Search for flavour-changing neutral-current interactions of a top quark and a gluon in pp collisions at √s=13 TeV with the ATLAS detector

Eur. Phys. J. C (2022) 82:334 https://doi.org/10.1140/epjc/s10052-022-10182-7 Regular Article - Experimental Physics Search for flavour-changing neutral-current interactions of a top quark and a gluon in pp collisions at √s=13 TeV with the ATLAS detector ATLAS Collaboration CERN, 1211 Geneva 23, Switzerland Received: 3 December 2021 / Accepted: 4 March 2022 / Published online: 19 April 2022 © CERN for the benefit of the ATLAS collaboration 2022 Abstract A search is presented for the production of a single top quark via left-handed flavour-changing neutralcurrent (FCNC) interactions of a top quark, a gluon and an up or charm quark. Two production processes are considered: u+g→tand c+g→t. The analysis is based on proton–protoncollisiondatatakenatacentre-of-massenergy of 13TeV with the ATLAS detector at the LHC. The data set corresponds to an integrated luminosity of 139 fb−1. Events with exactly one electron or muon, exactly one b-tagged jet and missing transverse momentum are selected, resembling the decay products of a singly produced top quark. Neural networks based on kinematic variables differentiate between events from the two signal processes and events from background processes. The measured data are consistent with the background-only hypothesis, and limits are set on the production cross-sections of the signal processes: σ(u+g→t)×B(t→Wb)×B(W→ν) < 3.0 pb and σ(c+g→t)×B(t→Wb)×B(W→ν) < 4.7pbatthe 95% confidence level, with B(W→ν) =0.325 being the sum of branching ratios of all three leptonic decay modes of the Wboson. Based on the framework of an effective field theory,thecross-sectionlimitsaretranslatedintolimitsonthe strengthsofthetugandtcgcouplingsoccurringinthetheory: |Cut uG|/2<0.057 TeV−2and |Cct uG|/2<0.14 TeV−2. These bounds correspond to limits on the branching ratios of FCNC-induced top-quark decays: B(t→u+g)< 0.61 ×10−4and B(t→c+g)<3.7×10−4. Contents 1 Introduction ..................... 1 2 The ATLAS detector ................. 2 3 Samples of data and simulated events ........ 3 3.1 Samples of simulated events from the ugt and cgt FCNC processes .............. 3 e-mail: [email protected] 3.2 Simulation of t¯ tand SM single-top-quark production ... 4 3.3 Simulation of W+jets and Z+jets production .. 4 3.4 Simulation of diboson and multijet production .5 4 Object reconstruction and event selection ...... 5 4.1 Object definitions ................ 5 4.2 Basic event selection .............. 6 4.3 Definition of signal and validation regions ... 7 5 Estimation of the multijet background ........ 8 6 Neural networks separating signal and background events ......................... 9 7 Systematic uncertainties ...............11 7.1 Experimental uncertainties ...........11 7.2 Modelling uncertainties .............12 8 Results ........................14 8.1 Results of the profile likelihood fit .......14 8.2 Upper limits on cross-sections, EFT coefficients and branching ratios ...............16 8.3 Comparison of expected upper limits ......17 9 Conclusions .....................18 References ........................19 1 Introduction Direct searches for on-shell production of new heavy particles at the Large Hadron Collider (LHC) have not yet been successful. For this reason, indirect searches targeting non-standard couplings among Standard Model (SM) particles attract increasing interest. Among these analyses are searches for flavour-changing neutral-current (FCNC) processes in the top-quark sector. The SM does not contain FCNC processes at tree level, and even though these processes exist at higher orders, they are suppressed due to the Glashow–Iliopoulous–Maiani mechanism [1]. Compared to the b-quark sector, where decays of b-hadrons via FCNCs were first observed in 1995 [2], FCNC decays of top quarks are even more suppressed. Depending on the decay mode, FCNC branching ratios (B) of the top quark are predicted to range from 10−12 to 10−17 [3], and are thus well below the 123 334 Page 2 of 35 Eur. Phys. J. C (2022) 82 :334 experimentally accessible regime, at present and in the foreseeable future. The observation of FCNC top-quark decays or top-quark production via FCNCs would therefore be an unambiguous signal of physics beyond the SM. Many extensions of the SM predict significantly higher rates for FCNC processes in the top-quark sector. These extensions include new scalar particles introduced in twoHiggs-doublet models [4,5] or in supersymmetry [6–8]. In certain regions of the parameter space of these models, the predicted branching ratios of top quarks decaying via FCNC can be as large as 10−5to 10−3and thus become detectable at the LHC. Searches for FCNCs involving a top quark and a gluon were performed at the Tevatron [9,10] and in data from Run 1 of the LHC [11–13]. Rather than looking for the top-quark decays t→u+gand t→c+gin top-quark–antiquark pair (t¯ t) production, these analyses searched for the production of a single top quark (t) via the FCNC processes u+g→t (ugt process)andc+g→t(cgt process),exploitingspecific kinematic features of single-top-quark production to separate a potential signal from the large W+jets and multijet backgrounds. The analysis presented in this paper extends the Run 1 ATLAS search to the Run 2 data set collected with the ATLAS detector in the years 2015 to 2018, during which the LHC operated at a centre-of-mass energy of 13TeV. Conceptually, the scope of the analysis is expanded by performing independently optimised searches for the ugt and cgt processes. Differences between these two processes are due to differences in the parton distribution functions (PDFs) for valence and sea quarks. For top antiquarks the charge-conjugate processes are implied. The FCNC interaction is assumed to be left-handed. Another novelty compared to the Run 1 analysis is the interpretation of the results in an effective field theory framework provided by the TopFCNC model [14]. The event selection targets the t→e+νband t→μ+νb decay modes of the top quark. However, there is also additional but lower acceptance for events with the decay t→ τ+νband the subsequent decay of the τ-lepton into e+νe¯ντ orμ+νμ¯ντ.Aleading-order(LO)Feynmandiagramillustrating the signature of the targeted scattering events is shown in Fig. 1. Consideringthesignature ofthesignalevents,therequired reconstructed objects are exactly one charged-lepton candidate (an electron or a muon) with high transverse momentum (pT), exactly one jet which is identified to originate with a high probability from a b-quark, and large missing transverse momentum as an indication of a high-pTneutrino. The main background processes are W+b¯ bproduction, t-channel single-top-quark (tq) production, t¯ tproduction and multijet production. Artificial neural networks (NNs) are used to separate signal events from background events. The observed distributions of the NN discriminants are analysed Fig. 1 Leading-order Feynman diagram of non-SM production of a single top quark via the FCNC process u(c)+g→t statistically with a profile maximum-likelihood fit in which all systematic uncertainties are treated as nuisance parameters. The structure of the paper is as follows. A brief description of the ATLAS detector is given in Sect. 2, followed by a comprehensive summary of the collision data and the samples of simulated events in Sect. 3. Section 4describes the reconstruction of detector-level objects and the event selection. The modelling of multijet background events and the estimation of their rate is discussed in Sect. 5. Section 6provides details about the separation of signal and background events using NNs. Systematic uncertainties are outlined in Sect. 7and the results are presented in Sect. 8. Conclusions are given in Sect. 9. 2 The ATLAS detector The ATLAS detector [15] at the LHC covers nearly the entire solid angle around the collision point.1It consists of an inner tracking detector surrounded by a thin superconducting solenoid, electromagnetic and hadronic calorimeters, and a muon spectrometer incorporating three large superconducting toroidal magnets. The inner-detector system (ID) is immersed in a 2T axial magnetic field and provides charged-particle tracking in the range |η|<2.5. The high-granularity silicon pixel detector covers the vertex region and typically provides four measurements per track, the first hit normally being in the insertable B-layer installed before Run 2 [16,17]. It is followed by the silicon microstrip tracker, which usually provides eight measurements per track. These silicon detectors are complemented by the transition radiation tracker (TRT), 1ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the centre of the detector and the zaxis along the beam pipe. The x-axis points from the IP to the centre of the LHC ring, and the y-axis points upwards. Cylindrical coordinates (r,φ) are used in the transverse plane, φbeing the azimuthal angle around the z-axis. The pseudorapidity is defined in terms of the polar angle θas η=−ln tan(θ/2). Angular distance is measured in units of R≡(η)2+(φ)2. 