Science, Faculty of
TRIUMF
Non UBC
Physics and Astronomy, Department of
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The European Physical Journal C. 2024 Jul 29;84(7):757
The Author(s)
ATLAS Collaboration
A search is presented for flavour-changing neutralcurrent interactions involving the top quark, the Higgs boson and an up-type quark (q = u, c) with the ATLAS detector at the Large Hadron Collider. The analysis considers leptonic decays of the top quark along with Higgs boson decays into two W bosons, two Z bosons or a τ +τ − pair. It focuses on final states containing either two leptons (electrons or muons) of the same charge or three leptons. The considered processes are tt ¯and Ht production. For the tt ¯production, one top quark decays via t → H q. The proton–proton collision data set analysed amounts to (140 fb−1) at ( √s = 13 TeV). No significant excess beyond Standard Model expectations is observed and upper limits are set on the t → H q branching ratios at 95 % confidence level, amounting to observed (expected) limits of B(t → H u) < 2.8 (3.0) × 10−4 and B(t → Hc) < 3.3 (3.8) × 10−4. Combining this search with other searches fortHq flavour-changing neutral-current interactions previously conducted by ATLAS, considering H → bb¯ and H → γ γ decays, as well as H → τ +τ − decays with one or two hadronically decaying τ -leptons, yields observed (expected) upper limits on the branching ratios of B(t → H u) < 2.6 (1.8)×10−4 and B(t → Hc) < 3.4 (2.3) × 10−4.
Eur. Phys. J. C (2024) 84:757 https://doi.org/10.1140/epjc/s10052-024-12994-1Regular Article - Experimental PhysicsSearch for flavour-changing neutral-current couplings betweenthe top quark and the Higgs boson in multi-lepton final statesin 13 TeV pp collisions with the ATLAS detectorATLAS CollaborationCERN, 1211 Geneva 23, SwitzerlandReceived: 4 April 2024 / Accepted: 7 June 2024© CERN for the benefit of the ATLAS Collaboration 2024Abstract A search is presented for flavour-changing neutral-current interactions involving the top quark, the Higgs bosonand an up-type quark (q = u, c) with the ATLAS detectorat the Large Hadron Collider. The analysis considers lep-tonic decays of the top quark along with Higgs boson decaysinto two W bosons, two Z bosons or a τ+τ− pair. It focuseson final states containing either two leptons (electrons ormuons) of the same charge or three leptons. The consideredprocesses are t t¯ and Ht production. For the t t¯ production, onetop quark decays via t → Hq. The proton–proton collisiondata set analysed amounts to (140 fb−1) at (√s = 13 TeV).No significant excess beyond Standard Model expectationsis observed and upper limits are set on the t → Hq branch-ing ratios at 95 % confidence level, amounting to observed(expected) limits of B(t → Hu) < 2.8 (3.0) × 10−4 andB(t → Hc) < 3.3 (3.8) × 10−4. Combining this searchwith other searches for t Hq flavour-changing neutral-currentinteractions previously conducted by ATLAS, consideringH → bb¯ and H → γ γ decays, as well as H → τ+τ−decays with one or two hadronically decaying τ -leptons,yields observed (expected) upper limits on the branchingratios of B(t → Hu) < 2.6 (1.8)×10−4 and B(t → Hc) <3.4 (2.3) × 10−4.Contents1 Introduction . . . . . . . . . . . . . . . . . . . . . .2 The ATLAS detector . . . . . . . . . . . . . . . . . .3 Samples of data and simulated events . . . . . . . . .3.1 Simulation of t Hq FCNC signal samples . . . . .3.2 Simulation of background processes . . . . . . .4 Object reconstruction and event preselection . . . . .5 Background estimate . . . . . . . . . . . . . . . . . .5.1 Non-prompt lepton background . . . . . . . . . .5.2 Charge misidentification . . . . . . . . . . . . . e-mail: atlas.publications@cern.ch5.3 Prompt-lepton background . . . . . . . . . . . .6 Event categorisation . . . . . . . . . . . . . . . . . .6.1 Definition of signal regions . . . . . . . . . . . .6.2 Control regions for non-prompt-lepton backgrounds6.3 Control regions for t t¯W and t t¯ Z backgrounds . .7 Separation of signal and background . . . . . . . . .7.1 Event reconstruction in signal regions . . . . . .7.2 Training of feed-forward neural networks . . . .8 Systematic uncertainties . . . . . . . . . . . . . . . .8.1 Experimental uncertainties . . . . . . . . . . . .8.2 Modelling uncertainties . . . . . . . . . . . . . .9 Statistical analysis . . . . . . . . . . . . . . . . . . .10 Results . . . . . . . . . . . . . . . . . . . . . . . . .10.1Cross-checks on the modelling of the neural net-work input variables . . . . . . . . . . . . . . . .10.2Full fit to data . . . . . . . . . . . . . . . . . . .11 Combination of results with other searches . . . . . .12 Conclusion . . . . . . . . . . . . . . . . . . . . . . .Appendix . . . . . . . . . . . . . . . . . . . . . . . . .References . . . . . . . . . . . . . . . . . . . . . . . . .1 IntroductionFollowing the discovery of the Higgs boson at the LargeHadron Collider (LHC) by the ATLAS and CMS experi-ments in 2012 [1,2], several measurements have probed prop-erties of the particle. In addition to Higgs boson couplingsto fermions and gauge bosons, which agree well with theStandard Model (SM) predictions [3,4], further interactionscan be investigated to search for evidence of possible newphysics in the Higgs sector. A possibility is that the Higgsboson has an interaction involving two up-type quarks of dif-ferent generations, denoted by t Hq where q = (u, c), lead-ing to gq → Ht production and t → Hq decay. Theseare flavour-changing neutral-current (FCNC) interactions,forbidden at tree-level in the SM and suppressed at higherorders due to the Glashow–Iliopoulos–Maiani (GIM) mech-0123456789().: V,-vol 123 757 Page 2 of 42 Eur. Phys. J. C (2024) 84:757 anism [5]. The SM predictions for the t → Hq branch-ing ratios B(t → Hq) are very small, around 10−15 [6–10], and beyond the sensitivity of the LHC. However, inthe framework of new physics models such as two-Higgs-doublet models (2HDMs) [11], the minimal supersymmetricSM (MSSM) [12–15], supersymmetric models with R-parityviolation [16], quark-singlet models [17], and warped extradimensions [18], the branching ratios of these processes aremodified making them large enough to be measured at theLHC. For example, branching ratios of up to 10−3 are possi-ble in 2HDMs without explicit flavour symmetry, since thereare no symmetries explicitly forbidding tree-level FCNCinteractions [19–26] in this model. The FCNC interactioncan also mediate the production of a Higgs boson with a sin-gle top quark (pp → t H ) [27]. The SM prediction of thepp → t H cross-section is 74.3+0.4−0.3 fb at√s = 13TeV [28].The FCNC interactions are introduced using an effectivefield theory (EFT) framework, which is used for indirectsearches for new physics [29]. Here the SM is regarded as alow-energy approximation of an ultraviolet complete theorycontaining new particles, whose masses are characterised byan energy scale  = 1 TeV. The new physics contributionsare parameterised in terms of operators with mass dimen-sion greater than four containing only the SM fields, scaledby dimensionless Wilson coefficients and inverse powers of. In the case where only the t Hu and t Hc interactions areconsidered, the relevant operators areOqtuφ =(φ†φ − v22)(q¯L tR)φ˜Otquφ =(φ†φ − v22)(t¯L qR)φ˜, (1)where q corresponds to an up or charm quark, dependingon the FCNC coupling. The index u is the coupling to anyup-type quark, t is the top-quark, φ denotes the Higgs bosonfield with v corresponding to the absolute value of its vac-uum expectation value. The two left-handed quark doubletfields are q¯L and t¯L , with qR and tR being the correspond-ing right-handed singlets. The operators are scaled with Wil-son coefficients Cqtuφ and Ctquφ , and 1/2 to give the relevantLagrangian:LEFT = LSM +∑q=u,c[Cqtuφ2Oqtuφ +Ctquφ2Otquφ]. (2)In the case of t t¯ production with a FCNC t → Hq