Measurements of t ¯ t differential cross-sections of highly boosted top quarks decaying to all-hadronic final states in p p collisions at √ s = 13 TeV using the ATLAS detector

Measurements of t¯ tdifferential cross-sections of highly boosted top quarks decaying to all-hadronic final states in pp collisions at ffiffi s p=13 TeV using the ATLAS detector M. Aaboud et al.* (ATLAS Collaboration) (Received 6 January 2018; published 25 July 2018) Measurements are made of differential cross-sections of highly boosted pair-produced top quarks as a function of top-quark and t¯ tsystem kinematic observables using proton-proton collisions at a center-ofmass energy of ffiffiffi s p¼13 TeV. The data set corresponds to an integrated luminosity of 36.1fb−1, recorded in 2015 and 2016 with the ATLAS detector at the CERN Large Hadron Collider. Events with two largeradius jets in the final state, one with transverse momentum pT>500 GeV and a second with pT>350 GeV, are used for the measurement. The top-quark candidates are separated from the multijet background using jet substructure information and association with a b-tagged jet. The measured spectra are corrected for detector effects to a particle-level fiducial phase space and a parton-level limited phase space, and are compared to several Monte Carlo simulations by means of calculated χ2values. The crosssection for t¯ tproduction in the fiducial phase-space region is 292 7ðstatÞ71ðsystÞfb, to be compared to the theoretical prediction of 384 36 fb. DOI: 10.1103/PhysRevD.98.012003 I. INTRODUCTION The large top-quark pair-production cross-section at the Large Hadron Collider (LHC) allows detailed studies of the characteristics of the production of top-antitop (t¯ t) quark pairs, providing an opportunity to further test the Standard Model (SM). Focusing on highly boosted final states probes the QCD t¯ tproduction processes in the TeV scale range, a kinematic region where theoretical calculations based on the SM still present large uncertainties [1–3]. High-precision measurements, especially in kinematic regions that have not been explored extensively, are necessary to better constrain the models currently in use. Furthermore, effects beyond the SM can appear as modifications of t¯ tdifferential distributions with respect to the SM predictions [4–6] that may not be detected with an inclusive cross-section measurement. In the SM, the top quark decays almost exclusively to a Wboson and a b-quark. The signature of a t¯ tfinal state is therefore determined by the Wboson decay modes. The ATLAS [7–14] and CMS [15–20] Collaborations have published measurements of the t¯ tdifferential cross-sections at center-of-mass energies of ffiffiffi s p¼7TeV, ffiffiffi s p¼8TeV, and ffiffiffi s p¼13 TeV in pp collisions using final states containing leptons. The CMS Collaboration has also published a measurement of t¯ tdifferential cross-sections as a function of the top quark transverse momenta (pT)in pp collisions at ffiffiffi s p¼8TeV using the all-hadronic final state [21]. The analysis presented here makes use of the allhadronic t¯ tdecay mode, where only top-quark candidates with high pTare selected. This highly boosted topology is easier to reconstruct than other final-state configurations as the top-quark decay products are collimated into a largeradius jet by the Lorentz boost of the top quarks. This analysis is performed on events with the leading top-quark jet having pt;1 T>500 GeV and the second-leading topquark jet having pt;2 T>350 GeV. These jets are reconstructed from calorimeter energy deposits and tagged as top-quark candidates to separate the t¯ tfinal state from background sources. The event selection and background estimation follows the approach used in Ref. [22], but with updated tagging methods and data-driven multijet background estimates. These measurements are based on data collected by the ATLAS detector in 2015 and 2016 from pp collisions at ffiffiffi s p¼13 TeV, corresponding to an integrated luminosity of 36.1fb−1. Measurements are made of the t¯ tdifferential cross-sections by unfolding the detector-level distributions to a particle-level fiducial phase-space region. The goal of unfolding to a particle-level fiducial phase space and of using variables directly related to detector observables is to allow precision tests of QCD by avoiding model-dependent *Full author list given at the end of the article. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3. PHYSICAL REVIEW D 98, 012003 (2018) 2470-0010=2018=98(1)=012003(39) 012003-1 © 2018 CERN, for the ATLAS Collaboration extrapolation of the measurements to a phase-space region outside the detector acceptance. Measurements of partonlevel differential cross-sections are also presented, where the detector-level distributions are unfolded to the top quark at the parton-level in a limited phase-space region. These allow comparisons to the higher-order calculations that are currently restricted to stable top quarks [1–3]. These differential cross-sections are similar to those studied in dijet measurements at large jet transverse momentum [23,24] and are sensitive to effects of initialand final-state radiation (ISR and FSR), to different parton distribution functions (PDF) and to different schemes for matching matrix-element calculations to parton shower models. Measurements are made of the differential cross-sections for the leading and second-leading top quarks as a function of pt;1 Tand pt;2 T, as well as the rapidities of the top quarks. The rapidities of the leading and second-leading top quarks in the laboratory frame are denoted by yt;1and yt;2, respectively, while their rapidities in the t¯ tcenter-of-mass frame are y⋆¼½ðyt;1−yt;2Þand −y⋆. These allow the construction of the variable χt¯ t¼exp2jy⋆j, which is of particular interest as many processes not included in the Standard Model are predicted to peak at low values of χt¯ t [25]. The longitudinal motion of the t¯ tsystem in the laboratory frame is described by the rapidity boost yt¯ t B¼ ½ðyt;1þyt;2Þand is sensitive to PDFs. Measurements are also made of the differential cross-sections as a function of the invariant mass, pTand rapidity of the t¯ tsystem; the absolute value of the azimuthal angle between the two top quarks, Δϕt¯ t; the absolute value of the out-of-plane momentum, jpt¯ t outj(i.e., the projection of the three-momentum of one of the top-quark jets onto the direction perpendicular to a plane defined by the other top quark and the beam axis (z) in the laboratory frame [24]); the cosine of the production angle in the Collins-Soper1 reference frame, cos θ⋆; and the scalar sum of the transverse momenta of the two top quarks, Ht¯ t T[26,27]. Some of the variables (e.g., Δϕt¯ tand jpt¯ t outj) are more sensitive to additional radiation in the main scattering process, and thus are more sensitive to effects beyond leading order (LO) in the matrix elements. All of these variables are sensitive to the kinematics of the t¯ tproduction process. The paper is organized as follows. Section II briefly describes the ATLAS detector, while Sec. III describes the data and simulation samples used in the measurements. The reconstruction of physics objects and the event selection is explained in Sec. IV and the background estimates are discussed in Sec. V. The procedure for unfolding to particle level and parton level are described in Sec. VI. The systematic uncertainties affecting the measurements are summarized in Sec. VII. The results of the measurements are presented in Sec. VIII and comparisons of these results with theoretical predictions are made in Sec. IX.A summary is presented in Sec. X. II. ATLAS DETECTOR The ATLAS experiment [28] at the LHC uses a multipurpose detector with a forward-backward symmetric cylindrical geometry and near 4πcoverage in solid angle.2 It consists of an inner tracking detector surrounded by a superconducting solenoid magnet creating a 2 T axial magnetic field, electromagnetic and hadronic calorimeters, and a muon spectrometer. The inner tracking detector covers the pseudorapidity range jηj<2.5. Consisting of silicon pixel, silicon microstrip, and transition radiation tracking detectors, the inner tracking detector allows highly efficient reconstruction of the trajectories of the charged particles produced in the pp interactions. An additional silicon pixel layer, the insertable B-layer,wasaddedbetween3and4cmfromthebeamline to improve b-hadron tagging [29]. Lead/liquid-argon (LAr) sampling calorimeters provide electromagnetic (EM) energy measurements with high granularity and showerdepth segmentation. A hadronic (steel/scintillator-tile) calorimeter covers the central pseudorapidity range (jηj<1.7). The endcap and forward regions are instrumented with LAr calorimeters for EM and hadronic energy measurements up tojηj¼4.9.Themuonspectrometerislocated outside ofthe calorimeter systems and is based on three large air-core toroid superconducting magnets with eight coils each. It includes a system of precision tracking chambers and detectors with sufficient timing resolution to enable triggering of events. A two-level trigger system is used to select events [30]. The first-level hardware-based trigger uses a subset of the detector information to reduce the rate of accepted events to a design maximum of 100 kHz. This is followed by a software-based trigger with a maximum average accepted event rate of 1 kHz. III. DATA SETS AND MONTE CARLO EVENT GENERATION The data used for this analysis were recorded with the ATLAS detector at a center-of-mass energy of 13 TeV in 2015 and 2016 and correspond to an integrated luminosity 1The Collins-Soper frame is the rest frame of the t¯ tpair, wherein the two top quarks have equal and opposite momenta; thus, each makes the same angle θ⋆with the beam direction. 2ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the center of the detector and the zaxis along the beam pipe. The xaxis points from the IP to the center of the LHC ring and the yaxis points upward. Cylindrical coordinates ðr; ϕÞare used in the transverse plane, ϕ being the azimuthal angle around the zaxis. The pseudorapidity is defined in terms of the polar angle θas η¼−ln tanðθ=2Þ. M. AABOUD et al. PHYS. REV. D 98, 012003 (2018) 012003-2 of 36.1fb−1. Only the data-taking periods in which all the subdetectors were operational are considered. The events for this analysis were collected using an inclusive anti-ktjet trigger with radius parameter R¼1.0 and nominal pTthresholds of 360 and 420 GeV for the 2015 and 2016 data-taking periods, respectively. These triggers were fully efficient for jets with pT>480 GeV [30]. The signal and several background processes are modeled using Monte Carlo (MC) event generators. Multiple overlaid proton-proton collisions (pileup) are simulated with the soft QCD processes of P YTHIA 8.186 [31] using a set of tuned parameters called the A2 tune [32] and the MSTW2008LO [33] PDF set. The detector response is simulated using the G EANT 4framework [34,35]. The data and MC events are reconstructed with the same software algorithms. Several next-to-leading-order (NLO) MC calculations of the t¯ tprocess are used in the analysis, and to compare with the measured differential cross-sections. The P OWHEG - B OX v2 [36],M AD G RAPH 5_ A MC [37], and S HERPA [38] Monte Carlo event generators encode different approaches to the matrix element calculation and different matching schemes between the NLO QCD matrix-element calculation and the parton shower algorithm. A more detailed explanation of the differences among these event generators can be found in Ref. [39]. The nominal sample uses the P OWHEG -B OX v2 [36] event generator employing the NNPDF30 PDF set interfaced with the P YTHIA 8parton shower and hadronization model (hereafter also referred to as PWG+PY8). The P OWHEG hdamp parameter, which controls the pTof the first additional emission beyond the Born configuration, is set to 1.5 times the top-quark mass [40]. The main effect of this is to regulate the high-pTemission against which the t¯ tsystem recoils. To enhance the production of top quarks in the high-pTregion, the P OWHEG parameter bornsuppfact is set to pT;supp ¼ 500 GeV [36,41].TheP YTHIA 8parameters are chosen for good agreement with ATLAS Run-1 data by employing the A14 tune [42] with the NNPDF23LO PDF set [43]. Two alternative P OWHEG +P YTHIA 8samples with systematic variations of the P OWHEG and P YTHIA 8parameters probe the effects of the experimental tuning of the MC event generators. One sample, which primarily increases the amount of initialand final-state radiation, uses hdamp ¼ 3mtop, the factorization and renormalization scale reduced by a factor of 2 and the A14 Var3c Up tune variation [42].The second sample, which decreases the amount of initialand final-state radiation, uses hdamp ¼1.5mtop, the factorization and renormalization scale increased by a factor of 2 and the A14 Var3c Down tune variation [42].Thesetwosamples will be also referred to as “more IFSR”and “less IFSR” respectively. An alternative matrix element calculation and matching with the parton shower is realized with the M AD G RAPH 5_ A MC event generator (hereafter referred to as MG5_ A MC@NLO) [37] interfaced with the P YTHIA 8parton shower and hadronization model using the same tune as the nominal sample. This sample requires the leading top quark in each event to have pT>300 GeV to ensure that the high-pTregion is adequately populated. The effects ofusingalternativepartonshowerandhadronization models is probed by interfacing the nominal P OWHEG setup with the H ERWIG 7parton shower and hadronization model [44] employing the H7UE tune (hereafter also referred to as PWG+H7). Another calculation using the S HERPA v2.2.1 event generator [38] with the default S HERPA parton shower and hadronization model merges the NLO t¯ tmatrix element with matrix element calculations including up to four additional jets using the MEPS @ NLO setup [45]. The Wt single-top-quark processes are modeled using the P OWHEG -B OX v2 event generator with the CT10 PDF set [46]. For the single-top-quark process, the top quarks are decayed using M AD S PIN [47]. The parton shower, fragmentation and the underlying event for these processes are simulated using the P YTHIA 6.428 event generator [48] with the CTEQ6L1 PDF sets and the corresponding Perugia 2012 tune (P2012) [49]. Electroweak tand s-channel single-top-quark events are not explicitly modeled because of the small cross-section of these processes and the low jet multiplicity in the final state. Their contribution is accounted for in the data-driven background estimate. The associated production of t¯ tpairs with W,Zand Higgs bosons is modeled using the MG5_ A MC@NLO event generator [37] coupled to the P YTHIA 8parton shower and hadronization model using the same PDF sets and tunes as the t¯ tsample. The top-quark mass is set to mtop ¼172.5GeV for all samples and the renormalization and factorization scales are set to μR=F¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi m2 top þ1 2ðpTðtÞ2þpTð¯ tÞ2Þ qfor all t¯ t samples except where explicitly noted above. The E VT G EN v1.2.0 program [50] is used for modeling the properties of the bottom and charm hadron decays for all event generator setups other than for the S HERPA sample. The t¯ tsamples are normalized using the next-to-next-toleading-order cross-section plus next-to-next-to-leadinglogarithm corrections (NNLO þNNLL) σt¯ t¼832þ46 −51 pb [51], where the uncertainties reflect the effect of scale and PDF variations. The single-top-quark cross-section is normalized to the NLO predictions [52]. The associated production of t¯ tpairs with W,Z, and Higgs bosons are normalized to 0.603, 0.586, and 0.231 pb, respectively, as predicted by the MG5_ A MC@NLO event generator. IV. EVENT RECONSTRUCTION AND SELECTION This analysis makes use of jets, electrons, and muons as well as event-based measures formed from their combinations. The event reconstruction and selection are summarized in the following subsections. MEASUREMENTS OF t¯ tDIFFERENTIAL …PHYS. REV. D 98, 012003 (2018) 012003-3 A. Event reconstruction Electron candidates are identified from high-quality inner detector tracks matched to calorimeter deposits consistent with an electromagnetic shower. The calorimeter deposits have to form a cluster with ET>25 GeV, jηj< 2.47 and be outside the transition region 1.37 ≤jηj≤1.52 between the barrel and endcap calorimeters. A likelihoodbased requirement is used to suppress misidentified jets (hereafter referred to as fakes), and calorimeterand trackbased isolation requirements are imposed [53,54]. Overall, these criteria result in electron identification efficiencies of ∼90% for electrons with pT>25 GeV and 96% for electrons with pT>60 GeV. Muon candidates are reconstructed using high-quality inner detector tracks combined with tracks reconstructed in the muon spectrometer. Only muon candidates with pT> 25 GeV and jηj<2.5are considered. Isolation criteria similar to those used for electrons are used [55]. To reduce the impact of nonprompt leptons, muons within ΔR¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðΔηÞ2þðΔϕÞ2 p¼0.4of a jet are removed. The anti-ktalgorithm implemented in the F AST J ET package [56,57] is used to define two types of jets for this analysis: small-Rjets with a radius parameter of R¼ 0.4and large-Rjets with R¼1.0. These are reconstructed independently of each other from topological clusters in the calorimeter. The clusters used as input to the large-Rjet reconstruction are calibrated using the local calibration method described in Ref. [58]. The small-Rjet energy scale is obtained by using an energyand η-dependent calibration scheme resulting from simulation and in situ corrections based on data [58–61]. Only small-Rjets that have jηj< 2.5and pT>25 GeV are considered. To reduce pileup effects, an algorithm that determines whether the primary vertex is the origin of the charged-particle tracks associated with a jet candidate is used to reject jets coming from other interactions [62]. This is done only for jet candidates with pT<50 GeV and jηj<2.4. The small-Rjet closest to an electron candidate is removed if they are separated by no more than ΔR¼0.2. Small-Rjets containing b-hadrons are identified (b-tagged) using a multivariate discriminant that combines information about secondary vertices and impact parameters. The small-Rjets are considered b-tagged if the value of the discriminant is larger than a threshold that provides 70% efficiency. The corresponding rejection factors for gluon/light-quark jets and charm-quark jets are approximately 125 and 4.5, respectively [63,64]. The large-Rjet energy scale is derived by using energyand η-dependent calibration factors derived from simulation and in situ measurements [58,59,65]. The largeRjet candidates are required to have jηj<2.0and pT>300 GeV. A trimming algorithm [66] with parameters Rsub ¼0.2and fcut ¼0.05 is applied to suppress gluon radiation and further mitigate pileup effects. A top-tagging algorithm [67] is applied that consists of pT-dependent requirements on two variables: the jet mass mJ, measured from clusters in the calorimeter, and the N-subjettiness ratio τ32 [68,69]. The N-subjettiness variable τNexpresses how well a jet can be described as containing Nor fewer subjets. The ratio τ32 ¼τ3=τ2allows discrimination between jets containing a three-prong structure and jets containing a two-prong structure. The pT-dependent requirements provide a 50% top-quark tagging efficiency independent of pT, with a light-quark and gluon jet rejection factor of ∼17 at pT¼500 GeV and decreasing with increasing pTto ∼10 at pT¼1TeV. This combination of variables used with trimmed large-Rjets provides the necessary rejection for this analysis, and is insensitive to the effects of pileup. B. Event selection The event selection identifies fully hadronic t¯ tevents where both top quarks have high pT. Each event is required to have a primary vertex with five or more associated tracks with pT>0.4GeV. In order to reject top-quark events where a top quark has decayed semileptonically, the events are required to contain no reconstructed electron or muon candidate. To identify the fully hadronic decay topology, events must have at least two large-Rjets with pT>350 GeV, jηj<2.0, and jmJ−mtopj<50 GeV, where the top-quark mass mtop is set to 172.5 GeV. The leading jet is required to have pT>500 GeV and the event must contain at least two small-Rjets with pT>25 GeV and jηj<2.5. This preselection results in an event sample of 22.7 million events. To reject multijet background events, the two highest pT large-Rjets must satisfy the top-tagging criteria described in Sec. IVA. Furthermore, both top-tagged large-Rjets are required to have an associated small-Rb-tagged jet. This association, hence referred to as b-matching, is made by requiring ΔR<1.0between the small-Rand large-Rjets. These two highest pTlarge-Rjets are the leading and second-leading top-quark candidate jets (or “top-quark jets” in what follows). The candidate t¯ tfinal state is defined as the sum of the four-momenta of the two large-Rtop-quark jets. This selection defines the signal region, which has 3541 events. V. BACKGROUND ESTIMATION There are two categories of background sources: those involving one or more top quarks in the final state and those sources where no top quark is involved. The background processes involving top quarks are estimated using MC calculations. The largest background source is events where the two leading jets both arise from gluons or u,d,s,c, or bquarks (which are referred to as “multijet”events). Monte Carlo predictions of multijet events have large uncertainties coming from the relatively poorly understood