Measurements of the charge asymmetry in top-quark pair productionin the dilepton final state at

ffiffis

p= 8 TeV with the ATLAS detector

G. Aad et al.*

(ATLAS Collaboration)(Received 20 April 2016; published 22 August 2016)

Measurements of the top-antitop quark pair production charge asymmetry in the dilepton channel,characterized by two high-pT leptons (electrons or muons), are presented using data corresponding to anintegrated luminosity of 20.3 fb−1 from pp collisions at a center-of-mass energy

ffiffiffis

p ¼ 8 TeV collectedwith the ATLAS detector at the Large Hadron Collider at CERN. Inclusive and differential measurementsas a function of the invariant mass, transverse momentum, and longitudinal boost of the tt̄ system areperformed both in the full phase space and in a fiducial phase space closely matching the detectoracceptance. Two observables are studied: AllC based on the selected leptons and A

tt̄C based on the

reconstructed tt̄ final state. The inclusive asymmetries are measured in the full phase space to beAllC ¼ 0.008� 0.006 and Att̄C ¼ 0.021� 0.016, which are in agreement with the Standard Modelpredictions of AllC ¼ 0.0064� 0.0003 and Att̄C ¼ 0.0111� 0.0004.DOI: 10.1103/PhysRevD.94.032006

I. INTRODUCTION

The top quark is the heaviest known elementary particle.Its large mass suggests that it may play a special role intheories of physics beyond the Standard Model (BSM)[1–5]. Such a role could be elucidated via precision tests ofthe Standard Model (SM) in large data samples of top-antitop quark pair (tt̄) events collected at the Large HadronCollider (LHC) in proton-proton (pp) collisions. One suchtest is the measurement of the charge asymmetry. Theproduction of tt̄ pairs at hadron colliders is symmetricunder charge conjugation at leading order (LO) in quantumchromodynamics (QCD), i.e., the probability of a top quarkflying in a given direction is the same as for an antitopquark [6]. At next-to-leading order (NLO) in QCD, anasymmetry arises from interference between differentFeynman diagrams [3]. In particular, interference betweenthe Born and one-loop diagram of the qq̄ → tt̄ processesand between qq̄ → tt̄g diagrams with initial-state and final-state radiation (ISR and FSR) processes lead to a chargeasymmetry. In the tt̄ rest frame, this asymmetry causes thetop quark to be preferentially emitted in the direction of theinitial quark, and causes the antitop quark to be emitted inthe direction of the initial antiquark. The size of theasymmetry can be enhanced by contributions beyond theSM, for example, tt̄ production via the exchange of newheavy particles such as axigluons [3], heavy Z particles [4],or colored Kaluza-Klein excitations of the gluon [5].

Inclusive and differential measurements of the tt̄asymmetry were first performed at the Tevatron proton-antiproton collider, where forward-backward asymmetrieswere measured. Several measurements were reported by theCDF and D0 experiments [7–12] in dileptonic and semi-leptonic tt̄ events. For these measurements, the directionof the initial quark can be assumed to be the direction ofthe proton, and the direction of the antiquark that of theantiproton, which yields straightforward access to theasymmetry. Initial tension between these measurementsand theory predictions have been reduced with the latestSM calculations at next-to-next-to-leading order (NNLO)QCD [13].Since the start of the LHC, measurements of tt̄ charge

asymmetries have been performed by the ATLAS and CMSexperiments. Two features complicate the measurement ofthe asymmetry at the LHC: in proton-proton collisionsthe initial state is symmetric, so there is no tt̄ forward-backward asymmetry, and the dominant production mecha-nism is gluon fusion, which is symmetric under chargeconjugation to all orders in perturbative QCD. However,valence quarks carry on average a larger fraction of theproton momentum than sea antiquarks, hence top anti-quarks produced through quark-antiquark annihilation aremore central than top quarks [14]. By using differencesbetween the absolute rapidity of the top and antitop quarks,ATLAS and CMS performed measurements of the chargeasymmetry in dileptonic and semileptonic events at

ffiffiffis

p ¼7 TeV and 8 TeV [15–22]. All asymmetry measurements atthe LHC show good agreement with the SM prediction[23], which is approximately an order of magnitude smallerthan the predicted asymmetry at the Tevatron.In this article, new measurements of the charge asymme-

try are presented using dileptonic tt̄ events atffiffiffis

p ¼ 8 TeV.The dileptonic channel is characterized by two charged

*Full author list given at the end of the article.

Published by the American Physical Society under the terms ofthe Creative Commons Attribution 3.0 License. Further distri-bution of this work must maintain attribution to the author(s) andthe published article’s title, journal citation, and DOI.

PHYSICAL REVIEW D 94, 032006 (2016)

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http://dx.doi.org/10.1103/PhysRevD.94.032006http://dx.doi.org/10.1103/PhysRevD.94.032006http://dx.doi.org/10.1103/PhysRevD.94.032006http://dx.doi.org/10.1103/PhysRevD.94.032006http://creativecommons.org/licenses/by/3.0/http://creativecommons.org/licenses/by/3.0/

leptons (denoted l ¼ e, μ), coming from either a directvector boson decay or through an intermediate τ leptondecay. Two different observables are used, based either onthe selected leptons or the reconstructed tt̄ final state.Inclusive and differential measurements as a function ofthe invariant mass of the tt̄ system (mtt̄), the transversemomentum of the tt̄ system (pT;tt̄), and the absolute value ofthe boost of the tt̄ system along the beam axis (βz;tt̄) areperformed. The inclusive and differential measurements areperformed in the full phase space as well as in a fiducialvolume based on the detector acceptance and selectionrequirements, using particle-level objects. The measurementin the fiducial region does not rely on extrapolating toregions of phase space that are not within the detectoracceptance, while the full phase space measurement has thebenefit of being comparable to theoretical calculations atthe parton level, including BSM models.In Sec. II, a brief description of the ATLAS detector is

given. Section III describes the data and Monte Carlo (MC)samples, and Sec. IV the event selection and backgroundestimation. The observables are described in Sec. V.Section VI outlines the measurement methods, includinga description of the tt̄ reconstruction, the definition offiducial volume, and a description of the unfolding pro-cedure. In Sec. VII, the sources of systematic uncertaintiesaffecting the measurements are discussed, and results areprovided in Sec. VIII. Finally, conclusions are given inSec. IX.

