Measurements of differential cross-sections in top-quark pair events with a high transverse momentum top quark and limits on beyond the Standard Model contributions to top-quark pair production with the ATLAS detector at root s=13 TeV

JHEP06(2022)063 Published for SISSA by Springer Received:February 25, 2022 Accepted:May 9, 2022 Published:June 13, 2022 Measurements of differential cross-sections in top-quark pair events with a high transverse momentum top quark and limits on beyond the Standard Model contributions to top-quark pair production with the ATLAS detector at √s= 13 TeV The ATLAS collaboration Abstract: Cross-section measurements of top-quark pair production where the hadronically decaying top quark has transverse momentum greater than 355 GeV and the other top quark decays into `νb are presented using 139 fb−1of data collected by the ATLAS experiment during proton-proton collisions at the LHC. The fiducial cross-section at √s= 13 TeV is measured to be σ= 1.267 ±0.005 ±0.053 pb, where the uncertainties reflect the limited number of data events and the systematic uncertainties, giving a total uncertainty of 4.2%. The cross-section is measured differentially as a function of variables characterising the t¯ tsystem and additional radiation in the events. The results are compared with various Monte Carlo generators, including comparisons where the generators are reweighted to match a parton-level calculation at next-to-next-to-leading order. The reweighting improves the agreement between data and theory. The measured distribution of the top-quark transverse momentum is used to search for new physics in the context of the effective field theory framework. No significant deviation from the Standard Model is observed and limits are set on the Wilson coefficients of the dimension-six operators OtG and O(8) tq , where the limits on the latter are the most stringent to date. Keywords: Top Physics, Beyond Standard Model, Hadron-Hadron Scattering ArXiv ePrint: 2202.12134 Open Access, Copyright CERN, for the benefit of the ATLAS Collaboration. Article funded by SCOAP3. https://doi.org/10.1007/JHEP06(2022)063 JHEP06(2022)063 Contents 1 Introduction 1 2 Data and simulated event samples 3 3 Event selection and reconstruction 6 4 Cross-section measurements 8 4.1 Background estimate 8 4.2 Correction of the jet energy 9 4.3 Fiducial requirements 10 4.4 Corrections for detector effects 11 4.5 Validation of the measurement technique 11 4.6 Choice of observables 12 4.7 Observed data distributions 14 5 Systematic uncertainties 15 5.1 Lepton reconstruction and identification 19 5.2 Jet reconstruction and b-tagging 19 5.3 JSF statistical uncertainty 21 5.4 t¯ tmodelling 21 5.5 Background modelling 22 5.6 Luminosity and other uncertainties 22 6 Results 22 7 Limits on EFT operators 34 8 Conclusions 37 A Normalised differential cross-section results 40 The ATLAS collaboration 56 1 Introduction The high mass of the top quark means that it is often intimately involved in models of physics beyond the Standard Model (SM). In effective models of new physics [1–4], nonresonant deviations from the SM often appear at high transverse momentum (pT) of the top quark and high invariant mass of the top-quark-top-antiquark (t¯ t) system [5–8]. The high rate of t¯ tproduction at the Large Hadron Collider (LHC) provides a unique opportunity – 1 – JHEP06(2022)063 to test for deviations from the SM predictions. This motivates precise differential t¯ tcrosssection measurements of high-pT(boosted) top quarks. In this paper, t¯ tevents containing a boosted top quark that has decayed hadronically are selected from data collected by the ATLAS detector in proton-proton collisions at √s= 13 TeV from 2015 to 2018. The selected events correspond to the semileptonic t¯ tdecay channel (t¯ t→WbWb →`νbqq0b) and the decay products are used to fully reconstruct the kinematics of the t¯ tsystem. The measured event properties are corrected for detector effects to obtain differential cross-sections as a function of various observables. These differential cross-section measurements characterise both the t¯ tsystem and the additional radiation in the events. The analysis introduces a novel use of the reconstructed topquark mass to reduce the impact of uncertainties from the jet energy scale compared to the previous ATLAS publication [9] and significantly improves the precision of the measurements. ATLAS has also measured the cross-section of t¯ tevents with boosted top quarks in the all-hadronic channel [10] and CMS has performed a measurement in the semileptonic channel [11]. These three measurements used smaller datasets, corresponding to an integrated luminosity of 36 fb−1, than the one used in this article, which corresponds to 139 fb−1. The measurements follow on from analyses performed at √s= 8 TeV [12,13]. The measured cross-sections are compared with available SM predictions. Precise predictions for SM t¯ tproduction are available at next-to-next-to-leading order (NNLO) in quantum chromodynamics (QCD) [14–16]. The predictions are fully differential but are only available for stable top quarks or in the dilepton channel (t¯ t→WbWb →`νb`νb) [17]. Predictions at NLO in QCD are available for the semileptonic decay channel including the full decay of the top quarks and parton shower and hadronisation effects in various Monte Carlo (MC) generators. The measured cross-sections are compared with the NLO MC predictions and the impact of the higher-order corrections is tested by reweighting the MC predictions at parton level to match predictions at NNLO in QCD. The measurements presented in this article are also used to test for the presence of new physics beyond the SM. The absence of direct evidence for the production of new particles beyond the SM at the LHC suggests that any new physics is separated in mass from the SM fields. In this situation the new physics can be parameterised in a model-independent way through the framework of effective field theory (EFT), in which the Lagrangian of the SM is modified by adding an infinite series of higher-dimensional effective operators [1–4] that are suppressed by the new-physics scale. Assuming that the energy scale is sufficiently large, the impact of new physics can be approximated by dimension-six operators. The ability of the presented measurements to constrain new physics is illustrated by using the measured top-quark pTdistribution to set limits on the effective operators OtG and O(8) tq , where the Warsaw basis [18] is used to define the operators. This paper is structured as follows. Section 2presents the data and simulated event samples. Section 3discusses the object and event selection and the reconstruction of the t¯ tsystem. The methodology of the cross-section measurement, including the new method to use the reconstructed top-quark mass to reduce the impact of the jet energy scale uncertainties, is described in section 4. The systematic uncertainties are discussed in section 5and the results of the measurement are compared with the theoretical predictions – 2 – JHEP06(2022)063 in section 6. Section 7presents the interpretation of the measured top-quark pTdistribution in the EFT framework. Finally, conclusions are presented in section 8. 2 Data and simulated event samples The ATLAS detector [19–21] surrounds one of the collision points at the LHC.1The detector consists of an inner tracking system surrounded by a superconducting solenoid producing a 2 T axial magnetic field, electromagnetic and hadronic calorimeters and an external muon spectrometer incorporating three toroidal magnet assemblies. An extensive software suite [22] is used in the reconstruction and analysis of real and simulated data, in detector operations, and in the trigger and data acquisition systems of the experiment. The analysis was performed on data collected from pp collisions at √s= 13 TeV during 2015–2018. The dataset must fulfil standard data quality requirements [23] and corresponds to an integrated luminosity of 139 fb−1. The uncertainty in the integrated luminosity is 1.7% [24], obtained using the LUCID-2 detector [25] for the primary luminosity measurements. Events are required to pass a single-electron or single-muon trigger [26,27]. MC simulated event samples are used to determine background contributions, derive corrections for detector effects, simulate potential new-physics contributions, and to compare with data. Samples were processed using either the full ATLAS detector simulation [28] based on Geant4 [29], or with a faster simulation making use of parameterised showers in the calorimeters [30]. The effects of multiple collisions during a single bunch crossing (pile-up) were simulated by overlaying additional inelastic pp collisions generated with Pythia 8 [31] and the A3 [32] set of tuned parameters (tune) onto the primary simulated events. These events were then processed with the same reconstruction software as the data. The top-quark mass (mt) is set to 172.5GeV in all samples aside from those used to study the impact of the uncertainty in mt. The nominal simulated t¯ tsample was generated using Powheg Box v2 [33–36] (hereafter referred to as Powheg), which provides matrix elements at NLO in the strong coupling constant, with the NNPDF3.0nlo [37] parton distribution functions (PDFs). The hdamp parameter, which controls the matching of the matrix element to the parton shower and effectively regulates the high-pTradiation against which the t¯ tsystem recoils, was set to 1.5mt[38]. The functional form of the renormalisation (µr) and factorisation (µf) scales was set to qm2 t+p2 T, where pTis the transverse momentum of the top quark. Pythia 8.230 was used to model the parton shower, hadronisation and underlying event, using the A14 tune [39] and the NNPDF2.3lo [40] set of PDFs. In the figures, this sample is referred to as PWG+PY8. 1ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the centre of the detector and the z-axis along the beam pipe. The x-axis points from the IP to the centre of the LHC ring, and the y-axis points upwards. Cylindrical coordinates (r, φ)are used in the transverse plane, φbeing the azimuthal angle around the z-axis. The pseudorapidity is defined in terms of the polar angle θas η=−ln tan(θ/2). The rapidity is defined as y= (1/2)[(E+pz)/(E−pz)]. Angular distance is measured in units of ∆R≡p(∆η)2+ (∆φ)2. – 3 – JHEP06(2022)063 Additional t¯ tsamples are used to assess the uncertainty in the modelling of t¯ tevents and to compare with the data measurements. The dependence of the analysis on the hdamp parameter is tested using a sample where the parameter is varied as described in ref. [41]. The impact of using a different parton shower and hadronisation model is evaluated using a sample produced with Powheg interfaced to Herwig 7.04 [42,43]. The settings in Powheg are the same as for the nominal sample, and the H7UE tune [43] and the MMHT2014lo PDF set [44] are used for Herwig. To assess the uncertainty due to the choice of generator, events were generated with MadGraph5_aMC@NLO 2.6.0 [45] and the NNPDF3.0nlo PDF set. The choice of µrand µfis the same as for the Powheg setup. The events were interfaced with Pythia 8.230. The uncertainty due to the top-quark mass is evaluated by using samples generated in the same way as the nominal t¯ tsample, but with the top-quark mass changed to 172,173,169 and 176 GeV. These samples were simulated using the fast simulation of the calorimeter, while all the previously described t¯ tsamples used the full simulation of the calorimeter. A version of the nominal sample was also produced using the fast simulation to ensure samples with consistent simulation settings were compared when evaluating the impact of the top-quark mass. All t¯ tsamples are normalised to the cross-section prediction at NNLO in QCD including the resummation of next-to-next-to-leading logarithmic (NNLL) soft-gluon terms calculated using Top++ 2.0 [46–52]. For proton-proton collisions at a centre-of-mass energy of √s=13 TeV, this cross-section corresponds to σ(t¯ t)NNLO+NNLL = 832 ±51 pb using a top-quark mass of mt= 172.5GeV. The uncertainties in the cross-section due to the PDF and αsare calculated using the PDF4LHC prescription [53] with the MSTW2008nnlo 68% CL [54,55], CT10nnlo [56,57] and NNPDF2.3 5f FFN [40] PDF sets, and are added in quadrature to the effect of the scale uncertainty. Predictions for t¯ tproduction at NNLO matched to the parton shower to produce particle-level predictions are not yet available for the semileptonic final state. In order to evaluate the impact of NNLO QCD corrections, the MC events are reweighted at parton level to match higher-order predictions. The reweighting is performed on the three variables pT(t),m(t¯ t)and pT(t¯ t), using the kinematics of the top quarks in the MC samples after initialand final-state radiation. The predictions for pT(t)and m(t¯ t)are calculated at NNLO in QCD with NLO electroweak (EW) corrections [15] with the NNPDF3.0qed PDF set using the dynamic renormalisation and factorisation scales mT(t)/2for pT(t)and HT/4for m(t¯ t)as proposed in ref. [15]. The prediction for pT(t¯ t)is calculated at NNLO in QCD [16,58] with the NNPDF3.0 PDF set and with µrand µfset to HT/4. All the predictions use mt= 173.3GeV.2 The reweighting was performed iteratively [59], such that at the end of the procedure the reweighted MC sample agrees well with the higher-order prediction for each of the three variables. These samples are referred to as being reweighted to the NNLO prediction in the remainder of the document. The reweighted predictions themselves are not equivalent to complete NNLO plus parton shower calculations and are used to estimate the effect of the NNLO contributions on the measured observables. 