ATLAS document

A search for flavour-changing neutral-current processes in top quark decays is presented. Data collected from proton-proton collisions at the Large Hadron Collider at a centre-of-mass energy of √ s = 13 TeV, corresponding to an integrated luminosity of 36 fb−1, are analysed. A search is performed using top-quark–top-antiquark events, with one top quark decaying through the t → qZ (q = u, c) flavour-changing neutral-current channel, and the other through the dominant Standard Model mode t → bW . Only decays of the Z boson to charged leptons and leptonic W boson decays are considered as signal. Consequently, the final-state topology is characterised by the presence of three isolated charged leptons, and at least two jets, one of them originating from a b-quark. Data are consistent with Standard Model background contributions and thus observed (expected) upper limits at 95% confidence level are set on the t → uZ branching ratio of 1.7 × 10−4 (2.4 × 10−4) and on the t → cZ branching ratio of 2.3 × 10−4 (3.2 × 10−4), constituting the most stringent limits to date.


Introduction
The top quark is the heaviest elementary particle known, with a mass m t = 173.1 ± 0.6 GeV [1]. In the the Standard Model of particle physics (SM), it decays almost exclusively to bW and flavour-changing neutral current (FCNC) decays such as t → qZ are forbidden at tree level. However, FCNC decays occur at one-loop level, but are strongly suppressed by the GIM mechanism [2] with a suppression factor of 14 orders of magnitude with respect to the dominant decay mode [3]. However, several SM extensions predict higher branching ratios (BRs) for the top-quark FCNC decays. Examples of such extensions are the quark-singlet model (QS) [4], the two-Higgs-doublet model with (FC 2HDM) or without (2HDM) flavour conservation [5], the Minimal Supersymmetric Standard Model (MSSM) [6], the MSSM with R-parity violation ( / R SUSY) [7], models with warped extra dimensions (RS) [8] or extended mirror fermion models (EMF) [9]. For a more comprehensive review of the various extensions of the SM that have been proposed, see Ref. [10]. The maximum values for the t → qZ BRs predicted by these models and by the SM are summarised in Table 1 [19][20][21][22]. Before the results reported here the most stringent limits, BR(t → uZ)< 2.2 × 10 −4 and BR(t → cZ)< 4.9 × 10 −4 at 95% confidence level, were the ones from the CMS Collaboration [22] using data collected at √ s = 8 TeV. For the same centre-of-mass energy, the ATLAS Collaboration derived a limit of BR(t → qZ)< 7 × 10 −4 [20]. Previous ATLAS results obtained at √ s = 7 TeV were also reported [19].
This analysis presents a search for the FCNC decay t → qZ in top-quark-top-antiquark (tt) events, in 36 fb −1 of data collected at √ s = 13 TeV, with one top quark decaying through FCNC mode and the other through the dominant SM mode (t → bW ). Only the decays of the Z boson into charged leptons and leptonic W boson decays are considered. Only electrons and muons are included. The final-state topology is thus characterised by the presence of three isolated charged leptons 1 , at least two jets with exactly one being tagged as a jet containing b-hadrons, and missing transverse momentum from the undetected neutrino. The main source of background events containing three real leptons are di-boson production, tt Z and t Z processes. An additional background originates from events with two or fewer real leptons and additional non-prompt 2 leptons. Besides the signal region, other regions are defined to control the main backgrounds. The result is obtained using a binned-likelihood fit to kinematic distributions in the signal and control regions.