II. ATLAS DETECTOR

The ATLAS detector [24] at the LHC covers nearlythe entire solid angle around the interaction point.1 Itconsists of an inner tracking detector surrounded by a thinsuperconducting solenoid, electromagnetic and hadroniccalorimeters, and a muon spectrometer incorporating super-conducting toroid magnets.The inner-detector system is immersed in a 2 T axial

magnetic field and provides charged-particle tracking in thepseudorapidity2 range jηj < 2.5. A high-granularity siliconpixel detector covers the interaction region and providestypically three measurements per track. It is surrounded by asilicon microstrip tracker designed to provide four two-dimensional measurement points per track. These silicondetectors are complemented by a transition radiation tracker,which enables radially extended track reconstruction up tojηj ¼ 2.0. The transition radiation tracker also provides

electron identification information based on the fraction ofhits (typically 30 in total) exceeding an energy-depositthreshold corresponding to transition radiation.The calorimeter system covers the pseudorapidity range

jηj < 4.9. Within the region jηj < 3.2, electromagneticcalorimetry is provided by barrel and endcap high-granularity lead/liquid-argon (LAr) electromagnetic calo-rimeters, with an additional thin LAr presampler coveringjηj < 1.8 to correct for energy loss in the material upstreamof the calorimeters. Hadronic calorimetry is providedby a steel/scintillator-tile calorimeter, segmented into threebarrel structures within jηj < 1.7, and two copper/LArhadronic endcap calorimeters. The solid angle coverageis completed with forward copper/LAr and tungsten/LArcalorimeters used for electromagnetic and hadronic mea-surements, respectively.The muon spectrometer comprises separate trigger and

high-precision tracking chambers measuring the deflectionof muons in a magnetic field generated by superconductingair-core toroids. The precision chamber system covers theregion jηj < 2.7 with drift tube chambers, complementedby cathode strip chambers. The muon trigger system coversthe range of jηj < 1.05 with resistive plate chambers inthe barrel, and the range of 1.05 < jηj < 2.4 with thin gapchambers in the endcap regions.A three-level trigger system is used to select interesting

events. The level-1 trigger is implemented in hardware anduses a subset of detector information to reduce the eventrate to a design value of at most 75 kHz. This is followed bytwo software-based trigger levels, which together reducethe event rate to about 300 Hz.

III. DATA AND MONTE CARLO SAMPLES

The data used for this analysis were collected duringthe 2012 LHC running period at a center-of-mass energyof 8 TeV. After applying data-quality selection criteria,the data sample used in the analysis corresponds to anintegrated luminosity of 20.3 fb−1.For the modeling of the signal processes and most

background contributions, several MC event generatorsare used. The main background contribution in thismeasurement comes from Drell-Yan production ofZ=γ� → ll, which is estimated by a combination ofsimulated samples modified with corrections derived fromdata, as described in Sec. IV. The smaller contributionsfrom diboson (WW, ZZ, and WZ) and single-top-quark(Wt channel) production are evaluated purely via MCsimulations. Further background contributions can arisefrom events including a jet or a lepton from a semileptonichadron decay misidentified as an isolated charged lepton aswell as leptons from photon conversions, together referredto as “fake leptons.” This contribution is estimated usingsimulated samples, modified with corrections derived fromdata. The samples mentioned above together with simu-lated samples of tt̄þW=Z, t-channel of single-top-quark

1ATLAS uses a right-handed coordinate system with its originat the nominal interaction point (IP) in the center of the detectorand the z axis along the beam pipe. The x axis points from the IPto the center of the LHC ring, and the y axis points upward.Cylindrical coordinates ðr;ϕÞ are used in the transverse plane, ϕbeing the azimuthal angle around the beam pipe.

2The pseudorapidity is defined in terms of the polar angle θ asη ¼ − ln½tan θ=2�, while the rapidity y is defined as y ¼ −ð1=2Þln½ðEþ pzÞ=ðE − pzÞ�.

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production, W þ jets, and W þ γ þ jets are included inthe estimation. The estimation procedure is describedin Sec. IV.The nominal tt̄ signal sample is generated at NLO in

QCD using POWHEG-hvq (version 1, r2330) [25–27] andthe CT10 [28] parton distribution function (PDF) set,setting the hdamp parameter to the top-quark mass of172.5 GeV. The hdamp parameter is the resummation scalethat is used in the damping function, which is designed tolimit the resummation of higher-order effects at largetransverse momentum without spoiling the NLO accuracyof the cross section. The parton shower, hadronization, andunderlying event are simulated using PYTHIA6 (version6.427) [29] with the CTEQ6L1 PDF [30] and the corre-sponding set of tunable parameters (Perugia 2011C tune[31]) intended to be used with this PDF. The tt̄ cross sectionfor pp collisions at a center-of-mass energy of 8 TeV is setto σtt̄ ¼ 253þ13−15 pb, calculated at NNLO in QCD inclu-ding resummation of next-to-next-to-leading logarithmic(NNLL) soft gluon terms with topþþ 2.0 [32–38]. ThePDF and αS uncertainties were calculated using thePDF4LHC prescription [39] with the MSTW200868% C.L. NNLO [40,41], CT10 NNLO [42,43], andNNPDF2.3 5f FFN [44] PDF sets, and added in quadratureto the scale uncertainty.Single-top-quark production in the Wt channel is

simulated using POWHEG-hvq with PYTHIA6 (version6.426) and the CT10 (NLO) PDF set. The cross sectionof 22.3� 1.5 pb is estimated at approximate NNLO inQCD including resummation of NNLL terms [45]. Theparton shower, hadronization, and underlying event aresimulated by PYTHIA6 using the Perugia 2011C tune. TheDrell-Yan process is modeled using ALPGEN (version2.14) [46] interfaced with PYTHIA6 with the CTEQ6L1[30] PDF set using the MLM matching scheme. Its heavy-flavor component is included in the matrix elementcalculations to model the Z=γ� þ bb̄ and Z=γ� þ cc̄processes. Diboson processes (WW, ZZ, and WZ) aresimulated using ALPGEN interfaced with HERWIG+JIMMY(version 4.31) [47,48] with the CTEQ6L1 [30] PDF set forparton fragmentation [49]. The only exceptions are thesame-charge Wþð−ÞWþð−Þ samples, which are simulatedusing MADGRAPH (version 5.1.4.8) [50] interfaced withPYTHIA8 (version 8.165) [51]. The samples are normalizedto the reference NLO QCD prediction, obtained using theMCFM generator [52]. The associated production of a tt̄pair with a vector boson (tt̄Z and tt̄W) is simulated withMADGRAPH interfaced with PYTHIA8 and normalizedto NLO cross-section calculations [53,54]. The W þ jetsevents are simulated using ALPGEN interfaced withPYTHIA6 and the W þ γ þ jets process is simulated usingALPGEN interfaced with JIMMY.To model the LHC environment properly, additional

inelastic pp collisions are generated with PYTHIA8 andoverlaid on the hard process. All the simulated samples are

then processed through a simulation of the ATLAS detector[55]. For most of the samples, a full simulation based onGEANT4 [56] is used. Some of the samples used toevaluate the generator modeling uncertainties are obtainedusing a faster detector simulation where only the calorim-eter simulation is modified and relies on parametrizedshowers [57]. The simulated events are passed through thesame reconstruction and analysis chain as data.