123 Eur. Phys. J. C (2022) 82 :334 Page 3 of 35 334 which enables radially extended track reconstruction up to |η|=2.0. The TRT also provides electron identification information based on the fraction of hits (typically 30 in total) above a higher energy-deposit threshold corresponding to transition radiation. The calorimeter system covers the pseudorapidity range |η|<4.9. Within the region |η|<3.2, electromagnetic calorimetry is provided by barrel and endcap highgranularity lead/liquid-argon (LAr) calorimeters, with an additional thin LAr presampler covering |η|<1.8 to correct for energy loss in material upstream of the calorimeters. Hadronic calorimetry is provided by the steel/scintillatortile calorimeter, segmented into three barrel structures within |η|<1.7, and two copper/LAr hadronic endcap calorimeters.Thesolidanglecoverage is completed with forwardcopper/LArandtungsten/LArcalorimetermodulesoptimisedfor electromagnetic and hadronic measurements respectively. The muon spectrometer (MS) comprises separate trigger and high-precision tracking chambers measuring the deflection of muons in a magnetic field generated by superconducting air-core toroids. The field integral of the toroids ranges between 2.0 and 6.0 T m across most of the detector. A set of precision chambers covers the region |η|<2.7 with three layers of monitored drift tubes, complemented by cathode-strip chambers in the forward region, where the background is highest. The muon trigger system covers the range |η|<2.4 with resistive-plate chambers in the barrel, and thin-gap chambers in the endcap regions. Interesting events are selected to be recorded by the first-level trigger system implemented in custom hardware, followed by selections made by algorithms implemented in software in the high-level trigger [18]. The first-level trigger accepts events from the 40 MHz bunch crossings at a rate below 100 kHz, which the high-level trigger reduces in order to record events to disk at about 1 kHz. An extensive software suite [19] is used in the reconstruction and analysis of real and simulated data, in detector operations, and in the trigger and data acquisition systems of the experiment. 3 Samples of data and simulated events The analysis uses proton–proton (pp) collision data recorded with the ATLAS detector in the years 2015 to 2018 at a centre-of-massenergyof13TeV.Afterapplyingdata-quality requirements [20], the data set corresponds to an integrated luminosity of 139fb−1with a relative uncertainty of 1.7% [21]. The LUCID-2 detector [22] was used for the primary luminosity measurements. At the high instantaneous luminosityreached atthe LHC, eventswereaffectedbyadditional inelastic pp collisions in the same and neighbouring bunch crossings (pile-up). The average number of interactions per bunch crossing was 33.7. Events were selected online during data taking by singleelectron or single-muon triggers [23,24]. Multiple triggers were used to increase the selection efficiency. The lowestthresholdtriggersutilisedisolationrequirementsforreducing the trigger rate. The isolated-lepton triggers had pTthresholds of 20 GeV for muons and 24 GeV for electrons in 2015 data, and 26GeV for both lepton types in 2016, 2017 and 2018 data. They were complemented by other triggers with higher pTthresholds but no isolation requirements in order to increase the trigger efficiency. Large sets of simulated events from signal and background processes were produced with event generator programs based on the Monte Carlo (MC) method to model the recorded and selected data. After event generation, the response of the ATLAS detector was simulated using the Geant4 toolkit [25] with a full detector model [26]ora fast simulation [27,28] which employed a parameterisation of the calorimeter response. To account for pile-up effects, minimum-bias interactions were superimposed on the hardscattering events and the resulting events were weighted to reproduce the observed pile-up distribution. The minimumbias events were simulated using Pythia 8.186 [29] with the A3 [30] set of tuned parameters and the NNPDF2.3lo PDF set [31]. Finally, the simulated events were reconstructed using the same software as applied to the collision data. Except for the multijet background, the same event selection requirements were applied and the selected events were passed through the same analysis chain. Small corrections were applied to simulated events such that the lepton trigger and reconstruction efficiencies, jet energy calibration and btagging efficiency were in better agreement with the response observed in data. More details of the simulated event samples are provided in the following subsections. 3.1 Samples of simulated events from the ugt and cgt FCNC processes Simulated events from the ugt and cgt processes were produced with the METOP1.0 event generator [32,33]at next-to-leading order (NLO) in quantum chromodynamics (QCD). The difference between LO and NLO is very relevant for the analysis since a veto on a second jet is applied in the event selection by requiring exactly one reconstructed jet with pT>30 GeV. Signalsamples generated atNLO predict a higher rate of events with two jets than samples generated at LO, leading to a lower acceptance for signal events due to the jet veto. The Lorentz structure of the vertex coupling was taken to be left-handed. It was verified that the shapes of kinematic distributions are independent of the value of the coupling constant used for the event generation. The top quark was assumed to decay as in the SM and the decay was 123 334 Page 4 of 35 Eur. Phys. J. C (2022) 82 :334 simulated using MadSpin [34,35]. Only leptonic decays of the Wboson originating from top-quark decay were considered, including e±,μ±and τ±leptons. The renormalisation scale μrand the factorisation scale μfwere set to the topquark mass mt, for which a value of mt=172.5GeVwas used. The CT10 set of PDFs [36] was used for event generation. Parton showers and the hadronisation were simulated with Pythia 8.235 [37] with the A14 set of tune parameters [38]. In the METOP + Pythia set-up, hard gluon emissions can arise in both the NLO matrix-element generator and the parton-showergenerator.The matching betweenthetwogenerators was achieved by limiting the phase-space region of the first parton-shower emission in a way that depends on the transverse momentum of the top quark. The matching scale between the matrix-element generator and the parton shower was set to 10 GeV. Samples with alternative generator settings were produced to estimate systematic uncertainties. Samples with μr=μf=2·mtand μr=μf=0.5·mtwere used to evaluate the impact of the scale choice on the signal model. The uncertainty in modelling parton showers was evaluated with METOPsignal samples in which parton showers were generated by Herwig7.0.4 [39,40] instead of Pythia .The METOP + Herwig set-upused the same PDF setas thenominal sample, CT10. In addition, METOP + Pythia samples with a different matching scale of 15 GeV were produced to evaluate the uncertainties due to the choice of this scale. All samples of the ugt and cgt processes were passed through the fast detector simulation. 3.2 Simulation of t¯ tand SM single-top-quark production Samples of simulated events from t¯ tand single-top-quark production were generated using the Powheg Boxv2 [41– 47]NLOmatrix-elementgenerator,settingmt=172.5GeV. For t¯ tand tW production as well as s-channel single-topquarkproduction(t¯ bproduction)theNNPDF3.0nlo PDFset [48] implementing the five-flavour scheme was used, while t-channel single-top-quark events (tq production) were produced with the NNPDF3.0nlo_nf4 PDF set, which implements the four-flavour scheme, following a recommendation given in Ref. [47]. Parton showers, hadronisation, and the underlying event were modelled using Pythia 8.230 with the A14 set of tuned parameters and the NNPDF2.3lo PDF set. The Powheg Box +Pythia generator set-up applies a matching scheme to the modelling of hard emissions in the two programs. The matrix-element-to-parton-shower matching is steered by the hdamp parameter, which controls the pT of the first additional gluon emission beyond the LO Feynman diagram in the parton shower and therefore regulates the high-pTemission against which the t¯ tsystem recoils. Event generation was run with hdamp =1.5×mt[49]. The renormalisation and factorisation scales were set dynamically on anevent-by-eventbasis, namely toμr=μf=m2 t+p2 T(t) for t¯ tproduction and to μr=μf=4m2 b+p2 T(b)for tq production, with pT(t)being the pTof the top quark and pT(b)beingthe pTofthe b-quarkoriginatingfromtheinitialstate gluon, splitting into a b¯ bpair. The scale choice for tq production followed a recommendation of Ref. [47]. When generating tW events, the diagram-removal scheme [50]was employed to handle the interference with t¯ tproduction [49]. In the case of t¯ tproduction, top-quark decays were handled by Powheg Boxdirectly, while in the case of singletop-quark production, top-quark decays were modelled by MadSpin . The decays of bottom and charm hadrons were simulated using the EvtGen 1.6.0 program [51] for all samples involving top-quark production. The t¯ tproduction cross-section was scaled to σ(t¯ t)= 832+47 −51 pb, the value obtained from next-to-next-to-leadingorder (NNLO) predictions from the Top++ 2.0 program (see Ref. [52] and references therein), which includes the resummation of next-to-next-to-leading logarithmic (NNLL) softgluon terms. The total cross-sections for tq and t¯ bproduction were computed at NLO in QCD with the Hathor v2.1 program [53,54] and the corresponding samples of simulated events were scaled to the following values: σ(tq)= 136.0+5.5 −4.7pb, σ(¯ tq)=81.0+4.1 −3.7pb and σ(t¯ b+¯ tb)= 10.3±0.38 pb. The cross-section used for normalising the tW sample is σ(tW +¯ tW)=71.7±3.8pb [55,56]. All cross-section calculations assumed mt=172.5 GeV as a fixed value. 