Measurements of top quark spin observables in \( t\overline{t} \) events using dilepton final states in \( \sqrt{s}=8 \) TeV pp collisions with the ATLAS detector

Journal of High Energy Physics, Mar 2017

Measurements of top quark spin observables in \( t\overline{t} \) events are presented based on 20.2 fb−1 of \( \sqrt{s}=8 \) TeV proton-proton collisions recorded with the ATLAS detector at the LHC. The analysis is performed in the dilepton final state, characterised by the presence of two isolated leptons (electrons or muons). There are 15 observables, each sensitive to a different coefficient of the spin density matrix of \( t\overline{t} \) production, which are measured independently. Ten of these observables are measured for the first time. All of them are corrected for detector resolution and acceptance effects back to the parton and stable-particle levels. The measured values of the observables at parton level are compared to Standard Model predictions at next-to-leading order in QCD. The corrected distributions at stable-particle level are presented and the means of the distributions are compared to Monte Carlo predictions. No significant deviation from the Standard Model is observed for any observable.

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Measurements of top quark spin observables in \( t\overline{t} \) events using dilepton final states in \( \sqrt{s}=8 \) TeV pp collisions with the ATLAS detector

Received: December Measurements of top quark spin observables in tt R.E. Blair T. Blazek I. Bloch C. Blocker A. Blue W. Blum U. Blumenschein 0 Dipartimento di Fisica e Astronomia, Universita di Bologna 1 INFN Sezione di Bologna 2 Dipartimento di Fisica, Universita di Roma Tor 3 INFN Sezione di Roma Tor Vergata Measurements of top quark spin observables in tt events are presented based on for detector resolution and acceptance e ects back to the parton and stable-particle levels. The measured values of the observables at parton level are compared to Standard Model predictions at next-to-leading order in QCD. The corrected distributions at stable-particle level are presented and the means of the distributions are compared to Monte Carlo predictions. No signi cant deviation from the Standard Model is observed for any observable. events; using; dilepton; pp; p; Hadron-Hadron scattering (experiments) - LHC. The analysis is performed in the dilepton nal state, characterised by the presence of two isolated leptons (electrons or muons). There are 15 observables, each sensitive to a di erent coe cient of the spin density matrix of tt production, which are measured independently. Ten of these observables are measured for the rst time. All of them are corrected 1 Introduction ATLAS detector Observables 2 Data and simulation samples Event selection and background estimation Kinematic reconstruction of the tt system Event yields and kinematic distributions Truth level de nitions Parton-level de nition Stable-particle de nition and ducial region Detector modelling uncertainties Background-related uncertainties The ATLAS collaboration The top quark, discovered in 1995 by the CDF and D0 experiments at the Tevatron at Fermilab [1, 2], is the heaviest fundamental particle observed so far. Its mass is of the order of the electroweak scale, which suggests that it might play a special role in electroweak symmetry breaking. Furthermore, since the top quark has a very short lifetime of O(10 25 s) [3{5] it decays before hadronisation and before any consequent spin- ip can take place. This o ers a unique opportunity to study the properties of a bare quark and, in particular, the properties of its spin. Top quarks at the LHC are mostly produced in tt pairs via the strong interaction, which conserves parity. The quarks1 and gluons of the initial state are unpolarised, which means that their spins are not preferentially aligned with any given direction. The top quarks produced in pairs are thus unpolarised except for the contribution of weak corrections and QCD absorptive parts at the per-mill level [6]. However, the spins of the top and antitop quarks are correlated with a strength depending on the spin quantisation axis and on the production process. Various new physics phenomena can alter the polarisation and spin correlation due to alternative production mechanisms [6{9]. The spins of the top quarks do not become decorrelated due to hadronisation, and so their spin information is transferred to their decay products. This makes it possible to measure the top quark pair's spin structure using angular observables of their decay products. The predictions for many of these observables are available at next-to-leading order (NLO) in quantum chromodynamics (QCD). A few of them have been measured by the experiments at the LHC and Tevatron and found to be in good agreement with the Standard Model (SM) predictions [10{18]. This paper presents the measurement of a set of 15 spin observables with a data set corresponding to an integrated luminosity of 20:2 fb 1 of proton-proton collisions at p s = 8 TeV, recorded by the ATLAS detector at the LHC in 2012. Each of the 15 observables is sensitive to a di erent coe cient of the top quark pair's spin density matrix, probing di erent symmetries in the production mechanism [19]. Ten of these observables have not been measured until now. The observables are corrected back to parton level in the full phase-space and to stable-particle level in a ducial phase-space. At parton level, the measured values of the polarisation and spin correlation observables are presented and compared to theoretical predictions. All observables allow a direct measurement of their corresponding expectation value. At stable-particle level, the distributions corrected for detector acceptance and resolution are provided. Because of the limited phase-space used at that level, the values of the polarisation and spin correlations are not proportional to the means of these distributions. Instead, the means of the distributions are provided and compared to the values obtained in Monte Carlo simulation. The ATLAS detector [20] at the LHC covers nearly the entire solid angle around the interaction point.2 It consists of an inner tracking detector surrounded by a thin superconducting solenoid, electromagnetic and hadronic calorimeters, and a muon spectrometer incorporating superconducting toroid magnets. 1Antiparticles are generally included in the discussions unless otherwise stated. 2ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the centre of the detector and the z-axis along the beam pipe. The x-axis points from the IP to the centre of the LHC ring, and the y-axis points upward. Cylindrical coordinates (r; ) are used in the transverse being the azimuthal angle around the beam pipe. The pseudorapidity is de ned in terms of the polar angle as = ln[tan( =2)]. The inner-detector system is immersed in a 2 T axial magnetic eld and provides charged-particle tracking in the pseudorapidity range j j < 2:5. A high-granularity silicon pixel detector covers the interaction region and typically provided three measurements per track in 2012. It is surrounded by a silicon microstrip tracker designed to provide eight twodimensional measurement points per track. These silicon detectors are complemented by a transition radiation tracker, which enables radially extended track reconstruction up to based on the fraction of hits (typically 30 in total) exceeding an energy-deposit threshold consistent with transition radiation. The calorimeter system covers the pseudorapidity range j j < 4:9. Within the region j j < 3:2, electromagnetic calorimetry is provided by barrel and endcap high-granularity lead/liquid-argon (LAr) electromagnetic calorimeters, with an additional thin LAr presampler covering j j < 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 j j < 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, respectively. The muon spectrometer comprises separate trigger and high-precision tracking chambers measuring the de ection of muons in a magnetic eld generated by superconducting air-core toroids. The precision chamber system covers the region j j < 2:7 with drift tube chambers, complemented by cathode strip chambers. The muon trigger system covers the range j j < 1:05 with resistive plate chambers, and the range 1:05 < j j < 2:4 with thin 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 400 Hz. The spin information of the top quarks, encoded in the spin density matrix, is transferred to their decay particles and a ects their angular distributions. The spin density matrix can be expressed by a set of several coe cients: one spin-independent coe cient, which determines the cross section and which is not measured here, three polarisation coe cients for the top quark, three polarisation coe cients for the antitop quark, and nine spin correlation coe cients. By measuring a set of 15 polarisation and spin correlation observables, the coe cient functions of the squared matrix element can be probed. The approach used in this paper was proposed in ref. [19]. The normalised double-di erential cross section for tt production and decay is of the form [6, 21] This means the di erential cross section has a linear dependence on the polarisation Ba, from which also follows All the observables are based on cos , which is de ned using three orthogonal spin where