IV. EVENT SELECTION AND BACKGROUNDESTIMATION

In order to enrich the data sample in dileptonic tt̄ events,requirements are imposed on reconstructed charged leptons(electrons and muons), jets, and the missing transversemomentum. Three different final states are considered inthe analysis: events with two electrons in the final state(ee), with one electron and one muon (eμ), and with twomuons (μμ).Electron candidates are reconstructed from an electro-

magnetic calorimeter energy depositmatched to a track in theinner detector and must pass the likelihood-based “medium”identification requirements [58]. They are required to havetransverse momentumpT > 25 GeV andmust also lie in theregion jηclj < 2.47, where ηcl is the pseudorapidity of thecalorimeter energy cluster associated with the electron,excluding the transition region between the calorimeterbarrel and endcaps 1.37 < jηclj < 1.52. Moreover, electronsare required to be isolated from surrounding activity in theinner detector. The scalar sum of the track pT within a coneof ΔR ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðΔηÞ2 þ ðΔϕÞ2

p¼ 0.3 (excluding the track of

the electron itself) divided by the electron pT shouldbe less than 0.12.Muon candidates are reconstructed using combined

information from the muon spectrometer and the innerdetector [59]. They are required to have pT > 25 GeV andjηj < 2.5. In addition, muons are required to satisfy track-based pT -dependent isolation criteria. The scalar sum ofthe track pT within a cone of size ΔR ¼ 10 GeV=pμTaround the muon (excluding the muon track itself) must beless than 5% of the muon pT (p

μT). Both the electrons and

muons have to be consistent with the primary vertex,3 byrequiring the absolute value of the longitudinal impactparameter to be less than 2 mm.Jets are reconstructed from clustered energy deposits in

the electromagnetic and hadronic calorimeters, using theanti-kt [60] algorithm with a radius parameter R ¼ 0.4. Themeasured energy of the jets is corrected to the hadronicscale using pT—and η-dependent scale factors derivedfrom simulation and validated in data [61]. After the energycorrection, the jets are required to have pT > 25 GeV, to bein the pseudorapidity range jηj < 2.5, and to have a jet

3The primary vertex is defined as the reconstructed vertex withat least five associated tracks (of pT > 0.4 GeV) and the highestsum of the squared transverse momenta of the associated tracks.

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vertex fraction jJVFj > 0.5 [62] if pT < 50 GeV. The jetvertex fraction is defined as the summed scalar pT of thetracks associated with both the jet and the primary vertexdivided by the summed scalar pT of all tracks in the jet.The jet that is the closest to a selected electron is removedfrom the event if their separation is ΔR < 0.2. After thisjet overlap removal, electrons and muons that are within acone of ΔR ¼ 0.4 around the closest jet are removed.Jets containing b-hadrons are identified (b-tagged) usinga multivariate algorithm (MV1) [63]. This is a neural-network-based algorithm that makes use of track impactparameters and reconstructed secondary vertices. Jets areidentified as b-tagged jets by requiring the MV1 outputdiscriminant to be above a certain threshold value. Thisvalue is chosen such that the overall tagging efficiency forb-jets with pT > 20 GeV and jηj < 2.5 originating fromtop-quark decays in dileptonic MC tt̄ events is 70%. Therejection factor for jets originating from gluons and lightquarks is about 130, while for c-quarks it is about 5.The magnitude of the missing transverse momentum

(EmissT ) is calculated from the negative vector sum of allcalorimeter energy deposits and the momenta of muons[64]. The calculation is refined by the application of theobject-level corrections for the contributions arising fromidentified electrons and muons.Events recorded with single-lepton triggers (e or μ)

under stable beam conditions with all detector subsystemsoperational are considered. The transverse momentumthresholds are 24 GeV for isolated single-lepton triggersand 60 (36) GeV for nonisolated single-electron (single-muon) triggers. The nonisolated triggers are used to selectevents that fail the isolation requirement at trigger level butpass it in the offline analysis. In all three final states, exactlytwo isolated leptons with opposite charge and an invariantmass mll > 15 GeV are required, together with at leasttwo jets. In the same-flavor channels (ee and μμ), theinvariant mass of the two charged leptons is requiredto be outside of the Z boson mass window such thatjmll −mZj > 10 GeV. Furthermore, it is required that

EmissT > 30 GeV and at least one of the jets must beb-tagged. These requirements suppress the dominantbackground contribution from Drell-Yan production ofZ=γ� → ll and also suppress diboson backgrounds. Inthe eμ channel, the background contamination is muchsmaller and the background suppression is achieved byrequiring the scalar sum of the pT of the two leading jetsand leptons ðHTÞ to be larger than 130 GeV. The eventselection requirements are summarized in Table I.The modeling of Drell-Yan events in the same-flavor

channels with EmissT > 30 GeV may not be accurate insimulation due to the mismodeling of the EmissT distribution.Moreover, after applying the b-tagging requirement, a largecontribution to the background comes from the associatedproduction of Z bosons with heavy-flavor jets, which isnot well predicted by MC simulation. The first source ofmismodeling depends on the reconstructed objects and istherefore different in each channel. The second source is alimitation of the MC simulation and is expected to be thesame in both channels. Thus, the normalization of theinclusive and heavy-flavor component of the Drell-Yanbackground in the same-flavor channels is computedsimultaneously using data in two control regions withthree scale factors. Two scale factors are applied to allDrell-Yan events to take into account the mismodeling fromthe EmissT requirement (one in the ee and one in the μμchannel) while another is applied only to Z þ heavy-flavor

TABLE I. The summary of the event selection requirementsapplied in different channels.

Requirements ee=μμ eμ

Leptons 2 2Jets ≥2 ≥2mll >15 GeV >15 GeVjmll −mZj >10 GeVEmissT >30 GeVb-tagged jets ≥1HT >130 GeV

TABLE II. Observed numbers of data events compared to the expected signal and background contributions in thethree decay channels. The uncertainty corresponds to the total uncertainty in the given process. Data-driven (DD)scale factors are applied to the Z þ jets and the NP and fake leptons contributions. The Z → ττ process in the eμchannel is estimated using MC simulation only.

Channel ee μμ eμ

tt̄ 10200� 800 12100� 800 36000� 2400Single-top 510� 50 590� 50 1980� 170Diboson 31� 5 40� 6 1320� 100Z → ee (DD) 1200� 260Z → μμ (DD) 1520� 300Z → ττ (DD/MC) 31� 15 58� 25 1120� 430NP and fake leptons (DD) 62þ119−29 45

þ36−24 480

þ240−220

Total expected 12000� 900 14400� 800 40900� 2500Data 12785 14453 42363

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events. The control regions are defined using the standardselection described previously but inverting the mll cut tobe within the Z mass window. The first control region isdefined without the b-tagging requirement while the secondis defined with at least one b-tagged jet. The simulatedmlldistribution in these control regions is simultaneously fit tothe data and the scale factors are extracted. The scalefactors derived in these two regions are 0.927� 0.005 and0.890� 0.004 for the ee and μμ channels, respectively, and1.70� 0.03 for the heavy-flavor component. The Z → ττprocess in the eμ channel is estimated using MC simulationonly: no data-driven correction is applied since neither theEmissT requirement nor b-tagging requirement are applied tothis channel.The background arising from misidentified and non-

prompt (NP) leptons is determined using both MC

simulation and data. The dominant sources of these fakeleptons are semileptonic b-hadron decays, long-livedweakly decaying states (such as π� or K� mesons), π0showers, photons reconstructed as electrons, and electronsfrom photon conversions. W þ jets, W þ γ þ jets, tt̄, tt̄Z,tt̄W, Drell-Yan, single-top-quark, and diboson productionare taken into account for the estimation of this back-ground. Multijet events do not contribute significantly tothis background, since the probability of having two jetsmisidentified as isolated leptons is very small. The shapesof the kinematic distributions are taken from simulatedevents where at least one of two selected leptons is requirednot to be matched with the MC generator-level leptons.Scale factors are derived from data in order to adjust thenormalization. A control region, enriched in fake leptons, isdefined by applying the same cuts as for the final selection

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FIG. 1. Distributions of the jet multiplicity, lepton pT , and lepton η for data (points) and predictions (histograms) for all channelscombined after event selection. The data/expected ratio is also shown. The shaded area corresponds to the detector systematicuncertainty, the signal modeling systematic uncertainty, and the normalization uncertainty in signal and background. In the lepton pTdistribution, the last bin includes the overflow.