decay,no kinematic differences between Oqtuφ and Otquφ are expectedbecause the top quarks are produced unpolarised and theHiggs boson is a scalar particle. For t → Hq production,comparisons of simulations using either Oqtuφ or Otquφ haveshown that differences between production rates and kine-matic distributions are negligible in the phase space consid-ered. Thus, the mean of both the couplings Cqt,tquφ =Cqtuφ+Ctquφ2is considered.Both the ATLAS and CMS Collaborations have under-taken various searches for t Hq FCNC processes, split byHiggs boson final state [30,30–38]. In this paper, a searchis conducted using final states containing either two leptons(electrons or muons) of the same charge (2SS,  = e, μ) orthree leptons, exactly two of which have the same charge(3,  = e, μ). The ATLAS Collaboration searched fort Hq FCNC couplings in 2SS and 3 final states using apartial Run 2 data sample of 36.1 fb−1 [32], resulting inobserved (expected) 95% CL upper limits of B(t → Hu) <19(15) × 10−4 and B(t → Hc) < 16(15) × 10−4. Thestrongest limits set by the ATLAS Collaboration come froma combination of searches in the H → bb¯, H → γ γ andH → τ+τ− channels using the full Run 2 data sample [35].The obtained limits are B(t → Hu) < 4.0(2.4) × 10−4 andB(t → Hc) < 5.8(3.0)×10−4. For the t Hc coupling, theseare the most stringent limits published to date. However, forthe t Hu coupling the strongest limits are set by a search con-ducted with the CMS detector in the H → γ γ channel [38],amounting to B(t → Hu) < 1.9(3.1) × 10−4.The dominant Higgs-boson decay mode resulting in 2SSand 3 final states across production and decay processesis H → W W ∗, with W W ∗ → ν j j or W W ∗ → ννfor the 2SS and 3 final state respectively. The correspond-ing Feynman diagrams are shown in Figs. 1, 2. Other Higgs-boson decay modes such as H → Z Z∗ and H → τ+τ− canalso meet the selection criteria. Based on the SM branch-ing ratios of the Higgs boson and the top quark, approx-imately 73 % of all 2SS signal events are expected fromthe H → W W ∗ decay mode, while the rest originate fromleptonic H → τ+τ− decays. Less than 1 % of events areattributable to the H → Z Z∗ decay mode. In the 3 finalstate, the latter contributes more significantly, being respon-sible for 14 % of all events. The majority, accounting for 54 %of the 3 signal events, originate from H → W W ∗ decays,while the remaining 32 % arise from H → τ+τ− events.These numbers do not take into account detector acceptanceeffects or selection requirements. Although the total numberof events meeting the 2SS and 3 criteria is modest, thelow statistical precision is balanced by minimal backgroundcontributions.The strategy of the analysis is to first identify kinematicregions enriched in the signal process. In these regions, var-ious reconstruction algorithms are implemented to createvariables that can distinguish between the signal and sev-eral background processes. These reconstructed variables arecombined into a single discriminant using a feed-forwardneural network [39]. The same kinematic regions are used forthe t Hu and the t Hc channel of the analysis, while individual123Eur. Phys. J. C (2024) 84:757 Page 3 of 42 757 Fig. 1 Example Feynmandiagrams of the t t¯(t → Hq)decay signal process resulting ina the 2SS final state and b the3 final state. The FCNC vertexis highlighted in redFig. 2 Example Feynmandiagrams of the gq → Htproduction signal processresulting in a the 2SS finalstate and b the 3 final state.The FCNC vertex is highlightedin redneural networks are trained for each of the channels. Asidefrom this, the analysis strategy is identical for the t Hu andthe t Hc channel. The distribution of the neural network out-put is then used as input to a maximum-likelihood fit, whichconsiders statistical and systematic uncertainties. In additionto the signal-enriched regions, several regions enriched inspecific background processes are included in the fit, to con-strain the normalisation of these processes. If the fit showsevidence of a signal, the corresponding significance is deter-mined. Otherwise, upper limits are set on the FCNC branch-ing ratios and the Wilson coefficients of the EFT dimension-6operators. Finally, the results of this analysis are statisticallycombined with those from other ATLAS searches for t HqFCNC interactions in different final states.2 The ATLAS detectorThe ATLAS detector [40] at the LHC covers nearly the entiresolid angle around the collision point.1 It consists of an1 ATLAS uses a right-handed coordinate system with its origin at thenominal interaction point (IP) in the centre of the detector and the z-axis along the beam pipe. The x-axis points from the IP to the centre ofinner tracking detector surrounded by a thin superconduct-ing solenoid, electromagnetic and hadron calorimeters, and amuon spectrometer incorporating three large superconduct-ing air-core toroidal magnets.The inner-detector system (ID) is immersed in a 2 T axialmagnetic field and provides charged-particle tracking in therange of |η| < 2.5. The high-granularity silicon pixel detec-tor covers the vertex region and typically provides fourmeasurements per track, the first hit normally being in theinsertable B-layer (IBL) installed before Run 2 [41,42]. Itis followed by the silicon microstrip tracker (SCT), whichusually provides eight measurements per track. These sili-con detectors are complemented by the transition radiationtracker (TRT), which enables radially extended track recon-struction up to |η| = 2.0. The TRT also provides electronidentification information based on the fraction of hits (typ-ically 30 in total) above a higher energy-deposit thresholdcorresponding to transition radiation.Footnote 1 continuedthe LHC ring, and the y-axis points upwards. Cylindrical coordinates(r, φ) are used in the transverse plane, φ being the azimuthal anglearound the z-axis. The pseudorapidity is defined in terms of the polarangle θ as η = − ln tan(θ/2). Angular distance is measured in units of R ≡ √( η)2 + ( φ)2.123 757 Page 4 of 42 Eur. Phys. J. C (2024) 84:757 The calorimeter system covers the pseudorapidity range|η| < 4.9. Within the region |η| < 3.2, electromag-netic calorimetry is provided by barrel and endcap high-granularity lead/liquid-argon (LAr) calorimeters, with anadditional thin LAr presampler covering |η| < 1.8 to cor-rect for energy loss in material upstream of the calorime-ters. Hadron calorimetry is provided by the steel/scintillator-tile calorimeter, segmented into three barrel structures within|η| = 1.7, and two copper/LAr hadron endcap calorimeters.The solid angle coverage is completed with forward cop-per/LAr and tungsten/LAr calorimeter modules optimised forelectromagnetic and hadronic energy measurements respec-tively.The muon spectrometer (MS) comprises separate triggerand high-precision tracking chambers measuring the deflec-tion of muons in a magnetic field generated by the supercon-ducting air-core toroidal magnets. The field integral of thetoroids ranges between 2.0 and 6.0 T m across most of thedetector. Three layers of precision chambers, each consistingof layers of monitored drift tubes, cover the region |η| < 2.7and are complemented by cathode-strip chambers in the for-ward region, where the detector occupancy is highest. Themuon trigger system covers the range of |η| < 2.4 withresistive-plate chambers in the barrel, and thin-gap chambersin the endcap regions.Recorded events are selected by the first-level trigger sys-tem implemented in custom hardware, followed by selectionsmade by algorithms implemented in software in the high-level trigger [43]. The first-level trigger accepts events fromthe 40 MHz bunch crossings at a rate below 100 kHz, whichthe high-level trigger further reduces to record events to diskat about 1 kHz.An extensive software suite [44] is used in data simulation,in the reconstruction and