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main.bib \addbibresourceatlaslatex/bib/ATLAS.bib \addbibresourceatlaslatex/bib/CMS.bib \addbibresourceatlaslatex/bib/ConfNotes.bib \addbibresourceatlaslatex/bib/PubNotes.bib \AtlasTitleMeasurements of fiducial and differential cross-sections of production with additional heavy-flavour jets in proton–proton collisions at  \TeV with the ATLAS detector \AtlasAbstractThis paper presents measurements of production in association with additional -jets in collisions at the LHC at a centre-of-mass energy of 13 \TeV. The data were recorded with the ATLAS detector and correspond to an integrated luminosity of \lumi. Fiducial cross-section measurements are performed in the dilepton and lepton-plus-jets decay channels. Results are presented at particle level in the form of inclusive cross-sections of final states with three and four -jets as well as differential cross-sections as a function of global event properties and properties of -jet pairs. The measured inclusive fiducial cross-sections generally exceed the predictions from various next-to-leading-order matrix element calculations matched to a parton shower but are compatible within the total uncertainties. The experimental uncertainties are smaller than the uncertainties in the predictions. Comparisons of state-of-the-art theoretical predictions with the differential measurements are shown and good agreement with data is found for most of them. \AtlasRefCodeTOPQ-2017-12 \PreprintIdNumberCERN-EP-2018-276 \AtlasJournalJHEP \AtlasCoverSupportingNoteDilepton notehttps://cds.cern.ch/record/2270265 \AtlasCoverSupportingNote\ljetsnotehttps://cds.cern.ch/record/2270273 \AtlasCoverCommentsDeadline11th October 2018 \AtlasCoverAnalysisTeamGeorges Aad, Henri Bachacou, Rafał Bielski, Nihal Brahimi, Yasiel Delabat, Frederic Deliot, Christoph Eckardt, Paul Glaysher, Stefan Guindon, Mahsana Haleem, Vivek Jain, Judith Katzy, Thorsten Kuhl, Tom Neep, Yvonne Peters, Matthieu Robin, Stewart Swift, Timothée Theveneaux-Pelzer, Laurent Vacavant, Akanksha Vishwakarma, Peter Weber \AtlasCoverEdBoardMemberJiri Kvita (chair), Michele Pinamonti, Jie Yu \AtlasCoverEgroupEditorsatlas-topq-2017-12-editors@cern.ch \AtlasCoverEgroupEdBoardatlas-topq-2017-12-editorial-board@cern.ch \pdfstringdefDisableCommands\pdfstringdefDisableCommands \LEcontactRichard Keeler rkeeler@uvic.ca

1 Introduction

Measurements of the production cross-section of top-antitop quark pairs (\ttbar) with additional jets provide important tests of quantum chromodynamics (QCD) predictions. Among these, the process of \ttbarproduced in association with jets originating from -quarks (-jets) is particularly important to measure, as there are many uncertainties in the calculation of the process. For example, calculating the amplitude for the process shown in Figure 0(a) is a challenge due to the non-negligible mass of the -quark. It is therefore important to compare the predictions with both inclusive and differential experimental cross-section measurements of \ttbarproduction with additional \bjets. State-of-the-art QCD calculations give predictions for the \ttbarproduction cross-section with up to two additional massless partons at NLO (NLO) in perturbation theory matched to a parton shower [Hoeche:2014qda], and the QCD production of \ttbbis calculated at NLO matched to a parton shower [Cascioli:2013era, Garzelli:2014aba, Bevilacqua:2017cru, Jezo:2018yaf].

Moreover, since the discovery of the Higgs boson [HIGG-2012-27, CMS-HIG-12-028], the determination of the Higgs coupling to the heaviest elementary particle, the top quark, is a crucial test of the Standard Model (SM). Direct measurements of the top-quark Yukawa coupling are performed in events where a Higgs boson is produced in association with a top-quark pair (\ttH[HIGG-2018-13, CMS-HIG-17-035]. The Higgs branching ratios are dominated by the decay, and therefore the \ttHprocess can be measured with the best statistical precision using events where the Higgs boson decays in this manner, leading to a \ttbbfinal state as shown in Figure 0(b). However, this channel suffers from a large background from QCD \ttbbproduction indicated in Figure 0(a) [HIGG-2017-03-FIXED, CMS-HIG-17-026].

Measurements of would benefit from a better understanding of the QCD production of \ttbbas predicted by the SM and, in particular, improved MC (MC) modelling. The measurements presented in this paper were chosen in order to provide data needed to improve the QCD MC modelling of the \ttbbprocess. The differential observables are particularly interesting as they are sensitive to the relative contribution of events from \ttbar-associated Higgs production (\ttH) with decays to QCD-produced \ttbbevents in various phase space regions. Even though the aim is to improve the modelling of QCD production of additional -jets in \ttbarevents, this analysis measures their production without separating the different production channels such as \ttHor \ttbarin association with a vector boson (\ttV), for example the process shown in Figure 0(c).

(a)
(b)
(c)
Figure 1: Example Feynman diagrams of processes leading to a \ttbbfinal state, including LABEL:sub@fig:ttbb QCD \ttbbproduction, LABEL:sub@fig:ttHbb , and LABEL:sub@fig:ttZ .

In this paper, measurements of fiducial cross-sections are presented using data recorded by the ATLAS detector during 2015 and 2016 in proton–proton () collisions at a centre-of-mass energy  \TeV, corresponding to a total integrated luminosity of \lumi. In addition, differential measurements at this centre-of-mass energy are presented as a function of various observables. Previous measurements of \ttbarproduction with additional heavy-flavour jets have been reported by ATLAS at  \TeV [TOPQ-2012-16] and both CMS and ATLAS at  \TeV [TOPQ-2014-10, CMS-TOP-12-041, CMS-TOP-13-010]. CMS has also reported a measurement of the inclusive \ttbbcross-section using 2.3

2 ATLAS detector

The ATLAS detector [PERF-2007-01] at the LHC covers nearly the entire solid angle around the collision point. It consists of an inner-tracking detector surrounded by a thin superconducting solenoid, electromagnetic and hadronic calorimeters, and a muon spectrometer incorporating three large superconducting toroidal magnets.

The ID (ID) system is immersed in a axial magnetic field and provides charged-particle tracking in the pseudorapidity range . The ID is composed of silicon detectors and the transition radiation tracker. The high-granularity silicon pixel detector covers the interaction region and is followed by the silicon microstrip tracker. The innermost silicon pixel layer, added to the inner detector before the start of Run-2 data taking [Capeans:2010jnh, Abbott:2018ikt], improves the identification of -jets. The tracking capabilities of the silicon detectors are augmented by the transition radiation tracker, which is located at a larger radius and enables track reconstruction up to . It also provides signals used to separate electrons from pions.

The calorimeter system covers the range . Within the region , electromagnetic calorimetry is provided by barrel and endcap high-granularity lead/liquid-argon (LAr) electromagnetic calorimeters, with an additional thin LAr presampler covering to correct for energy loss in material upstream of the calorimeters. Hadronic calorimetry is provided by the steel/scintillating-tile calorimeter, segmented into three barrel structures within , and two copper/LAr hadronic endcap calorimeters. The solid angle coverage is completed with forward copper/LAr and tungsten/LAr calorimeter modules optimised for electromagnetic and hadronic measurements, respectively.

The muon spectrometer (MS) comprises separate trigger and high-precision tracking chambers measuring the deflection of muons in a magnetic field generated by the superconducting air-core toroids. The field integral of the toroids ranges between and across most of the detector. A set of precision chambers covers the region with three layers of drift tubes, complemented by cathode strip chambers in the forward region, where the background is highest. The muon trigger system covers the range with resistive plate chambers in the barrel, and thin gap chambers in the endcap regions.

A two-level trigger system is used for event selection [PERF-2011-02, TRIG-2016-01]. The first trigger level is implemented in hardware and uses a subset of detector information to reduce the event rate to a design value of at most . This is followed by a software-based trigger that reduces the event rate to about .

3 Monte Carlo simulation

Monte Carlo simulations are used in three ways in this analysis: to estimate the signal and background composition of the selected data samples, to determine correction factors for detector and acceptance effects for unfolding, and finally to estimate systematic uncertainties. In addition, theoretical predictions are compared with the unfolded data. The computer codes used to generate the samples and how they were configured are described in the following. The signal MC samples used in the analysis are listed in Table 1.