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but requiring the two leptons to have the same charge. Theshapes of the distributions for various kinematic variablesof leptons, jets, and EmissT are checked and found to be wellmodeled in the MC simulation. The scale factors arederived in this region by comparing data and simulationand are then applied to the simulated events in the signalregion. The scale factor is 1.2� 0.3 in the ee channel,1.1� 0.2 in the eμ channel, and 3.7� 0.8 in the μμchannel, where the uncertainties are statistical. The sourcesof misidentified muons, such as heavy-flavor decays,are quite different from those of misidentified electrons.The large difference between the scale factor for the μμand the eμ channel is mainly due to the b-tagging require-ment, that is applied only in the μμ channel. However,the shapes of the distributions of the relevant kinematicvariables in the μμ channel are cross-checked in controlregions and found to be consistent with the distributionsfrom a purely data-driven method. The systematic uncer-tainties of both Drell-Yan background and the backgrounddue to events from misidentified and nonprompt leptons arediscussed in detail in Sec. VII B.The numbers of events for both expectation and data

after applying the selection criteria are shown in Table II forthe three final states. The uncertainties shown correspond tothe total uncertainty (including the statistical uncertaintiesfrom the limited size of the MC simulated samples, as wellas the systematic uncertainties). The eμ channel contributeswith the largest number of events, followed by μμ and ee.Figure 1 shows good agreement within the systematicuncertainties between data and the predictions as a functionof jet multiplicity, lepton pT and η, for all channelscombined.

V. OBSERVABLES

In dileptonic events, the charge asymmetry can bemeasured in two complementary ways: using the pseudor-apidity of the charged leptons or using the rapidity of the topquarks. The asymmetry based on the charged leptons usesthe difference of the absolute pseudorapidity values of thepositively and negatively charged leptons, jηlþj and jηl− j

Δjηj ¼ jηlþj − jηl− j: ð1Þ

The leptonic asymmetry is defined as

AllC ¼NðΔjηj > 0Þ − NðΔjηj < 0ÞNðΔjηj > 0Þ þ NðΔjηj < 0Þ ; ð2Þ

where NðΔjηj > 0Þ and NðΔjηj < 0Þ represent the numberof events with positive and negative Δjηj, respectively. TheSM prediction at NLO in QCD, including electroweakcorrections, is AllC ¼ 0.0064� 0.0003 [23], where theuncertainty includes variations in scale and choice ofPDF. The leptonic asymmetry, that is slightly diluted withrespect to the underlying top-quark asymmetry, has the

advantage that no reconstruction of the top-antitop quarksystem is required. Furthermore, it is also sensitive to top-quark polarization effects, which occur in some modelspredicting enhanced charge asymmetries.For the tt̄ charge asymmetry, the tt̄ system has to be

reconstructed and the absolute values of the top and antitopquark rapidities (jytj and jyt̄j, respectively) need to becomputed. Using

Δjyj ¼ jytj − jyt̄j; ð3Þ

the tt̄ charge asymmetry is defined as

Att̄C ¼NðΔjyj > 0Þ − NðΔjyj < 0ÞNðΔjyj > 0Þ þ NðΔjyj < 0Þ ; ð4Þ

where NðΔjyj > 0Þ and NðΔjyj < 0Þ represent thenumber of events with positive and negative Δjyj, respec-tively. The top (antitop) quarks are identified as thosegiving rise to positive (negative) leptons. The SM predic-tion at NLO QCD, including electroweak corrections, isAtt̄C ¼ 0.0111� 0.0004 [23].The measurements of AllC and A

tt̄C are performed inclu-

sively and differentially as a function of mtt̄, pT;tt̄, and βz;tt̄.The fractions of quark-antiquark annihilation and gluonfusion processes change as a function of mtt̄, and thus anincreasing asymmetry for increasing mtt̄ is expected. SincepT;tt̄ depends on the initial-state radiation, the asymmetryvalue is expected to change as a function of pT;tt̄. Inparticular, the contribution to the asymmetry from inter-ference of diagrams with initial- and final-state radiation isnegative, resulting in decreasing asymmetries with increas-ing pT;tt̄. While the initial antiquark is always a sea quark,the initial quark can be a valence quark. On average,valence quarks have higher momenta than sea quarks,which can result in a boost of the tt̄ system in the directionof the incoming quark. This results in an increased chargeasymmetry for increasing βz;tt̄. The asymmetry is alsoexpected to be different inclusively and differentially indifferent BSM models.

VI. ASYMMETRY MEASUREMENTS

The following measurements are performed:(i) inclusive measurements of the tt̄ and leptonic asym-

metries, corrected for reconstruction and acceptanceeffects to parton level in the full phase space;

(ii) inclusive measurements of the tt̄ and leptonicasymmetries, corrected for reconstruction effectsto particle level in the fiducial region;

(iii) differential measurements of the tt̄ and leptonicasymmetries as a function of mtt̄, pT;tt̄, and βz;tt̄in the fiducial region and the full phase space.

Particle-level results consider stable particles with amean lifetime larger than 0.3 × 10−10 s. For the parton-level measurements, MC generator-level objects are used.

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The parton-level top quarks and leptons are selected afterradiation.The leptonic asymmetry can be extracted directly using

the pseudorapidities of the measured charged leptons.For the tt̄ charge asymmetry, the reconstruction of the topand antitop quark four-momenta is necessary. A kinematicmethod is used for the reconstruction, as described inSec. VI A. Section VI B details the definition of the fiducialvolume and the particle-level objects used for the fiducialmeasurement. In order to correct the measured asymmetrydistributions for detector and acceptance effects, anunfolding method, described in Sec. VI C, is used for allasymmetry measurements. Section VI D describes how thevarious asymmetries are extracted.

A. Top and antitop quark reconstruction

For the reconstruction of the top and antitop quarkfour-momenta, a kinematic reconstruction is used. Thereconstruction is performed by solving the system ofequations that relates the particle momenta at each ofthe decay vertices in the tt̄ → WþbW−b̄ → lþνlbl−ν̄l b̄process. Two neutrinos are produced and escape unde-tected. Thus, an underconstrained system is obtained.This system is solved using the kinematic (KIN) method[65,66], assuming values of 172.5 GeV and 80.4 GeV forthe top quark and W boson masses, respectively, whichallows the system of equations to be solved numerically bythe Newton-Raphson method.If there are more than two reconstructed jets in a given

event, the two jets with the highest b-tagging weights (asdetermined by the MV1 b-tagging algorithm) are used.This improves the probability of choosing the correct jets,compared to just choosing the two jets with the highest pT ,from about 54% to about 69% in the inclusive selectedsample. The experimental uncertainties of the measuredobjects (described in Sec. VII) are taken into account bysampling the phase space of the measured jets and EmissTaccording to their resolution in simulation. The numberof sampled points is called Nsmear, whose optimizationis based on the time and efficiency of the top-pairreconstruction. The resolution functions, obtained fromthe tt̄ simulated sample, with respect to the jet pT (for jets)and the total transverse momentum in the event (for EmissT )are used for the sampling.For each sampling point, up to four solutions can be

