Measurement of the charge asymmetry in dileptonic decays of top quark pairs in pp collisions at √ s = 7 TeV using the ATLAS detector

: A measurement of the top-antitop ( t ¯ t ) charge asymmetry is presented using data corresponding to an integrated luminosity of 4.6 fb − 1 of LHC pp collisions at a centre-of-mass energy of 7 TeV collected by the ATLAS detector. Events with two charged leptons, at least two jets and large missing transverse momentum are selected. Two observables are studied: A `` C based on the identiﬁed charged leptons, and A t ¯ t C , based on the reconstructed t ¯ t ﬁnal state. The asymmetries are measured to be The measured values are in agreement with the Standard Model predictions.


Introduction
The top quark is the heaviest elementary particle known to date. It was discovered in 1995 at the Tevatron proton-antiproton (pp) collider by the CDF and D0 collaborations [1,2]. It is the only quark in the Standard Model (SM) that decays before hadronization occurs, and the only quark with Yukawa coupling to the Higgs boson close to unity. A precise study of top quark properties could shed light on possible physics models beyond the SM [3][4][5][6][7][8][9].
This analysis uses a data set corresponding to an integrated luminosity of 4.6 fb −1 of Large Hadron Collider (LHC) proton-proton (pp) collisions at a centre-of-mass energy of 7 TeV collected by the ATLAS detector. It is performed in the dilepton channel of the tt pair decay, realized when both W bosons decay to a charged lepton and a neutrino. The measured observables are the lepton-based charge asymmetry A C and the tt charge asymmetry A tt C . The observable A C is defined as an asymmetry between positively and negatively charged leptons (electrons and muons) in the dilepton decays of the tt pairs, where ∆|η| = |η + | − |η − |, (1.2) η + (η − ) is the pseudorapidity 1 of the positively (negatively) charged lepton and N is the number of events with positive or negative ∆|η|. While A C is defined in eq. (1.1) as an asymmetry between positively and negatively charged lepton pseudorapidities, A tt C corresponds to the asymmetry in top quark and antitop quark rapidities 2 , where ∆|y| = |y t | − |yt|, (1.4) y t (yt) is the rapidity of the top (antitop) quark, and N is the number of events with positive or negative ∆|y|.
In SM tt production, the asymmetry is absent at leading-order (LO) in Quantum Chromodynamics (QCD) and is introduced by the next-to-leading-order (NLO) QCD contributions to the tt differential cross-sections, which are odd with respect to the exchange of t andt. At the LHC, the contributions to the asymmetries defined in eq. (1.1) and eq. (1.3) are predominantly from qq-initiated tt production, and qg-initiated production also has a non-negligible contribution. The gg-initiated processes are symmetric [10]. The asymmetry predicted in the SM is slightly positive, implying that the top quark is preferentially emitted in the direction of the quark in the initial state. In qq interactions at the LHC, the quark is in most cases a valence quark whereas the antiquark is from the sea. The asymmetry translates to a higher boost along the beam direction for the t-quark than for thet-quark. The rapidity distribution of the t is thus slightly broader than the one of thet.
The SM predictions of A tt C and A C computed at NLO in QCD and including electroweak corrections (NLO QCD+EW) are [10] A tt C = 0.0123 ± 0.0005 (scale), (1.5) A C = 0.0070 ± 0.0003 (scale). (1.6) These asymmetries are evaluated without acceptance cuts. The uncertainties are due to scale variations, estimated by simultaneous variation of the renormalization and factorization scale by a factor of half or two with respect to the reference scale value, which is set to the top quark mass. Recent next-to-next-to-leading order (NNLO) calculations of the forward-backward asymmetry for the Tevatron suggest that varying these scales significantly underestimates the uncertainty due to higher order corrections [11], but no NNLO calculation has yet been published for pp interactions at the LHC energies. There is however a recent calculation obtained with the Principle of Maximum Conformality [12] which gives a consistent value of A tt C =0.0115 +0.0001 −0.0003 (scale). The predicted value of A C is smaller than 1 The pseudorapidity is defined in terms of the polar angle θ as η = − ln tan(θ/2). 2 The rapidity is defined as y = 1 2 ln E+pz E−pz where E is the energy of the particle and pz is the component of the momentum along the LHC beam axis. the prediction for A tt C , since the directions of the leptons do not fully follow the direction of the parent t andt quarks. However, A C can be measured more precisely, since it is determined without the need for a full reconstruction of t andt kinematics, which involves the use of jets and missing transverse momentum that are reconstructed with less precision than the kinematic variables of the leptons. The values of A C and A tt C as well as their correlation can be sensitive to new physics arising in top quark pair production [13][14][15][16][17].
The asymmetry A tt C has been measured in the single-lepton decay channel by the AT-LAS [18] and CMS [19] collaborations at √ s = 7 TeV. The CMS collaboration has reported measurements of A C and A tt C in the dilepton decay channel at √ s = 7 TeV [20]. The measured asymmetry values as well as those from a combination of ATLAS and CMS A tt C results in the single-lepton decay channel [21] are consistent with the SM predictions.
At the Tevatron collider, tt production has a forward-backward asymmetry with respect to the direction of the proton and antiproton beams. The asymmetry based on t andt quarks, A tt FB , is defined as where ∆y = y t − yt, (1.8) y t (yt) is the rapidity of the t (t) quark and N is the number of events with positive or negative ∆y. An analogously defined lepton-based forward-backward asymmetry in tt production has been studied as well. At the Tevatron, tt events are predominantly produced by qq annihilation, thus the predicted asymmetries are typically larger than at the LHC, where gg-initiated production dominates. The Tevatron experiments have reported deviations of forward-backward asymmetries from the SM predictions [22,23], which have motivated a number of further asymmetry measurements. Comparing the results with the latest NNLO calculations available at the Tevatron [11], the deviations reported by the CDF collaboration [24][25][26] are reduced, while the latest measurements by the D0 collaboration [27,28] are now in good agreement with the predictions. This paper is organized as follows. In section 2 the main components of the ATLAS detector relevant for this measurement are summarized. In section 3 the simulated samples used for the analysis are presented. In section 4 the object and event selection are described. In section 5 the kinematic reconstruction used for the A tt C measurement is detailed. For comparison with theory prediction, the measurements are corrected for detector resolution and acceptance effects, as presented in section 6. Sections 7 and 8 describe the systematic uncertainties and the measurement results, respectively. Finally, the conclusions are given in section 9.