The note is organised as follows. A brief description of the ATLAS detector is given in Section 2. The collected data samples and the simulations of signal and SM background processes are described in Section 3. Section 4 presents the object definitions, while the event analysis and kinematic reconstruction are explained in Section 5. Background evaluation and sources of systematic uncertainty are described in Sections 6 and 7. Results are presented in Section 8 and conclusions are drawn in Section 9. Table 1: Maximum allowed FCNC t → qZ (q = u, c) BRs as predicted by several models [3][4][5][6][7][8][9][10]

ATLAS detector and data samples
The ATLAS experiment [23] is a multi-purpose particle physics detector consisting of several sub-detector systems, which cover almost fully the solid angle 3 around the interaction point. It is composed of an inner tracking system close to the interaction point and immersed in a 2 T axial magnetic field produced by a thin superconducting solenoid. A lead/liquid-argon (LAr) electromagnetic calorimeter, a steel/scintillatortile hadronic calorimeter, copper/LAr hadronic endcap calorimeter and a muon spectrometer with three superconducting magnets, each one with eight toroid coils, complete the detector. The forward region is covered by additional LAr calorimeters with copper and tungsten absorbers. A new innermost silicon pixel layer has been added to the inner detector after the Run-1 data taking [24,25]. The combination of all these systems provides charged-particle momentum measurements, together with efficient and precise lepton and photon identification in the pseudorapidity range |η| < 2.5. Energy deposits over the full coverage of the calorimeters, |η| < 4.9 are used to reconstruct jets and missing transverse momentum (with magnitude E miss T ). A two-level trigger system is used to select interesting events [26]. The first level is implemented with custom hardware and uses a subset of detector information to reduce the event rate. It is followed by a software-based trigger level to reduce the event rate to approximately 1 kHz.
In this analysis, the combined 2015 and 2016 datasets from proton-proton (pp) collisions at √ s = 13 TeV corresponding to an integrated luminosity of 36 fb −1 are used. Analysed events are selected by either a single-electron or a single-muon trigger. Triggers with different transverse-momentum thresholds are used to increase the overall efficiency. The triggers using a low transverse momentum (p T ) threshold (p e T > 24 GeV or p µ T > 20 GeV for 2015 data and p e,µ T > 26 GeV for 2016 data) also have isolation requirements. At high p T values the isolation requirements incur small efficiency losses which are recovered by higher threshold triggers (p e T > 60 GeV, p e T > 120 GeV or p µ T > 50 GeV for 2015 data and p e T > 60 GeV, p e T > 140 GeV or p µ T > 50 GeV for 2016 data) without isolation requirements.

Signal and background simulation samples
At the LHC pp collider at a centre-of-mass energy of √ s = 13 TeV top quarks are produced according to the SM mainly in tt pairs with a predicted tt cross section of σ tt = 0.83 ± 0.05 nb for a top quark mass of 172.5 GeV, the uncertainty includes contributions from uncertainties on scales, parton distribution functions (PDF)+α S , and the top quark mass. The cross section is calculated at next-to-next-to leadingorder (NNLO) in QCD including resummation of next-to-next-to leading logarithmic soft gluon terms with Top++ 2.0 [27][28][29][30][31][32]. The PDF and α S uncertainties are calculated using the PDF4LHC prescription [33] with the MSTW 2008 68% CL NNLO [34,35], CT10 NNLO [36,37] and NNPDF 2.3 5f FFN [38] PDF sets and are added in quadrature to the renormalisation and factorisation scale uncertainties.
The next-to-leading-order (NLO) simulation of signal events is performed with MG5_aMC@NLO [39] interfaced to Pythia8 [40] with the A14 [41] tune and NNPDF2.3LO PDF set [38]. Dynamic factorisation and renormalisation scales are used. The factorisation and renormalisation scales were set equal to is the transverse momentum of the top quark (top antiquark). For the matrix element, PDF set NNPDF3.0NLO [42] is used. The top quark FCNC decay includes the effects of new physics at an energy scale Λ by adding dimension-six effective terms to the SM Lagrangian. No impact on the kinematical distributions in the events is observed by comparing the bWuZ and bW cZ processes. Due to the different b-tagging mistag rates for u and c quarks, different signal efficiencies at reconstruction level are expected when applying requirements on the b-tagged jet multiplicity. Hence limits on BR(t → qZ) are set separately for q = u, c. Only decays of the W and Z bosons involving charged leptons are generated at the matrix-element level (Z → e + e − , µ + µ − , τ + τ − and W → eν, µν, τν).