analysis of real and simulated data,in detector operations, and in the trigger and data acquisitionsystems of the experiment.3 Samples of data and simulated eventsProton–proton (pp) collision data are used recorded with theATLAS detector in the years 2015 to 2018 at a centre-of-mass energy of 13 TeV. After applying data-quality require-ments [45], the data sample corresponds to an integratedluminosity of 140.1(12) fb−1 [46]. The LUCID-2 detec-tor [47] was used for the primary luminosity measurements,complemented by measurements using the inner detector andcalorimeters.Events were selected online during data taking by single-electron or single-muon triggers [48,49]. Multiple unprescaledtriggers were combined in a logical OR to increase the selec-tion efficiency. The lowest-threshold triggers utilised isola-tion requirements to reduce the trigger rate. The higher-levellepton triggers had transverse momentum (pT) thresholds of20 GeV for muons and 24 GeV for electrons in 2015 data,and 26 GeV for both the lepton types in 2016, 2017 and 2018data. They were complemented by other triggers with higherpT thresholds but no isolation requirements to increase thetrigger efficiency.Large sets of simulated events from signal and backgroundprocesses were produced with Monte Carlo (MC) event gen-erator programs to model the selected data. After event sim-ulation, the response of the ATLAS detector was simulatedusing the Geant4 toolkit [50] with a full detector model [51]or a fast simulation [51,52] which employed a parameteri-sation of the calorimeter response. Samples relying on fastsimulation were used to evaluate systematic uncertainties inthe event generators and for the modelling of t t¯ productionwith two bosons.To account for additional inelastic pp collisions in thesame and neighbouring bunch crossings (pile-up), minimum-bias interactions were overlaid on the hard-scattering eventsat the level of energy depositions simulated using Geant4.The minimum-bias events were simulated using Pythia[8.186] [53] with the A3 [54] set of tuned parametersand the NNPDF[2.3lo] set of parton distribution functions(PDF) [55]. The resulting events were weighted to repro-duce the observed pile-up distribution. The average numberof interactions per bunch crossing during the entire data-taking period from 2015 to 2018 is 33.7.Finally, the simulated events were reconstructed using thesame software as applied to the collision data. The same eventselection requirements were applied and the selected eventswere passed through the same analysis chain. Small correc-tions were applied to simulated events such that the efficien-cies of the utilised reconstruction methods are in better agree-ment with the response observed in data. More details of thesimulated event samples are provided in the following sub-sections. Except for the events simulated with the Sherpagenerator [56,57], the Evtgen [58] program was used tosimulate bottom and charm hadron decays. If not mentionedotherwise, the top-quark mass was set to mt = 172.5 GeVand the Higgs-boson mass to m H = 125 GeV. All processesfor which the parton shower is simulated using Pythia[8] usethe A14 set of tuned parameters [59] and the NNPDF[2.3lo]PDF set.3.1 Simulation of t Hq FCNC signal samplesTwo different signal processes are studied: the t t¯(t → Hq)decay and the gq → Ht production process. The EFT oper-ators parametrising the FCNC coupling are implemented inthe TopFCNC [60] model using the Feynrules[2.0] frame-work [61], allowing for next-to-leading-order (NLO) cal-culations of the postulated processes. The decay processevents were simulated using the NLO matrix-element gen-123Eur. Phys. J. C (2024) 84:757 Page 5 of 42 757 erator Powhegbox[v2] [62–68], with the NNPDF[3.0nlo]PDF set [69]. The production of a top quark–antiquark pairis performed according to SM calculations in the five-flavourscheme, setting the masses of all quarks except for the topquark to zero. One top quark is required to decay via theSM decay mode t → W b, while the other performs theFCNC decay t → Hq. Both top-quark decays are modelledusing Madspin [70,71]. Only leptonic final states for theSM decay of the top quark are considered. The Higgs-bosondecay, and parton showers, hadronisation, and the underlyingevent, were modelled using Pythia[8.308] [72]. The matrix-element-to-parton-shower matching is steered by the hdampparameter, which controls the pT of the first additional gluonemission beyond the leading-order (LO) Feynman diagram inthe parton shower and therefore regulates the high-pT emis-sion against which the t t¯ system recoils. The event genera-tion was performed with hdamp = 1.5mt [73]. Four separatesamples are produced, modelling the t Hu/ t Hc couplingwith either the top quark or the top antiquark decaying viathe FCNC interaction. For consistency across searches, allt Hq FCNC samples are normalised to the cross-section cor-responding to a branching ratio of B(t → Hq) = 0.1 %.As explained previously, kinematic differences between theleft- and right-handed couplings are negligible in the caseof t → Hq decay process. Therefore, the same samples areused to model the left-handed and the right-handed FCNCcouplings. The matrix element generator Mgnlo[2.9.9] [74]was used to model the gq → Ht production signal usingthe TopFCNC model with the NNPDF[3.0nlo] PDF set andthe five-flavour scheme. Separate samples are produced, eachwith exactly one of the Wilson coefficients set to 1.0 and theothers set to zero, all of them at NLO in QCD.The SM top-quark and Higgs-boson decays are simu-lated using Madspin. The three relevant Higgs-boson decays(H → W W ∗, H → Z Z∗, H → τ+τ−) are modelled inseparate samples. All Higgs-boson decays, parton shower,hadronisation, and the underlying event, were modelled usingPythia[8.307]. The samples are normalised to the cross-section calculated with Mgnlo.3.2 Simulation of background processesSamples of simulated events from SM t t¯ and single-top-quark production were simulated using the NLO matrix-element generator Powhegbox[v2]. For t t¯ and tW pro-duction and s-channel single-top-quark production (t b¯ pro-duction) the Nnpdf[3.0nlo] PDF set was used with thefive-flavour scheme. Following a recommendation given inRef. [68], single top-quark production in the t-channel (tqproduction) was simulated with the Nnpdf[3.0nlo_nf4] PDFset, which implements the four-flavour scheme. Parton show-ers, hadronisation, and the underlying event were modelledusing Pythia[8.230]. The event simulation used a value ofhdamp = 1.5mt .The t t¯ production cross-section was scaled to σ(t t¯) =832 pb, the value obtained from next-to-next-to-leading-order predictions from the Top++2.0 program (see Ref. [75]and references therein), and it includes the resummationof next-to-next-to-leading logarithmic soft-gluon terms. Thepredicted cross-sections of tq and t¯q production used toscale the corresponding samples of simulated events areσ(tq) = 136 pb and σ(t¯q) = 81 pb and were calculatedat NLO in QCD with the Hathor[2.1] program [76,77].The total cross-section for t b¯ production was also com-puted at NLO in QCD with the Hathor[2.1] program andthe corresponding sample of simulated events was scaled toσ(t b¯ + t¯b) = 10.32 pb. The cross-section used for normal-ising the tW sample is σ(tW + t¯W ) = 71.7 pb [78].The production of a vector boson in association with jets(V +jets, V = W, Z ), including b- and c-jets, was simulatedwith the Sherpa[2.2.11] generator. NLO-accurate matrixelements for up to two partons and LO-accurate matrix ele-ments for three to five partons are calculated in the five-flavour scheme using the Comix [79] and Openloops [80–82] libraries. The default Sherpa parton shower [83] basedon Catani–Seymour dipole factorisation and the clusterhadronisation model [84] are used. The samples are simu-lated using a dedicated set of tuned parameters