2It was verified that the changes in the distributions from the reweighting procedure are much larger than those expected from changing mtby 0.8GeV. – 4 – JHEP06(2022)063 To examine the predictions provided by generators that use higher-order calculations for the additional jets in t¯ tevents, a sample was generated using Sherpa 2.2.10 [60]. The sample uses NLO-accurate matrix elements for up to one additional parton, and LOaccurate matrix elements for up to four additional partons, calculated with the Comix [61] and OpenLoops [62–64] libraries. They are matched with the Sherpa parton shower [65] using the MEPS@NLO prescription [66–69] and the set of tuned parameters developed by the Sherpa authors to match the NNPDF3.0nnlo set of PDFs [37]. The central scale has the functional form µ2=m2 t+1 2(p2 T,t +p2 T,¯ t). The CKKW matching scale [68] of the additional emissions was set to 30 GeV. As this sample contains parts of the inclusive NNLO corrections to t¯ tthere are two possibilities for normalising the sample: first to use the prediction provided by the generator (referred to as NLO norm. in the following) and second to normalise the sample to the NNLO+NNLL prediction in the same way as for t¯ tsamples from the other MC generators. The prediction of the inclusive t¯ tcross-section from the NNLO+NNLL calculation is 21% higher than the prediction from the Sherpa generator. The possible contributions from high-energy-scale new physics are modelled using an EFT approach. In this approach the SM Lagrangian is expanded with higher-dimensional operators according to: LEFT =LSM +X i,D CD i ΛD−4OD i, where each operator OD iof dimension Dhas a corresponding Wilson coefficient Ci, and Λis the energy scale associated with the new physics. Assuming that the energy scale is high, the sum can be truncated at dimension six, which is the first term that gives nonzero contributions when assuming lepton and baryon number conservation. At dimension six, assuming baryon number conservation and minimal flavour violation [70], there are 59 independent operators. The SM is recovered by setting all the Wilson coefficients to zero. This analysis is restricted to two operators in the Warsaw basis [18] that are expected to have a significant impact on t¯ tproduction: OtG and O(8) tq . MC samples were generated with the SMEFT@NLO 1.0.0 UFO model [71] at LO to provide events with CtG, C(8) tq = (±1or 0,±1or 0) and Λ=1TeV. The renormalisation and factorisation scales were set to µr=µf=mtand the {mW, mZ, Gµ}EW input scheme was used as outlined in ref. [72]. Two sets of samples were produced: one set includes contributions proportional to Λ−2, corresponding to the interference between the SM and dimension-six operators, and the second set additionally includes terms proportional to Λ−4, corresponding to the square of dimension-six operators. An additional sample including the Λ−2and Λ−4contributions was generated with CtG, C(8) tq = (0.2,0.2) and Λ = 1 TeV in order to test for possible biases in the EFT fit. The parton shower and hadronisation were performed using Pythia 8.244. Backgrounds from other processes that include the decay of at least one Wor Zboson into leptons were simulated using MC generators. Top-quark production in association with aWboson (tW) and the production of single top quarks in the s-channel were modelled by the Powheg [73,74] generator at NLO in QCD using the five-flavour scheme and the NNPDF3.0nlo set of PDFs interfaced to Pythia 8.230. The diagram removal scheme [75] – 5 – JHEP06(2022)063 was used to remove interference and overlap between tW and t¯ tproduction. The production of single top quarks in the t-channel was simulated using Powheg+Pythia in the fourflavour scheme [76] with the corresponding NNPDF3.0nlo set of PDFs. The production of V+jets (V=Wor Z) was simulated with Sherpa 2.2.1 using NLO matrix elements for up to two partons, and LO matrix elements for up to four partons, calculated with the Comix and OpenLoops libraries. They were matched with the Sherpa parton shower using the MEPS@NLO prescription. The NNPDF3.0nnlo set of PDFs was used and the samples were normalised to an NNLO prediction [77]. Events with diboson final states (V V ) were also simulated with the Sherpa generator using matrix elements at NLO accuracy in QCD for up to one additional parton and at LO accuracy for up to three additional parton emissions. The showering and hadronisation were performed in the same way as for the V+jets samples. Production of t¯ tV events forms a small background in the analysis and was modelled using the MadGraph5_aMC@NLO 2.3.3 [45] generator at NLO with the NNPDF3.0nlo parton distribution functions. Finally, t¯ tH events were modelled using the Powheg generator at NLO with the NNPDF3.0nlo PDF set. The events were interfaced to Pythia 8.230 in a similar way to the nominal t¯ tsample. 3 Event selection and reconstruction All events must contain a primary vertex with at least two associated tracks with pT> 0.5GeV. The vertex with the highest Pp2 Tof the associated tracks is taken as the primary vertex. Electrons are reconstructed from energy deposits in the electromagnetic (EM) calorimeter matched to a track in the inner detector. They must have transverse energy ET>27 GeV and pass the ‘Tight’ likelihood-based requirement [78]. They must have pseudorapidity |η|<2.47 and be outside the transition region between the barrel and endcap EM calorimeters (1.37 <|η|<1.52). Electrons are required to be isolated by applying the ‘Tight’ requirements on the sum of nearby energy in the calorimeter and the sum of the momenta of nearby tracks [78]. The track associated with the electron must satisfy a requirement of |d0|/σd0<5on the transverse impact parameter significance calculated relative to the beam line, and a requirement of |z0sin(θ)|<0.5mm on the longitudinal impact parameter calculated relative to the event primary vertex, where θis the polar angle of the track. Muons are reconstructed by combining a track found in the inner detector with a matching track found in the muon spectrometer. Selected muons must have pT>27 GeV and |η|<2.5, and pass the ‘Medium’ identification requirements and ‘Tight’ isolation requirements [79]. The muons must have impact parameters satisfying |d0|/σd0<3and |z0sin(θ)|<0.5mm. Jets are reconstructed using the anti-ktclustering algorithm [80,81] with radius parameter R= 0.4starting from particle-flow objects that exploit both calorimeter and track measurements [82]. Jets are calibrated using measurements in both simulation and data [83] and are required to have pT>26 GeV and |η|<2.5so that they are within the acceptance of the inner detector. Jets with pT<60 GeV must also pass a pile-up rejection threshold placed on the output of the multivariate jet-vertex tagger (JVT) [84]. Jets that are close to an electron, ∆R(e, j)<0.2, are removed to avoid double counting the energy of the elec- – 6 – JHEP06(2022)063 tron. Jets that have less than three tracks and are either close to a muon (∆R(µ, j)<0.2) or have a track that is part of the muon are also removed. This avoids counting the energy deposits of muons as jets. An additional requirement of ∆R(`, j)>0.4then ensures that electrons and muons are well separated from jets; leptons failing this requirement are rejected. Jets that contain b-hadrons (b-jets) are identified by the use of the DL1r multivariate algorithm [85,86]. The selected working point results in an efficiency of 77% per b-jet, as measured in simulated t¯ tevents. These jets are hereafter referred to as b-tagged jets. Highly boosted top quarks (pT&2mt) that decay hadronically can produce decay products that are not resolved as three separate jets. These boosted top quarks are therefore identified using large-radius jets so as to capture all the decay products in a single jet. These large-Rjets are reconstructed by applying the anti-ktclustering algorithm with radius parameter R= 1.0to the selected R= 0.4(small-R) jets [87]. Any small-Rjets that have less than 5% of the pTof the corresponding large-Rjet are removed from that large-R jet. This trimming procedure [87,88] is designed to remove jets that are more likely to originate from pile-up. The large-Rjets must have pT>355 GeV and |η|<2.0. In order to select jets consistent with a hadronically decaying top quark, the large-Rjets must contain at least one b-tagged jet and have an invariant mass in the range 120 <m<220 GeV. If more than one large-Rjet passes these requirements, the one with the highest pTis assumed to be the one originating from the hadronically decaying top quark. This selected large-Rjet is referred to as the top-tagged jet. The missing transverse momentum (Emiss T) is reconstructed from the negative vector sum of calibrated leptons, small-Rjets and the soft term (calculated using other tracks associated with the primary vertex) [89]. Events are required to have exactly one selected lepton, at least one top-tagged jet and at least two b-tagged jets. At least one of the b-tagged jets must not be a constituent of the top-tagged jet. The selected lepton must match a corresponding electron or muon trigger object. Consistency with the expected boosted topology is ensured by requiring the lepton to be close to a b-tagged jet, ∆R(`, b)<2.0, and the same b-tagged jet must not be a constituent of the top-tagged jet. A requirement of ∆R(e, t)>1.0 prevents the selection of large-Rjets seeded by a high-pTelectron. To reduce the multijet background, events must have Emiss T>20 GeV and Emiss T+mW T>60 GeV, where mW T=r2p` TEmiss T1−cos ∆φp` T, Emiss T is the transverse mass of the Wboson. The invariant mass of the lepton and the nearest b-tagged jet, m`b, must be less than 180 GeV. This selection requirement retains signal events where the lepton and b-jet originate from an on-shell top-quark decay, while rejecting events from tW single top-quark production [90]. The kinematics of the top quarks are obtained from the selected objects. The selected top-tagged jet is used as the estimate of the hadronically decaying top quark. The leptonically decaying top quark is reconstructed from the four-vector sum of the lepton, the closest b-tagged jet and the neutrino. The xand ycomponents of the missing transverse momentum provide estimates of the corresponding components of the neutrino four-vector. The z-component is calculated using the constraint that the lepton-neutrino system has invariant mass equal to the Wboson mass [91]. If there are two real solutions to the corresponding quadratic equation, the solution that gives the smallest value for the mass of the – 7 – JHEP06(2022)063 leptonically decaying top quark is used. In the case of complex solutions, only the real part is used. Any jets other than the constituents of the top-tagged jet and the b-tagged jet used in reconstructing the leptonically decaying top quark are referred to as additional jets. 4 Cross-section measurements The strategy used to measure differential cross-sections is to correct (unfold) the data for detector effects and can be summarised in the following equations: dσ dX =Nu i L∆Xi (4.1) Nu i=1 fi eff X j M−1 ij fj acc Nj d(JSF) −Nj b, where Xrepresents the variable being measured. The data are first corrected by applying a jet energy scale factor (JSF) that ensures that the mean of the reconstructed top-quark mass agrees with the simulation, as discussed in section 4.2. The number of events in each bin after that correction, Nj d(JSF), then have the background contributions (Nj b) subtracted. The yields are then corrected with the factor fj acc to account for t¯ tevents that do not pass the fiducial requirements. An iterative Bayesian unfolding [92] (denoted by M−1 ij ) implemented in RooUnfold [93] is used to correct for the limited resolution of the detector. The factor fi eff corrects for events that pass the fiducial requirements but do not pass the detector-level event selection. Finally, the events are corrected for the integrated luminosity (L) and the bin width (∆Xi). The same methodology is used for double-differential distributions. The inclusive cross-section is determined by using all the selected events in a single bin as input to eq. (4.1). All the correction factors are determined using the nominal t¯ tsimulation. In addition to the absolute differential cross-section measurements, normalised differential cross-section measurements are produced by dividing by the measured inclusive cross-section. The normalised measurements provide a way to evaluate how well a distribution’s shape agrees between data and theory without considering the overall normalisation. This is relevant, for example, in new-physics searches where the normalisation of t¯ tproduction can be fitted from the data, while the shape relies on the simulation [94]. As the normalised measurements contain less information than the absolute measurements, they are presented in appendix A. The different components of the measurement methodology are discussed in the following subsections and the section is concluded by comparing the observed data with the expectation from the t¯ tsimulation and the background estimates. 4.1 Background estimate The event selection is designed to reject the vast majority of background events such that the modelling of the background processes has a minor impact on the measurements. The main backgrounds to the signal process are expected to be from tW single top-quark production and W+jets production. These backgrounds, along with smaller backgrounds from t¯ tV ,t¯ tH,Z+jets and diboson production, are estimated from the simulated samples described in section 2. Events can also pass the selection if the lepton originates from the – 8 – JHEP06(2022)063 Process Expected events t¯ t084200 ±2600 Single top quark 001710 ±0280 t¯ tV (t¯ tW +t¯ tZ +t¯ tH)000850 ±0110 Multijet 000560 ±0370 W+jets 000420 ±0160 Z+jets 000084 ±0043 Diboson 00 0041 ±0021 Total prediction 087900 ±2700 Data 075743 Table 1. Event yields for measured data, simulated t¯ tsignal and background events. The uncertainty values are symmetrised and indicate the combined effect of statistical, detector and background modelling uncertainties. 