Measurement of the $t\bar{t}Z$ and $t\bar{t}W$ cross sections in proton-proton collisions at $\sqrt{s}=13$ TeV with the ATLAS detector

A measurement of the associated production of a top-quark pair ($t\bar{t}$) with a vector boson ($W$, $Z$) in proton-proton collisions at a center-of-mass energy of 13 TeV is presented, using $36.1$ fb$^{-1}$ of integrated luminosity collected by the ATLAS detector at the Large Hadron Collider. Events are selected in channels with two same- or opposite-sign leptons (electrons or muons), three leptons or four leptons, and each channel is further divided into multiple regions to maximize the sensitivity of the measurement. The $t\bar{t}Z$ and $t\bar{t}W$ production cross sections are simultaneously measured using a combined fit to all regions. The best-fit values of the production cross sections are $\sigma_{t\bar{t}Z} = 0.95 \pm 0.08_{\mathrm{stat.}} \pm 0.10_{\mathrm{syst.}}$ pb and $\sigma_{t\bar{t}W} = 0.87 \pm 0.13_{\mathrm{stat.}} \pm 0.14_{\mathrm{syst.}}$ pb in agreement with the Standard Model predictions. The measurement of the $t\bar{t}Z$ cross section is used to set constraints on effective field theory operators which modify the $t\bar{t}Z$ vertex.


Introduction
Properties of the top quark have been explored by the Large Hadron Collider (LHC) and previous collider experiments in great detail. The production cross sections of top-quark pairs and single top quarks, as well as the top-quark mass, spin correlations and W boson helicity fractions have all been measured. Other properties of the top quark are now becoming accessible, owing to the large center-of-mass energy and luminosity at the LHC. These include its coupling to the Higgs boson and electroweak neutral-current couplings, accessed by measurements of pair-produced top quarks in association with a Higgs boson [1-4] or a photon [5][6][7][8].
Measurements of top-quark pairs in association with a Z or W boson (tt Z and ttW) provide a direct probe of the weak couplings of the top quark [9][10][11]. These couplings may be modified in the presence of physics beyond the Standard Model (BSM). Any deviations from the SM predictions due to BSM effects can be parameterized in a model-independent way using the framework of the Standard Model Effective Field Theory (SMEFT) [12][13][14]. If no deviations are observed, measurements of the tt Z and ttW production cross sections, σ tt Z and σ ttW , can be used to set constraints on the weak couplings of the top quark in the SMEFT context. The tt Z and ttW processes were observed by ATLAS [15,16] and CMS [17,18], with measured cross sections compatible with the SM prediction.
The production of tt Z and ttW is often an important background in searches involving final states with multiple leptons and b-quarks. These processes also constitute an important background in measurements of the associated production of the Higgs boson with top quarks. This paper presents measurements of the tt Z and ttW cross sections using proton-proton (pp) collision data at a center-of mass energy √ s = 13 TeV corresponding to an integrated luminosity of 36.1 fb −1 , collected by the ATLAS detector in 2015 and 2016. The final states of top-quark pairs produced in association with a Z or a W boson contain up to four isolated, prompt leptons.1 In this analysis, events with two opposite-sign (OS) or same-sign (SS) leptons, three leptons or four leptons are considered. The dominant backgrounds in these four channels are Z+jets and tt, events with non-prompt or misidentified leptons, W Z, and Z Z production, respectively. An interpretation of the tt Z cross-section measurement in the SMEFT framework is also performed.