Several SM processes have final-state topologies similar to the signal, with at least three prompt charged leptons, especially dibosons (W Z and Z Z), ttV 4 , tt H, ggH, V H, t Z, Wt Z, ttt(t) and triboson (WWW , ZWW and Z Z Z) production. The theoretical estimates for these backgrounds are further constrained by the simultaneous fit to the signal-and control-regions described below. Events with non-prompt leptons or events in which at least one jet is misidentified as an isolated charged lepton (labelled as non-prompt leptons throughout this note) can also fulfil the event selection requirements. These events, typically Z+jets, tt and single-top (Wt), are estimated with the semi-data-driven method explained in Section 6, which also uses simulated samples which for the Z+jets events include Z production in association with heavy-flavour quarks. Table 2 summarises the information about the generators, parton shower and PDFs used to simulate the different event samples considered in the analysis. The associated production of a tt pair with one vector boson is generated at NLO with MG5_aMC@NLO interfaced to the Pythia8 with the A14 tune and the NNPDF2.3LO PDF set [38]. The tt Z and ttW samples are normalised to the NLO QCD+electroweak cross section calculation using fixed scale (m t + m V /2) [43]. In the case of the tt Z sample with the Z → + − decay mode, the Z/γ * interference is included with the cut m > 5 GeV applied. To assess systematic uncertainties an alternative tt Z sample is generated with Sherpa v2.2 using lowest order (LO) matrix element with up to one additional parton included in the matrix element calculation and merged with the Sherpa parton shower using the ME+PS@NLO prescription [44]. The t-channel production of a single top quark in association with a Z boson (t Z) is generated using MG5_aMC@NLO using the four-flavour PDF scheme. Alternative MG5_aMC@NLO_Pythia6 t Z samples with additional radiation are considered in order to estimate the effect of QCD radiation. The generation of Wt-channel production of a single top-quark together with a Z boson (Wt Z) is generated with MG5_aMC@NLO and the parton shower was simulated with Pythia8, using the PDF set NNPDF2.3LO and the A14 tune. Diagram removal is employed to remove the overlap of Wt Z with tt Z and with tt production followed by a three body top quark decay (t → W Z b). The procedure also removes the interference between Wt Z and these two processes. Diboson processes with four charged leptons (4 ), three charged leptons and one neutrino ( ν) or two charged leptons and two neutrinos ( νν), as well as diboson processes having additional hadronic contributions ( ν j j, j j, gg , νν j j) are simulated using the Sherpa 2.1 generator [45]. Matrix elements contain all diagrams with four electroweak vertices. They are calculated for up to one (4 , 2 + 2ν) or no additional partons (3 + 1ν) at NLO and up to three partons at LO using the Comix [46] and OpenLoops [47] matrix element generators and merged with the Sherpa parton shower using the ME+PS@NLO prescription. The CT10 PDF set is used in conjunction with a dedicated parton shower tuning developed by the Sherpa authors. Alternative diboson samples are simulated using the PowhegBox v2 [48] generator. The Higgs samples (tt H, Higgs boson production via gluon fusion and vector boson fusion and in association with a vector boson) are normalised to the theoretical calculations of Ref. [43]. Events containing Z bosons + jets are simulated with PowhegBox v2 interfaced to the Pythia8 parton shower model, using Photos++ version 3.52 [49] for QED emissions from electroweak vertices and charged leptons. The generation of tt and single top-quark in the Wt-channel is done with PowhegBox v2 and PowhegBox v1, respectively. Due to the high lepton-multiplicity requirement of the event selection and to increase the statistics, the tt sample is produced by selecting only true dilepton events in the final state. The SM production of three or four top quarks and the associated production of a tt pair with two W bosons are generated at LO with MG5_aMC@NLO+Pythia8. The production of three massive vector bosons with subsequent leptonic decays of all three bosons is modelled at LO with the Sherpa 2.1 generator. Up to two additional partons are included in the matrix element at LO.