The ATLAS detector
The ATLAS detector [29] at the LHC covers nearly the entire solid angle around the collision point. 3 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 toroid magnets. The inner-detector system is immersed in a 2 T axial magnetic field and provides charged-particle-tracking in the range |η| < 2.5.
A high-granularity silicon pixel detector covers the interaction region and typically provides three measurements per track. It is surrounded by a silicon microstrip tracker designed to provide four two-dimensional measurement points per track. These silicon detectors are complemented by a transition radiation tracker, which enables radially extended track reconstruction up to |η| = 2.0. The transition radiation tracker also provides electron identification information based on the fraction of hits (typically 30 in total) exceeding an energy-deposit threshold corresponding to transition radiation.
The calorimeter system covers the pseudorapidity range |η| < 4.9. Within the region |η| < 3.2, electromagnetic calorimetry is provided by barrel and end-cap high-granularity lead/liquid-argon (LAr) electromagnetic calorimeters, with an additional thin LAr presampler covering |η| < 1.8 to correct for energy loss in the material upstream of the calorimeters. Hadronic calorimetry is provided by a steel/scintillator-tile calorimeter, segmented into three barrel structures within |η| < 1.7, and two copper/LAr hadronic endcap calorimeters. The solid angle coverage is completed with forward copper/LAr and tungsten/LAr calorimeters used for electromagnetic and hadronic measurements.
The muon spectrometer comprises separate trigger and high-precision tracking chambers measuring the deflection of muons in a magnetic field generated by superconducting air-core toroids. The precision chamber system covers the region |η| < 2.7 with three layers of monitored drift tube chambers, complemented by cathode strip chambers in the forward region. The muon trigger system covers the range |η| < 2.4 with resistive plate chambers in the barrel, and thin gap chambers in the endcap regions.
A three-level trigger system is used to select interesting events. The Level-1 trigger is implemented in hardware and uses a subset of detector information to reduce the event rate to a design value of at most 75 kHz. This is followed by two software-based trigger levels, which together reduce the event rate to about 300 Hz.