The ATLAS detector
The ATLAS detector [19] consists of three main subsystems: an inner tracking system, electromagnetic (EM) and hadronic calorimeters, and a muon spectrometer (MS). The inner detector (ID) consists of a high-granularity silicon pixel detector, including the insertable B-layer [20,21], which is the innermost layer of the tracking system, and a silicon microstrip tracker, together providing precision tracking in the pseudorapidity2 range |η| < 2.5, followed by a transition radiation tracker covering |η| < 2.0. All these systems are immersed in a 2 T magnetic field provided by a thin superconducting solenoid. The EM sampling calorimeter uses lead and liquid argon (LAr) and is divided into barrel (|η| < 1.475) The t-channel production of a single top quark in association with a Z boson (t Z) was generated at leading order (LO) using MG5_aMC v2.2.3 interfaced to P v6.427 [38], referred to as P 6 in the following, with the CTEQ6L1 [39] PDF set and the Perugia2012 [40] set of tuned MC parameters at NLO in QCD. The four-flavor scheme was used in the generation, and the sample was normalized using the cross section computed at NLO in QCD using MG5_aMC.
The production of a single top quark together with a W and a Z boson (tW Z) was generated with MG5_aMC v2.3.3 using the NNPDF3.0NLO PDF set [35]. The generation was performed at NLO in QCD using the five-flavor scheme. Diagrams containing a top-quark pair were removed to avoid overlap with the tt Z process. The parton shower was modeled by P 8 with the A14 tune. The sample was normalized using the NLO cross section obtained from the generator.
Events containing Z or W bosons with associated jets were simulated using the S 2.2.1 event generator. The matrix-element calculation was performed using C [41] and O L [42] for up to two partons at NLO and four partons at LO, and merged with the S parton shower [43] according to the ME+PS@NLO prescription [44]. The NNPDF3.0NNLO PDF set was used in conjunction with dedicated parton-shower tuning developed by the S authors. The Z/W + jets samples were normalized to next-to-next-to-leading-order (NNLO) QCD cross sections for Z/W production calculated by the FEWZ program [45].
Diboson processes with four charged leptons (4 ), three charged leptons and one neutrino ( ν) or two charged leptons and two neutrinos ( νν) were simulated using the S 2.1.1 generator. The matrix elements included all diagrams with four electroweak vertices. They were calculated including up to three partons at LO, and the CT10 PDF set [46] was used in conjunction with a dedicated parton-shower tune developed by the S authors. The invariant mass of any two opposite-sign, same-flavor (OSSF) leptons was required to be greater than 5 GeV in the generated events.
The production of three massive vector bosons with subsequent leptonic decays of all three bosons was modeled at LO with the S 2.1.1 generator and the CT10 PDF set. Up to two additional partons were included in the matrix element at LO and the full NLO accuracy was used for the inclusive process.
Electroweak processes involving the vector-boson scattering (VBS) diagram and producing two same-sign leptons, two neutrinos and two partons were modeled using S 2.1.1 at LO accuracy and the CT10 PDF set. Processes of orders four and six in the electroweak coupling constant were considered, and up to one additional parton was included in the matrix element. Other VBS processes are found to be negligible in the analysis regions considered.
The P -B [47][48][49][50] v2 generator with the NNPDF3.0NLO PDF set was used for the generation of tt events. The parton shower and the underlying event were simulated using P 8 with the NNPDF2.3LO PDF set and the corresponding A14 tune. The h damp parameter, which controls the transverse momentum of the first gluon emission beyond the Born configuration, was set to 1.5 times the top-quark mass. The tt samples were normalized to the NNLO cross-section predictions, including soft-gluon resummation to next-to-next-to-leading-logarithm order, as calculated with the T ++2.0 [51] program.
Electroweak s-channel and t-channel single-top-quark events, and Wt final states, were generated with P -B v1, and the parton shower modeled by P v6.428. The CT10 PDF set was used for s-channel production and Wt events, while for t-channel production the four-flavor scheme was used for the NLO matrix element calculations together with the fixed four-flavor PDF set CT10f4. Diagram removal was employed to remove the overlap between tt and Wt production [52]. The single-top-quark samples were normalized to the cross sections computed at NLO reported in Refs. [53,54] for the sand t-channels and at NLO with next-to-next-to-leading-logarithm soft-gluon corrections for Wt production [55].
Samples of tt events produced in association with a Higgs boson (ttH) were generated using NLO matrix elements in MG5_aMC with the NNPDF3.0NLO PDF set and interfaced to P 8 for the modeling of the parton shower. Higgs boson production via gluon-gluon fusion (ggF) and vector-boson fusion (VBF) was generated using the P -B v2 generator with the CT10 PDF set. The parton shower and underlying event were simulated using P 8 with the CTEQ6L1 PDF set and AZNLO tune. Higgs boson production with a vector boson was generated at LO using P 8 with the NNPDF2.3LO PDF. All Higgs boson samples were normalized using theoretical calculations presented in Ref. [34].
The SM production of three and four top quarks was generated at LO with MG5_aMC+P 8, using the A14 tune together with the NNPDF2.3LO PDF set. The samples were normalized using cross sections computed at NLO [56,57].
The events with a Z or W boson in association with a photon were simulated with up to three partons at LO using S 2.1.1 (ME+PS mode) and the CT10 PDF set. They were normalized to the LO cross section obtained from the generator. The ttγ process was generated at LO with MG5_aMC+P 8, using the A14 tune together with the NNPDF2.3LO PDF set and normalized to the NLO cross section. Events in the tt sample with radiated photons of high transverse momentum were vetoed to avoid overlap with those from the ttγ sample.