A set of minimum-bias interactions generated with Pythia 8.186 using the A2 set of tuned parameters [50] and the MSTW2008LO [34] PDF set are overlaid on the hard-scattering event to account for additional pp collisions in the same or nearby bunch crossings (pile-up). MC samples are reweighted to match the pile-up conditions in data. Detailed and fast simulations of the detector and trigger system are performed with standard ATLAS software using GEANT4 [51,52] and ATLFASTII [52], respectively. The same offline reconstruction methods used on data are also applied to the samples of simulated events. Simulated events are corrected so that the object identification, reconstruction and trigger efficiencies, energy scales and energy resolutions match those determined from data control samples.

Object reconstruction
The final states of interest for this search include electrons, muons, E miss T , jets, and b-tagged jets. Electron candidates are reconstructed [57] from energy deposits (clusters) in the electromagnetic calorimeter, which are then matched to reconstructed charged-particle tracks in the inner detector. The candidates are required to have a transverse energy E T > 15 GeV and a pseudorapidity of the calorimeter cluster associated with the electron candidate |η cluster | < 2.47. The transition region between the central and forward regions of the calorimeters, in the range 1.37 ≤ |η| ≤ 1.52, exhibits poorer energy resolution and is therefore excluded. In order to reduce the background from non-prompt sources, electron candidates are also required to satisfy |d 0 |/σ(d 0 ) < 5 and |z 0 sin(θ)| < 0.5 mm criteria, where d 0 is the transverse impact parameter, with uncertainty σ(d 0 ), and z 0 is the distance from this impact parameter point along the beam line to the primary vertex. The sum of transverse energies of clusters in the calorimeter within a cone of ∆R = 0.2 around the electron candidate, excluding the p T of the electron candidate, is required to be less than 6% of the electron p T . The scalar sum of track transverse momentum around the electron candidate within a cone of min(10 GeV/p T , 0.2) has to be less than 6% of the electron candidate p T .
Muon candidates are reconstructed from tracks formed in the inner detector and muon spectrometer, which are combined to improve the reconstruction precision and to increase the background rejection [58]. They are required to have p T > 15 GeV and |η| < 2.5. Muons are also required to satisfy |d 0 |/σ(d 0 ) < 3 and |z 0 sin(θ)| < 0.5 mm criteria. Additionally, the scalar sum of track transverse momenta around the muon candidate within a cone of min(10 GeV/p T , 0.3) must be less than 6% of the muon candidate p T .
Jets are reconstructed from topological clusters of calorimeter cells that are noise-suppressed and calibrated to the electromagnetic scale [59] using the anti-k t algorithm [60] with a radius parameter R = 0.4 as implemented in FastJet [61]. Four-vector corrections are applied to the jets, starting with a subtraction procedure that removes the average estimated energy contributed by pile-up interactions based on the jet area [62]. This is followed by jet energy scale calibration that restores the jet energy to the mean response versus particle-level simulation, using a global sequential calibration to correct finer variations due to flavour and detector geometry and in situ corrections that match the data to the MC scale [63]. The jets used in the analysis are required to have p T > 25 GeV and |η| < 2.5.
In order to reduce the number of selected jets that originate from pile-up, an additional selection criterion based on a jet-vertex tagging (JVT) technique is applied. The JVT is a likelihood discriminant that combines information from several track-based variables [64] and the criterion is only applied to jets with p T < 60 GeV and |η| < 2.4.
Jets containing b-hadrons are identified ('b-tagged') [65] using an algorithm based on multivariate techniques. It combines information from the impact parameters of displaced tracks and from topological properties of secondary and tertiary decay vertices reconstructed within the jet. Using simulated tt events the tagging efficiency of jets originating from a b-quark is determined to be 77%, for the chosen working point, while the rejection factors for light flavour jets and charm jets are 133 and 6.2, respectively.
The missing transverse momentum E miss T is defined as the magnitude of the negative vector sum of the p T of all selected and calibrated objects in the event, including a term to account for energy from soft particles in the event that is not associated to any of the selected objects [66,67]. This soft term is calculated from inner detector tracks matched to the selected primary vertex to make it less prone to contamination from pile-up interactions.