Simulated samples
Several Monte Carlo (MC) simulated samples are used in the analysis to model the signal and background processes. The total background, estimated partly from these simulated samples, is subtracted from the data at a later stage of the analysis. The signal sample is used to correct the background subtracted data for detector, resolution and acceptance effects. The MC samples are also used to evaluate the systematic uncertainties of the measurement.
The nominal simulated tt sample is generated using the Powheg-hvq [30][31][32] (patch4) generator with the CT10 [33] parton distribution function (PDF) set. The NLO QCD matrix element is used for the tt hard-scattering process. The parton showers (PS) and the underlying event are simulated using Pythia6 [34] (v6.425) with the CTEQ6L1 [35] PDF and the corresponding Perugia 2011C set of tunable parameters (tune) [36] intended to be used with this PDF. The hard-scattering process renormalization and factorization scales are fixed at the generator default value Q that is defined by where m t and p T are the top quark mass and the top quark transverse momentum, evaluated for the underlying Born configuration (i.e. before radiation). Additional tt samples used to evaluate signal modelling uncertainties are described in section 7. Signal samples are normalized to a reference value of σ tt = 177 +10 −11 pb for a top quark mass of m t = 172.5 GeV. The cross-section has been calculated at next-to-next-to-leading-order (NNLO) in QCD including resummation of next-to-next-to-leading logarithmic (NNLL) soft gluon terms [37][38][39][40][41][42] with top++2.0 [43]. The PDF and strong coupling (α s ) uncertainties were calculated using the PDF4LHC prescription [44] with the MSTW2008 68% CL NNLO [45,46], CT10 NNLO [33,47] and NNPDF2.3 5f FFN [48] PDF sets, and added in quadrature to the scale uncertainty. The NNLO+NNLL cross-section value is about 3% larger than the exact NNLO prediction, as implemented in Hathor 1.5 [49].
The MC generators which are utilized to estimate the backgrounds are as follows. Single-top processes in the W t channel are generated with the MC@NLO event generator (v4.01) [50,51] with the CT10 PDF. The parton showers, hadronization and the underlying event are modelled using the Herwig (v6.520) [52,53] and Jimmy (v4.31) [54] generators. The CT10 PDF with the corresponding ATLAS AUET2 tune [55] is used for parton shower and hadronization settings. For Z/γ * +jets and diboson events (W W , W Z and ZZ), Alpgen (v2. 13) [56] interfaced to Herwig and Jimmy is used. The CTEQ6L1 PDF and the corresponding ATLAS AUET2 tune is used for the matrix element and parton shower settings. The W t background process is normalized to the reference NLO+NNLL QCD [57] prediction. Diboson production is normalized to the reference NLO QCD prediction obtained using MCFM [58] and MC@NLO generators with the MSTW2008 NLO PDF [45]. The Z/γ * → ee/µµ+jets cross-section is normalized using a control region in data as detailed in section 4. The Z/γ * → τ τ +jets events are normalized to a NNLO reference cross-section using the FEWZ [59] and ZWPROD [60] programs with the MSTW2008 NNLO PDF.
To realistically model the data, the simulated samples are generated with an average of eight additional inelastic pp interactions from the same bunch crossing (referred to as pileup) overlaid on the hard-scatter event. Simulated samples are processed through AT-LAS detector simulation. For the majority of the samples, a full detector simulation [61] based on GEANT4 [62] is used. Some of the samples used for assessment of generator modelling uncertainties are obtained using a faster detector simulation program that relies on parameterized showers in the calorimeters [61, 63]. Simulated events are then processed using the same reconstruction algorithms and analysis chain as the data. overall uncertainty of 1.8% [64]. The analysis makes use of reconstructed electrons, muons, jets and missing transverse momentum in the detector. Electrons are reconstructed as clusters of energy deposits in the electromagnetic calorimeter, matched to a track in the inner detector. They are required to pass a set of tight selection criteria [65]. The selected electrons have to satisfy a requirement on their transverse energy (E T ) and the pseudorapidity of the associated calorimeter cluster (|η cluster |): E T > 25 GeV and |η cluster | < 2.47. The electrons in the region 1.37 < |η cluster | < 1.52, which corresponds to a transition between the barrel and endcap electromagnetic calorimeters, are excluded. Electrons are required to be isolated, using the requirements described as follows (excluding calorimeter deposits and tracks from the electrons). The E T within a cone of size ∆R = (∆η) 2 + (∆φ) 2 = 0.2 and the scalar sum of track p T within a cone of ∆R = 0.3 around the electron are required to be below E T -and η-dependent thresholds. The efficiency of this isolation requirement on electrons is 90%, and its goal is to reduce the contribution from hadrons mimicking lepton signatures, as well as leptons produced in heavy-hadron decays or photon conversion. These are referred to as fake and non-prompt leptons (NP) in the following.
Muons are reconstructed by matching a track in the inner detector to a track segment in the muon spectrometer. They are required to pass tight selections [66]. The selected muons are required to have p T > 20 GeV and |η| < 2.5. To reject fake and non-prompt muons, the following isolation requirements are imposed: the calorimeter transverse energy within a cone of ∆R = 0.2 around the muon is required to be less than 4 GeV and the scalar sum of track p T within a cone of ∆R = 0.3 is required to be less than 2.5 GeV (excluding the calorimeter deposits and tracks from the muons).
Jets are reconstructed from energy deposits in the calorimeter, using the anti-k t algorithm with a distance parameter R = 0.4 [67]. The energy of the input clusters [68] is corrected to the level of stable particles using calibration factors derived from simulation and data [69]. The jets are required to have a p T of at least 25 GeV and |η| < 2.5. To suppress the contribution from low-p T jets originating from pileup interactions, tracks associated with the jet and emerging from the primary vertex are required to account for at least 75% of the scalar sum of the p T of all tracks associated with the jet. A primary vertex, originating from pp interactions, is a reconstructed vertex required to have at least five associated tracks with p T > 0.4 GeV. In the cases where more than one primary vertex is reconstructed, the vertex with the highest trk p 2 T is chosen and assumed to be associated with the hard-process, and the sum runs over all associated tracks.
The missing transverse momentum (E miss T ) is a measure of transverse momentum imbalance due to the presence of neutrinos. It is reconstructed from the transverse momenta of jets in the kinematic range of p T > 20 GeV and |η| < 4.5, electrons, muons, and calorimeter clusters not associated with any of the reconstructed objects, as detailed in ref. [70].
Using the objects reconstructed as above, an event selection optimized for signatures corresponding to tt events in which both W bosons from the t andt quarks decay to leptons is performed. Events are required to have been selected by a single-electron trigger with a threshold of 20 or 22 GeV (depending on the data-taking period), or a single-muon trigger with a threshold of 18 GeV. They are required to have exactly two isolated, oppositely charged, leptons. Depending on the lepton flavours, the sample is divided into three analysis channels referred to as ee, eµ and µµ. To reduce the Drell-Yan production of Z/γ * +jets background, the invariant mass of the two leptons (m ) is required to be above a threshold used to suppress γ * → production background and outside a Z boson mass window in the ee and µµ channel events. The following requirements are used: m > 15 GeV and |m −m Z | > 10 GeV. In the ee and µµ channels the Drell-Yan and diboson backgrounds are further reduced using a requirement on the missing transverse momentum, E miss T > 60 GeV. In the eµ channel the Z/γ * +jets background is smaller and suppressed by requiring the scalar sum of the p T of the two leading jets and leptons (H T ) to be larger than 130 GeV.
The background contributions are estimated using a combination of techniques using data and Monte Carlo events. In the case of single-top and diboson processes, both the shape and normalization of the distributions are taken from the simulation. For Z/γ * → ee/µµ+jets events, simulated MC events are used to model the shape of the distributions, but a data control region is used for normalization. Drell-Yan events with E miss T > 60 GeV are affected by energy mismeasurements, that are difficult to model in simulation. A control region with events with m in the Z-mass region is defined to study the effect of mismeasured E miss T . The relative E miss T , defined as the projection of the missing transverse momentum onto the direction of the jet or charged lepton with closest φ, is used to identify the events with mismeasured objects. Events with energy mismeasurements are characterized by high values of relative E miss T . A cut is applied to the relative E miss T , and data and simulation are then compared to derive a normalization correction factor which is applied to the simulated sample. The Z/γ * → τ τ contribution is estimated from MC simulation. The background stemming from events with at least one non-prompt or fake lepton is estimated from the data, since the lepton misidentification rates are difficult to model in MC simulation. A matrix method technique is used [71]. It consists of selecting data samples dominated either by real leptons or by fake leptons, and estimating the efficiencies for a real or fake lepton to satisfy the isolation criteria.
After the final selection, the data sample contains more than 8000 events, with an expected signal-to-background ratio of approximately six. The number of events in data and simulation, including statistical and systematic uncertainties, are compared in table 1. After selection, the largest number of events is observed in the eµ channel, which has the highest branching ratio and the loosest background suppression cuts. The ee channel has the lowest number of events because of the stringent requirements on lepton kinematics. Figure 1 shows good agreement between the data and the SM predictions for the jet multiplicity, lepton p T and lepton pseudorapidity distributions. The ∆|η| distributions are shown in figure 2 for the three channels separately.