obtained. The KIN method chooses the solution that leadsto the lowest reconstructed mass of the tt̄ system. Thereason for this is that the tt̄ cross section is a decreasingfunction of the partonic center-of-mass energy

ffiffiffîs

p ≃mtt̄, soevents with smaller mtt̄ are more likely. There is also atwofold ambiguity in the lepton and b-jet assignment. Thecorrect assignment to the top and antitop quarks is chosento be the one that has more reconstructed trials Nrecosmear, i.e.,the one that maximizes Nrecosmear=Nsmear. The chosen solutionis either the solution found using the nominal jet energies

and measured EmissT , if available, or the first solution foundduring the sampling. The kinematic reconstruction failsfor a given event if no solution is found in any of the Nsmearsampled points. This is possible if, for example, thesolution does not converge within a given number ofiterations. The performance of the method is quantifiedby evaluating the efficiency of reconstructing tt̄ eventsthat pass dilepton event selection, and the probability ofreconstructing the correct sign of Δjyj. These probabilitiesare found to be 90% and 76%, respectively. Thereconstruction efficiency is consistent between data andthe prediction.Figure 2 shows the distributions for data and prediction

of the pT , mass, and longitudinal boost of the tt̄ systemafter applying the reconstruction method. Good agreementbetween data and prediction is found.

B. Particle-level objects and fiducial region

A fiducial region is defined in order to closely matchthe phase space region accessed with the ATLAS detectorand the requirements made on the reconstructed objects.A fiducial measurement usually allows for MC generatordependencies to be reduced, since it avoids large extrapo-lation to the full phase space. In the fiducial region, onlyobjects defined at particle level are used.The considered charged leptons (electrons and muons)

are required not to originate from hadrons. Photons withinΔR ¼ 0.1 around the charged lepton are included in thefour-momentum calculation. The EmissT is calculated as thesummed four-momenta of neutrinos from the W=Z bosondecays, including those from τ decays. Jets are recon-structed using the anti-kt algorithm with a radius parameterR ¼ 0.4. The electrons, muons, neutrinos, and photons thatare used in the definition of the selected leptons areexcluded from the clustering. Finally, identification of jetsoriginating from b-quarks is achieved using ghost matching[67]. The MC generator-level b-hadrons are clustered intothe particle-level jets, with their momenta scaled to a verysmall value. If a clustered jet is found to contain a b-hadron,the particle-level jet is labeled as a b-jet.The fiducial volume is defined by requiring at least two

particle-level jets and at least two leptons in the event, bothobjects with pT > 25 GeV and jηj < 2.5. Events whereleptons and jets overlap, withinΔR of 0.4, are rejected. Theparticle-level jets are not required to be b-jets since thisrequirement is not shared between the three channels in theselection.Using these objects, the reconstruction of top quarks

(known as pseudotops [68]) can be performed. The assign-ment of the proper jet-lepton-neutrino permutation ischosen by first minimizing the difference between themass computed from each lepton-neutrino combination andthe W boson mass value used in the MC simulation. Then,the difference between the mass of each combination of thechosen lepton-neutrino pairs with a jet and the top quark

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mass value, used in the MC simulation, is minimized. Theb-jets are prioritized over the light jets for the proper jet-lepton-neutrino assignment. The correlation coefficientbetween Δjyj at the parton and particle levels is foundto be 79%, while for Δjηj it is 99%.The measurements of the asymmetry in the fiducial

volume require the treatment of an additional backgroundcontribution, in which signal events from outside of thefiducial region migrate into the detector acceptance due toresolution effects. This nonfiducial background constitutesabout 8% of the expected tt̄ events after selection, asestimated by using MC simulation, and it was found to beindependent of the charge asymmetry value of the simu-lated sample. A bin-by-bin scale factor derived fromsimulation is applied to background-subtracted data toestimate the contribution of these events.

C. Unfolding

The measurements are corrected for detector resolutionand acceptance effects. These corrections are performedusing the fully Bayesian unfolding (FBU) technique [69].The FBU procedure applies Bayes’ theorem to the problemof unfolding. This application can be stated in the followingterms: given an observed spectrumDwithNr reconstructedbins and a migration matrix M with Nr × Nt bins givingthe detector response to a true spectrum with Nt bins, theposterior probability of the true spectrum T with Nt binsfollows the probability density

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The selection and reconstruction efficiency, which is theprobability that an event produced in MC generator-level bint is reconstructed in one of the Nr bins included in M, istaken into account in the likelihood. An uninformative priorprobability density is chosen, such that equal probabilitiesare assigned to all T spectra within a wide range. Thebackground in each bin is taken into account when comput-ing LðDjTÞ. The unfolded spectrum and its associateduncertainty are extracted from the posterior probabilitydensity distribution.The migration matrix is obtained from the nominal tt̄

simulated sample using the top quarks before their decay(parton level) or pseudotops (particle level). The combinationof the threedecaychannels isperformedbyusinga rectangularmigration matrix, which maps the reconstructed distributionof the three channels to the same corrected distribution.To validate the method, a linearity test is performed for

the inclusive and differential measurements of the chargeasymmetry. A given asymmetry value is introduced byreweighting the samples according to a nonlinear functionof Δjyj and Δjηj based on a BSM axigluon model [70].The asymmetry values are in the range of −6% to 6% insteps of 2%. Good agreement between the unfolded valuesand the injected values is found, and the calibration curvesderived from this test are linear.For the treatment of systematic uncertainties in the

Bayesian inference approach, the likelihood LðDjTÞ isextended with nuisance parameter terms. This marginallikelihood is defined as

LðDjTÞ ¼Z

LðDjT; θÞ · πðθÞdθ; ð6Þ

where θ are the nuisance parameters, and πðθÞ their priorprobability densities, which are assumed to be normaldistributionsN with a mean value of zero and a variance of

one. A nuisance parameter is associated with each of theuncertainty sources. As is described in Sec. VII, fourcategories of uncertainties are considered in this analysis,but only two are included in the marginalization: thenormalizations of the background processes (θb), and theuncertainties associated with the object identification,reconstruction and calibration (θs). While the first onesonly affect the background predictions, the latter, referredto as object systematic uncertainties, affect both thereconstructed distribution for the tt̄ signal [RðT; θsÞ] andthe total background prediction [Bðθs; θbÞ]. The marginallikelihood then becomes

LðDjTÞ ¼Z

LðDjRðT; θsÞ;Bðθs; θbÞÞ ·N ðθsÞ

·N ðθbÞdθsdθb: ð7Þ

D. Binning optimization and asymmetry extraction

For each measurement, the choice of binning for theΔjyjand Δjηj distributions is optimized by minimizing the

TABLE III. Bins and ranges used for the inclusive and differ-ential measurements. The binning choices used in the Δjηj andΔjyj distributions are shown. The bins are symmetric aroundzero.

Δjηj ΔjyjInclusive [0.0, 0.3, 0.6, 0.9, 1.2,

1.5, 1.7, 1.9, 5.0][0.0, 0.75, 5.0]

mtt̄0–500 GeV [0.0, 0.8, 5.0] [0.0, 0.6, 5.0]

500–2000 GeV [0.0, 1.4, 5.0] [0.0, 1.2, 5.0]

βtt̄0–0.6 [0.0, 0.8, 5.0] [0.0, 0.5, 5.0]0.6–1.0 [0.0, 1.2, 5.0] [0.0, 0.9, 5.0]

ptt̄T0–30 GeV [0.0, 0.7, 5.0] [0.0, 0.8, 5.0]

30–1000 GeV [0.0, 0.7, 5.0] [0.0, 0.8, 5.0]

FIG. 3. Rectangular migration matrix for the Δjyj observable in the fiducial volume. The first four columns correspond to the eechannel, followed by μμ and eμ. The numbers are normalized by row for each channel.

