μ+jets channels have very similar corrections (as described in Sect. 8) and give con

sistent results at detector level, they are combined by summing the distributions. The event yields, in the resolved and boosted regimes, are shown in Table 4 for data, simulated signal, and backgrounds. The selection leads to a sample with an expected background of 11% and 15% for the resolved and boosted topologies, respectively. The overall difference between data and prediction is 1% and 8% in the resolved and boosted topologies, respectively. In the resolved topology 123 this is in good agreement within the experimental systematic uncertainties, while in the boosted topology the predicted event yield overestimates the data. Figures 1, 2, 3 and 4 show,2 for different distributions, the comparison between data and predictions. The reconstructed distributions, in the resolved topology, of the pT of the lepton, Emiss, jet multiplicty and pT are presented in Fig. 1 T and the b-jet multiplicity and υ in Fig. 2. The reconstructed distributions, in the boosted topology, of the reclustered jet multiplicity and jet pT are shown in Fig. 3 and the pT and υ W of the lepton, Emiss and min Fig. 4. In the resolved topol- TT ogy, good agreement between the prediction and the data is observed in all the distributions shown, while in the boosted topology the agreement lies at the edge of the uncertainty band. This is due to the overestimate of the predicted rate of events of about 10%, varying with the top quark pT, reﬂected in all the distributions. 6 Kinematic reconstruction ofthett¯system Since the tt¯production differential cross-sections are measured as a function of observables involving the top quark and the tt¯system, an event reconstruction is performed in each topology. 6.1 Resolved topology For the resolved topology, two reconstruction methods are employed: the pseudo-top algorithm [9] is used to reconstruct the objects to be used in the particle-level measurement; a kinematic likelihood ﬁtter (KLFitter) [105]isused to fully reconstruct the tt¯kinematics in the parton-level measurement. This approach performs better than the pseudo-top method in terms of resolution and bias for the reconstruction of the parton-level kinematics. The pseudo-top algorithm reconstructs the four-momenta of the top quarks and their complete decay chain from ﬁnalstate objects, namely the charged lepton (electron or muon), missing transverse momentum, and four jets, two of which are b-tagged. In events with more than two b-tagged jets, only the two with the highest transverse momentum values are considered as b-jets from the decay of the top quarks. The same algorithm is used to reconstruct the kinematic properties of top quarks as detector-and particle-level objects. The pseudo-top algorithm starts with the reconstruction of the neutrino four-momentum. While the x and ycomponents of the neutrino momentum are set to the corresponding components of the missing transverse momentum, the z component 2 Throughout this paper, all data as well as theory points are plotted at the bin centre of the x-axis. Moreover, the bin contents of all the histograms are divided by the corresponding bin width. is calculated by imposing the Wboson mass constraint on the invariant mass of the charged-lepton–neutrino system. If the resulting quadratic equation has two real solutions, the one with the smaller value of | pz| is chosen. If the discriminant is negative, only the real part is considered. The leptonically decaying W boson is reconstructed from the charged lepton and the neutrino. The leptonic top quark is reconstructed from the leptonic W and the b-tagged jet closest in /R to the charged lepton. The hadronic W boson is reconstructed from the two non-b-tagged jets whose invariant mass is closest to the mass of the W boson. This choice yields the best performance of the algorithm in terms of the correspondence between the detector and particle levels. Finally, the hadronic top quark is reconstructed from the hadronic W boson and the other b-jet. The advantage of using this method at particle level is that any dependence on the parton-level top quark is removed from the reconstruction and it is possible to have perfect consistency among the techniques used to reconstruct the top quarks at particle level and detector level. The kinematic likelihood ﬁt algorithm used for the partonlevel measurements relates the measured kinematics of the reconstructed objects (lepton, jets and Emiss) to the leading- T order representation of the tt¯ system decay. Compared to the pseudo-top algorithm, this procedure leads to better resolution (with an improvement of the order of 10% for the pT of tt¯system) in the reconstruction of the kinematics of the parton-level top quark. The kinematic likelihood ﬁt has not been employed for the particle-level measurement because its likelihood, described in the following, is designed to improve the jet-to-quark associations and so is dependent on partonlevel information. The likelihood is constructed as the product of Breit–Wigner distributions and transfer functions that associate the energies of parton-level objects with those at the detector level. Breit–Wigner distributions associate the missing transverse momentum, lepton, and jets with W bosons and top quarks, and make use of their known widths and masses, with the top-quark mass ﬁxed to 172.5 GeV. The transfer functions represent the experimental resolutions in terms of the probability that the given true energy for each of the tt¯decay products produces the observed energy at the detector level. The missing transverse momentum is used as a starting value for the neutrino transverse momentum, with its ν longitudinal component (p) as a free parameter in the kine z matic likelihood ﬁt. Its starting value is computed from the ν W mass constraint. If there are no real solutions for pthen z zero is used as a starting value. Otherwise, if there are two real solutions, the one giving the larger likelihood is used. The ﬁve highest-pT jets (or four if there are only four jets in the event) are used as input to the likelihood ﬁt. The input jets are deﬁned by giving priority to the b-tagged jets and then adding the hardest remaining light-ﬂavour jets. If there are more than four jets in the event satisfying pT > 25 GeV and |υ| < 2.5, all subsets of four jets from the ﬁve-jets collection 123 (a) (b) (c) Fig. 1 Kinematic distributions in the f+jets channel in the resolved topology at detector-level: a lepton transverse momentum and bmissing transverse momentum ETmiss, c jet multiplicity and d transverse momenta of selected jets. Data distributions are compared with predictions using Powheg+Pythia8 as the tt¯signal model. The hatched are considered. The likelihood is maximised as a function of the energies of the b-quarks, the quarks from the hadronic W boson decay, the charged lepton, and the components of the neutrino three-momentum. The maximisation is performed for each possible matching of jets to partons and the combination with the highest likelihood is retained. The event likelihood must satisfy log L > −52. This requirement provides good separation between well and poorly reconstructed events and improves the purity of the sample. Distributions of log L in the resolved topology for data and simulation are shown in Fig. 5 in the f+jets channel. The efﬁciency of the (d) area represents the combined statistical and systematic uncertainties (described in Sect. 9) in the total prediction, excluding systematic uncer

tainties related to the modelling of the tt¯events. Underﬂow and overﬂow events, if any, are included in the ﬁrst and last bins. The lower panel shows the ratio of the data to the total prediction likelihood requirement in data is found to be well modelled by the simulation. 6.2 Boosted topology In the boosted topology, the same detector-level reconstruction procedure is applied for both the particle-and partonlevel measurements. The leading reclustered jet that passes the selection described in Sect. 4 is considered the hadronic top quark. Once the hadronic top-quark candidate is identi 123 (a) Fig. 2 Kinematic distributions in the f+jets channel in the resolved topology at detector-level: a number of b-tagged jets and b b-tagged jet pseudorapidity. Data distributions are compared with predictions using Powheg+Pythia8 as the tt¯signal model. The hatched area represents the combined statistical and systematic uncertainties (described (b) in Sect. 9) in the total prediction, excluding systematic uncertainties related to the modelling of the tt¯events. Underﬂow and overﬂow events, if any, are included in the ﬁrst and last bins. The lower panel shows the ratio of the data to the total prediction (a) Fig. 3 Kinematic distributions in the f+jets channel in the boosted topology at detector-level: a number of reclustered jets and b reclustered jet pT. Data distributions are compared with predictions using Powheg+Pythia8 as the tt¯signal model. The hatched area represents the combined statistical and systematic uncertainties (described ﬁed, the leptonic top quark is reconstructed using the leading b-tagged jet that fulﬁls the following requirements: • π R(f, b-jet)< 2.0; () • π RjetR=1.0, b-jet> 1.5. (b) in Sect. 9) in the total prediction, excluding systematic uncertainties related to the modelling of the tt¯events. Underﬂow and overﬂow events, if any, are included in the ﬁrst and last bins. The lower panel shows the ratio of the data to the total prediction If there are no b-tagged jets that fulﬁl these requirements then the leading pT jet is used. The procedure for the reconstruction of the leptonically decaying W boson starting from the lepton and the missing transverse momentum is analogous to the pseudo-top reconstruction described in Sect. 6.1. 123 (a) (b) (c) Fig. 4 Kinematic distributions in the f+jets channel in the boosted topology at detector-level: a lepton pT and bpseudorapidity, c missing transverse momentum ETmiss and dtransverse mass of the Wboson. Data distributions are compared with predictions using Powheg+Pythia8 as the tt¯signal model. The hatched area represents the combined sta 7 Observables A set of measurements of the tt¯production cross-sections is presented as a function of kinematic observables. In the following, the indices had and lep refer to the hadronically and leptonically decaying top quarks, respectively. The indices 1 and 2 refer respectively to the leading and subleading top quark, where leading refers to the top quark with the largest transverse momentum. (d) tistical and systematic uncertainties (described in Sect. 9)inthe total prediction, excluding systematic uncertainties related to the modelling of the tt¯events. Underﬂow and overﬂow events, if any, are included in the ﬁrst and last bins. The lower panel shows the ratio of the data to the total prediction First, a set of baseline observables is presented: transverse t momentum ( pT) and absolute value of the rapidity (|yt|)of the top quarks, and the transverse momentum ( pT tt¯), absolute t¯ value of the rapidity (|yt|) and invariant mass (mtt¯)ofthe tt¯system and the transverse momentum of the leading ( pT t,1) and subleading ( pT t,2) top quarks. For parton-level measurements, the pT and rapidity of the top quark are measured from the pT and rapidity of the reconstructed hadronic top quarks. The differential cross-sections as a function of all 123 Fig. 5 Distribution in the f+jets channel of the logarithm of the likelihood obtained from the kinematic ﬁt in the resolved topology. Data distributions are compared with predictions using Powheg+Pythia8 as the tt¯signal model. The hatched area represents the combined statistical and systematic uncertainties in the total prediction, excluding systematic uncertainties related to the modelling of the tt¯events. Underﬂow and overﬂow events are included in the ﬁrst and last bins. The lower panel shows the ratio of the data to the total prediction. Only events with log L > −52 are considered in the parton-level measurement in resolved topology these observables, with the exception of the pT of the leading and subleading top quarks, were previously measured in the ﬁducial phase-space in the resolved topology by the ATLAS Collaboration using 13 TeV data [14], while in the t,had boosted topology only p and |yt,had|were measured. The T differential cross-sections as a function of the pT of the leading and subleading top quarks were previously measured, at particle-and parton-level, only in the boosted topology in the fully hadronic channel [106]. The detector-level distributions of the kinematic variables of the top quark and tt¯system in the resolved topology are presented in Figs. 6 and 7, respectively. The detector-level distributions of the same observables, reconstructed in the boosted topology, are shown in Figs. 8 and 9. Furthermore, angular variables sensitive to the momen tt¯ tum imbalance in the transverse plane (pout), i.e. to the emission of radiation associated with the production of the top-quark pair, are used to investigate the central production region [107]. The angle between the two top quarks is sensitive to non-resonant contributions from hypothetical new particles exchanged in the t-channel [108]. The rapidities of the two top quarks in the tt¯centre-of-mass frame are ( ≦ 1 t,had −yt,lep) y= yand −y≦. The longitudinal motion 2 of the tt¯system in the laboratory frame is described by the ( tt¯1 t,had +yt,lep) rapidity boost y= y. The production boost 2 polar angle is closely related to the variable ρtt¯, deﬁned as ρtt¯= e2|y≦|, which is included in the measurement since many signals due to processes not included in the SM are predicted to peak at low values of this distribution [108]. Finally, observables depending on the transverse momentum of the decay products of the top quark are sensitive to higher-order corrections [109,110]. In summary, the following additional observables are measured: • The absolute value of the azimuthal angle between the () two top quarks ( /φ t, t¯ ). • The out-of-plane momentum, i.e. the projection of the top-quark three-momentum onto the direction perpendicular to the plane deﬁned by the other top quark and the beam axis (z) in the laboratory frame [107]: pjt,lep ×jez t,had t,had p =jp· , out pjt,lep ×jez t,had ×j t,lep t,lep pjez p =jp· out pjt,had ×jez t,had In particular, |p |, introduced in Ref. [11], is used out in the resolved topology, while in the boosted topology, t,had where an asymmetry between pand pt,lep exists t,lep by construction, the variable |p |is measured. This out reduces the correlation between pout and pt,had,biased toward high values by construction, while keeping the sensitivity to the momentum imbalance. • The longitudinal boost of the tt¯system in the laboratory frame (ytt¯ boost)[108]. • ρtt¯=e2|y≦|[108], closely related to the production polar angle. • The scalar sum of the transverse momenta of the hadronic tt,had t,lep and leptonic top quarks (Ht¯= p + p )[109, TT T 110]. These observables were previously measured in the resolved topology by the ATLAS Collaboration using 8 TeV data [11] and, using 13 TeV data, as a function of the jet multiplicity [15]. Figures 10 and 11 show the distributions of these additional variables at detector-level in the resolved t,lep topology, while the distributions of |p |, ρ tt¯ and Htt¯ in out T the boosted topology are shown in Fig. 12. Finally, differential cross-sections have been measured at particle level as a function of the number of jets not employed in tt¯reconstruction in the resolved and boosted topology (Nextrajets). In addition, in the boosted topology, the crosssection as a function of the number of small-Rjets clustered inside a top candidate (Nsubjets) is measured. In the resolved topology, as shown in Figs. 6, 7, 10 and 11, good agreement between the prediction and the data is observed. Trends of deviations at the boundaries of 123 (a) (b) (c) Fig. 6 Distributions of observables in the f+jets channel reconstructed with the pseudo-top algorithm in the resolved topology at detector-level: a transverse momentum and b absolute value of the rapidity of the hadronic top quark, c transverse momentum of the leading top quark and dtransverse momentum of the subleading top quark. Data distributions are compared with predictions, using Powheg+Pythia8 as the tt¯ the uncertainty bands are seen for high values of mtt¯and pT tt¯. In the boosted topology, the predicted rate of events is overestimated at the level of 8.5%, leading to a corresponding offset in most distributions, as shown in Figs. 8, 9 and 12. A trend is observed in the Htt¯ distribution, where the pre- T dictions tend to overestimate the data at high values. This is more pronounced in the boosted topology, where the agree t ment lies outside the error band towards high values of HT t¯. (d) signal model. The hatched area represents the combined statistical and systematic uncertainties (described in Sect. 9) in the total prediction, excluding systematic uncertainties related to the modelling of the tt¯events. Underﬂow and overﬂow events, if any, are included in the ﬁrst and last bins. The lower panel shows the ratio of the data to the total prediction A summary of the observables measured in the particle and parton phase-spaces is given in Tables 5, 6 for the resolved topology and in Tables 7, 8 for the boosted topology. 8 Cross-section extraction The underlying differential cross-section distributions are obtained from the detector-level events using an unfolding 123 (a) (b) Fig. 7 Distributions of observables in the f+jets channel reconstructed with the pseudo-top algorithm in the resolved topology at detector-level: a invariant mass, btransverse momentum and c absolute value of the rapidity of the tt¯system. Data distributions are compared with predictions, using Powheg+Pythia8 as the tt¯signal model. The hatched technique that corrects for detector effects. The iterative Bayesian method [111] as implemented in RooUnfold [112] is used. Once the detector-level distributions are unfolded, the single-and double-differential cross-sections are extracted using the following equations: dξ 1 · Nunf ≧ dXi L· /Xi i d2ξ 1 · Nunf ≧ ij dXidYj L· /Xi/Yj (c) area represents the combined statistical and systematic uncertainties (described in Sect. 9) in the total prediction, excluding systematic uncer