Ba, Bb and C(a; b) are the polarisations and spin correlation along the spin quantisation axes a and b. The angles a and b are de ned as the angles between the momentum direction of a top quark decay particle in its parent top quark's rest frame and the axis a or b. The subscript +( ) refers to the top (antitop) quark. From equation (3.1) one can retrieve the following relation for the spin correlation between the axes a and b Integrating out one of the angles in equation (3.1) gives the single-di erential cross section C(a; b) = d cos a = Ba = 3hcos ai: The helicity axis is de ned as the top quark direction in the tt rest frame. In ref. [19] it is indicated by the letter k, a notation which is adopted in this paper. Measurements of the polarisation and spin correlation de ned along this axis at 7 and 8 TeV were consistent with the SM predictions [10{16]. The transverse axis is de ned to be transverse to the production plane [6, 22] created by the top quark direction and the beam axis. It is denoted by the letter n. The polarisation along that axis was measured by the D0 experiment [17]. The r-axis is an axis orthogonal to the other two axes, denoted by the letter r. No observable related to this axis has been measured previously. As the dominant initial state of tt production at the LHC (gluon-gluon fusion) is Bosesymmetric, cos calculations with respect to the transverse or r-axis are multiplied by the respect to the negatively charged lepton, the axes are multiplied by 1. The observables and corresponding expectation values, as well as their SM predictions at NLO, are shown in table 1. The rst six observables correspond to the polarisations of the top and antitop quarks along the various axes, the other nine to the spin correlations. In order to distinguish between the correlation observables, the correlations using only one axis are referred to as spin correlations and the last six as cross correlations. The predictions are computed for a top quark mass of 173.34 GeV [23]. In order to measure all observables, the nal-state particles of both decay chains must be reconstructed and correctly identi ed. As charged leptons retain more information about the spin state of the top quarks, and as they can be precisely reconstructed, the measurement in this paper is performed in the dileptonic nal state of tt events. The charged leptons considered in this analysis are electrons or muons, either originating directly from W and Z decays, or through an intermediate C(n; k) + C(k; n) C(n; r) + C(r; n) C(r; k) + C(k; r) The SM predictions at NLO are also shown [19]; expectation values predicted to be 0 at NLO are exactly 0 due to term cancellations. The expectation values can be obtained from the corresponding observables using the relations from Equations (3.2) and (3.4). The uncertainties on the predictions refer to scale uncertainties only; values below 10 4 are not quoted. Data and simulation samples The analysis is performed using the full 2012 proton-proton collision data sample at p s = 8 TeV recorded by the ATLAS detector. The data sample corresponds to an integrated luminosity of 20.2 fb 1 after requiring stable LHC beams and a fully operational detector. The analysis uses Monte Carlo (MC) simulations, in particular to estimate the sample composition and to correct the measurement to both parton and stable-particle level. The nominal tt signal MC sample is generated by Powheg-hvq (version 1, r2330) [24{27] with the top quark mass set to 172.5 GeV and the hdamp parameter3 set to the top quark mass. The PDF set used is CT10 [30]. The signal events are then showered with Pythia6 (version 6.426) [31] using a set of tuned parameters named the Perugia2011C tune [32]. The background processes are also modelled using a range of MC generators which are listed in table 2. An additional background originating from non-prompt and misreconstructed (called \fake") leptons is also estimated from MC simulation. To estimate this background, all samples listed in table 2 are used, and in particular those listed in the lower part of 3The hdamp parameter controls the hardness of the hardest emission which recoils against the tt sysSingle top (W t-channel) Dibosons (W W ,W Z,ZZ) ttV (V = W=Z= ) in the lower part of the table are used together with the other samples to estimate the fake-lepton background. The parton distribution functions (PDF) used by the generator and the tunes used for the parton shower are also shown. The versions of the di erent generators are 2.14 for Alpgen [39], 5.1.4.8 for MadGraph [40], 4.31 for Herwig 6+Jimmy [41], 1, r2330 for Powheg-hvq, 6.426 for Pythia6 [31] and 8.165 for Pythia8 [42]. Perugia2011C with various mass points for all of them. The version of the MC@NLO generator [43, 44] is 4.01. the table, which are generated speci cally for that background. Multijet events are not included in this list because the probability of having two jets misidenti ed as isolated leptons is very small. The contribution from these events is thus negligible. In order to account for systematic uncertainties in the signal modelling, di erent MC samples, documented in table 3, are compared with each other as described in section 6.3.3. The nominal signal and background samples were processed through a simulation of the detector geometry and response [33] using Geant4 [34]. MC samples used to estimate signal modelling uncertainties were processed with the ATLFAST-II [35] simulation. This employs a parameterisation of the response of the electromagnetic and hadronic calorimeters, and uses Geant4 for the other detector components. Reconstructed objects such as electrons, muons or jets are built from the detector information and used to form a tt-enriched sample by applying an event selection. Electron candidates are reconstructed by matching inner-detector tracks to clusters in the electromagnetic calorimeter. A requirement on the pseudorapidity of the cluster j clj < 2:47 is applied, with the transition region between barrel and endcap corresponding to 1:37 < j clj < 1:52 excluded. A minimum requirement on the transverse momentum (pT) of 25 GeV is applied to match the trigger criteria (see section 5.2). Furthermore, electron candidates are required to be isolated from additional activity in the detector. Two di erent criteria are used. The rst one considers the activity in the electromagnetic calorimeter in R = 0:2 around the electron. The second one sums the pT of all tracks in a cone of size 0.3 around the electron track. The requirements applied on both variables are -dependent and correspond to an e ciency on signal electrons of 90%. The nal selection e ciency for the electrons used in this analysis is between 85% and 90% depending on the of the electron [45]. Muon candidates are reconstructed by combining inner detector tracks with tracks constructed in the muon spectrometer. They are required to have a pT > 25 GeV and j j < 2:5. They are also required to be isolated from additional activity in the inner detector. An isolation criterion requiring the scalar sum of track pT around the muon in R = 10 GeV=pT to be less than 0:05pT is applied. Muons have a selection e ciency of about 95% [46]. Jets are reconstructed from energy clusters in the electromagnetic and hadronic calorimeters. The reconstruction algorithm used is the anti-kt [47] algorithm with a radius using pT- and -dependent scale factors derived from simulation and validated in data [48]. After the energy correction, they are required to have a transverse momentum pT > 25 GeV and a pseudorapidity j j < 2:5. For jets with pT < 50 GeV and j j < 2:4, the jet vertex fraction (JVF) must be greater than 0.5. The JVF is de ned as the fraction of the scalar pT sum of tracks associated with the jet and the primary vertex and the scalar pT sum of tracks associated with the jet and any vertex. It distinguishes between jets originating from the primary vertex and jets with a large contribution from other proton interactions in the same bunch crossing (pile-up). If separated by R < 0:2, the jet closest to a selected electron is removed to avoid double-counting of electrons reconstructed as jets. Next, all electrons and muons separated from a jet by R < 0:4 are removed from the list of selected leptons to reject semileptonic decays within a jet. Jets containing b-hadrons are identi ed (b-tagged) by using a multivariate algorithm (MV1) [49] which uses information about the tracks and secondary vertices. If the MV1 output for a jet is larger than a prede ned value, the jet is considered to be b-tagged. The value was chosen to achieve a b-tagging e ciency of 70%. With this algorithm, the probability to select a light jet (from gluons or u-, d-, s-quarks) is around 0.8%, and the probability to select a jet from a c-quark is 20%. The missing transverse momentum ETmiss is de ned as the magnitude of the negative vectorial sum of the transverse momenta of leptons, photons and jets, as well as energy deposits in the calorimeter not associated with any physics object [50]. The event selection aims at maximising the fraction of tt events with a dileptonic nal state. The nal states are then separated according to the lepton avours. Tau leptons are indirectly considered in the signal contribution when decaying leptonically. This leads to three di erent channels (ee, , e ). Di erent kinematic requirements have to be applied for