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expected statistical uncertainty while allowing only anegligible bias in the linearity of the calibration curve.The optimal binnings are found to be 4 and 16 bins in aninterval between −5 and 5 for the inclusive measurementsof the Δjyj and Δjηj distributions, respectively. For thedifferential measurements, 4 bins are used for the Δjyj andΔjηj distributions for each of the chosen mtt̄, pT;tt̄ and βz;tt̄ranges. Due to the limited size of the data sample, only tworanges of values are considered for the mtt̄, pT;tt̄ and βz;tt̄variables. The charge asymmetry predicted in the SM isexpected to increase as a function ofmtt̄ while it is expectedto be large for low pT;tt̄ and small and roughly constant forhigher pT;tt̄. The exact boundary between the bins for mtt̄was chosen to minimize the expected uncertainties in thebins. For pT;tt̄, the boundary was set at 30 GeV as a

compromise between the uncertainty optimization and theinterest in the pT;tt̄ dependence described above. For βz;tt̄,the boundary at 0.6 is motivated by the large differenceof the predicted asymmetry between SM and BSM modelsin the range (0.6,1.0) [19]. Table III summarizes thedifferential bins used in the analysis.For the optimized binning choice, more than 50% of the

events populate the diagonal bins of the migration matrixfor the Δjyj distribution, and more than 97% for Δjηj. Therectangular migration matrix, normalized by row for eachchannel, used for the inclusive tt̄ asymmetry measurementis shown in Fig. 3. Due to the nonuniform shape of the Δjyjdistribution, the matrix is not symmetric around thediagonal. The migrations are symmetric around zero anddo not affect the asymmetry value. The Δjyj and Δjηj input

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distributions used for the inclusive measurement are shownin Fig. 4.The asymmetry values are extracted by taking the mean

of the posterior probability density obtained during theunfolding procedure. The uncertainty is obtained from thestandard deviation of the posterior probability density.

VII. SYSTEMATIC UNCERTAINTIES

Four classes of systematic uncertainties affect the meas-urement of the charge asymmetry: detector modelinguncertainties, uncertainties related to the estimation ofthe backgrounds, signal modeling uncertainties, and otheruncertainties, which involve the top-quark reconstruction,the bias introduced by the unfolding procedure and the MCstatistical uncertainty.The first two categories are estimated within the

unfolding through the marginalization procedure wherethe total uncertainty includes these systematic uncertaintiestogether with the statistical uncertainty. In order to estimatethe impact of each source of systematic uncertainty,pseudodata corresponding to the sum of the nominal signaland background samples is used. The unfolding procedurewith marginalization is applied to the pseudodata andconstraints on the systematic uncertainties are obtained.These constraints are then used to build the �1σ variationsof the prediction. The varied pseudodata are then unfoldedwithout marginalization. The impact of each systematicuncertainty is computed by taking half of the differencebetween the results obtained from the �1σ variations ofpseudodata. Clearly, this is only an approximate estimate ofthe individual contribution of each source of systematicuncertainty within the overall marginalization procedure.The signal modeling uncertainties are not estimated

through the marginalization procedure. For these uncer-tainties, the migration matrix is fixed to the nominal tt̄sample and distributions obtained with different generatorsand different injected asymmetries are unfolded. Theunfolded asymmetries are compared with the injectedasymmetries and the calibration curves are obtained. Theslopes and offsets of the calibration curves are extrapolatedto the measured value in data.The final category of systematic uncertainties involves

different estimation methods. The uncertainty related tothe top-quark reconstruction is estimated on pseudodataby varying the starting point of the smearing procedurewithin the kinematic reconstruction and repeating theunfolding. The bias introduced by the unfolding pro-cedure is estimated by propagating the residual slope andoffset of the nominal calibration curve to the measuredvalue. The MC statistical uncertainty is estimated byvarying the nominal migration matrix within the MCstatistical uncertainty and the unfolding procedure isrepeated for each variation. All sources of systematicuncertainties are discussed below in detail.

A. Detector modeling uncertainties

1. Lepton-related uncertainties

The reconstruction and identification efficiencies of elec-trons andmuons, as well as the efficiency of the triggers usedto record the events, differ between data and simulation.Scale factors, and their uncertainties, are derived using tag-and-probe techniques on Z → lþl−ðl ¼ e; μÞ in data andin simulated samples to correct the simulation for thesedifferences [58,59,71,72]. Moreover, the accuracy of thelepton momentum scale and resolution in simulation is alsochecked using reconstructed distributions of the Z → lþl−and J=ψ → lþl− masses. In the case of electrons, E=pstudies using W → eν events are also used. Smalldifferences are observed between data and simulation.Corrections for the lepton energy scale and resolution,and their related uncertainties, are considered [58,59,72].The uncertainties are propagated through this analysis andrepresent a minor source of uncertainty in the measurements.

2. Jet-related uncertainties

The jet energy scale and its uncertainty are derivedcombining information from test-beam data, LHC collisiondata, and simulation [61]. The jet energy scale uncertaintyis split into 22 uncorrelated sources that have different jetpT and η dependencies and are treated independently in thisanalysis. The total jet energy scale uncertainty is one of thedominant uncertainties in Att̄C and in the differential mea-surements of AllC . The jet reconstruction efficiency is foundto be about 0.2% lower in simulation than in data for jetsbelow 30 GeV and consistent with data for higher jet pT .All jet-related kinematic variables (including the missingtransverse momentum) are recomputed by removing ran-domly 0.2% of the jets with pT below 30 GeVand the eventselection is repeated. The efficiency for each jet to satisfythe JVF requirement is measured in Z → lþl− þ 1-jetevents in data and simulation [62]. The correspondinguncertainty is evaluated in the analysis by changing thenominal JVF cut value and repeating the analysis usingthe modified cut value. The uncertainty related to the jetenergy resolution is estimated by smearing the energy ofjets in simulation by the difference between the jet energyresolutions for data and simulation [73]. Finally, theefficiencies to tag jets from b- and c-quarks, light quarks,and gluons in simulation are corrected by pT- andη-dependent data/MC scale factors [63,74,75]. The uncer-tainties in these scale factors are propagated to themeasured value. The impact on the measurement of thejet reconstruction efficiency, jet vertex fraction, jet reso-lution, and jet tagging efficiency is minor.

3. Missing transverse momentum

The systematic uncertainties associated with themomenta and energies of reconstructed objects (leptons

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and jets) are also propagated to the EmissT calculation. TheEmissT reconstruction also receives contributions from thepresence of low-pT jets and calorimeter cells not includedin reconstructed objects (“soft terms”). The systematicuncertainty of the soft terms is evaluated using Z→μþμ−events using methods similar to those used in Ref. [64].The uncertainty has a negligible effect on the measuredasymmetries.