In order to avoid double counting of single final state objects, such as an isolated electron being reconstructed both as an electron and as a jet with the requirements above, the following procedures are used to remove overlaps between final state objects. Electron candidates which share a track with a muon candidate are removed. If the distance in ∆R between a jet and an electron candidate is ∆R < 0.2, then the jet is dropped. If multiple jets are found with this requirement, only the closest one is dropped. If the distance in ∆R between a jet and a baseline electron is 0.2 < ∆R < 0.4, then the electron is dropped. If the distance in ∆R between a jet and a muon candidate is ∆R < 0.4, and if the jet has more than two associated tracks then the muon is dropped, otherwise the jet is removed.

Event selection and reconstruction
Events considered in the analysis must meet the criteria described in the following. At least one of the selected leptons must be matched, with ∆R < 0.15, to the appropriate trigger object and have transverse momentum greater than 25 GeV or 27 GeV for the data collected in 2015 or 2016, respectively. The events are required to have at least one primary vertex. The primary vertex must have at least two associated tracks, each with p T > 400 MeV. The primary vertex is chosen as the one with the highest p 2 T over all associated tracks. Exactly three isolated charged leptons with |η| < 2.5 and p T > 15 GeVare required. The Z boson candidate is reconstructed from the two leptons that have the same flavour, opposite charge and a reconstructed mass within 15 GeV of the Z boson mass (m Z ). If more than one compatible lepton-pair is found, the one with the reconstructed mass closest to m Z is chosen as the Z-boson candidate. According to the signal topology, the events are then required to have E miss T > 40 GeV and at least two jets. All jets are required to have p T > 25 GeV and |η| < 2.5. Exactly one of the jets must be b-tagged.
Applying energy-momentum conservation, the kinematic properties of the top quarks are reconstructed from the corresponding decay particles by minimising, without constraints, the following expression: where m reco j a a b , m reco j b c ν and m reco c ν are the reconstructed masses of the qZ, bW and ν systems, respectively. For each jet combination j b must correspond to the b-tagged jet, while any jet can be assigned to j a . Since the neutrino from the semileptonic decay of the top quark (t → bW → b ν) is undetected, its four-momentum must be estimated. This can be done by assuming that the lepton not previously assigned to the Z boson and the b-tagged jet (labelled b-jet) originate from the W boson and SM top-quark decays, respectively, and that E miss T is the transverse momentum of the neutrino in the W boson decay. The longitudinal component of the neutrino momentum (p ν z ) is then determined by the minimisation of Eq. 1. The central value for the masses and the widths of the top quarks and W boson are taken from reconstructed simulated signal events. This is done by matching the particles in the simulated events to the reconstructed ones, setting the longitudinal momentum of the neutrino to the p z of the simulated neutrino, and then performing Bukin fits 5 [68] to the masses of the matched reconstructed top quarks and W boson. The obtained values are m t FCNC = 169.6 GeV, σ t FCNC = 12.0 GeV, m t SM = 167.2 GeV, σ t SM = 24.0 GeV, m W = 81.2 GeV and σ W = 15.1 GeV. The χ 2 minimisation gives the most probable value for p ν z . From all combinations, the one with the minimum χ 2 is chosen, along with the corresponding p ν z value. The jet from the top-quark FCNC decay is referred to as the light-quark (q) jet. The fractions of correct assignments between the reconstructed top quarks and the true simulated particles (evaluated as a match within a cone of size ∆R = 0.4) are around t FCNC = 80% and t SM = 58%, where the difference comes from the fact that for the SM top quark decay it is less efficient to match the E miss T with the simulated neutrino.
The final requirements to define the signal region are | m reco j a a b − 172.5 GeV| < 40 GeV, |m reco j b c ν − 172.5 GeV| < 40 GeV and |m reco c ν − 80.4 GeV| < 30 GeV. Figure 1 shows the mass of the Z boson candidate as well as the E miss T and the masses of both top quark candidates for the events fulfilling these requirements. The stacked histograms are backgrounds with three real leptons, normalised to the theory prediction, and the scaled non-prompt leptons background as discussed in the next section.