Generator sample Process Matching Tune Use
\POWHEGBOXv2 + \PYTHIAV8.210 \ttbarNLO \powheg A14 nom.
\MGMCatNLO+ \PYTHIAV8.210 NLO MC@NLO A14 nom.
\POWHEGBOXv2 + \PYTHIAV8.210 RadLo \ttbarNLO \powheg A14Var3cDown syst.
\POWHEGBOXv2 + \PYTHIAV8.210 RadHi \ttbarNLO \powheg A14Var3cUp syst.
\POWHEGBOXv2 + \HERWIGV7.01 \ttbarNLO \powheg H7UE syst.
\SHERPAV2.2.1 \ttbar \ttbar+0,1 parton at NLO MePs@Nlo \SHERPA syst.
\ttbar+2,3,4 partons at LO
\MGMCatNLO+ \PYTHIAV8.210 \ttbarNLO MC@NLO A14 comp.
\SHERPAV2.2.1 \ttbb(4FS) \ttbbNLO MC@NLO \SHERPA comp.
\POWHEGBOXv2 + \PYTHIAV8.210 \ttbb(4FS) \ttbbNLO \powheg A14 comp.
\powhel+ \PYTHIAV8.210 (4FS) \ttbbNLO \powheg A14 comp.
\powhel+ \PYTHIAV8.210 (5FS) \ttbbNLO \powheg A14 comp.
Table 1: Summary of the MC sample set-ups used for modelling the signal processes () for the data analysis and for comparisons with the measured cross-sections and differential distributions. All samples used the NNPDF3.0NLO PDF set with the exception of the two \SHERPAsamples, which used NNPDF3.0NNLO. The different blocks indicate from top to bottom the samples used as nominal MC (nom.), systematic variations (syst.) and for comparison only (comp.). For details see Section 3.

The nominal \ttbarsample was generated using the \POWHEGBOXgenerator (version 2, r3026) [Nason:2004rx, Frixione:2007vw, Alioli:2010xd, Frixione:2007nw] at next-to-leading-order (NLO) in with the NNPDF3.0NLO set of parton distribution functions (PDF) in the matrix element calculation. The parton shower, fragmentation, and the underlying event were simulated using \PYTHIA8.210 [Sjostrand:Pythia8] with the NNPDF2.3LO PDF sets [RichardBalla:2013, RichardBalla:2015] and the corresponding A14 set of tuned parameters [ATL-PHYS-PUB-2014-021]. The parameter, which controls the \pTof the hardest additional parton emission beyond the Born configuration, was set to  [ATL-PHYS-PUB-2016-020], where denotes the top-quark mass. The \powheghardness criterion used in the matching (POWHEG:pTdef) is set to 2 following a study in Ref. [ATL-PHYS-PUB-2016-020]. The renormalisation and factorisation scales were set to , where is the transverse momentum of the top quark. Additional jets, including -jets, were generated by the hardest additional parton emission and from parton showering. This sample is called \ppyeightin the following.

Processes involving the production of a or Higgs boson in addition to a \ttbarpair were simulated using the \MGMCatNLOgenerator [Alwall:2014hca, ATL-PHYS-PUB-2016-005] at NLO in in the matrix element calculation. The parton shower, fragmentation and underlying event were simulated using \PYTHIAV8 with the A14 parton shower tune. A dynamic renormalisation and factorisation scale set to was used, where is defined as the scalar sum of the transverse mass, , of all partons in the partonic final state. The NNPDF3.0NLO PDF set was used in the matrix element calculation while the NNPDF2.3LO PDF set was used in the parton shower. In the case of , the Higgs boson mass was set to 125 \GeV and all possible Higgs decay modes were allowed, with the branching fractions calculated with HDECAY [yellowreport, Djouadi:1997yw]. The and samples are normalised to cross-sections calculated to NLO in with \MGMCatNLO. The sample is normalised to a cross-section calculated to NLO accuracy in QCD, including NLO electroweak corrections [yellowreport].

Alternative \ttbarsamples were generated to assess the uncertainties due to a particular choice of QCD MC model for the production of the additional -jets and to compare with unfolded data, as listed in Table 1. In order to investigate the effects of initial- and final-state radiation, two samples were generated using \ppyeightwith the renormalisation and factorisation scales varied by a factor of 2 (0.5) and using low-radiation (high-radiation) variations of the A14 tune and an value of (), corresponding to less (more) parton shower radiation [ATL-PHYS-PUB-2016-020]. These samples are called \ppyeight(RadLo) and \ppyeight(RadHi) in the following. To estimate the effect of the choice of parton shower and hadronisation algorithms, a MC sample was generated by interfacing \powhegwith \hwseven [herwig, herwig7tune] (v7.01) using the H7UE set of tuned parameters [herwig7tune].

In order to estimate the effects of QCD scales, and matching and merging algorithms used in the NLO \ttbarmatrix element calculation and the parton shower to predict additional -jets, events were generated with the \SHERPAV2.2.1 generator [Gleisberg:2008ta], which models the zero and one additional-parton process at NLO accuracy and up to four additional partons at LO accuracy, using the MePs@Nlo prescription [Hoeche:2012yf]. Additional -quarks were treated as massless and the NNPDF3.0NNLO PDF set was used. The calculation uses its own parton shower tune. This sample is referred to as \SHERPAtt.

In addition to the \ttbarsamples described above, a \ttbarsample was generated using the \MGMCatNLO [Alwall:2014hca] (v2.3.3) generator, interfaced to \PYTHIAV8.210 and is referred to as \amcnlopyeighthereafter. As with the nominal \ppyeight\ttbarsample, the NNPDF3.0NLO PDF set was used in the matrix element calculation and the NNPDF2.3LO PDF set was used in the parton shower. This sample is used to calculate the fraction of \ttbar+/ events in \ttbarevents and to compare with the data. The A14 set of tuned parameters was used for \PYTHIA.

The \ttbarsamples are normalised to a cross-section of pb as calculated with the Top++2.0 program to NNLO (NNLO) in perturbative QCD, including soft-gluon resummation to next-to-next-to-leading-log (NNLL) order (see Ref. [Czakon:2011xx] and references therein), and assuming  \GeV. The uncertainty in the theoretical cross-section comes from independent variations of the factorisation and renormalisation scales and variations in the PDF and , following the PDF4LHC prescription with the MSTW 2008 NNLO, CT10 NNLO and NNPDF2.3 5f FFN PDF sets (see Ref. [Botje:2011sn] and references therein, and Refs. [Martin:2009bu, Gao:2013xoa, Ball:2012cx]).

Four more predictions were calculated only for comparisons with data and are all based on \ttbbmatrix element calculations. These predictions all use the same renormalisation and factorisation scale definitions as the study presented in Ref. [yellowreport]. The renormalisation scale, , is set to , where refers to the transverse energy of the parton in the partonic final state, and the factorisation scale, , is set to which is defined as {linenomath}

where refers to the additional QCD-radiated partons at NLO.

Three of the four predictions are based on the \powhegmethod, and use the \PYTHIAV8 parton shower with the same parton shower tune and the same matching settings as the nominal \ppyeightsample, with the exception of the \hdampparameter, which is set to the same value as the factorisation scale, i.e. . In the \ttbbmatrix element calculations with massive -quarks, the -quark mass is set to  \GeV. The set-up of the four dedicated samples are described below.

A sample of \ttbbevents was generated using \SHERPAOL [Cascioli:2013era]. The \ttbbmatrix elements were calculated with massive -quarks at NLO, using the Comix [Gleisberg:2008fv] and OpenLoops [Cascioli:2011va] matrix element generators, and merged with the \SHERPAparton shower, tuned by the authors [Schumann:2007mg]. The four-flavour NNLO NNPDF3.0 PDF set was used. The resummation scale, , was set to the same value as . This sample is referred to as \SHERPAttbb(4FS). A sample of \ttbbevents was generated using the \powhelgenerator [Garzelli:2014aba], where the matrix elements were calculated at NLO assuming massless -quarks and using the five-flavour NLO NNPDF3.0 PDF set. Events were required to have the invariant mass, , of the system to be larger than 9.5 GeV and the of the -quark larger than 4.75 GeV as described in Ref. [yellowreport]. These events were matched to the \PYTHIAV8 parton shower using the \powhegmethod. This sample is referred to as \powhelpyeight(5FS).

A sample of \ttbbevents using the \powhelgenerator where the matrix elements were calculated at NLO with massive -quarks and using the four-flavour NLO NNPDF3.0 PDF set [Bevilacqua:2017cru]. Events were matched to the \PYTHIAV8 parton shower using the \powhegmethod. This sample is referred to as \powhelpyeight(4FS).

A sample of \ttbbevents using the \powheggenerator where \ttbbmatrix elements were calculated at NLO with massive -quarks and using the four-flavour NLO NNPDF3.0 PDF set [Jezo:2018yaf]. Events were matched to the \PYTHIAV8 parton shower using the \powhegmethod. This sample is referred to as \ppyeightttbb(4FS) to distinguish it from the nominal \ppyeightsample mentioned above.