3.3 Simulation of W+jets and Z+jets production The production of Wbosons and Zbosons in association with jets, including heavy-flavour jets in particular, was simulated with the Sherpa 2.2.1 generator [57]. In this set-up, NLO-accurate matrix elements for up to two partons and LO-accurate matrix elements for up to four partons were calculated with the Comix [58] and OpenLoops1[59–61] libraries. The default Sherpa parton shower [62] based on Catani–Seymour dipole factorisation and the cluster hadronisation model [63] were used. The generation employed the dedicated set of tuned parameters developed by the Sherpa authors and the NNPDF3.0nlo PDF set. The NLO matrix elements of a given jet multiplicity were matched to the parton shower using a colour-exact variant of the MC@NLO algorithm [64]. Different jet multiplicities werethenmergedinto aninclusivesample using animproved CKKW matching procedure [65,66] which was extended to NLOaccuracyusingtheMEPS@NLOprescription[67].The merging threshold wasset to20 GeV. The W+jets and Z+jets samples were normalised to NNLO predictions [68]ofthe total cross-sections, obtained with the FEWZ package [69]. 123 Eur. Phys. J. C (2022) 82 :334 Page 5 of 35 334 3.4 Simulation of diboson and multijet production Samples of on-shell diboson production (WW,WZand ZZ) were also simulated with the Sherpa 2.2.1 generator. Motivated by the targeted signature of the signal events, only semileptonic final states were produced, in which one boson decayed leptonically and the other hadronically. The considered matrix elements contain all diagrams with four electroweak vertices and they were calculated at NLO accuracy in QCD for up to one additional parton and at LO accuracy for up to three additional parton emissions. The matching of NLO matrix elements to the parton shower and the merging of different jet multiplicities was done in the same way as for W/Z+jets production. Virtual QCD corrections were provided by the OpenLoops1 library. The NNPDF3.0nlo PDF set was used along with the dedicated set of tuned parameters developed by the Sherpa authors. The diboson event samples were normalised to the total cross-sections provided by Sherpa at NLO in QCD. Events featuring generic high-pTmultijet production may pass the event selection if a jet is misidentified as an electron or muon, or if real electrons or muons coming from hadron decays inside the jets pass the isolation requirements. The former are called fake leptons, the latter non-prompt leptons. In addition, non-prompt electrons occur as a result of photon conversions in the detector material. Multijet events with fake electrons or non-prompt electrons were modelled with a sample of simulated dijet events, while events with non-prompt muons were modelled with collision data. The number of events with fake muons is negligible. The dijet event sample was generated using Pythia 8.186 with LO matrix elements for dijet production and interfaced to a pTordered parton shower. The scales μrand μfwere set to the square root of the geometric mean of the squared transverse masses of the two outgoing particles in the matrix element, μr=μf=4 (p2 T,1+m2 1)(p2 T,2+m2 2). At generator level, a filter was applied which required the existence of one particle-level jet with pT>17GeV. The generation used the NNPDF2.3lo PDF set and the A14 set of tuned parameters. The generated sample of dijet events was used to model the event kinematics and to produce template distributions in the electron channel, while the rate of the multijet background was estimated in a data-driven way as described in Sect. 5. 4 Object reconstruction and event selection The hard-scattering process was reconstructed by identifying the particles occurring at parton level with objects which were reconstructed at detector level, such as electron and muon candidates and hadronic jets. The presence of high-pT neutrinosis signalledby high missingtransversemomentum. 4.1 Object definitions Eventswere required to haveat least onevertexreconstructed from at least two ID tracks with transverse momenta of pT> 0.5GeV. The primary vertex of an event was defined as the vertex with the highest sum of p2 Tover all associated ID tracks [70]. Electron candidates were reconstructed from clusters of energy deposited in the electromagnetic calorimeter with a matched track reconstructed in the ID [71]. The pseudorapidity of clusters, ηcluster, was required to be in the range |ηcluster|<2.47. However, clusters were excluded if they are in the transition region 1.37 <|ηcluster|<1.52 between the central and the endcap electromagnetic calorimeters. Electron candidates had to have pT>10 GeV. A likelihoodbased method was used to simultaneously evaluate several properties of electron candidates, including shower shapes in the electromagnetic calorimeter, track quality, and detection of transition radiation produced in the TRT. Two categories of electrons with different quality were defined [71]: the first category implemented Tight identification criteria and featured a high rejection of non-prompt or fake electrons, while the second category with Loose criteria had higher efficiency at the price of lower purity in prompt electrons. Electrons from decays of weak gauge bosons pass the Tight criteria with an average efficiency of 80% and the Loose criteria with 93%. Muon candidates were reconstructed by combining tracks in the MS with tracks in the ID [72]. The tracks had to be in the range of |η|<2.5 and have pT>10 GeV. Similarly to electrons, two levels of identification criteria were applied, defining Medium and Loose quality categories of muon candidates. Muons orginating from Wbosons in t¯ tevents with pT>10 GeV pass the Medium quality criteria with an efficiency of 97% and the Loose criteria with 99%. The tracks matched to electron and muon candidates had to point to the primary vertex, which was ensured by requirements imposed on the transverse impact-parameter significance, |d0/σ(d0)|<5.0 for electrons and |d0/σ (d0)|< 3.0 for muons, and the longitudinal impact parameter, |z0sin(θ)|<0.5 mm for both lepton flavours. Isolated Tight electrons and Medium muons were selected by requiring the amount of energy in nearby energy depositions in the calorimeters and the scalar sum of the transverse momenta of nearby tracks in the ID to be small. Isolation requirements were not imposed on electrons and muons of Loose quality. Scale factors were used to correct the efficiencies in simulation in order to match the efficiencies measured for the electron [71] and muon [24] triggers, and the reconstruction, identification and isolation criteria. Jets were reconstructed from topological clusters [73,74] in the calorimeters with the anti-ktalgorithm [75] using FastJet [76] and a radius parameter of 0.4. Their energy was 123 334 Page 6 of 35 Eur. Phys. J. C (2022) 82 :334 calibrated [77], and they had to fulfil pT>20 GeV and |η|<4.5. Jets with pT<120 GeV and |η|<2.5were required to pass a requirement on the jet-vertex-tagger (JVT) discriminant [78] to suppress jets originating from pile-up collisions. The JVT-discriminant was required to be above 0.59,which corresponds toanefficiencyof 92% fornon-pileup jets. Similarly, a forward-JVT (fJVT) requirement was used for jets with pT<60 GeV and 2.5<|η|<4.5[79]. Differences in the efficiencies of the JVT and fJVT requirements between collision data and simulation were accounted for by corresponding scale factors. Jets containing b-hadrons were identified (b-tagged) with the MV2c10 algorithm [80], which used boosted decision treediscriminantswithseveralb-taggingalgorithmsasinputs [81]. The algorithms exploited the impact parameters of charged-particle tracks, the properties of reconstructed secondary vertices and the topology of band c-hadron decays inside the jets. In order to strongly reduce the misidentification rate of c-jets and light-flavour (u,dor s)/gluon jets, a specific working point of the MV2c10 algorithm was defined and calibrated, using the standard calibration technique [80]. With this working point, the b-tagging efficiency for jets that originate from the hadronisation of b-quarks is 30% in simulated t¯ tevents. The b-tagging rejection2for jets that originate from the hadronisation of c-quarks (u-, d-, squarks or gluons) is 900 (30,000). By using the high-purity b-tagging working point with 30% efficiency for b-jets the analysis performance was considerably improved in comparison to an analysis based on the tightest standard working point which features a tagging efficiency of 60% for b-jets. The improvement is mainly due to a reduced impact of the W+jets background, including uncertainties in mistagging cquark jets, light-flavour jets and gluon jets in W+jets production. Differences in b-tagging efficiency between simulated and collision events were corrected for by applying a pTdependent scale factor to simulated events. The scale factor rangesfrom0.96±0.04intheinterval30 <pT(b)≤40 GeV to 1.01 ±0.02 for 140 <pT(b)<175 GeV, which is the highest calibration interval relevant for this analysis. The btagging scale factors were obtained by comparing samples of collision data strongly enriched in t¯ tevents with samples of simulated events generated by Powheg+Pythia 8.230. The obtained scale factors depend on the parton-shower generator used to produce the t¯ tsamples. When using samples with a different parton-shower generator, for example Sherpa to model W+jets events, or when evaluating systematic uncertainties with