higher-order contributions that produce a pair of massive jets [70,71]. To avoid these large uncertainties the multijet M. AABOUD et al. PHYS. REV. D 98, 012003 (2018) 012003-4 background is determined using a data-driven technique. A similar method was used in previous work [22]. AP OWHEG +P YTHIA 8t¯ tsample is used to estimate the number of t¯ tevents in the sample that arise from at least one top quark decaying semileptonically. This includes contributions from decays resulting in τleptons, as no attempt is made to identify τlepton candidates and reject them. The rate is estimated to be only ∼4% in the signal region, primarily due to the top-tagging requirements. However, this category of t¯ tevents contributes to control and validation regions where the top-tagging and/or b-tagging requirements are relaxed. Thus, this MC prediction is used to estimate this contamination. Singletop-quark production in the Wt-channel makes a small contribution to the signal sample, which is estimated using the MC predictions described earlier. The t-channel singletop-quark process is not included, but is partially accounted for in the multijet background estimate. The data-driven multijet background estimate is performed using a set of control regions. Sixteen separate regions are defined by classifying each event in the preselection sample according to whether the leading and second-leading jets are top-tagged or b-tagged. Table I shows the 16 regions that are defined in this way, and illustrates the proportion of expected t¯ tevents in each region relative to the observed rate. Region Sis the signal region, while the regions with no b-tags (A, C, E, and F) and the regions with one b-tag and no top-tags (B and I) are dominated by multijet backgrounds. After subtracting the estimated contributions of the t¯ t signal and of the other background sources to each of the control regions, the number of events in region J divided by the number of events in region A gives an estimate of the ratio of the number of multijet events in region S to the number of multijet events in region O. Thus one can use these relationships to estimate the multijet background rate in region S, i.e., S¼O×J=A, where O,Jand Aare the number of observed events in each region, while Sis the estimate of the multijet background in region S. This “ABCD”estimate assumes that the mistagging rate of the leading jet does not depend on how the second-leading jet is tagged. This assumption is avoided by measuring the correlations in background-dominated regions, e.g., comparing the ratio of the numbers of events in regions F and E (giving the leading jet top-tagging rate when the second-leading jet is top-tagged) with the ratios of events in regions C and A (giving the leading jet top-tagging rate when the second leading jet is not toptagged). This results in a refined data-driven estimate of the size of the multijet background given by S¼J×O A·D×A B×C·G×A E×I·F×A E×C·H×A B×I ¼J×O×H×F×D×G×A3 ðB×E×C×IÞ2;ð1Þ where the region name is the number of observed events in that region. The measured correlations in the tagging of background jets result in an increase of ð12 3Þ%in the background estimate compared with the estimate assuming that the tagging rates are independent. This estimate is also valid when a variable characterizing the kinematics of the events in all the regions is further restricted to range between specific values. This provides a bin-by-bin data-driven background estimate with uncertainties that come from the number of events in the regions used in Eq. (1). Regions L and N are estimated to consist of approximately equal numbers of t¯ tsignal events and multijet background events. They are used as validation regions to verify that the signal and background estimates are robust. In these cases, the multijet background is estimated using different combinations of control regions, namely N¼ H×D=B and L¼H×G=I. The number of multijet events in the signal region is calculated by applying Eq. (1) to the number of events in the control regions. This results in an estimate of 810 50 multijet events in the signal region, where the uncertainty takes into account the statistical uncertainties as well as the systematic uncertainties in the t¯ tsignal subtraction. There is good agreement in the validation regions between the predicted and observed event yields, as well as in the shape of distributions that are sensitive to the proportion of t¯ tsignal and multijet background. This is illustrated in Fig. 1, which compares the large-Rjet mass distributions and the highest-pTsubjet mass distribution of the leading jets. A shift between the measured and predicted jet mass distributions, shown in Figs. 1(a) and 1(b), is consistent with the uncertainties arising from the TABLE I. Region labels and expected proportion of t¯ t events used for the data-driven background prediction of multijet events. A top-quark tagged jet is defined by the tagging algorithm described in the text, and denoted “1t”in the table, while a jet that is not top-tagged is labeled “0t.”Ab-match is defined as ΔRðJ; bÞ<1.0, where Jrepresents a large-Rjet and “b” represents a b-tagged jet. The labels “1b”and “0b”represent large-Rjets that either have or do not have a b-match. Regions K, L, N, and M have an expected contribution from sources involving one or more top quarks of at least 15% of the observed yield. In other regions, the expected contribution from signal and backgrounds involving top quarks is less than 15% of the observed event rate. 2nd large-Rjet 1t1b J (7.6%) K (21%) L (42%) S 0t1b B (2.2%) D (5.8%) H (13%) N (47%) 1t0b E (0.7%) F (2.4%) G (6.4%) M (30%) 0t0b A (0.2%) C (0.8%) I (2.2%) O (11%) 0t0b 1t0b 0t1b 1t1b Leading large-Rjet MEASUREMENTS OF t¯ tDIFFERENTIAL …PHYS. REV. D 98, 012003 (2018) 012003-5 calibration for large-Rjets [72]. The distributions for the leading and second-leading jet pTand rapidity in regions N and L are shown in Fig. 2, and can be compared with the signal region distributions in Fig. 3. The level of agreement between the observed and predicted distributions in the signal region can be seen in Fig. 3, which shows the distributions of the leading topquark pTand absolute value of rapidity, as well as the same distributions for the second-leading jet. The event yields are summarized in Table II for the simulated signal, the background sources, and the data sample. VI. UNFOLDING PROCEDURE The differential cross-sections are obtained from the data using an unfolding technique that corrects for detector effects suchasefficiency,acceptance,andresolution.Thiscorrection ismadetotheparticle levelusinga fiducialphasespacethatis defined to match the experimental acceptance and hence avoid large MC extrapolations. The parton-level differential cross-sections are obtained using a similar procedure, but in this case the correction is made to the top-quark parton after final-state radiation effects have been included in the Events / GeV 0 20 40 60 80 100 ATLAS -1 = 13 TeV, 36.1 fbs Validation region N (all-had)t t Data 2015+2016 (non all-had)tt Stat. Unc. Single top Det. Syst. Unc.⊕Stat. +W/Z/Htt Tot. Syst. Unc.⊕Stat. Multijet Leading large-R jet mass [GeV] 120 140 160 180 200 220 Predictio n Data 0.5 1 1.5 (a) Events / GeV 0 20 40 60 80 100 120 140 160 180 200 ATLAS -1 = 13 TeV, 36.1 fbs Signal region (all-had)t tData 2015+2016 (non all-had)tt Stat. Unc. Single top Det. Syst. Unc.⊕Stat. +W/Z/Htt Tot. Syst. Unc.⊕Stat. Multijet Leading large-R jet mass [GeV] 120 140 160 180 200 220 Predictio n Data 0.5 1 1.5 (b) Events / GeV 0 20 40 60 80 100 120 140 160 180 ATLAS -1 = 13 TeV, 36.1 fbs Validation region L (all-had)t t Data 2015+2016 (non all-had)tt Stat. Unc. Single top Det. Syst. Unc.⊕Stat. +W/Z/Htt Tot. Syst. Unc.⊕Stat. Multijet Lead. subjet mass in lead. large-R jet [GeV] 0 20 40 60 80 100 120 Predictio n Data 0.5 1 1.5 (c) Events / GeV 0 20 40 60 80 100 120 140 ATLAS -1 = 13 TeV, 36.1 fbs Signal region (all-had)t tData 2015+2016 (non all-had)tt Stat. Unc. Single top Det. Syst. Unc.⊕Stat. +W/Z/Htt Tot. Syst. Unc.⊕Stat. Multijet Lead. subjet mass in lead. large-R jet [GeV] 0 20406080100120 Predictio n Data 0.5 1 1.5 (d) FIG. 1. Kinematic distributions of top-quark candidate jets in the signal region S and in the two validation regions N and L. The leading large-Rjet mass distributions for the events in the validation region N and the signal region S are shown in (a) and (b), respectively. The mass distribution of the leading small-Rsubjet in the leading large-Rjet for events in the validation region L and in the signal region are shown in (c) and (d), respectively. The signal prediction (open histogram) is based on the P OWHEG +P YTHIA 8event generator normalized to the NNLO þNLL cross-section. The background is the sum of the data-driven multijet estimate (dark histogram) and the MC-based expectation for the contributions of non-all-hadronic t¯ tand single-top-quark processes. Events beyond the x-axis range are included in the last bin. The gray area indicates the combined statistical and systematic uncertainties, including t¯ t modeling uncertainties. M. AABOUD et al. PHYS. REV. D 98, 012003 (2018) 012003-6 generation process using a limited phase-space region matched to the kinematic acceptance of the analysis. In the following subsections, the particle-level fiducial phase space and the parton-level phase space are defined and the algorithm used for the unfolding is described. A. Particle-level fiducial phase-space and parton-level phase-space regions The particle-level fiducial phase-space definition models the kinematic requirements used to select the t¯ tprocess. In the MC signal sample, electrons and muons that do not originate from hadron decays are combined or “dressed”with any photons found in a cone of size ΔR¼0.1around the lepton direction. The four-momentum of each photon in the cone is added to the fourmomentum of the lepton to produce the dressed lepton. Jets are clustered using all stable particles except those used in the definition of dressed electrons and muons and neutrinos not from hadron decays, using the anti-kt algorithm with a radius parameter R¼0.4and R¼1.0 for small-Rand large-Rjets, respectively. The decay products of hadronically decaying τleptons are included. These jets do not include particles from pileup events but do include those from the underlying event. Large-Rjets Events / GeV 0 5 10 15 20 25 30 ATLAS -1 = 13 TeV, 36.1 fbs Validation region N Data 2015+2016 (all-had)tt (non all-had)tt Single top +W/Z/Htt Multijet Stat. Unc. Det. Syst. Unc.⊕Stat. Tot. Syst. Unc.⊕Stat. [GeV] t,1 T p 500 600 700 800 900 1000 1100 1200 Predictio n Data 0.5 1 1.5 (a) | t,1 Events / unit of |y 0 1000 2000 3000 4000 5000 ATLAS -1 = 13 TeV, 36.1 fbs Validation region N (all-had)t tData 2015+2016 (non all-had)tt Stat. Unc. Single top Det. Syst. Unc.⊕Stat. +W/Z/Htt Tot. Syst. Unc.