For all samples involving top quarks, was set to 172.5 \GeV and the EvtGen v1.2.0 program [EvtGen] was used for properties of the bottom and charm hadron decays except for the \SHERPAsamples. To preserve the spin correlation information, top quarks were decayed following the method of Ref. [Frixione:2007zp] which is implemented in \POWHEGBOXand by \MADSPIN [Artoisenet:2012st] in the \amcnlopyeightsamples. \SHERPAperforms its own calculation for spin correlation. Both of the \powhelpyeightsamples used \PYTHIAto decay the top quarks, with a top-quark decay width of , and hence these predictions do not include \ttbarspin correlations.

The production of single top-quarks in the - and -channels was simulated using the \POWHEGBOX(v2, r2819) NLO generator with the CT10 PDF set in the matrix element calculations. Electroweak -channel single-top-quark events were generated using the \POWHEGBOX(v1, r2556) generator. This generator uses the four-flavour scheme for the NLO matrix elements calculation together with the fixed four-flavour PDF set CT10f4. For all top processes, top-quark spin correlations are preserved (in the case of the -channel, top quarks were decayed using \MADSPIN). The interference between \ttbarand production is accounted for using the diagram-removal scheme [Frixione:2008yi]. The parton shower, fragmentation, and the underlying event were simulated using \PYTHIAV6.428 [Sjostrand:2006za] with the CTEQ6L1 PDF sets and the Perugia 2012 tune (P2012) [Pumplin:2002vw, Skands:2010ak]. The single-top MC samples for the - and -channels are normalised to cross-sections from NLO predictions [Aliev:2010zk, Kant:2014oha], while the -channel MC sample is normalised to approximate NNLO [Kidonakis:2010ux].

Events containing or bosons with associated jets were simulated using the \SHERPAV2.2.1 generator. Matrix elements were calculated for up to two partons at NLO and up to four partons at LO (LO) using the Comix and OpenLoops matrix element generators and merged with the \SHERPAparton shower using the MePs@Nlo prescription. The NNPDF3.0NNLO PDF set was used in conjunction with parton shower tuning developed by the \SHERPAauthors. The jets events are normalised to NNLO cross-sections, computed using Fewz [Anastasiou:2003ds] with the MSTW 2008 NNLO PDF set.

Diboson processes were simulated using the \SHERPAV2.1.1 generator. Matrix elements were calculated using the Comix and OpenLoops matrix element generators and merged with the \SHERPAparton shower using the MePs@Nlo prescription. In the case of both bosons decaying leptonically, matrix elements contain all diagrams with four electroweak vertices and were calculated for up to one (four charged leptons or two charged leptons and two neutrinos) or zero partons (three charged leptons and one neutrino) at NLO, and up to three partons at LO. In the cases where one of the bosons decays hadronically and the other leptonically, matrix elements were calculated with up to one () or zero () additional partons at NLO and up to three additional partons at LO. The CT10 PDF set was used in conjunction with parton shower tuning developed by the \SHERPAauthors.

In all MC simulation samples, the effect of multiple interactions per bunch crossing (pile-up) was modelled by adding multiple minimum-bias events simulated with \PYTHIAV8.186 [Sjostrand:Pythia8], the A2 set of tuned parameters [ATL-PHYS-PUB-2012-003] and the MSTW2008LO set of PDFs [MartinStirlingThrone:2009]. The MC simulation samples are re-weighted to reproduce the distribution of the mean number of interactions per bunch crossing observed in the data.

4 Object reconstruction and identification

4.1 Detector-level object reconstruction

A description of the main reconstruction and identification criteria applied for electrons, muons, jets and -jets is given below.

Electrons are reconstructed [ATLAS-CONF-2016-024] by matching ID tracks to clusters in the electromagnetic calorimeter. Electrons must satisfy the tight identification criterion, based on a likelihood discriminant combining observables related to the shower shape in the calorimeter and to the track matching the electromagnetic cluster, and are required to be isolated in both the ID and the EM calorimeter using the \pt-dependent isolation working point. Electrons are required to have  \GeV and . Electrons that fall in the transition region between the barrel and endcap calorimeters () are poorly measured and are therefore not considered in this analysis.

Muon candidates are reconstructed [PERF-2015-10] by matching ID tracks to tracks in the muon spectrometer. Track reconstruction is performed independently in the ID and MS before a combined track is formed with a global re-fit to hits in the ID and MS. Muon candidates are required to have  \GeV and , must satisfy the medium identification criteria and are required to be isolated using the \pt-dependent isolation working point.

Electron and muon tracks are required to be associated with the primary vertex. This association requires the electron (muon) track to have and , where and are the transverse and longitudinal impact parameters of the electron (muon) track, respectively, is the uncertainty in the measurement of , and is the angle of the track relative to the axis parallel to the beamline.

Reconstruction, identification and isolation efficiencies of electrons (muons) are corrected in simulation to match those observed in data using events, and the position and width of the observed boson peak is used to calibrate the electron (muon) energy (momentum) scale and resolution.

The \antiktalgorithm [Cacciari:2008gp] with a radius parameter of is used to reconstruct jets with a four-momentum recombination scheme, using energy deposits in topological clusters in the calorimeter as inputs [PERF-2014-07]. Jets are calibrated using a series of simulation-based corrections and in situ techniques [PERF-2016-04]. Calibrated jets are required to have  \GeV and so that data from the ID is available for determining whether they contain -hadrons. Jets with  \GeV and are required to be identified as originating from the primary vertex using a JVT (JVT) algorithm [ATLAS-CONF-2014-018].

Jets containing -hadrons are identified exploiting the lifetimes of -hadrons and their masses. A multivariate algorithm, MV2c10, that combines track and secondary-vertex information is used to distinguish -jets from other jets [ATL-PHYS-PUB-2016-012]. Four working points are defined by different -tagging discriminant output thresholds corresponding to efficiencies of 85%, 77%, 70% and 60% in simulated \ttbarevents for -jets with  \GeV and rejection factors ranging from 3–35 for -jets and 30–1500 for light-flavour jets [ATL-PHYS-PUB-2016-012, PERF-2016-05].

After selecting electrons, muons and jets as defined above, several criteria are applied to ensure that objects do not overlap. If a selected electron and muon share a track then the electron is rejected. If an electron is within of one or more jets then the closest jet to the electron is removed. If there are remaining jets within of an electron then the electron is removed. When a jet is within of a muon, it is removed if it has fewer than three tracks, otherwise the muon is removed.

4.2 Particle-level object definitions

Particle-level objects are selected in simulated events using definitions that closely match the detector-level objects defined in Section 4.1. Particle-level objects are defined using stable particles having a proper lifetime greater than 30 ps.

This analysis considers electrons and muons that do not come from hadron decays for the fiducial definition.111Electrons and muons from decays are thus included. In order to take into account final-state photon radiation, the four-momentum of each lepton is modified by adding to it the four-momenta of all photons, not originating from a hadron, that are located within a cone around the lepton. Electrons and muons are required to have  \GeV and .

Jets are clustered using the \antiktalgorithm with a radius parameter of 0.4. All stable particles are included except those identified as electrons and muons, and the photons added to them, using the definition above and neutrinos not from hadron decays. These jets do not include particles from pile-up events but do include those from the underlying event. The decay products of hadronically decaying -leptons are therefore included. Jets are required to have  \GeV and .

Jets are identified as -jets by requiring that at least one -hadron with  \GeV is matched to the jet by ghost association [Cacciari:2008gn]. Here, the ghost-association procedure includes -hadrons in the jet clustering after scaling their \ptto a negligible value. A similar procedure is followed to define -jets, with the -jet definition taking precedence, i.e. a jet containing one -hadron and one -hadron is defined as a -jet. Jets that do not contain either a -hadron or a -hadron are considered to be light-flavour jets.

Electrons and muons that meet the selection criteria defined above are required to be separated from selected jets by . This ensures compatibility with the detector-level selection defined in Section 4.1.

5 Event selection and definition of the fiducial phase space

5.1 Data event selection

The data analysed were collected by the ATLAS detector in 2015 and 2016 during stable collisions at  \TeV while all components of the ATLAS detector were fully operational. The total integrated luminosity recorded in this period is \lumi.

In order to ensure events originate from collisions, events are required to have at least one primary vertex with at least two tracks. The primary vertex is defined as the vertex with the highest of tracks assigned to it.

Single-electron or single-muon triggers are used to select the events. They require a \ptof at least 20 (26) \GeV for muons and 24 (26) \GeV for electrons for the 2015 (2016) data set and also include requirements on the lepton quality and isolation. These triggers are complemented by others with higher \ptrequirements but loosened isolation requirements to ensure maximum efficiencies at higher lepton \pt.

In the channel, events are required to have exactly one electron and one muon of  \GeV and with opposite electric charge. At least one of the two leptons must be matched in flavour and angle to a trigger object. In the \ljetschannel, exactly one selected lepton of  \GeV is required and must be matched to the trigger object that triggered the event.