developed bythe Sherpa authors and use the NNPDF[3.0nnlo] PDF set.The t t¯W process was simulated using the Sherpa[2.2.10]generator. The matrix elements were calculated for up to oneadditional parton at NLO and up to two partons at LO usingComix and Openloops, and merged with the Sherpa partonshower using the MEPS@NLO prescription [85]. In addi-tion to the nominal prediction at NLO in QCD, higher-ordercorrections related to electroweak (EWK) contributions arealso included. Event-by-event correction factors are appliedthat provide virtual NLO EWK corrections to O(α2α2s )and LO corrections to O(α3) [57,86,87]. An independentSherpa[2.2.10] sample was produced at LO to account forthe sub-leading EWK corrections to O(α3αs) [88]. The NLOQCD and NLO EWK contributions from Sherpa are com-bined following the method of Ref. [89]. The t t¯W samplesare normalised using a cross-section of 722 fb computed atNLO including the hard non-logarithmically enhanced radi-ation at NLO in QCD [89].The modelling of the production of a top quark–antiquarkpair with a Z boson decaying leptonically is done using theMgnlo[2.8.1] generator. It provides matrix elements at NLOin QCD, employing the NNPDF[2.3lo] PDF set. The gener-ated events are interfaced with Pythia[8.244] for the partonshower and hadronisation stages. The t t¯ Z/γ ∗(→ +−) pre-diction was normalised to the calculation at NLO QCD andNLO EWK accuracy based on Ref. [28] with the additionalinclusion of off-shell effects, corresponding to 162 fb.123 757 Page 6 of 42 Eur. Phys. J. C (2024) 84:757 The production of t t¯ H events was modelled usingthe Powhegbox[v2] generator at NLO in QCD with theNNPDF[3.0nlo] PDF set. The events were interfaced toPythia[8.230]. The cross-section was calculated at NLOQCD and NLO EWK using Mgnlo and amounts to 507 fb.The production of two or three weak vector bosons (V V ,V V V ) in 2, 3 and 4 final states was simulated usingthe Sherpa[2.2.12] generator including the off-shell contri-butions. Matrix elements including additional partons werecalculated at NLO in QCD for up to one parton and at LOaccuracy for two or three additional partons using Comixand Openloops. For the parton shower simulation, the samemethod as in the W +jets and Z+jets samples is used. The V Vand V V V samples are normalised to the total cross-sectionsprovided by Sherpa.The t Zq process was modelled at NLO with the Mgnlo[2.9.5] generator and the NNPDF[3.0nlo] PDF. The gen-erated events were interfaced with Pythia[8.230]. Matrixelements of the tW Z process were also calculated withMgnlo[2.2.2], using the same PDF set. The events wereinterfaced with Pythia[8.212] using the same tune and PDFset as used for t Zq production. The samples were normalisedto the theoretical cross-section at NLO QCD.Some rare processes are considered: t t¯ t , t t¯ t t¯ , t H W , t Hq,t t¯W W , t t¯ H H , t t¯W H , t t¯ Z Z , t t¯W Z and V H production.The processes involving at least one top quark were simu-lated with Mgnlo, while V H was produced with Powheg-box[v2]. Simulated events of all processes were interfacedto Pythia[8] to simulate parton showers and hadronisation.The processes are normalised to their predicted NLO cross-sections. Their combined contribution is nearly negligible,ranging from 0.1 to 1 %, depending on the kinematic regionconsidered.4 Object reconstruction and event preselectionEvents are required to have at least one vertex reconstructedfrom at least two ID tracks with transverse momenta of pT >0.5 GeV. The primary vertex of an event is defined as thevertex with the highest p2T summed over the ID tracks [90]matched to it.Electron candidates are reconstructed by matching a trackin the ID to clusters of energy deposits in the electro-magnetic calorimeter [91]. The pseudorapidity of clusters,ηcluster, is required to be in the range of |ηcluster| < 2.47.However, clusters are excluded if they are in the transitionregion 1.37 < |ηcluster| < 1.52 between the barrel and end-cap electromagnetic calorimeters. Electron candidates musthave pT > 10 GeV. A likelihood-based discriminant is con-structed to simultaneously evaluate several properties of elec-tron candidates, including shower shapes in the electromag-netic calorimeter, track quality, and the detection of transitionradiation produced in the TRT [92]. Applying a discrimi-nant requirement enhances the selection of prompt electronsproduced in W -, Z - or Higgs-boson decays and leptonic τ -lepton decays, while effectively rejecting photon conversionsand hadrons misidentified as electrons. All selected electronsmust meet the Tight selection criteria as defined in Ref. [92].ig Muon candidates are reconstructed by combining tracksin the MS with tracks in the ID [93]. The tracks must bein the range of |η| < 2.5 and have pT > 10 GeV. Simi-larly to electrons, likelihood-based identification criteria areapplied [93]. Muons are required to satisfy the Medium selec-tion defined in Ref. [93].The tracks matched to electron and muon candidates mustpoint to the primary vertex, which is ensured by require-ments imposed on the transverse impact-parameter signifi-cance, |d0/σ(d0)| < 5.0 for electrons and |d0/σ(d0)| < 3.0for muons, and on the longitudinal impact parameter, z0,for which |z0 sin(θ)| < 0.5 mm has to be satisfied for bothlepton flavours. Non-prompt electrons and muons are lep-tons produced by mechanisms other than W -, Z - or Higgs-boson decays and leptonic τ -lepton decays. They are effec-tively rejected by using multivariate discriminants computedwith boosted decision trees (BDT), which integrate elec-tromagnetic shower shapes and track information from theID [94]. Separate BDTs are trained for electrons in the barrel(|η| < 1.37) and endcap (|η| > 1.37) regions, while a sin-gle BDT is employed for muons. The efficiency for correctlyidentifying prompt muons (electrons) ranges from approxi-mately 80 % to 95 % (65 % to 90 %) for pT values between20 GeV and 45 GeV, with the efficiency plateauing beyond45 GeV. Overall, the BDTs achieve a 71 % (90 %) rejec-tion rate for muons (electrons) from B-hadron decay. Addi-tionally, the contribution of electrons reconstructed with anincorrectly reconstructed charge is significantly reduced byusing an additional BDT [91], which consolidates informa-tion about an electron candidate’s charge, impact parameter,energy, and ID track into a single discriminant. This achievesa 95 % efficiency for electrons with a correct charge assign-ment while rejecting 94 % of charge-misidentified electrons.Scale factors are used to correct the efficiencies in simula-tion to match the efficiencies measured for the electron [48]and muon [49] triggers, and the reconstruction, identificationand isolation criteria [91,93].Jets are reconstructed from particle-flow objects [95] withthe anti-kt clustering algorithm [96,97] using a radius param-eter of 0.4. This algorithm matches topological energy clus-ters [98] in the calorimeters to selected tracks in the ID. Theenergy of tracks is subtracted from the matched topologicalclusters and both the tracks and the energy-subtracted topo-logical clusters are used as input to the jet reconstruction.The jet energy is calibrated by applying several simulation-based corrections and techniques correcting for differences123Eur. Phys. J. C (2024) 84:757 Page 7 of 42 757 between simulation and data [99]. The jets must satisfypT > 20 GeV and |η| < 2.5.To suppress jets originating from pile-up collisions, sev-eral track-based variables are combined with a multivari-ate technique to form the jet-vertex-tagger (JVT) discrim-inant [100]. Jets with pT < 60 GeV and |η| < 2.4 arerequired to have a JVT discriminant above 0.5, which cor-responds to an efficiency of 92% for jets from the primaryvertex, while 98 % of jets from pile-up events are rejected.Identification of jets containing B hadrons (b-tagging)is performed with the DL1r