Background estimation and control regions
The main sources of background events containing three real prompt leptons are: di-boson production, tt Z and t Z processes. In addition, events where one or more of the reconstructed leptons are non-prompt, either mis-reconstructed or from heavy flavour decays, must be considered as potential background sources. To assess the agreement between data and the simulated samples of the expected background five control regions (CRs) are defined and described below. The control regions are included in the final fit to allow a tighter constraint of background expectations and of systematic uncertainties in the signal yield.
Backgrounds from events containing at least one non-prompt lepton are estimated by a semi-data-driven technique using dedicated selections. This technique is used to determine the normalisation of simulated Z+jets and tt events with a non-prompt lepton. Four different selections are applied to define regions enriched with non-prompt electrons or muons from Z+jets events ("light" region) and tt events ("heavy" region). The non-prompt lepton scale factors are determined by a simultaneous likelihood fit to the inclusive yields in the four regions, taking into account statistical and systematic uncertainties, leading to λ e Z+jets = 2.1 ± 0.8, λ µ Z+jets = 2.0 ± 1.1, λ e tt = 1.1 ± 0.3 and λ µ tt = 1.1 ± 0.7. Agreement between data and expectation in the CRs is significantly improved after applying the non-prompt lepton scale factors to the simulated samples. Table 3: Selection cuts applied to derive the four non-prompt scale factors. OS indicates pair of opposite sign leptons, OSSF indicates pair of opposite-sign same-flavour leptons. Additionally, events with at least 2 jets, one b-tag, 20 GeV < E miss T < 40 GeV and present in the SR are rejected from the "light" regions.
"light" region -electrons "light" region -µ "heavy" region -electrons "heavy" region -µ eee or eµµ, OSSF µµµ or µee, OSSF eµµ , OS no OSSF µee, OS no OSSF The following five CRs are used in the final fit to search for the signal (described in Section 8).
The tt Z CR is defined by requiring exactly three leptons, two of them with the same flavour, opposite charge and a reconstructed m within 15 GeV of the Z boson mass. Furthermore, the events are required to have at least four jets with p T > 25 GeV and |η| < 2.5, two of which must be b-tagged.
Another CR is chosen to study the W Z background. Events are required to have three leptons, two of them with the same flavour, opposite charge, and a reconstructed m within 15 GeV of the Z boson mass. Additional requirements include the presence of at least two jets in the event with p T > 25 GeV and |η| < 2.5 (additionally, the leading jet should have p T > 35 GeV), no b-tagged jets with p T > 25 GeV, E miss T > 40 GeV and a W boson transverse mass, built with the residual lepton momentum and E miss T , greater than 50 GeV.
The Z Z CR is defined by requiring two pairs of leptons with the same flavour, opposite charge, and a reconstructed m within 15 GeV of the Z boson mass. At least one jet with p T > 25 GeV and |η| < 2.5, no b-tagged jets with p T > 25 GeV and E miss T > 20 GeV is also required.
The CR for the non-prompt lepton backgrounds is defined by requiring that events have three leptons with two of them having the same flavour, opposite charge and a reconstructed m outside 15 GeV of the Z boson mass, at least one jet with p T > 25 GeV and E miss T > 20 GeV. This CR is split into two, with either zero (CR0) or exactly one (CR1) b-tagged jet. Table 4 summarises the selection requirements described above. The expected and observed yields in these regions, before the background fit described in Section 8, are shown in Table 5.

Systematic uncertainties
The background fit to the CRs, described in Section 8, reduces significantly some sources of systematic uncertainty, due to the constraints introduced by the data. The effect of each source of systematic uncertainty before the fit is studied by independently varying each parameter within its estimated uncertainty and propagating this through the full analysis chain. The relative impact of each type of systematic Table 5: Event yields in the background CRs for all significant sources of events before the combined fit under the background-only hypothesis described in Section 8. The uncertainties shown include all of the systematic uncertainties described in Section 7. The entry labelled "other backgrounds" includes all the remaining backgrounds described in Section 3 and in Table 2 uncertainty on the total background and signal yields is summarised before and after the fit in Table 6 and  Table 7, respectively.