B. Background-related uncertainties

The uncertainties in the single-top-quark and dibosonbackgrounds are about 7% and 5%, respectively. Thesecorrespond to the uncertainties in the theoretical crosssections used for the normalization of the MC simulatedsamples.The uncertainty in the normalization of the fake-lepton

background is evaluated by using various Monte Carlosimulations for each process contributing to this backgroundand propagating the change into the number of expectedevents in the signal region. In the μμ channel, the uncertaintyis obtained by comparing a purely data-driven method basedon the measurement of the efficiencies for real and fake looseleptons, and the estimation used in this analysis. Following aBayesian procedure assuming constant a priori probabilityfor a non-negative number of events, the resulting total

relative uncertainties are þ193%−47% in the ee,þ80%−53% in the μμ, andþ49%

−45% in the eμ channel, where the uncertainties correspondto the 68% central probability region.In the case of the Drell-Yan events, the detector modeling

systematic uncertainties described previously are propa-gated to the scale factors derived in the control regionby recalculating them for all the systematic uncertaintyvariations. An additional uncertainty of 6% is estimated byvarying the Z mass window of the control region used toobtain the scale factors and is added in quadrature to obtainthe final uncertainty in these scale factors.This category represents a minor source of uncertainty in

the measurement.

C. Signal modeling uncertainties

The uncertainty due to the choice of MC generator isobtained by taking the full difference between the POWHEG-hvq and MC@NLO predictions, both interfaced withHERWIG, while the uncertainty from parton showering andhadronization is obtained by comparing POWHEG-hvq inter-faced with either PYTHIA6 or HERWIG. These componentsare among the dominant uncertainties. The effect producedby the different amount of ISR and FSR in the events isestimated as half the difference between the asymmetriesobtained from MC samples with more or less ISR/FSR.

TABLE IV. Absolute uncertainties from the different sources affecting the leptonic asymmetry of the three channels combined in thefiducial and full phase space.

Absolute uncertainties in AllCFiducial volume Full phase space

Statistics Detector Bkg Signal modeling Other Statistics Detector Bkg Signal modeling Other

Inclusive 0.005 0.001 0.001 0.002 0.001 0.005 0.001 0.001 0.004 0.001

mtt̄0–500 GeV 0.008 0.002 0.001 0.005 0.005 0.008 0.002 0.001 0.005 0.006

500–2000 GeV 0.012 0.004 < 0.001 0.013 0.005 0.011 0.004 < 0.001 0.014 0.005

βtt̄0–0.6 0.007 0.003 < 0.001 0.004 0.004 0.007 0.002 < 0.001 0.005 0.0050.6–1.0 0.010 0.005 0.001 0.005 0.004 0.010 0.003 0.001 0.006 0.004

ptt̄T0–30 GeV 0.015 0.009 0.001 0.015 0.006 0.015 0.010 0.001 0.017 0.007

30–1000 GeV 0.011 0.004 0.001 0.012 0.005 0.010 0.004 0.001 0.013 0.006

TABLE V. Absolute uncertainties from the different sources affecting the tt̄ asymmetry of the three channels combined in the fiducialand full phase space.

Absolute uncertainties in Att̄CFiducial volume Full phase space

Statistics Detector Bkg Signal modeling Other Statistics Detector Bkg Signal modeling Other

Inclusive 0.013 0.008 < 0.001 0.007 0.007 0.011 0.006 < 0.001 0.008 0.006

mtt̄0–500 GeV 0.030 0.024 0.001 0.016 0.021 0.028 0.021 0.002 0.018 0.020

500–2000 GeV 0.018 0.007 < 0.001 0.015 0.009 0.015 0.006 < 0.001 0.016 0.008

βtt̄0–0.6 0.023 0.021 0.002 0.014 0.018 0.023 0.019 0.002 0.015 0.0170.6–1.0 0.021 0.009 0.001 0.013 0.011 0.018 0.009 0.001 0.013 0.010

ptt̄T0–30 GeV 0.035 0.019 0.003 0.018 0.020 0.031 0.015 0.004 0.019 0.017

30–1000 GeV 0.027 0.015 0.003 0.018 0.017 0.025 0.013 0.003 0.014 0.015

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These samples are generated with POWHEG-hvq interfacedwith PYTHIA6 for which the parameters of the generationwere varied to span the ranges compatible with the results ofmeasurements of tt̄ production in association with jets [76].Finally, PDF uncertainties are obtained by using the errorsets of CT10, MWST2008 and NNPDF2.3, and followingthe prescriptions recommended by the PDF4LHC workinggroup [39]. The impact of the last two uncertainties is small.

D. Other uncertainties

1. Top-quark kinematic reconstruction

There is an intrinsic uncertainty of the reconstructionmethod due to the randomness in the smearing procedure. Ifthe smearing starts from a different point it could lead to a

different solution. The uncertainty from this effect iscomputed by performing pseudoexperiments on MC events.For each event, the tt̄ system is reconstructed multiple timesvarying the starting point of the smearing procedure. Then,for each variation the unfolding procedure is repeated andthe standard deviation of the asymmetries obtained is takenas the uncertainty. This represents one of the major system-atic uncertainties for the measurements, but it is still onlyhalf of the statistical uncertainty for most of them.

2. Nonclosure uncertainties

When the calibration curve for the nominal signalPOWHEG-hvq sample is estimated a residual slope and anonzero offset are observed. This bias, introduced by theunfolding procedure, is propagated to the measured values in

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in the full phase spacellCA

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Bernreuther & Si. PRD 86, 034026.

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0.006±0.008

ATLAS-120.3 fb, = 8 TeVs

FIG. 5. Summary of all the measurements in this paper for theleptonic asymmetry in the fiducial volume (top) and full phasespace (bottom). The predictions shown in blue are obtained usingPOWHEG-hvq þ PYTHIA6 at NLO where the uncertainties arestatistical, and the corresponding theoretical uncertainties aresmall compared to the experimental precision. The inclusivemeasurement in the full phase space is compared to a NLOþ EWprediction [23].

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the same way as for the signal modeling uncertainties. Thissource of uncertainty is negligible in all the measurements.

3. MC sample size

The uncertainty associated with the limited size of thenominal signal POWHEG-hvq sample is evaluated byperforming pseudoexperiments on MC events. The migra-tion matrix is varied within the MC statistical uncertaintyand the unfolding procedure is repeated. The standarddeviation of the obtained asymmetries is taken as theuncertainty. This uncertainty has a minor impact on themeasurements.

E. Summary of systematic uncertainties

Tables IV and V show how each category of uncertaintyaffects the measurements of the lepton and tt̄ asymmetry,respectively. The statistical uncertainty gives the largestcontribution to the measurement, followed by thereconstruction and the signal modeling uncertainties. Thesignal modeling uncertainties are enhanced in the differ-ential measurements by the migrations between thedifferential bins across the different MC generators usedfor their estimation. The uncertainty obtained by the sumin quadrature of the individual systematic uncertainties isslightly larger than the total marginalized uncertainty in themeasurements.