tainties related to the modelling of the tt¯events. Underﬂow and overﬂow events, if any, are included in the ﬁrst and last bins. The lower panel shows the ratio of the data to the total prediction where the index i( j) iterates over bins of X(Y) at genera tor level, /Xi (/Yj) is the bin width, L is the integrated luminosity and Nunf represents the unfolded distribution, obtained as described in the following sections. Overﬂow and underﬂow events are never considered when evaluating Nunf, with the exception of the distributions as a function of jet multiplicities. The unfolding procedure described in the following is applied to both the single-and double-differential distri butions, the only difference being the creation of concate nated distributions in the double-differential case. In partic 123 (a) (b) (c) Fig. 8 Distributions of observables in the f+jets channel in the boosted topology at detector-level: a transverse momentum and b absolute value of the rapidity of the hadronic top quark, c transverse momentum of the leading top quark and dtransverse momentum of the subleading top quark. Data distributions are compared with predictions, using Powheg+Pythia8 as the tt¯signal model. The hatched area rep ular, Nunf is derived by introducing a new vector of size �nX m ==1 nY,i, where nX is the number of bins of the vari i able X and nY,i is the number of bins of the variable Y in the i-th bin of the variable X. The vector is constructed by concatenating all the bins of the original two-dimensional distribution. The total cross-section is obtained by integrating the unfolded differential cross-section over the kinematic bins, (d) resents the combined statistical and systematic uncertainties (described in Sect. 9) in the total prediction, excluding systematic uncertainties related to the modelling of the tt¯events. Underﬂow and overﬂow events, if any, are included in the ﬁrst and last bins. The lower panel shows the ratio of the data to the total prediction and its value is used to compute the normalised differential cross-section 1/ξ · dξ/dXi . 8.1 Particle level in the ﬁducial phase-space The unfolding procedure aimed to evaluate the particle-level distributions starts from the detector-level event distribution (Ndetector), from which the expected number of background events (Nbkg) is subtracted. Next, the bin-wise acceptance 123 (a) (c) Fig. 9 Kinematic distributions in the f+jets channel in the boosted topology at detector-level: a invariant mass, b transverse momentum and c absolute value of the rapidity of the tt¯system. Data distributions are compared with predictions, using Powheg+Pythia8 as the tt¯signal model. The hatched area represents the combined statistical and correction facc, deﬁned as Nparticle ≨detector facc = , Ndetector with Nparticle ≨detector being the number of detector-level events that satisfy the particle-level selection, corrects for events that are generated outside the ﬁducial phase-space but satisfy the detector-level selection. In the resolved topology, to separate resolution and combinatorial effects, distributions evaluated using a MC simulation are corrected to the level where detector-and particle (b) systematic uncertainties (described in Sect. 9) in the total prediction, excluding systematic uncertainties related to the modelling of the tt¯events. Underﬂow and overﬂow events, if any, are included in the ﬁrst and last bins. The lower panel shows the ratio of the data to the total prediction level objects forming the pseudo-top quarks are angularly well matched. The matching is performed using geometrical criteria based on the distance /R. Each particle-level e (μ) is required to be matched to the detector-level e (μ) within /R = 0.02. Particle-level jets forming the particlelevel hadronic top are required to be matched to the jets from the detector-level hadronic top within /R = 0.4. The same procedure is applied to the particle-and detector-level b-jet from the leptonically decaying top quark. If a detector-level jet is not matched to a particle-level jet, it is assumed to 123 (a) (b) (c) Fig. 10 Distributions of observables in the f+jets channel reconstructed with the pseudo-top algorithm in the resolved topology at detector-level: a azimuthal angle between the two top quarks () /φ t, t¯, b production angle ρtt¯and c absolute value of the longitt¯ tudinal boost yboost. Data distributions are compared with predictions, using Powheg+Pythia8 as the tt¯signal model.The hatched area rep- be either from pile-up or from matching inefﬁciency and is ignored. If two jets are reconstructed with a /R < 0.4from a single particle-level jet, the detector-level jet with smaller /Ris matched to the particle-level jet and the other detectorlevel jet is unmatched. The matching correction fmatch, which accounts for the corresponding efﬁciency, is deﬁned as: Nparticle ≨detector ≨match fmatch = , Nparticle ≨detector resents the combined statistical and systematic uncertainties (described in Sect. 9) in the total prediction, excluding systematic uncertainties related to the modelling of the tt¯events. Underﬂow and overﬂow events, if any, are included in the ﬁrst and last bins. The lower panel shows the ratio of the data to the total prediction where Nparticle ≨detector ≨match is the number of detector-level events that satisfy the particle-level selection and satisfy the matching requirement. The unfolding step uses a migration matrix (M) derived from simulated tt¯ events that maps the binned generated particle-level events to the binned matched detector-level events. The probability for particle-level events to remain in the same bin is therefore represented by the diagonal ele 123 (a) topology reconstructed with the pseudo-top algorithm at detector-level: t,had a absolute value of the out-of-plane momentum |p | and b scalar out sum of the transverse momenta of the hadronic and leptonic top t quarks HT t¯. Data distributions are compared with predictions, using Powheg+Pythia8 as the tt¯signal model.The hatched area repre ments, and the off-diagonal elements describe the fraction of particle-level events that migrate into other bins. Therefore, the elements of each row add up to unity as shown, for example, in Fig. 13d. The binning is chosen such that the fraction of events in the diagonal bins is always greater than 50%. The unfolding is performed using four iterations to balance the dependence on the prediction used to derive the corrections3 and the statistical uncertainty. The effect of varying the number of iterations by one is negligible. Finally, the efﬁciency correction 1/ς corrects for events that satisfy the particle-level selection but are not reconstructed at the detector level. The efﬁciency is deﬁned as the ratio Nparticle ≨ detector ς = , Nparticle where Nparticle is the total number of particle-level events. In the resolved topology, to account for the matching requirement, the numerator is replaced with Nparticle ≨ detector ≨ match. The inclusion of the matching requirement, in conjunction with the requirement on 2 b-tagged jets, identiﬁed with 70% efﬁciency, reﬂects in an overall efﬁciency below 25% in the resolved topology. This is lower than in the boosted topology, where the efﬁciency ranges between 35% and 50% thanks to 3 At every iteration the result of the previous iteration is taken as prior. This allows information derived from the data to be introduced into the prior and hence reduce the dependence on the prediction. (b) sents the combined statistical and systematic uncertainties (described in Sect. 9) in the total prediction, excluding systematic uncertainties related to the modelling of the tt¯events. Underﬂow and overﬂow events, if any, are included in the ﬁrst and last bins. The lower panel shows the ratio of the data to the total prediction the request of only one b-tagged jet and the absence of the matching correction. All corrections ( facc, fmatch and ς) and the migration matrices are evaluated with simulated events for all the distributions to be measured. As an example, Figs. 13 and 14 show the corrections and migration matrices for the case of the pT of the hadronically decaying top quark, in the resolved and boosted topologies, respectively. This variable is particularly representative since the kinematics of the decay products of the top quark change substantially in the observed range. In the resolved topology, the decrease in the efﬁciency at high values is primarily due to the increasingly large fraction of non-isolated leptons and to the partially or totally overlapping jets in events with high top-quark pT. An additional contribution is caused by the event veto removing the events passing the boosted selection from the resolved topology, as described in Sect. 4.4. This loss of efﬁciency is recovered by the measurement performed in the boosted topology. The unfolded distribution for an observable Xat particle level is given by: () 1 Nunf M−1 fj fjNj ≧···· , acc bkgi ςi ij match detector − Nj j where the index jiterates over bins of Xat detector level, while the iindex labels bins at particle level. The Bayesian unfolding is symbolised by Mij −1. No matching correction is applied in the boosted case ( fmatch =1). 123 (a) (b) (c) t,lep momentum |p |, b production angle ρtt¯and c scalar sum of the out t transverse momenta of the hadronic and leptonic top quarks HT t¯.Data distributions are compared with predictions, using Powheg+Pythia8 as the tt¯signal model.The hatched area represents the combined sta 8.2 Parton level in the full phase-space The measurements are extrapolated to the full phase-space of the parton-level tt¯system using a procedure similar to the one described in Sect. 8.1. At detector level, the only difference is in the deﬁnition of the reconstructed objects for the measurement in the resolved topology, where the event tistical and systematic uncertainties (described in Sect. 9)inthe total prediction, excluding systematic uncertainties related to the modelling of the tt¯events. Underﬂow and overﬂow events, if any, are included in the ﬁrst and last bins. The lower panel shows the ratio of the data to the total prediction reconstruction uses the kinematic ﬁt method instead of the pseudo-top method. To deﬁne f+jets ﬁnal states at the parton level, the contribution of tt¯ pairs decaying dileptonically (in all combinations of electrons, muons and τ -leptons) is removed by applying a bin-wise correction factor fdilep (dilepton correction) deﬁned 123 Table5 The single-and double-differential spectra, measured in the resolved topology at particle level 1D observables 2D combinations mtt¯In bins of: |ytt¯| and Nextrajets ptt¯In bins of: mtt¯, |ytt¯| and Nextrajets T t¯ |yt| In bins of: Nextrajets pt,had In bins of: mtt¯, pT tt¯, |yt,had| and Nextrajets T |yt,had| In bins of: Nextrajets t,1 p T t,2 p T ρtt¯ In bins of: Nextrajets tt¯|yboost | () /φ t, t¯In bins of: Nextrajets Htt¯ T In bins of: Nextrajets t,had | p | In bins of: Nextrajets out Nextrajets Table6 The single-differential and double-differential spectra, measured in the resolved topology at parton level 1D observables 2D combinations tt¯t¯ mIn bins of: |yt|tt¯t¯t¯ pIn bins of: mt and |yt| T t¯ |yt| pt,had In bins of: mtt¯, pT tt¯and |yt,had| T |yt,had| ρtt¯ tt¯|yboost | Htt¯ T Table7 The single-and double-differential spectra, measured in the boosted topology at particle level 1D observables 2D combinations t¯tt¯tt¯ mt In bins of: HT t¯, |yt|, pT and Nextrajets ptt¯In bins of: Nextrajets T t¯ |yt| pt,had In bins of: mtt¯, pT tt¯, |yt,had|, |ytt¯| and Nextrajets T |yt,had| t,1 p T t,2 p T ρtt¯Htt¯ T t,lep | p | out Nextrajets Nsubjets Table8 The single-differential and double-differential spectra, measured in the boosted topology at parton level 1D observables 2D combinations mt¯t In bins of: p t,had T p t,had T as Ndetector ≨ f+jets fdilep = , Ndetector which represents the fraction of the detector-level tt¯singlelepton events (Ndetector ≨ f+jets) in the total detector-level tt¯sample (Ndetector), where the lepton can be either an electron, muon or τ -lepton. The cross-section measurements correspond to the top quarks before decay (parton level) and after QCD radiation. Observables related to top quarks are extrapolated to the full phase-space starting from top quarks decaying hadronically at the detector level. The acceptance correction facc corrects for detector-level events that are generated at parton level outside the range of the given variable, and is deﬁned by a formula similar to the particle-level acceptance described in Sect. 8.1. The migra

tion matrix (M) is derived from simulated tt¯events decaying in the single-lepton channel and the efﬁciency correction 1/ς corrects for events that did not satisfy the detector-level selection where Ndetector ≨ f+jets ς = ,Nf+jets Ndetector ≨ f+jets is the number of parton-level events in the f+jets channel passing the detector-level selection and Nf+jets is the total number of events at parton level, as deﬁned in Sect. 4.3. All corrections and the migration matrices for the partonlevel measurement are evaluated with simulated events. As an example, Figs. 15 and 16 show the corrections and migration matrices for the case of the pT of the top quark, in the resolved and boosted topologies, respectively. The unfolding procedure is summarised by the expression Nunf M−1 ≧ 1 · 1 ·· fj · fj · Nj , i ςi ij dilep acc (detector − Nj ) bkg B j where the index jiterates over bins of the observable at the detector level, while the iindex labels the bins at the parton level, B = 0.438 is the f+jets branching ratio [113] and M−ij 1 represents the Bayesian unfolding. 8.3 Unfolding validation The statistical stability of the unfolding procedure has been tested with closure tests. With these tests it is checked that the 123 (a) (c) Fig. 13 The a acceptance facc, bmatching fmatch and c efﬁciency ς corrections (evaluated with the Monte Carlo samples used to assess the signal modelling uncertainties, as described in Sect. 9.2), and d the unfolding procedure is able to correctly recover a statistically independent sample generated with the same modelling used in the production of the unfolding corrections. These tests, performed on all the measured differential cross-sections, conﬁrm that good statistical stability is achieved for all the spectra. To ensure that the results are not biased by the MC generator used for the unfolding procedure, a study is performed in which the particle-level and parton-level spectra in the Powheg+Pythia8 simulation are altered by changing the shape of the distributions using continuous functions of the t particle-level and parton-level pT and of the actual data/MC (b) (d) migration matrix (evaluated with the nominal Powheg+Pythia8 simulation sample) for the hadronic top-quark transverse momentum in the resolved topology at particle level ratio observed at detector level. These tests are performed on all the measured distributions using the ﬁnal binning and employing the entire MC statistics available, and are referred to as stress tests. An additional stress test is performed on the distributions depending on mtt¯, where the spectra are modiﬁed to simulate the presence of a new resonance. Examples of stress tests performed by changing the distribution of the pT of the hadronic top employing a linear function of the t,had particle-level pT are presented, for both the resolved and boosted topologies, in Fig. 17. The studies conﬁrm that these altered shapes are preserved within statistical uncertainties by the unfolding procedure based on the nominal corrections. 123 (a) (b) (c) 9 Systematic uncertainties This section describes the estimation of systematic uncertainties related to object reconstruction and calibration, MC generator modelling and background estimation. As a result of the studies described in Sect. 8.3 no systematic uncertainty has been associated to the unfolding procedure. To evaluate the impact of each uncertainty after the unfolding, the reconstructed signal and background distributions in simulation are varied and unfolded using corrections from the nominal Powheg+Pythia8 signal sample. The unfolded distribution is compared with the corresponding particle-and (evaluated with the nominal Powheg+Pythia8 simulation sample) for the hadronic top-quark transverse momentum in the boosted topology at particle level parton-level spectrum and the relative difference is assigned as the uncertainty in the measured distribution. All detectorand background-related systematic uncertainties are evaluated using the same generator, while alternative generators and generator set-ups are employed to assess modelling systematic uncertainties. In these cases, the corrections, derived from the nominal generator, are used to unfold the detectorlevel spectra of the alternative generator and the comparison between the unfolded distribution and the alternative particleor parton-level spectrum is used to assess the corresponding uncertainty. 