5 Systematic uncertainties Systematic uncertainties affect the measured cross-section through the unfolding corrections discussed in section 4. The systematic uncertainty from each source is evaluated by creating pseudo-data where the source of uncertainty was varied in the simulation and background model. The modified pseudo-data sample is treated as if it is data and differential cross-sections are extracted using the analysis procedure described in section 4. Of particular relevance is the JSF, which is extracted for each pseudo-data sample as described in section 4.2. In this way, correlations between the different aspects of the analysis methodology are fully accounted for. The difference between the cross-sections extracted from the varied pseudo-data and the cross-sections extracted from the nominal simulation is used as an estimate of the impact of that uncertainty source. For the signal modelling components, where alternative t¯ tsimulations are employed, the cross-sections extracted from the pseudo-data are compared with the corresponding particle-level distributions to assess the impact of the uncertainty. The total uncertainty is then calculated assuming all the systematic uncertainties are uncorrelated. A description of the different uncertainty components is given in the following subsections. Table 2summarises the impact of the systematic uncertainties on the inclusive cross-section measurement. The benefit of the JSF correction procedure is evaluated by comparing the impact of each source for the case where no JSF correction is applied with the nominal analysis set-up. The precision of the measurement is seen to improve significantly due to the JSF correction. When examining the impact of the individual uncertainty sources, some distinct patterns are apparent. Uncertainty sources such as the b-tagging and lepton uncertainties are not affected by the JSF correction because they do not influence either the jet energy measurement or the mt,h distribution. The impact of the jet energy scale uncertainty is largely reduced because the JSF is able to absorb any overall jet energy scale differences between data and simulation. The top-quark mass uncertainty increases with the introduction of the JSF procedure be- – 15 – JHEP06(2022)063 1− 10 1 10 2 10 3 10 4 10 Events/GeV Data tt Single top ttV Multijet V(V)+jets Stat.+Syst. unc. -1 = 13 TeV, 139 fbs ATLAS Boosted Normalised to data 500 1000 1500 2000 [GeV] t,h T Reconstruction-level p 0.8 1 1.2 Data/Pred. (a) 1 10 2 10 3 10 4 10 Events/GeV Data tt Single top ttV Multijet V(V)+jets Stat.+Syst. unc. -1 = 13 TeV, 139 fbs ATLAS Boosted Normalised to data 0 200 400 600 800 1000 [GeV] t,l T Reconstruction-level p 0.8 1 1.2 Data/Pred. (b) 1− 10 1 10 2 10 3 10 Events/GeV Data tt Single top ttV Multijet V(V)+jets Stat.+Syst. unc. -1 = 13 TeV, 139 fbs ATLAS Boosted Normalised to data 1000 2000 3000 [GeV] t t Reconstruction-level m 0.8 1 1.2 Data/Pred. (c) 3 10 4 10 5 10 6 10 Events Data tt Single top ttV Multijet V(V)+jets Stat.+Syst. unc. -1 = 13 TeV, 139 fbs ATLAS Boosted Normalised to data 0 0.5 1 1.5 2 | t,h Reconstruction-level |y 0.8 1 1.2 Data/Pred. (d) 2 10 3 10 4 10 5 10 6 10 Events Data tt Single top ttV Multijet V(V)+jets Stat.+Syst. unc. -1 = 13 TeV, 139 fbs ATLAS Boosted Normalised to data 0 0.5 1 1.5 2 2.5 | t,l Reconstruction-level |y 0.8 1 1.2 Data/Pred. (e) 2 10 3 10 4 10 5 10 6 10 Events Data tt Single top ttV Multijet V(V)+jets Stat.+Syst. unc. -1 = 13 TeV, 139 fbs ATLAS Boosted Normalised to data 0 0.5 1 1.5 2 | t t Reconstruction-level |y 0.8 1 1.2 Data/Pred. (f) 1− 10 1 10 2 10 3 10 4 10 Events/GeV Data tt Single top ttV Multijet V(V)+jets Stat.+Syst. unc. -1 = 13 TeV, 139 fbs ATLAS Boosted Normalised to data 500 1000 1500 2000 2500 [GeV] t t T Reconstruction-level H 0.8 1 1.2 Data/Pred. (g) 3 10 4 10 5 10 6 10 7 10 Events Data tt Single top ttV Multijet V(V)+jets Stat.+Syst. unc. -1 = 13 TeV, 139 fbs ATLAS Boosted Normalised to data 0 0.2 0.4 0.6 0.8 1 ) h ,t l (b π φ∆ Reconstruction-level 0.8 1 1.2 Data/Pred. (h) Figure 4. Distributions of the observables sensitive to the kinematics of the top quarks: (a) pt,h T, (b) pt,` T, (c) mt¯ t, (d) |yt,h|, (e) |yt,`|, (f) |yt¯ t|, (g) Ht¯ t Tand (h) ∆φ(b`, th). The data are compared with the expectation from the simulation and background estimates. The total prediction is normalised to the same number of entries as the data. The lower panel in each subfigure shows the ratio of the data to the normalised expectation. The shaded band represents the uncertainties originating from the limited data sample size and systematic uncertainties (t¯ tmodelling uncertainties are not included). – 16 – JHEP06(2022)063 1− 10 1 10 2 10 3 10 4 10 Events/GeV Data tt Single top ttV Multijet V(V)+jets Stat.+Syst. unc. -1 = 13 TeV, 139 fbs ATLAS Boosted Normalised to data 0 500 1000 [GeV] t t T Reconstruction-level p 0.8 1 1.2 Data/Pred. (a) 3 10 4 10 5 10 6 10 7 10 Events Data tt Single top ttV Multijet V(V)+jets Stat.+Syst. unc. -1 = 13 TeV, 139 fbs ATLAS Boosted Normalised to data 0 0.2 0.4 0.6 0.8 1 ) l ,t h (t π φ∆ Reconstruction-level 0.8 1 1.2 Data/Pred. (b) 1− 10 1 10 2 10 3 10 Events/GeV Data tt Single top ttV Multijet V(V)+jets Stat.+Syst. unc. -1 = 13 TeV, 139 fbs ATLAS Boosted Normalised to data 500 1000 1500 2000 2500 [GeV] +jetstt T Reconstruction-level H 0.8 1 1.2 Data/Pred. (c) 2 10 3 10 4 10 5 10 6 10 Events Data tt Single top ttV Multijet V(V)+jets Stat.+Syst. unc. -1 = 13 TeV, 139 fbs ATLAS Boosted Normalised to data 0 1 2 4−3 >4 j Reconstruction-level N 0.8 1 1.2 Data/Pred. (d) 1 10 2 10 3 10 4 10 Events/GeV Data tt Single top ttV Multijet V(V)+jets Stat.+Syst. unc. -1 = 13 TeV, 139 fbs ATLAS Boosted Normalised to data 200 400 600 800 [GeV] j,1 T Reconstruction-level p 0.8 1 1.2 Data/Pred. (e) 1− 10 1 10 2 10 3 10 Events/GeV Data tt Single top ttV Multijet V(V)+jets Stat.+Syst. unc. -1 = 13 TeV, 139 fbs ATLAS Boosted Normalised to data 500 1000 1500 2000 2500 ) [GeV] h ,t 1 jReconstruction-level m( 0.8 1 1.2 Data/Pred. (f) 3 10 4 10 5 10 6 10 Events Data tt Single top ttV Multijet V(V)+jets Stat.+Syst. unc. -1 = 13 TeV, 139 fbs ATLAS Boosted Normalised to data 0 0.2 0.4 0.6 0.8 1 ) h ,t 1 j( π φ∆ Reconstruction-level 0.8 1 1.2 Data/Pred. (g) Figure 5. Distributions of observables sensitive to jets produced in association with the t¯ tsystem: (a) pt¯ t T, (b) ∆φ(th, t`), (c) Ht¯ t+jets T, (d) Nj, (e) pj,1 T, (f) m(j1, th)and (g) ∆φ(j1, th). The data are compared with the expectation from the simulation and background estimates. The total prediction is normalised to the same number of entries as the data. The lower panel in each subfigure shows the ratio of the data to the normalised expectation. The shaded band represents the uncertainties originating from the limited data sample size and systematic uncertainties (t¯ t modelling uncertainties are not included). – 17 – JHEP06(2022)063 3 10 4 10 5 10 6 10 Events Data tt Single top ttV Multijet V(V)+jets Stat.+Syst. unc. -1 = 13 TeV, 139 fbs ATLAS Boosted Normalised to data 0 0.2 0.4 0.6 0.8 1 ) h ,t 2 j( π φ∆ Reconstruction-level 0.8 1 1.2 Data/Pred. (a) 3 10 4 10 5 10 6 10 Events Data tt Single top ttV Multijet V(V)+jets Stat.+Syst. unc. -1 = 13 TeV, 139 fbs ATLAS Boosted Normalised to data 0 0.2 0.4 0.6 0.8 1 ) 2 j, 1 j( π φ∆ Reconstruction-level 0.8 1 1.2 Data/Pred. (b) 1− 10 1 10 2 10 3 10 4 10 Events/GeV Data tt Single top ttV Multijet V(V)+jets Stat.+Syst. unc. -1 = 13 TeV, 139 fbs ATLAS Boosted Normalised to data 100 200 300 400 500 [GeV] j,2 T Reconstruction-level p 0.8 1 1.2 Data/Pred. (c) Figure 6. Distributions of observables sensitive to the second leading additional jet: (a) ∆φ(j2, th), (b) ∆φ(j1, j2)and (c) pj,2 T. The data are compared with the expectation from the simulation and background estimates. The total prediction is normalised to the same number of entries as the data. The lower panel in each subfigure shows the ratio of the data to the normalised expectation. The shaded band represents the uncertainties originating from the limited data sample size and systematic uncertainties (t¯ tmodelling uncertainties are not included). cause the mean of the mt,h distribution is directly related to the top-quark mass. The data and MC statistical uncertainties are also increased by the use of mt,h; the increased statistical uncertainty is traded for the reduced systematic uncertainties. The reduction of the uncertainties is also shown in figure 7, which displays the effect of the JSF correction on the uncertainty for three differential distributions, both for the total uncertainty and for the jet energy scale (JES) uncertainty. In most bins the JES uncertainty is reduced due to the introduction of the JSF. There are a small number of bins where the JES uncertainty increases due to the JSF; this occurs when the kinematics of the jets in these bins are very different from the average jet kinematics in the sample and hence the average correction provided by the JSF causes the systematic uncertainty from the JES to increase. Figure 8 summarises the impact of the systematic uncertainties on three example observables. The modelling uncertainties generally have the largest impact on the measurement, while the JES and b-tagging uncertainties are important in particular phase-space regions. – 18 – JHEP06(2022)063 Source Uncertainty [%] Uncertainty [%] (no JSF) Statistical (data) ±0.4±0.4 JSF statistical (data) ±0.4— Statistical (MC) ±0.2±0.1 Hard scatter ±0.5±0.8 Hadronisation ±2.0±1.8 Radiation (ISR/FSR + hdamp)+1.0 +1.4 −1.6−2.3 PDF ±0.1±0.1 Top-quark mass +0.8±0.1 −1.1 Jets ±0.7±4.2 b-tagging ±2.4±2.4 Leptons ±0.8±0.8 Emiss T±0.1±0.1 Pile-up ±0.4±0.0 Luminosity ±1.8±1.8 Background modelling ±0.6±0.6 Total systematic uncertainty +4.1 +5.8 −4.3−6.0 Total +4.1 +5.8 −4.3−6.0 Table 2. Fractional uncertainty breakdown for the inclusive t¯ tcross-section both with and without the JSF method applied. 5.1 Lepton reconstruction and identification The uncertainty in the efficiency to reconstruct and identify electrons and muons was obtained by studying Z→ee/µµ events as discussed in refs. [78,79]. Similar studies were performed to determine the uncertainty in the trigger efficiencies for electrons and muons [26,27]. The impact of these uncertainties on the analysis is small, but they are the largest part of the ‘Leptons’ entry in table 2. The uncertainties in the electron and muon energy / momentum scales and resolutions were determined using resonance decays [78,105] and are found to have a negligible impact on the analysis. 5.2 Jet reconstruction and b-tagging The JES and jet energy resolution of small-Rjets were determined using a combination of simulation, test beam and in situ measurements [83]. The corresponding uncertainties are evaluated using a model with 30 independent components for the jet energy scale and 8 independent components for the jet energy resolution. The uncertainties are propagated to the large-Rjets such that the correlations between the energies of small-Rand large-Rjets – 19 – JHEP06(2022)063 Fractional Uncertainty [%] 20− 10− 0 10 20 Stat.+Syst. Unc. [No JSF] Stat.+Syst. Unc. JES Unc. [No JSF] JES Unc. ATLAS -1 = 13 TeV, 139 fbs Boosted Fiducial phase-space Absolute cross-section [GeV] t,h T p 400 600 800 1000 1200 1400 1600 1800 2000 No JSF JSF applied 0 1 2 JES Unc. Stat.+Syst. Unc. (a) Fractional Uncertainty [%] 20− 15− 10− 5− 0 5 10 15 20 Stat.+Syst. Unc. [No JSF] Stat.+Syst. Unc. JES Unc. [No JSF] JES Unc. ATLAS -1 = 13 TeV, 139 fbs Boosted Fiducial phase-space Absolute cross-section [GeV] t t m 500 1000 1500 2000 2500 3000 No JSF JSF applied 0 1 2JES Unc. Stat.+Syst. Unc. (b) Fractional Uncertainty [%] 30− 20− 10− 0 10 20 30 Stat.+Syst. Unc. [No JSF] Stat.+Syst. Unc. JES Unc. [No JSF] JES Unc. ATLAS -1 = 13 TeV, 139 fbs Boosted Fiducial phase-space Absolute cross-section j N No JSF JSF applied 0 1 2 0 1 2 3-4 >4 JES Unc. Stat.+Syst. Unc. (c) Figure 7. Effect of the JSF correction on the total uncertainty of the cross-section measurements as a function of (a) pTof the hadronically decaying top quark (pt,h T), (b) invariant mass of the t¯ tsystem (mt¯ t) and (c) the number of additional jets in the event (Nj). The yellow (grey) bands represent the total uncertainty with (without) the JSF correction applied. The red (grey) line in the upper pad shows the JES uncertainty with (without) the JSF method. The bottom pad shows the ratios of the absolute size of the uncertainty with and without the JSF correction applied, in red for the JES uncertainty and in yellow for the total uncertainty. [GeV] t,h T p 400 600 800 1000 1200 1400 1600 1800 2000 Fractional Uncertainty [%] 30− 20− 10− 0 10 20 30 Stat.+Syst. Unc. Stat. Unc. Jets top-quark Mass JSF Stat Unc. Flavor Tagging Modellingtt Other ATLAS -1 = 13 TeV, 139 fbs Boosted Fiducial phase-space Absolute cross-section (a) [GeV] t t m 500 1000 1500 2000 2500 3000 Fractional Uncertainty [%] 20− 15− 10− 5− 0 5 10 15 20 Stat.+Syst. Unc. Stat. Unc. Jets top-quark Mass JSF Stat Unc. Flavor Tagging Modellingtt Other ATLAS -1 = 13 TeV, 139 fbs Boosted Fiducial phase-space Absolute cross-section (b) j N Fractional Uncertainty [%] 20− 10− 0 10 20 0 1 2 3-4 >4 Stat.