⊕Stat. Multijet | t,1 |y 0 0.5 1 1.5 2 Predictio n Data 0.5 1 1.5 (b) Events / GeV 0 5 10 15 20 25 ATLAS -1 = 13 TeV, 36.1 fbs Validation region L Data 2015+2016 (all-had)tt (non all-had)tt Single top +W/Z/Htt Multijet Stat. Unc. Det. Syst. Unc.⊕Stat. Tot. Syst. Unc.⊕Stat. [GeV] t,2 T p 400 600 800 1000 1200 Predictio n Data 0.5 1 1.5 (c) | t,2 Events / unit of |y 0 1000 2000 3000 4000 5000 6000 7000 ATLAS -1 = 13 TeV, 36.1 fbs Validation region L (all-had)t tData 2015+2016 (non all-had)tt Stat. Unc. Single top Det. Syst. Unc.⊕Stat. +W/Z/Htt Tot. Syst. Unc.⊕Stat. Multijet | t,2 |y 0 0.5 1 1.5 2 Predictio n Data 0.5 1 1.5 (d) FIG. 2. Kinematic distributions of top-quark candidate jets in the two validation regions Nand L: (a) transverse momentum and (b) absolute value of the rapidity of the leading large-Rjet, (c) transverse momentum and (d) absolute value of the rapidity of the secondleading large-Rjet. The signal prediction (open histogram) is based on the P OWHEG +P YTHIA 8event generator normalized to the NNLO þNLL cross-section. The background is the sum of the data-driven multijet estimate (dark histogram) and the MC-based expectation for the contributions of non-all-hadronic t¯ tand single-top-quark processes. Events beyond the x-axis range are included in the last bin. The gray area indicates the combined statistical and systematic uncertainties, including t¯ tmodeling uncertainties. MEASUREMENTS OF t¯ tDIFFERENTIAL …PHYS. REV. D 98, 012003 (2018) 012003-7 are required to have pT>350 GeV and a mass within 50 GeV of the top-quark mass. The following requirements on particle-level electrons, muons, and jets in the all-hadronic t¯ tMC events define the particle-level fiducial phase space: (1) no dressed electrons or muons with pT>25 GeV and jηj<2.5be in the event, (2) at least two anti-ktR¼1.0jets with pT>350 GeV and jηj<2.0, (3) at least one anti-ktR¼1.0jet with pT>500 GeV and jηj<2.0, (4) the masses of the two large-Rjets be within 50 GeV of the top-quark mass of 172.5 GeV, (5) at least two anti-ktR¼0.4jets with pT>25 GeV and jηj<2.5and Events / GeV 0 10 20 30 40 50 ATLAS -1 = 13 TeV, 36.1 fbs Signal region Data 2015+2016 (all-had)tt (non all-had)tt Single top +W/Z/Htt Multijet Stat. Unc. Det. Syst. Unc.⊕Stat. Tot. Syst. Unc.⊕Stat. [GeV] t,1 T p 500 600 700 800 900 1000 1100 1200 Predictio n Data 0.5 1 1.5 (a) | t,1 Events / unit of |y 0 1000 2000 3000 4000 5000 6000 7000 ATLAS -1 = 13 TeV, 36.1 fbs Signal region (all-had)t tData 2015+2016 (non all-had)tt Stat. Unc. Single top Det. Syst. Unc.⊕Stat. +W/Z/Htt Tot. Syst. Unc.⊕Stat. Multijet | t,1 |y 0 0.5 1 1.5 2 Predictio n Data 0.5 1 1.5 (b) Events / GeV 0 5 10 15 20 25 30 ATLAS -1 = 13 TeV, 36.1 fbs Signal region Data 2015+2016 (all-had)tt (non all-had)tt Single top +W/Z/Htt Multijet Stat. Unc. Det. Syst. Unc.⊕Stat. Tot. Syst. Unc.⊕Stat. [GeV] t,2 T p 400 600 800 1000 1200 Predictio n Data 0.5 1 1.5 (c) | t,2 Events / unit of |y 0 1000 2000 3000 4000 5000 6000 7000 ATLAS -1 = 13 TeV, 36.1 fbs Signal region (all-had)t tData 2015+2016 (non all-had)tt Stat. Unc. Single top Det. Syst. Unc.⊕Stat. +W/Z/Htt Tot. Syst. Unc.⊕Stat. Multijet | t,2 |y 0 0.5 1 1.5 2 Predictio n Data 0.5 1 1.5 (d) FIG. 3. Kinematic distributions of top-quark candidate jets in the signal region S: (a) transverse momentum and (b) absolute value of the rapidity of the leading top-quark jet, (c) transverse momentum and (d) absolute value of the rapidity of the second-leading top-quark jet. The signal prediction (open histogram) is based on the P OWHEG +P YTHIA 8simulation normalized to the NNLO þNLL crosssection. The background is the sum of the data-driven multijet estimate (dark histogram) and the MC-based expectation for the contributions of non-all-hadronic t¯ tand single-top-quark processes. Events beyond the x-axis range are included in the last bin. The gray area indicates the combined statistical and systematic uncertainties in the total prediction, including t¯ tmodeling uncertainties. TABLE II. Event yields in the signal region for the expected t¯ t signal process and the background processes. The sum of these are compared to the observed yield. The uncertainties represent the sum in quadrature of the statistical and systematic uncertainties in each subsample. Neither modeling uncertainties nor uncertainties in the inclusive t¯ tcross-section are included in the systematic uncertainties. The single-top-quark background does not include the t-channel process. t¯ t(all-hadronic) 3250 470 t¯ t(non-all-hadronic) 200 40 Single-top-quark 24 12 t¯ tþW=Z=H 33 10 Multijet events 810 50 Prediction 4320 530 Data (36.1fb−1) 3541 M. AABOUD et al. PHYS. REV. D 98, 012003 (2018) 012003-8 (6) the two leading R¼1.0jets be matched to a b-hadron in the final state using a ghost-matching technique as described in Ref. [73] (called top-quark particle jets). The parton-level phase space is defined by requiring that the leading top quark have pT>500 GeV and the secondleading top quark have pT>350 GeV. No rapidity or other kinematic requirements are made. This definition avoids a large extrapolation in the unfolding procedure that results in large systematic uncertainties. B. Unfolding algorithm The iterative Bayesian method [74] as implemented in ROOUNFOLD [75] is used to correct the detector-level event distributions to their corresponding particleand partonlevel differential cross-sections. The unfolding starts from the detector-level event distributions after subtraction of the estimated backgrounds. An acceptance correction facc is applied that accounts for events that are generated outside the fiducial or parton phase space but pass the detector-level selection. In order to properly account for resolution and any combinatorial effects, the detector-level and particlelevel (parton-level) objects in MC events are required to bewell-matchedusingthe angulardifferenceΔR.Atparticle (parton) level, each top-quark particle-level jet (top quark) is matched to the closest detector-level jet within ΔR<1.0, a requirement that ensures high matching efficiency. The resulting acceptance corrections fj acc are illustrated in Fig. 4. The unfolding step uses a migration matrix (M) derived from simulated t¯ tevents with matching detector-level jets by binning these events in the particle-level and partonlevel phase spaces. The probability for particle-level [GeV] t,1 T p 500 600 700 800 900 1000 1100 1200 Correction 0 0.2 0.4 0.6 0.8 1ATLAS = 13 TeVsSimulation Fiducial phase space Acceptance Efficiency (a) [GeV] t,1 T p 500 600 700 800 900 1000 1100 1200 Correction 0 0.2 0.4 0.6 0.8 1ATLAS Simulation =13 TeVs > 350 GeV T t,2 > 500 GeV, p T t,1 Parton level, p Acceptance Efficiency (b) | t,1 |y 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Correction 0 0.2 0.4 0.6 0.8 1ATLAS = 13 TeVsSimulation Fiducial phase space Acceptance Efficiency (c) | t,1 |y 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Correction 0 0.2 0.4 0.6 0.8 1ATLAS Simulation =13 TeVs > 350 GeV T t,2 > 500 GeV, p T t,1 Parton level, p Acceptance Efficiency (d) FIG. 4. Acceptance and efficiency corrections as a function of pTand jyjof the leading top-quark jet for the particle-level phase space in (a) and (b) and for the parton-level phase space in (c) and (d). The P OWHEG +P YTHIA 8event generator is used as the nominal prediction to correct for detector effects. The blue and red areas represent statistical uncertainties. MEASUREMENTS OF t¯ tDIFFERENTIAL …PHYS. REV. D 98, 012003 (2018) 012003-9 IX. COMPARISONS WITH STANDARD MODEL PREDICTIONS The particle-level fiducial phase-space differential crosssections and the parton-level differential cross-sections are compared with several Standard Model calculations. The predicted total particle-level cross-section for top-quark pair production in the fiducial phase-space region is larger than the one observed. However, the effect is not statistically significant due to the large systematic uncertainties. A better agreement is found for P OWHEG + H ERWIG 7and to a lesser extent for the predictions of P OWHEG +P YTHIA 8with more initialand final-state radiation. The information provided by the shapes of the observed differential cross-section measurements is compared to the predictions using the χ2test described in Sec. VII B, which ] -1 [GeV tt T / d H tt σ d ⋅ tt σ1/ 5− 10 4− 10 3− 10 2− 10 1− 10 Data POWHEG+Py8 POWHEG+H7 MG5_aMC@NLO+Py8 Sherpa 2.2.1 Stat. Unc. Syst. Unc.⊕Stat. ATLAS -1 = 13 TeV, 36.1 fbs Fiducial phase space [GeV] tt T H 1000 1200 1400 1600 1800 2000 2200 Data Prediction 0 1 2 (a) tt B / d y tt σ d ⋅ tt σ1/ 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2Data POWHEG+Py8 POWHEG+H7 MG5_aMC@NLO+Py8 Sherpa 2.2.1 Stat. Unc. Syst. Unc.⊕Stat. ATLAS -1 = 13 TeV, 36.1 fbs Fiducial phase space tt B y 0 0.5 1 1.5 2 Data Prediction 0.8 1 1.2 (b) FIG. 9. Normalized particle-level fiducial phase-space differential cross-sections as a function of (a) the scalar sum of the transverse momenta of the two top-quark jets and (b) the longitudinal boost yt¯ t B. The gray bands indicate the total uncertainty in the data in each bin. The vertical bars indicate the statistical uncertainties in the theoretical models. The P OWHEG +P YTHIA 8event generator is used as the nominal prediction. Data points are placed at the center of each bin. ) 2 , t 1 (tφΔ / d tt σ d ⋅ tt σ1/ 3− 10 2− 10 1− 10 1 10 2 10 Data POWHEG+Py8 POWHEG+H7 MG5_aMC@NLO+Py8 Sherpa 2.2.1 Stat. Unc. Syst. Unc.⊕Stat. ATLAS -1 = 13 TeV, 36.1 fbs Fiducial phase space ) 2 , t 1 (tφΔ 0 0.5 1 1.5 2 2.5 3 Data Prediction 0.5 1 1.5 (a) ] -1tt out [GeV / d p tt σ d ⋅ tt σ1/ 5− 10 4− 10 3− 10 2− 10 1− 10 Data POWHEG+Py8 POWHEG+H7 MG5_aMC@NLO+Py8 Sherpa 2.2.1 Stat. Unc. Syst. Unc.⊕Stat. ATLAS -1 = 13 TeV, 36.1 fbs Fiducial phase space tt out [GeV]p 0 100 200 300 400 500 600 Data Prediction 0.5 1 1.5 (b) FIG. 10. Normalized particle-level fiducial phase-space differential cross-sections as a function of (a) the azimuthal angle between the two top-quark jets Δϕt¯ tand (b) the absolute value of the out-of-plane momentum pt¯ t out. The gray bands indicate the total uncertainty in the data in each bin. The vertical bars indicate the statistical uncertainties in the theoretical models. The P OWHEG +P YTHIA 8event generator is used as the nominal prediction. Data points are placed at the center of each bin. M. AABOUD et al. PHYS. REV. D 98, 012003 (2018) 012003-16 takes into account the correlations between the measured quantities. The largest correlations at the detector-level arise from sources of uncertainty that affect all bins equally, so that the most effective comparison is made using the normalized differential cross-sections where many of the common detector-level uncertainties largely cancel. The χ2 values and associated p-values that quantify the level of agreement between the measurements and the predictions are shown in Table IV for the normalized particle-level fiducial phase-space differential cross-sections and in Table Vfor the normalized parton-level differential crosssections. * θ tt σ d ⋅ tt σ1/ 0.5 1 1.5 2 2.5 Data POWHEG+Py8 POWHEG+H7 MG5_aMC@NLO+Py8 Sherpa 2.2.1 Stat. Unc. Syst. Unc.