123 (c) The covariance matrices of the statistical and systematic uncertainties are obtained for each observable by evaluating the covariance between the kinematic bins using pseudoexperiments, as explained in Sect. 10. 9.1 Object reconstruction and calibration The small-R jet energy scale (JES) uncertainty is derived using a combination of simulations, test-beam data and in situ measurements [93,114]. Additional contributions from jet ﬂavour composition, υ-intercalibration, punch-through, single-particle response, calorimeter response to different jet ﬂavours and pile-up are taken into account, resulting (evaluated with the nominal Powheg+Pythia8 simulation sample) for the hadronic top-quark transverse momentum in the resolved topology at parton level, for events selected with the kinematic likelihood cut in 29 independent subcomponents of systematic uncertainty, including the uncertainties in the jet energy resolution obtained with an in situ measurement of the jet response in dijet events [115]. This uncertainty is found to be in the range of 5%–10%, depending on the variable, increasing to 20% in regions with high jet multiplicity. The efﬁciency to tag jets containing b-hadrons is corrected in simulated events by applying b-tagging scale fac-tors, extracted from a tt¯dilepton sample, to account for the residual difference between data and simulation. Scale fac-tors are also applied for jets originating from light quarks that are misidentiﬁed as b-jets. The associated ﬂavour-tagging systematic uncertainties, split into eigenvector components, 123 (a) (b) (c) are computed by varying the scale factors within their uncertainties [94,116]. The uncertainties due to the b-tagging efﬁciencies are constant for most of the measured distributions, amounting to 10% and 2% for the absolute differential crosssections in the resolved and boosted topologies, respectively, and become negligible in most of the normalised differential cross-sections. The lepton reconstruction efﬁciency in simulated events is corrected by scale factors derived from measurements of these efﬁciencies in data using a control region enriched + in Z → ee− and Z → μ+μ− events. The lepton trigger and reconstruction efﬁciency scale factors, energy scale (evaluated with the nominal Powheg+Pythia8 simulation sample) for the hadronic top-quark transverse momentum in the boosted topology at parton level and energy resolution are varied within their uncertainties [85,87,117] derived using the same sample. The uncertainty associated with Emiss is calculated by T propagating the energy scale and resolution systematic uncertainties to all jets and leptons in the Emiss calculation. Addi- T tional Emiss uncertainties arising from energy deposits not T associated with any reconstructed objects are also included [102,103]. The systematic uncertainties due to the lepton and Emiss T reconstruction are generally subdominant (around 2%–3%) in both the resolved and boosted topologies. 123 (a) t,had level pT andunfolded using the nominal corrections. The pseudo 9.2 Signal modelling Uncertainties in the signal modelling affect the kinematic properties of simulated tt¯events as well as detector-and particle-level efﬁciencies. To assess the uncertainty related to the choice of MC generator for the tt¯signal process, events simulated with Sherpa 2.2.1 are unfolded using the migration matrix and correction factors derived from the nominal Powheg+Pythia8 sample. Sherpa 2.2.1 includes its own parton-shower and hadronisation model, which are consequently included in the variation and considered in the systematic uncertainty. This variation is indicated as ‘generator’ uncertainty. The symmetrised full difference between the unfolded distribution and the generated particle-and parton-level distribution of the Sherpa sample is assigned as the relative uncertainty in the distributions. This uncertainty is found to be in the range of 5%–10%, depending on the variable, increasing to 20% at very low mtt¯at particle level, and at high pT at parton level, in both the boosted and resolved topologies. To assess the impact of different parton-shower and hadronisation models, unfolded results using events simulated with Powheg+Pythia8 are compared with events simulated with Powheg+Herwig7, with the same procedure as described above to evaluate the uncertainty related to the tt¯generator. (b) data are compared to the nominal prediction and the prediction obtained by reweighting the particle-level distribution. The bands represent the uncertainty due to the Monte Carlo statistics. Pseudo-data points are placed at the centre of each bin. The lower panel shows the ratios of the predictions to pseudo-data This variation is indicated as ‘hadronisation’ uncertainty. The resulting systematic uncertainties, taken as the symmetrised full difference, are found to be typically at the level of 2%– 5% in the resolved and boosted topologies, increasing to 20% at high top and tt¯ transverse momentum. To evaluate the uncertainty related to the modelling of additional radiations (Rad.), two tt¯MC samples with modiﬁed hdamp, scales and showering tune are used. The MC samples used for the evaluation of this uncertainty were generated using the Powheg-Box generator interfaced to the Pythia shower model, where the parameters are varied as described in Sect. 3. This uncertainty is found to be in the range of 5%–10% for the absolute spectra in both the resolved and the boosted topology, increasing to 20% at high pT at parton level. The estimation of the uncertainty due to different partonshower models and additional radiation modelling is performed using samples obtained with the ‘fast’ simulation, introduced in Sect. 3. In most of the distributions the fast simulation gives the same result as the full simulation, and consequently the corrections obtained with the two samples are consistent as shown in Fig. 16a, comparing the two ver

sions of Powheg+Pythia8. However, in some distributions a difference between fast and full simulation is observed, as shown in Fig. 13ainthe low pT range. To completely disen 123 tangle this effect from the modelling uncertainties estimate, the AFII version of Powheg+Pythia8 is used to calculate the unfolding corrections when the alternative samples, used to evaluate the systematic uncertainty, are produced with the fast simulation. The impact of the uncertainty related to the PDF is assessed using the nominal signal sample generated with Powheg-Box interfaced to Pythia8. Acceptance, matching, efﬁciency and dilepton corrections and migration matrices for the unfolding procedure are obtained by reweighting the tt¯sample using the 30 eigenvectors of the PDF4LHC15 PDF set [118]. Using these corrections, the detector-level Powheg+Pythia8 distribution, obtained with the central eigenvector of the PDF4LHC15 set, is unfolded and the relative deviation from the expected particle-or parton-level spectrum obtained with the same PDF set is computed. The total uncertainty is then obtained by adding these relative differences in quadrature. This procedure, obtained applying the recommendation given in Ref. [118] to unfolded measurements, differs from the approach used for the other modelling uncertainties, where nominal corrections are used to unfold detector-level distributions obtained with alternative generators. In addition, a further source of uncertainty derived from the choice of the PDF set is considered. This is estimated in a similar way to the other component but comparing the central distribution of PDF4LHC15 and NNPDF3.0NLO sets. The two components are added in quadrature. The total PDFinduced uncertainty is found to be less than 1% in most of the bins of the measured cross-sections. 9.3 Background modelling Systematic uncertainties affecting the backgrounds are evaluated by varying the background distribution, while keeping the signal unchanged, in the input to the unfolding procedure. The shift between the resulting unfolded distribution and the nominal one is used to estimate the size of the uncertainty. For the single-top-quark background, three kind of uncertainties are considered: 1. Total normalisation uncertainty: the cross-section of the single-top-quark process is varied within its uncertainty for the t-channel (5%) [71], s-channel (3.6%) [73] and tW production (5.3%) [72]. 2. Additional radiation uncertainty: single-top-quark (tW production and t-channel) MC samples with modiﬁed scales and showering tunes are used in a similar way to those for estimating the equivalent systematic uncertainty for the signal sample. The samples are described in Sect. 3. 3. Diagram subtraction versus diagram removal (DR/DS) uncertainty: the uncertainty due to the overlap of tW pro duction of single top quarks and production of tt¯pairs is evaluated by comparing the single-top-quark samples obtained using the diagram removal and diagram subtraction schemes [77], using the samples described in Sect. 3. In the ﬁnal measurement, the sum of these components, dominated by the DR/DS uncertainty, gives a small contribution in the low pT region, while it reaches 9% and 12% in the high pT region of the resolved and boosted topologies, respectively. For the W+jets process, two different uncertainty components are constructed from two οS variations of ±0.002 around the nominal value of 0.118 and from an envelope formed from 7-point scale variations of the renormalisation and factorisation scales, following the prescriptions described in Ref. [81]. The uncertainty due to the PDF variations is found to be subdominant and consequently not included. An additional uncertainty in the fraction of the heavy-ﬂavour components is considered. This uncertainty is evaluated by applying a 50% shift to the cross-section of the samples in which the W boson is produced in association with at least one b-quark and also rescaling the other samples to keep the total W+jets cross-section constant. This uncertainty is considered sufﬁcient to cover a possible mismodelling of the heavy-ﬂavour composition since no disagreements among predictions and data are observed. The W+jets uncertainty on the ﬁnal result ranges from 2 to 4% in the resolved topology, depending on the variable and phasespace, and between 2 and 12% in the boosted topology. The uncertainty due to the background from non-prompt and fake leptons is evaluated by changing the parameterisation of the real-and fake-lepton efﬁciencies used in the matrix method calculation. In addition, an extra 50% uncertainty is assigned to this background to account for the remaining mismodelling observed in various control regions. The combination of all these components also affects the shape of this background and the overall impact of these systematic uncertainties on the measurement is at the 2% level in both topologies, increasing to almost 4% in the low pT region in the resolved topology. In the case of the Z+jets processes, a global uncertainty, binned in jet multiplicity and based on οS, PDF and scale variations calculated in Ref. [81], is applied to the MC prediction of the Z+jets background components. For diboson backgrounds, a 40% uncertainty is applied, including the uncertainty in the cross-section and a contribution due to the presence of at least two additional jets. For the t¯ tV background, an overall uncertainty of 14% is applied, covering the uncertainties related to the scale, οS and PDF for the tt¯+ Wand Zcomponents. The overall impact of these additional background uncertainties on the ﬁnal result is less than 1%, and the largest contribution comes from the Z+jets background. 123 9.4 Statistical uncertainty of the Monte Carlo samples To account for the ﬁnite number of simulated events, test distributions based on total predictions are varied in each bin according to their statistical uncertainty, excluding the datadriven fake-lepton background. The effect on the measured differential cross-sections is at most 1% in the resolved and boosted topologies, peaking at 6% in the highest top-quark pT bins in the boosted topology. 9.5 Integrated luminosity The uncertainty in the combined 2015–2016 integrated luminosity is 2.1% [119], obtained using the LUCID-2 detector [120] for the primary luminosity measurements. This uncertainty is not dominant for the absolute differential crosssection results and it mostly cancels out for the normalised differential cross-section results. 9.6 Systematic uncertainties summary Figures 18, 19, 20 and 21 present the uncertainties in the particle-and parton-level normalised differential crosssections as a function of some of the different observables in the resolved and boosted topologies, respectively. The dominant systematic uncertainties in many measured normalised differential cross-sections in the resolved topology are those related to the jet energy scale and resolution, especially for differential cross-sections sensitive to the jet multiplicity. While negligible in the normalised spectra, the uncertainties related to the ﬂavour tagging become dominant when measuring inclusive and absolute differential cross-sections. Other signiﬁcant uncertainties, dominant in the boosted topology, include those from the signal modelling with, depending on the observable, either the generator, hadronisation or the additional radiation component being the most dominant. For most distributions in the resolved topology and in large parts of the phase-space, the measurements have a precision of the order of 10%–15%, while for the boosted topology the precision obtained varies from 7 to about 30% at particle level, increasing to 40% at parton level. 10 Results In this section, comparisons between the measured single-and double-differential cross-sections and several SM predictions are presented for the observables discussed in Sect. 7. The results are presented for both the resolved and boosted topologies, at particle level in the ﬁducial phase-spaces and at parton level in the full phase-space. For the comparisons at the particle level, the predictions are obtained using different MC generators. The Powheg-Box generator, denoted ‘PWG’ in the ﬁgures, is used with two different parton-shower and hadronisation models, as implemented in Pythia8 and Herwig7, as well as two extra settings for the radiation modelling. In addition the Sherpa 2.2.1 generator is also compared with the data. All the MC samples are detailed in Sect. 3.1. The measured differential cross-sections at the parton level are compared with NNLO pQCD theoretical predictions [4,5]. An additional comparison is performed, for a sub-set of the differential parton-level cross-sections, with existing ﬁxed-order predictions at NNLO pQCD accuracy and including electroweak (EW) corrections [121]. To quantify the level of agreement between the measured cross-sections and the different theoretical predictions, ρ 2 values are calculated, using the total covariance matrices evaluated for the measured cross-sections, according to the following relation 2 ρ= VT · Cov−1 · VNb , Nb Nb where Nb is the number of bins of the spectrum under consideration, VNb is the vector of differences between the measured and predicted cross-sections and CovNb represents the covariance matrix. This includes both the statistical and systematic uncertainties and is evaluated by performing 10 000 pseudo-experiments, following the procedure described in Ref. [14]. No uncertainties in the theoretical predictions are included in the ρ2 calculation. The p-values are then evaluated from the ρ2 and the number of degrees of freedom (NDF). For normalised cross-sections, VNb must be replaced with VNb−1, which is the vector of differences between data and prediction obtained by discarding one of the Nb elements and, consequently, CovNb−1 is the (Nb − 1) × (Nb − 1) sub-matrix derived from the full covariance matrix discarding the corresponding row and column. The sub-matrix obtained in this way is invertible and allows the ρ2 to be computed. The ρ2 value does not depend on the choice of the element discarded for the vector VNb−1 and the corresponding sub-matrix CovNb−1. The determination of statistical correlations within each spectrum and among different spectra are evaluated using the Bootstrap Method [122]. The method is based on the extraction of 1000 Bootstrap samples (pseudo-experiments) obtained by reweighting the measured data sample on an event-by-event basis with a Poisson distribution. To allow comparisons to be made between the shapes of the measured cross-sections and the predictions, all the results included in this section are presented as normalised cross-sections: the measurement of the normalised cross 123 (a) (b) (c) Fig. 18 Uncertainties in the particle-level normalised differential cross-sections as a function of a the transverse momentum, bthe mass of the tt¯system, and c the transverse momentum of the tt¯system as sections signiﬁcantly reduces the contribution of uncertainties common to all bins of the distributions, highlighting shape differences relative to the absolute case. Examples to a function of the jet multiplicity in the resolved topology. The bands represent the statistical and total uncertainty in the data illustrate this features are presented in Sect. 10.1, while the results of ρ2 and p-value calculations are always reported for both the normalised and absolute cross-sections. 123 (a) (b) (c) Fig. 19 Uncertainties in the particle-level normalised differential as a function of the number of additional jets in the boosted topology. cross-sections as a function of athe transverse momentum, bthe rapid-The bands represent the statistical and total uncertainty in the data ity of the hadronically decaying top quark and c the pT of the tt¯system 123 (a) (b) (c) Fig. 20 Uncertainties in the parton-level normalised differential cross quark as a function of the mass of the t¯t system in the resolved topology. sections as a function of a the t¯t system transverse momentum bthe The bands represent the statistical and total uncertainty in the data absolute value of the rapidity and cthe transverse momentum of the top 123 (a) (b) (c) Fig. 21 Uncertainties in the parton-level normalised differential cross- of the pT of the top quark in the boosted topology. The bands represent sections as a function of a the transverse momentum of the top quark, the statistical and total uncertainty in the data bthe mass of the t¯t system and cthe mass of the t¯t system as a function 123 (a) (b) Fig. 22 Particle-level normalised differential cross-sections as a func resent the statistical and total uncertainty in the data. Data points are tion of a the transverse momentum and b the absolute value of the placed at the centre of each bin. The lower panel shows the ratios of the rapidity of the hadronically decaying top quark in the resolved topol simulations to data ogy, compared with different Monte Carlo predictions. The bands rep (a) (b) Fig. 23 Particle-level normalised differential cross-sections as a func predictions. The bands represent the statistical and total uncertainty in tion of the transverse momentum of a the leading and bthe subleading the data. Data points are placed at the centre of each bin. The lower top quark in the resolved topology, compared with different Monte Carlo panel shows the ratios of the simulations to data 123 (a) 10.1 Results at particle level in the ﬁducial phase-spaces 10.1.1 Resolved topology The normalised single-differential cross-sections are measured as a function of the transverse momentum and absolute value of the rapidity of the hadronically decaying top quark, as well as of the mass and transverse momentum of the tt¯ () t,had system and of the additional variables p , /φ t, t¯, out Htt¯ T and jet multiplicity. Moreover, the differential crosssection as a function of the pT of the top quark is measured separately for the leading and subleading top quark. The results are shown in Figs. 22, 23, 24 and 25. The quantita