a set-up based on Herwig, additional correction factors called MC-to-MC scale factors were applied. Toavoiddouble-countingobjectssatisfyingmorethanone selection criterion, a procedure called overlap removal was applied. Reconstructed objects defined with Loose quality 2The rejection is defined as the inverse of the efficiency. criteria were removed in the following order: electrons sharing an ID track with a muon; jets within R=0.2ofan electron, thereby avoiding double-counting electron energy deposits as jets; electrons within R=0.4ofaremaining jet, for reducing the impact of non-prompt electrons; jets within R=0.2 of a muon if they have two or fewer associated tracks; muons within R=0.4 of a remaining jet, reducing the rate of non-prompt muons. The Tight and Medium criteriawere applied tothose objectswhich survived overlap removal. The missing transverse momentum pmiss Twas reconstructed as the negative vector sum of the pTof the reconstructed leptons and jets, as well as ID tracks that pointed to the primary vertex but were not associated with a reconstructed object [82]. The magnitude of pmiss Tis denoted by Emiss T. 4.2 Basic event selection To be selected, events were required to have exactly one electron of Tight quality or exactly one muon of Medium quality, both with pT>27 GeV. The charged lepton was required to match the object which triggered the event. To reduce contributions from t¯ tevents in the dilepton decay channel, any event with an additional lepton satisfying the Loose quality conditions with pT>10 Gev was rejected (dilepton veto). Multijet events containing fake or non-prompt leptons tend to have, in contrast to events with prompt leptons from Wand Zdecays, low Emiss Tand low Wtransverse mass, which is defined as mT(W)=2pT()Emiss T1−cos φ , pmiss T.(1) To reduce the multijet background, Emiss T>30 GeV and mT(W)>50 Gev were applied as additional selection requirements. At least one jet with pT>30 GeV was required. In order to even further suppress the multijet background and to remove poorly reconstructed leptons with low pT,the event selection applied an additional requirement based on the azimuthal angle between the primary lepton () and the leading jet (j1), i.e. the jet with the largest pT. This quantity is denoted by φ (j1, ). The imposed requirement was pT()>50 Gev ·1−π−|φ (j1, )| π−1, which led to a tighter pTrequirement on the charged lepton if the leading jet and the lepton had a back-to-back topology, namely if |φ( j1,)|>0.687π. For the maximum separation |φ( j1,)|=πbetween the two objects, pT() > 50 Gev had to be satisfied. 123 Eur. Phys. J. C (2022) 82 :334 Page 7 of 35 334 4.3 Definition of signal and validation regions A signal region (SR) and three validation regions (VRs) were defined by applying further requirements to the sample of eventspassingthebasicselection. Only eventsintheSRwere used at a later stage of the analysis for a profile-likelihood fit to the data in the search for a signal contribution, while the VRs were used to validate the modelling of different background contributions. A summary of the selection requirements used to define the four analysis regions is given in Table 1. All requirements mentioned before are common to all regions considered. The SR was defined by narrowing the jet requirement relative to the basic event selection. Each event had to have exactly one jet with pT>30 GeV and |η|<2.5, i.e. events with additional central jets were vetoed. This single jet had to be b-tagged. The selection efficiency for signal events in which the top quark decays into Wband the resulting Wboson decays leptonically was 1.36% for ugt events and 2.30% for cgt events. For the ugt search, the SR was split according to the sign of the charge of the primary lepton sgnq(). Two NN discriminants D1and D2, described in Sect. 6, were formed to separate signal and background events in these three SRs. The first VR was defined for validating the modelling of the events kinematics of W+jets production (W+jetsVR) by the Sherpa 2.2.1 generator. To suppress top-quark backgrounds a less stringent b-tagging requirement was used. Exactly one jet with pT>30 GeV was required to be btagged at a working point with an efficiency of 60%. All other selection requirements were the same as for the SR. However, events in the SR were vetoed. The modified btagging requirement leads to a different flavour composition of the jets in the W+jetsVR compared to the SR; the components of W+c-jets and W+light-flavour jets are increased relative to W+b-jets. To enrich the region further in W+jets events and reduce the number of signal events, the NN discriminant D1, specified in Sect. 6, was required to be in the range 0.3<D1<0.6. The modelling of events with positive lepton charge was separately checked by requiring the NN discriminant D2to be in the range 0.3<D2<0.6, defining the +W+jetsVR. When normalising the FCNC processes to the observed limits from the previous ATLAS results obtained at a centre-of-mass energy of 8TeV, the FCNC signal contamination is 1.2% in the W+jetsVR and 0.9% in the +W+jetsVR. The second VR was enriched in t¯ tevents by selecting events with exactly two b-tagged jets using the 30% btagging working point (t¯ tVR). When normalising the FCNC processes to the observed limits from the previous ATLAS results obtained at a centre-of-mass energy of 8TeV, the FCNC signal contamination is at a very low level of a few times 10−4. The third VR checked the modelling of tq events (tqVR). Events with exactly two jets were required. Exactly one of the jets had to be b-tagged at the 30% efficiency working point, while the second jet was required to be in the forward region with |η|>2.5, which is a characteristic feature of tq events. Thus, the tqVR was a subset of the SR, since Table 1 Summary of selection requirements used to define the four analysis regions. The left column lists the observables on which the requirements are based. The first part of the table lists requirements which are common to all four analysis regions and define the basic event selectiondescribedinSect.4.2.Tightelectronsandmediummuonswere counted based on a pTthreshold of 27GeV and they are a subset of the corresponding Loose quality category. Loose charged leptons had to exceed a threshold of pT() =10 GeV. The transverse mass of the W boson, mT(W), is defined in Eq. (1). The efficiency of the b-tagging working point used to identify b-jets is denoted by b. The symbol D1 represents one of the NN discriminants defined in Sect. 6 Observable Common requirements nTight(e)+nMedium(μ) =1 nLoose(e)+nLoose(μ) =1 Emiss T>30 GeV mT(W) > 50 Gev n(j)≥1 pT()>50 Gev ·1−π−|φ(j1,)| π−1 Analysis regions SR W+jetsVR t¯ tVR tqVR n(|η(j)|<2.5)=1=1=2=1 n(b)=1=1=2=1 b30% 60% (veto 30%) 30% 30% n(|η(j)|>2.5)≥0≥0≥0=1 D1(2)–0.3<D1(2)<0.6– 0.2<D1(2)<0.4 123 334 Page 8 of 35 Eur. Phys. J. C (2022) 82 :334 there was no condition on jets in the forward region when defining the SR. To further enhance the fraction of tq events and to suppress signal events, the NN discriminant D1was required to be in the range 0.2<D1<0.4. The modelling of events with positive lepton charge was separately checked by requiring the NN discriminant D2to be in the range 0.2<D2<0.4, defining the +tqVR. When normalising the FCNC processes to the observed limits from the previous ATLAS results obtained at a centre-of-mass energy of8TeV,theFCNCsignalcontaminationis1.2%inthetqVR (cgt analysis) and 0.8% in the +tqVR. 5 Estimation of the multijet background By requiring electron and muon candidates to be isolated, the object definition and the event selection strongly favour prompt leptons originating from decays of Wbosons or Zbosons. However, there is a small probability for nonpromptelectronsormuonsoccurringinhadrondecays, either directly or through the decay of a τ-lepton, to be reconstructed as isolated leptons. The main source is b-hadron decays in jets, but c-hadrons and long-lived weakly decaying states such as π±and Kmesons also contribute. In addition, prompt electrons are mimicked by fake electrons which arise from the misidentification of direct photons, photons from π0decays, or bremsstrahlung and photon conversions. Even though the probabilities of misidentification are relatively low, some multijet events still pass the selection and contribute to the background, since their production crosssection is approximately three orders of magnitude higher thanthecross-sectionsoftop-quarkproductionprocesses.As themechanismsofmisidentificationare notwellmodelledby the detector simulation, the rate of the multijet background was determined in a data-driven way by fitting the Emiss Tdistribution for events with an electron (electron channel) and the mT(W)distribution for events with a muon (muon channel). In the electron channel, the multijet background was modelled using the jet-electron method [83]. Simulated events from dijet production (see Sect. 3.4 for a description of the sample) were selected if they contained a jet depositing a large fraction (>80%) of its energy in the electromagnetic calorimeter. This jet was classified as an electron, the jetelectron, and treated in the subsequent steps of the analysis in the same way as a properly identified prompt electron. The jet-electrons had to pass the nominal pTand |η| requirements, but electron identification requirements were not applied. Since the relative numbers of electrons detected in the barrel (|η|<1.37) and endcap (|η|>1.52) sections of the electromagnetic calorimeter were