+Syst. Unc. Stat. Unc. Jets top-quark Mass JSF Stat Unc. Flavor Tagging Modellingtt Other ATLAS -1 = 13 TeV, 139 fbs Boosted Fiducial phase-space Absolute cross-section (c) Figure 8. Fractional uncertainties of the absolute cross-section measurement as a function of (a) pTof the hadronically decaying top quark (pt,h T), (b) invariant mass of the t¯ tsystem (mt¯ t) and (c) the number of additional jets in the event (Nj). The line labelled ‘Jets’ includes the uncertainties from the JES, JER and JVT requirements. The line labelled ‘t¯ tModelling’ includes all the uncertainties discussed in section 5.4, with the exception of the uncertainty in the top-quark mass, which is shown separately. are maintained. The impact of the JES uncertainties on the measurement is significantly reduced by the JSF procedure; for example, the uncertainty in the inclusive cross-section due to the JES is reduced from 4.0% to 0.4%. The JES uncertainties have their largest impact in regions with high jet multiplicity. The impact of the jet energy resolution uncertainty is generally smaller than that due to the jet energy scale uncertainty. The uncertainty in the efficiency of the JVT requirement for pile-up suppression is also considered [84]. The performance of the b-tagging algorithm has been calibrated in the data [85]. The corresponding uncertainties are propagated to the analysis by using an uncertainty model – 20 – JHEP06(2022)063 containing 9/4/4independent variations for the b-/c-/light-jet calibrations and two components for the MC-based extrapolation to jets with very high pT. These uncertainties have a moderate impact on the fiducial cross-section measurement as seen in table 2and do not significantly vary in size as a function of the measured observables, as seen in figure 8. 5.3 JSF statistical uncertainty The statistical uncertainty due to the limited number of data events in the determination of the JSF is evaluated by performing pseudo-experiments in which the data yields in the mt,h distribution are varied according to a Poisson distribution. As the mt,h distribution is found to be largely uncorrelated with all measured observables, this uncertainty is assumed to be uncorrelated with the statistical uncertainty of the cross-section measurement. A similar procedure is used to assess the statistical uncertainty of the JSF due to the limited size of the simulated event samples. 5.4 t ¯ tmodelling Uncertainties in the modelling of t¯ tproduction affect the unfolding corrections as well as the mt,h distribution that is used to determine the JSF. Several separate variations of the t¯ tmodel are considered in the analysis. The uncertainty due to the choice of parton shower and hadronisation models is assessed by using the events generated by Powheg+Herwig to build pseudo-data, repeating the analysis, and comparing the unfolded distributions with the particle-level prediction of Powheg+Herwig. The impact of this uncertainty is quite important and largest at low pt,h T. The uncertainty originating from the choice of generator is assessed by using pseudo-data created from the MadGraph5_aMC@NLO+Pythia sample. The impact of this uncertainty is relatively small. The uncertainty originating from the scales used in the matrix elements and the parton shower is evaluated by using pseudo-data built from the samples with variations of the hdamp parameter, and by using pseudo-data created by reweighting the nominal sample to correspond to different values of the µrand µfscales in the matrix elements, the parameters in the showering tune [41], and the µrscale in the final-state parton shower. The reweighted samples using the changes in the scales in the matrix elements and the changes in the parameter values in the showering tune are referred to as the ISR variations. The reweighted samples using the varied scale in the final-state parton shower are referred to as the FSR variations. These modelling uncertainties are found to be particularly important at high pt,h T(figure 8a). The extraction of the JSF relies on the measured value of the top-quark mass, which is known to a precision of around 0.5GeV [100,101]. This uncertainty is evaluated by using pseudo-data built from MC samples where the top-quark mass is varied from its nominal value of 172.5GeV. Thanks to the high precision of the top-quark mass measurements, the impact on the analysis is small, although the use of the JSF method increases the impact of this uncertainty, as seen in table 2. The uncertainty in the parton distribution functions is evaluated using the 30 eigenvectors of PDF4LHC30 [53]. The impact of the uncertainty is found to be very small. – 21 – JHEP06(2022)063 5.5 Background modelling The uncertainty in the modelling of single top-quark production is assessed by using samples where the scales are varied in a similar way to the t¯ tsamples described above. The uncertainty in the subtraction of the t¯ tevents from the tW sample is assessed by using an alternative sample that uses the diagram subtraction scheme [75] instead of the diagram removal scheme. Uncertainties in the cross-sections of the single-top-quark processes are also included. The uncertainties in the W+jets background are evaluated by reweighting the MC samples to correspond to different values of the scales in the matrix elements and the parton shower [106]. The small Z+ jets and diboson backgrounds are assigned uncertainties of 50% to cover potential mismodelling of these backgrounds. The t¯ tV and t¯ tH processes are assigned an uncertainty of 13% [107]. The uncertainty in the multijet background is assessed by comparing the estimate from the matrix method with the estimate from an alternative method based on fitting MC templates to the Emiss Tand Emiss T+mW Tdistributions. These comparisons result in an uncertainty of 65% in the multijet background estimate. The impact of the background uncertainties on the measurements is generally small, and less than in the previous ATLAS measurement thanks to the tighter selection requirements (particularly the one on m`b). 5.6 Luminosity and other uncertainties The calibration of the integrated luminosity has an uncertainty of 1.7% [24]. The uncertainty is important for the inclusive cross-section measurement but less so for the differential measurements. The uncertainty in the pile-up modelling is evaluated by varying the mean number of interactions in the simulation and this uncertainty is found to be small. The uncertainty in the Emiss Toriginates from the possible miscalibration of the tracks in the soft term and it was derived from the pTimbalance between the soft and hard components in data-simulation comparisons [89]. The uncertainty due to the limited number of simulated events is evaluated by varying the number of events according to the statistical uncertainties of the simulated samples and is found to be smaller than the statistical uncertainty of the data. 6 Results The fiducial cross-section (as defined in section 4.3) is measured to be 1.267 ±0.005 ± 0.053 pb, where the first uncertainty is due to the size of the data sample and the second originates from the systematic uncertainties. This cross-section is measured to a relative precision of 4.2%. This is smaller than the calculated uncertainty of 6.1% in the inclusive t¯ tcross-section at NNLO+NNLL, which is composed of 4.2% from PDF uncertainties, 3% from scale variations and 2.8% from the uncertainty in the top-quark mass. A comparison with the SM predictions obtained with different MC set-ups (each normalised to the inclusive NNLO+NNLL t¯ tcross-section) is shown in figure 9. All MC – 22 – JHEP06(2022)063 Inclusive fiducial cross-section [pb] 1 1.5 2 PWG+PY8 PWG+PY8 (NNLO rw.) PWG+H7 PWG+H7 (NNLO rw.) MCatNLO+PY8 MCatNLO+PY8 (NNLO rw.) Sherpa ATLAS -1 = 13 TeV, 139 fbs Fiducial phase-space Boosted calculation* prior to any further re-weighting t t inc σ All predictions normalised to NNLO+NNLL *M. Czakon and A. Mitov, Comp. Phys. Com. 185 (2014) 2930 uncertainty on the NNLO+NNLL calculation t +m s αError bars correspond to scale+PDF+ Stat. unc. Stat.+Syst. unc. Data Figure 9. The fiducial cross-section at particle level for boosted t¯ tproduction measured in data (dashed line) is compared with several NLO predictions (closed markers). All the MC samples are normalised to the NNLO+NNLL prediction for the total t¯ tcross-section (σinc t¯ t). The open markers show the predictions from the MC generators after they were reweighted at parton level to match NNLO predictions for pT(t),m(t¯ t)and pT(t¯ t). The yellow band represents the total uncertainty of the measured cross-section, while the orange band shows the statistical component. The uncertainties in the predictions are evaluated as the quadrature sum of the αs, PDF, mt and scale uncertainties present in the NNLO+NNLL prediction. PWG+PY8 corresponds to the Powheg+Pythia sample, PWG+H7 to the Powheg+Herwig sample, and MCatNLO+PY8 to the MadGraph5_aMC@NLO+Pythia sample. set-ups give predictions that are higher than the data, with the Powheg+Pythia and MadGraph5_aMC@NLO+Pythia predictions being around two standard deviations above the data.4Significantly better agreement is seen after reweighting the MC simulations to the differential NNLO predictions, indicating the corrections are relevant given the precision of the measurement. The level of agreement for the differential cross-section measurements is quantified by calculating χ2values according to: χ2=VTC−1V where Vis the vector of residuals between the measured and predicted cross-sections and Cis the covariance matrix of the measured data (including both the statistical and systematic uncertainties). No uncertainties in the theoretical predictions are included in the χ2calculation. The observed χ2and the number of degrees of freedom are used to calculate p-values. Table 3shows the χ2values for the different NLO generators discussed in section 2. The effect of the NNLO reweighting is quantified in this table by also showing the 4The estimate of the uncertainty of the ratio between data and expectation includes the experimental uncertainty and the 6.1% uncertainty on the t¯ tcross-section, assuming the two are uncorrelated. – 23 – JHEP06(2022)063 Observable PWG+PY8 PWG+PY8(NNLO weight) MC@NLO+PY8 MC@NLO+PY8(NNLO weight) PWG+H7 PWG+H7(NNLO weight) 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,h T26/8 <0.01 5/8 0.79 18/8 0.03 4/8 0.85 7/8 0.56 3/8 0.94 pt,` T78/8 <0.01 28/8 <0.01 144/8 <0.01 10/8 0.27 43/8 <0.01 18/8 0.02 pt¯ t T162/7 <0.01 46/7 <0.01 171/7 <0.01 22/7 <0.01 122/7 <0.01 39/7 <0.01 Ht¯ t+jets T36/7 <0.01 7/7 0.42 17/7 0.02 23/7 <0.01 21/7 <0.01 12/7 0.10 Ht¯ t T86/10 <0.01 37/10 <0.01 110/10 <0.01 16/10 0.10 47/10 <0.01 28/10 <0.01 |yt,h|47/17 <0.01 27/17 0.06 37/17 <0.01 23/17 0.15 30/17 0.03 26/17 0.07 |yt,`|40/14 <0.01 17/14 0.26 29/14 0.01 12/14 0.58 28/14 0.01 19/14 0.16 |yt¯ t|30/10 <0.01 8/10 0.58 23/10 0.01 6/10 0.81 14/10 0.19 7/10 0.74 mt¯ t52/10 <0.01 24/10 <0.01 81/10 <0.01 7/10 0.74 29/10 <0.01 22/10 0.02 pj,1 T115/15 <0.01 38/15 <0.01 413/15 <0.01 194/15 <0.01 143/15 <0.01 69/15 <0.01 pj,2 T46/9 <0.01 19/9 0.02 25/9 <0.01 74/9 <0.01 42/9 <0.01 29/9 <0.01 Nj32/5 <0.01 12/5 0.03 76/5 <0.01 78/5 <0.01 57/5 <0.01 62/5 <0.01 ∆φ(j1, th)17/9 0.05 8/9 0.53 150/9 <0.01 80/9 <0.01 42/9 <0.01 30/9 <0.01 ∆φ(j2, th)8/9 0.56 5/9 0.84 8/9 0.57 25/9 <0.01 85/9 <0.01 76/9 <0.01 ∆φ(b`, th)95/13 <0.01 34/13 <0.01 145/13 <0.01 16/13 0.23 52/13 <0.01 25/13 0.02 ∆φ(th, t`)111/5 <0.01 36/5 <0.01 134/5 <0.01 82/5 <0.01 90/5 <0.01 36/5 <0.01 ∆φ(j1, j2)24/11 0.01 16/11 0.13 31/11 <0.01 69/11 <0.01 237/11 <0.01 215/11 <0.01 m(j1, th)50/12 <0.01 20/12 0.06 221/12 <0.01 48/12 <0.01 41/12 <0.01 19/12 0.08 pj,1 Tvs Nj355/21 <0.01 205/21 <0.01 633/21 <0.01 316/21 <0.01 263/21 <0.01 159/21 <0.01 pj,1 Tvs pt,h T115/17 <0.01 53/17 <0.01 383/17 <0.01 152/17 <0.01 121/17 <0.01 74/17 <0.01 ∆φ(j1, th)vs pt,h T69/21 <0.01 43/21 <0.01 427/21 <0.01 223/21 <0.01 78/21 <0.01 60/21 <0.01 ∆φ(j1, th)vs Nj109/19 <0.01 64/19 <0.01 545/19 <0.01 250/19 <0.01 85/19 <0.01 60/19 <0.01 Table 3. χ2and p-values quantifying the level of agreement between the absolute unfolded spectra, several NLO+PS predictions and the respective NNLO reweighted spectrum. PWG+PY8 corresponds to the Powheg+Pythia sample, PWG+H7 to the Powheg+Herwig sample and MC@NLO+PY8 to the MadGraph5_aMC@NLO+Pythia sample. Observable PWG+PY8 PWG+PY8(ISR Down) PWG+PY8(ISR Up) PWG+PY8(hdamp = 3mt) SHERPA SHERPA (NLO norm.) 