algorithm, which uses a deepfeed-forward neural network with several b-tagging algo-rithms as inputs [101]. These input algorithms exploit theimpact parameters of charged-particle tracks, the propertiesof reconstructed secondary vertices and the topology of b-and c-hadron decays inside the jets. The requirement on theDL1r discriminant is chosen such that the average taggingefficiency of b-jets from simulated dileptonic t t¯ events is70 %. The corresponding pT-dependent c-jet rejection fac-tors range from 10 to 14, while those for light-flavour jetsrange from 100 to 900. Differences between the b-taggingefficiency between collision data and simulation are cor-rected using simulation-to-data scale factors derived from t t¯events. The scale factors depend on the pT of the jets and areconsistent with unity within the uncertainties. The obtainedscale factors depend on the parton-shower generator used toproduce the t t¯ samples. When using samples produced witha different parton-shower generator, for example Sherpa, tomodel W +jets events, or when evaluating systematic uncer-tainties with a setup based on Herwig, additional correctionfactors called MC-to-MC scale factors are applied. Since theDL1r algorithm uses measurements from the ID, the identi-fication of b-jets is limited to the region with |η| < 2.5.With the above definitions of physical objects it is possi-ble for ambiguities to arise, since all objects are reconstructedindependently of each other. To avoid the double-counting ofcandidates which satisfy more than one selection criterion, aprocedure called overlap removal is applied. Reconstructedphysical objects are removed in the following order: elec-trons sharing an ID track with a muon; jets within R = 0.2of an electron, thereby avoiding double-counting electronenergy deposits as jets; electrons within R = 0.4 of aremaining jet, for reducing the impact of non-prompt elec-trons; jets within R = 0.2 of a muon if they have two orfewer matched tracks; muons within R = 0.4 of a remain-ing jet, reducing the rate of non-prompt muons.The missing transverse momentum p missT is reconstructedas the negative vector sum of the transverse momentum ofthe reconstructed leptons and jets, and ID tracks that pointto the primary vertex but are not matched to a reconstructedobject [102]. The magnitude of p missT is denoted by EmissT .Events selected by this analysis are required to have at leastone charged lepton with pT > 28 GeV. Additional leptonsTable 1 Overview of the preselections applied in the analysis. Theseselections ensure jet and b-tag multiplicities, lepton momenta, anddefine the 2SS and 3 final statesPreselectionNjets ≥ 1Nb-tags ≥ 1pT(jet) ≥ 20 GeVpT() ≥ 10 GeVpT(0) ≥ 28 GeV2SS 3N = 2 = 3∑q(i ) = ±2e = ±1emust satisfy a pT threshold of 10 GeV. In the 2SS final state,exactly two leptons of the same charge are required, while inthe 3 final state the requirement is three leptons with a totalcharge of ±1e. The lepton with the highest pT is referred toas 0. The lepton with the second highest pT is denoted by 1and, for events in the 3 final state, the lepton with the lowestpT is called 2. In the 3 final state an alternative labelling ofleptons is introduced based on their charge. In any given 3event two leptons have the same charge while the remaininglepton has an opposite charge. The latter is labelled OS, theformer SS,0 and SS,1 with the number indexing the leptonin order of decreasing pT. In addition to the requirements onleptons, considered events need to contain at least one jet, atleast one of which is b-tagged. A summary of the preselectionapplied to events is given in Table 1.5 Background estimateSeveral SM background processes are present in the sig-nal regions. Many of these processes can be simulated byusing MC, others require dedicated treatment. Particularlythe modelling of background from non-prompt leptons mustbe validated and potentially corrected. This background isseparated into various categories, encompassing electronsfrom prompt muon decay, electrons from photon conversionand leptons produced in a hadronic jet, where further dif-ferentiation depending on the jet primary particle are made.Jets initiated by b-quarks, by other quarks or gluons, and byτ -leptons are considered, where leptons from b-jets are fur-ther categorised into electrons and muons. The productionof these non-prompt leptons is fully accounted for by thesimulated SM samples. By navigating through the generator-level parent particles of a given lepton, this lepton is sortedinto one of the previously discussed lepton-origin categories.Based on this, several MC templates are defined containingthe events corresponding to exactly one non-prompt lepton-origin category. The remaining events include only prompt123 757 Page 8 of 42 Eur. Phys. J. C (2024) 84:757 leptons and remain in their original SM background tem-plate. All background estimate methods discussed in thefollowing are based on these prompt and non-prompt MCtemplates. Several of the processes discussed in this sectionare assigned unconstrained (free-floating) normalisation fac-tors in the final maximum-likelihood fit. These normalisationfactors are constrained in the fit through dedicated controlregions, enriched in the respective processes. It should benoted that the QCD multijet background is negligible in thisanalysis, owing to the rarity of the considered 2SS and 3final states.5.1 Non-prompt lepton backgroundThe primary source of non-prompt lepton background is thedecay of B-hadrons. These particular objects are also referredto as heavy-flavour (HF) decay leptons. They mainly con-sist of events from t t¯ production (75 %), while the remain-ing events are split evenly between V +jets and single-top-quark production. The Template fit method [103] is usedto determine the rates of HF-decay electrons and HF-decaymuons. It assumes the kinematic distributions of the corre-sponding processes are well described, while their normal-isation may require corrections. The normalisation factorsare determined in the final maximum-likelihood fit, which isperformed simultaneously in the 2SS and the 3 final states.As explained above, various other non-prompt lepton pro-cesses contribute to this analysis. Their contribution is minorcompared with the HF-decay e and HF-decay μ processes. Inthe fit, they are assigned normalisation uncertainties of 50 %.5.2 Charge misidentificationIn addition to the processes discussed above, the phase spaceof the 2SS final state is contaminated by events contain-ing prompt electrons with a misidentified charge. The mod-elling of such objects is strongly dependent on their pT. Fur-thermore, electrons can radiate hard bremsstrahlung throughinteraction with the detector material, which then undergoesasymmetric conversion into an electron-positron-pair. Theprobability for electrons to interact with the detector mate-rial increases with the absolute value of the pseudorapid-ity |η|. Both, charge misidentified electrons and electronsfrom bremsstrahlung, are considered as a single backgroundlabelled Q-misID, which is modelled using a data-drivenmethod based on the one described in Ref. [103]. To avoiddouble-counting Q-misID events, MC events featuring anelectron from any of the considered processes are identifiedusing generator level information and are excluded from theanalysis.The data-driven Q-misID background estimate is per-formed as follows. Events containing two isolated electronswith an invariant mass around the mass of the Z boson areconsidered, where the electrons can have either an opposite-sign charge (OS) or the same-sign charge (SS). To maintainorthogonality to the kinematic regions of the main analysis,there is an Nb-tags = 0 requirement. The mee distribution inthe vicinity of m Z = 91.19 GeV [104] is fitted separatelyfor OS and SS events using Breit–Wigner functions. Thefitted centres