not modelled well enough by the sample of simulated dijet events, the electron channel was divided into two subchannels: a barrel-electron channel and an endcap-electron channel. In the muon channel, multijet events were modelled with collision events highly enriched in non-prompt muons [83]. Starting from the same sample of collision events as the nominal selection, a subset of events enriched in non-prompt muons was obtained by inverting or modifying some of the muon isolation requirements, such that the resulting sample did not overlap with the nominal sample. The kinematic requirements on muon pTand |η|remained the same as for the nominal selection. The rate of the multijet background was normalised by performing a binned maximum-likelihood fit to the Emiss T and mT(W)distributions observed in the electron and muon channels, respectively. All selection criteria were applied, except for the Emiss Trequirement in the electron channels (barrel and endcap) and the requirement on mT(W)in the muon channel. The three channels were further split according to the sign of the charge of the primary lepton sgnq(), leading to six channels per analysis region. Separate fits were performed for the SR and the three VRs. In each region, all six channels were fit simultaneously. Since the multijet background is expected to be independent of lepton charge, its rates in the +and the −channels were assumed to be the same. On the other hand, the rates of some of the other background processes, i.e. tq,t¯ band W+jets production, are different in the +and the −channels due to the PDFs. For the purpose of these fits, scattering processes other than multijet production were grouped in the following way: (1) top-quark production comprises t¯ tproduction and all three single-top-quark production processes (tq,t¯ b and tW production), (2) W+jets production, including the production of light-quark, gluon, b-quark and c-quark jets in association with a Wboson, and (3) Z+jets and diboson production (WW,WZ and ZZ production). The templates of the fit distributions for these three groups of processes were derived from simulated events and the rates were normalised to the theory predictions reported in Sect. 3.Asthe shapes of the distributions for Z+jets and diboson production are very similar to those of W+jets production, the rates of Z+jets and diboson production were fixed in the fitting process to the values predicted by simulation. Uncertainties in the normalisation of top-quark production and W+jets production were accounted for by Gaussian constraints on the normalisation factors of these groups of processes. In the W+jetsVR, only the rate of W+jets production was varied, while the top-quark background was fixed. Similarly, in the t¯ tVR and tqVR only the rate of top-quark production was varied, while the rate of W+jets production was fixed. In the SR, both rates were free to vary within uncertainties. The fits yielded estimates of the rates of the multijet background in the four analysis regions before applying 123 Eur. Phys. J. C (2022) 82 :334 Page 9 of 35 334 0 20000 40000 Events / 10 GeV 0 50 100 150 [GeV] miss T E 0.8 1 1.2 Pred. Data barrel SR + e ATLAS -1 139 fb,=13 TeVs Data qt,tq bt,b,Wt,ttt +jetsW VV+jets,Z Multijet Uncertainty 0 20000 40000 60000 Events / 10 GeV 0 50 100 150 200 (W) [GeV] T m 0.8 1 1.2 Pred. Data SR + μ ATLAS -1 139 fb,=13 TeVs Data qt,tq bt,b,Wt,ttt +jetsW VV+jets,Z Multijet Uncertainty (a) (b) Fig. 2 Illustration of the estimation of the multijet background by fitting the Emiss Tand mT(W)distributions in the analysis regions. As representative examples, the Emiss Tdistribution is shown in the e+barrel channel in (a)andthemT(W)distribution is shown in the μ+channel in (b). Both distributions are in the SR. The stacked histograms were normalised to the fit result. The uncertainty band represents the uncertainty due to limited sample size and the rate uncertainties of the different processes (20% for W+jets production, 30% for the multijet background and 6% for the top-quark processes). The ratio of observed to predicted (Pred.) numbers of events in each bin is shown in the lower panel. Events beyond the axis range are included in the last bin the requirements on Emiss Tand mT(W). An uncertainty of 30% was assigned to the estimates, covering alternative results obtained in studies of fits to different discriminating observables. As examples illustrating the fit results, Fig. 2 shows the Emiss Tdistribution in the e+barrel channel of the SR and the mT(W)distributionintheμ+channel of the SR. The stacked histograms were normalised to the fit result. The low Emiss Tand mT(W)regions drove the estimate of the multijet background, since its fraction of the total yield was larger there than at higher values of the two observables. The yield of the multijet background after applying the requirements of Emiss T>30 GeV and mT(W)>50 GeV is based on the normalised histograms of the multijet background normalised to the fit result and was later used as a starting value for the profile-likelihood fit in the final statistical analysis. The normalisation factors obtained for top-quark production and W+jets production were applied to normalise the respectivebackgroundswhenvalidating the modelling ofkinematic distributions prior to the statistical analysis of the NN discriminants, but they were not used in the statistical analysis itself. All backgrounds other than the multijet background were modelled by simulated events and the event rate was estimated by scaling the samples of simulated events to the integrated luminosity of the sample of collision data being analysed. The event kinematics of the multijet background is described with the jet-electron model and with non-prompt muon events, normalising the rate of the multijet background to the results of the fits to the Emiss Tand mT(W)distributions. Figure 3provides a summary of the fractional contributions of the different background processes to the expected event yield in the SR. +jets 36.8%W 4.8%VV+jets,Z Multijet 7.6% 22.2%qt ,tq 28.7%bt ,b,Wt,ttt SR ATLAS -1 139 fb,=13 TeVs Fig. 3 Pie chart of the background composition of the SR. The SR comprises the two electron channels (barrel and endcap) and the muon channel. The pre-fit event yields are reported in Table 3 The three largest backgrounds are W+jets production, the combined t¯ t-tW-t¯ bbackground, and tq production. 6 Neural networks separating signal and background events Two NNs were employed to enhance the separation of signal events from background events by combining several kinematic (input) variables to form two discriminants named D1and D2. The kinematics of signal events depends on whether the quark (antiquark) in the initial state is a valence quark or a sea quark (antiquark). Sea quarks (antiquarks) and valence quarks of the proton carry, on average, different fractions xof the proton momentum and this difference leads to different rapidity distributions for the corresponding produced top quarks (antiquarks) and their decay prod123 334 Page 16 of 35 Eur. Phys. J. C (2022) 82 :334 Table 3 Expected pre-fit and post-fit event yields along with the observed event yield in the SR. The quoted uncertainties include the statistical and systematic uncertainties of the event yields. Correlations, includinganticorrelations, among thenuisance parameters relatedtothe uncertainties were taken into account as determined in the maximumlikelihood fit Process Pre-fit Post-fit cgt Post-fit ugt ugt FCNC process 0 0 1200 ±2100 cgt FCNC process 0 4100 ±4500 0 tq 138,600 ±9300 149,200 ±9400 150,000 ±10,000 t¯ t,tW,t¯ b179,000 ±17,000 179,000 ±14,000 175,200 ±9700 W+jets 229,000 ±30,000 281,000 ±21,000 292,000 ±18,000 Z+jets, VV 29,700 ±6000 30,000 ±6000 29,800 ±6000 Multijet 47,000 ±14,000 45,000 ±14000 40,000 ±12,000 Total 650,000 ±46,000 688,600 ±2400 688,700 ±3500 Observed 688,380 688,380 688,380 Fig. 7 The NN discriminant D1of the cgt search is shown with the post-fit normalisation applied to the stacked histograms of the different hard-scattering processes. The histogram in ashows the full discriminant range. The histogram bshows a zoomed-in view of the high discriminant region between 0.7and1.0. The hatched bands represent the post-fit uncertainty of the total event yield in each bin. Correlations among uncertainties were taken into account as determined in the fit The observed discriminant distributions are very well described by the fitted model and they are compatible with the background-only hypothesis. 