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,h T26/8 <0.01 26/8 <0.01 25/8 <0.01 36/8 <0.01 12/8 0.15 11/8 0.19 pt,` T78/8 <0.01 144/8 <0.01 20/8 0.01 50/8 <0.01 12/8 0.13 11/8 0.22 pt¯ t T162/7 <0.01 243/7 <0.01 340/7 <0.01 108/7 <0.01 70/7 <0.01 57/7 <0.01 Ht¯ t+jets T36/7 <0.01 38/7 <0.01 96/7 <0.01 52/7 <0.01 39/7 <0.01 34/7 <0.01 Ht¯ t T86/10 <0.01 119/10 <0.01 46/10 <0.01 72/10 <0.01 28/10 <0.01 22/10 0.01 |yt,h|47/17 <0.01 46/17 <0.01 46/17 <0.01 55/17 <0.01 25/17 0.10 20/17 0.29 |yt,`|40/14 <0.01 45/14 <0.01 34/14 <0.01 45/14 <0.01 24/14 0.05 18/14 0.19 |yt¯ t|30/10 <0.01 32/10 <0.01 23/10 <0.01 35/10 <0.01 22/10 0.02 20/10 0.03 mt¯ t52/10 <0.01 78/10 <0.01 75/10 <0.01 53/10 <0.01 31/10 <0.01 25/10 <0.01 pj,1 T115/15 <0.01 136/15 <0.01 272/15 <0.01 74/15 <0.01 140/15 <0.01 98/15 <0.01 pj,2 T46/9 <0.01 12/9 0.23 196/9 <0.01 81/9 <0.01 41/9 <0.01 19/9 0.02 Nj32/5 <0.01 51/5 <0.01 27/5 <0.01 41/5 <0.01 23/5 <0.01 16/5 <0.01 ∆φ(j1, th)17/9 0.05 34/9 <0.01 22/9 <0.01 23/9 <0.01 10/9 0.38 11/9 0.25 ∆φ(j2, th)8/9 0.56 7/9 0.67 22/9 0.01 19/9 0.03 6/9 0.74 3/9 0.96 ∆φ(b`, th)95/13 <0.01 116/13 <0.01 294/13 <0.01 119/13 <0.01 51/13 <0.01 28/13 0.01 ∆φ(th, t`)111/5 <0.01 164/5 <0.01 207/5 <0.01 79/5 <0.01 36/5 <0.01 39/5 <0.01 ∆φ(j1, j2)24/11 0.01 17/11 0.12 41/11 <0.01 38/11 <0.01 26/11 <0.01 20/11 0.05 m(j1, th)50/12 <0.01 111/12 <0.01 93/12 <0.01 43/12 <0.01 65/12 <0.01 40/12 <0.01 pj,1 Tvs Nj355/21 <0.01 495/21 <0.01 488/21 <0.01 254/21 <0.01 193/21 <0.01 137/21 <0.01 pj,1 Tvs pt,h T115/17 <0.01 192/17 <0.01 256/17 <0.01 87/17 <0.01 133/17 <0.01 87/17 <0.01 ∆φ(j1, th)vs pt,h T69/21 <0.01 104/21 <0.01 56/21 <0.01 73/21 <0.01 42/21 <0.01 32/21 0.06 ∆φ(j1, th)vs Nj109/19 <0.01 201/19 <0.01 66/19 <0.01 91/19 <0.01 35/19 0.01 26/19 0.14 Table 4. χ2and p-values quantifying the level of agreement between the absolute unfolded spectra and several NLO+PS predictions. PWG+PY8 corresponds to the Powheg+Pythia sample. SHERPA (NLO norm.) refers to the Sherpa sample with its default normalisation. All other samples are normalised to the inclusive NNLO+NNLL t¯ tcross-section prediction. χ2values for the different generators with the NNLO reweighting applied. Table 4shows the observed χ2values for the different Powheg+Pythia set-ups discussed in section 2. Figure 10 shows the measured top-quark transverse momentum distributions, the invariant mass of the t¯ tsystem, the rapidities of the top quarks and the t¯ tsystem, Ht¯ t Tand ∆φ(b`, th). In this figure, the distributions are compared with those from the nominal MC sample (with and without NNLO reweighting), the variations of the nominal MC sam- – 24 – JHEP06(2022)063 100 200 300 400 500 600 700 800 [GeV] j,1 T p 7− 10 6− 10 5− 10 4− 10 3− 10 2− 10 1− 10 1 10 2 10 ] 2 ) [pb/GeV t,h T dp j,1 T /(dp t t σd ATLAS -1 = 13 TeV, 139 fbs Boosted Fiducial phase-space 398≤ [GeV] t,h T ), 355 < p 4 (x10 496≤ [GeV] t,h T ), 398 < p 2 (x10 2000≤ [GeV] t,h T ), 496 < p 0 (x10 PWG+PY8 (a) 2 10 0.6 0.8 1 1.2 1.4 1.6 Data Prediction 30 2 10×3 [GeV] < 398 t,h T p≤355 2 10 30 2 10×3 [GeV] < 496 t,h T p≤398 2 10 30 2 10×3 [GeV] < 2000 t,h T p≤496 Stat+Syst Stat Only Data t =1.5 m damp PWG+PY8 h PWG+PY8 (NNLO rw.) PWG+H7 MC@NLO+PY8 Sherpa Sherpa (NLO norm.) t =3 m damp PWG+PY8 h PWG+PY8 ISR Up PWG+PY8 ISR Down -1 = 13 TeV, 139 fbs ATLAS Boosted Fiducial phase-space Absolute cross-section [GeV] j,1 T p (b) Figure 15. (a) Differential cross-section measurements as a function of the pTof the leading additional jet in bins of pt,h Tare compared with the prediction from the Powheg+Pythia MC generator. The measurement and the predictions are normalised by the factors shown in parentheses to aid visibility. (b) Ratio of the measured absolute cross-section to different NLO, and NLO reweighted to NNLO, predictions of t¯ tsignal for the same differential variables. PWG+PY8 corresponds to the Powheg+Pythia sample, PWG+H7 to the Powheg+Herwig sample and MCatNLO+PY8 to the MadGraph5_aMC@NLO+Pythia sample. The yellow band represents the total uncertainty of the measured differential cross-section while the orange band shows the statistical component. – 31 – JHEP06(2022)063 0 0.2 0.4 0.6 0.8 1 ) h ,t 1 j( π φ∆ 4− 10 3− 10 2− 10 1− 10 1 10 2 10 3 10 4 10 5 10 ) [pb/GeV] t,h T dp) h ,t 1 j( π φ∆ /(d t t σd ATLAS -1 = 13 TeV, 139 fbs Boosted Fiducial phase-space 398≤ [GeV] t,h T ), 355 < p 4 (x10 496≤ [GeV] t,h T ), 398 < p 2 (x10 2000≤ [GeV] t,h T ), 496 < p 0 (x10 PWG+PY8 (a) 0 0.5 1 0.6 0.8 1 1.2 1.4 Data Prediction [GeV] < 398 t,h T p≤355 0 0.5 1 [GeV] < 496 t,h T p≤398 0 0.5 1 [GeV] < 2000 t,h T p≤496 Stat+Syst Stat Only Data t =1.5 m damp PWG+PY8 h PWG+PY8 (NNLO rw.) PWG+H7 MC@NLO+PY8 Sherpa Sherpa (NLO norm.) t =3 m damp PWG+PY8 h PWG+PY8 ISR Up PWG+PY8 ISR Down -1 = 13 TeV, 139 fbs ATLAS Boosted Fiducial phase-space Absolute cross-section ) h ,t 1 j( π φ∆ (b) Figure 16. (a) Differential cross-section measurements as a function of the ∆φangle between the leading additional jet and the hadronically decaying top quark in bins of pt,h Tare compared with the prediction from the Powheg+Pythia MC generator. The measurement and the predictions are normalised by the factors shown in parentheses to aid visibility. (b) Ratio of the measured absolute cross-section to different NLO, and NLO reweighted to NNLO, predictions of t¯ tsignal for the same differential variables. PWG+PY8 corresponds to the Powheg+Pythia sample, PWG+H7 to the Powheg+Herwig sample and MCatNLO+PY8 to the MadGraph5_aMC@NLO+Pythia sample. The yellow band represents the total uncertainty of the measured differential cross-section while the orange band shows the statistical component. – 32 – JHEP06(2022)063 0 0.2 0.4 0.6 0.8 1 ) h ,t 1 j( π φ∆ 2− 10 1− 10 1 10 2 10 3 10 4 10 5 10 6 10 ) [pb] j dN) h ,t 1 j( π φ∆ /(d t t σd ATLAS -1 = 13 TeV, 139 fbs Boosted Fiducial phase-space = 1 j ), N 4 (x10 = 2 j ), N 2 (x10 > 2 j ), N 0 (x10 PWG+PY8 (a) 0 0.5 1 0.6 0.8 1 1.2 1.4 1.6 Data Prediction = 1 j N 0 0.5 1 = 2 j N 0 0.5 1 > 2 j N Stat+Syst Stat Only Data t =1.5 m damp PWG+PY8 h PWG+PY8 (NNLO rw.) PWG+H7 MC@NLO+PY8 Sherpa Sherpa (NLO norm.) t =3 m damp PWG+PY8 h PWG+PY8 ISR Up PWG+PY8 ISR Down -1 = 13 TeV, 139 fbs ATLAS Boosted Fiducial phase-space Absolute cross-section ) h ,t 1 j( π φ∆ (b) Figure 17. (a) Differential cross-section measurements as a function of the ∆φangle between the leading additional jet and the hadronically decaying top quark in bins of additional jet multiplicity are compared with the prediction from the Powheg+Pythia MC generator. The measurement and the predictions are normalised by the factors shown in parentheses to aid visibility. (b) Ratio of the measured absolute cross-section to different NLO, and NLO reweighted to NNLO, predictions of t¯ tsignal for the same differential variables. PWG+PY8 corresponds to the Powheg+Pythia sample, PWG+H7 to the Powheg+Herwig sample and MCatNLO+PY8 to the MadGraph5_aMC@NLO+Pythia sample. The yellow band represents the total uncertainty of the measured differential cross-section while the orange band shows the statistical component. – 33 – JHEP06(2022)063 7 Limits on EFT operators The sensitivity of the analysis to potential new physics in t¯ tproduction is explored by interpreting the measured pt,h Tdistribution in terms of dimension-six operators within the effective field theory framework. The interpretation allows two Wilson coefficients that are sensitive to t¯ tproduction to be non-zero: CtG and C(8) tq . All other Wilson coefficients, for both the dimension-six and higher-dimensional operators, are assumed to be zero. The OtG operator primarily changes the overall rate of t¯ tproduction while the O(8) tq operator results in additional t¯ tevents at high energy. Example LO Feynman diagrams for the two operators are shown in figure 18. The two operators can be disentangled by fitting a differential cross-section measurement. The pt,h Tdistribution, shown in figure 10a, is chosen as the observable, based on simulation studies that considered the sensitivity of the variables as well as the stability of the variables when going from LO to NLO QCD. The differential cross-section is parameterised as a polynomial of second degree in the two Wilson coefficients under consideration: σj(CtG, C(8) tq ) = pj 0+pj 1·CtG +pj 2·C(8) tq +pj 3·(CtG)2+pj 4·(C(8) tq )2+pj 5·CtG ·C(8) tq where the index jlabels the bins of the differential distribution. The parameters pj iwith i≥1are extracted from fits to the EFT samples with (CtG, C(8) tq )=(±1or 0,±1or 0); see section 2for a description of the samples. Two separate fits are performed, one using samples containing the full EFT contributions (i.e. proportional to Λ−2and Λ−4), and the second containing only EFT contributions proportional to Λ−2. This allows the impact of the Λ−4terms on the sensitivity of the results to be examined and the two set-ups are referred to as the Λ−4and Λ−2models in the rest of this section. The parameters pj 0determine the Standard Model prediction and are taken from the Powheg+Pythia sample after reweighting it to the NNLO prediction. The parameterisation of the EFT effects assumes that the background estimate is independent of the tested operators, which is reasonable given the high purity of the selected event sample. The EFTfitter [109] package is used to extract the limits on the Wilson coefficients by minimising the likelihood: −2 ln p(CtG, C(8) tq |m) = m−σ(CtG, C(8) tq )TM−1m−σ(CtG, C(8) tq ) ggt ¯ t g (a) ¯q q t ¯ t (b) Figure 18. Example LO Feynman diagrams for EFT contributions from (a) CtG and (b) C(8) tq . Couplings affected by EFT contributions are marked by the black dots. – 34 – JHEP06(2022)063 where mis the vector of measurements of each bin of the observed distribution and σ(CtG, C(8) tq )is the vector of corresponding predictions for each bin that depends on the two Wilson coefficients of interest (CtG,C(8) tq ). The covariance matrix, M, is a sum of the matrices corresponding to the experimental and theoretical uncertainties, M=Me+Mt. This procedure assumes that the theoretical uncertainties in the predicted cross-section are not correlated with the theoretical uncertainties in the experimental measurement (described in section 5.4). The covariance matrix for the experimental uncertainties corresponds exactly to the uncertainties described in section 5. The theoretical uncertainties are determined using the Powheg+Pythia t¯ tsample reweighted to NNLO. The scales µrand µfare varied to 2µand µ/2, with the condition 1/2≤µr/µf≤2, giving seven variations. The envelope of those variations is used to define alternative shapes for the three parton-level distributions used in the NNLO reweighting procedure. The difference between each alternative prediction and the nominal one gives an estimate of the uncertainty in the shape of the distributions provided by the NNLO calculations. The uncertainty in all three distributions is included and assumed to be uncorrelated with the uncertainty in the other distributions. The uncertainty due to the choice of PDF set is also included. Since all these uncertainties cover only the shape differences, an additional 6%uncertainty is included for the uncertainty in the inclusive t¯ tcross-section, covering the variations of the scales, PDFs, αsand mt. The posterior probability distribution for the Wilson coefficients is extracted using the equation of Bayes and Laplace, as implemented in the Bayesian Analysis Toolkit [110]. The prior probability distribution for the Wilson coefficients is taken to be uniform. To make the dependence of the sensitivity to the Wilson coefficients on the energy scale of the new physics explicit, the results are presented for the product Ci(TeV/Λ)2. This also facilitates straightforward comparisons with results where Λ=1TeV. The credible interval for each Wilson coefficient is extracted by marginalising over the other coefficient. The fit is also performed with only one Wilson coefficient as a free parameter and the other fixed to zero; these are referred to as individual fits. The measured pt,h Tdifferential cross-section is compared with the SM prediction and uncertainty in figure 19. The figure also displays the best fit for the EFT models, where the fitted Wilson coefficients are CtG =−0.11+0.16 −0.25 (Λ/TeV)2,C(8) tq =−0.43+0.40 −0.06 (Λ/TeV)2 for Λ−4and CtG =−0.24 ±0.23 (Λ/TeV)2,C(8) tq = 0.03 ±0.17 (Λ/TeV)2for Λ−2. These values agree with zero within two standard deviations, indicating there is no evidence of new physics in the data. The fit prefers negative values for CtG because the measured cross-section is lower than the SM prediction. Table 5shows the expected and observed marginalised credible intervals for the nominal fit and the individual fits. The expected and observed posterior distributions are shown in figure 20. The expected and observed credible intervals are asymmetric in the Λ−4model because the linear and quadratic terms can cancel out to some extent when the Wilson coefficients are negative. The impact of the different bins in the distribution is investigated by repeating the fit with a subset of the measured bins. Figure 21 shows the evolution of the posterior distribution as bins are added to the interpretation. With only a single bin, the operators are largely degenerate and the fit can only constrain the combination of the two. As bins are added to the fit, the – 35 – JHEP06(2022)063 5− 10 4− 10 3− 10 2− 10 [pb/GeV] T t,h / d p t t σd Data =-0.43) (8) tq =-0.11, C tG C model ( -4 Λ PWG+PY8 (NNLO rw.) Prediction uncertainty -1 = 13 TeV, 139 fbs ATLAS 500 1000 1500 2000 [GeV] T t,h p 0.8 1 1.2 SM Data or EFT (a) 5− 10 4− 10 3− 10 2− 10 [pb/GeV] T t,h / d p t t σd Data =0.03) (8) tq =-0.24, C tG C model ( -2 Λ PWG+PY8 (NNLO rw.) Prediction uncertainty -1 = 13 TeV, 139 fbs ATLAS 500 1000 1500 2000 [GeV] T t,h p 0.8 1 1.2 SM Data or EFT (b) Figure 19. Differential cross-section measurement of pt,h Tused in the EFT interpretation. The data are compared with the SM prediction in red and the EFT model prediction in blue at the respective global modes for (a) the Λ−4model and (b) the Λ−2model. The lower panel in each plot displays the ratio of the data or EFT model to the SM prediction. The shaded red band shows the uncertainty in the SM prediction used in the EFT fit. Model Ci(Λ/TeV)2Marginalised 95% intervals Individual 95% intervals Global fit 95% Expected Observed Expected Observed limits [111] Λ−4CtG [−0.44, 0.35] [−0.53, 0.21] [−0.44, 0.28] [−0.52, 0.15] [0.006, 0.107] C(8) tq [−0.57, 0.17] [−0.60, 0.13] [−0.57, 0.18] [−0.64, 0.12] [−0.48, 0.39] Λ−2CtG [−0.44, 0.44] [−0.68, 0.21] [−0.41, 0.42] [−0.63, 0.20] [0.007, 0.111] C(8) tq [−0.35, 0.35] [−0.30, 0.36] [−0.35, 0.36] [−0.34, 0.27] [−0.40, 0.61] Table 5. Expected and observed 95% intervals for the Wilson coefficients (Ci). The marginalised results show the intervals extracted from the nominal fit where both Wilson coefficients are allowed to vary. The individual intervals are extracted from fits where only the Wilson coefficient under study is allowed to differ from zero. The results are compared with the individual limits obtained in ref. [111]. ability of the fit to distinguish between the operators is improved. The figure also shows that the constraint on C(8) tq is dominated by the measurements at high pt,h T. The observed constraints are compared in table 5with the individual limits obtained in a recent global analysis based on multiple measurements [111]. The limits on CtG obtained in this paper are significantly weaker than these, but the limits on C(8) tq are more stringent than those obtained in the global fit, which, given the use of only a single dataset, indicates that the data presented here can provide important constraining power in future global EFT fits. – 36 – JHEP06(2022)063 1.0 0.5 0.0 0.5 1.0 C tG (TeV/ )2 1.00 0.75 0.50 0.25 0.00 0.25 0.50 0.75 1.00 C(8) tq (TeV/ )2 ATLAS s= 13 TeV, 139 fb 1 Expected limits, 4 SM Global Mode 99.7% region 95.5% region 68.4% region (a) 1.0 0.5 0.0 0.5 1.0 C tG (TeV/ )2 1.00 0.75 0.50 0.25 0.00 0.25 0.50 0.75 1.00 C(8) tq (TeV/ )2 ATLAS s= 13 TeV, 139 fb 1 Observed limits, 4 SM Global Mode 99.7% region 95.5% region 68.4% region (b) 1.0 0.5 0.0 0.5 1.0 C tG (TeV/ )2 1.00 0.75 0.50 0.25 0.00 0.25 0.50 0.75 1.00 C(8) tq (TeV/ )2 ATLAS s= 13 TeV, 139 fb 1 Expected limits, 2 SM Global Mode 99.7% region 95.5% region 68.4% region (c) 1.0 0.5 0.0 0.5 1.0 C tG (TeV/ )2 1.00 0.75 0.50 0.25 0.00 0.25 0.50 0.75 1.00 C(8) tq (TeV/ )2 ATLAS s= 13 TeV, 139 fb 1 Observed limits, 2 SM Global Mode 99.7% region 95.5% region 68.4% region (d) Figure 20. Two-dimensional posterior distributions for the two Wilson coefficients CtG and C(8) tq obtained from fitting the pt,h Tdistribution. (a) Shows the posterior distribution expected from the SM prediction and (b) shows the distribution obtained from the data, both for the Λ−4model. The same distributions are shown in (c) and (d) for the Λ−2model. The 68.4 %,95.5 % and 99.7 % regions are shown in green, yellow and red respectively. 