tive comparisons among the particle-level results and predictions, obtained with a ρ2 test statistic, are shown in Tables 9 and 10, for normalised and absolute single-differential cross

sections, respectively. The normalised double-differential cross-sections, presented in Figs. 26, 27, 28, 29, 30, 31, 32, 33, 34 and 35, are measured as a function of the pT of the hadronically decaying top quark and of the tt¯system in bins of the mass t,had the tt¯system, as a function of p in bins of the pT of out the hadronically decaying top quark and ﬁnally as a func () t,had tt¯tt¯t,had t tion of p , m, pp , /φ t, t¯and Ht¯in bins T T, out T of jet multiplicity. The quantitative comparisons among the particle-level results and predictions, obtained with a ρ2 test statistic, are shown in Tables 11 and 12, for normalised and (b) tions. The bands represent the statistical and total uncertainty in the data. Data points are placed at the centre of each bin. The lower panel shows the ratios of the simulations to data absolute double-differential cross-sections, respectively. An example of an absolute differential cross-section, as a function of mtt¯in bins of jet multiplicity, is given in Fig. 31.In this case, the total uncertainty is larger than the uncertainty in the corresponding normalised differential cross-section, as shown Fig. 30. Additionally, the total cross-section is measured in the ﬁducial phase-space of the resolved topology and is compared with the MC predictions previously described, as shown in Fig. 36. The total cross-section predicted by each NLO MC generator is normalised to the NNLO + NNLL prediction as quoted in Ref. [55] and the corresponding uncertainty only includes the uncertainty affecting the kfactor used in the normalisation. The differences between the quoted ﬁducial cross-sections hence result from different acceptance predictions from each model. All the measured differential cross-sections are compared with the MC predictions. Overall, these MC predictions give a good description of the measured single-differential crosssections. Poorer agreement is observed in speciﬁc regions of the probed phase-space. In Figs. 24b and 25a, showing the tt¯ t,had differential cross-sections as a function of pand | p |, T out the predictions overestimate the data in the high pT tt¯region, with the exception of Powheg+Pythia8 prediction with the Var3cDown tuning, and several generators overestimate t,had the high | p | region. A similar trend is observed in the out double-differential cross-sections as a function of the pT of 123 (a) (c) Fig. 25 Particle-level normalised differential cross-sections as a func () t,had tion of a pout, b/φ t, t¯, c HT tt¯ and dadditional jet multiplicity in the resolved topology, compared with different Monte Carlo predic the tt¯ system in bins of jet multiplicity (Fig. 32), in particular for bins of higher jet multiplicities. The Var3cUp tuning of Powheg+Pythia8, in combination with the increase of the hdamp value to 3mt, is the prediction that shows the largest disagreement with the data. Overall, the NLO+PS generator that gives the better description of several double-differential distributions is Powheg+Pythia8. (b) (d) tions. The bands represent the statistical and total uncertainty in the data. Data points are placed at the centre of each bin. The lower panel shows the ratios of the simulations to data The measured single-and double-differential cross-sections are often able to discriminate between the different features exhibited by the MC predictions and this sensitivity is hence relevant for the tuning of the MC generators and will contribute to improving the description of the tt¯ ﬁnal state and to reducing the systematic uncertainties related to topquark modelling. A relevant example is the ﬁducial single 123 Table9 Comparison of the measured particle-level normalised single-calculated using the covariance matrix of the measured spectrum. The differential cross-sections in the resolved topology with the predictions NDF is equal to the number of bins in the distribution minus one from several MC generators. For each prediction a ρ 2 and a p-value are Observable Pwg+Py8 Pwg+Py8Rad. Up Pwg+Py8 Rad. Down Pwg+H7 Sherpa 2.2.1 ρ2/NDF p-value ρ2/NDF p-value ρ2/NDF p-value ρ2/NDF p-value ρ2/NDF p-value Htt¯ T 9.5/17 0.92 12.3/17 0.78 12.1/17 0.80 7.6/17 0.97 7.7/17 0.97 t,had |p | 6.3/7 0.51 71.3/7 < 0.01 6.3/7 0.51 12.9/7 0.07 24.6/7 < 0.01 out tt¯ |yboost | 5.9/14 0.97 7.4/14 0.92 5.1/14 0.98 8.4/14 0.87 7.8/14 0.90 ρtt¯ 18.1/12 0.11 10.5/12 0.57 36.0/12 < 0.01 14.6/12 0.26 22.7/12 0.03 |/φ(t, t¯)| 3.3/6 0.77 45.8/6 < 0.01 8.0/6 0.24 5.7/6 0.46 21.6/6 < 0.01 pT t,1 6.0/10 0.81 10.0/10 0.44 6.8/10 0.74 3.1/10 0.98 3.0/10 0.98 pT t,2 4.2/8 0.84 3.4/8 0.91 5.3/8 0.73 1.9/8 0.98 0.9/8 1.00 |yt,had | 9.1/19 0.97 9.6/19 0.96 9.0/19 0.97 10.4/19 0.94 14.6/19 0.74 t,had pT 11.7/18 0.86 11.1/18 0.89 14.3/18 0.71 6.4/18 0.99 6.8/18 0.99 t¯ |yt| 8.2/15 0.91 11.1/15 0.75 7.4/15 0.95 9.1/15 0.87 10.6/15 0.78 mtt¯16.0/15 0.38 14.8/15 0.46 19.8/15 0.18 14.7/15 0.48 15.3/15 0.43 pT tt¯19.6/10 0.03 165.0/10 < 0.01 17.5/10 0.07 28.6/10 < 0.01 71.2/10 < 0.01 Nextrajets 5.8/6 0.44 14.4/6 0.03 29.2/6 < 0.01 94.0/6 < 0.01 8.8/6 0.19 Table10 Comparison of the measured particle-level absolute single-calculated using the covariance matrix of the measured spectrum. The differential cross-sections in the resolved topology with the predictions NDF is equal to the number of bins in the distribution from several MC generators. For each prediction a ρ 2 and a p-value are Observable Pwg+Py8 Pwg+Py8Rad. Up Pwg+Py8 Rad. Down Pwg+H7 Sherpa 2.2.1 ρ2/NDF p-value ρ2/NDF p-value ρ2/NDF p-value ρ2/NDF p-value ρ2/NDF p-value Htt¯ T 11.1/18 0.89 17.7/18 0.48 10.5/18 0.91 11.4/18 0.88 11.9/18 0.85 t,had | p | 9.2/8 0.32 97.3/8 < 0.01 8.3/8 0.41 11.2/8 0.19 27.8/8 < 0.01 out tt¯ |yboost | 7.0/15 0.96 8.7/15 0.89 6.1/15 0.98 9.8/15 0.83 10.2/15 0.81 ρtt¯ 20.4/13 0.09 12.3/13 0.51 38.3/13 < 0.01 17.7/13 0.17 22.5/13 0.05 |/φ(t, t¯)| 3.0/7 0.89 57.7/7 < 0.01 12.3/7 0.09 4.7/7 0.70 22.1/7 < 0.01 pT t,1 9.2/11 0.60 15.0/11 0.18 8.8/11 0.64 7.8/11 0.73 6.5/11 0.84 pT t,2 5.3/9 0.80 5.2/9 0.81 6.0/9 0.74 2.5/9 0.98 2.1/9 0.99 |yt,had | 12.7/20 0.89 13.5/20 0.86 12.5/20 0.90 13.2/20 0.87 19.5/20 0.49 t,had pT 19.0/19 0.46 23.3/19 0.23 18.0/19 0.52 15.0/19 0.72 14.5/19 0.75 t¯ |yt| 9.2/16 0.90 11.5/16 0.78 8.3/16 0.94 9.8/16 0.88 13.5/16 0.64 mtt¯17.8/16 0.34 16.4/16 0.43 20.2/16 0.21 15.5/16 0.49 17.1/16 0.38 pT tt¯23.1/11 0.02 196.0/11 < 0.01 16.9/11 0.11 33.4/11 < 0.01 88.0/11 < 0.01 Nextra jets 9.5/7 0.22 7.7/7 0.36 28.3/7 < 0.01 104.0/7 < 0.01 11.5/7 0.12 t¯t,had differential cross-section as a function of mt and pT that is well described by all the NLO MC predictions, as shown in Figs. 22a and 24a and Table 9, while the double-differential cross-section where these two variables are combined shows strong disagreement with several predictions, as shown in Fig. 26. The comparison of the NLO MC predictions with the measured double-differential cross-sections reveals, overall, poorer agreement than in the single-differential case. In particular, it is observed that no generator is able to describe any double-differential observable that includes pT tt¯as a probed variable. 10.1.2 Boostedtopology The single-differential cross-sections are measured as a function of the transverse momentum and absolute value of the rapidity of the hadronically decaying top quark as well as of the mass, transverse momentum and rapidity of the tt¯system 123 (a) Fig. 26 aParticle-level normalised differential cross-section as a func t,had t¯ tion of pT in bins of mt in the resolved topology compared with the prediction obtained with the Powheg+Pythia8 MC generator. Data (a) Fig. 27 aParticle-level normalised differential cross-section as a func tt¯t¯ tion of pT in bins of mt in the resolved topology compared with the prediction obtained with the Powheg+Pythia8 MC generator. Data t,lep t and of the additional variables p , HT t¯, ρ tt¯, additional out jet multiplicity and the number of small-R jets reclustered inside the hadronic top. The differential cross-section as a function of the pT of the top quark is also measured separately for the leading and subleading top quark. The results are shown in Figs. 37, 38, 39, 40, 41, and 42. The quantita

tive comparisons among the particle-level results and predictions, obtained with a ρ2 test statistic, are shown in Tables 13 and 14, for normalised and absolute single-differential cross

sections, respectively. In Fig. 40b an example of an absolute differential cross-section in the boosted topology is given. The total uncertainty in the differential cross-section as a (b) points are placed at the centre of each bin. bThe ratio of the measured cross-section to different Monte Carlo predictions. The bands represent the statistical and total uncertainty in the data (b) points are placed at the centre of each bin. bThe ratio of the measured cross-section to different Monte Carlo predictions. The bands represent the statistical and total uncertainty in the data function of mtt¯is reduced relative to the corresponding normalised cross-section, Fig. 40a. The double-differential cross-sections, presented in Figs. 43, 44, 45, 46, 47, 48, 49, 50, 51, and 52, are mea

t,had tt¯tt¯t suredasafunctionof p in bins of py,yand T T, t¯tt¯ tt¯ mt as well as a function of mtt¯ in bins of pT,yand Htt¯ t,had tt¯t¯ and ﬁnally as a function of p , pand mt in bins T TT of jet multiplicity. The quantitative comparisons among the particle-level results and predictions, obtained with a ρ2 test statistic, are shown in Tables 15 and 16, for normalised and absolute double-differential cross-sections, respectively. 123 (a) (b) Fig. 28 aParticle-level normalised differential cross-section as a func-points are placed at the centre of each bin. bThe ratio of the measured t,had t,had cross-section to different Monte Carlo predictions. The bands represent tion of p in bins of p in the resolved topology compared with outT the statistical and total uncertainty in the data the prediction obtained with the Powheg+Pythia8 MC generator. Data (a) Fig. 29 aParticle-level normalised differential cross-section as a func t,had tion of pT in bins of the jet multiplicity in the resolved topology compared with the prediction obtained with the Powheg+Pythia8 MC Additionally, the total cross-section is measured in the ﬁducial phase-space of the boosted topology and is compared with the MC predictions previously described, as shown in Fig. 53. The total cross-section predicted by each NLO MC generator is normalised to the NNLO+NNLL prediction as quoted in Ref. [55] and the corresponding uncertainty only includes the uncertainty affecting the k-factor used in the normalisation. As in the case of the inclusive ﬁducial cross-section in the resolved topology, the differences between the quoted ﬁducial cross-sections result from different acceptance predictions from each model. It is (b) generator. Data points are placed at the centre of each bin. bThe ratio of the measured cross-section to different Monte Carlo predictions. The bands represent the statistical and total uncertainty in the data observed that several NLO+PS predictions, with the exception of Powheg+Herwig7 and Powheg+Pythia8 Rad. down, overestimate the measurement of the inclusive crosssection. The MC predictions are not always able to describe the measured single-differential cross-sections in the entire ﬁducial phase-space; mismodelling is observed, in particular, for the differential cross-section as a function of the pT of the hadronic top quark, shown in Fig. 37a, for the differential cross-section as a function of mtt¯, shown in Fig. 40a, and t for the observable HT t¯, shown in Fig. 41c, where all the MC 123 (a) (b) Fig. 30 aParticle-level normalised differential cross-section as a func-generator. Data points are placed at the centrer of each bin. bThe ratio tion of mtt¯in bins of the jet multiplicity in the resolved topology com-of the measured cross-section to different Monte Carlo predictions. The pared with the prediction obtained with the Powheg+Pythia8 MC bands represent the statistical and total uncertainty in the data (a) Fig. 31 aParticle-level absolute differential cross-section as a function of mtt¯in bins of the jet multiplicity in the resolved topology compared with the prediction obtained with the Powheg+Pythia8 MC genera predictions tend to overestimate the data in the tails of the distributions. A similar trend is observed for the differential cross-sections as a function of the transverse momentum of the leading and subleading top quark (shown in Fig. 38). To a smaller extent, discrepancies are observed at high values t,lep tt¯ ofy, shown in Fig. 39b, and in the tails of thep outdistribution, shown in Fig. 41b. The tensions between the MC predictions and the data are observed also in the measured double-differential crosssections, in particular for the cross-sections as a function t,had t¯ t t t¯ of pT in bins ofy,yand mt (shown in Figs. 44, 45, 46) and as a function of mtt¯ in bins ofytt¯ (shown (b) tor. Data points are placed at the centre of each bin. bThe ratio of the measured cross-section to different Monte Carlo predictions. The bands represent the statistical and total uncertainty in the data in Fig. 49). As in the case of the double-differential cross

sections in the resolved topology, the measurements allow discrimination between the different MC predictions. Overall, for the double-differential cross-sections, the MC predictions obtained from Powheg+Herwig7 provide the better description of the data while those from Sherpa 2.2.1 and Powheg+Pythia8 with the Var3cDown tuning show a signiﬁcant disagreement with the data, as also observed in the resolved topology to a smaller extent. Since the deﬁnitions of the phase-space and the particlelevel hadronic top quark differ between the resolved and boosted topologies, a direct comparison of the measured dif 123 (a) (b) Fig. 32 aParticle-level normalised differential cross-section as a func-generator. Data points are placed at the centre of each bin. bThe ratio tion of pT tt¯in bins of the jet multiplicity in the resolved topology com-of the measured cross-section to different Monte Carlo predictions. The pared with the prediction obtained with the Powheg+Pythia8 MC bands represent the statistical and total uncertainty in the data (a) Fig. 33 aParticle-level normalised differential cross-section as a func t,had tion of p in bins of the jet multiplicity in the resolved topology outcompared with the prediction obtained with the Powheg+Pythia8 MC ferential cross-sections is not possible. However, it can be seen in Fig. 54 that the ratio of data to prediction is consistent between the measured absolute differential cross-sections in the overlap region of the two topologies. 10.2 Results at parton level in the full phase-space 10.2.1 Resolved topology The single-differential normalised cross-sections are measured as a function of the transverse momentum and absolute value of the rapidity of the top quark and as a func (b) generator. Data points are placed at the centre of each bin. bThe ratio of the measured cross-section to different Monte Carlo predictions. The bands represent the statistical and total uncertainty in the data tion of the mass, transverse momentum and absolute value of the rapidity of the tt¯system and of the additional vari tt¯, Htt¯ ablesyand ρ tt¯. The results are shown in Figs. 55, boostT 56 and 57. The quantitative comparisons among the parton