8.2 Upper limits on cross-sections, EFT coefficients and branching ratios Since the observed NN-discriminant distributions were found to be compatible with the background-only hypothesis, upper limits were set on the cross-sections of the ugt and the cgt processes at the 95% confidence level (CL). The limits were computed by applying the CLsmethod [93,94]as implemented in the RooFit package [95] to the test statistic 123 Eur. Phys. J. C (2022) 82 :334 Page 17 of 35 334 ˜qμ= ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ −2ln⎛ ⎝ Lμ,ˆ ˆ  θ(μ) L0,ˆ ˆ  θ(0)⎞ ⎠if ˆμ<0, −2ln⎛ ⎝ Lμ,ˆ ˆ  θ(μ) Lˆμ,ˆ  θ⎞ ⎠if 0 ≤ˆμ≤μ, 0ifˆμ>μ. (2) In Eq. (2), the symbols ˆμand ˆ  θrepresent the values of the parameters maximising the likelihood function and ˆ ˆ  θare the values of the nuisance parameters which maximise the likelihood function for a fixed value of μ. The obtained upper limits on the cross-sections times branching ratio are σ(ugt)×B(t→Wb)×B(W→ν) < 3.0 pb and (3) σ(cgt)×B(t→Wb)×B(W→ν) < 4.7pb,(4) with B(W→ν) =0.325 being the sum of branching ratios of all three leptonic decay modes of the Wboson. The expected cross-section-times-branching-ratio limits are 2.4 pb and 2.5 pb, respectively. The observed limits are larger than the expected ones because non-zero signal yields are fitted. The cross-section limits are interpreted within the TopFCNC model [14], which implements an effective operator formalism and is based on the FeynRules 2.0 framework [96]usedinsidetheMadGraph5_aMC@NLOevent generator. With this set-up the cross-sections of the FCNC processes under consideration were calculated at NLO in QCD, providing a significant improvement on LO calculations, since NLO corrections for this class of processes were found to be between 30% and 80% [14].4In the TopFCNC model, thetwooperators Out uG andOct uG generatetheugt andcgt processes, and the coupling strengths of the corresponding vertices are given by the two coefficients Cut uG and Cct uG divided by the square of the new-physics scale . The total crosssections are found to be related to the EFT coefficients by σ(u+g→t)=2773 ×Cut uG 22 pbTeV4and (5) σ(c+g→t)=719 ×Cct uG 22 pbTeV4.(6) Using Eqs. (5) and (6) the cross-section limits of Eqs. (3) and (4) become limits on the EFT coefficients: |Cut uG| 2<0.057TeV−2and |Cct uG| 2<0.14 TeV−2at the 95% CL.(7) 4While MadGraph5_aMC@NLOcan be used for a fixed-order calculation at NLO, events for which a matching to a parton-shower program is needed can only be generated at LO in the current implementation. Since the u-quark is a valence quark of the proton, it carries on average a much larger momentum fraction than the c-quark, and thus the cross-section of the ugt process is much larger than the cross-section of the cgt process, when considering the same value of the corresponding coefficient (Cut uG =Cct uG). For a certain experimental sensitivity, the sensitivity to Cut uG is therefore higher than to Cct uG. However, in the two-Higgs-doublet models mentioned in Sect. 1the predicted FCNC couplings to charm quarks are much higher thantoupquarks.Forthis reason, thelimitsonCct uG havephenomenological relevance even though they are weaker than the limits on Cut uG. The limits presented in Eq. (7) tighten constraints set by the CMS Collaboration using dilepton events recorded in Run 2 of the LHC [97] by more than a factor of three. The CMS analysis searched for tW production crosssection via FCNC. An alternative and very accessible way of comparing the upper limits on the EFT coefficient with previous results uses the branching ratios of FCNC top-quark decays: B(t→u+ g)and B(t→c+g). These branching ratios are given as a function of the EFT coefficients by the relation B(t→q+g)=0.0186 ×Cqt uG 22 TeV4, with q=u,c[98], assuming the top-quark width to be t= 1.32 GeV. The resulting upper limits at the 95% CL are B(t→u+g)<0.61 ×10−4and B(t→c+g)<3.7×10−4.(8) These new bounds are approximately a factor of two more restrictive than the previous ATLAS results obtained at a centre-of-mass energy of 8 TeV [12]. The bound on the cgt mode is comparable to that of the CMS analysis combining 7 and 8 TeV data [11], while the bound on the ugt mode is significantly weaker than the CMS one. 8.3 Comparison of expected upper limits For assessing the sensitivity of this analysis and comparing it with the sensitivity of other results, and for evaluating the impact of different groups of systematic uncertainties, the computation of expected upper limits is more suitable than using the observed results, since biases caused by statistical fluctuations are avoided and the signal contribution is set to zero. The expected limits were derived by using the expected distributions of the NN discriminants, considering background processes only. The initially predicted rate of the W+jets process was scaled by a factor of μ(W+b)=1.22 or μ(W−b)=1.30 for the ugt analysis and by a factor of μ(Wb)=1.18 for the cgt analysis. These normalisation factors were obtained from background-only fits to the observed NN discriminants in background-dominated regions, namely 123 334 Page 18 of 35 Eur. Phys. J. C (2022) 82 :334 Table 4 Impact of systematic uncertainties on the expected upper limits on the branching ratios of the FCNC decay modes B(t→u+g) and B(t→c+g). Four scenarios are considered: (1) include only data statistical uncertainties, (2) include the experimental systematic uncertainties in addition, (3) include all systematic uncertainties except for the MC statistical uncertainties and (4) include all uncertainties Scenario Description Bexp 95 (t→u+g)Bexp 95 (t→c+g) (1) Data statistical only 1.1×10−52.4×10−5 (2) Experimental uncertainties also 3.1×10−512 ×10−5 (3) All uncertainties except MC statistical 3.9×10−518 ×10−5 (4) All uncertainties 4.9×10−520 ×10−5 the ranges 0.0to0.7fortheD1discriminant and 0.0to0.55 for the D2discriminant. The resulting expected upper limits in terms of branching ratios are Bexp 95 (t→u+g)=0.49 ×10−4and Bexp 95 (t→c+g)=2.0×10−4.(9) Compared to the ATLAS analysis at 8 TeV centre-of-mass energy, significant improvements in sensitivity are obtained for both the ugt and cgt analyses. However, the improvements in sensitivity are smaller than expected from a simple scaling of the number of expected events with the increase in integrated luminosity and the increase in signal crosssections. The main reason for this effect is that the crosssections of the top-quark background processes rise faster with the centre-of-mass energy than the cross-sections of the FCNC signal processes. The expected upper limits are lower than the observed upper limits in Eq. (8), since non-zero, yet insignificant, signalsareobserved,whiletheexpectedlimitsareobtainedfrom expected distributions without any signal events included. The effect is larger for the cgt analysis than for the ugt analysis because the fitted signal event yield is more than three times larger in the cgt case, as seen in Table 3. In order to quantify the impact of different groups of systematic uncertainties, expected upper limits were computed for different scenarios: (1) include only data statistical uncertainties,(2)includetheexperimentalsystematicuncertainties in addition, (3) include all systematic uncertainties except for the MC statistical uncertainties and (4) include all uncertainties. The last case leads to the limits quoted in Eq. (9). The results of this study are reported in Table 4and clearly demonstrate how large the impact of systematic uncertainties is. Both the experimental and modelling uncertainties are relevant. MC statistical uncertainties increase the expected upper limits by approximately 20% in the ugt case and by about 10% for the cgt process. 9 Conclusions A search for the production of a single top quark via lefthanded FCNC interactions of a top quark, a gluon and an up or charm quark was performed. The analysis used the full LHCRun2proton–protoncollisiondatasetrecordedwiththe ATLAS detector at a centre-of-mass energy of 13TeV, corresponding to an integrated luminosity of 139 fb−1. Events with exactly one electron or muon, exactly one b-tagged jet andmissingtransversemomentumwereselected,resembling the decay products of a single top quark. A dedicated highpurity working point was devised for the identification of b-jets, reducing the background of W+c-jets and W+lightflavour jets considerably. Neural networks were used to separate signal events from background events, and a binned maximum-likelihood fit to the neural-network discriminants wasperformedtosearchforacontributionfromtheu+g→t and c+g→tprocesses. The observed distributions were found to be compatible with the background-only hypothesis and therefore upper limits on the production cross-sections times branching ratios were derived, leading to σ(ugt)×B(t→Wb)×B(W→ν) < 3.0 pb and σ(cgt)×B(t→Wb)×B(W→ν) < 4.7pb. The cross-section limits were interpreted in the framework of an effective field theory, yielding limits on the coefficients of the operators producing the FCNC processes under investigation: |Cut uG|/2<0.057 TeV−2and |Cct uG|/2< 0.14 TeV−2at the 95% confidence level. These limits are also expressed in terms of branching ratios of corresponding FCNC top-quark decays, resulting in B(t→u+g)<0.61 ×10−4and B(t→c+g) <3.7×10−4. The new bounds improve on previous ATLAS results obtained at a centre-of-mass energy of 8 TeV by approximately a factor of two. Acknowledgements We thank CERN for the very successful operation of the LHC, as well as the support staff from our institutions without whom ATLAS could not be operated efficiently. We acknowledge the support of ANPCyT, Argentina; YerPhI, Armenia; ARC, Australia; BMWFWandFWF,Austria;ANAS,Azerbaijan; SSTC,Belarus;CNPq and FAPESP, Brazil; NSERC, NRC and CFI, Canada; CERN; ANID, Chile; CAS, MOST and NSFC, China; Minciencias, Colombia; MSMT CR, MPO CR and VSC CR, Czech Republic; DNRF and DNSRC, Denmark; IN2P3-CNRS and CEA-DRF/IRFU, France; SRNSFG, Georgia; 123 Eur. Phys. J. C (2022) 82 :334 Page 19 of 35 334 BMBF, HGF and MPG, Germany; GSRI, Greece; RGC and Hong Kong SAR, China; ISF and Benoziyo Center, Israel; INFN, Italy; MEXT and JSPS, Japan; CNRST, Morocco; NWO, Netherlands; RCN, Norway; MEiN,Poland;FCT,Portugal;MNE/IFA,Romania;JINR;MESofRussiaandNRCKI,RussianFederation;MESTD,Serbia;MSSR,Slovakia; ARRS and MIZŠ, Slovenia; DSI/NRF, South Africa; MICINN, Spain; SRC and Wallenberg Foundation, Sweden; SERI, SNSF and Cantons of Bern and Geneva, Switzerland; MOST, Taiwan; TAEK, Turkey; STFC, United Kingdom; DOE and NSF, United States of America. In addition, individual groups and members have received support from BCKDF, CANARIE, Compute Canada and CRC, Canada; COST, ERC, ERDF, Horizon 2020 and Marie Skłodowska-Curie Actions, European Union; Investissements d’Avenir Labex, Investissements d’Avenir Idex and ANR, France; DFG and AvH Foundation, Germany; Herakleitos, Thales and Aristeia programmes co-financed by EU-ESF and the Greek NSRF, Greece; BSF-NSF and GIF, Israel; Norwegian Financial Mechanism 2014-2021, Norway; NCN and NAWA, Poland; La Caixa Banking Foundation, CERCA Programme Generalitat de Catalunya and PROMETEO and GenT Programmes Generalitat Valenciana, Spain; Göran Gustafssons Stiftelse, Sweden; The Royal Society and Leverhulme Trust, United Kingdom. 