mpeak and widths σ are used to define the Z -windows up to 4σ from the centres, and sideband regions[mpeak − 8σ, mpeak − 4σ ] ∪ [mpeak + 4σ, mpeak + 8σ ]. Theassumption is made, that events in the Z -window consist ofprompt Z → e+e− events and a uniform background. Theuniform background is estimated from the average yield inthe sideband regions, separately for the OS and SS events,and are subtracted in the Z -window.Q-misID efficiencies are extracted in bins of |η| and pT,corresponding to the probability for an electron in a givenbin to be charge-misidentified. These relate the number ofbackground-corrected SS and OS events in the Z -windowand can thus be determined from the obtained event yields.The Q-misID events in a given region of the 2SS phase spaceare then modelled by selecting data events with two opposite-charge leptons while keeping all other selection requirementsof the region unmodified, and weighting these data eventswith the obtained efficiencies. It should be noted that dueto the high accuracy of the ATLAS muon spectrometer, themuon charge misidentification is negligible in this analysis.5.3 Prompt-lepton backgroundThe t t¯W and t t¯ Z processes represent the primary back-ground sources from prompt leptons. While measurementsof t t¯W production deviate from theoretical predictions by1.4σ [105], measurements of t t¯ Z production align closelywith SM expectations. However, it’s worth noting that the lat-est measurement of t t¯ Z production is conducted in regionswith a jet multiplicity of at least four [106]. This analysisextends to kinematic regions with fewer jets, which may notbe adequately modelled by MC simulations. To address thisdiscrepancy, the normalisation of t t¯W and t t¯ Z productionis left unconstrained in the maximum-likelihood fit. Similarto the non-prompt templates, a single normalisation factoris applied per process across the entire phase space, encom-passing both the 2SS and the 3 final states.The 2SS and 3 event selection requires at least one b-jetin the final state. In the V V MC samples used in the analy-sis these quarks must be produced by the shower generator.To account for potential mismodeling of the jet flavour com-position, the V V background is split according to the num-ber of leptons (2, 3, 4) and the generator-level flavour ofadditional jets. If the event contains at least one jet originat-ing from the decay of either a bottom or a charm hadron issorted into the b/c category. If it exclusively contains jetsfrom light quarks or τ -leptons it is included in the l/τ cat-123Eur. Phys. J. C (2024) 84:757 Page 9 of 42 757 egory. The V V 3 + b/c template has the largest contribu-tion in the phase space and its normalisation is left free-floating in the maximum-likelihood fit. The remaining tem-plates (V V 2+l/τ , V V 2+b/c, V V 3+l/τ , V V 4+b/cand V V 4 + l/τ ) are assigned individual 50 % normalisa-tion uncertainties. These minor V V templates, alongside theminor non-prompt templates and several SM processes arecombined into one Others category in the following. Therates of the majority of processes in this category are similarin the analysis phase space.6 Event categorisationPreselected events are categorised into several kinematicregions. These regions are either enriched in signal events, toimprove the overall sensitivity of the analysis, or in certainbackground events, to control the normalisation of specificprocesses.6.1 Definition of signal regionsAfter event preselection, four signal regions are defined inthis analysis, two in the 2SS final state and two in the 3 finalstate. One region per final state is enriched in the t → Hqdecay signal. These two regions are referred to as SR2Decand SR3Dec. The other two signal regions contain a largerfraction of gq → t H production signal and are correspond-ingly named SR2Prod and SR3Prod.Both the 2SS signal regions require exactly one b-taggedjet. Given that a higher jet multiplicity is anticipated for thedecay signal compared to the production signal, the SR2Decis defined by requiring Njets ≥ 4. A cut of Njets ≤ 3 in theSR2Prod ensures the orthogonality of the two regions. Tominimise the contribution from HF-decay leptons, the pTof 1 is required to be larger than 12 GeV in the SR2Decand 16 GeV in the SR2Prod. As Q-misID events stronglycontaminate the 2SS final state, a cut on the invariant massof the two leptons is imposed in both the regions. If both theleptons are identified as electrons, |m(e, e)−m Z | ≥ 10 GeVmust be satisfied.Similar to the 2SS final state, both the signal regionsin the 3 final state require exactly one b-tagged jet. Theprimary difference between the two regions is again the jetmultiplicity. Overall fewer jets are expected for the signalin the 3 final state. Hence, Njets ≥ 3 is required for theSR3Dec, while Njets ≤ 2 is required for the SR3Prod. Toreduce the HF-decay contribution, the definition of both theregions require cuts on the pT of the two sub-leading leptons:pT(1) ≥ 20 GeV and pT(2) ≥ 16 GeV. As the Q-misIDprocess does not contribute to the 3 final state, no furtherrestrictions to the event selection are made. The definitionof all signal regions is summarised in Table 2, while theirTable 2 Overview of the event selections applied to define the signalregions of the analysisSR2Dec SR2Prod SR3Dec SR3ProdNjets ≥ 4 ≤ 3 ≥ 3 ≤ 2Nb-tags = 1 = 1 = 1 = 1pT(1) ≥ 12 GeV ≥ 16 GeV ≥ 20 GeV ≥ 20 GeVpT(2) – – ≥ 16 GeV ≥ 16 GeV|m(e, e) − m Z | ≥ 10 GeV ≥ 10 GeV – –respective composition in terms of background processes isshown in Fig. 3.6.2 Control regions for non-prompt-lepton backgroundsThe template-fit method assumes that corrective normalisa-tion factors are applicable independently of the consideredfinal state. To ensure this assumption is correct, two controlregions are defined for each of the HF-decay processes: onein the 2SS final state (CR2HFe and CR2HFμ) and one inthe 3 final state (CR3HFe and CR3HFμ).Overall, the average pT of leptons originating from aHF decay is smaller than that of prompt leptons. Thus, allHF-decay control regions are defined by imposing upperboundaries on the pT of the lowest-pT lepton. The boundariesare chosen such that an orthogonality to the signal regionsof the respective final state is ensured. Requiring the flavourof the lowest-pT lepton to be either e or μ ensures that theregion is exclusively enriched in HF-decay e or HF-decay μevents. In the CR2HFe and the CR2HFμ the pT-leadinglepton is required to be a muon, reducing the contamina-tion of Q-misID events. Due to high statistical uncertainty,only the event yields of the CR2HFe and the CR2HFμenter the maximum-likelihood fit. For the CR3HFe andthe CR3HFμ, the distributions of the pT(1) variable areincluded. A summary of the definition of all non-prompt con-trol regions can be found in Table 3.6.3 Control regions for t t¯W and t t¯ Z backgroundsThree additional control regions are defined to determinethe normalisation of the background from t t¯W and t t¯ Z pro-duction. Studies on various kinematic distributions in thesignal regions of the 2SS final state show a strong similar-ity between the two processes. Therefore, in this final stateonly one control region (denoted CR2t t¯V ) is defined toconstrain the sum of t t¯W and t t¯ Z . This region requires atleast four jets, exactly two of which are b-tagged, becauseboth the top quarks in the process are expected to producea b-quark. An additional requirement of pT(1) ≥ 18 GeVfurther increases the purity of the region in t t¯V events by123 757 Page 10 of 42 Eur. Phys. J. C (2024) 84:757 Fig. 3 The composition ofbackground processes in the aSR2Dec, b SR2Prod, cSR3Dec and d SR3Prod. TheOthers template containsvarious minor processes, whichindividually only have smallcontributions. No correction tothe normalisation of any processis appliedreducing contamination from HF-decay events. The pT(1)variable is used as