The main uncertainty, both on the background and on the signal estimations, comes from the uncertainty on their modelling. This uncertainty receives contributions from theoretical normalisation uncertainties and uncertainties from the modelling of background processes in the simulation.
The theoretical normalisation uncertainties are estimated to be 12% for tt Z, 13% for ttW [39], and 30% for t Z production [69]. For dibosons, the normalisation uncertainties on the cross-section [70] and on the choice of the electroweak parameters [71] were added in quadrature yielding a 12.5% uncertainty. An uncertainty of +10% and -28% is assigned to the Wt Z background cross section following the methodology of Refs. [72,73]. For the remaining small backgrounds a 50% uncertainty is assumed. The tt production cross section uncertainties coming from the independent variation of the factorisation and renormalisation scales, as well as the PDF choise and α S variations (see Refs. [32,33] and references therein and Refs. [35,37,38]) lead to a 5% uncertainty on the signal normalisation.
The uncertainties on the modelling of tt Z and W Z processes in the simulation are taken from alternative generators (Sherpa v2.2 and PowhegBox v2 interfaced to the Pythia8, respectively) which yield 4% and 50% uncertainties in the SR, respectively. The Wt Z parton-shower uncertainty is estimated as 6% in the SR using a sample interfaced to Herwig++. The uncertainty due to the choice of NLO generator for the tt event production is evaluated using the alternative sample generated with MG5_aMC@NLO interfaced to Pythia8. This leads to 24% uncertainty on the total non-prompt leptons background in the SR. To evaluate the uncertainty due to the choice of the parton shower algorithm, tt samples generated using Powheg interfaced to Herwig7 are used, yielding 2% uncertainty on the total non-prompt leptons background in the SR. In order to estimate the effect of QCD radiation on the tt samples, alternative samples generated with Powheg+Pythia8 are considered where the factorisation and renormalisation scales are varied up and down by a factor of two and the A14 tune variant was changed correspondingly to RadLo and RadHi [41]. This leads to 10% uncertainty on the total non-prompt leptons background in the SR. Non-prompt lepton scale factor uncertainties are considered on the estimation of the backgrounds from events containing at least one non-prompt lepton.
For both the estimated signal and background event yields, experimental uncertainties resulting from detector effects are considered. Sources of uncertainty include the lepton reconstruction, identification and trigger efficiencies, as well as lepton momentum scales and resolutions [57,74,75]. Uncertainties of the E miss T scale [66], pile-up effects, jet energy scale and resolution [76,77] are considered as well. The b-tagging uncertainty component, which includes the uncertainty of the b-, c-, mistagged-and τ-jet scale factors (the τ and charm uncertainties are highly correlated and evaluated as such) is evaluated by varying the η-, p T -and flavour-dependent scale factors applied to each jet in the simulated samples.
The uncertainty related to the integrated luminosity for the dataset used in this analysis is 2.1%. It is derived following the methodology described in Ref. [78] and only affects the estimations obtained from simulated samples.

Results
A simultaneous fit to the SR and all CRs defined in Table 4 is used to search for a signal from FCNC decays of the top-quark. A maximum-likelihood fit is performed to the kinematic distributions in the signal and control regions to test for the presence of signal events. Signal contamination of the CRs is negligible but inclusion of the CRs in a combined fit with the signal region allows tighter constraints of backgrounds and systematic uncertainties. The distributions used in the fit are: the χ 2 of the kinematical reconstruction for the SR, the leading lepton p T for the non-prompt leptons and tt Z CRs, the W boson transverse mass for the W Z CR and the reconstructed mass of the four leptons for the Z Z CR.