Object reconstruction
Electron candidates [58] are reconstructed from energy deposits (clusters) in the EM calorimeter that are associated with reconstructed tracks in the ID. Electrons are required to pass the 'medium' likelihood identification requirements described in Ref. [58]. In the SS dilepton channel, the 'tight' likelihood requirement is used instead. The electrons are also required to have transverse momentum p T > 7 GeV and |η cluster | < 2.47, where η cluster is the pseudorapidity of the calorimeter energy deposit associated with the electron candidate. Candidates in the EM calorimeter barrel/endcap transition region 1.37 < |η cluster | < 1.52 are excluded.
Muon candidates are reconstructed from a fit to track segments in the various layers of the muon spectrometer, matched with tracks identified in the inner detector. Muons are required to have p T > 7 GeV and |η| < 2.5 and to pass the 'medium' identification requirements defined in Ref. [59]. The 'medium' criteria include requirements on the numbers of hits in the ID and MS as well as a compatibility requirement between momentum measurements in the ID and MS. They provide a high efficiency and purity of selected muons. Electron candidates sharing a track with a muon candidate are removed.
To reduce the background due to non-prompt leptons from hadron decays, photon conversions or jets misidentified as leptons (labeled as "fake leptons" throughout this paper), electron and muon candidates are required to be isolated. In the OS dilepton and the tetralepton channels, as well as in those trilepton regions that target the tt Z process, the total sum of the track transverse momenta in a surrounding cone of size ∆R η ≡ (∆η) 2 + (∆φ) 2 = min(10 GeV/p T , r e,µ ), excluding the track of the candidate, is required to be less than 6% of the candidate p T , where r e = 0.2 and r µ = 0.3. In addition, the sum of the cluster transverse energies in the calorimeter within a cone of size ∆R η = 0.2 around any electron candidate, excluding energy deposits of the candidate itself, is required to be less than 6% of the candidate p T .
In the SS dilepton channel and those trilepton regions targeting the ttW process, where the fake-lepton background is particularly important, tighter isolation requirements are imposed on candidate leptons. A multivariate discriminant is built to distinguish prompt leptons from leptons arising from heavy-hadron decays inside jets [1]. The discriminant uses information from charged-particle tracks in a cone around the lepton candidate. Jets are reconstructed from these tracks to obtain a track-jet, and the discriminant is constructed from information such as the angular distance between the lepton and the track-jet, the number of tracks in the track-jet and the ratio of the lepton candidate p T to the track-jet p T . The rejection factor obtained for leptons from b-hadron decays is about 20, while the prompt-lepton efficiency is about 85% (80%) for p T ∼ 20 GeV and reaches a plateau of ∼ 98% (96%) for muons (electrons) at high p T . Simulated events are corrected to account for differences in the prompt-lepton tagging discriminant between data and simulation.
Another important background in the SS dilepton channel arises from electrons with misidentified charge. To suppress this background, another multivariate discriminant is used, which takes as inputs various track and cluster properties of the electron candidates [1]. The discriminant provides a 95% efficiency for electrons with correct charge reconstruction while achieving a rejection factor of ∼ 17 for electrons with misidentified charge that pass the 'tight' likelihood identification requirement. Correction factors are applied to selected electrons to match the efficiency of the discriminant in simulation to that measured in data.
For both the electrons and muons, the longitudinal impact parameter of the associated track relative to the primary vertex,4 z 0 , is required to satisfy |z 0 sin θ| < 0.5 mm. The significance of the transverse impact parameter d 0 is required to satisfy |d 0 |/σ(d 0 ) < 5 for electrons and |d 0 |/σ(d 0 ) < 3 for muons, where σ(d 0 ) is the uncertainty in d 0 .
Jets are reconstructed using the anti-k t algorithm [60,61] with radius parameter R = 0.4, starting from topological energy clusters in the calorimeters [62]. The effect of pileup on jet energies is accounted for by a jet-area-based correction [63] and the energy resolution of the jets is improved by using global sequential corrections [64]. Jets are calibrated to the hadronic energy scale using energy-and pseudorapidity-dependent calibration factors derived from data. Jets are accepted if they fulfill the requirements p T > 25 GeV and |η| < 2.5. To reduce the contribution from jets associated with pileup, jets with p T < 60 GeV and |η| < 2.4 are required to satisfy pileup rejection criteria (JVT), based on a multivariate combination of track-based variables [65].
Jets are tagged as likely to contain b-hadrons (b-tagged) with a multivariate discriminant making use of the long lifetime, large decay multiplicity, hard fragmentation and high mass of b-hadrons [66]. For the working point used in this analysis, the average efficiency for correctly tagging a b-jet is approximately 77%, as determined in simulated tt events. In simulation, the tagging algorithm gives a rejection factor of 134 against light-quark and gluon jets, and 6.2 against charm-quark jets. The b-tagging efficiency and mistagging rates in simulation are corrected to reproduce those in data [66].
The missing transverse momentum p miss T , with magnitude E miss T , is a measure of the transverse momentum imbalance due to particles escaping detection. It is computed [67] as the negative sum of the transverse momenta of all electrons, muons and jets and an additional soft term. The soft term is constructed from all tracks that are associated with the primary vertex but not with any lepton or jet. In this way, the E miss T is adjusted for the best calibration of the jets and the other identified objects, while maintaining pileup independence in the soft term [67, 68].
To prevent double-counting of electron energy deposits as jets, the closest jet within ∆R y = 0.2 of a reconstructed electron is removed, where ∆R y ≡ (∆y) 2 + (∆φ) 2 and y is the rapidity of the electron. If the nearest jet surviving the above criterion is within ∆R y = 0.4 of an electron, the electron is discarded to ensure that selected electrons are sufficiently separated from nearby jet activity. To reduce the background from muons originating from heavy-flavor particle decays inside jets, muons are removed if they are separated from the nearest jet by ∆R y < 0.4. However, if this jet has fewer than three associated tracks, the muon is kept and the jet is removed instead; this ensures that high-energy muons undergoing significant energy loss in the calorimeter are retained. Table 1 lists the analysis channels and the targeted decay modes of the tt Z and ttW processes. Each channel is divided into multiple analysis regions in order to enhance the sensitivity to the signal. Simultaneous fits to the signal regions and dedicated control regions are performed to extract the cross sections for tt Z and ttW production.

Tetralepton
Only events collected using single-electron or single-muon triggers are accepted. Events are required to have at least one reconstructed primary vertex. In all regions considered, at least one reconstructed lepton with p T > 27 GeV is required to match (∆R η < 0.15) a lepton with the same flavor reconstructed by the trigger algorithm. Four channels are defined: same-sign dilepton, opposite-sign dilepton, trilepton and tetralepton.
The shapes of background distributions containing prompt leptons are modeled by simulation. The normalizations for the W Z and Z Z processes, as well as the production of a Z boson in association with heavy-flavor (HF) jets, are taken from data control regions as defined in this section and which are included in the fit discussed in Section 7. The yields in these data control regions are extrapolated to the signal regions using simulation. Systematic uncertainties in the extrapolation are taken into account in the overall uncertainty in the background estimate.
The contribution from events containing an electron with misidentified charge (referred to as "charge-flip" in the following) is estimated from data. The charge-flip probability is extracted in events containing a pair of electrons with m close to the Z boson mass. It is parameterized in p T and η and is found to range from around 0.01% to 2%, depending on p T and η, for electrons passing the identification and isolation criteria applied in the SS dilepton channel. The probability is extracted by maximizing a likelihood which relates the number of events in which the two electrons have the same charge to the total number of observed events. The background contribution from events other than charge-flip electrons in the same-sign region is estimated from a sideband of the m distribution and subtracted before performing the likelihood fit.
The charge-flip background contribution in any SS dilepton region is estimated by constructing a control region with identical requirements, apart from requiring two leptons with opposite sign, and applying the appropriate charge-flip probabilities.
Background sources involving one or more fake leptons are modeled using data events from dedicated regions. For the SS dilepton (2 -SS) and trilepton channels the fake-lepton background is estimated using the matrix method [69]. The matrix method makes use of events with the same selection as the region of interest, but for which the electron identification criteria are relaxed to the 'loose' likelihood requirement of Ref.
[58], and neither electrons nor muons are required to be isolated. These leptons are referred to as "loose" leptons, whereas leptons satisfying the full set of identification and isolation criteria of Section 4 are referred to as "tight" leptons. The fake-lepton background in any region of interest is obtained from the aforementioned events using efficiencies for prompt and fake leptons to satisfy the tight criteria.
The lepton efficiencies are extracted in control regions with a likelihood fit, by using the model of the matrix method, and assuming that the number of events with two fake leptons is negligible. The control regions are defined in dilepton events, separately for events with exactly one b-tagged jet and ≥ 2b-tagged jets. The prompt lepton efficiencies are measured in inclusive OSSF events, while fake-lepton efficiencies are measured in events with same-sign leptons. Both the prompt and fake-lepton efficiencies are parameterized as a function of the lepton p T . The measurement of fake-lepton efficiencies is performed after subtracting the estimated contribution from charge-flip events. Contributions from processes with two prompt same-sign leptons or one real lepton and a photon conversion (arising mainly from ttγ production) are estimated from simulation and are also subtracted. The prompt and fake-lepton efficiencies are extracted separately for the regions targeting tt Z and those targeting ttW, due to the different lepton isolation requirements applied in the two sets of regions.
In the tetralepton channel, the matrix method is not used due to the small number of events in data with four selected leptons. Instead, the contribution from backgrounds containing fake leptons is estimated from simulation and corrected with scale factors determined in control regions. The contributions from events containing a photon conversion (denoted by γ + X) in the SS dilepton and trilepton channels are estimated from simulation and scaled with these correction factors, obtained separately for lepton type and origin.