⊕Stat. ATLAS -1 = 13 TeV, 36.1 fbs Fiducial phase space * θ / d cos cos 0 0.2 0.4 0.6 0.8 1 Data Prediction 0.8 1 1.2 (a) tt χ / d tt σ d ⋅ tt σ1/ 3− 10 2− 10 1− 10 1 10 Data POWHEG+Py8 POWHEG+H7 MG5_aMC@NLO+Py8 Sherpa 2.2.1 Stat. Unc. Syst. Unc.⊕Stat. ATLAS -1 = 13 TeV, 36.1 fbs Fiducial phase space tt χ 12 3 4 5 6 7 8 9 10 Data Prediction 0.8 1 1.2 (b) FIG. 11. Normalized particle-level fiducial phase-space differential cross-sections as a function of (a) the production angle in the Collins-Soper reference frame and (b) the variable χt¯ t. The gray bands indicate the total uncertainty in the data in each bin. The vertical bars indicate the statistical uncertainties in the theoretical models. The P OWHEG +P YTHIA 8event generator is used as the nominal prediction. Data points are placed at the center of each bin. ] -1 [GeV t T / d p tt σ d ⋅ tt σ1/ 5− 10 4− 10 3− 10 2− 10 1− 10 Data PWG+Py8 PWG+H7 MG5_aMC@NLO+Py8 Sherpa 2.2.1 Stat. Unc. Syst. Unc.⊕Stat. ATLAS -1 = 13 TeV, 36.1 fbs Parton level > 350 GeV T t,2 > 500 GeV, p T t,1 p [GeV] t T p 500 600 700 800 900 1000 1100 1200 Data Prediction 0.5 1 1.5 (a) t / d y tt σ d ⋅ tt σ1/ 0.2 0.4 0.6 0.8 1 1.2 Data PWG+Py8 PWG+H7 MG5_aMC@NLO+Py8 Sherpa 2.2.1 Stat. Unc. Syst. Unc.⊕Stat. ATLAS -1 = 13 TeV, 36.1 fbs Parton level > 350 GeV T t,2 > 500 GeV, p T t,1 p | t |y 0 0.5 1 1.5 2 Data Prediction 0.5 1 1.5 (b) FIG. 12. The normalized parton-level differential cross-sections as a function of (a) the transverse momentum and (b) the rapidity of the top quark. The orange bands indicate the total uncertainty in the data in each bin. The vertical bars indicate the statistical uncertainties in the theoretical models. The P OWHEG +P YTHIA 8event generator is used as the nominal prediction to correct for detector effects, parton showering and hadronization. Data points are placed at the center of each bin. The unfolding has required the leading topquark pT>500 GeV and the second-leading top-quark pT>350 GeV. MEASUREMENTS OF t¯ tDIFFERENTIAL …PHYS. REV. D 98, 012003 (2018) 012003-17 The particle-level differential cross-sections are generally well described by the P OWHEG +P YTHIA 8,P OWHEG +H ERWIG 7, MG5_aMC+P YTHIA 8and S HERPA event generator predictions. The t¯ tdifferential cross-section as a function of the absolute value of the leading top-quark rapidity [Fig. 7(c)] is broader in the data than the predictions of all Monte Carlo event generators. A similar effect is observed in the t¯ tsystem rapidity differential cross-section [Fig. 8(c)]. However, the p-values arising from the χ2comparisons are mostly within 0.15 to 0.55, reflecting the overall reasonable agreement of the predictions with the measured differential cross-sections. There are modest differences in the distributions of the production angle cosθ[Fig. 11(a)] and the variable χt¯ t[Fig. 11(b)], both showing p-values that are generally below 0.2. The most significant deviations are in the MG5_ A MC@NLO particle-level fiducial phase-space differential cross-sections as a function of pt¯ t T[Fig. 8(a)], Δϕt¯ t [Fig. 10(a)], and jpt¯ t outj[Fig. 10(b)] for which the MG5_aMC+P YTHIA 8MC event generator predicts a harder pt¯ t Tspectrum, a broader azimuthal opening angle differential cross-section than what is measured, and a slower decline than observed as a function of jpt¯ t outj. ] -1 [GeV t,1 T / d p tt σ d ⋅ tt σ1/ 5− 10 4− 10 3− 10 2− 10 1− 10 Data PWG+Py8 PWG+H7 MG5_aMC@NLO+Py8 Sherpa 2.2.1 Stat. Unc. Syst. Unc.⊕Stat. ATLAS -1 = 13 TeV, 36.1 fbs Parton level > 350 GeV T t,2 > 500 GeV, p T t,1 p [GeV] t,1 T p 500 600 700 800 900 1000 1100 1200 Data Prediction 0.5 1 1 . 5 (a) ] -1 [GeV t,2 T / d p tt σ d ⋅ tt σ1/ 5− 10 4− 10 3− 10 2− 10 1− 10 Data PWG+Py8 PWG+H7 MG5_aMC@NLO+Py8 Sherpa 2.2.1 Stat. Unc. Syst. Unc.⊕Stat. ATLAS -1 = 13 TeV, 36.1 fbs Parton level > 350 GeV T t,2 > 500 GeV, p T t,1 p [GeV] t,2 T p 400 600 800 1000 1200 Data Prediction 0.5 1 1 . 5 (b) | t,1 / d |y tt σ d ⋅ tt σ1/ 0 0.2 0.4 0.6 0.8 1 1.2 Data PWG+Py8 PWG+H7 MG5_aMC@NLO+Py8 Sherpa 2.2.1 Stat. Unc. Syst. Unc.⊕Stat. ATLAS -1 = 13 TeV, 36.1 fbs Parton level > 350 GeV T t,2 > 500 GeV, p T t,1 p | t,1 |y 0 0.5 1 1.5 2 Data Prediction 0.8 1 1.2 (c) | t,2 / d |y tt σ d ⋅ tt σ1/ 0 0.2 0.4 0.6 0.8 1 1.2 Data PWG+Py8 PWG+H7 MG5_aMC@NLO+Py8 Sherpa 2.2.1 Stat. Unc. Syst. Unc.⊕Stat. ATLAS -1 = 13 TeV, 36.1 fbs Parton level > 350 GeV T t,2 > 500 GeV, p T t,1 p | t,2 |y 0 0.5 1 1.5 2 Data Prediction 0.8 1 1.2 (d) FIG. 13. The normalized parton-level differential cross-sections as a function of (a) the transverse momentum of the leading top quark, (b) the transverse momentum of the second-leading top quark, (c) the absolute value of the rapidity of the leading top quark, and (d) the absolute value of the rapidity of the second-leading top quark. The orange bands indicate the total uncertainty in the data in each bin. The vertical bars indicate the statistical uncertainties in the theoretical models. The P OWHEG +P YTHIA 8event generator is used as the nominal prediction to correct for detector effects, parton showering and hadronization. Data points are placed at the center of each bin. The unfolding has required the leading top-quark pT>500 GeV and the second-leading top-quark pT>350 GeV. M. AABOUD et al. PHYS. REV. D 98, 012003 (2018) 012003-18 There is similar good agreement between the partonlevel differential cross-sections and the P OWHEG +P YTHIA 8, P OWHEG +H ERWIG 7, MG5_aMC+P YTHIA 8, and S HERPA predictions, confirming the results of the fiducial phase-space measurements, but with larger uncertainties. As shown in Fig. 14(a), the P OWHEG +P YTHIA 8and P OWHEG +H ERWIG 7event generators predict a softer pT spectrum of the t¯ tsystem, while the MG5_aMC+P YTHIA 8 event generator predicts a harder spectrum. The S HERPA event generator offers a good description of the differential cross-section behavior for pt¯ t Tin the range 100 to 500 GeV but predicts a steeper distribution for lower momenta and a higher rate for pt¯ t T>500 GeV than observed. The modeling uncertainties generally play a dominant role in determining the significance of the difference between the measurements and the nominal P OWHEG +P YTHIA 8prediction. It suggests that future work should seek the sources for this potential discrepancy, considering variations in parton shower and hadronization models as well as the matching of higher-order matrix elements with the parton shower model. In summary, all of these results are in agreement with earlier differential cross-section measurements in the t¯ t final states involving at least one lepton [7–21]. Those studies observed a “softer”pTspectrum for the top-quark final states, although the statistical and systematic ] -1 [GeV tt T / d p tt σ d ⋅ tt σ1/ 5− 10 4− 10 3− 10 2− 10 1− 10 Data PWG+Py8 PWG+H7 MG5_aMC@NLO+Py8 Sherpa 2.2.1 Stat. Unc. Syst. Unc.⊕Stat. ATLAS -1 = 13 TeV, 36.1 fbs Parton level > 350 GeV T t,2 > 500 GeV, p T t,1 p [GeV] tt T p 0 100 200 300 400 500 600 700 800 Data Prediction 0.5 1 1.5 (a) ] -1 [TeV tt / d m tt σ d ⋅ tt σ1/ 2− 10 1− 10 1 10 2 10 Data PWG+Py8 PWG+H7 MG5_aMC@NLO+Py8 Sherpa 2.2.1 Stat. Unc. Syst. Unc.⊕Stat. ATLAS -1 = 13 TeV, 36.1 fbs Parton level > 350 GeV T t,2 > 500 GeV, p T t,1 p [TeV] tt m 1 1.5 2 2.5 3 Data Prediction 0.5 1 1.5 (b) | tt / d |y tt σ d ⋅ tt σ1/ 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 Data PWG+Py8 PWG+H7 MG5_aMC@NLO+Py8 Sherpa 2.2.1 Stat. Unc. Syst. Unc.⊕Stat. ATLAS -1 = 13 TeV, 36.1 fbs Parton level > 350 GeV T t,2 > 500 GeV, p T t,1 p | tt |y 0 0.5 1 1.5 2 Data Prediction 0.8 1 1.2 (c) FIG. 14. The normalized parton-level differential cross-sections as a function of (a) the t¯ tp T, (b) the t¯ tinvariant mass, and (c) the absolute value of t¯ trapidity. The orange bands indicate the total uncertainty in the data in each bin. The vertical bars indicate the statistical uncertainties in the theoretical models. The P OWHEG +P YTHIA 8event generator is used as the nominal prediction to correct for detector effects, parton showering and hadronization. Data points are placed at the center of each bin. The unfolding has required the leading top-quark pT>500 GeV and the second-leading top-quark pT>350 GeV. MEASUREMENTS OF t¯ tDIFFERENTIAL …PHYS. REV. D 98, 012003 (2018) 012003-19 ] -1 [GeV tt T / d H tt σ d ⋅ tt σ1/ 5− 10 4− 10 3− 10 2− 10 1− 10 Data PWG+Py8 PWG+H7 MG5_aMC@NLO+Py8 Sherpa 2.2.1 Stat. Unc. Syst. Unc.⊕Stat. ATLAS -1 = 13 TeV, 36.1 fbs Parton level > 350 GeV T t,2 > 500 GeV, p T t,1 p [GeV] tt T H 1000 1200 1400 1600 1800 2000 2200 2400 Data Prediction 0.5 1 1.5 (a) tt B / d y tt σ d ⋅ tt σ1/ 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 Data PWG+Py8 PWG+H7 MG5_aMC@NLO+Py8 Sherpa 2.2.1 Stat. Unc. Syst. Unc.⊕Stat. ATLAS -1 = 13 TeV, 36.1 fbs Parton level > 350 GeV T t,2 > 500 GeV, p T t,1 p tt B y 0 0.5 1 1.5 2 Data Prediction 0.8 1 1.2 (b) FIG. 15. The normalized parton-level differential cross-sections as a function of (a) Ht¯ tand (b) yt¯ t B. The orange bands indicate the total uncertainty in the data in each bin. The vertical bars indicate the statistical uncertainties in the theoretical models. The P OWHEG +P YTHIA 8event generator is used as the nominal prediction to correct for detector effects, parton showering and hadronization. Data points are placed at the center of each bin. The unfolding has required the leading top-quark pT>500 GeV and the second-leading topquark pT>350 GeV. ) 2 , t 1 (tφΔ / d tt σ d ⋅ tt σ1/ 1 2 3 4 5 6Data PWG+Py8 PWG+H7 MG5_aMC@NLO+Py8 Sherpa 2.2.1 Stat. Unc. Syst. Unc.⊕Stat. ATLAS -1 = 13 TeV, 36.1 fbs Parton level > 350 GeV T t,2 > 500 GeV, p T t,1 p ) 2 , t 1 (tφΔ 0 0.5 1 1.5 2 2.5 3 Data Prediction 0.5 1 1.5 (a) ] -1 tt out [GeV / d p tt σ d ⋅ tt σ1/ 4− 10 3− 10 2− 10 1− 10 Data PWG+Py8 PWG+H7 MG5_aMC@NLO+Py8 Sherpa 2.2.1 Stat. Unc. Syst. Unc.⊕Stat. ATLAS -1 = 13 TeV, 36.1 fbs Parton level > 350 GeV T t,2 > 500 GeV, p T t,1 p tt out [GeV]p 0 100 200 300 400 500 600 Data Prediction 0.5 1 1.5 (b) FIG. 16. The normalized parton-level differential cross-sections as a function of (a) Δϕðt1;t 2Þand (b) jpt¯ t outj. The orange bands indicate the total uncertainty in the data in each bin. The vertical bars indicate the statistical uncertainties in the theoretical models. The P OWHEG +P YTHIA 8event generator is used as the nominal prediction to correct for detector effects, parton showering, and hadronization. Data points are placed at the center of each bin. The unfolding has required the leading top-quark pT>500 GeV and the second-leading top-quark pT>350 GeV. M. AABOUD et al. PHYS. REV. D 98, 012003 (2018) 012003-20 * θ / d cos tt σ d ⋅ tt σ1/ 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 Data PWG+Py8 PWG+H7 MG5_aMC@NLO+Py8 Sherpa 2.2.1 Stat. Unc. Syst. Unc.