level results and MC predictions, obtained with a ρ2 test statistic, are shown in Tables 17 and 18, for normalised and absolute single-differential distributions, respectively. The double-differential cross-sections, presented in Figs. 58, 59, t 60, 61, 62, and 63, are measured as a function of pT in bins tt¯tt¯ ttt¯ of m, pandy, as a function of pin bins of mtt¯ and TT t t yt¯and ﬁnally as a function of mtt¯ in bins ofyt¯.The quantitative comparisons among the parton-level results and 123 (a) Fig. 34 aParticle-level normalised differential cross-section as a func () tion of/φ t, t¯ in bins of the jet multiplicity in the resolved topology compared with the prediction obtained with the Powheg+Pythia8 MC (a) Fig. 35 aParticle-level normalised differential cross-section as a func t tion of Ht¯in bins of the jet multiplicity in the resolved topology com- T pared with the prediction obtained with the Powheg+Pythia8 MC MC predictions, obtained with a ρ 2 test statistic, are shown in Tables 21 and 22, for normalised and absolute single

differential distributions, respectively. The measured differential cross-sections are compared with the ﬁxed-order NNLO pQCD predictions and with the Powheg+Pythia8 NLO+PS parton-level predictions. In the case of the top-quark pT and rapidity, NNLO predictions are available for the distributions of the top/anti-top average, which are calculated not on an event-by-event basis but by averaging the results of the histograms of the distributions (b) generator. Data points are placed at the centre of each bin. bThe ratio of the measured cross-section to different Monte Carlo predictions. The bands represent the statistical and total uncertainty in the data (b) generator. Data points are placed at the centre of each bin. bThe ratio of the measured cross-section to different Monte Carlo predictions. The bands represent the statistical and total uncertainty in the data of the top and anti-top quark [121]. For these variables, the measured differential cross-sections are taken as a function of the hadronic top quark’s kinematics. The NNLO pQCD predictions are obtained, for the optimised binning of this analysis, using the NNLO NNPDF3.1 PDF set [123] with the renormalisation (μR) and factorisation (μF) scales both set to HT/4 (with HT equal to the sum of the transverse masses of the top and anti-top quark) for all the measured differential cross-sections with the excep t tion of the differential cross-section as a function of pT,for 123 Table 11 Comparison of the measured particle-level normalised p-value are calculated using the covariance matrix of the measured double-differential cross-sections in the resolved topology with the pre-spectrum. The NDF is equal to the number of bins in the distribution dictions from several MC generators. For each prediction a ρ2 and a minus one Observable Pwg+Py8 Pwg+Py8Rad. Up Pwg+Py8 Rad. Down Pwg+H7 Sherpa 2.2.1 ρ2/NDF p-value ρ2/NDF p-value ρ2/NDF p-value ρ2/NDF p-value ρ2/NDF p-value Htt¯vs Nextrajets T 9.7/19 0.96 57.9/19 < 0.01 19.4/19 0.43 48.7/19 < 0.01 27.4/19 0.10 | pt,had | vs Nextrajets 10.8/9 0.29 89.2/9 < 0.01 31.9/9 < 0.01 32.6/9 < 0.01 19.2/9 0.02 out ρtt¯ vs Nextrajets 37.6/19 < 0.01 31.6/19 0.03 88.9/19 < 0.01 84.8/19 < 0.01 23.7/19 0.21 |/φ(t, t¯)| vs Nextrajets 21.8/18 0.24 125.0/18 < 0.01 31.0/18 0.03 44.4/18 < 0.01 36.7/18 < 0.01 |yt,had | vs Nextrajets 9.5/12 0.66 19.1/12 0.09 26.8/12 < 0.01 30.8/12 < 0.01 10.4/12 0.58 |yt,had | vs pt,had 14.9/12 0.25 11.9/12 0.45 18.1/12 0.11 8.4/12 0.75 9.4/12 0.67 T t,had t,had p vs |p | 10.5/12 0.57 74.5/12 < 0.01 25.3/12 0.01 13.4/12 0.34 22.4/12 0.03 T out t,had vs Nextrajets pT 14.2/16 0.58 45.7/16 < 0.01 37.3/16 < 0.01 67.5/16 < 0.01 13.9/16 0.60 |ytt¯| vs Nextrajets 8.2/12 0.77 14.6/12 0.26 25.4/12 0.01 55.5/12 < 0.01 13.9/12 0.30 t¯tt¯ |yt| vs m18.0/14 0.21 12.0/14 0.60 23.1/14 0.06 13.2/14 0.51 14.8/14 0.40 t¯tt¯ |yt| vs p28.5/12 < 0.01 149.0/12 < 0.01 23.2/12 0.03 31.8/12 < 0.01 70.7/12 < 0.01 T tt¯vs Nextrajets m29.1/16 0.02 25.5/16 0.06 49.6/16 < 0.01 24.6/16 0.08 11.5/16 0.78 tt¯t,had mvs pT 58.9/31 < 0.01 51.4/31 0.01 92.3/31 < 0.01 35.6/31 0.26 44.8/31 0.05 tt¯tt¯ mvs pT 43.6/21 < 0.01 260.0/21 < 0.01 47.0/21 < 0.01 44.7/21 < 0.01 149.0/21 < 0.01 tt¯vs Nextrajets pT 69.1/19 < 0.01 283.0/19 < 0.01 58.5/19 < 0.01 82.8/19 < 0.01 102.0/19 < 0.01 tt¯t,had pT vs pT 39.2/19 < 0.01 282.0/19 < 0.01 51.5/19 < 0.01 55.8/19 < 0.01 137.0/19 < 0.01 Table12 Comparison of the measured particle-level absolute double-calculated using the covariance matrix of the measured spectrum. The differential cross-sections in the resolved topology with the predictions NDF is equal to the number of bins in the distribution from several MC generators. For each prediction a ρ 2 and a p-value are Observable Pwg+Py8 Pwg+Py8Rad. Up Pwg+Py8 Rad. Down Pwg+H7 Sherpa 2.2.1 ρ2/NDF p-value ρ2/NDF p-value ρ2/NDF p-value ρ2/NDF p-value ρ2/NDF p-value Htt¯vs Nextrajets T 13.8/20 0.84 72.9/20 < 0.01 31.3/20 0.05 56.6/20 < 0.01 40.5/20 < 0.01 | pt,had | vs Nextrajets 16.3/10 0.09 165.0/10 < 0.01 15.7/10 0.11 35.6/10 < 0.01 50.9/10 < 0.01 out ρtt¯ vs Nextrajets 44.4/20 < 0.01 60.3/20 < 0.01 88.3/20 < 0.01 62.2/20 < 0.01 24.6/20 0.21 |/φ(t, t¯)| vs Nextrajets 41.6/19 < 0.01 183.0/19 < 0.01 43.6/19 < 0.01 44.2/19 < 0.01 60.0/19 < 0.01 |yt,had | vs Nextrajets 11.3/13 0.59 50.3/13 < 0.01 23.1/13 0.04 28.7/13 < 0.01 14.8/13 0.32 |yt,had | vs pt,had 13.3/13 0.42 12.9/13 0.45 15.6/13 0.27 8.7/13 0.80 9.8/13 0.71 T t,had t,had p vs |p | 8.6/13 0.80 79.6/13 < 0.01 28.8/13 < 0.01 9.7/13 0.72 16.0/13 0.25 T out t,had vs Nextrajets pT 19.3/17 0.31 59.5/17 < 0.01 43.3/17 < 0.01 65.3/17 < 0.01 24.7/17 0.10 |ytt¯| vs Nextrajets 7.0/13 0.90 26.7/13 0.01 22.1/13 0.05 51.5/13 < 0.01 31.5/13 < 0.01 t¯tt¯ |yt| vs m22.3/15 0.10 15.0/15 0.45 29.8/15 0.01 15.8/15 0.40 19.1/15 0.21 t¯tt¯ |yt| vs p32.7/13 < 0.01 143.0/13 < 0.01 21.2/13 0.07 36.8/13 < 0.01 81.4/13 < 0.01 T tt¯vs Nextrajets m28.0/17 0.04 29.0/17 0.03 49.2/17 < 0.01 36.3/17 < 0.01 14.0/17 0.67 tt¯t,had mvs pT 56.2/32 < 0.01 59.9/32 < 0.01 79.9/32 < 0.01 31.9/32 0.47 48.5/32 0.03 tt¯tt¯ mvs pT 49.0/22 < 0.01 310.0/22 < 0.01 53.3/22 < 0.01 55.1/22 < 0.01 175.0/22 < 0.01 tt¯vs Nextrajets pT 93.2/20 < 0.01 412.0/20 < 0.01 51.9/20 < 0.01 91.8/20 < 0.01 163.0/20 < 0.01 tt¯t,had pT vs pT 38.6/20 < 0.01 294.0/20 < 0.01 66.5/20 < 0.01 46.1/20 < 0.01 128.0/20 < 0.01 123 Fig. 36 Comparison of the measured inclusive ﬁducial cross-section in the resolved topology with the predictions from several MC generators. The bands represent the statistical and total uncertainty in the data. The uncertainty on the cross-section predicted by each NLO MC generator only includes the uncertainty (due to PDFs, mt and οs) affecting the k-factor used in the normalisation which both scales were set to mT/2[5].4 The top-quark pole mass is set to 172.5 GeV. The theoretical uncertainty in the central NNLO predictions is obtained by summing in quadrature the uncertainty due to the higher-order terms, estimated from the envelope of the predictions obtained by independently increasing and decreasing μR and μF by a factor of two relative to the central scale choice, and the uncertainty due to the PDFs obtained according to the prescription of the NNPDF Collaboration. The quantitative comparisons among the parton-level results and the NNLO pQCD predictions, obtained with a ρ2 test statistic, are shown in Tables 19 and 20 and Tables 23 and 24, for single-and double-differential dis

tributions, respectively. For the single-differential cross-sections the NNLO and NLO+PS predictions give a good and comparable description of the data, with the exception of mtt¯that is poorly described by several NLO+PS predictions. Regarding the measured 4 22 mT = mt + p. T,t double-differential cross-sections, tensions are observed for several variables with respect to the NLO+PS predictions while a better description is observed when comparing the measurements with the NNLO calculations. In the double- t tt¯ differential cross-sections as a function of pT in bins of m, showninFig. 60, the NNLO and NLO+PS central predictions show a contrasting behaviour, with the Powheg+Pythia8 predictions giving a better description of the data in the low mtt¯region while the NNLO predictions better model the measurements in the high mtt¯ region. The absolute differential cross-sections as a function of t ttt¯tt¯t¯ pT, y, pT, yand mt are also measured using a coarser binning,5 used in a recent measurement from the CMS Collaboration [21], to test the impact of including EW corrections in the NNLO pQCD predictions. These EW corrections [121] include the NLO EW effects of O(οS2ο), all subleading NLO (O(οSο2) and O(ο3)) terms as well as the LO (O(οSο) and O(ο2)) contributions in the QCD and EW coupling constants. For these predictions, the mass of the top quark is set to 173.3 GeV. These additional measurements are shown in Figs. 64 and 65 and are compared with theoretical predictions obtained, with and without EW corrections, with two different PDF sets: the NNLO NNPDF3.1 PDF set and the LUXQED17 PDF set [124], the latter includes in addition to the standard partonic structure of the proton its photon component. The still rather limited range covered by the trans-verse momenta of top and anti-top quarks does not yet allow quantitative tests of the impact of the EW corrections as well as the contribution of the PDF of the photon in the proton to the production of top-quark pairs. 10.2.2 Boostedtopology In the boosted topology, the parton-level normalised differential cross-sections are extracted in a region of the phasespace where the top quark is produced with pT > 350 GeV. The single-differential cross-sections are measured as a function of the transverse momentum of the top quark and of the invariant mass of the tt¯system. The results are shown in Fig. 66. The parton-level double-differential cross-sections, presented in Fig. 67, are measured as a function of mtt¯in t bins of pT. 5 The binning used for this comparison is tested and fully validated against the stability of the unfolding procedure. 123 (a) (b) Fig. 37 Particle-level normalised differential cross-sections as a func resent the statistical and total uncertainty in the data. Data points are tion of a the transverse momentum and b the absolute value of the placed at the centre of each bin. The lower panel shows the ratios of the rapidity of the hadronically decaying top quark in the boosted topol simulations to data ogy, compared with different Monte Carlo predictions. The bands rep (a) (b) Fig. 38 Particle-level normalised differential cross-sections as a func predictions. The bands represent the statistical and total uncertainty in tion of the transverse momentum of a the leading and bthe subleading the data. Data points are placed at the centre of each bin. The lower top quark in the boosted topology, compared with different Monte Carlo panel shows the ratios of the simulations to data 123 (a) (b) Fig. 39 Particle-level normalised differential cross-sections as a func ferent Monte Carlo predictions. The bands represent the statistical and tion of a the transverse momentum and b the absolute value of the total uncertainty in the data. Data points are placed at the centre of each rapidity of the t¯t system in the boosted topology, compared with dif bin. The lower panel shows the ratios of the simulations to data (a) (b) Fig. 40 Particle-level a normalised and babsolute differential cross-and total uncertainty in the data. Data points are placed at the centre of sections as a function of mtt¯in the boosted topology, compared with each bin. The lower panel shows the ratios of the simulations to data different Monte Carlo predictions. The bands represent the statistical 123 tt,lep t tion of a ρt¯, b p and c Ht¯in the boosted topology, compared of each bin. The lower panel shows the ratios of the simulations to data out T with different Monte Carlo predictions. The bands represent the statisti 123 (a) Table 13 Comparison of the measured particle-level normalised single-differential cross-sections in the boosted topology with the predictions from several MC generators. For each prediction a ρ2 and a (b) the statistical and total uncertainty in the data. Data points are placed at the centre of each bin. The lower panel shows the ratios of the simulations to data p-value are calculated using the covariance matrix of the measured spectrum. The NDF is equal to the number of bins in the distribution minus one Observable Pwg+Py8 Pwg+Py8Rad. Up Pwg+Py8 Rad. Down Pwg+H7 Sherpa 2.2.1 ρ2/NDF p-value ρ2/NDF p-value ρ2/NDF p-value ρ2/NDF p-value ρ2/NDF p-value p t,1 T 6.2/7 0.51 10.3/7 0.17 2.8/7 0.90 2.4/7 0.93 11.1/7 0.14 p t,2 T 4.0/6 0.68 3.9/6 0.69 4.1/6 0.66 3.2/6 0.78 4.4/6 0.62 Ht¯t T 9.0/9 0.44 7.1/9 0.62 24.1/9 < 0.01 10.4/9 0.32 7.8 /9 0.56 p t,lep out 7.1/ 6 0.31 17.2/6 < 0.01 43.3/6 < 0.01 25.4/6 < 0.01 2.9/6 0.82 ρtt¯ 3.5/6 0.74 1.0/6 0.98 18.4/6 < 0.01 3.2/6 0.79 8.9/6 0.18 Nextrajets 5.5/4 0.24 15.7/4 < 0.01 17.0/4 < 0.01 2.5/4 0.64 8.6/4 0.07 p t,had T 6.2/7 0.52 11.0/7 0.14 3.2/7 0.86 3.5/7 0.83 10.6/7 0.16 Nsubjets 0.3/3 0.95 4.3/3 0.23 0.7/3 0.86 2.1/3 0.55 2.6/3 0.46 |yt,had | |yt¯t| mt¯t 0.6/3 3.2/3 7.5/9 0.90 0.36 0.59 0.5/3 1.9/3 11.8/9 0.93 0.60 0.23 1.5/3 4.5/3 16.2/9 0.68 0.21 0.06 0.6/3 5.2/3 8.1/9 0.90 0.16 0.52 1.2/3 4.2/3 8.3/9 0.75 0.24 0.50 pt¯t T 3.5/5 0.63 25.6/5 < 0.01 35.7/5 < 0.01 9.8/5 0.08 19.7/5 < 0.01 123 Table14 Comparison of the measured particle-level absolute single-calculated using the covariance matrix of the measured spectrum. The differential cross-sections in the boosted topology with the predictions NDF is equal to the number of bins in the distribution from several MC generators. For each prediction a ρ 2 and a p-value are Observable Pwg+Py8 Pwg+Py8Rad. Up Pwg+Py8 Rad. Down Pwg+H7 Sherpa 2.2.1 ρ2/NDF p-value ρ2/NDF p-value ρ2/NDF p-value ρ2/NDF p-value ρ2/NDF p-value t,1 pT 7.8/8 0.46 14.1/8 0.08 3.9/8 0.86 2.8/8 0.95 12.9/8 0.11 pT t,2 5.3/7 0.62 6.6/7 0.47 5.7/7 0.58 5.6/7 0.59 4.8/7 0.68 Htt¯ T 10.9/10 0.37 10.5/10 0.40 15.5/10 0.12 7.0/10 0.72 11.4/10 0.33 t,lep p 24.2/7 < 0.01 21.7/7 < 0.01 72.0/7 < 0.01 31.9/7 < 0.01 9.9/7 0.19 out ρtt¯ 12.9/7 0.07 9.2/7 0.24 32.0/7 < 0.01 4.5/7 0.72 17.2/7 0.02 Nextrajets 38.5/5 < 0.01 46.0/5 < 0.01 57.0/5 < 0.01 4.7/5 0.45 33.4/5 < 0.01 t,had pT 9.2/8 0.33 16.0/8 0.04 5.9/8 0.66 4.5/8 0.81 12.0/8 0.15 Nsubjets 7.6/4 0.11 11.2/4 0.02 8.1/4 0.09 1.3/4 0.87 3.6/4 0.46 |yt,had| 4.0/4 0.41 5.8/4 0.21 3.9/4 0.42 2.3/4 0.68 10.6/4 0.03 t¯ |yt| 8.8/4 0.07 10.3/4 0.04 8.1/4 0.09 6.7/4 0.15 10.5/4 0.03 mtt¯16.5/10 0.09 28.5/10 < 0.01 24.3/10 <0.01 11.2/10 0.34 25.5/10 < 0.01 pT tt¯21.0/6 < 0.01 59.3/6 < 0.01 107.0/6 < 0.01 27.8/6 < 0.01 38.4/6 < 0.01 (a) (b) Fig. 43 aParticle-level normalised differential cross-section as a func-points are placed at the centre of each bin. bThe ratio of the measured t,had tt¯ tion of p in bins of pT in the boosted topology compared with the cross-section to different Monte Carlo predictions. The bands represent T prediction obtained with the Powheg+Pythia8 MC generator. Data the statistical and total uncertainty in the data (a)(b) Fig. 44 aParticle-level normalised differential cross-section as a func-tre of each bin. bThe ratio of the measured cross-section to different t,had tion of pT in bins of the absolute value of the rapidity of the tt¯system Monte Carlo predictions. The bands represent the statistical and total in the boosted topology compared with the prediction obtained with the uncertainty in the data Powheg+Pythia8 MC generator.Data points are placed at the cen 123 (a) (b) Fig. 45 aParticle-level normalised differential cross-section as a func-are placed at the centre of each bin. bThe ratio of the measured cross- t,had tion of pT in bins of the absolute value of the rapidity of the hadroni-section to different Monte Carlo predictions. The bands represent the cally decaying top quark in the boosted topology compared with the pre-statistical and total uncertainty in the data diction obtained with the Powheg+Pythia8 MC generator.Data points (a)(b) Fig. 46 aParticle-level normalised differential cross-section as a func-generator. Data points are placed at the centre of each bin. bThe ratio t,had tion of pT in bins of the mass of the tt¯system in the boosted topology of the measured cross-section to different Monte Carlo predictions. The compared with the prediction obtained with the Powheg+Pythia8 MC bands represent the statistical and total uncertainty in the data (a) (b) Fig. 47 aParticle-level normalised differential cross-section as a func-generator. Data points are placed at the centre of each bin. bThe ratio t tion of the mass of the tt¯system in bins of Ht¯in the boosted topology of the measured cross-section to different Monte Carlo predictions. The T compared with the prediction obtained with the Powheg+Pythia8 MC bands represent the statistical