Opposite-sign dilepton analysis
The OS dilepton analysis targets the tt Z process, where both top quarks decay hadronically and the Z boson decays to a pair of leptons (electrons or muons). Events are required to have exactly two OSSF leptons. Events with additional isolated leptons are rejected. The invariant mass of the lepton pair is required to be in the Z boson mass window, |m − m Z | < 10 GeV. The leading (subleading) lepton is required to have a transverse momentum of at least 30 (15) GeV.
The OS dilepton analysis is affected by large backgrounds from Z+jets or tt production, both characterized by the presence of two leptons. In order to improve the signal-to-background ratio and constrain these backgrounds from data, three separate analysis regions are considered, depending on the number of jets (n jets ) and number of b-tagged jets (n b-tags ): 2 -Z-5j2b, 2 -Z-6j1b and 2 -Z-6j2b. The signal region requirements are summarized in Table 2. In signal region 2 -Z-5j2b, exactly five jets are required, of which at least two must be b-tagged. In 2 -Z-6j1b (2 -Z-6j2b), at least six jets are required with exactly one (at least two) being b-tagged jets.  >30 GeV p T (subleading lepton) >15 GeV In order to separate signal from background, boosted decision trees (BDTs) are used. The BDTs are constructed and trained separately for each region against all the contributing backgrounds, using as input 15, 14 and 17 variables for 2 -Z-6j1b, 2 -Z-5j2b and 2 -Z-6j2b, respectively. Fourteen of the variables are common to the three regions. The details of the variables used are given in Table 11 in the Appendix. In all three regions, the variables with the largest discriminative power are found to be: • the η of the dilepton system, • the scalar sum of transverse momenta of all jets divided by the sum of their energies, Each of the signal regions is further divided into 19 equal-size bins of the BDT distribution. To avoid relying on simulation for the normalization of Z+HF jet production, the Z+jets background is constrained by using events with low values of the BDT discriminant. The simulated Z+jets background is split into three components, Z+0HF, Z+1HF and Z+2HF, depending on the number of reconstructed jets which are matched to a generator-level bor c-hadron (heavy-flavor, or HF jets). The normalization factors of the Z+1HF and Z+2HF components of the Z+jets background are determined from the fit to data, as described in Section 7, while the normalization of the Z+0HF component is taken from simulation.
A data-driven method is used to estimate the tt background in the OS dilepton signal regions. Control regions are defined which are identical to the signal regions, except that the requirement of two leptons with the same flavor and opposite sign is replaced by the requirement of two leptons with different flavors and opposite sign. In this manner, three regions enriched in tt background are obtained. The number of tt events in each same-flavor dilepton region is estimated from corresponding opposite-flavor regions, corrected for non-tt backgrounds and differences in contributions from leptonic τ-lepton decays. This procedure is applied to each bin of the distribution under consideration. Figure 1 shows the BDT distributions for the tt control regions. Agreement between the data and the expectation is observed.

Same-sign dilepton analysis
The SS dilepton signal regions target the ttW process. Events are required to have two lepton candidates with the same sign and p T > 27 GeV. The scalar sum of the p T of selected leptons and jets, H T , is Other Uncertainty The shaded band represents the total uncertainty. The 'Other' background contains SM processes with small cross sections producing two opposite-sign prompt leptons, including the tt Z process, whose contribution is negligible. required to be above 240 GeV. Events containing additional loose leptons (with p T > 7 GeV) are vetoed. Twelve signal regions are defined in total, categorized by the number of b-tagged jets (one or ≥ 2) as well as the charge and the flavor of the selected leptons. The signal regions are denoted by 2 -SSp-1b, 2 -SSm-1b, 2 -SSp-2b and 2 -SSm-2b, where "p" or "m" indicates the charge of the selected leptons. Considering separate signal regions for positive and negative charges of the leptons increases the sensitivity of the analysis since ttW events are preferentially produced with positively charged W bosons, while the fake-lepton background and other processes such as tt Z and ttH are expected to be charge symmetric.
The event selection requirements in the SS dilepton regions are summarized in Table 3. The presence of at least four jets and E miss T > 40 GeV is required in all signal regions except 2µ-SSp-2b and 2µ-SSm-2b. In these regions, the E miss T requirement is loosened to E miss T > 20 GeV, and at least two jets are required. In the 2e and 2µ signal regions, events containing a pair of leptons whose invariant mass is within 10 GeV of the Z boson mass are vetoed.
GeV in the 2e and 2µ regions The control regions used to measure the fake-lepton efficiencies, as explained in Section 5, are defined to be orthogonal to the SS dilepton signal regions: either the E miss T , H T or jet multiplicity requirements of the signal regions are not satisfied. The ttW signal contribution in the control regions where both leptons satisfy the "tight" criteria is found to be non-negligible. To enhance the sensitivity of the analysis, the latter regions are also included in the final fit used to measure the ttW cross section, as discussed in Section 7. These six regions are further split according to the charge of the leptons, and the resulting twelve regions are denoted by 2 -SS(p,m)-(1, 2)b-CR, following the same notation as for the signal regions defined above. In each control region, both leptons are required to have p T > 27 GeV, and at least one (two) jets are required in the 1b (2b) regions. In addition, events containing a pair of leptons whose invariant mass is compatible with the Z boson mass are vetoed. The largest contamination from ttW is found to be 25%, in the region 2µ-SSp2b-CR.
The dominant background in the 2 -SS signal regions arises from events containing fake leptons. Backgrounds from the production of prompt leptons with correctly identified charge come primarily from ttH and W Z production. The charge-flip background is also significant in signal regions with two electrons. In regions with two muons, this background is negligible as the probability of misidentifying the charge of a muon in the relevant p T range is very small. To validate the charge-flip background, a validation region called 2e-SS-1b-VR is constructed similarly to the 2e-SS signal regions, except that the number of jets is required to be between one and three, to ensure orthogonality with the signal regions. The requirement on H T is also removed, exactly one jet is required to be b-tagged, and the invariant mass of the lepton pair is required to be greater than 15 GeV. The distributions of m and the leading lepton p T are shown in Figure 2, demonstrating good modeling of the charge-flip background.