In the channel, at least two jets are required and at least two of these must be -tagged at the 77% efficiency -tagging working point for the baseline selection. The measurement of the fiducial cross-section with one (two) additional -jets requires at least three (at least four) jets to be -tagged. For the measurement of the -jet multiplicity distribution, at least two jets are required and at least two of them must be -tagged. All other differential cross-section measurements in the channel require at least three jets and at least three of these must be -tagged.

In the \ljetschannel, at least five jets are required and at least two of these must be -tagged for the baseline selection. For the measurement of the fiducial cross-section with one (two) additional -jets, five (six) jets are required, of which at least three (at least four) must be -tagged. For the measurement of the differential cross-sections, at least six jets, at least four of which are -tagged, are required. In this channel, -jets are identified using the tighter 60% efficiency -tagging working point to better suppress -jets from or decays.

5.2 Fiducial phase-space definition

The phase space in which the fiducial cross-section is measured is defined using particle-level objects with kinematic requirements similar to those placed on reconstructed objects in the event selection. The definitions of the fiducial phase spaces used for the cross-sections measurements are given below. The data are corrected to particle level using slightly different definitions of the fiducial phase space depending on the top-pair decay channel and on the observable.

In the channel, fiducial cross-sections are determined by requiring exactly one electron and one muon with opposite-sign charge at particle level and at least three (at least four) -jet(s) for the fiducial cross-section with one (two) additional -jets. The normalised differential cross-sections are measured in the fiducial volume containing the leptons and at least two -jets for the distribution differential in number of -jets and at least three -jets for all other differential measurements.

In the \ljetschannel, the fiducial phase space for the measurement of the integrated cross-section with one (two) additional -jet(s) is defined as containing exactly one particle-level electron or muon and five (six) jets, at least three (four) of which are -jets. Differential cross-sections are measured in a fiducial volume containing at least six jets and where at least four of them are required to be -jets.

6 Background estimation

The baseline selection with at least two -tagged jets results in a sample with only small backgrounds from processes other than \ttbarproduction. As mentioned before, events with additional \bjetsproduced in \ttVor \ttHproduction are treated as signal. The estimation of \ttbarproduction in association with additional light-flavour jets or -jets is described in Section 7.1 and is performed simultaneously with the extraction of fiducial cross-sections.

The remaining background events are classified into two types: those with prompt leptons from single top, or decays (including those produced via leptonic decays), which are discussed in Section 6.1, and those where at least one of the reconstructed lepton candidates is non-prompt or “fake” (NP & fake lep.), i.e. a non-prompt lepton from the decay of a - or -hadron, an electron from a photon conversion, hadronic jet activity misidentified as an electron, or a muon produced from an in-flight decay of a pion or kaon. This is estimated using a combined data-driven and simulation-based approach in the channel, and a data-driven approach in the \ljetschannel, both of which are described in Section 6.2.

6.1 Background from single-top, jets and \Wjetsevents

The background from single top-quark production is estimated from the MC simulation predictions in both the and \ljetschannels. This background contributes 3% of the event yields in both channels, with slightly smaller contributions in the four \bjetsselections.

In the channel, a very small number of events from Drell–Yan production and +jets fulfil the selection criteria. This background is estimated from MC simulation scaled to the data with separate scale factors for the two--tagged jets and three--tagged jets cases. The scale factors are derived from data events that have a reconstructed mass of the dilepton system corresponding to the boson mass and that fulfil the standard selection except that the lepton flavour is or . The fraction of background events from +jets is below two per mill for all -tagged jet multiplicities. A small number of +jets events, where the is decaying into any lepton flavour pair, can enter in the \ljetschannel and is estimated from MC simulation.

In the \ljetschannel, a small background from \Wjetsremains after the event selection; however, this contribution is below 2% in events that have at least three -tagged jets. This background is estimated directly from MC simulation.

6.2 Background from non-prompt and fake leptons

In the channel, the normalisation of this background is estimated from data using events in which the electron and muon have the same-sign electric charge. The method is described in Ref. [TOPQ-2015-09]. Known sources of same-sign prompt leptons are subtracted from the data and the non-prompt and fake background is extracted by scaling the remaining data events by a transfer factor determined from MC simulation. This transfer factor is defined as the ratio of predicted opposite-sign to predicted same-sign non-prompt and fake leptons.

In the \ljetschannel, the background from non-prompt and fake leptons is estimated using the matrix method [ATLAS-CONF-2014-058]. A sample enriched in non-prompt and fake leptons is obtained by removing the isolation and impact parameter requirements on the lepton selections defined in Section 4. The efficiency for these leptons, hereafter referred to as loose leptons, to meet the identification criteria defined in Section 4.1 is then measured separately for prompt and fake leptons. 222Here fake leptons also include non-prompt leptons. For both electrons and muons the efficiency for a prompt loose lepton to pass the identification criteria defined in Section 4.1 is measured using a sample of boson decays. The efficiency for fake loose leptons to pass the identification criteria is measured using events that have low missing transverse momentum for electrons and high lepton impact-parameter significance for muons. These efficiencies allow the number of fake leptons selected in the signal region to be estimated.

(a)
(b)
(a)
(b)
Figure 2: Comparison of the data distributions with predictions for the number of -tagged jets, in events with at least 2 -tagged jets, in the LABEL:sub@fig:nbjets_emu_prefit and LABEL:sub@fig:nbjets_ljets_prefit \ljetschannels. The systematic uncertainty band, shown in grey, includes all uncertainties from experimental sources.
Figure 3: Comparison of the data distributions with predictions for the leading -tagged jet \pt, in events with at least 3 -tagged jets, in the LABEL:sub@fig:leadbjetpt_emu_prefit and LABEL:sub@fig:leadbjetpt_ljets_prefit \ljetschannels. The systematic uncertainty band, shown in grey, includes all uncertainties from experimental sources. Events that fall outside of the range of the -axis are not included in the plot.
Figure 2: Comparison of the data distributions with predictions for the number of -tagged jets, in events with at least 2 -tagged jets, in the LABEL:sub@fig:nbjets_emu_prefit and LABEL:sub@fig:nbjets_ljets_prefit \ljetschannels. The systematic uncertainty band, shown in grey, includes all uncertainties from experimental sources.
Process
Signal ()
   
   
   
Background
    Single top
    NP and fake lep.
    +jets
    Diboson
Expected
Observed
Table 2: Predicted and observed channel event yields in 2, 3 and 4 selections. The quoted errors are symmetrised and indicate total statistical and systematic uncertainties in predictions due to experimental sources.
Process , , , ,
Signal ()
    \ttbar
   
   
Background
    Single top
    NP and fake lep.
    +jets
    +jets
    Diboson
Expected
Observed
Table 3: Predicted and observed \ljetsevent yields in the , , , and selections. The quoted uncertainties are symmetrised and indicate total statistical and systematic uncertainties in predictions due to experimental sources.

6.3 Data and prediction comparison of baseline selection

The overall number of events fulfilling the baseline selection is well described by the prediction in both channels, as seen in Tables 2 and 3 and Figure 3, where and denote a -jet and a jet of any flavour, respectively. However, the number of events with more than two -tagged jets is slightly underestimated, as shown in Figures 3 and 3. Therefore, data-driven scale factors are derived to correct the predictions of additional -jets or light jets in the \ttbarMC simulation, as described in the next section.

7 Extraction of the fiducial cross-sections

Fiducial cross-sections in the phase spaces defined in Section 5.2 for the different observables are extracted from detector-level distributions obtained after the event selections described in Section 5.1 and subtracting the number of background events produced by the non-\ttbar processes described in Section 6. After the subtraction of non-\ttbar background, the data suffer from backgrounds from \ttbarevents with additional light-flavour jets (\ttlight) or -jets (\ttc) that are misidentified as \bjetsby the -tagging algorithm. The correction factors for these backgrounds are measured in data, as presented in Section 7.1. The data are then unfolded using the corrected MC simulation as described in Section 7.2.

7.1 Data-driven correction factors for flavour composition of additional jets in \ttbarevents

The measurement of -jets production is dependent on the determination of the background from other \ttbarprocesses. For example, according to simulation studies in the channel, only about 50% of the events selected at detector level with at least three -tagged jets at the efficiency working point and within the fiducial phase space of the analysis, also have at least three \bjetsat particle level. The other events contain at least one \cjetor light-flavour jet which is misidentified as a \bjet. While the -jet mis-tag efficiency is known with a precision of 6%–22% [ATLAS-CONF-2018-001], depending on the jet \ptand the -tagging working point, the cross-section for the production of \ttbarin association with a charm-quark pair is poorly known. The cross-section of \ttbar+ light-flavour jets is better known as this process has been measured with uncertainty in the production cross-section for events with two (three) additional jets [TOPQ-2015-17]. However, the uncertainty in the light-flavour jet mis-tag efficiency ranges from 15% to 75% [ATLAS-CONF-2018-006-FIXED], depending on the jet \ptand the -tagging working point. Due to these large uncertainties, template fits to data are performed to extract the \ttbsignal yields and estimate the \ttcand \ttlightbackgrounds as described in the following. The templates are constructed from \ttbar, \ttHand \ttVMC simulated samples, as the signal includes the contributions from \ttVand \ttH.