Kinematic reconstruction
For the measurement of the tt charge asymmetry, the direction of the top and antitop quarks needs to be determined. The four-momenta of top quarks in selected events are computed with a kinematic reconstruction using the objects observed in the detector. The reconstruction is based on solving the kinematic equations obtained when imposing energy-momentum conservation at each of the decay vertices of the process. In the dilepton channel, at least Channel ee eµ µµ tt 621 ± 5 ± 59 4670 ± 10 ± 325 1780 ± 10 ± 120 Single top 31.6 ± 1.7 ± 3.8 230 ± 5 ± 21 83.9 ± 2.7 ± 8.3 19 ± 4 ± 19 99 ± 10 ± 63 26.8 ± 5.1 ± 1.9 Total expected 734 ± 8 ± 63 5350 ± 20 ±340 2100 ± 10 ±130 Data 740 5328 2057 Table 1: Observed number of data events in comparison to the expected number of signal events and all relevant background contributions after the event selection. The backgrounds are estimated from the MC simulation or from the data-driven methods (DD) described in section 4. Events with one or more non-prompt or fake leptons are referred to as "NP & fake". The first uncertainty is statistical, the second corresponds to systematic uncertainties on background normalization and detector modelling described in section 7. The values labeled with "-" are estimated to be smaller than 0.5.
two neutrinos are produced and escape undetected. Consequently, the system is underconstrained and its kinematics cannot be fully determined without further assumptions (for example on the W boson and top quark masses, and the pseudorapidities of the neutrinos from the W boson decays). Moreover, several ambiguities have to be resolved to find the correct solution. For example, the lepton and jet from the same decay chain have to be associated. In an event with two leptons and two jets, this leads to two possible associations. In this analysis, the neutrino weighting technique [72] is used. This procedure steps through different hypotheses for the pseudorapidity of the two neutrinos in the final state. These hypotheses are made independently for the two neutrinos. For each hypothesis, the algorithm calculates the full event kinematics, assuming the W boson and the top quark masses. It then assigns a weight to the resulting solution based on the level of agreement between the calculated and measured missing transverse momentum. The weight is defined as with E miss,obs d being the projection of the measured missing transverse momentum along the axes defining the transverse plane (d = x, y) and E miss,calc d the projection calculated with the assumed η values of the neutrino pair. The resolution on the missing transverse momentum is denoted σ E miss T , and defined as σ E miss . The total transverse energy, struction efficiency, corresponding to the fraction of events in which solutions for t andt four-momenta are found, is estimated to be about 80% in the data. In the other 20% of events, no solution to the system of the kinematic equations could be found, and the events are not used for the measurement of A tt C . The performance of the reconstruction algorithm for key variables, such as the top quark rapidities and ∆|y|, is evaluated using the nominal tt simulated sample. The fraction of reconstructed MC events where the sign of ∆|y| is determined correctly is about 70%. In figure 3 the distributions of the top quark transverse momentum, top quark rapidity and the tt invariant mass are shown for the combined ee, eµ and µµ channels. In figure 4 the ∆|y| distribution is shown separately for each of the ee, eµ and µµ channels. Good agreement between the observed and expected distributions is found.