and total uncertainty in the data 123 (a)(b) Fig. 48 aParticle-level normalised differential cross-section as a func-generator. Data points are placed at the centre of each bin. bThe ratio tion of the mass of the tt¯system in bins of pT tt¯in the boosted topology of the measured cross-section to different Monte Carlo predictions. The compared with the prediction obtained with the Powheg+Pythia8 MC bands represent the statistical and total uncertainty in the data (a) (b) Fig. 49 aParticle-level normalised differential cross-section as a func-generator. Data points are placed at the centre of each bin. bThe ratio t¯ tion of the mass of the tt¯system in bins of |yt| in the boosted topology of the measured cross-section to different Monte Carlo predictions. The compared with the prediction obtained with the Powheg+Pythia8 MC bands represent the statistical and total uncertainty in the data (a) (b) Fig. 50 aParticle-level normalised differential cross-section as a func points are placed at the centre of each bin. bThe ratio of the measured tion of the pT of the hadronically decaying top quark in bins of the cross-section to different Monte Carlo predictions. The bands represent number of additional jets in the boosted topology compared with the the statistical and total uncertainty in the data prediction obtained with the Powheg+Pythia8 MC generator. Data 123 (a) (b) Fig. 51 aParticle-level normalised differential cross-section as a func tre of each bin. bThe ratio of the measured cross-section to different tion of the pT of the t¯t system in bins of the number of additional jets Monte Carlo predictions. The bands represent the statistical and total in the boosted topology compared with the prediction obtained with the uncertainty in the data Powheg+Pythia8 MC generator. Data points are placed at the cen (a)(b) Fig. 52 aParticle-level normalised differential cross-section as a func-Powheg+Pythia8 MC generator. Data points are placed at the centre tion of the mass of the tt¯system in bins of the number of additional jets of each bin. bThe ratio of the measured cross-section to different Monte in the boosted topology compared with the prediction obtained with the Carlo predictions Table 15 Comparison of the measured particle-level normalised p-value are calculated using the covariance matrix of the measured double-differential cross-sections in the boosted topology with the pre-spectrum. The NDF is equal to the number of bins in the distribution dictions from several MC generators. For each prediction a ρ2 and a minus one Observable Pwg+Py8 Pwg+Py8Rad. Up Pwg+Py8 Rad. Down Pwg+H7 Sherpa 2.2.1 ρ2/NDF p-value ρ2/NDF p-value ρ2/NDF p-value ρ2/NDF p-value ρ2/NDF p-value tt¯vs Nextrajets m14.3/12 0.28 30.4/12 < 0.01 28.7/12 < 0.01 5.4/12 0.94 19.1/12 0.09 tt¯vs Nextrajets pT 13.5/10 0.20 43.0/10 < 0.01 41.9/10 < 0.01 13.0/10 0.22 22.7/10 0.01 tt¯t mvs Ht¯7.3/8 0.51 16.5/8 0.04 15.7/8 0.05 7.1/8 0.53 20.8/8 < 0.01 T mtt¯vs |ytt¯| 4.8/13 0.98 11.5/13 0.57 15.9/13 0.26 5.8/13 0.95 16.4/13 0.23 tt¯tt¯ mvs pT 7.8/12 0.80 34.6/12 < 0.01 40.6/12 < 0.01 18.6/12 0.10 18.0/12 0.12 t,had p vs |yt| 8.6/9 0.47 12.7/9 0.17 6.5/9 0.69 5.7/9 0.77 12.5/9 0.18 T t,had t¯ p vs |yt| 10.0/9 0.35 11.6/9 0.24 8.5/9 0.48 8.9/9 0.45 13.5/9 0.14 T t,had vs Nextrajets p T 16.3/14 0.29 42.6/14 < 0.01 30.3/14 < 0.01 18.6/14 0.18 30.8/14 < 0.01 t,had tt¯ p T vs m6.9/7 0.44 18.7/7 < 0.01 8.9/7 0.26 4.4/7 0.73 25.6/7 < 0.01 t,had tt¯ pT vs pT 16.1/13 0.24 50.4/13 < 0.01 63.2/13 < 0.01 26.0/13 0.02 33.9/13 < 0.01 123 Table16 Comparison of the measured particle-level absolute double-calculated using the covariance matrix of the measured spectrum. The differential cross-sections in the boosted topology with the predictions NDF is equal to the number of bins in the distribution from several MC generators. For each prediction a ρ 2 and a p-value are Observable Pwg+Py8 Pwg+Py8Rad. Up Pwg+Py8 Rad. Down Pwg+H7 Sherpa 2.2.1 ρ2/NDF p-value ρ2/NDF p-value ρ2/NDF p-value ρ2/NDF p-value ρ2/NDF p-value tt¯vs Nextrajets m38.9/13 < 0.01 53.2/13 < 0.01 73.4/13 < 0.01 9.1/13 0.77 35.9/13 < 0.01 tt¯vs Nextrajets pT 41.6/11 < 0.01 86.5/11 < 0.01 102.0/11 < 0.01 25.4/11 < 0.01 45.9/11 < 0.01 tt¯t mvs Ht¯12.7/9 0.17 17.8/9 0.04 25.3/9 < 0.01 11.8/9 0.22 24.4/9 < 0.01 T tt¯ mvs |ytt¯| 18.4/14 0.19 17.3/14 0.24 36.5/14 < 0.01 14.2/14 0.43 22.1/14 0.08 tt¯tt¯ mvs pT 15.5/13 0.28 70.1/13 < 0.01 86.4/13 < 0.01 27.8/13 < 0.01 28.8/13 < 0.01 t,had p vs |yt| 11.2/10 0.34 15.9/10 0.10 7.3/10 0.70 6.7/10 0.75 15.3/10 0.12 T t,had t¯ p vs |yt| 9.7/10 0.47 10.6/10 0.39 8.1/10 0.62 8.5/10 0.58 13.4/10 0.20 T t,had vs Nextrajets p T 35.7/15 < 0.01 74.2/15 < 0.01 61.1/15 < 0.01 22.5/15 0.09 59.6/15 < 0.01 t,had tt¯ p T vs m14.8/8 0.06 29.8/8 < 0.01 16.4/8 0.04 4.4/8 0.82 32.6/8 < 0.01 t,had tt¯ pT vs pT 24.6/14 0.04 70.1/14 < 0.01 94.3/14 < 0.01 30.0/14 < 0.01 48.7/14 < 0.01 123 (a) (b) uncertainty in the NNLO prediction. The solid bands represent the statistical and total uncertainty in the data. Data points are placed at the centre of each bin. The lower panel shows the ratios of the predictions to data 123 (a) (b) (c) Fig. 56 Parton-level normalised differential cross-sections as a function of a the mass, b pT and c absolute value of the rapidity of the tt¯system in the resolved topology, compared with the NNLO predictions obtained using the NNPDF3.1 NNLO PDF set and the predictions obtained with the Powheg+Pythia8 MC generator. The hatched band represents the total uncertainty in the NNLO prediction. The solid bands represent the statistical and total uncertainty in the data. Data points are placed at the centre of each bin. The lower panel shows the ratios of the predictions to data 123 (a) (b) (c) Fig. 57 Parton-level normalised differential cross-sections as a func-erator. The hatched band represents the total uncertainty in the NNLO tt¯Htt¯ tion of a |yboost |, b T and c ρtt¯ in the resolved topology, compared prediction. The solid bands represent the statistical and total uncertainty with the NNLO predictions obtained using the NNPDF3.1 NNLO PDF in the data. Data points are placed at the centre of each bin. The lower set and the predictions obtained with the Powheg+Pythia8 MC gen-panel shows the ratios of the predictions to data 123 Table17 Comparison of the measured parton-level normalised single-calculated using the covariance matrix of the measured spectrum. The differential cross-sections in the resolved topology with the predictions NDF is equal to the number of bins in the distribution minus one from several MC generators. For each prediction a ρ 2 and a p-value are Observable Pwg+Py8 Pwg+Py8Rad. Up Pwg+Py8 Rad. Down Pwg+H7 Sherpa 2.2.1 ρ2/NDF p-value ρ2/NDF p-value ρ2/NDF p-value ρ2/NDF p-value ρ2/NDF p-value Htt¯ T 3.8/8 0.88 2.9/8 0.94 4.0/8 0.86 2.1/8 0.98 10.1/8 0.26 tt¯ |yboost | 4.9/8 0.77 5.3/8 0.73 5.1/8 0.74 4.8/8 0.78 5.6/8 0.70 ρtt¯ 9.7/3 0.02 4.2/3 0.24 20.9/3 < 0.01 5.8/3 0.12 19.1/3 < 0.01 |yt| 9.4/4 0.05 8.8/4 0.07 10.3/4 0.03 8.4/4 0.08 9.8/4 0.04 t pT 6.4/7 0.49 5.8/7 0.56 6.8/7 0.45 4.7/7 0.69 7.6/7 0.37 t¯ |yt| 4.1/6 0.67 4.5/6 0.61 4.3/6 0.63 4.1/6 0.66 4.4/6 0.62 tt¯ m32.1/8 < 0.01 26.7/8 < 0.01 37.6/8 < 0.01 29.6/8 < 0.01 17.1/8 0.03 ptt¯7.8/8 0.45 41.7/8 < 0.01 25.0/8 < 0.01 11.9/8 0.15 22.1/8 < 0.01 T Table 18 Comparison of the measured parton-level absolute single-calculated using the covariance matrix of the measured spectrum. The differential cross-sections in the resolved topology with the predictions NDF is equal to the number of bins in the distribution from several MC generators. For each prediction a ρ 2 and a p-value are Observable Pwg+Py8 Pwg+Py8Rad. Up Pwg+Py8 Rad. Down Pwg+H7 Sherpa 2.2.1 ρ2/NDF p-value ρ2/NDF p-value ρ2/NDF p-value ρ2/NDF p-value ρ2/NDF p-value Htt¯ T 9.9/9 0.36 10.1/9 0.34 9.9/9 0.36 6.7/9 0.67 19.6/9 0.02 tt¯ |yboost | 5.9/9 0.75 6.4/9 0.70 6.2/9 0.72 5.8/9 0.76 6.4/9 0.70 ρtt¯ 10.7/4 0.03 4.5/4 0.34 23.6/4 < 0.01 6.3/4 0.18 22.1/4 < 0.01 |yt| 10.8/5 0.06 10.0/5 0.08 12.2/5 0.03 9.5/5 0.09 10.9/5 0.05 t pT 9.9/8 0.27 8.8/8 0.36 10.8/8 0.21 8.2/8 0.42 11.9/8 0.15 t¯ |yt| 5.0/7 0.66 5.5/7 0.60 5.2/7 0.63 4.9/7 0.67 5.2/7 0.63 mtt¯29.1/9 < 0.01 22.9/9 < 0.01 36.8/9 < 0.01 25.6/9 < 0.01 15.4/9 0.08 pT tt¯8.6/9 0.47 42.4/9 < 0.01 24.3/9 < 0.01 14.1/9 0.12 20.6/9 0.01 (a) (b) Fig. 58 a Parton-level normalised differential cross-section as a func-cross-section to the NNLO prediction and the prediction obtained with tt tion of pT in bins of yin the resolved topology compared with the the Powheg+Pythia8 MC generator. The hatched band represents the NNLO prediction obtained using the NNPDF3.1 NNLO PDF set. Data total uncertainty in the NNLO prediction. The solid bands represent the points are placed at the centre of each bin. bThe ratio of the measured statistical and total uncertainty in the data 123 (a) Fig. 59 a Parton-level normalised differential cross-section as a func tt tion of pT in bins of pt¯in the resolved topology compared with the T NNLO prediction obtained using the NNPDF3.1 NNLO PDF set. Data points are placed at the centre of each bin. bThe ratio of the measured (a) Fig. 60 a Parton-level normalised differential cross-section as a function of pT t in bins of mtt¯in the resolved topology compared with the NNLO prediction obtained using the NNPDF3.1 NNLO PDF set. Data points are placed at the centre of each bin. bThe ratio of the measured (a) Fig. 61 a Parton-level normalised differential cross-section as a func t tt¯ tion of pt¯in bins ofyin the resolved topology compared with the T NNLO prediction obtained using the NNPDF3.1 NNLO PDF set. Data points are placed at the centre of each bin. bThe ratio of the measured (b) cross-section to the NNLO prediction and the prediction obtained with the Powheg+Pythia8 MC generator. The hatched band represents the total uncertainty in the NNLO prediction. The solid bands represent the statistical and total uncertainty in the data (b) cross-section to the NNLO prediction and the prediction obtained with the Powheg+Pythia8 MC generator. The hatched band represents the total uncertainty in the NNLO prediction. The solid bands represent the statistical and total uncertainty in the data (b) cross-section to the NNLO prediction and the prediction obtained with the Powheg+Pythia8 MC generator. The hatched band represents the total uncertainty in the NNLO prediction. The solid bands represent the statistical and total uncertainty in the data 123 (a) Fig. 62 a Parton-level normalised differential cross-section as a func tt¯t¯ tion of pT in bins of mt in the resolved topology compared with the NNLO prediction obtained using the NNPDF3.1 NNLO PDF set. Data points are placed at the centre of each bin. bThe ratio of the measured (a) Fig. 63 a Parton-level normalised differential cross-section as a func t¯ tt¯ tion of mt in bins ofyin the resolved topology compared with the NNLO prediction obtained using the NNPDF3.1 NNLO PDF set. Data points are placed at the centre of each bin. bThe ratio of the measured Table19 Comparison of the measured parton-level normalised single-differential in the resolved topology cross-sections with the NNLO predictions and the nominal Powheg+Pythia8 predictions. For each prediction a ρ2 and a p-value are calculated using the covariance matrix of the measured spectrum. The NDF is equal to the number of bins in the distribution minus one (b) cross-section to the NNLO prediction and the prediction obtained with the Powheg+Pythia8 MC generator. The hatched band represents the total uncertainty in the NNLO prediction. The solid bands represent the statistical and total uncertainty in the data (b) cross-section to the NNLO prediction and the prediction obtained with the Powheg+Pythia8 MC generator. The hatched band represents the total uncertainty in the NNLO prediction. The solid bands represent the statistical and total uncertainty in the data Observable NNPDF31 NNLO Pwg+Py8 ρ2/NDF p-value ρ2/NDF p-value Ht¯t T 5.0/8 0.76 3.8/8 0.88 |yt¯t boost | ρt¯t 8.60/8 2.40/3 0.38 0.50 4.9/8 9.7/3 0.77 0.02 |yt,had | pt T 8.20/4 6.30/7 0.09 0.51 9.4/4 6.4/7 0.05 0.49 |yt¯t| mt¯t 6.10/6 17.20/8 0.41 0.03 4.1/6 32.1/8 0.67 < 0.01 pt¯t T 3.70/8 0.88 7.8/8 0.45 123 Table20 Comparison of the Observable NNPDF31 NNLO Pwg+Py8 measured parton-level absolute single-differential in the ρ2/NDF p-value ρ2/NDF p-value resolved topology cross-sections Htt¯ with the NNLO predictions and T 10.4/9 0.32 9.9/9 0.36 the nominal Powheg+Pythia8 tt¯ |yboost | 10.9/9 0.28 5.9/9 0.75 predictions. For each prediction ρtt¯ 2.6/4 0.63 10.7/4 0.03 a ρ2 and a p-value are calculated using the covariance |yt,had | 9.5/5 0.09 10.8/5 0.06 matrix of the measured t pT 7.8/8 0.45 9.9/8 0.27 spectrum. The NDF is equal to t¯|yt| 7.2/7 0.41 5.0/7 0.66 the number of bins in the tt¯ distribution m14.0/9 0.12 29.1/9 < 0.01 pT tt¯4.9/9 0.84 8.6/9 0.47 Table21 Comparison of the measured parton-level normalised double-calculated using the covariance matrix of the measured spectrum. The differential cross-sections in the resolved topology with the predictions NDF is equal to the number of bins in the distribution minus one from several MC generators. For each prediction a ρ 2 and a p-value are Observable Pwg+Py8 Pwg+Py8Rad. Up Pwg+Py8 Rad. Down Pwg+H7 Sherpa 2.2.1 ρ2/NDF p-value ρ2/NDF p-value ρ2/NDF p-value ρ 2/NDF p-value ρ2/NDF p-value t |yt| vs p30.9/12 < 0.01 30.2/12 < 0.01 34.7/12 < 0.01 22.9/12 0.03 44.3/12 < 0.01 T t¯tt¯ |yt| vs m51.8/19 < 0.01 47.0/19 < 0.01 56.6/19 < 0.01 49.4/19 < 0.01 41.4/19 < 0.01 t¯tt¯ |yt| vs p17.6/13 0.17 61.8/13 < 0.01 32.4/13 < 0.01 28.3/13 < 0.01 39.5/13 < 0.01 T tt¯t mvs pT 64.6/14 < 0.01 118.0/14 < 0.01 129.0/14 < 0.01 60.9/14 < 0.01 63.4/14 < 0.01 tt¯tt¯ mvs pT 62.6/16 < 0.01 163.0/16 < 0.01 82.1/16 < 0.01 66.4/16 < 0.01 118.0/16 < 0.01 tt¯t pT vs pT 37.4/16 < 0.01 87.1/16 < 0.01 95.0/16 < 0.01 50.7/16 < 0.01 47.2/16 < 0.01 Table22 Comparison of the measured parton-level absolute double-calculated using the covariance matrix of the measured spectrum. The differential cross-sections in the resolved topology with the predictions NDF is equal to the number of bins in the distribution from several MC generators. For each prediction a ρ 2 and a p-value are Observable Pwg+Py8 Pwg+Py8Rad. Up Pwg+Py8 Rad. Down Pwg+H7 Sherpa 2.2.1 ρ2/NDF p-value ρ2/NDF p-value ρ2/NDF p-value ρ 2/NDF p-value ρ2/NDF p-value t |yt| vs p33.2/13 < 0.01 32.4/13 < 0.01 37.3/13 < 0.01 24.5/13 0.03 48.5/13 < 0.01 T t¯tt¯ |yt| vs m55.6/20 < 0.01 50.4/20 < 0.01 61.3/20 < 0.01 52.9/20 < 0.01 44.6/20 < 0.01 t¯tt¯ |yt| vs p18.8/14 0.17 67.1/14 < 0.01 35.1/14 < 0.01 30.2/14 < 0.01 42.9/14 < 0.01 T tt¯t mvs pT 70.5/15 < 0.01 126.0/15 < 0.01 138.0/15 < 0.01 65.5/15 < 0.01 73.3/15 < 0.01 tt¯tt¯ mvs pT 69.8/17 < 0.01 174.0/17 < 0.01 89.5/17 < 0.01 75.5/17 < 0.01 128.0/17 < 0.01 tt¯t pT vs pT 44.2/17 < 0.01 92.7/17 < 0.01 112.0/17 < 0.01 57.6/17 < 0.01 51.4/17 < 0.01 123 Table23 Comparison of the measured parton-level normalised double-diction a ρ2 and a p-value are calculated using the covariance matrix differential cross-sections in the resolved topology with the NNLO pre-of the measured spectrum. The NDF is equal to the number of bins in dictions and the nominal Powheg+Pythia8 predictions. For each pre-the distribution minus one Observable NNPDF31 NNLO Pwg+Py8 ρ2/NDF p-value ρ2/NDF p-value t |yt| vs p25.4/12 0.01 30.9/12 < 0.01 T t¯tt¯ |yt| vs m39.9/19 < 0.01 51.8/19 < 0.01 t¯tt¯ |yt| vs p15.9/13 0.26 17.6/13 0.17 T tt¯t mvs pT 55.7/14 < 0.01 64.4/14 < 0.01 tt¯tt¯ mvs pT 40.6/16 < 0.01 62.6/16 < 0.01 tt¯t,had pT vs pT 22.2/16 0.14 37.4/16 < 0.01 Table24 Comparison of the measured parton-level absolute double-diction a ρ2 and a p-value are calculated using the covariance matrix differential cross-sections in the resolved topology with the NNLO pre-of the measured spectrum. The NDF is equal to the number of bins in dictions and the nominal Powheg+Pythia8 predictions. For each pre-the distribution Observable NNPDF31 NNLO Pwg+Py8 ρ2/NDF p-value ρ2/NDF p-value t |yt| vs p26.8/13 0.01 33.2/13 < 0.01 T t¯tt¯ |yt| vs m43.7/20 < 0.01 55.6/20 < 0.01 t¯tt¯ |yt| vs p17.1/14 0.17 18.8/14 0.17 T tt¯t mvs pT 60.7/15 < 0.01 70.5/15 < 0.01 tt¯tt¯ mvs pT 47.4/17 < 0.01 69.8/17 < 0.01 tt¯t,had pT vs pT 25.6/17 0.08 44.2/17 < 0.01 (a) t of a pT and b yt in the resolved topology. The results are compared with NNLO QCD and NNLO QCD+NLO EW theoretical calculations using the NNPDF3.1 and LUXQED17 PDF sets. The vertical bars on each marker represents the total uncertainty in the prediction. The solid (b) line is the nominal NLO Powheg+Pythia8 prediction. The bands represent the statistical and total uncertainty in the data. Data points are placed at the centre of each bin. The lower panel shows the ratios of the predictions to data. The binning adopted in these distributions is the same used in a recent measurement from the CMS collaboration [21] 123 tt¯tt¯ of a m, b pT and c ytt¯ in the resolved topology. The results are compared with NNLO QCD and NNLO QCD+NLO EW theoretical calculations using the NNPDF3.1 and LUXQED17 PDF sets. The vertical bars on each marker represents the total uncertainty in the prediction. The solid line is the nominal NLO Powheg+Pythia8 prediction. The bands represent the statistical and total uncertainty in the data. Data points are placed at the centre of each bin. The lower panel shows the ratios of the predictions to data. The binning adopted in these distributions is the same used in a recent measurement from the CMS collaboration [21] 123 (a) Fig. 66 a Parton-level normalised differential cross-section