The events in the channel are selected within an analysis region consisting of at least three -tagged jets at the 77% -tagging working point as specified in Section 5.1. This avoids extrapolation of the background shapes determined outside the selected region into the analysis region. The fit in the \ljetschannel is performed on a sample with at least five jets, at least two of which are -tagged with a -tagging efficiency of . While this means that the MC simulation is needed to extrapolate the results of the fit into the signal regions, it allows the \ttlightbackground to be extracted in what is effectively a control region. The \ljetschannel suffers from an additional background due to or corresponding decays in the inclusive \ttbarprocess, where the -jet is misidentified as a -jet. In order to separate this background from +-jets events, events containing only one particle-level -jet are attributed to this background and grouped into a \ttlightclass, while those with two particle-level -jets are placed into a \ttcclass, as summarised in Table 4. In this sample, of the events with exactly one particle-level -jet are found to contain decays, according to \ttbarMC simulation.

Category \ljets
\ttb 3 -jets 3 -jets
\ttc 3 -jets and 1 -jet 3 -jets and 2 -jets
\ttlight events that do not meet above criteria events that do not meet above criteria
Table 4: Event categorisation (for the definition of the MC templates) based on the particle-level selections of -jets, -jets and light-flavour jets.

Templates are created for events in the different categories described in Table 4 using the -tagging discriminant value of the jet with the third-highest -tagging discriminant in the channel, and the two jets with the third- and fourth-highest -tagging discriminant values in the \ljetschannel. The discriminant values are divided into five -tagging discriminant bins such that each bin corresponds to a certain range of -tagging efficiencies defined by the working points. The bins range from 1 to 5, corresponding to efficiencies of 100%–85%, 85%–77%, 77%–70%, 70%–60%, and respectively. In the channel, one-dimensional templates with three bins are formed corresponding to -tagging efficiencies between 77% and 0% for the jet with the third highest -tagging discriminant value. In the \ljetschannel, two-dimensional templates are created using the -tagging discriminant values of the two jets with the third- and fourth-highest -tagging discriminant values, corresponding to -tagging efficiencies between 100% and 0% for the two jets.

In both channels, one template is created from the sum of all backgrounds described in Section 6 and three templates are created from \ttbar, \ttVand \ttHMC simulations, to account for \ttb, \ttcand \ttlightevents, as detailed in Table 4. These templates are then fitted to the data using a binned maximum-likelihood fit, with a Poisson likelihood

where is the number of events in bin of the data template and is the expected number of events, and depends upon a number of free parameters, .

In the channel, two free parameters are used, such that the expected number of events in bin is

where , , and are the numbers of events in bin of the \ttb, \ttc, \ttlightand non-\ttbarbackground templates, respectively. The scale factors obtained from the fit are and , where the quoted uncertainties are statistical only. Figure 3(a) shows the distributions of the templates before and after scaling the templates by these scale factors.

In the \ljetschannel, three free parameters, , and , are used in the maximum-likelihood fit, such that the expected number of events in bin is

(1)

The best-fit values of the free parameters are , and where the quoted uncertainties are statistical only. Including systematic uncertainties, the values of extracted in the and \ljetschannels are found to be compatible at a level better than standard deviations. Some of the dominant common systematic uncertainties have small correlations between the two channels, while the uncertainty in due to the modelling of the \ttctemplate in the channel, as discussed in Section 8.3 is uncorrelated between the two channels. Taking only this uncertainty as uncorrelated, the values of extracted from the two channels are found be compatible at a level better than standard deviations. Figure 3(b) shows the distribution of the -tagging discriminant before and after the fit. For clarity, the two-dimensional \ljetstemplates are flattened into a single dimension.

(a)
(b)
Figure 4: The -tagging distribution of the third-highest -tagging discriminant-ranked jet for the LABEL:sub@fig:fit_dilepton channel, and of the third and fourth -tagging discriminant-ranked jet for the LABEL:sub@fig:fit_lepjets \ljetschannel. For clarity, the two-dimensional \ljetstemplates have been flattened into one dimension. The ratios of total predictions before and after the fit to the data are shown in the lower panel. The vertical bar in each ratio represents only the statistical uncertainty, and the grey bands represent the total error including systematic uncertainties from experimental sources. The extracted scale factors are given considering only statistical uncertainties.
(a)
(b)
(a)
(b)
Figure 5: Comparison of the data distributions with predictions, after applying scale factors, for the number of -tagged jets, in events with at least 2 -tagged jets, in the LABEL:sub@fig:nbjets_emu_postfit and LABEL:sub@fig:nbjets_ljets_postfit \ljetschannels. The systematic uncertainty band, shown in grey, includes all uncertainties from experimental sources.
Figure 6: Comparison of the data distributions with predictions for the leading -tagged jet \pt, after applying scale factors, in events with at least 3 -tagged jets, in the LABEL:sub@fig:leadbjetpt_emu_postfit and LABEL:sub@fig:leadbjetpt_ljets_postfit \ljetschannels. The systematic uncertainty band, shown in grey, includes all uncertainties from experimental sources. Events that fall outside of the range of the -axis are not included in the plot.
Figure 5: Comparison of the data distributions with predictions, after applying scale factors, for the number of -tagged jets, in events with at least 2 -tagged jets, in the LABEL:sub@fig:nbjets_emu_postfit and LABEL:sub@fig:nbjets_ljets_postfit \ljetschannels. The systematic uncertainty band, shown in grey, includes all uncertainties from experimental sources.

Figures 6 and 6 show the comparison of data and predictions for the -tagged jet multiplicity and the leading -tagged jet in the and \ljetschannels after the \ttbsignal, and the and backgrounds, are scaled by the extracted scale factors. The data are described much better by the prediction after the scaling is applied.

7.2 Unfolding

The measured distributions at detector level are unfolded to the particle level. The unfolding procedure corrects for resolution effects and for detector efficiencies and acceptances.

First, the number of non-\ttbarbackground events in bin (), described in Section 6, is subtracted from the data distribution at the detector level in bin (). This retains a mixture of signal and \ttbar-related backgrounds, the latter coming from mis-tagged events as described in Section 7.1. A series of corrections are then applied, with all corrections derived from simulated \ttbar, and events. Following the subtraction of non-\ttbarbackground, the data are first corrected for mis-tagged events by applying a correction

where is defined in the previous section, is the number of detector-level \ttbevents predicted by MC simulation, and is the number of detector-level \ttcand \ttlightevents in bin , after being scaled by the fit parameters, or and , defined in the previous section. In the channel,

and in the \ljetschannel,

where and are the numbers of reconstructed \ttcand \ttlightevents in bin , as predicted by MC simulation, respectively. Next, an acceptance correction, , is applied, which corrects for the fiducial acceptance and is defined as the probability of a \ttbevent passing the detector-level selection in a given bin () to also fall within the fiducial particle-level phase space (). It is estimated as

The detector-level objects are required to be matched within to the corresponding particle-level objects. This requirement leads to a better correspondence between the particle and detector levels and improves the unfolding performance. The matching factor is defined as

where is the subset of reconstructed events falling in the particle-level fiducial volume which are matched to the corresponding particle-level objects.

The remaining part of the unfolding procedure consists of effectively inverting the migration matrix to correct for the resolution effects and subsequently correcting for detector inefficiencies. An iterative Bayesian unfolding technique [DAgostini:1994fjx], as implemented in the RooUnfold software package [Adye:2011gm], is used. The matrix, , represents the probability for a particle-level event in bin to be reconstructed in bin . The chosen binning is optimised for each distribution to have a migration matrix with a large fraction of events on the diagonal and a sufficient number of events in each bin. The Bayesian unfolding technique performs the effective matrix inversion, , iteratively. Four iterations are used for all measured distributions.

Finally, the factor corrects for the reconstruction efficiency and is defined as

where is the number of \ttbevents passing the particle-level selection in bin and is the number of \ttbevents at particle level in bin that also pass the detector-level selection, containing matched objects.

The unfolding procedure for an observable at particle level can be summarised by the following expression

where is the bin width, is the number of events in bin of the unfolded distribution and is the integrated luminosity. In this paper, the integrated fiducial cross-section \sigmafid is obtained from

and is used as a normalisation factor such that results are presented in terms of a relative differential cross-section as .

8 Systematic uncertainties

In this section, the statistical and systematic uncertainties considered in this analysis are described. Experimental sources of uncertainty are described in Section 8.1, sources of uncertainty due to \ttbarmodelling are described in Section 8.2 and uncertainties due to the treatment of the \ttbar(\ttcand \ttlight) and non-\ttbarbackground processes are described in Sections 8.3 and 8.4, respectively. The method used to propagate the effects of systematics uncertainties to the final results are described in Section 8.5. The impact of these uncertainties on the fiducial and differential cross-section measurements are discussed in Section 9.