Trilepton analysis
Eight signal regions defined in Tables 4 and 5 with exactly three leptons are considered. The regions are divided into two groups depending on whether or not a pair of OSSF leptons with invariant mass within 10 GeV of the Z boson mass is present. The signal regions are further categorized according to jet and b-tagged jet multiplicities.
The four signal regions in the first group are sensitive to tt Z. In the 3 -Z-1b4j region, at least four jets are required, exactly one of which is b-tagged. In the 3 -Z-2b3j region, exactly three jets with at least two b-tagged jets are required. In the 3 -Z-2b4j region, at least four jets are required, of which at least two are b-tagged. In the 3 -noZ-2b4j region, targeting events with an off-shell Z * or γ * , at least four jets are required, of which at least two are b-tagged; no OSSF lepton pair is allowed in the Z boson mass window. The sum of the lepton charges must be ±1.
The remaining four trilepton signal regions target the ttW process. These regions require two or three jets and veto events that contain an OSSF pair of leptons whose invariant mass is within 10 GeV of the Z boson mass. In the first two regions, 3 p-noZ-2b2j and 3 m-noZ-2b2j, at least two jets are required Charge-flips  Events / 20 GeV  to be b-tagged. In the other two regions, 3 p-noZ-1b2j and 3 m-noZ-1b2j, exactly one jet is required to be b-tagged. The sum of lepton charges is required to be +1 (-1) in 3 p-noZ-2b2j and 3 p-noZ-1b2j (3 m-noZ-2b2j and 3 m-noZ-1b2j). In regions 3 p-noZ-1b2j and 3 m-noZ-1b2j, H T > 240 GeV is also required. The signal region definitions for the trilepton channel are summarized in Tables 4 and 5 for the signal regions targeting tt Z and ttW, respectively.
The dominant backgrounds in the 3 -Z-1b4j, 3 -Z-2b3j and 3 -Z-2b4j signal regions arise from diboson production, the production of a single top quark in association with a Z boson (t Z and tW Z) and Z+jets production with a fake lepton.
Leading lepton A control region is used to determine the normalization of the W Z+jets background in data. Exactly three leptons are required, at least one pair of which must be an OSSF pair with an invariant mass within 10 GeV of the Z boson mass. There must be exactly three jets, none of which pass the b-tagging requirement. This region is referred to as 3 -WZ-CR and it is included in the fit. Distributions comparing data with SM predictions in 3 -WZ-CR are shown in Figure 5, demonstrating good modeling of the W Z background. Figure 6 shows the leading lepton p T and E miss T for events belonging to any of the four trilepton regions targeting ttW. Distributions of the number of jets, the p T and mass of the reconstructed Z boson candidate in the signal region most sensitive to tt Z, 3 -Z-2b4j, are shown in Figure 7.

Tetralepton analysis
The tetralepton channel targets the tt Z process for the case where both W bosons, resulting from top-quark decays, and the Z boson decay leptonically. Events with two pairs of opposite-sign leptons are selected, and at least one pair must have the same flavor. The OSSF lepton pair with reconstructed invariant mass     closest to m Z is attributed to the Z boson decay and denoted in the following by Z 1 . The two remaining leptons are used to define Z 2 . The signal region definitions for the tetralepton channel are summarized in Table 6. Four signal regions are defined according to the relative flavor of the two Z 2 leptons, different flavor (DF) or same flavor (SF), and the number of b-tagged jets: one, or at least two (1b, 2b). The signal regions are thus 4 -DF-1b, 4 -DF-2b, 4 -SF-1b and 4 -SF-2b.
In the same-flavor regions, requirements on E miss T are applied to suppress the Z Z background. In the 4 -SF-1b signal region, the E miss T is required to be greater than 80 GeV (40 GeV) for events with |m Z 2 − m Z | < 10 GeV (|m Z 2 − m Z | > 10 GeV). In the 4 -SF-2b signal region, a requirement of E miss T > 40 GeV is applied for events with |m Z 2 − m Z | < 10 GeV.
To suppress events with fake leptons in the 1-b-tag multiplicity regions, additional requirements on the scalar sum of the transverse momenta of the third and fourth leptons (p T34 ) are imposed. In the 4 -SF-1b and 4 -DF-1b regions, events are required to satisfy p T34 > 25 GeV and p T34 > 35 GeV, respectively, while in the other regions all leptons are required to satisfy p T > 10 GeV. Region

Systematic uncertainties
The signal and background yields in each signal and control region may be affected by several sources of systematic uncertainty. These are implemented as nuisance parameters in the fit, explained in Section 7, are constrained by Gaussian probability density functions and are described in the following subsections.