as a func t tion of pT in the boosted topology, compared with the NNLO predictions obtained using the NNPDF3.1 NNLO PDF set and the predictions obtained with the Powheg+Pythia8 MC generator. The hatched band represents the total uncertainty in the NNLO prediction. bParton-level (b) t¯ normalised differential cross-section as a function of mt in the boosted topology, compared with predictions obtained with different MC generators. The bands represent the statistical and total uncertainty in the data. Data points are placed at the centre of each bin. The lower panel shows the ratios of the predictions to data ( a ) (b) Fig. 67 a Parton-level normalised differential cross-section as a func-cross-section to the NNLO prediction and the prediction obtained with t tion of mtt¯ in bins of pT in the boosted topology compared with the the Powheg+Pythia8 MC generator. The hatched band represents the NNLO prediction obtained using the NNPDF3.1 NNLO PDF set. Data total uncertainty in the NNLO prediction. The bands represent the stapoints are placed at the centre of each bin. bThe ratio of the measured tistical and total uncertainty in the data 123 The inclusive parton-level cross-section measured in the boosted topology is shown in Fig. 68, where it is compared with the MC predictions previously described and the NNLO calculation. The total cross-section predicted by each NLO MC generator is normalised to the NNLO + NNLL prediction as quoted in Ref. [55] and the corresponding uncertainty only includes the uncertainty affecting the k-factor used in the normalisation. Since the parton-level deﬁnition in the boosted topology doesn’t cover the full phase space, the inclusive cross-section predicted is different for each generator and differs from the normalisation value described in Sect. 3. The prediction given by the NNLO calculation shows better agreement with the measured inclusive cross-section, while several NLO predictions overestimate data. The measured single-and double-differential crosssections are compared with the ﬁxed-order NNLO pQCD predictions, obtained using the same parameter settings already described for the resolved topology, and with the Powheg+Pythia8 NLO + PS parton-level predictions. A trend is observed in the agreement between the predictions and the measured single-differential cross-sections in the high pT t and mtt¯regions, where both the NLO + PS and NNLO (when available) predictions lie at the edge of the uncertainty band. Both the predictions, however, give a good description of the double-differential cross-section as a function of mtt¯in bins of pTt . Tables 25 and 26 and Tables 27 and 28 show the quantitative comparisons among the parton-level results and the Monte Carlo and NNLO predictions. The normalised and absolute single-and double-differential cross-sections are shown. Unlike the particle-level measurements, at parton level the deﬁnition of the top-quark observables is identical between the resolved and boosted topologies. This allows a direct comparison to be made between the measured differential cross-sections as a function of the pT of the top quark in the two topologies, shown in Fig. 69. The two measurements are consistent in the overlap region. 11 Conclusion Single-and double-differential cross-sections for the production of top-quark pairs are measured in the f+jets channel at particle and parton level, in the resolved and boosted topolo √ gies, using data from pp collisions at s = 13 TeV collected in 2015 and 2016 by the ATLAS detector at the CERN Large Hadron Collider and corresponding to an integrated luminosity of 36.1fb−1. The differential cross-sections are presented as a function of the main kinematic variables of the tt¯system, jet multiplicities and observables sensitive to extra QCD radiation and PDFs. Fig. 68 Comparison of the measured inclusive parton-level crosssection in the boosted topology with the predictions from several MC generators and the NNLO prediction obtained using the NNPDF3.1 NNLO PDF set. The uncertainties associated to the NNLO prediction have been calculated starting from the scale and PDF uncertainties associated to the NNLO prediction of the differential cross-section as a func t tion of pT. The uncertainty on the cross-section predicted by each NLO MC generator only includes the uncertainty (due to PDFs, mt and οs) affecting the k-factor used in the normalisation. The bands represent the statistical and total uncertainty in the data The particle-level measurements are compared with NLO+ PS MC predictions as implemented in state-of-the-art MC generators. At the particle level, the predictions agree with the single-differential measurements over a wide kinematic region for both the resolved and boosted topologies, although poorer modelling is observed in speciﬁc regions of the probed phase-space. In the boosted topology, which is focused in the region where the hadronic top quark is produced with high pT, a disagreement between the measured inclusive cross-section and several predictions is observed. Overall, the NLO+PS MC generators show poorer modelling of the double-differential distributions and no combination that includes pT tt¯can be described by the generators in the resolved topology. Overall, the Powheg+Pythia8 and, in the boosted topology, Powheg+Herwig7 are the two generators able to give a good prediction of the largest fraction of the probed variables. The measurements show high sensitivity to the different aspects of the predictions of the MC generators and are hence relevant for the tuning of the MC generators and will contribute to improving the description of the tt¯ﬁnal state and to reducing the systematic uncertainties related to top-quark modelling. 123 Table25 Comparison of the measured parton-level normalised differ-calculated using the covariance matrix of the measured spectrum. The ential cross-sections in the boosted topology with the predictions from NDF is equal to the number of bins in the distribution minus one several MC generators. For each prediction a ρ2 and a p-value are Observable Pwg+Py8 Pwg+Py8Rad. Up Pwg+Py8 Rad. Down Pwg+H7 Sherpa 2.2.1 ρ2/NDF p-value ρ2/NDF p-value ρ2/NDF p-value ρ2/NDF p-value ρ2/NDF p-value tt¯t mvs pT 0.5/4 0.97 11.6/4 0.02 4.9/4 0.30 0.7/4 0.95 9.0/4 0.06 t pT 4.9/5 0.43 6.9/5 0.23 5.0/5 0.41 4.6/5 0.46 10.4/5 0.07 mtt¯4.3/6 0.64 7.5/6 0.28 19.2/6 < 0.01 5.4/6 0.49 5.0/6 0.55 Table26 Comparison of the measured parton-level absolute differen-calculated using the covariance matrix of the measured spectrum. The tial cross-sections in the boosted topology with the predictions from NDF is equal to the number of bins in the distribution several MC generators. For each prediction a ρ2 and a p-value are Observable Pwg+Py8 Pwg+Py8Rad. Up Pwg+Py8 Rad. Down Pwg+H7 Sherpa 2.2.1 ρ2/NDF p-value ρ2/NDF p-value ρ2/NDF p-value ρ2/NDF p-value ρ2/NDF p-value tt¯t mvs pT 6.2/5 0.29 29.6/5 < 0.01 18.7/5 < 0.01 3.9/5 0.56 41.5/5 < 0.01 t pT 4.7/6 0.58 6.2/6 0.41 5.8/6 0.45 4.1/6 0.67 9.7/6 0.14 mtt¯5.9/7 0.55 18.8/7 < 0.01 18.5/7 < 0.01 6.0/7 0.54 23.8/7 < 0.01 Table27 Comparison of the measured parton-level normalised differential cross-sections in the boosted topology with the NNLO predictions and the nominal Powheg+Pythia8 predictions. For each prediction a ρ2 and a p-value are calculated using the covariance matrix of the measured spectrum. The NDF is equal to the number of bins in the distribution minus one Observable NNPDF3.1 NNLO PWG+PY8 ρ2/NDF p-value ρ2/NDF p-value mt¯t vs pt T 6.2/4 0.18 0.5/4 0.97 pt T 4.8/5 0.44 4.9/5 0.43 The measured parton-level differential cross-sections are compared with state-of-the-art ﬁxed-order NNLO QCD predictions and a general improvement relative to the NLO+PS MC generators is found in the level of agreement of the single-and double-differential cross-sections in both the resolved and boosted regimes. The comparison of doubledifferential distributions with NNLO predictions provides a very stringent test of the SM description of tt¯production. The comparison with the NNLO pQCD predictions including Table28 Comparison of the measured parton-level absolute differential cross-sections in the boosted topology with the NNLO predictions and the nominal Powheg+Pythia8 predictions. For each prediction a ρ2 and a p-value are calculated using the covariance matrix of the measured spectrum. The NDF is equal to the number of bins in the distribution Observable NNPDF3.1 NNLO PWG+PY8 ρ2/NDF p-value ρ2/NDF p-value mt¯t vs pt T 6.3/5 0.28 6.2/5 0.29 pt T 4.3/6 0.64 4.7/6 0.58 EW corrections, due to the still rather limited range probed for the measured transverse momenta of the top and anti-top quarks, does not yet allow the impact of the EW corrections in the production of top-quark pairs to be quantiﬁed. The measured differential cross-sections at the parton level will be able to be used in detailed phenomenological studies and in particular to improve the determination of the gluon density in the proton and of the top-quark pole mass. 123 (a) Acknowledgements We thank CERN for the very successful operation of the LHC, as well as the support staff from our institutions without whom ATLAS could not be operated efﬁciently. We acknowledge the support of ANPCyT, Argentina; YerPhI, Armenia; ARC, Australia; BMWFW and FWF, Austria; ANAS, Azerbaijan; SSTC, Belarus; CNPq and FAPESP, Brazil; NSERC, NRC and CFI, Canada; CERN; CONICYT, Chile; CAS, MOST and NSFC, China; COLCIENCIAS, Colombia; MSMT CR, MPO CR and VSC CR, Czech Republic; DNRF and DNSRC, Denmark; IN2P3-CNRS, CEA-DRF/IRFU, France; SRNSFG, Georgia; BMBF, HGF, and MPG, Germany; GSRT, Greece; RGC, Hong Kong SAR, China; ISF and Benoziyo Center, Israel; INFN, Italy; MEXT and JSPS, Japan; CNRST, Morocco; NWO, The Netherlands; RCN, Norway; MNiSW and NCN, Poland; FCT, Portugal; MNE/IFA, Romania; MES of Russia and NRC KI, Rus-sian Federation; JINR; MESTD, Serbia; MSSR, Slovakia; ARRS and MIZŠ, Slovenia; DST/NRF, South Africa; MINECO, Spain; SRC and Wallenberg Foundation, Sweden; SERI, SNSF and Cantons of Bern and Geneva, Switzerland; MOST, Taiwan; TAEK, Turkey; STFC, UK; DOE and NSF, USA. In addition, individual groups and members have received support from BCKDF, CANARIE, CRC and Compute Canada, Canada; COST, ERC, ERDF, Horizon 2020, and Marie Skłodowska-Curie Actions, European Union; Investissements d’ Avenir Labex and Idex, ANR, France; DFG and AvH Foundation, Germany; Herakleitos, Thales and Aristeia programmes co-ﬁnanced by EU-ESF and the Greek NSRF, Greece; BSF-NSF and GIF, Israel; CERCA Programme Generalitat de Catalunya, Spain; The Royal Society and Leverhulme Trust, United Kingdom. The crucial computing support from all WLCG partners is acknowledged gratefully, in particular from CERN, the ATLAS Tier-1 facilities at TRIUMF (Canada), NDGF (Denmark, Norway, Sweden), CC-IN2P3 (France), KIT/GridKA (Germany), INFN-CNAF (Italy), NL-T1 (The Netherlands), PIC (Spain), ASGC (Taiwan), RAL (UK) and BNL (USA), the Tier-2 facilities worldwide and large non-WLCG resource providers. Major contributors of computing resources are listed in Ref. [125]. DataAvailability Statement This manuscript has no associated data or the data will not be deposited. [Authors’ comment: All ATLAS scientiﬁc output is published in journals, and preliminary results are made available in Conference Notes. All are openly available, without restriction on use by external parties beyond copyright law and the standard conditions agreed by CERN. Data associated with journal publications are also made available: tables and data from plots (e.g. cross section values, likelihood proﬁles, selection efﬁciencies, cross section limits, ...) are stored in appropriate repositories such as HEPDATA (http:// hepdata.cedar.ac.uk/). ATLAS also strives to make additional material (b) sections to the NNLO predictions in the resolved and boosted topologies as a function of the transverse momentum of the top quark. The bands indicate the statistical and total uncertainties of the data in each bin related to the paper available that allows a reinterpretation of the data in the context of new theoretical models. For example, an extended encapsulation of the analysis is often provided for measurements in the framework of RIVET (http://rivet.hepforge.org/).” This information is taken from the ATLAS Data Access Policy, which is a public document that can be downloaded from http://opendata.cern.ch/record/413 [opendata.cern.ch].] Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, pro-vide a link to the Creative Commons licence, and indicate if changes were made. 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Zwalinski36 1 Department of Physics, University of Adelaide, Adelaide, Australia 2 Physics Department, SUNY Albany, Albany, NY, USA 3 Department of Physics, University of Alberta, Edmonton, AB, Canada 4 (a)Department of Physics, Ankara University, Ankara, Turkey; (b)Istanbul Aydin University, Istanbul, Turkey; (c)Division of Physics, TOBB University of Economics and Technology, Ankara, Turkey 5 LAPP, Université Grenoble Alpes, Université Savoie Mont Blanc, CNRS/IN2P3, Annecy, France 6 High Energy Physics Division, Argonne National Laboratory, Argonne, IL, USA 7 Department of Physics, University of Arizona, Tucson, AZ, USA 8 Department of Physics, University of Texas at Arlington, Arlington, TX, USA 9 Physics Department, National and Kapodistrian University of Athens, Athens, Greece 10 Physics Department, National Technical University of Athens, Zografou, Greece 11 Department of Physics, University of Texas at Austin, Austin, TX, USA 123 12 (a)Bahcesehir University, Faculty of Engineering and Natural Sciences, Istanbul, Turkey; (b)Istanbul Bilgi University, Faculty of Engineering and Natural Sciences, Istanbul, Turkey; (c)Department of Physics, Bogazici University, Istanbul, Turkey; (d)Department of Physics Engineering, Gaziantep University, Gaziantep, Turkey 13 Institute of Physics, Azerbaijan Academy of Sciences, Baku, Azerbaijan 14 Institut de Física d’Altes Energies (IFAE), Barcelona Institute of Science and Technology, Barcelona, Spain 15 (a)Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China; (b)Physics Department, Tsinghua University, Beijing, China; (c)Department of Physics, Nanjing University, Nanjing, China; (d)University of Chinese Academy of Science (UCAS), Beijing, China 16 Institute of Physics, University of Belgrade, Belgrade, Serbia 17 Department for Physics and Technology, University of Bergen, Bergen, Norway 18 Physics Division, Lawrence Berkeley National Laboratory and University of California, Berkeley, CA, USA 19 Institut für Physik, Humboldt Universität zu Berlin, Berlin, Germany 20 Albert Einstein Center for Fundamental Physics and Laboratory for High Energy Physics, University of Bern, Bern, Switzerland 21 School of Physics and Astronomy, University of Birmingham, Birmingham, UK 22 Facultad de Ciencias y Centro de Investigaciónes, Universidad Antonio Nariño, Bogotá, Colombia 23 (a)Dipartimento di Fisica, INFN Bologna and Universita’ di Bologna, Bologna, Italy; (b)INFN Sezione di Bologna, Bologna, Italy 24 Physikalisches Institut, Universität Bonn, Bonn, Germany 25 Department of Physics, Boston University, Boston, MA, USA 26 Department of Physics, Brandeis University, Waltham, MA, USA 27 (a)Transilvania University of Brasov, Brasov, Romania; (b)Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest, Romania; (c)Department of Physics, Alexandru Ioan Cuza University of Iasi, Iasi, Romania; (d)National Institute for Research and Development of Isotopic and Molecular Technologies, Physics Department, Cluj Napoca, Romania; (e)University Politehnica Bucharest, Bucharest, Romania; (f)West University in Timisoara, Timisoara, Romania 28 (a)Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovak Republic; (b)Department of Subnuclear Physics, Institute of Experimental Physics of the Slovak Academy of Sciences, Kosice, Slovak Republic 29 Physics Department, Brookhaven National Laboratory, Upton, NY, USA 30 Departamento de Física, Universidad de Buenos Aires, Buenos Aires, Argentina 31 California State University, California, CA, USA 32 Cavendish Laboratory, University of Cambridge, Cambridge, UK 33 (a)Department of Physics, University of Cape Town, Cape Town, South Africa; (b)Department of Mechanical Engineering Science, University of Johannesburg, Johannesburg, South Africa; (c)School of Physics, University of the Witwatersrand, Johannesburg, South Africa 34 Department of Physics, Carleton University, Ottawa, ON, Canada 35 (a)Faculté des Sciences Ain Chock, Réseau Universitaire de Physique des Hautes Energies -Université Hassan II, Casablanca, Morocco; (b)Faculté des Sciences, Université Ibn-Tofail, Kénitra, Morocco; (c)Faculté des Sciences Semlalia, Université Cadi Ayyad, LPHEA-Marrakech, Morocco; (d)Faculté des Sciences, Université Mohamed Premier and LPTPM, Oujda, Morocco; (e)Faculté des sciences, Université Mohammed V, Rabat, Morocco 36 CERN, Geneva, Switzerland 37 Enrico Fermi Institute, University of Chicago, Chicago, IL, USA 38 LPC, Université Clermont Auvergne, CNRS/IN2P3, Clermont-Ferrand, France 39 Nevis Laboratory, Columbia University, Irvington, NY, USA 40 Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark 41 (a)Dipartimento di Fisica, Università della Calabria, Rende, Italy; (b)INFN Gruppo Collegato di Cosenza, Laboratori Nazionali di Frascati, Frascati, Italy 42 Physics Department, Southern Methodist University, Dallas, TX, USA 43 Physics Department, University of Texas at Dallas, Richardson, TX, USA 44 National Centre for Scientiﬁc