8.1 Experimental uncertainties

The uncertainty in the combined 2015+2016 integrated luminosity is 2.1%. It is derived, following a methodology similar to that detailed in Ref. [DAPR-2013-01], and using the LUCID-2 detector for the baseline luminosity measurements [LUCID2], from a calibration of the luminosity scale using beam-separation scans.

The uncertainty in the pile-up reweighting of the reconstructed events in the MC simulation is estimated by comparing the distribution of the number of primary vertices in the MC simulation with the one in data as a function of the instantaneous luminosity. Differences between these distributions are adjusted by scaling the mean number of interactions per bunch crossing in the MC simulation and the uncertainties are assigned to these scaling factors. The pile-up weights are recalculated after varying the scale factors within their uncertainties.

As discussed in Section 4, scale factors to correct differences seen in the lepton reconstruction, identification and trigger efficiency between the data and MC simulation are derived using a tag-and-probe technique in and events [PERF-2015-10, ATLAS-CONF-2016-024, ATL-PHYS-PUB-2016-015]. The electron (muon) momentum scale and resolution are determined using the measurement of the position and width of the boson peak in events [PERF-2015-10, ATLAS-CONF-2016-024, ATL-PHYS-PUB-2016-015]. The lepton uncertainties considered in this analysis are considerably smaller than the jet and flavour-tagging uncertainties.

The JVT is calibrated using + jet events where the jet balances the \ptof the boson. Scale factors binned in jet \ptare applied to each event in order to correct for small differences in the JVT efficiency between the data and MC simulation. The scale factors are for jets with  \GeV, getting closer to one with smaller uncertainties as the jet \ptincreases. The uncertainty in the efficiency to pass the JVT requirement is evaluated by varying the scale factors within their uncertainties [PERF-2014-03].

Jets are calibrated using a series of simulation-based corrections and in situ techniques [PERF-2016-04]. The uncertainties due to the JES (JES) are estimated using a combination of simulations, test-beam data and in situ measurements. Contributions from the jet-flavour composition, -intercalibration, leakage of the hadron showers beyond the extent of the hadronic calorimeters (punch-through), single-particle response, calorimeter response to different jet flavours, and pile-up are taken into account, resulting in 21 orthogonal uncertainty components. The total uncertainty due to the JES is one of the dominant uncertainties in this analysis.

The JER (JER) is measured using both data and simulation. First, the “true” resolution is measured by comparing the particle and reconstructed jet \ptin MC simulation as a function of the jet \ptand . Second, an in situ measurement of the JER is made using the bisector method in dijet events [PERF-2011-04]. The resolution in data and MC simulation are compared and the energies of jets in the MC simulation are smeared to match the resolution observed in data. The uncertainties in the JER stem from uncertainties in both the modelling and the data-driven method.

Differences in the -tagging and -jet mis-tag efficiencies between the data and MC simulation are corrected using scale factors derived from dilepton \ttbarevents and \ljets\ttbarevents, respectively. A negative-tag method is used to calibrate mis-tagged light-flavour (, , ) jets [ATLAS-CONF-2018-006-FIXED]. The scale factors are measured for different -tagging working points and as a function of jet kinematics, namely the jet \ptfor the -tagging efficiency and -jet mis-tag scale factors, and the jet \ptand for the light-flavour jet mis-tag scale factors. The associated flavour-tagging uncertainties, split into eigenvector components, are computed by varying the scale factors within their uncertainties. In total, there are 30 components related to the -tagging efficiencies and 15 (80) components related to the mis-tag rates of -jets (light-flavour jets). Due to the large number of -tagged jets in each event used in this analysis, the total uncertainty due to -tagging is one of the dominant uncertainties in this analysis.

8.2 Modelling systematic uncertainties

Uncertainties due to the choice of \ttbarMC generator are evaluated by unfolding alternative \ttbarsamples, described in Section 3 and presented in Table 1, with the nominal unfolding set-up. Uncertainties related to the choice of matrix element generator (labelled “generator” uncertainty) are evaluated using the \SHERPAttsample. This generator comes with its own parton shower and hadronisation model; hence these are included in the variation. Uncertainties due to the choice of parton shower and hadronisation model are evaluated using the \phwsevensample, in which only the parton shower and hadronisation model is varied relative to the nominal \ppyeightsample. Additionally, two MC samples are used to evaluate an uncertainty in the modelling of initial- and final-state radiation, namely the RadHi and RadLo samples described in Section 3.

The uncertainty due to the choice of PDF is evaluated following the PDF4LHC prescription [Butterworth:2015oua] using event weights that are available in the nominal \ppyeightsample. The uncertainty in the cross-section is evaluated by scaling the component of the prediction by factors of zero and two, with the nominal values being taken from theoretical predictions. A factor of two is chosen as this is the current 95% confidence-level upper limit on the signal strength as measured by ATLAS [HIGG-2017-03-FIXED].

The uncertainty in the cross-section is evaluated by varying the component of the prediction up and down by 30% to cover the measured uncertainty in this process [TOPQ-2015-22].

8.3 Uncertainty in \ttcand background

Since the and backgrounds in the channel are determined within a single fit, the uncertainty in this result is determined by changing the sample composition. This is achieved by loosening the -tagging requirement on the jet with the third-highest -tagging discriminant value, such that it is tagged at the 85% -tagging efficiency working point or not required to be -tagged at all. This results in the templates having more bins and allows the likelihood to be modified such that three free parameters are used in the fit. The number of expected events is then given by Eq. (1). With these looser selections the values of vary by about and this is used as a systematic uncertainty in the \ttctemplate. The validity of this uncertainty is checked by investigating the variations in the values of the \ttcscale factors after fitting to pseudo-data from alternative MC samples and it is found to cover the uncertainties in the \ttctemplate modelling. The values of remain consistent within the statistical uncertainty in fits with looser selections. After propagating the uncertainty in the \ttctemplate through the nominal fit set-up, by varying the input \ttctemplate by before performing the fit, the value of is found to change by , while the value of changes by .

Double counting of the uncertainties associated with the inclusive \ttb, \ttcand \ttlightcomposition differences in the channel when evaluating \ttbarmodelling uncertainties is avoided by factoring out differences in model composition by repeating the fits for each systematic model. In the \ljetschannel uncertainties in the flavour composition are taken directly from the samples used to evaluate systematic uncertainties in the modelling, as described in Section 8.2.

8.4 Uncertainty in non-\ttbarbackground estimation

The uncertainty in the single-top background is evaluated by comparing the nominal single-top sample (with overlap with \ttbarremoved via the diagram-removal scheme) with an alternative sample generated using the diagram-subtraction scheme [Frixione:2008yi]. Potential effects of QCD radiation on the single-top background are estimated using MC simulation predictions where the renormalisation and factorisation scales were varied by factors of 0.5 and 2. The uncertainty in the inclusive single-top cross-section [Kidonakis:2010ux] is taken to be .

The uncertainty attributed to the \Wjetsbackground normalisation is evaluated by varying the renormalisation and factorisation scales in the MC simulation prediction by a factor of two up and down. Furthermore, the uncertainty due to PDFs is estimated by using a set of 100 different PDF eigenvectors recommended in Ref. [Butterworth:2015oua]. An additional uncertainty of 30% is assumed for the normalisation of the heavy-flavour jets cross-section, based on MC simulation comparisons performed in the context of Ref. [HIGG-2017-03-FIXED].

The uncertainty in the non-prompt or fake lepton background is obtained by varying the estimate of this background by a factor of () in the \ljets() channel. No shape uncertainty is applied, as this background is small in both channels.

The uncertainty in the Drell–Yan background normalisation is evaluated by varying the estimate of this background by . It accounts for the impact of the reconstructed-mass resolution of the boson in the and events, for the background contribution of the \ttbarevents in the \Zjetsselection, and for differences in the scale factors obtained from each of the individual and decay channels relative to the nominal scale factor obtained from the combined and sample.

8.5 Propagation of uncertainties

Pseudo-experiments based on 10 000 histogram replicas are performed to evaluate statistical uncertainties for each distribution considered. Each entry for every event is given a random weight drawn from a Poisson distribution with a mean of one. Each of these histograms is then unfolded using the unfolding procedure described in Section 7.2. The standard deviation of each bin across all unfolded histogram replicas is then taken as the statistical uncertainty in that bin. This procedure is similar to simply obtaining pseudo-experiments by directly Poisson-fluctuating the measured data distributions, but has the added advantage that correlations between bins of different distributions are conserved.