Luminosity
The uncertainty in the integrated luminosity of the dataset is 2.1%. It is derived, following a methodology similar to that detailed in Ref.
[23], and using the LUCID-2 detector for the baseline luminosity measurements [24], from a calibration of the luminosity scale using x-y beam-separation scans. This systematic uncertainty affects all processes modeled using Monte Carlo simulations, apart from Z+1HF, Z+2HF, W Z and Z Z, whose normalizations are taken from data control regions.

Uncertainties associated with reconstructed objects
Uncertainties associated with the lepton selection arise from the trigger, reconstruction, identification and isolation efficiencies, and lepton momentum scale and resolution [59, 71-73].
Uncertainties associated with the jet selection arise from the jet energy scale (JES), the JVT requirement and the jet energy resolution (JER). The JES and its uncertainty are derived by combining information from test-beam data, collision data and simulation [64]. The uncertainties in the JER and JVT have a significant effect at low jet p T .
The efficiency of the flavor-tagging algorithm is measured for each jet flavor using control samples in data and in simulation. From these measurements, correction factors are derived to correct the tagging rates  Figure 9: Distributions, for all tetralepton signal regions combined, of (a) the number of jets, (b) the invariant mass of the OSSF lepton pair closest to the Z boson mass, m Z 1 , (c) the pseudorapidity separation ∆η for that pair of leptons and (d) the azimuthal angle ∆φ between the remaining two leptons. The 'Other' background contains SM processes with small cross sections producing four prompt leptons. The distributions are shown before the fit. The shaded band represents the total uncertainty. The first and last bin include the underflow and overflow, respectively. in the simulation. In the case of b-jets, correction factors and their uncertainties are estimated from data using dileptonic tt events [66]. In the case of c-jets, they are derived using jets from W boson decays in tt events [74]. In the case of light-flavor jets, correction factors are derived using dijet events [75]. Sources of uncertainty affecting the band c-tagging efficiencies are considered as a function of jet p T , including bin-to-bin correlations [76]. The uncertainty in the efficiency for tagging light-flavor jets depends on the jet p T and on η. These systematic uncertainties are taken as uncorrelated between b-jets, c-jets, and light-flavor jets. An additional uncertainty is assigned to account for the extrapolation of the b-tagging efficiency measurement from the p T region used to determine the correction factors to regions with higher transverse momentum.
The treatment of the uncertainties associated with reconstructed objects is common to all analysis channels, and thus these are considered as fully correlated among different analysis regions.

Uncertainties in the signal modeling
Four sources of systematic uncertainties in the theoretical predictions of the tt Z and ttW processes are considered. These signal modeling uncertainties are treated as uncorrelated between the two processes, and correlated among channels. Taking instead the uncertainties as correlated between the two processes has a negligible impact on the results. Acceptance effects due to the choice of scale and PDF in the nominal MG5_aMC+P 8 (A14 tune) sample are considered. The renormalization and factorization scales µ = µ are varied simultaneously by factors 2.0 and 0.5. In addition, the effects of a set of variations in the tune parameters (A14 eigentune variations), sensitive to initial-and final-state radiation, multiple parton interactions and color reconnection, are evaluated [36]. Studies performed at particle level show that the largest impact comes from variations in initial-state radiation [77]. The systematic uncertainty due to the choice of generator for the tt Z and ttW acceptance is estimated by comparing the nominal sample with one generated with S v2.2. The S sample uses the LO matrix element with up to one (two) additional parton(s) included in the matrix element calculation for tt Z (ttW) and merged with the S parton shower [43] using the ME+PS@LO prescription. The NNPDF3.0NLO PDF set is used in conjunction with a dedicated parton-shower tune developed by the S authors.

Uncertainties in the background modeling
The Z+jets process is, together with tt production, the dominant background in the OS dilepton channel. Its normalization is extracted from data as described in Section 5.1, but the shape of the BDT distribution is obtained from simulation. To assess the systematic uncertainty in the shape, the renormalization, factorization and resummation scales used in the MC generation are varied by a factor of two with respect to the nominal values.
The normalization and shape of the tt background in the OS dilepton channel is obtained using the data-driven method detailed in Section 5.1. A systematic uncertainty arises from the factor used to obtain tt background yields in the same-flavor signal regions from corresponding opposite-flavor dilepton control regions. The uncertainty is due to the finite size of the samples of simulated events used, and the difference between the values of the factor obtained with the nominal P -B +P 8 sample and an alternative sample generated using MG5_aMC+P 8. The total uncertainty in the factor is found to be 3%.
In the trilepton regions sensitive to tt Z, the normalization of the W Z background is treated as a free parameter in the fit used to extract the tt Z and ttW signals. The uncertainty in the extrapolation of the W Z background estimate from the control region to signal regions with specific jet and b-tag multiplicities is evaluated by comparing predictions obtained by varying the renormalization, factorization and resummation scales used in MC generation. The uncertainties vary from 30% to 50%, depending on the signal region.
The normalization of the Z Z background is treated as a free parameter in the fit. An additional uncertainty arises from the extrapolation from the 4 -ZZ-CR control region to the signal regions. It is assessed by varying the renormalization, factorization and resummation scales used in MC generation, and found to be in the range 20-40%.
The uncertainty in the ttH background is evaluated by varying the factorization and renormalization scales up and down by a factor of two with respect to the nominal values. It is found to be around 10%.
An overall normalization uncertainty of 30% is assigned to the t Z background, motivated by the measurements of this process presented in Refs. [78,79]. An additional uncertainty affecting the distribution of this background as a function of jet and b-tagged jet multiplicities is evaluated by varying the factorization and renormalization scales, as well as the amount of radiation in the Perugia2012 parton-shower tune.
An uncertainty of 10% is assigned to the tW Z background cross section, resulting from different prescriptions for removing the interference with the tt Z process. The shape uncertainty is evaluated by varying the factorization and renormalization scales up and down by a factor of two with respect to the nominal value.
For other prompt-lepton backgrounds, uncertainties of 20% are assigned to the normalizations of the W H and Z H processes, based on calculations from Ref. [34]. An uncertainty of 50% is considered for triboson and same-sign WW processes.
A 10% uncertainty is applied to the charge-flip background, resulting from uncertainties in the charge-flip rates extracted from a control sample as described in Section 5.
A 30% uncertainty is assigned to the contribution from events with two prompt leptons or one prompt lepton and a photon conversion in the control regions used to measure the fake-lepton efficiency. In the SS dilepton channel regions and trilepton regions targeting ttW, there are 22 nuisance parameters corresponding to the statistical uncertainty in the measurement of the fake-lepton efficiencies. One nuisance parameter is used for each p T bin used in the measurement of the fake-lepton efficiencies. For fake-lepton efficiencies in events with one (at least two) b-tagged jet(s), seven (four) bins are used, and there is one nuisance parameter for each of the two lepton flavors. In the trilepton signal regions targeting tt Z, where the fake-lepton background is less important, a simplified description of the fake-lepton uncertainties is used, with one nuisance parameter for each of the two lepton flavors. These nuisance parameters correspond to the maximum of the up and down shifts of the fake-lepton efficiencies resulting from statistical uncertainties and the prompt lepton background subtraction in the control regions used to measure the fake-lepton efficiency. The uncertainties in the fake-lepton background in the tt Z and ttW analysis regions are considered to be uncorrelated, due to the different lepton selection requirements used in the two sets of regions.
Uncertainties in scale factors applied to the fake-lepton background are taken into account in the fake-lepton background yield in the tetralepton channel and the ttγ background contribution in the trilepton and 2 -SS channels. These uncertainties are associated with reconstructed objects and the limited sizes of control regions in which the scale factors are obtained. The scale factors have uncertainties between 10% and 50%, depending on the fake-lepton flavor and source. The 2 -SS and trilepton fake-lepton systematic uncertainties from the matrix method are assumed to be uncorrelated with the systematic uncertainties in the fake-lepton scale factors.