Research “Demokritos”, Agia Paraskevi, Greece 45 (a)Department of Physics, Stockholm University, Sweden; (b)Oskar Klein Centre, Stockholm, Sweden 46 Deutsches Elektronen-Synchrotron DESY, Hamburg and Zeuthen, Germany 47 Lehrstuhl für Experimentelle Physik IV, Technische Universität Dortmund, Dortmund, Germany 123 48 Institut für Kern-und Teilchenphysik, Technische Universität Dresden, Dresden, Germany 49 Department of Physics, Duke University, Durham, NC, USA 50 SUPA -School of Physics and Astronomy, University of Edinburgh, Edinburgh, UK 51 INFN e Laboratori Nazionali di Frascati, Frascati, Italy 52 Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Freiburg, Germany 53 II. Physikalisches Institut, Georg-August-Universität Göttingen, Göttingen, Germany 54 Département de Physique Nucléaire et Corpusculaire, Université de Genève, Geneva, Switzerland 55 (a)Dipartimento di Fisica, Università di Genova, Genoa, Italy; (b)INFN Sezione di Genova, Genoa, Italy 56 II. Physikalisches Institut, Justus-Liebig-Universität Giessen, Giessen, Germany 57 SUPA -School of Physics and Astronomy, University of Glasgow, Glasgow, UK 58 LPSC, Université Grenoble Alpes, CNRS/IN2P3, Grenoble INP, Grenoble, France 59 Laboratory for Particle Physics and Cosmology, Harvard University, Cambridge, MA, USA 60 (a)Department of Modern Physics and State Key Laboratory of Particle Detection and Electronics, University of Science and Technology of China, Hefei, China; (b)Institute of Frontier and Interdisciplinary Science and Key Laboratory of Particle Physics and Particle Irradiation (MOE), Shandong University, Qingdao, China; (c)School of Physics and Astronomy, Shanghai Jiao Tong University, KLPPAC-MoE, SKLPPC, Shanghai, China; (d)Tsung-Dao Lee Institute, Shanghai, China 61 (a)Kirchhoff-Institut für Physik, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany; (b)Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany 62 Faculty of Applied Information Science, Hiroshima Institute of Technology, Hiroshima, Japan 63 (a)Department of Physics, Chinese University of Hong Kong, Shatin, N.T., Hong Kong, China; (b)Department of Physics, University of Hong Kong, Hong Kong, China; (c)Department of Physics and Institute for Advanced Study, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China 64 Department of Physics, National Tsing Hua University, Hsinchu, Taiwan 65 Department of Physics, Indiana University, Bloomington, IN, USA 66 (a)INFN Gruppo Collegato di Udine, Sezione di Trieste, Udine, Italy; (b)ICTP, Trieste, Italy; (c)Dipartimento Politecnico di Ingegneria e Architettura, Università di Udine, Udine, Italy 67 (a)INFN Sezione di Lecce, Lecce, Italy; (b)Dipartimento di Matematica e Fisica, Università del Salento, Lecce, Italy 68 (a)INFN Sezione di Milano, Milan, Italy; (b)Dipartimento di Fisica, Università di Milano, Milan, Italy 69 (a)INFN Sezione di Napoli, Naples, Italy; (b)Dipartimento di Fisica, Università di Napoli, Naples, Italy 70 (a)INFN Sezione di Pavia, Pavia, Italy; (b)Dipartimento di Fisica, Università di Pavia, Pavia, Italy 71 (a)INFN Sezione di Pisa, Pisa, Italy; (b)Dipartimento di Fisica E. Fermi, Università di Pisa, Pisa, Italy 72 (a)INFN Sezione di Roma, Rome, Italy; (b)Dipartimento di Fisica, Sapienza Università di Roma, Rome, Italy 73 (a)INFN Sezione di Roma Tor Vergata, Rome, Italy; (b)Dipartimento di Fisica, Università di Roma Tor Vergata, Rome, Italy 74 (a)INFN Sezione di Roma Tre, Rome, Italy; (b)Dipartimento di Matematica e Fisica, Università Roma Tre, Rome, Italy 75 (a)INFN-TIFPA, Rome, Italy; (b)Università degli Studi di Trento, Trento, Italy 76 Institut für Astro-und Teilchenphysik, Leopold-Franzens-Universität, Innsbruck, Austria 77 University of Iowa, Iowa City, IA, USA 78 Department of Physics and Astronomy, Iowa State University, Ames, IA, USA 79 Joint Institute for Nuclear Research, Dubna, Russia 80 (a)Departamento de Engenharia Elétrica, Universidade Federal de Juiz de Fora (UFJF), Juiz de Fora, Brazil; (b)Universidade Federal do Rio De Janeiro COPPE/EE/IF, Rio de Janeiro, Brazil; (c)Universidade Federal de São João del Rei (UFSJ), São João del Rei, Brazil; (d)Instituto de Física, Universidade de São Paulo, São Paulo, Brazil 81 KEK, High Energy Accelerator Research Organization, Tsukuba, Japan 82 Graduate School of Science, Kobe University, Kobe, Japan 83 (a)AGH University of Science and Technology, Faculty of Physics and Applied Computer Science, Kraków, Poland; (b)Marian Smoluchowski Institute of Physics, Jagiellonian University, Kraków, Poland 84 Institute of Nuclear Physics Polish Academy of Sciences, Kraków, Poland 85 Faculty of Science, Kyoto University, Kyoto, Japan 86 Kyoto University of Education, Kyoto, Japan 87 Research Center for Advanced Particle Physics and Department of Physics, Kyushu University, Fukuoka, Japan 88 Instituto de Física La Plata, Universidad Nacional de La Plata and CONICET, La Plata, Argentina 123 89 Physics Department, Lancaster University, Lancaster, UK 90 Oliver Lodge Laboratory, University of Liverpool, Liverpool, UK 91 Department of Experimental Particle Physics, Jožef Stefan Institute and Department of Physics, University of Ljubljana, Ljubljana, Slovenia 92 School of Physics and Astronomy, Queen Mary University of London, London, UK 93 Department of Physics, Royal Holloway University of London, Egham, UK 94 Department of Physics and Astronomy, University College London, London, UK 95 Louisiana Tech University, Ruston, LA, USA 96 Fysiska institutionen, Lunds universitet, Lund, Sweden 97 Centre de Calcul de l’Institut National de Physique Nucléaire et de Physique des Particules (IN2P3), Villeurbanne, France 98 Departamento de Física Teorica C-15 and CIAFF, Universidad Autónoma de Madrid, Madrid, Spain 99 Institut für Physik, Universität Mainz, Mainz, Germany 100 School of Physics and Astronomy, University of Manchester, Manchester, UK 101 CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France 102 Department of Physics, University of Massachusetts, Amherst, MA, USA 103 Department of Physics, McGill University, Montreal, QC, Canada 104 School of Physics, University of Melbourne, Victoria, Australia 105 Department of Physics, University of Michigan, Ann Arbor, MI, USA 106 Department of Physics and Astronomy, Michigan State University, East Lansing, MI, USA 107 B.I. Stepanov Institute of Physics, National Academy of Sciences of Belarus, Minsk, Belarus 108 Research Institute for Nuclear Problems of Byelorussian State University, Minsk, Belarus 109 Group of Particle Physics, University of Montreal, Montreal, QC, Canada 110 P.N. Lebedev Physical Institute of the Russian Academy of Sciences, Moscow, Russia 111 National Research Nuclear University MEPhI, Moscow, Russia 112 D.V. Skobeltsyn Institute of Nuclear Physics, M.V. Lomonosov Moscow State University, Moscow, Russia 113 Fakultät für Physik, Ludwig-Maximilians-Universität München, Munich, Germany 114 Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), Munich, Germany 115 Nagasaki Institute of Applied Science, Nagasaki, Japan 116 Graduate School of Science and Kobayashi-Maskawa Institute, Nagoya University, Nagoya, Japan 117 Department of Physics and Astronomy, University of New Mexico, Albuquerque, NM, USA 118 Institute for Mathematics, Astrophysics and Particle Physics, Radboud University Nijmegen/Nikhef, Nijmegen, The Netherlands 119 Nikhef National Institute for Subatomic Physics and University of Amsterdam, Amsterdam, The Netherlands 120 Department of Physics, Northern Illinois University, DeKalb, IL, USA 121 (a)Budker Institute of Nuclear Physics and NSU, SB RAS, Novosibirsk, Russia; (b)Novosibirsk State University Novosibirsk, Novosibirsk, Russia 122 Institute for High Energy Physics of the National Research Centre Kurchatov Institute, Protvino, Russia 123 Institute for Theoretical and Experimental Physics named by A.I. Alikhanov of National Research Centre “Kurchatov Institute”, Moscow, Russia 124 Department of Physics, New York University, New York, NY, USA 125 Ochanomizu University, Otsuka, Bunkyo-ku, Tokyo, Japan 126 Ohio State University, Columbus, OH, USA 127 Faculty of Science, Okayama University, Okayama, Japan 128 Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma, Norman, OK, USA 129 Department of Physics, Oklahoma State University, Stillwater, OK, USA 130 Palacký University, RCPTM, Joint Laboratory of Optics, Olomouc, Czech Republic 131 Center for High Energy Physics, University of Oregon, Eugene, OR, USA 132 LAL, Université Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, Orsay, France 133 Graduate School of Science, Osaka University, Osaka, Japan 134 Department of Physics, University of Oslo, Oslo, Norway 135 Department of Physics, Oxford University, Oxford, UK 136 LPNHE, Sorbonne Université, Université de Paris, CNRS/IN2P3, Paris, France 123 137 Department of Physics, University of Pennsylvania, Philadelphia, PA, USA 138 Konstantinov Nuclear Physics Institute of National Research Centre “Kurchatov Institute”, PNPI, St. Petersburg, Russia 139 Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA, USA 140 (a)Laboratório de Instrumentação e Física Experimental de Partículas -LIP, Lisbon, Portugal; (b)Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Lisbon, Portugal; (c)Departamento de Física, Universidade de Coimbra, Coimbra, Portugal; (d)Centro de Física Nuclear da Universidade de Lisboa, Lisbon, Portugal; (e)Departamento de Física, Universidade do Minho, Braga, Portugal; (f)Departamento de Física Teórica y del Cosmos, Universidad de Granada, Granada, Spain; (g)Dep Física and CEFITEC of Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Caparica, Portugal; (h)Instituto Superior Técnico, Universidade de Lisboa, Lisbon, Portugal 141 Institute of Physics of the Czech Academy of Sciences, Prague, Czech Republic 142 Czech Technical University in Prague, Prague, Czech Republic 143 Charles University, Faculty of Mathematics and Physics, Prague, Czech Republic 144 Particle Physics Department, Rutherford Appleton Laboratory, Didcot, UK 145 IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette, France 146 Santa Cruz Institute for Particle Physics, University of California Santa Cruz, Santa Cruz, CA, USA 147 (a)Departamento de Física, Pontiﬁcia Universidad Católica de Chile, Santiago, Chile; (b)Universidad Andres Bello, Department of Physics, Santiago, Chile; (c)Departamento de Física, Universidad Técnica Federico Santa María, Valparaíso, Chile 148 Department of Physics, University of Washington, Seattle, WA, USA 149 Department of Physics and Astronomy, University of Shefﬁeld, Shefﬁeld, UK 150 Department of Physics, Shinshu University, Nagano, Japan 151 Department Physik, Universität Siegen, Siegen, Germany 152 Department of Physics, Simon Fraser University, Burnaby, BC, Canada 153 SLAC National Accelerator Laboratory, Stanford, CA, USA 154 Physics Department, Royal Institute of Technology, Stockholm, Sweden 155 Departments of Physics and Astronomy, Stony Brook University, Stony Brook, NY, USA 156 Department of Physics and Astronomy, University of Sussex, Brighton, UK 157 School of Physics, University of Sydney, Sydney, Australia 158 Institute of Physics, Academia Sinica, Taipei, Taiwan 159 (a)E. Andronikashvili Institute of Physics, Iv. Javakhishvili Tbilisi State University, Tbilisi, Georgia; (b)High Energy Physics Institute, Tbilisi State University, Tbilisi, Georgia 160 Department of Physics, Technion, Israel Institute of Technology, Haifa, Israel 161 Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv, Israel 162 Department of Physics, Aristotle University of Thessaloniki, Thessaloniki, Greece 163 International Center for Elementary Particle Physics and Department of Physics, University of Tokyo, Tokyo, Japan 164 Graduate School of Science and Technology, Tokyo Metropolitan University, Tokyo, Japan 165 Department of Physics, Tokyo Institute of Technology, Tokyo, Japan 166 Tomsk State University, Tomsk, Russia 167 Department of Physics, University of Toronto, Toronto, ON, Canada 168 (a)TRIUMF, Vancouver, BC, Canada; (b)Department of Physics and Astronomy, York University, Toronto, ON, Canada 169 Division of Physics and Tomonaga Center for the History of the Universe, Faculty of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Japan 170 Department of Physics and Astronomy, Tufts University, Medford, MA, USA 171 Department of Physics and Astronomy, University of California Irvine, Irvine, CA, USA 172 Department of Physics and Astronomy, University of Uppsala, Uppsala, Sweden 173 Department of Physics, University of Illinois, Urbana, IL, USA 174 Instituto de Física Corpuscular (IFIC), Centro Mixto Universidad de Valencia -CSIC, Valencia, Spain 175 Department of Physics, University of British Columbia, Vancouver, BC, Canada 176 Department of Physics and Astronomy, University of Victoria, Victoria, BC, Canada 177 Fakultät für Physik und Astronomie, Julius-Maximilians-Universität Würzburg, Würzburg, Germany 178 Department of Physics, University of Warwick, Coventry, UK 179 Waseda University, Tokyo, Japan 180 Department of Particle Physics, Weizmann Institute of Science, Rehovot, Israel 123 181 Department of Physics, University of Wisconsin, Madison, WI, USA 182 Fakultät für Mathematik und Naturwissenschaften, Fachgruppe Physik, Bergische Universität Wuppertal, Wuppertal, Germany 183 Department of Physics, Yale University, New Haven, CT, USA 184 Yerevan Physics Institute, Yerevan, Armenia a Also at Borough of Manhattan Community College, City University of New York, New York NY, USA b Also at CERN, Geneva, Switzerland c Also at CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France d Also at Département de Physique Nucléaire et Corpusculaire, Université de Genève, Geneva, Switzerland e Also at Departament de Fisica de la Universitat Autonoma de Barcelona, Barcelona, Spain f Also at Departamento de Física, Instituto Superior Tècnico, Universidade de Lisboa, Lisbon, Portugal g Also at Department of Applied Physics and Astronomy, University of Sharjah, Sharjah, United Arab Emirates h Also at Department of Financial and Management Engineering, University of the Aegean, Chios, Greece i Also at Department of Physics and Astronomy, Michigan State University, East Lansing MI, USA j Also at Department of Physics and Astronomy, University of Louisville, Louisville, KY, USA k Also at Department of Physics, Ben Gurion University of the Negev, Beer Sheva, Israel l Also at Department of Physics, California State University, East Bay, USA m Also at Department of Physics, California State University, Fresno, USA n Also at Department of Physics, California State University, Sacramento, USA o Also at Department of Physics, King’s College London, London, UK p Also at Department of Physics, St. Petersburg State Polytechnical University, St. Petersburg, Russia q Also at Department of Physics, Stanford University, Stanford CA, USA r Also at Department of Physics, University of Adelaide, Adelaide, Australia s Also at Department of Physics, University of Fribourg, Fribourg, Switzerland t Also at Department of Physics, University of Michigan, Ann Arbor MI, USA u Also at Dipartimento di Matematica, Informatica e Fisica, Università di Udine, Udine, Italy v Also at Faculty of Physics, M.V. Lomonosov Moscow State University, Moscow, Russia w Also at Giresun University, Faculty of Engineering, Giresun, Turkey x Also at Graduate School of Science, Osaka University, Osaka, Japan y Also at Hellenic Open University, Patras, Greece z Also at Institucio Catalana de Recerca i Estudis Avancats, ICREA, Barcelona, Spain aa Also at Institut für Experimentalphysik, Universität Hamburg, Hamburg, Germany ab Also at Institute for Mathematics, Astrophysics and Particle Physics, Radboud University Nijmegen/Nikhef, Nijmegen, The Netherlands ac Also at Institute for Nuclear Research and Nuclear Energy (INRNE) of the Bulgarian Academy of Sciences, Soﬁa, Bulgaria ad Also at Institute for Particle and Nuclear Physics, Wigner Research Centre for Physics, Budapest, Hungary ae Also at Institute of Particle Physics (IPP), Vancouver, Canada af Also at Institute of Physics, Academia Sinica, Taipei, Taiwan ag Also at Institute of Physics, Azerbaijan Academy of Sciences, Baku, Azerbaijan ah Also at Institute of Theoretical Physics, Ilia State University, Tbilisi, Georgia ai Also at Instituto de Fisica Teorica, IFT-UAM/CSIC, Madrid, Spain aj Also at Joint Institute for Nuclear Research, Dubna, Russia ak Also at LAL, Université Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, Orsay, France al Also at Louisiana Tech University, Ruston LA, USA am Also at LPNHE, Sorbonne Université, Université de Paris, CNRS/IN2P3, Paris, France an Also at Manhattan College, New York NY, USA ao Also at Moscow Institute of Physics and Technology State University, Dolgoprudny, Russia ap Also at National Research Nuclear University MEPhI, Moscow, Russia aq Also at Physics Department, An-Najah National University, Nablus, Palestine ar Also at Physics Dept, University of South Africa, Pretoria, South Africa as Also at Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Freiburg, Germany 123 at Also at School of Physics, Sun Yat-sen University, Guangzhou, China au Also at The City College of New York, New York NY, USA av Also at The Collaborative Innovation Center of Quantum Matter (CICQM), Beijing, China aw Also at Tomsk State University, Tomsk, and Moscow Institute of Physics and Technology State University, Dolgoprudny, Russia ax Also at TRIUMF, Vancouver BC, Canada ay Also at Universita di Napoli Parthenope, Naples, Italy ≦ Deceased 123