⊕Stat. ATLAS -1 = 13 TeV, 36.1 fbs Parton level > 350 GeV T t,2 > 500 GeV, p T t,1 p * θcos 0 0.2 0.4 0.6 0.8 1 Data Prediction 0.8 1 1.2 (a) tt χ / d tt σ d ⋅ tt σ1/ 3− 2− 10 1− 10 1 10 Data PWG+Py8 PWG+H7 MG5_aMC@NLO+Py8 Sherpa 2.2.1 Stat. Unc. Syst. Unc.⊕Stat. ATLAS -1 = 13 TeV, 36.1 fbs Parton level > 350 GeV T t,2 > 500 GeV, p T t,1 p tt χ 12 3 4 5 6 7 8 9 10 Data Prediction 0.8 1 1.2 (b) 10 FIG. 17. The normalized parton-level differential cross-sections as a function of (a) cos θand (b) χt¯ t. The orange bands indicate the total uncertainty in the data in each bin. The vertical bars indicate the statistical uncertainties in the theoretical models. The P OWHEG +P YTHIA 8event generator is used as the nominal prediction to correct for detector effects, parton showering, and hadronization. Data points are placed at the center of each bin. The unfolding has required the leading top-quark pT>500 GeV and the second-leading topquark pT>350 GeV. Inclusive fiducial cross-section [fb] 200 300 400 500 600 700 800 PDF Unc.)⊕ Scale ⊕Nominal (Th. Stat. POWHEG+Pythia8 , NNPDF 3.0 NLO, A14 top =1.5m damp h Alternative PDF (Th. Stat. Unc.) POWHEG+Pythia8 , MMHT2014, A14 top =1.5m damp h POWHEG+Pythia8 , CT14, A14 top =1.5m damp h POWHEG+Pythia8 , PDF4LHC15, A14 top =1.5m damp h Alternative ISR/FSR (Th. Stat. Unc.) POWHEG+Pythia8 (less IFSR) =2, NNPDF 3.0 NLO, A14v3cDo R μ=2 F μ , top =1.5m damp h POWHEG+Pythia8 (more IFSR) =0.5, NNPDF 3.0 NLO, A14v3cUp R μ=0.5 F μ , top =3.0m damp h Alternative ME/PS (Th. Stat. Unc.) POWHEG+Herwig7 , NNPDF 3.0 NLO, H7UE top =1.5m damp h MG5_aMC@NLO+Pythia8 NNPDF 3.0 NLO, A14 Sherpa 2.2.1 NNPDF 3.0 NNLO ATLAS -1 = 13 TeV, 36.1 fbs Stat. Unc. Det. Syst. Unc.⊕Stat. Mod. Syst. Unc.⊕ Det. ⊕Stat. FIG. 18. Particle-level fiducial phase-space cross-section. The shaded (blue) bands indicate the statistical, detector, and modeling uncertainties in the measurement. The P OWHEG +P YTHIA 8event generator is used as the nominal prediction to correct for detector effects. The uncertainty associated with the P OWHEG +P YTHIA 8signal model is the sum in quadrature of statistical, scale, and PDF uncertainties as well as the uncertainty in the inclusive cross-section prediction. Other predictions show only the statistical uncertainty of the MC sample. MEASUREMENTS OF t¯ tDIFFERENTIAL …PHYS. REV. D 98, 012003 (2018) 012003-21 uncertainties for top quarks with pT>500 GeV are larger than the measurements reported here. Together, the previous measurements and these results provide a coherent picture that the current NLO Monte Carlo models for t¯ t production and decay overestimate the production of highly boosted top quarks. X. CONCLUSION Measurements of differential cross-sections of highly boosted pair-produced top quarks in 13 TeV pp collisions are presented in a data sample of 36.1fb−1collected by the ATLAS detector at the LHC. The top-quark pairs are TABLE IV. Comparison between the measured normalized particle-level fiducial phase-space differential cross-sections and the predictions from several SM event generators. For each variable and prediction, a χ2and a p-value are calculated using the covariance matrix described in the text, which includes all sources of uncertainty. The number of degrees of freedom is equal to Nb−1, where Nbis the number of bins in the distribution. PWG+PY8 A MC@NLO+PY8PWG+H7 PWG+PY8 (more IFSR) PWG+PY8 (less IFSR) S HERPA 2.2.1 Observable χ2=NDF p-value χ2=NDF p-value χ2=NDF p-value χ2=NDF p-value χ2=NDF p-value χ2=NDF p-value pt;1 T7.7=70.36 8.2=70.32 8.0=70.33 9.1=70.24 8.7=70.27 9.3=70.23 jyt;1j7.5=50.18 12.2=50.03 6.8=50.24 8.8=50.12 8.1=50.15 4.0=50.55 pt;2 T8.6=60.20 2.6=60.86 9.9=60.13 12.2=60.06 5.0=60.54 5.0=60.55 jyt;2j3.7=50.59 4.6=50.46 3.1=50.68 3.5=50.63 3.2=50.67 2.9=50.72 mt¯ t4.5=90.88 4.7=90.86 4.0=90.91 5.3=90.81 5.2=90.82 10.0=90.35 pt¯ t T7.8=50.17 20.9=5<0.01 12.6=50.03 15.0=50.01 1.9=50.86 1.9=50.87 jyt¯ tj1.1=50.95 2.2=50.83 0.9=50.97 0.8=50.98 1.8=50.88 1.7=50.89 χt¯ t14.2=60.03 12.7=60.05 13.6=60.03 16.9=6<0.01 10.1=60.12 18.5=6<0.01 yt¯ t B2.5=60.87 3.3=60.77 2.2=60.90 2.6=60.86 2.8=60.84 3.0=60.81 jpt¯ t outj1.9=60.93 53.1=6<0.01 3.1=60.80 4.2=60.64 4.8=60.57 5.9=60.44 Δϕt¯ t0.9=30.84 16.3=3<0.01 2.0=30.58 3.0=30.40 0.6=30.89 3.4=30.33 Ht¯ t T4.8=60.57 5.2=60.52 4.5=60.61 5.0=60.54 5.0=60.55 3.1=60.80 cos θ⋆9.9=50.08 10.5=50.06 9.3=50.10 12.8=50.03 6.5=50.26 18.7=5<0.01 TABLE V. Comparison between the measured normalized parton-level differential cross-sections and the predictions from several MC event generators. For each variable and prediction, a χ2and a p-value are calculated using the covariance matrix described in the text, which includes all sources of uncertainty. The number of degrees of freedom is equal to Nb−1, where Nbis the number of bins in the distribution. PWG+PY8 A MC@NLO+PY8PWG+H7 PWG+PY8 (more IFSR) PWG+PY8 (less IFSR) S HERPA 2.2.1 Observable χ2=NDF p-value χ2=NDF p-value χ2=NDF p-value χ2=NDF p-value χ2=NDF p-value χ2=NDF p-value pt T3.7=60.72 4.5=60.61 4.0=60.67 3.9=60.69 4.0=60.68 4.3=60.64 jytj4.3=70.75 4.1=70.77 4.0=70.78 4.4=70.73 4.3=70.74 5.3=70.62 pt;1 T5.9=70.55 7.0=70.43 5.9=70.55 6.4=70.50 6.2=70.52 7.6=70.37 jyt;1j5.5=70.60 8.3=70.31 5.1=70.65 5.9=70.55 5.5=70.60 4.7=70.70 pt;2 T5.7=60.46 2.8=60.83 6.1=60.41 4.6=60.60 7.4=60.29 7.0=60.32 jyt;2j4.4=70.73 5.1=70.65 4.2=70.76 4.4=70.73 4.3=70.74 5.9=70.55 mt¯ t4.0=90.91 3.7=90.93 3.9=90.92 3.9=90.92 4.3=90.89 4.6=90.86 pt¯ t T5.1=70.65 7.0=70.42 6.2=70.52 3.7=70.81 6.8=70.45 30.1=7<0.01 yt¯ t1.8=70.97 2.9=70.90 2.0=70.96 2.0=70.96 1.9=70.97 4.2=70.76 χt¯ t7.9=60.24 5.0=60.55 7.3=60.29 6.4=60.38 9.0=60.17 7.6=60.27 yt¯ t B1.0=60.99 1.4=60.96 1.0=60.98 1.1=60.98 1.0=60.99 1.0=60.99 jpt¯ t outj1.7=60.94 16.9=6<0.01 1.2=60.98 1.9=60.93 2.7=60.84 3.9=60.69 Δϕt¯ t0.5=30.93 13.1=3<0.01 0.7=30.87 0.1=31.00 1.1=30.78 0.2=30.98 Ht¯ t T5.2=90.81 5.7=90.77 7.4=90.60 6.9=90.64 5.6=90.78 5.9=90.75 cos θ⋆5.5=50.35 3.2=50.66 5.3=50.38 5.0=50.42 6.2=50.29 7.8=50.17 M. AABOUD et al. PHYS. REV. D 98, 012003 (2018) 012003-22 observed in their all-hadronic decay modes. With a combination of top-tagging and b-tagging techniques, an event sample with a t¯ tsignal-to-background ratio of approximately 3-to-1 is selected. Because most of the decay products of the top quarks are observed in a large-Rjet, the kinematics of the top quarks and the t¯ tsystem are well measured compared with final states involving energetic neutrinos. The measurements are corrected to a fiducial phase space and normalized to the total cross-section for events with leading top quarks with pT>500 GeV and second-leading top quarks with pT>350 GeV. Partonlevel differential cross-sections are also determined. The leading and second-leading top-quark pTdifferential cross-sections fall by 2 orders of magnitude over the pTrange from 500 GeV to 1 TeV. The top-quark rapidity distributions show a plateau out to jytj∼0.6and then fall rapidly, reflecting the central production of these top-quark pairs. The measurements show that the t¯ tsystem is produced centrally with limited transverse momentum, though events are observed up to a pt¯ t Tof 500 GeV. The normalized differential cross-sections are compared with several Standard Model predictions for highly boosted pair-produced top quarks, and there is generally good agreement of the predictions with the particle-level and parton-level differential results. In particular, the P OWHEG +P YTHIA 8,P OWHEG +H ERWIG 7and S HERPA predictions are consistent with the observed differential cross-sections at particle level and parton level. The most significant discrepancy is in the aMC+P YTHIA 8predictions for the kinematics of the t¯ tsystem. Qualitatively, both particleand parton-level rapidity distributions of the leading top quark and of the t¯ tsystem are broader in the data compared with the Monte Carlo generator predictions. Also, there are more modest differences between predicted and observed differential cross-sections as a function of the production angle cosθand the variable χt¯ t. The cross-section for t¯ tproduction in the particle-level fiducial phase space is 292 7ðstatÞ71ðsystÞfb, which can be compared with the P OWHEG +P YTHIA 8prediction of 384 36 fb, where the total cross-section has been calculated up to NNLO þNNLL corrections. Improvements in this measurement will come from a better understanding of the models of t¯ tproduction that are the source of the modeling uncertainties. This analysis shows that studies of boosted top-quark jets can be done with good efficiency and signal-to-background ratios in the all-hadronic channel. This creates opportunities for more detailed studies of high-pTStandard Model processes, and provides data to test and improve models of t¯ tproduction. ACKNOWLEDGMENTS We thank CERN for the very successful operation of the LHC,aswell asthesupportstafffromourinstitutionswithout 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, andMPG,Germany;GSRT,Greece;RGC,HongKongSAR, China; ISF, I-CORE and Benoziyo Center, Israel; INFN, Italy; MEXT and JSPS, Japan; CNRST, Morocco; NWO, Netherlands; RCN, Norway; MNiSW and NCN, Poland; FCT, Portugal; MNE/IFA, Romania; MES of Russia and NRC KI, Russian 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, United Kingdom; DOE and NSF, United States of America. In addition, individual groups and members have received support from BCKDF, the Canada Council, CANARIE, CRC, Compute Canada, FQRNT, and the Ontario Innovation Trust, Canada; EPLANET, ERC, ERDF, FP7, Horizon 2020 and Marie Skłodowska-Curie Actions, European Union; Investissements d’Avenir Labex and Idex, ANR, R´egion Auvergne and Fondation Partager le Savoir, France; DFG and AvH Foundation, Germany; Herakleitos, Thales and Aristeia programmes co-financed by EU-ESF and the Greek NSRF; BSF, GIF and Minerva, Israel; BRF, Norway; CERCA Programme Generalitat de Catalunya, Generalitat Valenciana, Spain; the Royal Society and Leverhulme Trust, United Kingdom. 