the e and ee/ channels due to their di erent background contributions. Only events selected from dedicated electron or muon triggers are considered. The pT thresholds of the triggers are 24 GeV for isolated leptons and 60 (36) GeV for single-electron (-muon) triggers without an isolation requirement. Events containing muons compatible with cosmic-ray interactions are removed. Exactly two oppositely charged electrons or muons with pT > 25 GeV are required. A requirement on the dilepton invariant mass of m`` > 15 GeV is required in all channels. In addition, jm`` mZ j > 10 GeV, where mZ is the Z boson mass, is required channels to suppress the Drell-Yan background. In these channels the missing transverse momentum is required to be greater than 30 GeV. In the e channel, the scalar sum of the pT of the jets and leptons in the event (HT) is required to be HT > 130 GeV. At least two jets with at least one of them being b-tagged are required in each channel. Background estimation are di cult to model. Since real ETmiss is present in Z ! Single-top-quark and diboson backgrounds are estimated using MC simulation only. The MC estimate for the Drell-Yan and fake-lepton background is normalised using data-driven scale factors (SF). The Drell-Yan background does not contain any real ETmiss. negligible ETmiss can appear in a fraction of events with misreconstructed objects, which events, no scale factors are applied to this sample. Another issue is the correct normalisation of Drell-Yan events with additional heavy- avour (HF) jets from b- and c-quarks after the b-tagging requirement. In order to correct for these e ects, three control regions are de ned, from which three SF are extracted. Two correspond to the ETmiss modelling in Z ! ee (SFee) and Z ! ), and one for the heavy- avour normalisation in Z+jets events (SFHF) common to the three dilepton channels. All control regions require the same selection as the signal region with the exception that the invariant mass of the two leptons should be within 10 GeV of the Z mass. The control regions are then distinguished by dividing them into a into the ee and 0) and a b-tag region (nb-tag 1), additionally dividing the pretag region channels. The purity of the pretag control region is 97% on average for both channels. The purity of the b-tag region is 75%. The SF are extracted by solving a system of equations which relates the number of events in data and in simulation in the three control regions. The lepton- avour-dependent scale factors SFee= 0:004 respectively for the ee and channels while the heavy- avour scale factor SFHF is 1:70 0:03, where the uncertainties are only statistical. The shape of the fake and non-prompt lepton background distributions are taken from MC simulation but the normalisation is derived from data in a control region enriched in fake leptons. This is achieved by applying the same requirements as for the signal region, except that two leptons of the same charge are required. As fake leptons have approximately the same probability of having negative or positive charge, the same number of fake-lepton events should populate the opposite-sign and same-sign selection regions. The same-sign control region has a smaller background contribution from other processes, allowing the study of the modelling of the fake-lepton background. Channel-dependent scale factors are derived by normalising the predictions to data in the control regions, while the shapes of the distributions are taken from MC simulation. The SF in the ee and e around 1.0 and 1.5, whereas the SF in the channel is about 4. The di erences between the three scale factors originate from the sources of misidenti ed electrons and muons, which seem to be modelled better in MC simulation for the electrons. However, the shapes of the distributions of several kinematic variables in the channel are cross-checked in control regions and found to be consistent with the distributions from a purely data-driven method. The relative statistical uncertainties are about 20% in the same- avour channels and 10% in the e channel. Kinematic reconstruction of the tt system The dileptonic tt nal state consists of two charged leptons, two neutrinos and at least two jets originating from the top quark decay. As the neutrinos cannot be directly observed in the detector, the kinematics of the tt system, which is necessary to construct the observables, cannot be simply reconstructed from the measured information. To solve the kinematic equations and reconstruct the tt system, the neutrino weighting technique [51, 52] As input, the method uses the measured lepton and jet momenta. The masses of the top quarks are set to their generated mass of 172.5 GeV whereas the masses of the W bosons are set to their PDG values [53] in the calculations. A hypothesis is made for the value of the pseudorapidity of each neutrino and the kinematics of the system is then solved. For each solution found, a weight is assigned to quantify the level of agreement between the vectorial sum of neutrino transverse momenta and the measured ETmiss components. The pseudorapidities of the neutrinos are scanned independently between xed steps of 0.025 in the range [ 2, 2] and of 0.05 outside of that range. All possible combinations of jets and leptons are tested. Additionally, the resolution of the jet energy measurement is taken into account by smearing the energy of each jet 50 times. The smearing is done using transfer functions mapping the energy at particle level to the energy after detector simulation. Out of all the solutions obtained, the one with the highest weight is selected. The reconstruction e ciency of the kinematic reconstruction in the tt signal sample is about 88%. No solution is found for the remaining events. Event yields and kinematic distributions Figure 1 shows the jet multiplicity, lepton pT and jet pT for all three channels. Figure 2 shows kinematic distributions of the top quark and the tt system after the event recons = 8 TeV, 20.2 fb-1 5eG 105 irse 104 t E 103 itrne 104 predictions after the event selection in the combined dilepton channel. The ratio between the data and prediction is also shown. The grey area shows the statistical and systematic uncertainty on the signal and background. The ttV , diboson and fake-lepton backgrounds are shown together in the \Others" category. Only the events passing the kinematic reconstruction are considered in the struction. The data are well modelled by the MC predictions. The corrections to the Drell-Yan and fake-lepton backgrounds are applied. Only the events passing the kinematic reconstruction are considered in the distributions. The total number of predicted events is slightly lower than the number of observed events, but the two are compatible within the systematic uncertainties. The measurement is insensitive to a di erence of normalisation of the signal. There is also a slight slope in the ratio between data and prediction for the lepton and top quark pT distributions. This is related to a known issue in the modelling of the top quark pT, described in section 6.3.3. The nal yields for each channel as well as for the inclusive channel combining ee, e , along with their combined statistical and systematic uncertainties, can be found in table 4. The predictions agree with data within uncertainties in all channels. e i trn 104 /s2 105 e i r tnE 104 /20 105 0 50 100 150 200 250 300 350 400 450 500 s = 8 TeV, 20.2 fb-1 s = 8 TeV, 20.2 fb-1 combined dilepton channel. The distributions of the top quark pT and are shown, as well as the tt pT and mass. The ratio between the data and prediction is also shown. The grey area shows the statistical and systematic uncertainty on the signal and background. The ttV , diboson and fakelepton backgrounds are shown together in the \Others" category. The last bin of the distribution corresponds to the over ow. Analysis Two di erent measurements of the spin observables are performed. One set of measurements is corrected to parton level and the other set is corrected to stable-particle level. These two levels are de ned in the next section, as well as the phase-spaces to which the measurements are corrected. Truth level de nitions Parton-level de nition At parton level, the considered top quarks are taken from the MC history after radiation but before decay. Parton-level leptons include tau leptons before they decay into an electron the kinematic reconstruction. The given uncertainties correspond to the combination of statistical and systematic uncertainties of the individual processes. The last column represents the inclusive or muon and before radiation. With these de nitions, the polarisation can be extracted from the slope of the cos distribution of parton-level particles (equation (3.3)) and the correlation can be extracted from the mean value of the distribution (equation (3.2)). The measurement corrected to parton level is extrapolated to the full phase-space, where all generated dilepton events are considered. Stable-particle de nition and Stable-particle level includes only particles with a lifetime larger than 30 ps. The charged leptons are required not to originate from hadrons. Photons within a cone of R = 0:1 around the lepton direction are considered as bremsstrahlung and so their four-momenta are added to the lepton four-momentum. Selected leptons are required to have pT > 25 GeV and