Corrections
For comparison with theoretical calculations, the measurements are corrected for detector resolution and acceptance effects. The corrections are applied to the observed ∆|η| and ∆|y| spectra. Apart from the corrected inclusive asymmetry values, particle-or parton-level ∆|η| and ∆|y| distributions are obtained and presented as normalized differential cross-sections in section 8. Acceptance corrections are included, thus all the results correspond to an extrapolation to the full phase-space for tt production.
In case of the A C , the resolution of the measured lepton ∆|η| is very good. Figure 5(a) shows, for the eµ channel, the probability of an event with a generated value ∆|η| in the j-th bin to be reconstructed in the i-th bin of the corresponding distribution. This probability distribution is defined to be the response matrix for the observable ∆|η|. The diagonal bins of the response matrix account for more than 90% of the events. The acceptance and the small migrations are accounted for by the bin-by-bin correction described in subsection 6.1.
In case of the A tt C , the top quark direction, which is necessary to determine the tt asymmetry, is evaluated using the kinematic reconstruction of the events, described in section 5. In addition to lepton directions and energies measured with very good resolution, jet four-momenta and E miss T measured with worse resolution are used in reconstructing the t andt four-momenta. The resolution of tt ∆|y| ( figure 5(b)) is thus much worse than that for the lepton ∆|η|. In order to correct for detector resolution and acceptance effects in A tt C , the fully Bayesian unfolding (FBU) technique [73] described in subsection 6.2 is used.

Correction of the lepton-based asymmetry
For A C , bin-by-bin correction factors that also extrapolate to the full acceptance for the tt production are used. The goal of this procedure is to find an estimate of the true distribution, given an observed distribution and an expected background distribution. For the lepton-based results, true distributions are obtained at particle level using leptons before Quantum Electrodynamics (QED) final-state radiation 4 . The following notation is used: µ andμ are vectors of true distribution values and its estimate, respectively. An observed distribution is denoted by n and its expected value from simulation by ν MC . An expected background distribution is denoted by β. For the i-th bin of the asymmetry distribution, the estimate of the true value is obtained by applying a correction factor C i to the difference between the observed number of events and the expected number of background events, The C i are estimated using the tt MC simulated sample as The bin-by-bin correction of A C is tested on simulation samples reweighted such that different levels of asymmetry ∆|η| are introduced. Samples are reweighted according to a linear function of ∆|η| with a slope between −6% and 6% in steps of 2%. Corrected values obtained from reweighted distributions are found to be in good agreement with the input value, following a linear relationship. The choice of the binning is done by optimizing the linearity of the method and the expected statistical uncertainty of the asymmetry. The results in section 8 are obtained with ∆|η| distribution binned in 14 bins in the interval between −3 and 3.
The correction factors depend strongly on the channel and the bin, with the outer bins receiving larger fractional corrections. The ee channel has the lowest acceptance and thus the highest correction factors, reaching values of 500 in the outer bins, in which the events are mostly outside the detector fiducial acceptance. The eµ channel has a much higher acceptance, and the correction factors vary between 10 and 60. The dependence of the correction factors on the MC model and PDF is small, up to approximately 5%.

Unfolding of the tt asymmetry
In case of sizeable migrations across the bins of the considered distribution, the migrations need to be taken into account without introducing a significant bias during the correction procedure. Unfolding is better suited for the purpose than the bin-by-bin correction factors described in subsection 6.1. Using the response matrix (R), the true distribution (µ) is related to the expected reconstruction-level distribution (ν) and the expected background (β) by In the FBU technique, the maximum likelihood estimator of µ, L(µ), is given by log P (n i ; ν i ) − αS(µ) ; p(µ) ∝ L(µ) , (6.4) with P the Poisson distribution, n the observed distribution, S a regularization function and α a regularization parameter. The sum in i runs over all N bins of the distributions. The probability density of the unfolded spectra p(µ) is proportional to L(µ). The regularization function S is selected such that the spectra with a desired quality, such as smoothness, are preferred. The regularization parameter α controls the relative strength of the regularization when evaluating the likelihood. The unfolded spectrum and its associated uncertainty are extracted from the probability density p(µ). The statistical uncertainty corresponds to the width of the shortest interval covering 68% probability, and the unfolded spectrum corresponds to the middle of that interval. The response matrix is obtained using information from the nominal tt simulated sample and, in particular, using the top quarks before their decay (parton level) and after QCD radiation 5 .
As explained for the lepton-based asymmetry, the correction is done at the level of true dilepton events (where the two top quarks decay to electrons or muons, either from a direct W boson decay or through an intermediate τ lepton decay).
Using the vector of the true distribution's estimated valuesμ, the regularization function is defined based on the curvature S(µ) = |C(µ) − C(μ)|, with As in the case of the lepton-based asymmetry, linearity tests are performed. A given asymmetry value is introduced by reweighting the samples according to a linear function of tt ∆|y| with a slope between -6% and 6% in steps of 2%. Unfolded values obtained from reweighted distributions are observed to be in good agreement with the injected values of A tt C , following a linear relationship. This linearity test is performed with and without regularization and yields similar performance. The binning used for the ∆|y| distribution as well as the regularization parameter are optimized simultaneously to minimise the expected statistical uncertainty while achieving good linearity. The results in section 8 are obtained with a regularization parameter α = 10 −7 . The ∆|y| distribution is binned in 4 bins in the interval between −5 and 5. For this binning choice, at least 50% of the events populate the response matrix diagonal bins for each of the ee, eµ and µµ channels ( figure 5(b)).
The overall correction which is applied to the distribution varies between factors of 10 and 100, depending on the channel and the bin. As shown in figure 5 the bins used for the tt ∆|y| distribution are wider than the bins used for the lepton ∆|η| distribution. The acceptance correction applied to the outer bins of ∆|y| is thus smaller than the correction obtained for the outer bins of ∆|η| distribution.