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Zwalinski32 (ATLAS Collaboration) 1Department of Physics, University of Adelaide, Adelaide, Australia 2Physics Department, SUNY Albany, Albany, New York, USA 3Department of Physics, University of Alberta, Edmonton, Alberta, Canada 4aDepartment of Physics, Ankara University, Ankara, Turkey 4bIstanbul Aydin University, Istanbul, Turkey 4cDivision of Physics, TOBB University of Economics and Technology, Ankara, Turkey 5LAPP, University of Grenoble Alpes, University of Savoie Mont Blanc, CNRS/IN2P3, Annecy, France 6High Energy Physics Division, Argonne National Laboratory, Argonne, Illinois, USA 7Department of Physics, University of Arizona, Tucson, Arizona, USA 8Department of Physics, The University of Texas at Arlington, Arlington, Texas, USA 9Physics Department, National and Kapodistrian University of Athens, Athens, Greece 10Physics Department, National Technical University of Athens, Zografou, Greece 11Department of Physics, The University of Texas at Austin, Austin, Texas, USA 12Institute of Physics, Azerbaijan Academy of Sciences, Baku, Azerbaijan 13Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Barcelona, Spain 14Institute of Physics, University of Belgrade, Belgrade, Serbia 15Department for Physics and Technology, University of Bergen, Bergen, Norway 16Physics Division, Lawrence Berkeley National Laboratory and University of California, Berkeley, California, USA 17Department of Physics, Humboldt University, Berlin, Germany 18Albert Einstein Center for Fundamental Physics and Laboratory for High Energy Physics, University of Bern, Bern, Switzerland 19School of Physics and Astronomy, University of Birmingham, Birmingham, United Kingdom 20aDepartment of Physics, Bogazici University, Istanbul, Turkey 20bDepartment of Physics Engineering, Gaziantep University, Gaziantep, Turkey 20dIstanbul Bilgi University, Faculty of Engineering and Natural Sciences, Istanbul, Turkey 20eBahcesehir University, Faculty of Engineering and Natural Sciences, Istanbul, Turkey 21Centro de Investigaciones, Universidad Antonio Narino, Bogota, Colombia 22aINFN Sezione di Bologna, Italy 22bDipartimento di Fisica e Astronomia, Universit`a di Bologna, Bologna, Italy 23Physikalisches Institut, University of Bonn, Bonn, Germany 24Department of Physics, Boston University, Boston, Massachusetts, USA 25Department of Physics, Brandeis University, Waltham, Massachusetts, USA 26aUniversidade Federal do Rio De Janeiro COPPE/EE/IF, Rio de Janeiro, Brazil 26bElectrical Circuits Department, Federal University of Juiz de Fora (UFJF), Juiz de Fora, Brazil 26cFederal University of Sao Joao del Rei (UFSJ), Sao Joao del Rei, Brazil 26dInstituto de Fisica, Universidade de Sao Paulo, Sao Paulo, Brazil 27Physics Department, Brookhaven National Laboratory, Upton, New York, USA 28aTransilvania University of Brasov, Brasov, Romania 28bHoria Hulubei National Institute of Physics and Nuclear Engineering, Romania 28cDepartment of Physics, Alexandru Ioan Cuza University of Iasi, Iasi, Romania 28dNational Institute for Research and Development of Isotopic and Molecular Technologies, Physics Department, Cluj Napoca, Romania 28eUniversity Politehnica Bucharest, Bucharest, Romania 28fWest University in Timisoara, Timisoara, Romania 29Departamento de Física, Universidad de Buenos Aires, Buenos Aires, Argentina 30Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom 31Department of Physics, Carleton University, Ottawa, Ontario, Canada M. AABOUD et al. PHYS. REV. D 98, 012003 (2018) 012003-34 32CERN, Geneva, Switzerland 33Enrico Fermi Institute, University of Chicago, Chicago, Illinois, USA 34aDepartamento de Física, Pontificia Universidad Católica de Chile, Santiago, Chile 34bDepartamento de Física, Universidad T´ecnica Federico Santa María, Valparaíso, Chile 35aInstitute of High Energy Physics, Chinese Academy of Sciences, Beijing, China 35bDepartment of Physics, Nanjing University, Jiangsu, China 35cPhysics Department, Tsinghua University, Beijing, China 35dUniversity of Chinese Academy of Science (UCAS), Beijing, China 36aSchool of Physics, Shandong University, Shandong, China 36bSchool of Physics and Astronomy, Key Laboratory for Particle Physics, Astrophysics and Cosmology, Ministry of Education; Shanghai Key Laboratory for Particle Physics and Cosmology, Shanghai Jiao Tong University, Shanghai, China 36cDepartment of Modern Physics and State Key Laboratory of Particle Detection and Electronics, University of Science and Technology of China, Anhui, China 37Universit´e Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France 38Nevis Laboratory, Columbia University, Irvington, New York, USA 39Niels Bohr Institute, University of Copenhagen, Kobenhavn, Denmark 40aINFN Gruppo Collegato di Cosenza, Laboratori Nazionali di Frascati, Cosenza, Italy 40bDipartimento di Fisica, Universit`a della Calabria, Rende, Italy 41aAGH University of Science and Technology, Faculty of Physics and Applied Computer Science, Krakow, Poland 41bMarian Smoluchowski Institute of Physics, Jagiellonian University, Krakow, Poland 42Institute of Nuclear Physics Polish Academy of Sciences, Krakow, Poland 43Physics Department, Southern Methodist University, Dallas, Texas, USA 44Physics Department, University of Texas at Dallas, Richardson, Texas, USA 45DESY, Hamburg and Zeuthen, Germany 46Lehrstuhl für Experimentelle Physik IV, Technische Universität Dortmund, Dortmund, Germany 47Institut für Kern-und Teilchenphysik, Technische Universität Dresden, Dresden, Germany 48Department of Physics, Duke University, Durham, North Carolina, USA 49SUPA–School of Physics and Astronomy, University of Edinburgh, Edinburgh, United Kingdom 50INFN e Laboratori Nazionali di Frascati, Frascati, Italy 51Fakultät für Mathematik und Physik, Albert-Ludwigs-Universität, Freiburg, Germany 52Departement de Physique Nucleaire et Corpusculaire, Universit´e de Gen`eve, Geneva, Switzerland 53aINFN Sezione di Genova, Genova, Italy 53bDipartimento di Fisica, Universit`a di Genova, Genova, Italy 54aE. Andronikashvili Institute of Physics, Iv. Javakhishvili Tbilisi State University, Tbilisi, Georgia 54bHigh Energy Physics Institute, Tbilisi State University, Tbilisi, Georgia 55II. Physikalisches Institut, Justus-Liebig-Universit Germany, Giessen, Germany 56SUPA–School of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom 57LPSC, Universit´e Grenoble Alpes, CNRS-IN2P3, Grenoble INP, Grenoble, France 58II Physikalisches Institut, Georg-August-Universität, Göttingen, Germany 59Laboratory for Particle Physics and Cosmology, Harvard University, Cambridge, Massachusetts, USA 60aKirchhoff-Institut für Physik, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany 60bPhysikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany 61Faculty of Applied Information Science, Hiroshima Institute of Technology, Hiroshima, Japan 62aDepartment of Physics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong, China 62bDepartment of Physics, The University of Hong Kong, Hong Kong, China 62cDepartment of Physics and Institute for Advanced Study, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China 63Department of Physics, National Tsing Hua University, Hsinchu, Taiwan 64Department of Physics, Indiana University, Bloomington, Indiana, USA 65Institut für Astro-und Teilchenphysik, Leopold-Franzens-Universität, Innsbruck, Austria 66University of Iowa, Iowa City, Iowa, USA 67Department of Physics and Astronomy, Iowa State University, Ames Iowa, USA 68Joint Institute for Nuclear Research, JINR Dubna, Dubna, Russia 69KEK, High Energy Accelerator Research Organization, Tsukuba, Japan 70Graduate School of Science, Kobe University, Kobe, Japan 71Faculty of Science, Kyoto University, Kyoto, Japan 72Kyoto University of Education, Kyoto, Japan MEASUREMENTS OF t¯ tDIFFERENTIAL …PHYS. REV. D 98, 012003 (2018) 012003-35 73Research Center for Advanced Particle Physics and Department of Physics, Kyushu University, Fukuoka, Japan 74Instituto de Física La Plata, Universidad Nacional de La Plata and CONICET, La Plata, Argentina 75Physics Department, Lancaster University, Lancaster, United Kingdom 76aINFN Sezione di Lecce, Lecce, Italy 76bDipartimento di Matematica e Fisica, Universit`a del Salento, Lecce, Italy 77Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom 78Department of Experimental Particle Physics, Jožef Stefan Institute and Department of Physics, University of Ljubljana, Ljubljana, Slovenia 79School of Physics and Astronomy, Queen Mary University of London, London, United Kingdom 80Department of Physics, Royal Holloway University of London, Surrey, United Kingdom 81Department of Physics and Astronomy, University College London, London, United Kingdom 82Louisiana Tech University, Ruston, Louisiana, USA 83Laboratoire de Physique Nucl´eaire et de Hautes Energies, UPMC and Universit´e Paris-Diderot and CNRS/IN2P3, Paris, France 84Fysiska institutionen, Lunds universitet, Lund, Sweden 85Departamento de Fisica Teorica C-15 and CIAFF, Universidad Autonoma de Madrid, Madrid, Spain 86Institut für Physik, Universität Mainz, Mainz, Germany 87School of Physics and Astronomy, University of Manchester, Manchester, United Kingdom 88CPPM, Aix-Marseille Universit´e and CNRS/IN2P3, Marseille, France 89Department of Physics, University of Massachusetts, Amherst, Massachusetts, USA 90Department of Physics, McGill University, Montreal, Quebec, Canada 91School of Physics, University of Melbourne, Victoria, Australia 92Department of Physics, The University of Michigan, Ann Arbor, Michigan, USA 93Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan, USA 94aINFN Sezione di Milano, Milano, Italy 94bDipartimento di Fisica, Universit`a di Milano, Milano, Italy 95B.I. Stepanov Institute of Physics, National Academy of Sciences of Belarus, Minsk, Republic of Belarus 96Research Institute for Nuclear Problems of Byelorussian State University, Minsk, Republic of Belarus 97Group of Particle Physics, University of Montreal, Montreal, Quebec, Canada 98P.N. Lebedev Physical Institute of the Russian Academy of Sciences, Moscow, Russia 99Institute for Theoretical and Experimental Physics (ITEP), Moscow, Russia 100National Research Nuclear University MEPhI, Moscow, Russia 101D.V. Skobeltsyn Institute of Nuclear Physics, M.V. Lomonosov Moscow State University, Moscow, Russia 102Fakultät für Physik, Ludwig-Maximilians-Universität München, München, Germany 103Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), München, Germany 104Nagasaki Institute of Applied Science, Nagasaki, Japan 105Graduate School of Science and Kobayashi-Maskawa Institute, Nagoya University, Nagoya, Japan 106aINFN Sezione di Napoli, Napoli, Italy 106bDipartimento di Fisica, Universit`a di Napoli, Napoli, Italy 107Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico, USA 108Institute for Mathematics, Astrophysics and Particle Physics, Radboud University Nijmegen/Nikhef, Nijmegen, Netherlands 109Nikhef National Institute for Subatomic Physics and University of Amsterdam, Amsterdam, Netherlands 110Department of Physics, Northern Illinois University, DeKalb, Illinois, USA 111Budker Institute of Nuclear Physics, SB RAS, Novosibirsk, Russia 112Department of Physics, New York University, New York, New York, USA 113The Ohio State University, Columbus, Ohio, USA 114Faculty of Science, Okayama University, Okayama, Japan 115Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma, Norman, Oklahoma, USA 116Department of Physics, Oklahoma State University, Stillwater, Oklahoma, USA 117Palacký University, RCPTM, Olomouc, Czech Republic 118Center for High Energy Physics, University of Oregon, Eugene, Oregon, USA 119LAL, Univ. Paris-Sud, CNRS/IN2P3, Universit´e Paris-Saclay, Orsay, France 120Graduate School of Science, Osaka University, Osaka, Japan 121Department