8 Conclusions This article presents precise cross-section measurements of t¯ tevents containing a high transverse momentum top quark that has decayed hadronically (pt,h T>355 GeV). The events were selected from the full 139 fb−1Run-2 ATLAS dataset of 13 TeV proton-proton collisions at the LHC and the cross-sections were extracted by unfolding the reconstructed distributions. The precision of the results is significantly better than in previous measurements. This improvement in precision is largely driven by the introduction of a novel technique to use the invariant mass of the selected large-radius jet from the hadronically decaying top quark to reduce the impact of jet energy scale uncertainties. In addition, the background from W+jets and single top-quark production is reduced compared to the – 37 – JHEP06(2022)063 (a) (b) Figure 21. Evolution of the 95% observed credible region when adding the bins of the measured pt,h Tdistribution to the interpretation one-by-one for (a) the Λ−4model and (b) the Λ−2model. The coloured ellipses show the 95% regions obtained from fitting the pt,h Trange indicated in the legend. previous ATLAS measurement by requiring at least two b-tagged jets and m`b <180 GeV, which reduces the impact of the background uncertainties on the measurements. The fiducial cross-section is measured to be 1.267 ±0.005 (stat.)±0.053 (syst.)pb. The measurements are compared with predictions from NLO+PS MC generators. No single generator is able to describe all the measured variables well. Applying parton-level reweighting to match NNLO QCD predictions gives better agreement with the data for all generators, indicating that these corrections are relevant given the precision of the measurements. The number of additional jets is best modelled by the Sherpa generator, which provides NLO accuracy for the first additional jet, but the details of the additional radiation are not well described by any of the MC predictions. The sensitivity of the measurement to new physics beyond the Standard Model is illustrated by using the transverse momentum distribution of the hadronically decaying top quark to set limits in the context of effective field theory. No evidence of new physics is seen and the 95% credible intervals of the Wilson coefficients are CtG ∈[−0.53,0.21] (Λ/TeV)2and C(8) tq ∈[−0.60,0.13] (Λ/TeV)2when including EFT contributions proportional to Λ−2and Λ−4. The results demonstrate that the analysis can disentangle the OtG and O(8) tq operators, and the stringent limits placed on C(8) tq demonstrate the data will be highly relevant in future global fits. Acknowledgments 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; ANID, Chile; CAS, MOST and NSFC, China; Minciencias, Colombia; MEYS CR, Czech Republic; DNRF and DNSRC, – 38 – JHEP06(2022)063 Denmark; IN2P3-CNRS and CEA-DRF/IRFU, France; SRNSFG, Georgia; BMBF, HGF and MPG, Germany; GSRI, Greece; RGC and Hong Kong SAR, China; ISF and Benoziyo Center, Israel; INFN, Italy; MEXT and JSPS, Japan; CNRST, Morocco; NWO, Netherlands; RCN, Norway; MEiN, Poland; FCT, Portugal; MNE/IFA, Romania; JINR; MES of Russia and NRC KI, Russian Federation; MESTD, Serbia; MSSR, Slovakia; ARRS and MIZŠ, Slovenia; DSI/NRF, South Africa; MICINN, 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, CANARIE, Compute Canada and CRC, Canada; COST, ERC, ERDF, Horizon 2020 and Marie Skłodowska-Curie Actions, European Union; Investissements d’Avenir Labex, Investissements d’Avenir Idex and 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; Norwegian Financial Mechanism 2014-2021, Norway; NCN and NAWA, Poland; La Caixa Banking Foundation, CERCA Programme Generalitat de Catalunya and PROMETEO and GenT Programmes Generalitat Valenciana, Spain; Göran Gustafssons Stiftelse, Sweden; 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 (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. [112]. – 39 – JHEP06(2022)063 Observable PWG+PY8 PWG+PY8(NNLO weight) MC@NLO+PY8 MC@NLO+PY8(NNLO weight) PWG+H7 PWG+H7(NNLO weight) 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,h T3/7 0.84 2/7 0.95 3/7 0.85 3/7 0.89 3/7 0.90 3/7 0.92 pt,` T24/7 <0.01 15/7 0.03 76/7 <0.01 7/7 0.39 24/7 <0.01 13/7 0.07 pt¯ t T95/6 <0.01 34/6 <0.01 109/6 <0.01 20/6 <0.01 96/6 <0.01 35/6 <0.01 Ht¯ t+jets T9/6 0.17 4/6 0.71 5/6 0.57 21/6 <0.01 14/6 0.03 11/6 0.08 Ht¯ t T39/9 <0.01 28/9 <0.01 63/9 <0.01 13/9 0.14 33/9 <0.01 26/9 <0.01 |yt,h|21/16 0.18 23/16 0.12 21/16 0.20 21/16 0.17 23/16 0.10 25/16 0.06 |yt,`|14/13 0.40 13/13 0.44 12/13 0.50 11/13 0.63 20/13 0.09 18/13 0.16 |yt¯ t|7/9 0.61 6/9 0.77 8/9 0.51 5/9 0.85 8/9 0.51 6/9 0.72 mt¯ t18/9 0.03 19/9 0.02 51/9 <0.01 6/9 0.74 20/9 0.02 21/9 0.01 pj,1 T84/14 <0.01 35/14 <0.01 318/14 <0.01 168/14 <0.01 125/14 <0.01 65/14 <0.01 pj,2 T29/8 <0.01 18/8 0.02 20/8 <0.01 51/8 <0.01 37/8 <0.01 28/8 <0.01 Nj7/4 0.12 8/4 0.08 48/4 <0.01 72/4 <0.01 47/4 <0.01 58/4 <0.01 ∆φ(j1, th)9/8 0.32 7/8 0.51 113/8 <0.01 68/8 <0.01 37/8 <0.01 29/8 <0.01 ∆φ(j2, th)5/8 0.78 5/8 0.80 6/8 0.67 15/8 0.06 67/8 <0.01 61/8 <0.01 ∆φ(b`, th)35/12 <0.01 21/12 0.06 92/12 <0.01 13/12 0.35 32/12 <0.01 19/12 0.08 ∆φ(th, t`)62/4 <0.01 28/4 <0.01 74/4 <0.01 76/4 <0.01 71/4 <0.01 33/4 <0.01 ∆φ(j1, j2)16/10 0.11 16/10 0.10 26/10 <0.01 51/10 <0.01 197/10 <0.01 186/10 <0.01 m(j1, th)30/11 <0.01 19/11 0.06 166/11 <0.01 34/11 <0.01 34/11 <0.01 18/11 0.07 pj,1 Tvs Nj261/20 <0.01 194/20 <0.01 470/20 <0.01 273/20 <0.01 231/20 <0.01 154/20 <0.01 pj,1 Tvs pt,h T80/16 <0.01 50/16 <0.01 291/16 <0.01 127/16 <0.01 105/16 <0.01 71/16 <0.01 ∆φ(j1, th)vs pt,h T48/20 <0.01 39/20 <0.01 333/20 <0.01 196/20 <0.01 68/20 <0.01 56/20 <0.01 ∆φ(j1, th)vs Nj68/18 <0.01 58/18 <0.01 404/18 <0.01 210/18 <0.01 73/18 <0.01 58/18 <0.01 Table 6. χ2and p-values quantifying the level of agreement between the relative unfolded spectra, several NLO+PS predictions and the respective NNLO reweighted spectrum. PWG+PY8 corresponds to the Powheg+Pythia sample, PWG+H7 to the Powheg+Herwig sample and MC@NLO+PY8 to the MadGraph5_aMC@NLO+Pythia sample. A Normalised differential cross-section results In this appendix, the differential cross-section results after normalising to the cross-section measured in the fiducial region are presented. These results allow comparisons of the shape of the measured observables with MC predictions. Tables 6and 7show the χ2 values for the normalised distributions for the different MC models. Figure 22 shows the differential cross-section measurements of pt,h T,pt,` T,mt¯ t,|yt,h|,|yt,`|,|yt¯ t|,Ht¯ t Tand ∆φ(b`, th) compared with the predictions from different NLO generator set-ups. The same variables are compared in figure 23 with the MC generators with and without the reweighting to the NNLO prediction. The variables sensitive to additional radiation are shown in figures 24 and 25. The double-differential measurements are shown in figures 26–29. – 40 – JHEP06(2022)063 0 0.2 0.4 0.6 0.8 1 ) h ,t 1 j( π φ∆ 4− 10 3− 10 2− 10 1− 10 1 10 2 10 3 10 4 10 5 10 ) [1/GeV] t,h T dp) h ,t 1 j( π φ∆ /(d t t σ d tt σ1/ ATLAS -1 = 13 TeV, 139 fbs Boosted Fiducial phase-space 398≤ [GeV] t,h T ), 355 < p 4 (x10 496≤ [GeV] t,h T ), 398 < p 2 (x10 2000≤ [GeV] t,h T ), 496 < p 0 (x10 PWG+PY8 (a) 0 0.5 1 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 Data Prediction [GeV] < 398 t,h T p≤355 0 0.5 1 [GeV] < 496 t,h T p≤398 0 0.5 1 [GeV] < 2000 t,h T p≤496 Stat+Syst Stat Only Data t =1.5 m damp PWG+PY8 h PWG+PY8 (NNLO rw.) PWG+H7 MC@NLO+PY8 Sherpa t =3 m damp PWG+PY8 h PWG+PY8 ISR Up PWG+PY8 ISR Down -1 = 13 TeV, 139 fbs ATLAS Boosted Fiducial phase-space Relative cross-section ) h ,t 1 j( π φ∆ (b) Figure 28. (a) Normalised differential cross-section measurements as a function of the ∆φangle between the leading additional jet and the hadronically decaying top quark in bins of pt,h T are compared with the prediction from the Powheg+Pythia MC generator. The measurement and the predictions are further normalised by the factors shown in parentheses to aid visibility. (b) Ratio of the measured normalised cross-section to different NLO, and NLO reweighted to NNLO, predictions of t¯ tsignal for the same differential variables. PWG+PY8 corresponds to the Powheg+Pythia sample, PWG+H7 to the Powheg+Herwig sample and MCatNLO+PY8 to the MadGraph5_aMC@NLO+Pythia sample. The yellow band represents the total uncertainty of the measured differential cross-section while the orange band shows the statistical component. – 47 – JHEP06(2022)063 0 0.2 0.4 0.6 0.8 1 ) h ,t 1 j( π φ∆ 2− 10 1− 10 1 10 2 10 3 10 4 10 5 10 6 10 ) j dN) h ,t 1 j( π φ∆ /(d t t σ d tt σ1/ ATLAS -1 = 13 TeV, 139 fbs Boosted Fiducial phase-space = 1 j ), N 4 (x10 = 2 j ), N 2 (x10 > 2 j ), N 0 (x10 PWG+PY8 (a) 0 0.5 1 0.6 0.8 1 1.2 1.4 Data Prediction = 1 j N 0 0.5 1 = 2 j N 0 0.5 1 > 2 j N Stat+Syst Stat Only Data t =1.5 m damp PWG+PY8 h PWG+PY8 (NNLO rw.) PWG+H7 MC@NLO+PY8 Sherpa t =3 m damp PWG+PY8 h PWG+PY8 ISR Up PWG+PY8 ISR Down -1 = 13 TeV, 139 fbs ATLAS Boosted Fiducial phase-space Relative cross-section ) h ,t 1 j( π φ∆ (b) Figure 29. (a) Normalised differential cross-section measurements as a function of the ∆φangle between the leading additional jet and the hadronically decaying top quark in bins of additional jet multiplicity are compared with the prediction from the Powheg+Pythia MC generator. The measurement and the predictions are further normalised by the factors shown in parentheses to aid visibility. (b) Ratio of the measured normalised cross-section to different NLO, and NLO reweighted to NNLO, predictions of t¯ tsignal for the same differential variables. PWG+PY8 corresponds to the Powheg+Pythia sample, PWG+H7 to the Powheg+Herwig sample and MCatNLO+PY8 to the MadGraph5_aMC@NLO+Pythia sample. The yellow band represents the total uncertainty of the measured differential cross-section while the orange band shows the statistical component. – 48 – JHEP06(2022)063 Open Access. 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Schune142,A. Schwartzman150,T.A. Schwarz104,Ph. Schwemling142, R. Schwienhorst105,A. Sciandra143,G. Sciolla26,F. Scuri71a, F. Scutti103,C.D. Sebastiani90, K. Sedlaczek47,P. Seema18,S.C. Seidel115,A. Seiden143,B.D. Seidlitz29,T. Seiss37,C. Seitz46, J.M. Seixas80b,G. Sekhniaidze69a,S.J. Sekula42,L. Selem4,N. Semprini-Cesari23b,23a,S. Sen49, V. Senthilkumar170,L. Serin64,L. Serkin66a,66b,M. Sessa74a,74b,H. Severini126,S. Sevova150, F. Sforza55b,55a,A. Sfyrla54,E. Shabalina53,R. Shaheen151,J.D. Shahinian134, N.W. Shaikh45a,45b,D. Shaked Renous176,L.Y. Shan14a,M. Shapiro17,A. Sharma36, A.S. Sharma1,S. Sharma46,P.B. Shatalov121,K. Shaw153,S.M. Shaw99,P. Sherwood94,L. Shi94, C.O. Shimmin179,Y. Shimogama175,J.D. Shinner93,I.P.J. Shipsey132,S. Shirabe54, M. Shiyakova79,J. Shlomi176,M.J. Shochet37,J. Shojaii103,D.R. Shope151,S. Shrestha125, E.M. Shrif33g,M.J. Shroff172,P. Sicho138,A.M. Sickles169,E. Sideras Haddad33g, O. Sidiropoulou36,A. Sidoti23b,F. Siegert48,Dj. Sijacki15,F. Sili88,J.M. Silva20, M.V. Silva Oliveira36,S.B. Silverstein45a, S. Simion64,R. Simoniello36,E.L. Simpson57, N.D. Simpson96,S. Simsek21d,S. Sindhu53,P. Sinervo163,V. Sinetckii111,S. Singh149, S. Singh163,S. Sinha46,S. Sinha33g,M. Sioli23b,23a,I. Siral129,S.Yu. Sivoklokov111, J. Sjölin45a,45b,A. Skaf53,E. Skorda96,P. Skubic126,M. Slawinska84, V. Smakhtin176, B.H. Smart141,J. Smiesko140,S.Yu. Smirnov110,Y. Smirnov110,L.N. Smirnova111,q, O. Smirnova96,E.A. Smith37,H.A. Smith132, R. Smith150,M. Smizanska89,K. Smolek139, A. Smykiewicz84,A.A. Snesarev109,H.L. Snoek117,S. Snyder29,R. Sobie172,v,A. Soffer158, C.A. Solans