This procedure is extended to include all experimental systematic uncertainties. For each systematic uncertainty effect considered, the relative variation due to that uncertainty is obtained at the detector level, using the nominal MC sample. Rather than unfolding each shifted histogram individually, each Poisson-fluctuated data distribution is smeared by all experimental systematic uncertainties simultaneously. For each pseudo-experiment, and for each uncertainty considered, the size of the shift applied is obtained randomly from a Gaussian distribution with a mean of zero and width equal to the relative shift at detector level in each bin due to that uncertainty, producing a new detector-level distribution. The same procedure that is followed for the statistical uncertainty alone is then followed to get the sum of the statistical and experimental systematic uncertainty.

In the case of \ttbarmodelling systematic uncertainties, detector-level distributions from alternative MC samples are unfolded using the unfolding procedure described in Section 7.2, with the unfolding corrections derived from the nominal \ppyeightsample. The unfolded distributions are compared with the particle-level distribution from the alternative sample and the relative difference in each bin is taken as the systematic uncertainty.

9 Fiducial and differential cross-section results

The unfolded results are presented in this section as fiducial cross-sections and as normalised differential cross-sections as a function of the \bjetmultiplicity, global event properties and kinematic variables. Table 5 lists the measured fiducial cross-sections for \ttbarproduction in association with additional at least one and at least two \bjetsand Table 6 lists the contributions to the uncertainty in these cross-sections. The most precise cross-section measurements are for the phase space in the channel, which has an uncertainty of 13%, and the , phase space in the \ljetschannel, which has an uncertainty of 17%. The uncertainties are dominated by systematic uncertainties, which are mainly caused by the uncertainties due to \ttbarmodelling and the uncertainties related to -tagging and the jet energy scale. In the channel, the uncertainty due to the fit variations is also significant. This measurement is more precise than the uncertainties in the theoretical predictions of the inclusive cross-section for this process, which are 20%–30% [yellowreport]. The results are summarised in Figure 7 after subtracting the \amcnlopyeightpredicted values of \ttHand \ttVcross-sections from the measured fiducial \ttbbcross-section, and compared with \ttbbpredictions from \SHERPAttbb, \ppyeightand \powhelpyeight. This procedure of \ttHand \ttVsubtraction is also employed for all following figures showing the normalised differential distributions.

[fb] \ljets[fb]
Measured 181 27 2450 359
MC
Measured 177 25 2370 331
\SHERPAttbb(4FS)
\ppyeightttbb(4FS) 104 16.5 1520 260
\powhelpyeight(5FS) 152 18.7 1360 290
\powhelpyeight(4FS) 105 18.2 1690 300
Table 5: Measured and predicted fiducial cross-section results for additional \bjetproduction in the and the \ljetsdecay channels.
Source Fiducial cross-section phase space
\ljets
unc. [] unc. [] unc. [] unc. []
Data statistics
Luminosity
Jet
-tagging
Lepton
Pile-up
fit variation - -
Non-\ttbarbkg
Detector+background total syst.
Parton shower
Generator
ISR/FSR
PDF
MC sample statistics
\ttbarmodelling total syst.
Total syst.
Total
Table 6: Main systematic uncertainties in percentage for particle-level measurement of inclusive cross-sections in 3 and 4 phase space.
Figure 7: The measured fiducial cross-sections, with \ttHand \ttVcontributions subtracted from data, compared with predictions obtained using \SHERPAttbbwith uncertainties obtained by varying the renormalisation and factorisation scales by factors of 0.5 and 2.0 and including PDF uncertainties. Comparisons with the central values of the predictions of \ppyeightand \powhelpyeightare also made. No uncertainties are included in the subtraction of the \ttHor \ttVpredictions.

Figure 8 shows the normalised fiducial cross-section as a function of the -jet multiplicity compared with predictions from various MC generator set-ups. A quantitative assessment of the level of agreement between data and the various predictions is performed by calculating a for each prediction. The is defined as

where is the inverse of the covariance matrix , calculated for each variable including all statistical and systematic uncertainties and is a vector of the differences between the measured and predicted cross-sections being tested. The resulting value of the calculation is converted into a -value using the number of degrees of freedom for each variable, which is the number of bins minus one in the case of the normalised differential cross-sections to reflect the normalisation constraint.

As normalised distributions are used, one element of is discarded in the calculation along with the corresponding row and column of the covariance matrix. The resulting does not depend on the element of or the row and column of the covariance matrix that is discarded. The resulting values are shown in Table 7, where the second column is for the normalised \bjetsmultiplicity distribution with and the last column is for the normalised \bjetsmultiplicity distribution with . All MC predictions that calculate the top-quark pair production matrix element at NLO, but rely on the parton shower for high jet multiplicities, predict too few events with three or four \bjets. This suggests that the \bjetproduction by the parton shower is not optimal in these set-ups. The situation does not improve significantly when the renormalisation and factorisation scales in the matrix element calculation and in the parton shower are changed by factors of 0.5 and 2, as shown in the middle ratio panel of Figure 8. \SHERPAtt, which models one additional-parton process at NLO accuracy and up to four additional partons at LO accuracy, is the only one of the presented generators that describes the \bjetproduction well over the full phase space.

Predictions that include additional massive -quarks in the matrix element calculation (\SHERPAttbb (4FS), \powhelpyeight (4FS), \ppyeightttbb (4FS)) do not provide top-pair production without additional \bjetsand cannot be compared with the region with less than three \bjets. Table 7 therefore also includes values where the total additional -jet production has been adjusted through the normalisation to . The relative rate of one, two and more than two additional -jets is described well by all predictions. It is also interesting to note that parton shower generators predict the relative rate of one and two additional -jets well once the total additional -jet production has also been adjusted through the normalisation to .

The comparison of the predictions from various MC generators with the data are made after subtracting the simulation-estimated contributions of \ttVand \ttHproduction from the data. The third ratio panel of Figure 8 shows the ratio of predictions of normalised differential cross-sections from \amcnlopyeightincluding (numerator) and not including (denominator) the contributions from the \ttVand \ttHprocesses. The impact of including these processes in the prediction increases with \bjetmultiplicity, resulting in a change of about 10% relative to the QCD \ttbarprediction alone in the inclusive four-\bjetbin.

Figure 8: The relative differential cross-section as a function of the -jet multiplicity in events with at least two -jets in the channel compared with various MC generators. The \ttHand \ttVcontributions are subtracted from data. Three ratio panels are shown, the first two of which show the ratios of various predictions to data. The third panel shows the ratio of predictions of normalised differential cross-sections from \amcnlopyeightincluding (numerator) and not including (denominator) the contributions from \ttVand \ttHproduction. Uncertainty bands represent the statistical and total systematic uncertainties as described in Section 8.
Generators
/ NDF -value / NDF -value
channel
\ppyeight / 1
\amcnlopyeight 0.05 / 1
\SHERPAtt 0.65 0.06 / 1
\SHERPAttbb(4FS) - - 0.37 / 1
\powhelpyeight(5FS) - - 0.33 / 1
\powhelpyeight(4FS) - - 0.76 / 1
\phwseven 0.26 / 1
\ppyeightttbb(4FS) - - 0.28 / 1
\ppyeightradhi 0.01 0.08 / 1
\ppyeightradlo 0.01 / 1
Table 7: Values of per degree of freedom and -values between the unfolded normalised cross-section and the predictions for -jet multiplicity measurements in the channel. The number of degrees of freedom is equal to the number of bins minus one. Calculations are performed after subtracting estimated contributions from \ttHand \ttVfrom the data. In the two right columns, data and predictions are normalised to cross-section for before calculating per degree of freedom and -values.

Observables sensitive to the details of the QCD modelling of additional \bjetproduction are studied in events with at least three \bjetsin the channel and in events with at least four \bjetsin the \ljetschannel. While the sample with at least four \bjetshas high signal purity, leading to smaller dependence on the MC models, the channel benefits from an order of magnitude larger size of the sample containing at least three \bjets.

Distributions for and \hthadare shown in Figures 9 and 10. Assessments of the level of agreement between data and the various MC predictions are presented in Table 8. The data are well described by all MC models in both channels within uncertainties of %–%, except for \amcnlopyeight, which shows poor agreement in the \ljetschannel. Major contributions of systematics uncertainties in the measurement from various sources are illustrated in Figure 11. Parton shower modelling is the dominant uncertainty in most regions of \hthad. Similar uncertainties are found in the measurement of , where the low region has relatively larger uncertainties due to QCD radiation scale variations because of softer jets contributing to this region.