j j < 2:5. Jets are clustered from all stable particles, excluding the already selected clustered within jets. Intermediate b-hadrons have their momentum set to zero, and are allowed to be clustered into the jets along with the stable particles [54]. If after clustering a b-hadron is found in a jet, the jet is considered as b-tagged [54]. Jets must have a transverse momentum of at least 25 GeV and have a pseudorapidity of j j < 2:5. Events are rejected if a lepton and a jet are separated by ducial phase-space close to the detector and selection acceptance is de ned by requiring the presence of at least two leptons and at least two jets satisfying the kinematic selection criteria. Around 32% of all generated events satisfy the ducial requirements. No b-jet is required in the de nition of the ducial region to keep it common with other analyses not using b-tagging. The b-jets are used in the kinematic reconstruction described in the following. The top quarks (called pseudo-top-quarks [55]) are reconstructed from the stable particles de ned above. If no jets are b-tagged, the two highest-pT jets are considered for the pseudo-top-quark reconstruction. Neutrinos are required not to originate from hadrons, but from W or Z decays or from intermediate tau decays. For the reconstruction, only the two neutrinos with the highest pT are taken in MC events. The correct lepton-neutrino pairings are chosen as those with reconstructed masses closer to the W boson mass. The correct jet-lepton-neutrino pairings are then chosen as those with masses closer to the generated top quark mass of 172.5 GeV. In contrast to the parton-level measurement where all events are included, events from outside the ducial region can still pass the event selection at reconstruction level and have to be treated as additional background (called the non- ducial background). This contribution is estimated from background-subtracted data by applying the binwise ratio of nonducial to total reconstructed signal events obtained from MC simulation, which is found to be constant for di erent levels of polarisation and correlation with an average of about 6.5%. RNt . This can be expressed as Selection requirements and detector resolution distort the reconstructed distributions. An unfolding procedure is applied to correct for these distortions. The Fully Bayesian Unfolding [56] method is used. It is based on Bayes' theorem and estimates the probability (p) of T 2 RNt being the true spectrum given the observed data D 2 NNr .4 This probability is proportional to the likelihood (L) of obtaining the data distribution given a true spectrum p (T jD; M) / L (DjT ; M) is the prior probability density for the true spectrum T and is taken to be uniform. The background is estimated as described in section 5.3 and included in the computation of the likelihood by taking into account its contribution in data when comparing it with the true spectrum. The response matrix M, in which each entry Mij gives the probability of an event generated in bin i to be reconstructed in bin j, is calculated from the nominal signal sample. By taking a rectangular response matrix connecting the three di erent analysis channels to the same true spectrum, the channels are combined within the unfolding method. The unfolded value is taken to be the mean of the posterior distribution with its root mean square taken as the uncertainty. Di erent systematic uncertainties are estimated within the unfolding by adding nuisance parameter terms ( ) to the likelihood for each systematic uncertainty considered. The so-called marginal likelihood is then de ned as L (DjT ) = where ( ) is the prior probability density for each nuisance parameter . They are dened as Gaussian distributions G with a mean of zero and a width of one. Systematic 4R and N are the sets of real and natural numbers. Nt and Nr are the number of bins for the true and uncertainties can be distinguished between normalisation-changing uncertainties ( n) and uncertainties changing both the normalisation and the shape ( s) of the reconstructed distribution of signal R(T ; s) and background B( s; n). The marginal likelihood can then L (DjT ) = L (DjR(T ; s); B( s; b)) G( s) G( b)d sd b: The method is validated by performing a linearity test in which distributions with known values of the polarisation and spin correlations are unfolded. The distributions of observables are reweighted to inject di erent values of the polarisations and correlations. For the polarisations and spin correlations, the double-di erential cross section (equation (3.1)) is used, while a linear reweighting is used for the cross correlations. The unfolded value for each reweighted distribution is then compared to the true value of polarisation or spin correlation and a calibration curve is built. Non-closure in the linearity test appears as a slope di erent from one in the calibration curve. The number of bins and the bin widths for each observable are chosen based on its resolution and optimised by evaluating the expected statistical uncertainty and by limiting the bias in the linearity test. The binning optimisation leads to a four-bin con guration for the polarisation observables and six-bin con gurations for the di erent correlation observables. An uncertainty is added to cover the non-closure of the linearity test, which is at most 10%. The input distribution and the response matrix normalised per true bin are shown for one example of polarisation, spin correlation, and cross correlation in gures 3 and 4. Systematic uncertainties The measurement of the spin observables is a ected in various ways by systematic uncertainties. Three di erent types of systematic uncertainties are considered: detector modelling uncertainties a ecting both the signal and background, normalisation uncertainties of the background, and modelling uncertainties of the signal. The rst two types are included in the marginalisation procedure. The reconstructed distribution, varied to re ect a systematic uncertainty, is compared to the nominal distribution and the average change per bin is taken as the width of the Gaussian prior, as discussed in section 6.2. In order to estimate the impact of each source of systematic uncertainty individually, pseudodata corresponding to the sum of the nominal signal and background samples are used. The unfolding procedure with marginalisation is applied to the pseudodata and constraints on the systematic uncertainties are obtained. The strongest constraint is on the uncertainty related to the electron identi cation and it reduces this systematic uncertainty by 50%. The other constraints are of the order of a few percent. The constrained systematic uncertainties are then used variations of the prediction. The varied pseudodata are then unfolded without marginalisation. The impact of each systematic uncertainty is computed by taking half of the di erence between the results obtained from the 1 variations of pseudodata. Modelling systematic uncertainties for the signal process are estimated separately by building calibration curves for each sample. The unfolded value in data is calibrated to generator level using the calibration curves for the nominal sample and the sample varied to re ect the uncertainty. The di erence is taken as the systematic uncertainty. 0.8−1 −0.5 s = 8 TeV, 20.2 fb-1 s = 8 TeV, 20.2 fb-1 taa .rde1.11 D P0.9 taa .rde1.11 D P0.9 taa .rde1.11 0.8−1 1−1 −0.5 0.8−1 −0.5 1−1 −0.5 Input distributions for the unfolding procedure of cos +k, cos +n cos n , and cos +r cos n . The ratio between the data and prediction is also shown. The grey area shows the total uncertainty on the signal and background. The ttV , diboson and fake-lepton backgrounds are shown together in the \Others" category. at parton level. They are divided into ee, , and e channels. The matrices are normalised per truth bin (rows) for each channel separately. All sources of detector modelling uncertainty are discussed below. Lepton-related uncertainties. Reconstruction, identi cation and trigger. The reconstruction and identi cation e ciencies for electrons and muons, as well as the e ciency of the triggers used to record the events di er between data and simulation. Scale factors and their events in data and in simulated samples to correct the simulation for these di er Momentum scale and resolution. The accuracy of the lepton momentum scale and resolution in simulation is checked using the Z ! `+` and J= also used. Small di erences are observed between data and simulation. Corrections to the lepton energy scale and resolution, and their related uncertainties are also considered [57, 58]. Jet-related uncertainties. Reconstruction e ciency. The jet reconstruction e ciency is found to be about 0:2% lower in the simulation than in data for jets below 30 GeV and it is consistent with data for higher jet pT. To evaluate the systematic uncertainty due to this small ine ciency, 0:2% of the jets with pT below 30 GeV are removed randomly and all jet-related kinematic variables (including the missing transverse momentum) are recomputed. The event selection is repeated using the modi ed number of jets. Vertex fraction e ciency. The per-jet e ciency to satisfy the jet vertex fraction requirement is measured in Z ! `+` + 1-jet events in data and simulation, selecting separately events enriched in hard-scatter jets and events enriched in