Systematic uncertainties
The systematic uncertainties considered in this analysis are classified into three categories: detector modelling uncertainties, signal modelling uncertainties and uncertainties related to the estimation of the backgrounds. The contributions of these sources of uncertainty are summarized in table 2 for the lepton-based asymmetry A C and in table 3 for the tt asymmetry A tt C . The resulting variations are assumed to be of the same size in both directions and are therefore symmetrized. Apart from one-sided uncertainties, as in the case of the comparison of different MC models, the symmetrization does not notably modify the uncertainty values.
Detector modelling uncertainties are evaluated by performing corrections for detector effects for A C and A tt C , with the response matrices corresponding to the systematic variations. Effects of detector modelling uncertainties on the background are included by subtracting the background, varied accordingly, from the data. The following sources are considered.

• Lepton reconstruction
The uncertainty due to lepton reconstruction includes several sources. Lepton momentum scale and resolution modelling correction factors and associated uncertainties are derived from comparisons of data and simulation in Z → events [65, 66]. Uncertainties in the modelling of trigger, reconstruction and lepton identification efficiencies are also included. Data-to-simulation efficiency corrections, and their uncertainties, are derived from J/ψ → , Z → and W → eν events.

• Jet reconstruction
The effects include the jet energy scale and jet resolution uncertainties. Jet energy scale uncertainty is derived using information from test-beam data, LHC collision  The uncertainties from the energy scale and resolution corrections for leptons and jets are propagated to the E miss T . The category accounts for uncertainties in the energies of calorimeter cells not associated with the reconstructed objects and the uncertainties from cells associated with low-p T jets (7 GeV< p T < 20 GeV) [70] as well as the dependence of their energy on the number of pileup interactions.
The uncertainties due to the modelling of the signal tt distributions are evaluated by performing the linearity test for signal model samples generated with various assumptions. The following sources are quoted.

• Signal modelling
The uncertainty is evaluated by adding in quadrature the MC generator uncertainties, initial-and final-state radiation (ISR and FSR), underlying event (UE) and colour reconnection (CR) uncertainties described in the following. The systematic uncertainty related to the choice of a MC generator includes the difference between the nominal sample generated with Powheg-hvq + Pythia6 and samples generated with MC@NLO + Herwig, Powheg-hvq + Herwig and Alpgen + Herwig. The effects of renormalization and factorization scale choice are evaluated with a dedicated pair of samples generated with MC@NLO + Herwig. In these samples renormalization and factorization scales are varied simultaneously by a factor of two with respect to the reference scale. The reference scale is fixed at the MC@NLO generator default, which is defined as the average of the t and thet transverse masses, where p Tt(t) corresponds to the transverse momentum of the t ort. Since the effects covered by generator comparisons and scale variations partially overlap, only the largest contribution from all comparisons is used. For the lepton-based asymmetry the dominant contribution was found to stem from the difference between the nominal sample and the sample generated with Alpgen + Herwig. For the tt asymmetry the contributions of the comparison of the baseline sample result to the results obtained with each of MC@NLO + Herwig, Powheg-hvq + Herwig and Alpgen + Herwig samples are of comparable size and significantly larger than the contribution of the renormalization and factorization scale uncertainty. The amount of ISR and FSR are treated as an additional source of signal modelling uncertainty. It is evaluated using samples generated with Alpgen + Pythia6 with variations of parameters controlling the renormalization scale used in Alpgen and in the Pythia6 parton shower. The renormalization scale is varied by factors of 0.5 and 2. The Pythia6 settings correspond to Perugia radLO and radHi tunes [36]. Apart from this, the UE and CR uncertainties are evaluated by comparing samples generated with Powheg-hvq + Pythia6, using Perugia2011, Perugia2011 mpiHi and Perugia2011 noCR tunes [36]. For A C , the contributions from the choice of MC generator and from ISR and FSR exceed the non-perturbative UE and CR contributions. For A tt C , the contributions from the choice of MC generator and from radiation and non-perturbative modelling uncertainties are comparable.

• PDF uncertainty
The uncertainty due to the PDF is evaluated by performing linearity tests with samples obtained from the nominal signal sample, generated with CT10 PDF, reweighted to other PDFs. The CT10 error set as well as MSTW2008 68% CL NLO [45] and NNPDF2.3 NLO (α s = 0.118) [48] central predictions are used. For each asymmetry value, the largest value of the three sources is quoted as uncertainty.
The uncertainties on the modelling of the SM backgrounds are divided into two categories described below.