Results
The signal strengths µ tt Z and µ ttW , defined as the ratios of the measured values of the inclusive production cross sections to the corresponding SM predictions discussed in Section 3, are extracted simultaneously using a binned maximum-likelihood fit to the numbers of events in the dilepton, trilepton and tetralepton signal and control regions. In the OS dilepton channel signal regions 2 -Z-6j1b, 2 -Z-5j2b and 2 -Z-6j2b, the BDT output distribution is fitted. In the SS dilepton channel, the twelve signal regions 2 -SSp-1b, 2 -SSm-1b, 2 -SSp-2b and 2 -SSm-2b are fitted together with the twelve control regions 2 -SSp-1b-CR, 2 -SSm-1b-CR, 2 -SSp-2b-CR and 2 -SSm-2b-CR defined in Section 5. The contribution from the ttW signal in the SS dilepton control regions is taken into account in the fit. The dependence of the fake-lepton background in these regions on the ttW signal strength is also taken into account. In the trilepton channel, the eight signal regions described in Section 5 are included in the fit, as is the 3 -WZ-CR control region. Finally, in the tetralepton channel, the four signal regions 4 -DF-1b, 4 -DF-2b, 4 -SF-1b and 4 -SF-2b and the control region 4 -ZZ-CR are included in the fit.
The fit is based on the profile-likelihood technique, where systematic uncertainties are included in the fit as nuisance parameters constrained by Gaussian functions. None of the uncertainty parameters are found to be significantly constrained or pulled in the fit. The calculation of confidence intervals and hypothesis testing is performed using a modified frequentist method as implemented in RooStats [80,81]. Figure 10 shows the BDT output distribution in signal regions 2 -Z-6j1b, 2 -Z-5j2b and 2 -Z-6j2b after performing the fit. Figures 11 and 12 summarize the comparison between data and the post-fit signal and background yields for regions sensitive to tt Z and ttW production, together with the relevant control regions. In all cases, good agreement between observed values and the expectation is seen. The normalization corrections for the W Z and Z Z backgrounds with respect to the predictions are obtained from the fits as described in Section 5 and found to be compatible with unity: 0.91 ± 0.10 for the W Z background and 1.11 ± 0.17 for the Z Z background. The normalizations of the Z+1HF and Z+2HF backgrounds are mainly constrained in the low BDT output bins of the OS dilepton channel signal regions, where the signal contamination is low. Their values are found to be 1.19 ± 0.25 and 1.09 ± 0.13, respectively.
In addition to the combined fit described above, fits in individual channels are performed. The tt Z signal strength is extracted through fits to the opposite-sign dilepton regions alone, to the trilepton channel regions alone and to the tetralepton channel signal regions alone. The ttW signal strength is extracted using the four trilepton signal regions targeting ttW and the same-sign dilepton regions considered in the combined fit. The measured values of the signal strengths µ tt Z and µ ttW are reported in Table 7 for each channel separately and for the combined fit. Agreement is observed for the measured values between all the different fit configurations.
The measured signal strengths from the combined fit and their uncertainties are converted to inclusive cross-section measurements using the signal simulation described in Section 3 and the central values of the theoretical predictions. The results are: σ tt Z = 0.95 ± 0.08 stat. ± 0.10 syst. pb = 0.95 ± 0.13 pb and σ ttW = 0.87 ± 0.13 stat. ± 0.14 syst. pb = 0.87 ± 0.19 pb. Figure 13 shows a comparison of the fit results with theoretical predictions, σ th tt Z = 0.88 +0.09 −0.11 pb and σ th ttW = 0.60 +0.08 −0.07 pb, demonstrating good agreement between the measured and predicted cross sections.     Figure 11: Event yields in data compared with the results of the fit that extracts σ tt Z and σ ttW simultaneously in the (a) trilepton and (b) tetralepton signal regions targeting the tt Z process. Yields for the control regions used to extract the normalization of the W Z and Z Z backgrounds are also shown. The 'Other' background summarizes all small SM backgrounds described in Section 3. The shaded band represents the total uncertainty. For the tt Z process, both the observed and the expected significances are found to be much larger than five standard deviations. For the ttW process, an excess of events over the expected background-only hypothesis is found with an observed (expected) significance of 4.3 (3.4) standard deviations. The significance values are computed using the asymptotic approximation described in Ref. [82].  Figure 13: The result of the simultaneous fit to the tt Z and ttW cross sections along with the 68% and 95% confidence level (CL) contours. The cross shows the SM calculations and their uncertainties, including renormalization and factorization scale uncertainties as well as uncertainties including α S variations. Table 8 shows the uncertainties in the measured tt Z and ttW cross sections, grouped in categories, along with the total uncertainties. For both processes, the precision of the measurement is affected by statistical and systematic uncertainties in similar proportions. For the tt Z determination, the dominant systematic uncertainty sources are the modeling of the backgrounds and of the signal. For the ttW determination, the dominant systematic uncertainty sources are the modeling of the signal and the limited amount of data available in the control regions and simulated event samples. Table 8: List of relative uncertainties in the measured cross sections of the tt Z and ttW processes from the fit, grouped in categories. All uncertainties are symmetrized. The sum in quadrature may not be equal to the total due to correlations between uncertainties introduced by the fit.