jets from pile-up. The corresponding uncertainty is estimated by changing the nominal JVF requirement value and repeating the analysis using the modi ed value. Energy scale. The jet energy scale (JES) and its uncertainty were derived by combining information from test-beam data, LHC collision data and simulation [48]. The jet energy scale uncertainty is split into 22 uncorrelated sources, which have di erent jet pT and dependencies and are treated independently. Energy resolution. The jet energy resolution was measured separately for data and simulation. A systematic uncertainty is de ned as the di erence in quadrature between the jet energy resolutions for data and simulation. To estimate the corresponding systematic uncertainty, the jet energy in simulation is smeared by this residual di erence. b-tagging/mistag e ciency. E ciencies to tag jets from b- and c-quarks in the simulation are corrected by pT- and -dependent data/MC scale factors. The uncertainties on these scale factors are about 2% for the e ciency for b-jets, between 8% and 15% for c-jets, and between 15% and 43% for light jets [59, 60]. The dominant uncertainties in this category are related to lepton reconstruction, identi cation and trigger, jet energy scale and jet energy resolution. The contribution from this category to the total uncertainty is small (less than 20% for all observables). Missing transverse momentum. The systematic uncertainties associated with the momenta and energies of reconstructed objects (leptons and jets) are propagated to the ETmiss calculation. The ETmiss reconstruction also receives contributions from the presence of low-pT jets and calorimeter energy deposits not included in reconstructed objects (the \soft term"). The systematic uncertainty associated with the soft term is estimated using procedure on the measured observables is minor. Background-related uncertainties events using methods similar to those used in ref. [61]. The e ect of this The uncertainties on the single-top-quark, ttV , and diboson backgrounds are 6.8%, 10%, and 5%, respectively [62{64]. These correspond to the uncertainties on the theoretical cross sections used to normalise the MC simulated samples. The uncertainty on the normalisation of the fake-lepton background is estimated by using various MC generators for each process contributing to this background. The scale factor in the control region is recomputed for each variation and the change is propagated to the expected number of events in the signal region. In the channel, the uncertainty is obtained by comparing a purely data-driven method based on the measurement of the e ciencies of real and fake loose leptons, and the estimation used in this analysis. The resulting relative total uncertainties are 170% in the ee channel, 77% in the and 49% in the e channel. For the Drell-Yan background the detector modelling uncertainties described previously are propagated to the scale factors derived in the control region by recalculating them for all the uncertainties. An additional uncertainty of 5% is obtained by varying the Uncertainties on the shape of the di erent backgrounds were also estimated but found to be negligible. This category represents a minor source of uncertainty on the measure Modelling uncertainties These systematic uncertainties are estimated using the samples listed in table 3. Choice of MC generator. The uncertainty is obtained by comparing samples generated with either the Powheg-hvq or the MC@NLO generator, both interfaced with Herwig. It is one of the dominant uncertainties of the measurement. Parton shower and hadronisation. This e ect is estimated by comparing samples generated with Powheg-hvq interfaced either with Pythia6 or Herwig, and is one of the dominant systematic uncertainties. nal-state radiations. The uncertainty associated with the ISR/FSR modelling is estimated using Powheg-hvq interfaced with Pythia6 where the parameters of the generation were varied to be compatible with the results of a measurement of tt production with a veto on additional jet activity in a central rapidity interval [65]. The di erence obtained between the two samples is divided by two. This uncertainty is large and even dominant for some of the observables. Colour reconnection and underlying event. The uncertainties associated with colour reconnection and the underlying event are obtained by comparing dedicated samples with a varied colour-reconnection strength and underlying-event activity to a reference sample. All samples are generated by Powheg-hvq and interfaced with Pythia6. The reference sample uses the Perugia2012 tune, the colour-reconnection sample uses the Perugia2012loCR tune, and the underlying-event sample uses the Perugia2012mpiHi tune. This uncertainty is large and even dominant for some of Parton distribution functions. PDF uncertainties are obtained by using the error sets of CT10 [30], MWST2008 [66], and NNPDF23 [67], and following the recommendations of the PDF4LHC working group [68]. The impact of this uncertainty is small. Top quark pT modelling. The top quark pT spectrum is not satisfactorily modelled in MC simulation [69, 70]. The impact of the mismodelling is estimated by reweighting the simulation to data and unfolding the di erent distributions using the nominal response matrix. The di erences with respect to the nominal values are negligible compared to the other modelling uncertainties. The impact of this mismodelling is thus considered negligible, and no uncertainty is added to the total uncertainty. Polarisation and spin correlation. The response matrices used in the unfolding are calculated using the SM polarisation and spin correlation. An uncertainty related to a di erent polarisation and spin correlation is obtained by changing their values in the linearity test. In the reweighting procedure of the spin correlation observables, the polarisation is changed by 0:5%, while for the polarisation observables, the spin correlation is changed by 0:1. This uncertainty cannot be applied to the cross correlation observables as no analytic description of these observables is available. Instead, a linear reweighting is used, not depending on the polarisation or spin correlation along any axis as described in section 6.2. The impact of this category is large and can represent up to 85% of the total uncerNon-closure uncertainties. When the calibration curve for the nominal signal Powheg-hvq sample is estimated a residual slope and a non-zero o set are observed. This bias, introduced by the unfolding procedure, is propagated to the measured values. This uncertainty is small compared to the total uncertainty. The crucial computing support from all WLCG partners is acknowledged gratefully, in particular from CERN, the ATLAS Tier-1 facilities at TRIUMF (Canada), NDGF (Denmark, Norway, Sweden), CC-IN2P3 (France), KIT/GridKA (Germany), INFN-CNAF (Italy), NL-T1 (Netherlands), PIC (Spain), ASGC (Taiwan), RAL (U.K.) and BNL (U.S.A.), the Tier-2 facilities worldwide and large non-WLCG resource providers. Major contributors of computing resources are listed in ref. [73]. 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Gramstad121, S. Grancagnolo17, V. Gratchev125, P.M. Gravila28e, H.M. Gray32, E. Graziani136a, Z.D. Greenwood82;u, C. Grefe23, K. Gregersen81, I.M. Gregor45, P. Grenier145, K. Grevtsov5, J. Gri ths8, A.A. Grillo139, K. Grimm75, S. Grinstein13;v, Ph. Gris37, J.-F. Grivaz119, S. Groh86, E. Gross175, J. Grosse-Knetter57, G.C. Grossi82, Z.J. Grout81, L. Guan92, W. Guan176, J. Guenther65, F. Guescini52, D. Guest166, O. Gueta155, B. Gui113, E. Guido53a;53b, T. Guillemin5, S. Guindon2, U. Gul56, C. Gumpert32, J. Guo36c, W. Guo92, Y. Guo36a;s, R. Gupta43, S. Gupta122, G. Gustavino134a;134b, P. Gutierrez115, N.G. Gutierrez Ortiz81, C. Gutschow81, C. Guyot138, C. Gwenlan122, C.B. Gwilliam77, A. Haas112, C. Haber16, H.K. Hadavand8, A. Hadef88, S. Hagebock23, M. Hagihara164, H. Hakobyan180; , M. Haleem45, J. Haley116, G. Halladjian93, G.D. Hallewell88, K. Hamacher178, P. Hamal117, K. Hamano172, A. Hamilton147a, G.N. Hamity141, P.G. Hamnett45, L. Han36a, S. Han35a, K. Hanagaki69;w, K. Hanawa157, M. Hance139, B. Haney124, P. Hanke60a, R. Hanna138, J.B. Hansen39, J.D. Hansen39, M.C. Hansen23, P.H. Hansen39, K. Hara164, K.H. Hiller45, S.J. Hillier19, I. Hinchli e16, E. Hines124, M. Hirose51, D. Hirschbuehl178, O. Hladik129, X. Hoad49, J. Hobbs150, N. Hod163a, M.C. Hodgkinson141, P. Hodgson141, P. Krieger161, K. Krizka33, K. Kroeninger46, H. Kroha103, J. Kroll124, J. Kroseberg23, J. Krstic14, U. Kruchonak68, H. Kruger23, N. Krumnack67, M.C. Kruse48, M. Kruskal24, T. Kubota91, H. Kucuk81, S. Kuday4b, J.T. Kuechler178, S. Kuehn51, A. Kugel60c, F. Kuger177, T. Kuhl45, V. Kukhtin68, R. Kukla138, Y. Kulchitsky95, S. Kuleshov34b, M. Kuna134a;134b, T. Kunigo71, A. Kupco129, O. Kuprash155, H. Kurashige70, L.L. Kurchaninov163a, Y.A. Kurochkin95, M.G. Kurth44, V. Kus129, E.S. Kuwertz172, M. Kuze159, J. Kvita117, T. Kwan172, D. Kyriazopoulos141, A. La Rosa103, J.L. La Rosa Navarro26d, L. La Rotonda40a;40b, C. Lacasta170, F. Lacava134a;134b, J. Lacey31, H. Lacker17, D. Lacour83, E. Ladygin68, R. Lafaye5, B. Laforge83, T. Lagouri179, S. Lai57, S. Lammers64, W. Lampl7, E. Lancon138, U. Landgraf51, N.C. Mc Fadden107, G. Mc Goldrick161, S.P. Mc