of Physics, University of Oslo, Oslo, Norway 122Department of Physics, Oxford University, Oxford, United Kingdom 123aINFN Sezione di Pavia, Pavia, Italy M. AABOUD et al. PHYS. REV. D 98, 012003 (2018) 012003-36 123bDipartimento di Fisica, Universit`a di Pavia, Pavia, Italy 124Department of Physics, University of Pennsylvania, Philadelphia, Pennsylvania, USA 125National Research Centre “Kurchatov Institute”B.P.Konstantinov Petersburg Nuclear Physics Institute, St. Petersburg, Russia 126aINFN Sezione di Pisa, Pisa, Italy 126bDipartimento di Fisica E. Fermi, Universit`a di Pisa, Pisa, Italy 127Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania, USA 128aLaboratório de Instrumentação e Física Experimental de Partículas–LIP, Lisboa, Portugal 128bFaculdade de Ciências, Universidade de Lisboa, Lisboa, Portugal 128cDepartment of Physics, University of Coimbra, Coimbra, Portugal 128dCentro de Física Nuclear da Universidade de Lisboa, Lisboa, Portugal 128eDepartamento de Fisica, Universidade do Minho, Braga, Portugal 128fDepartamento de Fisica Teorica y del Cosmos, Universidad de Granada, Granada (Spain), Spain 128gDep Fisica and CEFITEC of Faculdade de Ciencias e Tecnologia, Universidade Nova de Lisboa, Caparica, Portugal 129Institute of Physics, Academy of Sciences of the Czech Republic, Praha, Czech Republic 130Czech Technical University in Prague, Praha, Czech Republic 131Charles University, Faculty of Mathematics and Physics, Prague, Czech Republic 132State Research Center Institute for High Energy Physics (Protvino), NRC KI, Russia 133Particle Physics Department, Rutherford Appleton Laboratory, Didcot, United Kingdom 134aINFN Sezione di Roma, Roma, Italy 134bDipartimento di Fisica, Sapienza Universit`a di Roma, Roma, Italy 135aINFN Sezione di Roma Tor Vergata, Roma, Italy 135bDipartimento di Fisica, Universit`a di Roma Tor Vergata, Roma, Italy 136aINFN Sezione di Roma Tre, Roma, Italy 136bDipartimento di Matematica e Fisica, Universit`a Roma Tre, Roma, Italy 137aFacult´e des Sciences Ain Chock, R´eseau Universitaire de Physique des Hautes Energies–Universit´e Hassan II, Casablanca, Morocco 137bCentre National de l’Energie des Sciences Techniques Nucleaires, Rabat, Morocco 137cFacult´e des Sciences Semlalia, Universit´e Cadi Ayyad, LPHEA-Marrakech, Morocco 137dFacult´e des Sciences, Universit´e Mohamed Premier and LPTPM, Oujda, Morocco 137eFacult´e des sciences, Universit´e Mohammed V, Rabat, Morocco 138Institut de Recherches sur les Lois Fondamentales de l’Univers, DSM/IRFU, CEA Saclay, Gif-sur-Yvette, France 139Santa Cruz Institute for Particle Physics, University of California Santa Cruz, Santa Cruz, California, USA 140Department of Physics, University of Washington, Seattle, Washington, USA 141Department of Physics and Astronomy, University of Sheffield, Sheffield, United Kingdom 142Department of Physics, Shinshu University, Nagano, Japan 143Department Physik, Universität Siegen, Siegen, Germany 144Department of Physics, Simon Fraser University, Burnaby, British Columbia, Canada 145SLAC National Accelerator Laboratory, Stanford, California, USA 146aFaculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovak Republic 146bDepartment of Subnuclear Physics, Institute of Experimental Physics of the Slovak Academy of Sciences, Kosice, Slovak Republic 147aDepartment of Physics, University of Cape Town, Cape Town, South Africa 147bDepartment of Mechanical Engineering Science, University of Johannesburg, Johannesburg, South Africa 147cSchool of Physics, University of the Witwatersrand, Johannesburg, South Africa 148aDepartment of Physics, Stockholm UniversityStockholm, Sweden 148bThe Oskar Klein Centre, Stockholm, Sweden 149Physics Department, Royal Institute of Technology, Stockholm, Sweden 150Departments of Physics and Astronomy, Stony Brook University, Stony Brook, New York, USA 151Department of Physics and Astronomy, University of Sussex, Brighton, United Kingdom 152School of Physics, University of Sydney, Sydney, Australia 153Institute of Physics, Academia Sinica, Taipei, Taiwan 154Department of Physics, Technion: Israel Institute of Technology, Haifa, Israel 155Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv, Israel 156Department of Physics, Aristotle University of Thessaloniki, Thessaloniki, Greece MEASUREMENTS OF t¯ tDIFFERENTIAL …PHYS. REV. D 98, 012003 (2018) 012003-37 157International Center for Elementary Particle Physics and Department of Physics, The University of Tokyo, Tokyo, Japan 158Graduate School of Science and Technology, Tokyo Metropolitan University, Tokyo, Japan 159Department of Physics, Tokyo Institute of Technology, Tokyo, Japan 160Tomsk State University, Tomsk, Russia 161Department of Physics, University of Toronto, Toronto, Ontario, Canada 162aINFN-TIFPA, Trento, Italy 162bUniversity of Trento, Trento, Italy 163aTRIUMF, Vancouver, British Columbia, Canada 163bDepartment of Physics and Astronomy, York University, Toronto, Ontario, Canada 164Division of Physics and Tomonaga Center for the History of the Universe, Faculty of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Japan 165Department of Physics and Astronomy, Tufts University, Medford, Massachusetts, USA 166Department of Physics and Astronomy, University of California Irvine, Irvine, California, USA 167aINFN Gruppo Collegato di Udine, Sezione di Trieste, Udine, Italy 167bICTP, Trieste, Italy 167cDipartimento di Chimica, Fisica e Ambiente, Universit`a di Udine, Udine, Italy 168Department of Physics and Astronomy, University of Uppsala, Uppsala, Sweden 169Department of Physics, University of Illinois, Urbana, Illinois, USA 170Instituto de Fisica Corpuscular (IFIC), Centro Mixto Universidad de Valencia–CSIC, Spain 171Department of Physics, University of British Columbia, Vancouver, British Columbia, Canada 172Department of Physics and Astronomy, University of Victoria, Victoria, British Columbia, Canada 173Department of Physics, University of Warwick, Coventry, United Kingdom 174Waseda University, Tokyo, Japan 175Department of Particle Physics, The Weizmann Institute of Science, Rehovot, Israel 176Department of Physics, University of Wisconsin, Madison, Wisconsin, USA 177Fakultät für Mathematik und Naturwissenschaften, Fachgruppe Physik, Bergische Universität Wuppertal, Wuppertal, Germany 178Fakultät für Physik und Astronomie, Julius-Maximilians-Universität, Würzburg, Germany 179Department of Physics, Yale University, New Haven, Connecticut, USA 180Yerevan Physics Institute, Yerevan, Armenia 181Centre de Calcul de l’Institut National de Physique Nucl´eaire et de Physique des Particules (IN2P3), Villeurbanne, France 182Academia Sinica Grid Computing, Institute of Physics, Academia Sinica, Taipei, Taiwan aDeceased. bAlso at Department of Physics, King’s College London, London, United Kingdom. cAlso at Institute of Physics, Azerbaijan Academy of Sciences, Baku, Azerbaijan. dAlso at Novosibirsk State University, Novosibirsk, Russia. eAlso at TRIUMF, Vancouver, British Columbia, Canada. fAlso at Department of Physics and Astronomy, University of Louisville, Louisville, KY, USA. gAlso at Department of Physics, California State University, Fresno, CA, USA. hAlso at Department of Physics, University of Fribourg, Fribourg, Switzerland. iAlso at II Physikalisches Institut, Georg-August-Universität, Göttingen, Germany. jAlso at Departament de Fisica de la Universitat Autonoma de Barcelona, Barcelona, Spain. kAlso at Tomsk State University, Tomsk, and Moscow Institute of Physics and Technology State University, Dolgoprudny, Russia. lAlso at The Collaborative Innovation Center of Quantum Matter (CICQM), Beijing, China. mAlso at Universita di Napoli Parthenope, Napoli, Italy. nAlso at Institute of Particle Physics (IPP), Canada. oAlso at Dipartimento di Fisica E. Fermi, Universit`a di Pisa, Pisa, Italy. pAlso at Horia Hulubei National Institute of Physics and Nuclear Engineering, Romania. qAlso at CPPM, Aix-Marseille Universit´e and CNRS/IN2P3, Marseille, France. rAlso at Department of Physics, St. Petersburg State Polytechnical University, St. Petersburg, Russia. sAlso at Borough of Manhattan Community College, City University of New York, New York City, NY, USA. tAlso at Department of Financial and Management Engineering, University of the Aegean, Chios, Greece. uAlso at Centre for High Performance Computing, CSIR Campus, Rosebank, Cape Town, South Africa. vAlso at Louisiana Tech University, Ruston, LA, USA. wAlso at Institucio Catalana de Recerca i Estudis Avancats, ICREA, Barcelona, Spain. xAlso at Department of Physics, The University of Michigan, Ann Arbor, MI, USA. yAlso at LAL, Univ. Paris-Sud, CNRS/IN2P3, Universit´e Paris-Saclay, Orsay, France. M. AABOUD et al. PHYS. REV. D 98, 012003 (2018) 012003-38 zAlso at Graduate School of Science, Osaka University, Osaka, Japan. aaAlso at Fakultät für Mathematik und Physik, Albert-Ludwigs-Universität, Freiburg, Germany. bbAlso at Institute for Mathematics, Astrophysics and Particle Physics, Radboud University Nijmegen/Nikhef, Nijmegen, Netherlands. ccAlso at Department of Physics, The University of Texas at Austin, Austin, TX, USA. ddAlso at Near East University, Nicosia, North Cyprus, Mersin 10, Turkey. eeAlso at Institute of Theoretical Physics, Ilia State University, Tbilisi, Georgia. ffAlso at CERN, Geneva, Switzerland. ggAlso at Georgian Technical University (GTU), Tbilisi, Georgia. hhAlso at Ochadai Academic Production, Ochanomizu University, Tokyo, Japan. iiAlso at Manhattan College, New York, NY, USA. jjAlso at The City College of New York, New York, NY, USA. kkAlso at Departamento de Fisica Teorica y del Cosmos, Universidad de Granada, Granada (Spain), Spain. llAlso at Department of Physics, California State University, Sacramento, CA, USA. mmAlso at Moscow Institute of Physics and Technology State University, Dolgoprudny, Russia. nnAlso at Departement de Physique Nucleaire et Corpusculaire, Universit´e de Gen`eve, Geneva, Switzerland. ooAlso at Institut de Física d’Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Barcelona, Spain. ppAlso at School of Physics, Sun Yat-sen University, Guangzhou, China. qqAlso at Institute for Nuclear Research and Nuclear Energy (INRNE) of the Bulgarian Academy of Sciences, Sofia, Bulgaria. rrAlso at Faculty of Physics, M.V.Lomonosov Moscow State University, Moscow, Russia. ssAlso at National Research Nuclear University MEPhI, Moscow, Russia. ttAlso at Department of Physics, Stanford University, Stanford, CA, USA. uuAlso at Institute for Particle and Nuclear Physics, Wigner Research Centre for Physics, Budapest, Hungary. vvAlso at Giresun University, Faculty of Engineering, Turkey. wwAlso at Department of Physics, Nanjing University, Jiangsu, China. xxAlso at Institute of Physics, Academia Sinica, Taipei, Taiwan. yyAlso at University of Malaya, Department of Physics, Kuala Lumpur, Malaysia. MEASUREMENTS OF t¯ tDIFFERENTIAL …PHYS. REV. D 98, 012003 (2018) 012003-39