(a)
(b)
Figure 9: Relative differential cross-sections as a function of LABEL:sub@fig:HT_emu , LABEL:sub@fig:HThad_emu in events with at least three -jets in the channel compared with various MC generators. The \ttHand \ttVcontributions are subtracted from data. Four ratio panels are shown, the first three of which show the ratios of various predictions to data. The last panel shows the ratio of predictions of normalised differential cross-sections from \amcnlopyeightincluding (numerator) and not including (denominator) the contributions from \ttVand \ttHproduction. Uncertainty bands represent the statistical and total systematic uncertainties as described in Section 8. Events with () values outside the axis range are not included in the plot.
(a)
(b)
Figure 10: Relative differential cross-sections as a function of LABEL:sub@fig:HT_ljets , LABEL:sub@fig:HThad_ljets in events with at least four -jets in the \ljetschannel compared with various MC generators. The \ttHand \ttVcontributions are subtracted from data. Four ratio panels are shown, the first three of which show the ratios of various predictions to data. The last panel shows the ratio of predictions of normalised differential cross-sections from \amcnlopyeightincluding (numerator) and not including (denominator) the contributions from \ttVand \ttHproduction. Uncertainty bands represent the statistical and total systematic uncertainties as described in Section 8. Events with () values outside the axis range are not included in the plot.
/ NDF -value / NDF -value
Generator
channel, -jets
\ppyeight 0.95 / 4 2.68 / 3 0.44
\amcnlopyeight 3.71 / 4 3.72 / 3 0.29
\SHERPAtt 0.58 / 4 2.26 / 3 0.52
\SHERPAttbb(4FS) 0.35 / 4 0.40 / 3 0.94
\powhelpyeight(5FS) 4.88 / 4 1.85 / 3 0.60
\powhelpyeight(4FS) 1.39 / 4 3.33 / 3 0.32
\phwseven 0.26 / 4 2.28 / 3 0.52
\ppyeightttbb(4FS) 0.63 / 4 3.93 / 3 0.27
\ppyeightradhi 4.09 / 4 6.43 / 3 0.09
\ppyeightradlo 0.14 / 4 1.06 / 3 0.79
lepton+jets channel, jets, -jets
\ppyeight 0.60 / 4 1.41 / 4 0.84
\amcnlopyeight 9.88 / 4 17.6 / 4
\SHERPAtt 0.72 / 4 1.38 / 4 0.85
\SHERPAttbb(4FS) 1.09 / 4 2.58 / 4 0.63
\powhelpyeight(5FS) 0.81 / 4 1.40 / 4 0.84
\powhelpyeight(4FS) 1.38 / 4 2.38 / 4 0.67
\phwseven 4.27 / 4 7.00 / 4 0.14
\ppyeightttbb(4FS) 0.72 / 4 1.71 / 4 0.79
\ppyeightradhi 0.94 / 4 0.96 / 4 0.92
\ppyeightradlo 1.15 / 4 2.57 / 4 0.63
Table 8: Values of per degree of freedom and -values between the unfolded normalised cross-sections and the various predictions for the and measurements in the and \ljetschannels. The number of degrees of freedom is equal to the number of bins in the measured distribution minus one.
(a)
(b)
Figure 11: Relative systematic uncertainties from various theoretical and experimental sources for variable measured in the LABEL:sub@fig:syst_hthad:emu and LABEL:sub@fig:syst_hthad:ljets \ljetschannels.

The \ptdistributions of the \pt-ordered \bjetsare shown in Figure 12 and Figure 13 for events with \bjetsin the channel and \bjetsin the \ljetschannel, respectively, with quantitative assessments of the level of data–MC agreement shown in Table 9. Most MC predictions describe the data well, except \powhelpyeight(5FS) for the leading and third-highest \pt-jets in events with \bjetsin the channel. As the \bjetsfrom the top-quark decays have a tendency to be harder than the \bjetsfrom additional -quark production via gluon splitting, the leading and sub-leading \bjetdistributions have relatively higher probability to contain the \bjetsfrom the top-quark decays, while the third and the fourth \bjetdistributions contain mainly jets from gluon splitting. The measurement uncertainties are between 10% and 25% depending on the \ptof the jet and the top-quark decay channel. Statistical uncertainties are dominant in only the highest \ptbins. The uncertainties are dominated by systematic uncertainties in the jet-energy scale and the -tagging algorithm.

(a)
(b)
(c)
Figure 12: Relative differential cross-sections as a function of -jets for \pt-ordered -jets in events with at least three -jets in the channel compared with various MC generators. The \ttHand \ttVcontributions are subtracted from data. LABEL:sub@fig:leadpt_emu leading -jet \pt, LABEL:sub@fig:subleadpt_emu sub-leading -jet \pt, LABEL:sub@fig:thirdleadpt_emu third-leading -jet \pt. Four ratio panels are shown, the first three of which show the ratios of various predictions to data. The last panel shows the ratio of predictions of normalised differential cross-sections from \amcnlopyeightincluding (numerator) and not including (denominator) the contributions from \ttVand \ttHproduction. Uncertainty bands represent the statistical and total systematic uncertainties as described in Section 8. Events with -jets values outside the axis range are not included in the plot.
(a)
(b)
(c)
(d)
Figure 13: Relative differential cross-sections as a function of -jets for \pt-ordered -jets in events with at least four -jets in the \ljetschannel compared with various MC generators. The \ttHand \ttVcontributions are subtracted from data. LABEL:sub@fig:leadpt_ljets leading -jet \pt, LABEL:sub@fig:subleadpt_ljets sub-leading -jet \pt, LABEL:sub@fig:thirdleadpt_ljets third-leading -jet \pt, LABEL:sub@fig:fourthleadpt_ljets fourth-leading -jet \pt. Four ratio panels are shown, the first three of which show the ratios of various predictions to data. The last panel shows the ratio of predictions of normalised differential cross-sections from \amcnlopyeightincluding (numerator) and not including (denominator) the contributions from \ttVand \ttHproduction. Uncertainty bands represent the statistical and total systematic uncertainties as described in Section 8. Events with -jets values outside the axis range are not included in the plot.
/ NDF -value / NDF -value / NDF -value / NDF -value
Generator
channel, -jets
\ppyeight 0.72 0.50 / 3 0.92 0.09 / 2 0.95 - -
\amcnlopyeight 0.62 0.27 / 3 0.97 0.33 / 2 0.85 - -
\SHERPAtt 0.91 0.67 / 3 0.88 0.02 / 2 0.99 - -
\SHERPAttbb(4FS) 0.47 0.68 / 3 0.88 0.21 / 2 0.90 - -
\powhelpyeight(5FS) 0.03 2.58 / 3 0.46 3.91 / 2 0.14 - -
\powhelpyeight(4FS) 0.18 1.96 / 3 0.58 1.30 / 2 0.52 - -
\phwseven 0.89 1.02 / 3 0.80 0.02 / 2 0.99 - -
\ppyeightttbb(4FS) 0.62 0.53 / 3 0.91 0.46 / 2 0.80 - -
\ppyeightradhi 0.61 0.56 / 3 0.91 0.26 / 2 0.88 - -
\ppyeightradlo 0.75 0.64 / 3 0.89 0.05 / 2 0.97 - -
lepton+jets channel, jets, -jets
\ppyeight 0.72 2.98 / 3 0.40 1.42 / 3 0.70 0.20 / 2 0.90
\amcnlopyeight 0.27 5.31 / 3 0.15 1.87 / 3 0.60 0.08 / 2 0.96
\SHERPAtt 0.73 2.46 / 3 0.48 1.75 / 3 0.63 0.15 / 2 0.93
\SHERPAttbb(4FS) 0.73 2.82 / 3 0.42 1.23 / 3 0.75 0.52 / 2 0.77
\powhelpyeight(5FS) 0.72 3.65 / 3 0.30 1.73 / 3 0.63 0.85 / 2 0.65
\powhelpyeight(4FS) 0.64 2.37 / 3 0.50 2.41 / 3 0.49 0.18 / 2 0.91
\phwseven 0.63 3.50 / 3 0.32 1.30 / 3 0.73 0.26 / 2 0.88
\ppyeightttbb(4FS) 0.78 2.02 / 3 0.57 1.83 / 3 0.61 0.84 / 2 0.66
\ppyeightradhi 0.83 2.39 / 3 0.50 1.74 / 3 0.63 0.37 / 2 0.83
\ppyeightradlo 0.70 3.75 / 3 0.29 1.42 / 3 0.70 0.17 / 2 0.92
Table 9: Values of per degree of freedom and -values between the unfolded normalised cross-sections and the various predictions for the three (four) leading -jet \ptmeasurements in the (\ljets) channel. The number of degrees of freedom is equal to the number of bins in the measured distribution minus one.

Figures 14 and 15 show the distribution of the mass, the angular distance and \ptof the system built from the two highest-\pt\bjets. The \ptof the system is measured with a precision of 10%–15% over the full range in the channel and with an uncertainty of 20%–25% in the \ljetschannel. It is well described by the different MC predictions, which vary significantly less than the experimental uncertainty. The distributions of the between the two -jets and the invariant mass of the pair are measured with slightly higher uncertainties and also show little variation between the different predictions. Good agreement between the data and the models is confirmed by the -values listed in Table 10.

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(c)
Figure 14: Relative differential cross-sections as a function of LABEL:sub@fig:mb1b2_emu , LABEL:sub@fig:ptb1b2_emu , and LABEL:sub@fig:drb1b2_emu