Sanchez36,E.Yu. Soldatov110,U. Soldevila170,A.A. Solodkov120,S. Solomon52, A. Soloshenko79,K. Solovieva52,O.V. Solovyanov120,V. Solovyev135,P. Sommer146,H. Son166, A. Sonay13,W.Y. Song164b,A. Sopczak139, A.L. Sopio94,F. Sopkova28b, V. Sothilingam61a, S. Sottocornola70a,70b,R. Soualah122c,A.M. Soukharev119b,119a,Z. Soumaimi35e,D. South46, S. Spagnolo67a,67b,M. Spalla113,M. Spangenberg174,F. Spanò93,D. Sperlich52,G. Spigo36, M. Spina153,S. Spinali89,D.P. Spiteri57,M. Spousta140, E.J. Staats34,A. Stabile68a,68b, R. Stamen61a,M. Stamenkovic117,A. Stampekis20,M. Standke24,E. Stanecka84,B. Stanislaus17, M.M. Stanitzki46,M. Stankaityte132,B. Stapf46,E.A. Starchenko120,G.H. Stark143,J. Stark100, D.M. Starko164b,P. Staroba138,P. Starovoitov61a,S. Stärz102,R. Staszewski84, G. Stavropoulos44,J. Steentoft168,P. Steinberg29,A.L. Steinhebel129,B. Stelzer149,164a, H.J. Stelzer136,O. Stelzer-Chilton164a,H. Stenzel56,T.J. Stevenson153,G.A. Stewart36, M.C. Stockton36,G. Stoicea27b,M. Stolarski137a,S. Stonjek113,A. Straessner48, J. Strandberg151,S. Strandberg45a,45b,M. Strauss126,T. Strebler100,P. Strizenec28b, R. Ströhmer173,D.M. Strom129,L.R. Strom46,R. Stroynowski42,A. Strubig45a,45b, – 64 – JHEP06(2022)063 S.A. Stucci29,B. Stugu16,J. Stupak126,N.A. Styles46,D. Su150,S. Su60a,W. Su60d,145,60c, X. Su60a,64,K. Sugizaki160,V.V. Sulin109,M.J. Sullivan90,D.M.S. Sultan75a,75b, L. Sultanaliyeva109,S. Sultansoy3b,T. Sumida85,S. Sun104,S. Sun177, O. Sunneborn Gudnadottir168,M.R. Sutton153,M. Svatos138,M. Swiatlowski164a,T. Swirski173, I. Sykora28a,M. Sykora140,T. Sykora140,D. Ta98,K. Tackmann46,u,A. Taffard167, R. Tafirout164a,R.H.M. Taibah133,R. Takashima86,K. Takeda82,E.P. Takeva50,Y. Takubo81, M. Talby100,A.A. Talyshev119b,119a,K.C. Tam62b, N.M. Tamir158,A. Tanaka160,J. Tanaka160, R. Tanaka64, J. Tang60c,Z. Tao171,S. Tapia Araya78,S. Tapprogge98, A. Tarek Abouelfadl Mohamed105,S. Tarem157,K. Tariq60b,G. Tarna27b,G.F. Tartarelli68a, P. Tas140,M. Tasevsky138,E. Tassi41b,41a,G. Tateno160,Y. Tayalati35e,G.N. Taylor103, W. Taylor164b, H. Teagle90,A.S. Tee177,R. Teixeira De Lima150,P. Teixeira-Dias93,J.J. Teoh163, K. Terashi160,J. Terron97,S. Terzo13,M. Testa51,R.J. Teuscher163,v,N. Themistokleous50, T. Theveneaux-Pelzer18, O. Thielmann178, D.W. Thomas93,J.P. Thomas20,E.A. Thompson46, P.D. Thompson20,E. Thomson134,E.J. Thorpe92,Y. Tian53,V. Tikhomirov109,aa, Yu.A. Tikhonov119b,119a, S. Timoshenko110,E.X.L. Ting1,P. Tipton179,S. Tisserant100, S.H. Tlou33g,A. Tnourji38,K. Todome23b,23a,S. Todorova-Nova140, S. Todt48, M. Togawa81, J. Tojo87,S. Tokár28a,K. Tokushuku81,R. Tombs32,M. Tomoto81,114,L. Tompkins150, P. Tornambe101,E. Torrence129,H. Torres48,E. Torró Pastor170,M. Toscani30,C. Tosciri37, D.R. Tovey146, A. Traeet16,I.S. Trandafir27b,C.J. Treado123,T. Trefzger173,A. Tricoli29, I.M. Trigger164a,S. Trincaz-Duvoid133,D.A. Trischuk171, W. Trischuk163,B. Trocmé58, A. Trofymov64,C. Troncon68a,F. Trovato153,L. Truong33c,M. Trzebinski84,A. Trzupek84, F. Tsai152,M. Tsai104,A. Tsiamis159, P.V. Tsiareshka106,A. Tsirigotis159,s,V. Tsiskaridze152, E.G. Tskhadadze156a,M. Tsopoulou159,Y. Tsujikawa85,I.I. Tsukerman121,V. Tsulaia17, S. Tsuno81, O. Tsur157,D. Tsybychev152,Y. Tu62b,A. Tudorache27b,V. Tudorache27b, A.N. Tuna36,S. Turchikhin79,I. Turk Cakir3a,R. Turra68a,P.M. Tuts39,S. Tzamarias159, P. Tzanis10,E. Tzovara98, K. Uchida160,F. Ukegawa165,P.A. Ulloa Poblete144c,G. Unal36, M. Unal11,A. Undrus29,G. Unel167,K. Uno160,J. Urban28b,P. Urquijo103,G. Usai8, R. Ushioda161,M. Usman108,Z. Uysal21b,V. Vacek139,B. Vachon102,K.O.H. Vadla131, T. Vafeiadis36,C. Valderanis112,E. Valdes Santurio45a,45b,M. Valente164a,S. Valentinetti23b,23a, A. Valero170,A. Vallier100,J.A. Valls Ferrer170,T.R. Van Daalen145,P. Van Gemmeren6, S. Van Stroud94,I. Van Vulpen117,M. Vanadia73a,73b,W. Vandelli36,M. Vandenbroucke142, E.R. Vandewall127,D. Vannicola158,L. Vannoli55b,55a,R. Vari72a,E.W. Varnes7,C. Varni17, T. Varol155,D. Varouchas64,K.E. Varvell154,M.E. Vasile27b, L. Vaslin38,G.A. Vasquez172, F. Vazeille38,D. Vazquez Furelos13,T. Vazquez Schroeder36,J. Veatch53,V. Vecchio99, M.J. Veen117,I. Veliscek132,L.M. Veloce163,F. Veloso137a,137c,S. Veneziano72a, A. Ventura67a,67b,A. Verbytskyi113,M. Verducci71a,71b,C. Vergis24,M. Verissimo De Araujo80b, W. Verkerke117,J.C. Vermeulen117,C. Vernieri150,P.J. Verschuuren93,M. Vessella101, M.L. Vesterbacka123,M.C. Vetterli149,ae,A. Vgenopoulos159,N. Viaux Maira144f,T. Vickey146, O.E. Vickey Boeriu146,G.H.A. Viehhauser132,L. Vigani61b,M. Villa23b,23a, M. Villaplana Perez170, E.M. Villhauer50,E. Vilucchi51,M.G. Vincter34,G.S. Virdee20, A. Vishwakarma50,C. Vittori23b,23a,I. Vivarelli153, V. Vladimirov174,E. Voevodina113, M. Vogel178,P. Vokac139,J. Von Ahnen46,E. Von Toerne24,B. Vormwald36,V. Vorobel140, K. Vorobev110,M. Vos170,J.H. Vossebeld90,M. Vozak117,L. Vozdecky92,N. Vranjes15, M. Vranjes Milosavljevic15, V. Vrba139,*,M. Vreeswijk117,N.K. Vu100,R. Vuillermet36, O.V. Vujinovic98,I. Vukotic37,S. Wada165, C. Wagner101,W. Wagner178,S. Wahdan178, H. Wahlberg88,R. Wakasa165,M. Wakida114,V.M. Walbrecht113,J. Walder141,R. Walker112, W. Walkowiak148,A.M. Wang59,A.Z. Wang177,C. Wang60a,C. Wang60c,H. Wang17, J. Wang62a,P. Wang42,R.-J. Wang98,R. Wang59,R. Wang6,S.M. Wang155, S. Wang60b, – 65 – JHEP06(2022)063 T. Wang60a,W.T. Wang77,W.X. Wang60a,X. Wang14c,X. Wang169,X. Wang60c,Y. Wang60d, Z. Wang104,Z. Wang60d,49,60c,Z. Wang104,A. Warburton102,R.J. Ward20,N. Warrack57, A.T. Watson20,M.F. Watson20,G. Watts145,B.M. Waugh94,A.F. Webb11,C. Weber29, M.S. Weber19,S.A. Weber34,S.M. Weber61a, C. Wei60a,Y. Wei132,A.R. Weidberg132, J. Weingarten47,M. Weirich98,C. Weiser52,T. Wenaus29,B. Wendland47,T. Wengler36, N.S. Wenke113,N. Wermes24,M. Wessels61a,K. Whalen129,A.M. Wharton89,A.S. White59, A. White8,M.J. White1,D. Whiteson167,L. Wickremasinghe130,W. Wiedenmann177,C. Wiel48, M. Wielers141, N. Wieseotte98,C. Wiglesworth40,L.A.M. Wiik-Fuchs52, D.J. Wilbern126, H.G. Wilkens36,D.M. Williams39, H.H. Williams134,S. Williams32,S. Willocq101, P.J. Windischhofer132,F. Winklmeier129,B.T. Winter52, M. Wittgen150,M. Wobisch95, A. Wolf98,R. Wölker132, J. Wollrath167,M.W. Wolter84,H. Wolters137a,137c,V.W.S. Wong171, A.F. Wongel46,S.D. Worm46,B.K. Wosiek84,K.W. Woźniak84,K. Wraight57,J. Wu14a,14d, S.L. Wu177,X. Wu54,Y. Wu60a,Z. Wu142,60a,J. Wuerzinger132,T.R. Wyatt99,B.M. Wynne50, S. Xella40,L. Xia14c, M. Xia14b,J. Xiang62c,X. Xiao104,M. Xie60a,X. Xie60a, I. Xiotidis153, D. Xu14a, H. Xu60a,H. Xu60a,L. Xu60a,R. Xu134,T. Xu60a,W. Xu104,Y. Xu14b,Z. Xu60b, Z. Xu150,B. Yabsley154,S. Yacoob33a,N. Yamaguchi87,Y. Yamaguchi161,H. Yamauchi165, T. Yamazaki17,Y. Yamazaki82, J. Yan60c,S. Yan132,Z. Yan25,H.J. Yang60c,60d,H.T. Yang17, S. Yang60a,T. Yang62c,X. Yang60a,X. Yang14a,Y. Yang42,Z. Yang104,60a,W-M. Yao17, Y.C. Yap46,H. Ye14c,J. Ye42,S. Ye29,X. Ye60a,I. Yeletskikh79,M.R. Yexley89,P. Yin39, K. Yorita175,C.J.S. Young52,C. Young150,M. Yuan104,R. Yuan60b,i,X. Yue61a,M. Zaazoua35e, B. Zabinski84,G. Zacharis10, E. Zaid50,A.M. Zaitsev120,z,T. Zakareishvili156b,N. Zakharchuk34, S. Zambito36,D. Zanzi52,O. Zaplatilek139,S.V. Zeißner47,C. Zeitnitz178,J.C. Zeng169, D.T. Zenger Jr26,O. Zenin120,T. Ženiš28a,S. Zenz92,S. Zerradi35a,D. Zerwas64,B. Zhang14c, D.F. Zhang146,G. Zhang14b,J. Zhang6,K. Zhang14a,L. Zhang14c,M. Zhang169,R. Zhang177, S. Zhang104,X. Zhang60c,X. Zhang60b,Z. Zhang64, H. Zhao145,P. Zhao49,T. Zhao60b, Y. Zhao143,Z. Zhao60a,A. Zhemchugov79,Z. Zheng150,D. Zhong169, B. Zhou104,C. Zhou177, H. Zhou7,N. Zhou60c, Y. Zhou7,C.G. Zhu60b,C. Zhu14a,14d,H.L. Zhu60a,H. Zhu14a,J. Zhu104, Y. Zhu60a,X. Zhuang14a,K. Zhukov109,V. Zhulanov119b,119a,D. Zieminska65,N.I. Zimine79, S. Zimmermann52,*, J. Zinsser61b,M. Ziolkowski148,L. Živković15,A. Zoccoli23b,23a,K. Zoch54, T.G. Zorbas146,O. Zormpa44,W. Zou39,L. Zwalinski36 1Department of Physics, University of Adelaide, Adelaide; Australia 2Department of Physics, University of Alberta, Edmonton AB; Canada 3 (a)Department of Physics, Ankara University, Ankara;(b)Division of Physics, TOBB University of Economics and Technology, Ankara; Turkey 4LAPP, Univ. Savoie Mont Blanc, CNRS/IN2P3, Annecy; France 5Université de Paris, CNRS/IN2P3, AstroParticule et Cosmologie, Paris; France 6High Energy Physics Division, Argonne National Laboratory, Argonne IL; United States of America 7Department of Physics, University of Arizona, Tucson AZ; United States of America 8Department of Physics, University of Texas at Arlington, Arlington TX; United States of America 9Physics 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; United States of America 12 Institute of Physics, Azerbaijan Academy of Sciences, Baku; Azerbaijan 13 Institut de Física d’Altes Energies (IFAE), Barcelona Institute of Science and Technology, Barcelona; Spain 14 (a)Institute of High Energy Physics, Chinese Academy of Sciences, Beijing;(b)Physics Department, Tsinghua University, Beijing;(c)Department of Physics, Nanjing University, Nanjing;(d)University of Chinese Academy of Science (UCAS), Beijing; China 15 Institute of Physics, University of Belgrade, Belgrade; Serbia – 66 – JHEP06(2022)063 16 Department for Physics and Technology, University of Bergen, Bergen; Norway 17 Physics Division, Lawrence Berkeley National Laboratory and University of California, Berkeley CA; United States of America 18 Institut für Physik, Humboldt Universität zu Berlin, Berlin; Germany 19 Albert Einstein Center for Fundamental Physics and Laboratory for High Energy Physics, University of Bern, Bern; Switzerland 20 School of Physics and Astronomy, University of Birmingham, Birmingham; United Kingdom 21 (a)Department of Physics, Bogazici University, Istanbul;(b)Department of Physics Engineering, Gaziantep University, Gaziantep;(c)Department of Physics, Istanbul University, Istanbul;(d)Istinye University, Sariyer, Istanbul; Turkey 22 (a)Facultad de Ciencias y Centro de Investigaciónes, Universidad Antonio Nariño, Bogotá;(b)Departamento de Física, Universidad Nacional de Colombia, Bogotá; Colombia 23 (a)Dipartimento di Fisica e Astronomia A. Righi, Università di Bologna, Bologna;(b)INFN Sezione di Bologna; Italy 24 Physikalisches Institut, Universität Bonn, Bonn; Germany 25 Department of Physics, Boston University, Boston MA; United States of America 26 Department of Physics, Brandeis University, Waltham MA; United States of America 27 (a)Transilvania University of Brasov, Brasov;(b)Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest;(c)Department of Physics, Alexandru Ioan Cuza University of Iasi, Iasi;(d)National Institute for Research and Development of Isotopic and Molecular Technologies, Physics Department, Cluj-Napoca;(e)University Politehnica Bucharest, Bucharest;(f)West University in Timisoara, Timisoara; Romania 28 (a)Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava;(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; United States of America 30 Departamento de Física (FCEN) and IFIBA, Universidad de Buenos Aires and CONICET, Buenos Aires; Argentina 31 California State University, CA; United States of America 32 Cavendish Laboratory, University of Cambridge, Cambridge; United Kingdom 33 (a)Department of Physics, University of Cape Town, Cape Town;(b)iThemba Labs, Western Cape;(c)Department of Mechanical Engineering Science, University of Johannesburg, Johannesburg;(d)National Institute of Physics, University of the Philippines Diliman (Philippines);(e)University of South Africa, Department of Physics, Pretoria;(f)University of Zululand, KwaDlangezwa;(g)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;(b)Faculté des Sciences, Université Ibn-Tofail, Kénitra;(c)Faculté des Sciences Semlalia, Université Cadi Ayyad, LPHEA-Marrakech;(d)LPMR, Faculté des Sciences, Université Mohamed Premier, Oujda;(e)Faculté des sciences, Université Mohammed V, Rabat;(f)Mohammed VI Polytechnic University, Ben Guerir; Morocco 36 CERN, Geneva; Switzerland 37 Enrico Fermi Institute, University of Chicago, Chicago IL; United States of America 38 LPC, Université Clermont Auvergne, CNRS/IN2P3, Clermont-Ferrand; France 39 Nevis Laboratory, Columbia University, Irvington NY; United States of America 40 Niels Bohr Institute, University of Copenhagen, Copenhagen; Denmark 41 (a)Dipartimento di Fisica, Università della Calabria, Rende;(b)INFN Gruppo Collegato di Cosenza, Laboratori Nazionali di Frascati; Italy 42 Physics Department, Southern Methodist University, Dallas TX; United States of America 43 Physics Department, University of Texas at Dallas, Richardson TX; United States of America 44 National Centre for Scientific Research “Demokritos”, Agia Paraskevi; Greece – 67 – JHEP06(2022)063 45 (a)Department of Physics, Stockholm University;(b)Oskar Klein Centre, Stockholm; Sweden 46 Deutsches Elektronen-Synchrotron DESY, Hamburg and Zeuthen; Germany 47 Fakultät Physik , Technische Universität Dortmund, Dortmund; Germany 48 Institut für Kernund Teilchenphysik, Technische Universität Dresden, Dresden; Germany 49 Department of Physics, Duke University, Durham NC; United States of America 50 SUPA - School of Physics and Astronomy, University of Edinburgh, Edinburgh; United Kingdom 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, Genève; Switzerland 55 (a)Dipartimento di Fisica, Università di Genova, Genova;(b)INFN Sezione di Genova; Italy 56 II. Physikalisches Institut, Justus-Liebig-Universität Giessen, Giessen; Germany 57 SUPA - School of Physics and Astronomy, University of Glasgow, Glasgow; United Kingdom 58 LPSC, Université Grenoble Alpes, CNRS/IN2P3, Grenoble INP, Grenoble; France 59 Laboratory for Particle Physics and Cosmology, Harvard University, Cambridge MA; United States of America 60 (a)Department of Modern Physics and State Key Laboratory of Particle Detection and Electronics, University of Science and Technology of China, Hefei;(b)Institute of Frontier and Interdisciplinary Science and Key Laboratory of Particle Physics and Particle Irradiation (MOE), Shandong University, Qingdao;(c)School of Physics and Astronomy, Shanghai Jiao Tong University, Key Laboratory for Particle Astrophysics and Cosmology (MOE), SKLPPC, Shanghai;(d)Tsung-Dao Lee Institute, Shanghai; China 61 (a)Kirchhoff-Institut für Physik, Ruprecht-Karls-Universität Heidelberg, Heidelberg;(b)Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg; Germany 