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 (UK) and BNL (USA), the Tier-2 facilities worldwide and large non-WLCG resource providers. Major contributors of computing resources are listed in Ref. [99]. Open Access This article is licensed under a Creative Commons Attribution4.0InternationalLicense,whichpermits use,sharing,adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. 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J. Kareem163b , I. Karkanias158 , S. N. Karpov77 , Z. M. Karpova77 , V. Kartvelishvili87 , A. N. Karyukhin118 ,E.Kasimi 158 ,C.Kato 58d , J. Katzy44 , K. Kawade146 , K. Kawagoe85 , T. Kawaguchi112 , T. Kawamoto140 , G. Kawamura51,E.F.Kay 171 , F. I. Kaya165 , S. Kazakos12 , V. F. Kazanin117a,117b ,Y.Ke 151 , J. M. Keaveney31a , R. Keeler171 , J. S. Keller32 ,D.Kelsey 152 , J. J. Kempster19 , J. Kendrick19 , K. E. Kennedy37 , O. Kepka136 , S. Kersten177 , B. P. Kerševan89 , S. Ketabchi Haghighat162 , M. Khandoga131 , A. Khanov125 , A. G. Kharlamov117a,117b , T. Kharlamova117a,117b , E. E. Khoda144 , T.J.Khoo 17 , G. Khoriauli172 , E. Khramov77 , J. Khubua155b , S. Kido80 , M. Kiehn34 , A. Kilgallon127 ,E.Kim 160 ,Y.K.Kim 35 ,N.Kimura 92 , A. Kirchhoff51 , D. Kirchmeier46 ,C.Kirfel 22 ,J.Kirk 139 , A. E. Kiryunin111 , T. Kishimoto159 , D. P. Kisliuk162, C. Kitsaki9, O. Kivernyk22 , T. Klapdor-Kleingrothaus50 , M. Klassen59a , C. Klein32 , L. Klein172 ,M.H.Klein 102 , M. Klein88 , U. Klein88 , P. Klimek34 , A. Klimentov27 , F. Klimpel111 , T. Klingl22 , T. Klioutchnikova34 , F. F. Klitzner110 , P. Kluit115 , S. Kluth111 , E. Kneringer74 , T. M. Knight162 , A. Knue50 , D. Kobayashi85, R. Kobayashi83 , M. Kobel46 , M. Kocian149 , T. Kodama159, P. Kodys138 , D. M. Koeck152 , P. T. Koenig22 , T. Koffas32 , N. M. Köhler34 ,M.Kolb 140 , I. Koletsou4, T. Komarek126 , K. Köneke50 , A.X.Y.Kong 1, T. Kono122 , V. Konstantinides92, N. Konstantinidis92 , B. Konya94 , R. Kopeliansky63 , S. Koperny81a , K. Korcyl82 , K. Kordas158 , G. Koren157,A.Korn 92 ,S.Korn 51 , I. Korolkov12 , E. V. Korolkova145, N. Korotkova109 , B. Kortman115 , O. Kortner111 , S. Kortner111 , W. H. Kostecka116 , V. V. Kostyukhin147,161 , A. Kotsokechagia62 ,A.Kotwal 47 , A. Koulouris34 , A. Kourkoumeli-Charalampidi68a,68b , C. Kourkoumelis8, 123 334 Page 32 of 35 Eur. Phys. J. C (2022) 82 :334 47 Department of Physics, Duke University, Durham, NC, USA 48 SUPA-School of Physics and Astronomy, University of Edinburgh, Edinburgh, UK 49 INFN e Laboratori Nazionali di Frascati, Frascati, Italy 50 Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Freiburg, Germany 51 II. Physikalisches Institut, Georg-August-Universität Göttingen, Göttingen, Germany 52 Département de Physique Nucléaire et Corpusculaire, Université de Genève, Geneva, Switzerland 53 (a)Dipartimento di Fisica, Università di Genova, Genoa, Italy; (b)INFN Sezione di Genova, Genoa, Italy 54 II. Physikalisches Institut, Justus-Liebig-Universität Giessen, Giessen, Germany 55 SUPA-School of Physics and Astronomy, University of Glasgow, Glasgow, UK 56 LPSC, Université Grenoble Alpes, CNRS/IN2P3, Grenoble INP, Grenoble, France 57 Laboratory for Particle Physics and Cosmology, Harvard University, Cambridge, MA, USA 58 (a)Department of Modern Physics and State Key Laboratory of Particle Detection and Electronics, University of Science and Technology of China, Hefei, China; (b)Institute of Frontier and Interdisciplinary Science and Key Laboratory of Particle Physics and Particle Irradiation (MOE), Shandong University, Qingdao, China; (c)School of Physics and Astronomy, Key Laboratory for Particle Astrophysics and Cosmology (MOE), SKLPPC, Shanghai Jiao Tong University, Shanghai, China; (d)Tsung-Dao Lee Institute, Shanghai, China 59 (a)Kirchhoff-Institut für Physik, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany; (b)Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany 60 (a)Department of Physics, Chinese University of Hong Kong, Shatin, N.T., Hong Kong, China; (b)Department of Physics, University of Hong Kong, Hong Kong, China; (c)Department of Physics and Institute for Advanced Study, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China 61 Department of Physics, National Tsing Hua University, Hsinchu, Taiwan 62 IJCLab, CNRS/IN2P3, Université Paris-Saclay, 91405 Orsay, France 63 Department of Physics, Indiana University, Bloomington, IN, USA 64 (a)INFN Gruppo Collegato di Udine, Sezione di Trieste, Udine, Italy; (b)ICTP, Trieste, Italy; (c)Dipartimento Politecnico di Ingegneria e Architettura, Università di Udine, Udine, Italy 65 (a)INFN Sezione di Lecce, Lecce, Italy; (b)Dipartimento di Matematica e Fisica, Università del Salento, Lecce, Italy 66 (a)INFN Sezione di Milano, Milan, Italy; (b)Dipartimento di Fisica, Università di Milano, Milan, Italy 67 (a)INFN Sezione di Napoli, Naples, Italy; (b)Dipartimento di Fisica, Università di Napoli, Naples, Italy 68 (a)INFN Sezione di Pavia, Pavia, Italy; (b)Dipartimento di Fisica, Università di Pavia, Pavia, Italy 69 (a)INFN Sezione di Pisa, Pisa, Italy; (b)Dipartimento di Fisica E. Fermi, Università di Pisa, Pisa, Italy 70 (a)INFN Sezione di Roma, Rome, Italy; (b)Dipartimento di Fisica, Sapienza Università di Roma, Rome, Italy 71 (a)INFN Sezione di Roma Tor Vergata, Rome, Italy; (b)Dipartimento di Fisica, Università di Roma Tor Vergata, Rome, Italy 72 (a)INFN Sezione di Roma Tre, Rome, Italy; (b)Dipartimento di Matematica e Fisica, Università Roma Tre, Rome, Italy 73 (a)INFN-TIFPA, Povo, Italy; (b)Università degli Studi di Trento, Trento, Italy 74 Institut für Astround Teilchenphysik, Leopold-Franzens-Universität, Innsbruck, Austria 75 University of Iowa, Iowa City, IA, USA 76 Department of Physics and Astronomy, Iowa State University, Ames, IA, USA 77 Joint Institute for Nuclear Research, Dubna, Russia 78 (a)Departamento de Engenharia Elétrica, Universidade Federal de Juiz de Fora (UFJF), Juiz de Fora, Brazil; (b)Universidade Federal do Rio De Janeiro COPPE/EE/IF, Rio de Janeiro, Brazil; (c)Instituto de Física, Universidade de São Paulo, São Paulo, Brazil 79 KEK, High Energy Accelerator Research Organization, Tsukuba, Japan 80 Graduate School of Science, Kobe University, Kobe, Japan 81 (a)AGH University of Science and Technology, Faculty of Physics and Applied Computer Science, Kraków, Poland; (b)Marian Smoluchowski Institute of Physics, Jagiellonian University, Kraków, Poland 82 Institute of Nuclear Physics Polish Academy of Sciences, Kraków, Poland 83 Faculty of Science, Kyoto University, Kyoto, Japan 84 Kyoto University of Education, Kyoto, Japan 85 Research Center for Advanced Particle Physics and Department of Physics, Kyushu University, Fukuoka , Japan 86 Instituto de Física La Plata, Universidad Nacional de La Plata and CONICET, La Plata, Argentina 87 Physics Department, Lancaster University, Lancaster, UK 123 Eur. Phys. J. C (2022) 82 :334 Page 33 of 35 334 88 Oliver Lodge Laboratory, University of Liverpool, Liverpool, UK 89 Department of Experimental Particle Physics, Jožef Stefan Institute and Department of Physics, University of Ljubljana, Ljubljana, Slovenia 90 School of Physics and Astronomy, Queen Mary University of London, London, UK 91 Department of Physics, Royal Holloway University of London, Egham, UK 92 Department of Physics and Astronomy, University College London, London, UK 93 Louisiana Tech University, Ruston, LA, USA 94 Fysiska institutionen, Lunds universitet, Lund, Sweden 95 Departamento de Física Teorica C-15 and CIAFF, Universidad Autónoma de Madrid, Madrid, Spain 96 Institut für Physik, Universität Mainz, Mainz, Germany 97 School of Physics and Astronomy, University of Manchester, Manchester, UK 98 CPPM, CNRS/IN2P3, Aix-Marseille Université, Marseille, France 99 Department of Physics, University of Massachusetts, Amherst, MA, USA 100 Department of Physics, McGill University, Montreal, QC, Canada 101 School of Physics, University of Melbourne, Victoria, Australia 102 Department of Physics, University of Michigan, Ann Arbor, MI, USA 103 Department of Physics and Astronomy, Michigan State University, East Lansing, MI, USA 104 B.I. Stepanov Institute of Physics, National Academy of Sciences of Belarus, Minsk, Belarus 105 Research Institute for Nuclear Problems of Byelorussian State University, Minsk, Belarus 106 Group of Particle Physics, University of Montreal, Montreal, QC, Canada 107 P.N. Lebedev Physical Institute of the Russian Academy of Sciences, Moscow, Russia 108 National Research Nuclear University MEPhI, Moscow, Russia 109 D.V. Skobeltsyn Institute of Nuclear Physics, M.V. Lomonosov Moscow State University, Moscow, Russia 110 Fakultät für Physik, Ludwig-Maximilians-Universität München, Munich, Germany 111 Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), Munich, Germany 112 Graduate School