VIII. RESULTS

Figures 5 and 6 show the inclusive and differentialresults for the leptonic and tt̄ charge asymmetry in thefiducial region and in the full phase space. All the results arecompatible with the Standard Model predictions [23,25–27].Figure 7 shows the unfolded distributions of the Δjηj and

Δjyj observables for the inclusive measurement in thefiducial volume. The distributions are compared withMonte Carlo predictions at NLO provided by POWHEG-hvq. The measured inclusive values in the full phase spaceare AllC ¼ 0.008� 0.006 and Att̄C ¼ 0.021� 0.016. Theyare in agreement with the Standard Model predictionsAllC ¼ 0.0064� 0.0003 and Att̄C ¼ 0.0111� 0.0004 [23].The measurements are consistent with other LHC asymme-try measurements at 8 TeV [19–21].The statistical uncertainty is in most cases the dominant

contribution to the total uncertainty. The dominantsystematic uncertainties across all the measurements arethe signal modeling and the kinematic reconstructionuncertainty. The signal modeling uncertainties are reducedin most of the cases by performing the measurements in thefiducial region, since the extrapolation from detectoracceptance to the full phase space is avoided. The statisticaluncertainty is slightly larger in the fiducial region thanin the full phase space; this is expected because somereconstructed events fail the fiducial requirements in thefiducial analysis.Figure 8 compares the values of AllC and A

tt̄C from the

inclusive measurements in the full phase space to the SMpredictions and two BSM models [77] compatible with theTevatron results. Two BSM models with a new color-octetparticle that is exchanged in the s-channel are considered.In the model with the light octet, the new particle’s mass(m ¼ 250 GeV) is below the tt̄ production threshold and itswidth is assumed to be Γ ¼ 0.2 m. The model with theheavy octet uses an octet mass beyond current limits fromdirect searches at the LHC. The corrections to tt̄ productionare independent of the mass but instead depend on theratio of coupling to mass, which is assumed to be 1 TeV−1.The new particles in both BSMmodels would not be visible

|η| Δdσd

σ1

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FIG. 7. Data distribution after the unfolding procedure compared with the POWHEG-hvq þ PYTHIA6 prediction at NLO for theinclusive Δjηj (left) and Δjyj (right) observables in the fiducial volume. The data/expected ratio is also shown.

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as resonances in the mtt̄ spectrum at the Tevatron or at theLHC. In the figures, model predictions for different left-handed, right-handed, and axial coupling constants to topquarks are shown. The ellipses correspond to the 1σ and 2σtotal uncertainty in the measurements. The correlationbetween these two measurements is taken into account.The statistical and detector systematic uncertainty correla-tion between AllC and A

tt̄C is found to be 30%. The modeling

systematic uncertainties are assumed to be 100% corre-lated. The resulting correlation between AllC and A

tt̄C is

about 48%. The measurements are compatible with the SMand do not exclude the two sets of BSMmodels considered.

IX. CONCLUSION

Measurements of the leptonic and tt̄ charge asymmetryin the dilepton channel, characterized by two high-pTleptons (electrons or muons), are presented. The measure-ments, corrected for detector resolution and acceptanceeffects, are performed using data corresponding to anintegrated luminosity of 20.3 fb−1 of pp collisions atffiffiffis

p ¼ 8 TeV collected by the ATLAS detector at theLHC. The inclusive asymmetries are measured in the fullphase space to be

AllC ¼ 0.008� 0.006

and

Att̄C ¼ 0.021� 0.016:

They are in agreement with the Standard Model predictionsAllC ¼ 0.0064� 0.0003 and Att̄C ¼ 0.0111� 0.0004.Differential measurements of the asymmetries as a function

of the invariant mass, transverse momentum, and longi-tudinal boost of the tt̄ system are also performed and theyare found to be in agreement with the SM predictions,although they have relatively large uncertainties. Allmeasurements are also performed in a fiducial region atparticle level where the modeling uncertainties are reduced.For all measurements, the statistical uncertainty is thedominant contribution to the total uncertainty. Theunfolded distributions of lepton Δjηj and tt̄ Δjyj areprovided. Good agreement between the corrected distribu-tions and the predictions of POWHEG-hvq þ PYTHIA6 isobserved.

ACKNOWLEDGMENTS

We thank CERN for the very successful operation of theLHC, as well as the support staff from our institutionswithout 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 andFAPESP, Brazil; NSERC, NRC and CFI, Canada; CERN;CONICYT, Chile; CAS, MOST and NSFC, China;COLCIENCIAS, Colombia; MSMT CR, MPO CR andVSC CR, Czech Republic; DNRF and DNSRC, Denmark;IN2P3-CNRS, CEA-DSM/IRFU, France; GNSF, Georgia;BMBF, HGF, and MPG, Germany; GSRT, Greece; RGC,Hong Kong SAR, China; ISF, I-CORE and BenoziyoCenter, Israel; INFN, Italy; MEXT and JSPS, Japan;CNRST, Morocco; FOM and NWO, Netherlands; RCN,Norway; MNiSWand NCN, Poland; FCT, Portugal; MNE/IFA, Romania; MES of Russia and NRC KI, RussianFederation; JINR; MESTD, Serbia; MSSR, Slovakia;ARRS and MIZŠ, Slovenia; DST/NRF, South Africa;

ttCA

0.02− 0.01− 0 0.01 0.02 0.03 0.04 0.05 0.06

ll CA

0.02−

0.01−

0

0.01

0.02

0.03

Bernreuther & Si. PRD 86, 034026.light octet, LEFTlight octet, RIGHTlight octet, AXIAL

ATLAS data

σATLAS 1σATLAS 2

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Inclusive - Parton level

ttCA

0.02− 0.01− 0 0.01 0.02 0.03 0.04 0.05 0.06

ll CA

0.02−

0.01−

0

0.01

0.02

0.03

Bernreuther & Si. PRD 86, 034026.heavy octet, LEFTheavy octet, RIGHTheavy octet, AXIAL

ATLAS data

σATLAS 1σATLAS 2

ATLAS-120.3 fb = 8 TeV,s

Inclusive - Parton level

FIG. 8. Comparison of the inclusive AllC and Att̄C measurement values in the full phase space to the SM NLO QCDþ EW prediction

[23] and to two benchmark BSM models [77], one with a light octet with mass below the tt̄ production threshold (left) and one with aheavy octet with mass beyond the reach of the LHC (right), for various couplings as described in the legend. Ellipses corresponding to1σ and 2σ combined statistical and systematic uncertainties of the measurement, including the correlation between AllC and A

tt̄C, are also

shown.

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MINECO, Spain; SRC and Wallenberg Foundation,Sweden; SERI, SNSF and Cantons of Bern and Geneva,Switzerland; MOST, Taiwan; TAEK, Turkey; STFC,United Kingdom; DOE and NSF, United States ofAmerica. In addition, individual groups and members havereceived support from BCKDF, the Canada Council,CANARIE, CRC, Compute Canada, FQRNT, and theOntario Innovation Trust, Canada; EPLANET, ERC,FP7, Horizon 2020 and Marie Skłodowska-CurieActions, European Union; Investissements d’AvenirLabex and Idex, ANR, Région Auvergne and FondationPartager le Savoir, France; DFG and AvH Foundation,Germany; Herakleitos, Thales and Aristeia programmes

co-financed by EU-ESF and the Greek NSRF; BSF, GIFand Minerva, Israel; BRF, Norway; Generalitat deCatalunya, Generalitat Valenciana, Spain; the RoyalSociety and Leverhulme Trust, United Kingdom. Thecrucial computing support from all WLCG partners isacknowledged gratefully, in particular from CERN, theATLAS 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 largenon-WLCG resource providers. Major contributors ofcomputing resources are listed in Ref. [78].

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