• NP & fake
This source corresponds to the uncertainty in the estimation of processes fulfilling the event selection due to non-prompt or misidentified leptons. The uncertainties are obtained by varying the efficiencies for a real or fake lepton to pass the tight selection, and are affecting both the normalization of the background and its shape.

• Background
The uncertainties in the modelling of diboson, Z+jets and single-top SM processes are quoted in the background category. They are evaluated by varying the normalization of each of these processes by the uncertainty on its cross-section. The uncertainty on the overall luminosity of 1.8% is also entering this category [64].
For both the lepton-based asymmetry A C and the tt asymmetry A tt C , the statistical uncertainty is larger than the total systematic uncertainty. The A C measurement has a combined statistical uncertainty of 1.5%, whereas the combined systematic uncertainty is 0.9%. The largest source of A C systematic uncertainty is the lepton reconstruction uncertainty, which accounts for approximately 90% of the total systematic uncertainty. The uncertainty on the asymmetry A C measured in the ee channel receives a sizeable contribution from the NP & fake leptons category (1.6%). This, however, does not significantly impact the combined systematic uncertainty since the ee channel receives a small weight in the combination, as detailed in section 8. The tt asymmetry A tt C has a combined statistical uncertainty of 2.5% and a combined systematic uncertainty of 1.7%. The detector modelling uncertainties account for approximately 80% of the combined systematic uncertainty, with comparable large contributions from the lepton reconstruction, the E miss T (0.7%) and the jet reconstruction uncertainty (0.9%). The NP & fake contribution to the A tt C systematic uncertainty is also sizeable (0.8%).
The uncertainties related to detector and background modelling are evaluated in each bin of the corrected distributions and presented in section 8.

Results
After the event selection and reconstruction but before the correction described in section 6 the inclusive lepton and tt asymmetries measured in the data are A C = 0.021 ± 0.011 (stat.) and A tt C = 0.003 ± 0.012 (stat.), respectively for the combination of the ee,eµ and µµ channels. After the subtraction of the background contribution, the measured data asymmetries are A C = 0.029 ± 0.013 (stat.) and A tt C = 0.006 ± 0.014 (stat.). The corresponding asymmetry predictions in the nominal simulated tt sample are A C = 0.005 ± 0.003 (stat.) and A tt C = 0.008 ± 0.003 (stat.). This sample is generated with the Powheg-hvq + Pythia6 generator with a particle-level lepton asymmetry of A C = 0.0045 ± 0.0009 (stat.) and a parton-level tt asymmetry of A tt C = 0.0071 ± 0.0009 (stat.), evaluated in the full phase-space.
After the correction for detector, resolution and acceptance effects, the normalized differential cross-sections corrected to particle and parton level are obtained for ∆|η| and ∆|y| separately for the three channels. From these distributions, the inclusive asymmetry values can be extracted. The inclusive results obtained in the ee, eµ and µµ channels (see tables 2 and 3) are then combined using the best linear unbiased estimator (BLUE) method [75,76]. All systematic uncertainties are assumed to be 100% correlated, except for the uncertainties on electrons and muons and on the NP & fake lepton background.
The normalized differential cross-sections for ∆|η| and ∆|y| are presented in figure 6 for the eµ channel. Good agreement is observed between the measured distributions and the ones predicted by Powheg-hvq + Pythia6. The normalized differential cross-sections in that channel are also presented with statistical and systematic uncertainties in tables 4 and 5. The systematic uncertainties for the differential distributions do not include the signal modelling uncertainties, which could not be evaluated with sufficient precision due to the limited statistics of the simulated samples. For both distributions, the statistical uncertainty is somewhat larger than the systematic uncertainty. In appendix A the contributions from each source of systematic uncertainty, described in section 7, to the total  0.0361 ± 0.0076 ± 0.0035 Table 4: Normalized differential cross-sections for ∆|η| in the eµ channel presented with statistical and systematic uncertainties.
The results for the inclusive lepton-based asymmetry A C and the tt asymmetry A tt 0.0470 ± 0.0032 ± 0.0024 Table 5: Normalized differential cross-sections for ∆|y| in the eµ channel presented with statistical and systematic uncertainties.
21 81 Weights (ee/eµ/µµ in %) 7 / 68 / 25 9 / 57 / 34 Table 7: Information about the combination of the three channels using the best linear unbiased estimator method: χ 2 and probability of the combination, as well as the weight of each channel.
after corrections for detector and resolution effects are shown in table 6. The values in the ee, eµ and µµ channels as well as for their combination are presented, together with statistical and systematic uncertainties.
Detailed information about the combination of the inclusive values is given in table 7. The combination probabilities are 21% and 81% for A C and A tt C respectively, demonstrating the compatibility of the measurements in the three channels (ee, eµ and µµ). The weight of each channel in the combination is also reported in table 7. The eµ channel dominates the combination, reflecting the larger data statistics compared to that of the ee and µµ channels.
The inclusive measurements after the detector and resolution effects corrections can be compared with the state-of-the-art theoretical predictions calculated at NLO QCD, including the electromagnetic and weak-interaction corrections [10]: A C = 0.0070 ± 0.0003 (scale) C measurement values to the theory predictions (SM NLO QCD+EW prediction [10] and the prediction of the Powheg-hvq + Pythia6 generator). Ellipses corresponding to 1σ and 2σ combined statistical and systematic uncertainties of the measurement, including the correlation between A C and A tt C , are also shown.
and A tt C = 0.0123 ± 0.0005 (scale). In figure 7 the measured values of A C and A tt C are compared to these predictions and Powheg-hvq + Pythia6 predictions. In the figure, ellipses corresponding to 1σ and 2σ combined statistical and systematic uncertainties of the measurement, including the correlation between A C and A tt C , are also shown. The statistical correlation between A C and A tt C is evaluated to be 37±5% using pseudo-experiments based on simulation. The systematic uncertainties are treated as 100% correlated. The resulting correlation between A C and A tt C is about 55%. The measured values are both consistent with the theory predictions within the uncertainties. The measured A tt C values are consistent with but less precise than measurements in the single-lepton decay channel by the ATLAS [18] and CMS [19] collaborations. The measurements of A C and A tt C are also consistent with the CMS collaboration measurements in the dilepton decay channel [20].
The inclusive measurement of A C and A tt C is furthermore compared to two models of physics beyond the Standard Model (BSM) [9] that could be invoked to explain an anomalous forward-backward asymmetry at the Tevatron, such as reported by the CDF experiment [24]. Two models with a new colour octet particle exchanged in the s-channel are considered. In the model with the light octet, the new particle mass is below the tt production threshold. The model with the heavy octet uses the octet mass beyond the reach of the LHC. The new particles would not be visible as resonances in the m tt spectrum at the Tevatron or at the LHC. The light octet is assumed to have a mass of m = 250 GeV and a width of Γ = 0.2m. For the heavy octet, the corrections to tt production are independent of the mass but instead depend on the ratio of coupling to mass, which is assumed to be 1/TeV. In figure 8 the measured A C and A tt C values are compared to the light (figure 8(a)) and heavy ( figure 8(b)) colour octet model predictions in order to assess whether any of the BSM predictions can be excluded. Models with left-handed, right-handed and axial coupling to  Figure 8: Comparison of the measured inclusive A C and A tt C values to two benchmark BSM models, one a light octet with mass below tt production threshold (left) and one with a heavy octet with mass beyond LHC reach (right), for various couplings as described in the legend. the up, down and top quarks are shown. The considered couplings to the quarks are such that the global fit to tt observables at the Tevatron and the LHC, including total crosssections, various asymmetries, the top polarisation and spin correlations, is consistent with the measurements within two standard deviations [9]. The LHC asymmetry measurements in the dilepton decay channel are excluded from the fit. While the models span a sizeable range of values in the A C and A tt C plane in figure 8, their predictions are consistent with the measured value within the present uncertainties. Thus the potential BSM contributions cannot be excluded beyond the reach of the previous Tevatron and LHC measurements. Future A C and A tt C measurements with a larger dataset could however further constrain the allowed couplings of the colour octet models if both statistical and systematic uncertainties can be reduced further.