Kee92, A. McCarn92, R.L. McCarthy150, T.G. McCarthy103, L.I. McClymont81, E.F. McDonald91, J.A. Mcfayden81, G. Mchedlidze57, S.J. McMahon133, R.A. McPherson172;o, M. Medinnis45, S. Meehan140, S. Mehlhase102, A. Mehta77, K. Meier60a, C. Meineck102, B. Meirose44, D. Melini170;ah, B.R. Mellado Garcia147c, M. Melo146a, F. Meloni18, S.B. Menary87, L. Meng77, X.T. Meng92, A. Mengarelli22a;22b, S. Menke103, E. Meoni165, S. Mergelmeyer17, P. Mermod52, L. Merola106a;106b, C. Meroni94a, F.S. Merritt33, A. Messina134a;134b, J. Metcalfe6, A.S. Mete166, C. Meyer86, C. Meyer124, J-P. Meyer138, J. Meyer109, H. Meyer Zu Theenhausen60a, F. Miano151, R.P. Middleton133, S. Miglioranzi53a;53b, L. Mijovic49, G. Mikenberg175, M. Mikestikova129, M. Mikuz78, M. Milesi91, A. Milic27, D.W. Miller33, C. Mills49, A. Milov175, D.A. Milstead148a;148b, A.A. Minaenko132, Y. Minami157, I.A. Minashvili68, A.I. Mincer112, B. Mindur41a, M. Mineev68, Y. Minegishi157, Y. Ming176, L.M. Mir13, K.P. Mistry124, T. Mitani174, J. Mitrevski102, V.A. Mitsou170, A. Miucci18, P.S. Miyagawa141, A. Mizukami69, J.U. Mjornmark84, M. Mlynarikova131, T. Moa148a;148b, K. Mochizuki97, P. Mogg51, S. Mohapatra38, S. Molander148a;148b, R. Moles-Valls23, R. Monden71, M.C. Mondragon93, K. Monig45, J. Monk39, E. Monnier88, A. Montalbano150, J. Montejo Berlingen32, F. Monticelli74, S. Monzani94a;94b, R.W. Moore3, N. Morange119, D. Moreno21, M. Moreno Llacer57, P. Morettini53a, S. Morgenstern32, D. Mori144, T. Mori157, M. Morii59, M. Morinaga157, V. Morisbak121, S. Moritz86, A.K. Morley152, G. Mornacchi32, J.D. Morris79, L. Morvaj150, P. Moschovakos10, M. Mosidze54b, H.J. Moss141, J. Moss145;ai, K. Motohashi159, R. Mount145, E. Mountricha27, E.J.W. Moyse89, S. Muanza88, R.D. Mudd19, F. Mueller103, J. Mueller127, R.S.P. Mueller102, T. Mueller30, D. Muenstermann75, P. Mullen56, G.A. Mullier18, F.J. Munoz Sanchez87, J.A. Murillo Quijada19, W.J. Murray173;133, H. Musheghyan57, M. Muskinja78, A.G. Myagkov132;aj, M. Myska130, B.P. Nachman16, O. Nackenhorst52, K. Nagai122, R. Nagai69;ad, K. Nagano69, Y. Nagasaka61, K. Nagata164, M. Nagel51, E. Nagy88, A.M. Nairz32, Y. Nakahama105, K. Nakamura69, T. Nakamura157, I. Nakano114, R.F. Naranjo Garcia45, R. Narayan11, D.I. Narrias Villar60a, I. Naryshkin125, T. Naumann45, G. Navarro21, R. Nayyar7, H.A. Neal92, P.Yu. Nechaeva98, T.J. Neep87, A. Negri123a;123b, M. Negrini22a, S. Nektarijevic108, C. Nellist119, A. Nelson166, S. Nemecek129, P. Nemethy112, A.A. Nepomuceno26a, M. Nessi32;ak, M.S. Neubauer169, M. Neumann178, R.M. Neves112, P. Nevski27, P.R. Newman19, T. Nguyen Manh97, R.B. Nickerson122, R. Nicolaidou138, J. Nielsen139, V. Nikolaenko132;aj, I. Nikolic-Audit83, K. Nikolopoulos19, J.K. Nilsen121, P. Nilsson27, Y. Ninomiya157, A. Nisati134a, R. Nisius103, T. Nobe157, M. Nomachi120, I. Nomidis31, T. Nooney79, S. Norberg115, M. Nordberg32, N. Norjoharuddeen122, O. Novgorodova47, S. Nowak103, M. Nozaki69, L. Nozka117, K. Ntekas166, E. Nurse81, F. Nuti91, D.C. O'Neil144, A.A. O'Rourke45, V. O'Shea56, F.G. Oakham31;d, H. Oberlack103, T. Obermann23, J. Ocariz83, A. Ochi70, I. Ochoa38, J.P. Ochoa-Ricoux34a, S. Oda73, S. Odaka69, H. Ogren64, A. Oh87, S.H. Oh48, C.C. Ohm16, H. Ohman168, H. Oide53a;53b, H. Okawa164, Y. Okumura157, T. Okuyama69, A. Olariu28b, L.F. Oleiro Seabra128a, S.A. Olivares Pino49, D. Oliveira Damazio27, A. Olszewski42, J. Olszowska42, A. Onofre128a;128e, K. Onogi105, P.U.E. Onyisi11;z, M.J. Oreglia33, Y. Oren155, D. Orestano136a;136b, N. Orlando62b, R.S. Orr161, B. Osculati53a;53b; , R. Ospanov87, G. Otero y Garzon29, H. Otono73, M. Ouchrif137d, F. Ould-Saada121, A. Ouraou138, K.P. Oussoren109, Q. Ouyang35a, M. Owen56, R.E. Owen19, V.E. Ozcan20a, N. Ozturk8, K. Pachal144, A. Pacheco Pages13, L. Pacheco Rodriguez138, C. 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Schweiger87, Ph. Schwemling138, R. Schwienhorst93, J. Schwindling138, T. Schwindt23, G. Sciolla25, F. Scuri126a;126b, F. Scutti91, J. Searcy92, P. Seema23, S.C. Seidel107, A. Seiden139, F. Seifert130, J.M. Seixas26a, G. Sekhniaidze106a, K. Sekhon92, S.J. Sekula43, N. Semprini-Cesari22a;22b, C. Serfon121, L. Serin119, L. Serkin167a;167b, M. Sessa136a;136b, R. Seuster172, H. Severini115, T. S ligoj78, F. Sforza32, A. Sfyrla52, E. Shabalina57, N.W. Shaikh148a;148b, L.Y. Shan35a, R. Shang169, J.T. Shank24, M. Shapiro16, P.B. Shatalov99, K. Shaw167a;167b, S.M. Shaw87, A. Shcherbakova148a;148b, C.Y. Shehu151, P. Sherwood81, L. Shi153;ap, S. Shimizu70, C.O. Shimmin166, M. Shimojima104, S. Shirabe73, M. Shiyakova68;aq, A. Shmeleva98, D. Shoaleh Saadi97, M.J. Shochet33, S. Shojaii94a, D.R. Shope115, S. Shrestha113, E. Shulga100, M.A. Shupe7, Z. Sibb, P. Sicho129, A.M. Sickles169, P.E. Sidebo149, E. Sideras Haddad147c, O. Sidiropoulou177, D. Sidorov116, A. Sidoti22a;22b, F. Siegert47, Dj. Sijacki14, J. Silva128a;128d, S.B. Silverstein148a, V. Simak130, Lj. Simic14, S. Simion119, E. Simioni86, B. Simmons81, D. Simon37, M. Simon86, P. Sinervo161, N.B. Sinev118, M. Sioli22a;22b, G. Siragusa177, I. Siral92, S.Yu. Sivoklokov101, J. Sjolin148a;148b, M.B. Skinner75, H.P. Skottowe59, P. Skubic115, M. Slater19, T. Slavicek130, M. Slawinska109, K. Sliwa165, R. Slovak131, V. Smakhtin175, B.H. Smart5, L. Smestad15, J. Smiesko146a, S.Yu. Smirnov100, Y. Smirnov100, L.N. Smirnova101;ar, O. Smirnova84, J.W. Smith57, M.N.K. Smith38, R.W. Smith38, M. Smizanska75, K. Smolek130, A.A. Snesarev98, I.M. Snyder118, S. Snyder27, R. Sobie172;o, F. Socher47, A. So er155, D.A. Soh153, G. Sokhrannyi78, C.A. Solans Sanchez32, M. Solar130, E.Yu. Soldatov100, U. Soldevila170, A.A. Solodkov132, A. Soloshenko68, O.V. Solovyanov132, V. Solovyev125, P. Sommer51, H. Son165, H.Y. Song36a;as, A. Sood16, A. Sopczak130, V. Sopko130, V. Sorin13, D. Sosa60b, C.L. Sotiropoulou126a;126b, R. Soualah167a;167c, A.M. 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Wosiek42, 1 Department of Physics, University of Adelaide, Adelaide, Australia 2 Physics Department, SUNY Albany, Albany NY, United States of America 3 Department of Physics, University of Alberta, Edmonton AB, Canada 4 (a) Department of Physics, Ankara University, Ankara; (b) Istanbul Aydin University, Istanbul; (c) Division of Physics, TOBB University of Economics and Technology, Ankara, Turkey 5 LAPP, CNRS/IN2P3 and Universite Savoie Mont Blanc, Annecy-le-Vieux, France 6 High Energy Physics Division, Argonne National Laboratory, Argonne IL, United States of America 7 Department of Physics, University of Arizona, Tucson AZ, United States of America 8 Department of Physics, The University of Texas at Arlington, Arlington TX, United States of 9 Physics Department, National and Kapodistrian University of Athens, Athens, Greece 10 Physics Department, National Technical University of Athens, Zografou, Greece 11 Department of Physics, The University of Texas at Austin, Austin TX, United States of America 12 Institute of Physics, Azerbaijan Academy of Sciences, Baku, Azerbaijan 13 Institut de F sica d'Altes Energies (IFAE), The Barcelona Institute of Science and Technology, 14 Institute of Physics, University of Belgrade, Belgrade, Serbia 15 Department for Physics and Technology, University of Bergen, Bergen, Norway 16 Physics Division, Lawrence Berkeley National Laboratory and University of California, Berkeley CA, United States of America University of Bern, Bern, Switzerland 17 Department of Physics, Humboldt University, Berlin, Germany 18 Albert Einstein Center for Fundamental Physics and Laboratory for High Energy Physics, 19 School of Physics and Astronomy, University of Birmingham, Birmingham, United Kingdom 20 (a) Department of Physics, Bogazici University, Istanbul; (b) Department of Physics Engineering, Gaziantep University, Gaziantep; (d) Istanbul Bilgi University, Faculty of Engineering and Natural Sciences, Istanbul,Turkey; (e) Bahcesehir University, Faculty of Engineering and Natural Sciences, 21 Centro de Investigaciones, Universidad Antonio Narino, Bogota, Colombia 23 Physikalisches Institut, University of Bonn, Bonn, Germany 24 Department of Physics, Boston University, Boston MA, United States of America 25 Department of Physics, Brandeis University, Waltham MA, United States of America 26 (a) Universidade Federal do Rio De Janeiro COPPE/EE/IF, Rio de Janeiro; (b) Electrical Circuits Department, Federal University of Juiz de Fora (UFJF), Juiz de Fora; (c) Federal University of Sao Joao del Rei (UFSJ), Sao Joao del Rei; (d) Instituto de Fisica, Universidade de Sao Paulo, Sao 27 Physics Department, Brookhaven National Laboratory, Upton NY, United States of America 28 (a) Transilvania University of Brasov, Brasov, Romania; (b) Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest; (c) National Institute for Research and Development of Isotopic and Molecular Technologies, Physics Department, Cluj Napoca; (d) University Politehnica Bucharest, Bucharest; (e) West University in Timisoara, Timisoara, Romania 29 Departamento de F sica, Universidad de Buenos Aires, Buenos Aires, Argentina 30 Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom 31 Department of Physics, Carleton University, Ottawa ON, Canada 32 CERN, Geneva, Switzerland 33 Enrico Fermi Institute, University of Chicago, Chicago IL, United States of America 34 (a) Departamento de F sica, Ponti cia Universidad Catolica de Chile, Santiago; (b) Departamento de F sica, Universidad Tecnica Federico Santa Mar a, Valpara so, Chile 35 (a) Institute of High Energy Physics, Chinese Academy of Sciences, Beijing; (b) Department