input for the maximum-likelihood fit.In the 3 final state, distinct shape differences betweent t¯W and t t¯ Z production are observed due to the absenceof any requirement on the invariant mass of lepton pairs.Therefore, two control regions, CR3t t¯W and CR3t t¯ Z , aredefined. Both the regions require at least two jets, two ofwhich are b-tagged. Events are then assigned to the CR3t t¯ Zif at least one pair of leptons with the same flavour and oppo-site charge can be found satisfying |m(+, −) − m Z | <10 GeV. In cases where this criterion is not met, events areassigned to CR3t t¯W . In both the control regions, the trans-verse momentum of the pT-leading b-tagged jet pT(b-jet0)is used as input for the maximum-likelihood fit. A summaryof the definition of all t t¯V control regions can be found inTable 4.7 Separation of signal and backgroundArtificial neural networks (NNs) are used to separate signaland background in all four signal regions combining sev-eral kinematic variables into optimised NN discriminants. Inaddition to variables derived from the reconstructed objectsTable 3 Overview of the event selections applied to define the non-prompt lepton background control regions of the analysisCR2HFe CR2HFμ CR3HFe CR3HFμNjets ≤ 3 ≤ 3 ≥ 1 ≥ 1Nb-tags ≥ 1 ≥ 1 = 1 = 10 flavour μ μ – –1 flavour e μ – –pT(1) < 16 GeV < 16 GeV ≥ 20 GeV ≥ 20 GeV2 flavour – – e μpT(2) – – < 16 GeV < 16 GeVthe NNs build on a diverse range of reconstructed kinematicvariables. Detailed information regarding the reconstructionalgorithms is provided in Sect. 7.1, while a comprehen-sive description of the NN training process can be foundin Sect. 7.2.7.1 Event reconstruction in signal regionsThe reconstruction algorithms employed are described below.In t Hq FCNC interactions, multiple decay modes of theHiggs boson that contribute to the 2SS and 3 final states are123Eur. Phys. J. C (2024) 84:757 Page 11 of 42 757 Table 4 Overview of the eventselections applied to define thet t¯W and t t¯ Z control regions ofthe analysisCR2t t¯V CR3t t¯W CR3t t¯ ZNjets ≥ 4 ≥ 2 ≥ 2Nb-tags = 2 = 2 = 20 flavour μ – –pT(1) ≥ 18 GeV ≥ 20 GeV ≥ 20 GeVpT(2) – ≥ 16 GeV ≥ 16 GeV|m(+, −) − m Z | – ≥ 10 GeV < 10 GeVconsidered. However, the H → W W ∗ decay mode has byfar the largest contribution with ≥ 75 % in all signal regions.Thus, all reconstruction efforts presented here focus on thisspecific Higgs-boson decay mode. Most algorithms are cus-tomised to fit one of the two considered final states. Therelevant final states for each algorithm are given in parenthe-ses.Recursive jigsaw reconstruction (2SS and 3)The Recursive Jigsaw Reconstruction (RJR) technique [107]is a method for resolving combinatorial and kinematic ambi-guities which arise in hadron collider events. RJR relies ondecay trees which describe the topologies of interest, andrelates the reference frames of the intermediate particles inthe decay. Lepton and jet assignment, along with the split-ting of EmissT , is governed by a set of jigsaw rules which relyon known properties of the decay tree. For instance the top-quark and Higgs-boson masses can be used to constrain theassignment of the jets, or the W -boson mass can be used tofacilitate EmissT splitting and matching to leptons.This process leads to the computation of four-vectors ofthe reconstructed intermediate states, accessible in any ofthe frames defined in the decay tree. For each of the fourtopologies (21b2 j , 21b3 j , 31b0 j , 31b1 j , where b refersto Nb-jets and j to Njets) there are different intermediate states,split by production versus decay and again by final state. Theparticles that are reconstructed for each individual regionare listed in Table 5. These include W and Higgs bosons,and top quarks. Figure 4 depicts the probability densitiesof two RJR reconstructed variables for the t Hu signal andthe combination of all background processes, showing clearshape differences between the two.Neutrino independent combinatorics estimator (3) Theconsidered decay scenario of a signal event in the 3 finalstate involves one top quark decaying into a b-quark, a lep-ton and a neutrino, while the Higgs-boson decay is expectedto yield two leptons and two neutrinos. Studies of the MCsignal samples show that on average the two leptons from theHiggs-boson decay have the smallest angular separation outof any lepton pair in the event. Based on this information,the two leptons with the smallest angular separation R arelabelled H,0 and H,1, ordered by their transverse momen-tum. The remaining lepton is labelled t , while the b-taggedjet is denoted bt . Various kinematic parameters are calcu-lated for these objects, two of which are shown as examplesin Fig. 5 for the full t Hu signal and the combination of allbackground processes, demonstrating their high separationpower. However, these parameters are discarded, if the angu-lar separation of bt from either H,i is smaller than the sep-aration from t . Conversely, when the angular separation ofbt from t is found to be smaller than from any other lepton,and further, when H,0 and H,1 have opposite charges theNeutrino independent combinatorics estimator reconstruc-tion (NICE Reco) condition is defined as satisfied. In thisscenario, the calculated kinematic parameters have a partic-ularly high separation power between signal and backgroundprocesses. This information is provided as additional inputto the NNs.7.2 Training of feed-forward neural networksThe NNs are implemented using the NeuroBayes pack-age [108,109], which combines a three-layer feed-forwardNN with a complex and robust preprocessing of the inputvariables before they are presented to the NN. The prepro-cessing produces a ranking of the input variables based on analgorithm employing the total correlation of a set of variablesto the target function which assumes the value 1 for signaland 0 for background events. The input variable selection isperformed once per signal region.The selected variables of all signal regions are listed inTables 11, 12, 13, 14. Overall, invariant masses of recon-structed objects, including RJR objects, compose the largestfraction. The most significant variables in both the 3 sig-nal regions are the invariant mass of the opposite chargeand either of the two same charge leptons m(OS, SS,0) andm(OS, SS,1). In the SR2Prod, the invariant mass of thesubleading-pT lepton and the RJR Higgs boson m(1, H)is the most important variable, followed by the number ofjets Njets. The most significant variable of the SR2Dec isthe scalar pT sum of all jets HT (jets), a quantity that is alsohighly ranked in other trainings. The invariant mass of theleading-pT lepton and the event’s b-jet m(0, b-jet) is thesecond-highest ranked in the training.123 757 Page 12 of 42 Eur. Phys. J. C (2024) 84:757 Table 5 Particles from the t Hqprocesses which arereconstructed using theRecursive JigsawReconstruction (RJR) in therespective signal regionsRegions Particle name DescriptiontSM The top quark decaying via t → W bSR2Dec/ Wt The W boson from the SM top-quark decaySR3Dec tFCNC The top quark decaying via t → HqH The Higgs boson originating from th FCNC top-quark decaySR2Dec Whad The hadronically decaying W boson from the H → W W ∗ decaySR2Prod/ tSM The top quark produced in the gq → Ht processSR3Prod Wt The W boson from the top-quark decayH The Higgs boson produced in the gq → Ht processFig. 4 Probability densities of a m(1, tFCNC) in the SR2Dec and b m(Wt ) in the SR3Dec for the t Hu signal process and the sum of allbackground processes. The vertical lines on bins represent MC-statistical uncertainties. The last bin includes the overflowFig. 