Conclusion
Measurements of the tt charge asymmetry in the dilepton channel are presented. The measurements are performed using data corresponding to an integrated luminosity of 4.6 fb −1 of pp collisions at √ s = 7 TeV collected by the ATLAS detector at the LHC. Selected events are required to have exactly two charged leptons (electron or muon), large missing transverse momentum and at least two jets. Both the lepton-based asymmetry A C and the tt asymmetry A tt C are extracted in three channels: ee, eµ and µµ. The measurement of A tt C requires the kinematic reconstruction of the tt system, which is performed using the neutrino weighting technique. Agreement between predictions and data is checked after selection and kinematic reconstruction. Good agreement is obtained for all the kinematic observables studied. The ∆|η| and tt ∆|y| distributions and inclu-sive asymmetries are corrected for detector and acceptance effects. Corrections are applied using bin-by-bin corrections for A C and fully bayesian unfolding for A tt C . The distributions of lepton ∆|η| and tt ∆|y| after the detector smearing corrections are provided for the eµ channel. Good agreement between the corrected values and predictions of the Monte Carlo generator models is observed in these distributions. The combined values of lepton-based inclusive asymmetry A C and tt inclusive asymmetry A tt C are measured to be A C = 0.024±0.015 (stat.)±0.009 (syst.) and A tt C = 0.021±0.025 (stat.)±0.017 (syst.). The measured values are in agreement with previous LHC measurements and with the Standard Model prediction [10]: A C = 0.0070 ± 0.0003 (scale) and A tt C = 0.0123 ± 0.0005 (scale). The measurements are limited by statistical uncertainties. The predictions of benchmark light and heavy colour octet models with parameters selected such that the models are consistent with previous LHC and Tevatron data [9] are found to be consistent with the measured asymmetries.

A Additional tables
Additional information about the normalized differential cross-sections in the eµ channel are provided in this appendix.
The detail of the systematic uncertainties in each bin of the distributions are reported in tables 8 and 9.  Table 8: Systematic uncertainties in each bin of the ∆|η| distribution in the eµ channel. Hyphens are used when the uncertainties are lower than 0.0005. The signal modelling and the PDF uncertainty, (labeled as n/r) are limited by the statistical fluctuations in the simulated samples and are thus not reported in the table.
The statistical correlations between the different bins of each distribution are reported in tables 10 and 11. They were estimated using bootstrapping.