62 (a)Department of Physics, Chinese University of Hong Kong, Shatin, N.T., Hong Kong;(b)Department of Physics, University of Hong Kong, Hong Kong;(c)Department of Physics and Institute for Advanced Study, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong; China 63 Department of Physics, National Tsing Hua University, Hsinchu; Taiwan 64 IJCLab, Université Paris-Saclay, CNRS/IN2P3, 91405, Orsay; France 65 Department of Physics, Indiana University, Bloomington IN; United States of America 66 (a)INFN Gruppo Collegato di Udine, Sezione di Trieste, Udine;(b)ICTP, Trieste;(c)Dipartimento Politecnico di Ingegneria e Architettura, Università di Udine, Udine; Italy 67 (a)INFN Sezione di Lecce;(b)Dipartimento di Matematica e Fisica, Università del Salento, Lecce; Italy 68 (a)INFN Sezione di Milano;(b)Dipartimento di Fisica, Università di Milano, Milano; Italy 69 (a)INFN Sezione di Napoli;(b)Dipartimento di Fisica, Università di Napoli, Napoli; Italy 70 (a)INFN Sezione di Pavia;(b)Dipartimento di Fisica, Università di Pavia, Pavia; Italy 71 (a)INFN Sezione di Pisa;(b)Dipartimento di Fisica E. Fermi, Università di Pisa, Pisa; Italy 72 (a)INFN Sezione di Roma;(b)Dipartimento di Fisica, Sapienza Università di Roma, Roma; Italy 73 (a)INFN Sezione di Roma Tor Vergata;(b)Dipartimento di Fisica, Università di Roma Tor Vergata, Roma; Italy 74 (a)INFN Sezione di Roma Tre;(b)Dipartimento di Matematica e Fisica, Università Roma Tre, Roma; Italy 75 (a)INFN-TIFPA;(b)Università degli Studi di Trento, Trento; Italy 76 Institut für Astround Teilchenphysik, Leopold-Franzens-Universität, Innsbruck; Austria 77 University of Iowa, Iowa City IA; United States of America 78 Department of Physics and Astronomy, Iowa State University, Ames IA; United States of America 79 Joint Institute for Nuclear Research, Dubna; Russia 80 (a)Departamento de Engenharia Elétrica, Universidade Federal de Juiz de Fora (UFJF), Juiz de Fora;(b)Universidade Federal do Rio De Janeiro COPPE/EE/IF, Rio de Janeiro;(c)Instituto de Física, Universidade de São Paulo, São Paulo;(d)Rio de Janeiro State University, Rio de Janeiro; Brazil – 68 – JHEP06(2022)063 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, Krakow;(b)Marian Smoluchowski Institute of Physics, Jagiellonian University, Krakow; Poland 84 Institute of Nuclear Physics Polish Academy of Sciences, Krakow; 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 89 Physics Department, Lancaster University, Lancaster; United Kingdom 90 Oliver Lodge Laboratory, University of Liverpool, Liverpool; United Kingdom 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; United Kingdom 93 Department of Physics, Royal Holloway University of London, Egham; United Kingdom 94 Department of Physics and Astronomy, University College London, London; United Kingdom 95 Louisiana Tech University, Ruston LA; United States of America 96 Fysiska institutionen, Lunds universitet, Lund; Sweden 97 Departamento de Física Teorica C-15 and CIAFF, Universidad Autónoma de Madrid, Madrid; Spain 98 Institut für Physik, Universität Mainz, Mainz; Germany 99 School of Physics and Astronomy, University of Manchester, Manchester; United Kingdom 100 CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille; France 101 Department of Physics, University of Massachusetts, Amherst MA; United States of America 102 Department of Physics, McGill University, Montreal QC; Canada 103 School of Physics, University of Melbourne, Victoria; Australia 104 Department of Physics, University of Michigan, Ann Arbor MI; United States of America 105 Department of Physics and Astronomy, Michigan State University, East Lansing MI; United States of America 106 B.I. Stepanov Institute of Physics, National Academy of Sciences of Belarus, Minsk; Belarus 107 Research Institute for Nuclear Problems of Byelorussian State University, Minsk; Belarus 108 Group of Particle Physics, University of Montreal, Montreal QC; Canada 109 P.N. Lebedev Physical Institute of the Russian Academy of Sciences, Moscow; Russia 110 National Research Nuclear University MEPhI, Moscow; Russia 111 D.V. Skobeltsyn Institute of Nuclear Physics, M.V. Lomonosov Moscow State University, Moscow; Russia 112 Fakultät für Physik, Ludwig-Maximilians-Universität München, München; Germany 113 Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), München; Germany 114 Graduate School of Science and Kobayashi-Maskawa Institute, Nagoya University, Nagoya; Japan 115 Department of Physics and Astronomy, University of New Mexico, Albuquerque NM; United States of America 116 Institute for Mathematics, Astrophysics and Particle Physics, Radboud University/Nikhef, Nijmegen; Netherlands 117 Nikhef National Institute for Subatomic Physics and University of Amsterdam, Amsterdam; Netherlands 118 Department of Physics, Northern Illinois University, DeKalb IL; United States of America 119 (a)Budker Institute of Nuclear Physics and NSU, SB RAS, Novosibirsk;(b)Novosibirsk State University Novosibirsk; Russia 120 Institute for High Energy Physics of the National Research Centre Kurchatov Institute, Protvino; Russia 121 Institute for Theoretical and Experimental Physics named by A.I. Alikhanov of National Research Centre “Kurchatov Institute”, Moscow; Russia – 69 – JHEP06(2022)063 122 (a)New York University Abu Dhabi, Abu Dhabi;(b)United Arab Emirates University, Al Ain;(c)University of Sharjah, Sharjah; United Arab Emirates 123 Department of Physics, New York University, New York NY; United States of America 124 Ochanomizu University, Otsuka, Bunkyo-ku, Tokyo; Japan 125 Ohio State University, Columbus OH; United States of America 126 Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma, Norman OK; United States of America 127 Department of Physics, Oklahoma State University, Stillwater OK; United States of America 128 Palacký University, Joint Laboratory of Optics, Olomouc; Czech Republic 129 Institute for Fundamental Science, University of Oregon, Eugene, OR; United States of America 130 Graduate School of Science, Osaka University, Osaka; Japan 131 Department of Physics, University of Oslo, Oslo; Norway 132 Department of Physics, Oxford University, Oxford; United Kingdom 133 LPNHE, Sorbonne Université, Université de Paris, CNRS/IN2P3, Paris; France 134 Department of Physics, University of Pennsylvania, Philadelphia PA; United States of America 135 Konstantinov Nuclear Physics Institute of National Research Centre “Kurchatov Institute”, PNPI, St. Petersburg; Russia 136 Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh PA; United States of America 137 (a)Laboratório de Instrumentação e Física Experimental de Partículas - LIP, Lisboa;(b)Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Lisboa;(c)Departamento de Física, Universidade de Coimbra, Coimbra;(d)Centro de Física Nuclear da Universidade de Lisboa, Lisboa;(e)Departamento de Física, Universidade do Minho, Braga;(f)Departamento de Física Teórica y del Cosmos, Universidad de Granada, Granada (Spain);(g)Instituto Superior Técnico, Universidade de Lisboa, Lisboa; Portugal 138 Institute of Physics of the Czech Academy of Sciences, Prague; Czech Republic 139 Czech Technical University in Prague, Prague; Czech Republic 140 Charles University, Faculty of Mathematics and Physics, Prague; Czech Republic 141 Particle Physics Department, Rutherford Appleton Laboratory, Didcot; United Kingdom 142 IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette; France 143 Santa Cruz Institute for Particle Physics, University of California Santa Cruz, Santa Cruz CA; United States of America 144 (a)Departamento de Física, Pontificia Universidad Católica de Chile, Santiago;(b)Millennium Institute for Subatomic physics at high energy frontier (SAPHIR), Santiago;(c)Instituto de Investigación Multidisciplinario en Ciencia y Tecnología, y Departamento de Física, Universidad de La Serena;(d)Universidad Andres Bello, Department of Physics, Santiago;(e)Instituto de Alta Investigación, Universidad de Tarapacá, Arica;(f)Departamento de Física, Universidad Técnica Federico Santa María, Valparaíso; Chile 145 Department of Physics, University of Washington, Seattle WA; United States of America 146 Department of Physics and Astronomy, University of Sheffield, Sheffield; United Kingdom 147 Department of Physics, Shinshu University, Nagano; Japan 148 Department Physik, Universität Siegen, Siegen; Germany 149 Department of Physics, Simon Fraser University, Burnaby BC; Canada 150 SLAC National Accelerator Laboratory, Stanford CA; United States of America 151 Department of Physics, Royal Institute of Technology, Stockholm; Sweden 152 Departments of Physics and Astronomy, Stony Brook University, Stony Brook NY; United States of America 153 Department of Physics and Astronomy, University of Sussex, Brighton; United Kingdom 154 School of Physics, University of Sydney, Sydney; Australia 155 Institute of Physics, Academia Sinica, Taipei; Taiwan 156 (a)E. Andronikashvili Institute of Physics, Iv. Javakhishvili Tbilisi State University, Tbilisi;(b)High Energy Physics Institute, Tbilisi State University, Tbilisi; Georgia – 70 – JHEP06(2022)063 157 Department of Physics, Technion, Israel Institute of Technology, Haifa; Israel 158 Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv; Israel 159 Department of Physics, Aristotle University of Thessaloniki, Thessaloniki; Greece 160 International Center for Elementary Particle Physics and Department of Physics, University of Tokyo, Tokyo; Japan 161 Department of Physics, Tokyo Institute of Technology, Tokyo; Japan 162 Tomsk State University, Tomsk; Russia 163 Department of Physics, University of Toronto, Toronto ON; Canada 164 (a)TRIUMF, Vancouver BC;(b)Department of Physics and Astronomy, York University, Toronto ON; Canada 165 Division of Physics and Tomonaga Center for the History of the Universe, Faculty of Pure and Applied Sciences, University of Tsukuba, Tsukuba; Japan 166 Department of Physics and Astronomy, Tufts University, Medford MA; United States of America 167 Department of Physics and Astronomy, University of California Irvine, Irvine CA; United States of America 168 Department of Physics and Astronomy, University of Uppsala, Uppsala; Sweden 169 Department of Physics, University of Illinois, Urbana IL; United States of America 170 Instituto de Física Corpuscular (IFIC), Centro Mixto Universidad de Valencia - CSIC, Valencia; Spain 171 Department of Physics, University of British Columbia, Vancouver BC; Canada 172 Department of Physics and Astronomy, University of Victoria, Victoria BC; Canada 173 Fakultät für Physik und Astronomie, Julius-Maximilians-Universität Würzburg, Würzburg; Germany 174 Department of Physics, University of Warwick, Coventry; United Kingdom 175 Waseda University, Tokyo; Japan 176 Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot; Israel 177 Department of Physics, University of Wisconsin, Madison WI; United States of America 178 Fakultät für Mathematik und Naturwissenschaften, Fachgruppe Physik, Bergische Universität Wuppertal, Wuppertal; Germany 179 Department of Physics, Yale University, New Haven CT; United States of America aAlso at Borough of Manhattan Community College, City University of New York, New York NY; United States of America bAlso at Bruno Kessler Foundation, Trento; Italy cAlso at Center for High Energy Physics, Peking University; China dAlso at Centro Studi e Ricerche Enrico Fermi; Italy eAlso at CERN, Geneva; Switzerland fAlso at Département de Physique Nucléaire et Corpusculaire, Université de Genève, Genève; Switzerland gAlso at Departament de Fisica de la Universitat Autonoma de Barcelona, Barcelona; Spain hAlso at Department of Financial and Management Engineering, University of the Aegean, Chios; Greece iAlso at Department of Physics and Astronomy, Michigan State University, East Lansing MI; United States of America jAlso at Department of Physics and Astronomy, University of Louisville, Louisville, KY; United States of America kAlso at Department of Physics, Ben Gurion University of the Negev, Beer Sheva; Israel lAlso at Department of Physics, California State University, East Bay; United States of America mAlso at Department of Physics, California State University, Sacramento; United States of America nAlso at Department of Physics, King’s College London, London; United Kingdom oAlso at Department of Physics, St. Petersburg State Polytechnical University, St. Petersburg; Russia – 71 – JHEP06(2022)063 pAlso at Department of Physics, University of Fribourg, Fribourg; Switzerland qAlso at Faculty of Physics, M.V. Lomonosov Moscow State University, Moscow; Russia rAlso at Graduate School of Science, Osaka University, Osaka; Japan sAlso at Hellenic Open University, Patras; Greece tAlso at Institucio Catalana de Recerca i Estudis Avancats, ICREA, Barcelona; Spain uAlso at Institut für Experimentalphysik, Universität Hamburg, Hamburg; Germany vAlso at Institute of Particle Physics (IPP); Canada wAlso at Institute of Theoretical Physics, Ilia State University, Tbilisi; Georgia xAlso at Instituto de Fisica Teorica, IFT-UAM/CSIC, Madrid; Spain yAlso at Joint Institute for Nuclear Research, Dubna; Russia zAlso at Moscow Institute of Physics and Technology State University, Dolgoprudny; Russia aa Also at National Research Nuclear University MEPhI, Moscow; Russia ab Also at Physics Department, An-Najah National University, Nablus; Palestine ac Also at Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Freiburg; Germany ad Also at The City College of New York, New York NY; United States of America ae Also at TRIUMF, Vancouver BC; Canada af Also at Universita di Napoli Parthenope, Napoli; Italy ag Also at University of Chinese Academy of Sciences (UCAS), Beijing; China ah Also at Yeditepe University, Physics Department, Istanbul; Turkey ∗Deceased – 72 –