The statistical analysis to extract the signal is based on a binned likelihood function L(µ, θ) constructed as a product of Poisson probability terms over all bins in each considered distribution, and several Gaussian constraint terms for θ, a set of nuisance parameters that parametrise effects of statistical uncertainty and all sources of systematical uncertainties on the signal and background expectations. This function depends on the signal strength parameter µ, a multiplicative factor for the number of signal events normalised to a reference branching ratio BR ref (t → qZ ) = 0.1%. The nuisance parameters adjust the expectations for signal and background according to the corresponding systematic uncertainties, and their fitted values correspond to the adjustment that best fits the data.
The test statistic q µ is defined as the profile likelihood ratio: q µ = −2 ln(L(µ,θ µ )/L(μ,θ)), whereμ and θ are the values of the parameters that maximise the likelihood function (with the constraints 0 ≤μ ≤ µ), andθ µ are the values of the nuisance parameters that maximise the likelihood function for a given value of µ. This test statistic is used to measure the compatibility of the observed data with the background-only hypothesis (i.e. for µ = 0), and to make statistical inferences about µ.
The distributions used in the fit are presented in Figures 2 and 3, obtained before and after the combined fit under the background-only hypothesis, respectively. Table 8 shows the expected number of background events, number of selected data events and signal yields in the SR before and after the fit. The post-fit signal yield changes due to the fitted nuisance parameters. The obtained yields in the CRs after the fit are shown in Table 9. Good agreement between data and expectation from the background-only hypothesis is observed and no evidence for an FCNC signal is found. We compute upper limits on BR(t → qZ ) with the CL s method [79,80] using the asymptotic properties of q µ [81][82][83] and assuming that only one FCNC mode contributes. Figure 4 shows the observed CL s for BR(t → uZ ) and BR(t → cZ ) together with the ±1σ and ±2σ bands for the expected values. From these we derive the 95% CL limits on these branching ratios shown in Table 10.
Using the effective field theory framework developed in the TopFCNC model [84,85], assuming a cut-off scale Λ = 1 TeV and that only one operator has a non-zero value, the upper limits on the B(t → uZ ) and B(t → cZ ) are converted into 95% CL upper limits on the modulus of the operators contributing to the FCNC decay t → qZ presented in Table 11. Table 8: Expected number of background events, number of selected data events and signal events (arbitrarily normalised to a branching ratio of BR(t → qZ) = 0.1%), in the signal region before and after the combined fit under the background-only hypothesis. The uncertainties shown include all of the systematic uncertainties described in Section 7. The entry labelled "other backgrounds" includes all the remaining backgrounds described in Section 3 and in Table 2. The uncertainties on the post-fit yields are calculated using the full correlation matrix resulting from the fit to data.  Table 9: Event yields in the background control regions for all significant sources of events after the combined fit under the background-only hypothesis. The uncertainties shown include all of the systematic uncertainties described in Section 7. The entry labelled "other backgrounds" includes all the remaining backgrounds described in Section 3 and in Table 2. The uncertainties on the post-fit yields are calculated using the full correlation matrix resulting from the fit to data.

Conclusions
The analysis presented a search for tt events, with one top quark decaying through the t → qZ FCNC (q = u, c) channel, and the other through the dominant Standard Model mode t → bW , where only decays of the Z boson into charged leptons and leptonic W boson decays are considered as signal. Data collected in pp collisions corresponding to an integrated luminosity of 36 fb −1 at the LHC at a centre-of-mass energy of √ s = 13 TeV by the ATLAS experiment agree with the Standard Model expectations, no evidence for signal events is found. A 95% CL limit for the t → qZ branching fraction is established at BR(t → uZ ) < 1.7 × 10 −4 and BR(t → cZ ) < 2.3 × 10 −4 , with the expected 95% CL limit of BR(t → uZ ) < 2.4 × 10 −4 and BR(t → cZ ) < 3.2 × 10 −4 , respectively. These limits constrain the values of effective field theory operators contributing to the t → uZ and t → cZ FCNC decays of the top-quark.