of Physics, Nanjing University, Jiangsu; (c) Physics Department, Tsinghua University, Beijing 36 (a) Department of Modern Physics, University of Science and Technology of China, Anhui; (b) School of Physics, Shandong University, Shandong; (c) Department of Physics and Astronomy, Key Laboratory for Particle Physics, Astrophysics and Cosmology, Ministry of Education; Shanghai Key Laboratory for Particle Physics and Cosmology, Shanghai Jiao Tong University, Shanghai(also at 37 Universite Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France 38 Nevis Laboratory, Columbia University, Irvington NY, United States of America 39 Niels Bohr Institute, University of Copenhagen, Kobenhavn, Denmark 40 (a) INFN Gruppo Collegato di Cosenza, Laboratori Nazionali di Frascati; (b) Dipartimento di Fisica, Universita della Calabria, Rende, Italy 41 (a) AGH University of Science and Technology, Faculty of Physics and Applied Computer Science, Krakow; (b) Marian Smoluchowski Institute of Physics, Jagiellonian University, Krakow, Poland 42 Institute of Nuclear Physics Polish Academy of Sciences, Krakow, Poland 43 Physics Department, Southern Methodist University, Dallas TX, United States of America 44 Physics Department, University of Texas at Dallas, Richardson TX, United States of America 45 DESY, Hamburg and Zeuthen, Germany 46 Lehrstuhl fur Experimentelle Physik IV, Technische Universitat Dortmund, Dortmund, Germany 47 Institut fur Kern- und Teilchenphysik, Technische Universitat Dresden, Dresden, Germany 48 Department of Physics, Duke University, Durham NC, United States of America 49 SUPA - School of Physics and Astronomy, University of Edinburgh, Edinburgh, United Kingdom 50 INFN Laboratori Nazionali di Frascati, Frascati, Italy 51 Fakultat fur Mathematik und Physik, Albert-Ludwigs-Universitat, Freiburg, Germany 52 Departement de Physique Nucleaire et Corpusculaire, Universite de Geneve, Geneva, Switzerland 53 (a) INFN Sezione di Genova; (b) Dipartimento di Fisica, Universita di Genova, Genova, Italy 54 (a) E. Andronikashvili Institute of Physics, Iv. Javakhishvili Tbilisi State University, Tbilisi; (b) High Energy Physics Institute, Tbilisi State University, Tbilisi, Georgia 55 II Physikalisches Institut, Justus-Liebig-Universitat Giessen, Giessen, Germany 56 SUPA - School of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom 58 Laboratoire de Physique Subatomique et de Cosmologie, Universite Grenoble-Alpes, CNRS/IN2P3, 59 Laboratory for Particle Physics and Cosmology, Harvard University, Cambridge MA, United States 60 (a) Kirchho -Institut fur Physik, Ruprecht-Karls-Universitat Heidelberg, Heidelberg; (b) Physikalisches Institut, Ruprecht-Karls-Universitat Heidelberg, Heidelberg; (c) ZITI Institut fur technische Informatik, Ruprecht-Karls-Universitat Heidelberg, Mannheim, Germany 61 Faculty of Applied Information Science, Hiroshima Institute of Technology, Hiroshima, Japan 62 (a) Department of Physics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong; (b) Department of Physics, The University of Hong Kong, Hong Kong; (c) Department of Physics and Institute for Advanced Study, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China 63 Department of Physics, National Tsing Hua University, Taiwan, Taiwan 64 Department of Physics, Indiana University, Bloomington IN, United States of America 65 Institut fur Astro- und Teilchenphysik, Leopold-Franzens-Universitat, Innsbruck, Austria 66 University of Iowa, Iowa City IA, United States of America 67 Department of Physics and Astronomy, Iowa State University, Ames IA, United States of America 68 Joint Institute for Nuclear Research, JINR Dubna, Dubna, Russia 69 KEK, High Energy Accelerator Research Organization, Tsukuba, Japan 70 Graduate School of Science, Kobe University, Kobe, Japan 71 Faculty of Science, Kyoto University, Kyoto, Japan 72 Kyoto University of Education, Kyoto, Japan 73 Research Center for Advanced Particle Physics and Department of Physics, Kyushu University, 74 Instituto de F sica La Plata, Universidad Nacional de La Plata and CONICET, La Plata, Argentina 75 Physics Department, Lancaster University, Lancaster, United Kingdom 76 (a) INFN Sezione di Lecce; (b) Dipartimento di Matematica e Fisica, Universita del Salento, Lecce, 77 Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom 78 Department of Experimental Particle Physics, Jozef Stefan Institute and Department of Physics, University of Ljubljana, Ljubljana, Slovenia 79 School of Physics and Astronomy, Queen Mary University of London, London, United Kingdom 80 Department of Physics, Royal Holloway University of London, Surrey, United Kingdom 81 Department of Physics and Astronomy, University College London, London, United Kingdom 82 Louisiana Tech University, Ruston LA, United States of America 83 Laboratoire de Physique Nucleaire et de Hautes Energies, UPMC and Universite Paris-Diderot and CNRS/IN2P3, Paris, France 84 Fysiska institutionen, Lunds universitet, Lund, Sweden 85 Departamento de Fisica Teorica C-15, Universidad Autonoma de Madrid, Madrid, Spain 86 Institut fur Physik, Universitat Mainz, Mainz, Germany 87 School of Physics and Astronomy, University of Manchester, Manchester, United Kingdom 88 CPPM, Aix-Marseille Universite and CNRS/IN2P3, Marseille, France 89 Department of Physics, University of Massachusetts, Amherst MA, United States of America 90 Department of Physics, McGill University, Montreal QC, Canada 91 School of Physics, University of Melbourne, Victoria, Australia 92 Department of Physics, The University of Michigan, Ann Arbor MI, United States of America 93 Department of Physics and Astronomy, Michigan State University, East Lansing MI, United States 94 (a) INFN Sezione di Milano; (b) Dipartimento di Fisica, Universita di Milano, Milano, Italy 95 B.I. Stepanov Institute of Physics, National Academy of Sciences of Belarus, Minsk, Republic of 96 Research Institute for Nuclear Problems of Byelorussian State University, Minsk, Republic of 97 Group of Particle Physics, University of Montreal, Montreal QC, Canada 98 P.N. Lebedev Physical Institute of the Russian Academy of Sciences, Moscow, Russia 99 Institute for Theoretical and Experimental Physics (ITEP), Moscow, Russia 100 National Research Nuclear University MEPhI, Moscow, Russia 101 D.V. Skobeltsyn Institute of Nuclear Physics, M.V. Lomonosov Moscow State University, Moscow, 102 Fakultat fur Physik, Ludwig-Maximilians-Universitat Munchen, Munchen, Germany 103 Max-Planck-Institut fur Physik (Werner-Heisenberg-Institut), Munchen, Germany 104 Nagasaki Institute of Applied Science, Nagasaki, Japan 105 Graduate School of Science and Kobayashi-Maskawa Institute, Nagoya University, Nagoya, Japan 106 (a) INFN Sezione di Napoli; (b) Dipartimento di Fisica, Universita di Napoli, Napoli, Italy 107 Department of Physics and Astronomy, University of New Mexico, Albuquerque NM, United States Nijmegen/Nikhef, Nijmegen, Netherlands 108 Institute for Mathematics, Astrophysics and Particle Physics, Radboud University 109 Nikhef National Institute for Subatomic Physics and University of Amsterdam, Amsterdam, 110 Department of Physics, Northern Illinois University, DeKalb IL, United States of America 111 Budker Institute of Nuclear Physics, SB RAS, Novosibirsk, Russia 112 Department of Physics, New York University, New York NY, United States of America 113 Ohio State University, Columbus OH, United States of America 114 Faculty of Science, Okayama University, Okayama, Japan 115 Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma, Norman OK, United States of America 116 Department of Physics, Oklahoma State University, Stillwater OK, United States of America 117 Palacky University, RCPTM, Olomouc, Czech Republic 118 Center for High Energy Physics, University of Oregon, Eugene OR, United States of America 119 LAL, Univ. Paris-Sud, CNRS/IN2P3, Universite Paris-Saclay, Orsay, France 120 Graduate School of Science, Osaka University, Osaka, Japan 121 Department of Physics, University of Oslo, Oslo, Norway 122 Department of Physics, Oxford University, Oxford, United Kingdom 123 (a) INFN Sezione di Pavia; (b) Dipartimento di Fisica, Universita di Pavia, Pavia, Italy 124 Department of Physics, University of Pennsylvania, Philadelphia PA, United States of America 125 National Research Centre \Kurchatov Institute" B.P.Konstantinov Petersburg Nuclear Physics Institute, St. Petersburg, Russia 126 (a) INFN Sezione di Pisa; (b) Dipartimento di Fisica E. Fermi, Universita di Pisa, Pisa, Italy 127 Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh PA, United States of 128 (a) Laboratorio de Instrumentaca~o e F sica Experimental de Part culas - LIP, Lisboa; (b) Faculdade de Ci^encias, Universidade de Lisboa, Lisboa; (c) Department of Physics, University of Coimbra, Coimbra; (d) Centro de F sica Nuclear da Universidade de Lisboa, Lisboa; (e) Departamento de Fisica, Universidade do Minho, Braga; (f) Departamento de Fisica Teorica y del Cosmos and CAFPE, Universidad de Granada, Granada (Spain); (g) Dep Fisica and CEFITEC of Faculdade de Ciencias e Tecnologia, Universidade Nova de Lisboa, Caparica, Portugal 129 Institute of Physics, Academy of Sciences of the Czech Republic, Praha, Czech Republic 130 Czech Technical University in Prague, Praha, Czech Republic 131 Charles University, Faculty of Mathematics and Physics, Prague, Czech Republic 132 State Research Center Institute