of Science and Kobayashi-Maskawa Institute, Nagoya University, Nagoya, Japan 113 Department of Physics and Astronomy, University of New Mexico, Albuquerque, NM, USA 114 Institute for Mathematics, Astrophysics and Particle Physics, Radboud University/Nikhef, Nijmegen, The Netherlands 115 Nikhef National Institute for Subatomic Physics and University of Amsterdam, Amsterdam, The Netherlands 116 Department of Physics, Northern Illinois University, DeKalb, IL, USA 117 (a)Budker Institute of Nuclear Physics and NSU, SB RAS, Novosibirsk, Russia; (b)Novosibirsk State University Novosibirsk, Novosibirsk, Russia 118 Institute for High Energy Physics of the National Research Centre Kurchatov Institute, Protvino, Russia 119 Institute for Theoretical and Experimental Physics named by A.I. Alikhanov of National Research Centre “Kurchatov Institute”, Moscow, Russia 120 (a)New York University Abu Dhabi, Abu Dhabi, United Arab Emirates; (b)United Arab Emirates University, Al Ain, United Arab Emirates; (c)University of Sharjah, Sharjah, United Arab Emirates 121 Department of Physics, New York University, New York, NY, USA 122 Ochanomizu University, Otsuka, Bunkyo-ku, Tokyo, Japan 123 Ohio State University, Columbus, OH, USA 124 Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma, Norman, OK, USA 125 Department of Physics, Oklahoma State University, Stillwater, OK, USA 126 Palacký University, Joint Laboratory of Optics, Olomouc, Czech Republic 127 Institute for Fundamental Science, University of Oregon, Eugene, OR, USA 128 Graduate School of Science, Osaka University, Osaka, Japan 129 Department of Physics, University of Oslo, Oslo, Norway 130 Department of Physics, Oxford University, Oxford, UK 131 LPNHE, CNRS/IN2P3, Sorbonne Université, Université de Paris, Paris, France 132 Department of Physics, University of Pennsylvania, Philadelphia, PA, USA 133 Konstantinov Nuclear Physics Institute of National Research Centre “Kurchatov Institute”, PNPI, St. Petersburg, Russia 134 Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA, USA 135 (a)Laboratório de Instrumentação e Física Experimental de Partículas - LIP, Lisbon, Portugal; (b)Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Lisbon, Portugal; (c)Departamento de Física, Universidade de Coimbra, 123 334 Page 34 of 35 Eur. Phys. J. C (2022) 82 :334 Coimbra, Portugal; (d)Centro de Física Nuclear da Universidade de Lisboa, Lisbon, Portugal; (e)Departamento de Física, Universidade do Minho, Braga, Portugal; (f)Departamento de Física Teórica y del Cosmos, Universidad de Granada, Granada, Spain; (g)Instituto Superior Técnico, Universidade de Lisboa, Lisbon, Portugal 136 Institute of Physics of the Czech Academy of Sciences, Prague, Czech Republic 137 Czech Technical University in Prague, Prague, Czech Republic 138 Charles University, Faculty of Mathematics and Physics, Prague, Czech Republic 139 Particle Physics Department, Rutherford Appleton Laboratory, Didcot, UK 140 IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette, France 141 Santa Cruz Institute for Particle Physics, University of California Santa Cruz, Santa Cruz, CA, USA 142 (a)Departamento de Física, Pontificia Universidad Católica de Chile, Santiago, Chile; (b)Instituto de Investigación Multidisciplinario en Ciencia y Tecnología, y Departamento de Física, Universidad de La Serena, Santiago, Chile; (c)Universidad Andres Bello, Department of Physics, Santiago, Chile; (d)Instituto de Alta Investigación, Universidad de Tarapacá, Arica, Chile; (e)Departamento de Física, Universidad Técnica Federico Santa María, Valparaiso, Chile 143 Universidade Federal de São João del Rei (UFSJ), São João del Rei, Brazil 144 Department of Physics, University of Washington, Seattle, WA, USA 145 Department of Physics and Astronomy, University of Sheffield, Sheffield, UK 146 Department of Physics, Shinshu University, Nagano, Japan 147 Department Physik, Universität Siegen, Siegen, Germany 148 Department of Physics, Simon Fraser University, Burnaby, BC, Canada 149 SLAC National Accelerator Laboratory, Stanford, CA, USA 150 Department of Physics, Royal Institute of Technology, Stockholm, Sweden 151 Departments of Physics and Astronomy, Stony Brook University, Stony Brook, NY, USA 152 Department of Physics and Astronomy, University of Sussex, Brighton, UK 153 School of Physics, University of Sydney, Sydney, Australia 154 Institute of Physics, Academia Sinica, Taipei, Taiwan 155 (a)E. Andronikashvili Institute of Physics, Iv. Javakhishvili Tbilisi State University, Tbilisi, Georgia; (b)High Energy Physics Institute, Tbilisi State University, Tbilisi, Georgia 156 Department of Physics, Technion, Israel Institute of Technology, Haifa, Israel 157 Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv, Israel 158 Department of Physics, Aristotle University of Thessaloniki, Thessaloníki, Greece 159 International Center for Elementary Particle Physics and Department of Physics, University of Tokyo, Tokyo, Japan 160 Department of Physics, Tokyo Institute of Technology, Tokyo, Japan 161 Tomsk State University, Tomsk, Russia 162 Department of Physics, University of Toronto, Toronto, ON, Canada 163 (a)TRIUMF, Vancouver, BC, Canada; (b)Department of Physics and Astronomy, York University, Toronto, ON, Canada 164 Division of Physics and Tomonaga Center for the History of the Universe, Faculty of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Japan 165 Department of Physics and Astronomy, Tufts University, Medford, MA, USA 166 Department of Physics and Astronomy, University of California Irvine, Irvine, CA, USA 167 Department of Physics and Astronomy, University of Uppsala, Uppsala, Sweden 168 Department of Physics, University of Illinois, Urbana, IL, USA 169 Instituto de Física Corpuscular (IFIC), Centro Mixto Universidad de Valencia - CSIC, Valencia, Spain 170 Department of Physics, University of British Columbia, Vancouver, BC, Canada 171 Department of Physics and Astronomy, University of Victoria, Victoria, BC, Canada 172 Fakultät für Physik und Astronomie, Julius-Maximilians-Universität Würzburg, Würzburg, Germany 173 Department of Physics, University of Warwick, Coventry, UK 174 Waseda University, Tokyo, Japan 175 Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot, Israel 176 Department of Physics, University of Wisconsin, Madison, WI, USA 177 Fakultät für Mathematik und Naturwissenschaften, Fachgruppe Physik, Bergische Universität Wuppertal, Wuppertal, Germany 178 Department of Physics, Yale University, New Haven, CT, USA 123 Eur. Phys. J. C (2022) 82 :334 Page 35 of 35 334 aAlso at Borough of Manhattan Community College, City University of New York, New York, NY, USA bAlso at Bruno Kessler Foundation, Trento, Italy cAlso at Center for High Energy Physics, Peking University, Beijing, China dAlso at Centro Studi e Ricerche Enrico Fermi, Rome, Italy eAlso at CERN, Geneva, Switzerland fAlso at Département de Physique Nucléaire et Corpusculaire, Université de Genève, Geneva, Switzerland gAlso at Departament de Fisica de la Universitat Autonoma de Barcelona, Barcelona, Spain hAlso at Department of Financial and Management Engineering, University of the Aegean, Chios, Greece iAlso at Department of Physics and Astronomy, Michigan State University, East Lansing, MI, USA jAlso at Department of Physics and Astronomy, University of Louisville, Louisville, KY, USA kAlso at Department of Physics, Ben Gurion University of the Negev, Beer Sheva, Israel lAlso at Department of Physics, California State University, East Bay, USA mAlso at Department of Physics, California State University, Fresno, USA nAlso at Department of Physics, California State University, Sacramento, USA oAlso at Department of Physics, King’s College London, London, UK pAlso at Department of Physics, St. Petersburg State Polytechnical University, St. Petersburg, Russia qAlso at Department of Physics, University of Fribourg, Fribourg, Switzerland rAlso at Faculty of Physics, M.V. Lomonosov Moscow State University, Moscow, Russia sAlso at Faculty of Physics, Sofia University, ’St. Kliment Ohridski’, Sofia, Bulgaria tAlso at Graduate School of Science, Osaka University, Osaka, Japan uAlso at Hellenic Open University, Patras, Greece vAlso at Institucio Catalana de Recerca i Estudis Avancats, ICREA, Barcelona, Spain wAlso at Institut für Experimentalphysik, Universität Hamburg, Hamburg, Germany xAlso at Institute for Particle and Nuclear Physics, Wigner Research Centre for Physics, Budapest, Hungary yAlso at Institute of Particle Physics (IPP), Victoria, Canada zAlso at Institute of Physics, Azerbaijan Academy of Sciences, Baku, Azerbaijan aa Also at Institute of Theoretical Physics, Ilia State University, Tbilisi, Georgia ab Also at Instituto de Fisica Teorica, IFT-UAM/CSIC, Madrid, Spain ac Also at Department of Physics, Istanbul University, Istanbul, Turkey ad Also at Joint Institute for Nuclear Research, Dubna, Russia ae Also at Moscow Institute of Physics and Technology State University, Dolgoprudny, Russia af Also at National Research Nuclear University MEPhI, Moscow, Russia ag Also at Physics Department, An-Najah National University, Nablus, Palestine ah Also at Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Freiburg, Germany ai Also at The City College of New York, New York, NY, USA aj Also at TRIUMF, Vancouver, BC, Canada ak Also at Universita di Napoli Parthenope, Naples, Italy al Also at University of Chinese Academy of Sciences (UCAS), Beijing, China am Also at Yeditepe University, Physics Department, Istanbul, Turkey ∗Deceased 123