Interpretation
The effective field theory (EFT) framework provides a model-independent approach to the parameterization of possible deviations from the SM predictions. In this framework, effects due to BSM physics are described by adding additional operators of dimension six or higher to the SM Lagrangian. Each EFT operator O i is associated with a Wilson coefficient C i , and the operators enter the modified Lagrangian in the form where Λ is the characteristic energy scale of the BSM physics.
The complete set of independent, gauge-invariant and baryon-number conserving EFT operators at dimension six contains 59 different operators [83,84]. In the present analysis, five of these operators are considered, all of which modify the tt Z vertex: The operators are defined in Table 9, following Ref.
[85]. The first two operators enter the tt Z vertex as a linear combination, such that the measurement is sensitive to the difference C (3) φQ − C (1) φQ . For this paper, the effect of this combination is evaluated by varying C (3) φQ with C (1) φQ set to zero.
Considering only one EFT operator at a time, any observable, such as the tt Z event rate in a certain signal region, can be expressed as a quadratic function of the coefficient C i : ii .
(1) Operator Expression The values of σ (1) i and σ (2) ii are computed using simulated event samples generated with MG5_aMC interfaced to P 8 [11, 86, 87]. The computation is performed at NLO, separately for all trilepton and tetralepton signal regions. The detector reconstruction efficiency is verified to be compatible between SM tt Z samples and samples with non-zero values of C i , for ranges of C i considered here.
A fit is then performed to extract C i /Λ 2 . The fit is similar to the one described in Section 7, except that only the four trilepton and four tetralepton signal regions targeting tt Z are used and a normalization uncertainty of 12%, corresponding to the uncertainty in the NLO cross-section computation, is applied to the SM tt Z prediction. Uncertainties resulting from the limited sizes of MC samples used to derive the values of σ (1) i and σ (2) ii are propagated to the measured values of C i /Λ 2 .
The profile-likelihood test statistic is defined as −∆ log(L) = log(L(Ĉ i )/L(C i )), where L is the profile likelihood as a function of the Wilson coefficient C i , andĈ i is the best-fit value of C i . Approximate confidence intervals for the Wilson coefficients are computed using the formula −∆ log(L) = ε, where the threshold ε is set to 0.5 and 1.92 for the 68% (1σ) and 95% confidence levels (CL), respectively.
The confidence intervals for C i are computed considering only the minimum of λ(C i ) near C i = 0. For coefficient C (3) φQ (C φt ), another, deeper minimum exists for negative values of C i ∼ 30 (20), which is excluded by previous constraints. The 68% and 95% confidence intervals are shown in Table 10, together with previous constraints on the EFT coefficients obtained from Refs. [10,[88][89][90]. The lower boundary of the 95% confidence interval for C φt is at large negative values, which are excluded by indirect constraints. The tt Z measurement provides competitive constraints for positive C φt values. The full likelihood scans are shown in Figure 14 in the Appendix.
The fits are repeated while assuming that the quadratic terms are zero, and the results of these fits are also reported in Table 10. For C tW and C t B , where the quadratic terms dominate, the fits do not converge. Compared with the nominal fits for C (3) φQ and C φt , the limits shift to larger values, consistent with removing a positive term from the prediction. The most notable change is the improvement in the lower limit for C φt at 95% CL, as the second minimum disappears when a linear expression is assumed. Coefficients

Conclusion
Measurements of the production cross sections of a top-quark pair in association with a Z or W boson using 36.1 fb −1 of data collected by the ATLAS detector in √ s = 13 TeV pp collisions at the LHC are presented. Final states with two same-or opposite-sign leptons, three leptons or four leptons are analyzed. The tt Z and ttW production cross sections are determined to be σ tt Z = 0.95 ± 0.08 stat. ± 0.10 syst. pb = 0.95 ± 0.13 pb and σ ttW = 0.87 ± 0.13 stat. ± 0.14 syst. pb = 0.87 ± 0.19 pb. The measured values are consistent with the SM predictions. The measurements are used to derive confidence intervals for the Wilson coefficients of dimension-6 effective field theory operators involving the top quark and the Z boson.  [72] ATLAS Collaboration, Electron efficiency measurements with the ATLAS detector using the 2012 LHC proton-proton collision data, ATLAS-CONF-2014-032, 2014, : https://cds.cern.ch/record/1706245.   [80] W. Verkerke and D. Kirkby, The RooFit toolkit for data modeling, arXiv: physics/0306116.     φQ and C φt distributions, another, deeper minimum exists for large negative values of C i , which is excluded by indirect measurements. There, the vertical axis is chosen such that the value of the likelihood at the minimum near C i = 0 is zero.  Average ∆R η of all jet pairs 5 4 5

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