for High Energy Physics (Protvino), NRC KI, Russia 133 Particle Physics Department, Rutherford Appleton Laboratory, Didcot, United Kingdom 134 (a) INFN Sezione di Roma; (b) Dipartimento di Fisica, Sapienza Universita di Roma, Roma, Italy 136 (a) INFN Sezione di Roma Tre; (b) Dipartimento di Matematica e Fisica, Universita Roma Tre, 137 (a) Faculte des Sciences Ain Chock, Reseau Universitaire de Physique des Hautes Energies Universite Hassan II, Casablanca; (b) Centre National de l'Energie des Sciences Techniques Nucleaires, Rabat; (c) Faculte des Sciences Semlalia, Universite Cadi Ayyad, LPHEA-Marrakech; (d) Faculte des Sciences, Universite Mohamed Premier and LPTPM, Oujda; (e) Faculte des sciences, Universite Mohammed V, Rabat, Morocco 138 DSM/IRFU (Institut de Recherches sur les Lois Fondamentales de l'Univers), CEA Saclay (Commissariat a l'Energie Atomique et aux Energies Alternatives), Gif-sur-Yvette, France 139 Santa Cruz Institute for Particle Physics, University of California Santa Cruz, Santa Cruz CA, United States of America 140 Department of Physics, University of Washington, Seattle WA, United States of America 141 Department of Physics and Astronomy, University of She eld, She eld, United Kingdom 142 Department of Physics, Shinshu University, Nagano, Japan 143 Department Physik, Universitat Siegen, Siegen, Germany 144 Department of Physics, Simon Fraser University, Burnaby BC, Canada 145 SLAC National Accelerator Laboratory, Stanford CA, United States of America 146 (a) Faculty of Mathematics, Physics & Informatics, Comenius University, Bratislava; (b) Department of Subnuclear Physics, Institute of Experimental Physics of the Slovak Academy of Sciences, Kosice, Slovak Republic 147 (a) Department of Physics, University of Cape Town, Cape Town; (b) Department of Physics, University of Johannesburg, Johannesburg; (c) School of Physics, University of the Witwatersrand, Johannesburg, South Africa United States of America 148 (a) Department of Physics, Stockholm University; (b) The Oskar Klein Centre, Stockholm, Sweden 149 Physics Department, Royal Institute of Technology, Stockholm, Sweden 150 Departments of Physics & Astronomy and Chemistry, Stony Brook University, Stony Brook NY, of Tokyo, Tokyo, Japan 151 Department of Physics and Astronomy, University of Sussex, Brighton, United Kingdom 152 School of Physics, University of Sydney, Sydney, Australia 153 Institute of Physics, Academia Sinica, Taipei, Taiwan 154 Department of Physics, Technion: Israel Institute of Technology, Haifa, Israel 155 Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv, 156 Department of Physics, Aristotle University of Thessaloniki, Thessaloniki, Greece 157 International Center for Elementary Particle Physics and Department of Physics, The University 158 Graduate School of Science and Technology, Tokyo Metropolitan University, Tokyo, Japan 159 Department of Physics, Tokyo Institute of Technology, Tokyo, Japan 160 Tomsk State University, Tomsk, Russia, Russia 161 Department of Physics, University of Toronto, Toronto ON, Canada 162 (a) INFN-TIFPA; (b) University of Trento, Trento, Italy, Italy 163 (a) TRIUMF, Vancouver BC; (b) Department of Physics and Astronomy, York University, Toronto 164 Faculty of Pure and Applied Sciences, and Center for Integrated Research in Fundamental Science and Engineering, University of Tsukuba, Tsukuba, Japan 165 Department of Physics and Astronomy, Tufts University, Medford MA, United States of America 166 Department of Physics and Astronomy, University of California Irvine, Irvine CA, United States of 167 (a) INFN Gruppo Collegato di Udine, Sezione di Trieste, Udine; (b) ICTP, Trieste; (c) Dipartimento di Chimica, Fisica e Ambiente, Universita di Udine, Udine, Italy 169 Department of Physics, University of Illinois, Urbana IL, United States of America 170 Instituto de Fisica Corpuscular (IFIC) and Departamento de Fisica Atomica, Molecular y Nuclear and Departamento de Ingenier a Electronica and Instituto de Microelectronica de Barcelona (IMB-CNM), University of Valencia and CSIC, Valencia, Spain 171 Department of Physics, University of British Columbia, Vancouver BC, Canada 172 Department of Physics and Astronomy, University of Victoria, Victoria BC, Canada 173 Department of Physics, University of Warwick, Coventry, United Kingdom Waseda University, Tokyo, Japan 175 Department of Particle Physics, The Weizmann Institute of Science, Rehovot, Israel 176 Department of Physics, University of Wisconsin, Madison WI, United States of America 177 Fakultat fur Physik und Astronomie, Julius-Maximilians-Universitat, Wurzburg, Germany 178 Fakultat fur Mathematik und Naturwissenschaften, Fachgruppe Physik, Bergische Universitat Wuppertal, Wuppertal, Germany 179 Department of Physics, Yale University, New Haven CT, United States of America 180 Yerevan Physics Institute, Yerevan, Armenia 181 Centre de Calcul de l'Institut National de Physique Nucleaire et de Physique des Particules (IN2P3), Villeurbanne, France a Also at Department of Physics, King's College London, London, United Kingdom b Also at Institute of Physics, Azerbaijan Academy of Sciences, Baku, Azerbaijan c Also at Novosibirsk State University, Novosibirsk, Russia d Also at TRIUMF, Vancouver BC, Canada e Also at Department of Physics & Astronomy, University of Louisville, Louisville, KY, United f Also at Physics Department, An-Najah National University, Nablus, Palestine g Also at Department of Physics, California State University, Fresno CA, United States of America h Also at Department of Physics, University of Fribourg, Fribourg, Switzerland i Associated at Department of Physics, Aachen, Tech. Hochsch., Aachen, Germany j Also at Departament de Fisica de la Universitat Autonoma de Barcelona, Barcelona, Spain k Also at Departamento de Fisica e Astronomia, Faculdade de Ciencias, Universidade do Porto, Also at The Collaborative Innovation Center of Quantum Matter (CICQM), Beijing, China l Also at Tomsk State University, Tomsk, Russia, Russia n Also at Universita di Napoli Parthenope, Napoli, Italy o Also at Institute of Particle Physics (IPP), Canada p Also at Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest, Romania q Also at Department of Physics, St. Petersburg State Polytechnical University, St. Petersburg, r Also at Borough of Manhattan Community College, City University of New York, New York City, United States of America s Also at Department of Physics, The University of Michigan, Ann Arbor MI, United States of t Also at Centre for High Performance Computing, CSIR Campus, Rosebank, Cape Town, South u Also at Louisiana Tech University, Ruston LA, United States of America v Also at Institucio Catalana de Recerca i Estudis Avancats, ICREA, Barcelona, Spain Also at Graduate School of Science, Osaka University, Osaka, Japan x Also at Fakultat fur Mathematik und Physik, Albert-Ludwigs-Universitat, Freiburg, Germany y Also at Institute for Mathematics, Astrophysics and Particle Physics, Radboud University aa Also at Institute of Theoretical Physics, Ilia State University, Tbilisi, Georgia ab Also at CERN, Geneva, Switzerland ac Also at Georgian Technical University (GTU),Tbilisi, Georgia ad Also at Ochadai Academic Production, Ochanomizu University, Tokyo, Japan ae Also at Manhattan College, New York NY, United States of America af Also at Academia Sinica Grid Computing, Institute of Physics, Academia Sinica, Taipei, Taiwan ag Also at School of Physics, Shandong University, Shandong, China ah Also at Departamento de Fisica Teorica y del Cosmos and CAFPE, Universidad de Granada, ai Also at Department of Physics, California State University, Sacramento CA, United States of aj Also at Moscow Institute of Physics and Technology State University, Dolgoprudny, Russia ak Also at Departement de Physique Nucleaire et Corpusculaire, Universite de Geneve, Geneva, al Also at Eotvos Lorand University, Budapest, Hungary Also at International School for Advanced Studies (SISSA), Trieste, Italy an Also at Department of Physics and Astronomy, University of South Carolina, Columbia SC, United ao Also at Institut de F sica d'Altes Energies (IFAE), The Barcelona Institute of Science and ap Also at School of Physics, Sun Yat-sen University, Guangzhou, China aq Also at Institute for Nuclear Research and Nuclear Energy (INRNE) of the Bulgarian Academy of ar Also at Faculty of Physics, M.V.Lomonosov Moscow State University, Moscow, Russia as Also at Institute of Physics, Academia Sinica, Taipei, Taiwan at Also at National Research Nuclear University MEPhI, Moscow, Russia au Also at Department of Physics, Stanford University, Stanford CA, United States of America av Also at Institute for Particle and Nuclear Physics, Wigner Research Centre for Physics, Budapest, Also at Giresun University, Faculty of Engineering, Turkey ax Also at Flensburg University of Applied Sciences, Flensburg, Germany ay Also at CPPM, Aix-Marseille Universite and CNRS/IN2P3, Marseille, France az Also at University of Malaya, Department of Physics, Kuala Lumpur, Malaysia ba Also at LAL, Univ. 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M. Aaboud, G. Aad, B. Abbott, J. Abdallah, O. Abdinov. Measurements of top quark spin observables in \( t\overline{t} \) events using dilepton final states in \( \sqrt{s}=8 \) TeV pp collisions with the ATLAS detector, Journal of High Energy Physics, 2017, 113, DOI: 10.1007/JHEP03(2017)113