5 Probability densities of a m(H,0, H,1) and b m(t , bt ) in the SR3Dec for the t Hu signal process and the sum of all background processes.The vertical lines on bins represent MC-statistical uncertainties. The last bin includes the overflow123Eur. Phys. J. C (2024) 84:757 Page 13 of 42 757 Individual NNs are created for both the signal processesand every signal region, summing up to a total of eight NNarchitectures. The training uses the data-driven Q-misID esti-mate together with unmodified MC templates as input, beforeany corrections to their normalisation by the maximum-likelihood fit. Cross-training is employed to prevent over-fitting, where the signal and background MC events are splitinto half. The splitting is performed in a pseudo-random waybased on the parity of the unique event identification number.For each half, a separate NN model is trained, which is thenapplied to the other half of MC events in the final analysis.During the training process of all the NNs, the signal istrained against all considered backgrounds with a fraction of50 % signal events and 50 % background events. The differ-ent background processes are weighted relative to each otheraccording to their expected number of events. NeuroBayesuses Bayesian regularisation techniques for the training pro-cess to improve the generalisation performance and to avoidoverfitting. The network infrastructure consists of one inputnode for each input variable, a single hidden layer, andone output node giving a continuous output in the inter-val (−1,+1). The number of nodes in the hidden layer isoptimised individually for each NN model. As a non-linearactivation function NeuroBayes uses the symmetric sigmoidfunction. In the region close to zero, the sigmoid function hasa linear response. The final discriminant DNN is obtained bylinearly scaling the output of the NNs to the interval (0, 1).8 Systematic uncertaintiesSeveral sources of systematic uncertainty affect the expectedevent yield from signal and background processes and theshape of the NN discriminants used in the maximum-likelihood fits. The systematic uncertainties are divided intotwo major categories. There are experimental uncertaintiesin the reconstruction of the four-momenta of the final-stateobjects: electrons, muons, jets, b-tagged jets, and EmissT as asign of a high-pT neutrino. The second category of uncertain-ties is related to the modelling of scattering processes withevent generators and of the interaction of particles with thedetector. All uncertainties are propagated through the anal-ysis and their effects on the expected event yields and dis-criminant distributions are accounted for by including cor-responding nuisance parameters in the fit. In the following,the estimate of experimental and modelling uncertainties isexplained in more detail.8.1 Experimental uncertaintiesThe uncertainty in the integrated luminosity of the combined2015–2018 data set is 0.83% and is based on a calibration ofthe luminosity scale using x–y beam-separation scans [46].The luminosity uncertainty is applied to the expected signaland background event yields.Scale factors are applied to simulated events to correctfor reconstruction, identification, isolation and trigger per-formance differences between data and detector simulationfor electrons and muons. These scale factors and their sys-tematic uncertainties, and the lepton momentum scale andresolution, were assessed using Z → e+e− and Z → μ+μ−events in simulation and data [91,93].The jet energy scale (JES) was calibrated using a combina-tion of test-beam data, simulation and in situ techniques [99].The JES is parameterised in bins of jet pT and η. Its uncer-tainty is decomposed into a set of 30 uncorrelated compo-nents, of which 29 are non-zero in a given event depend-ing on the type of simulation used. Sources of uncertaintycontributing to the JES uncertainties include the η intercal-ibration of forward jets in the range of 0.8 < |ηdet| < 4.5with those in the central barrel region (|ηdet| < 0.8), pile-up modelling, jet flavour composition and response, differ-ences between jets induced by b-quarks and those from glu-ons or light-quarks, single-particle response, detector mod-elling, non-closure, and effects of jets not fully contained inthe calorimeter.The uncertainty of the jet energy resolution (JER) is eval-uated by smearing jet energies according to a Gaussian func-tion [99]. Thirteen orthogonal components account for jet-pT and η-dependent differences between simulation and datawhich were determined using dijet events and noise measure-ments based on random cones. The smearing is applied tosimulated events if the resolution in data is larger than in MCsimulation, and to pseudo-data when the resolution is largerin simulation than in collision data. The JER uncertaintiesare defined by comparing both types of smearing and therebytaking the anti-correlation between different components intoaccount. The nominal data remains unchanged. The uncer-tainty in the efficiency to satisfy the JVT requirement forpile-up suppression was derived in Z(→ μ+μ−)+jets eventsand is also considered [100]. The uncertainty in EmissT dueto a possible miscalibration of its soft-track component wasderived from data–simulation comparisons of the pT balancebetween the hard and soft EmissT components [102].The b-tagging requirement made in the measurement hasuncertainties in the b-tagging efficiency of true b-jets andin the mistagging rates of light-quark jets and c-jets. Theb-tagging efficiency is measured in dileptonic t t¯ events. Dif-ferences between data and detector simulation are correctedby pT-dependent scale factors applied to simulated events.The uncertainty in the scale factors is decomposed into 45orthogonal components [110]. The uncertainties are propa-gated through the analysis as weights. The set of uncertaintiesused covers both the 70 % working point used in this analysis,as well as other working points of theDL1rdiscriminant. Therate of mistagging c-jets as b-jets was measured in semilep-123 757 Page 14 of 42 Eur. Phys. J. C (2024) 84:757 tonic t t¯ events, where one of the W bosons decays into anelectron or a muon and a neutrino and the other decays intoa quark–antiquark pair [111]. This event sample allows toutilise the relatively large and known W → cs contribution.The mistagging rate of c-jets depends on the jet pT and has atotal uncertainty in the range of 317%. The uncertainties aredecomposed into 20 orthogonal components. The misiden-tification rate of light-quark jets was evaluated based on thetechniques described in Ref. [112]. The resulting calibrationfactors are in the range of about 1.5–3.0 with uncertaintiesup to 50 %. The uncertainties are decomposed into 20 inde-pendent eigenvectors.To account for differences between simulation and data inthe pile-up distribution, the pile-up profile in the simulationis corrected to match the one in data. The uncertainty in thecorrection factor is applied in the measurement as a variationof the event weight.8.2 Modelling uncertaintiesNormalisation uncertainties are applied to all processes,except for the ones whose normalisation is a free parameterof the maximum-likelihood fit, specifically for the HF-decaytemplates, for t t¯W and t t¯ Z production, and for the largestV V template V V 3 + b/c. Thus, no normalisation uncer-tainty is applied to t t¯ , single-top-quark, Z+jets and W +jetsproduction, all of which exclusively contribute to non-prompttemplates. Minor non-prompt templates are assigned 50 %normalisation uncertainties. The same is true for the minorV V templates and all rare processes discussed in Sect. 3.2.For t Zq and tW Z production, a respective uncertainty of30 % is assigned based on a previous ATLAS measurementof the processes [113]. Asymmetric uncertainties of +7%−10%are assigned to t t¯ H production, estimated by varying therenormalisation and factorisation scales, and the combinedPDF+αs uncertainties [28].Uncertainties in modelling parton showers and hadroni-sation are assigned to the t Hq signal samples, and the back-ground originating from t t¯ , t t¯ H , t t¯ Z and t t¯W production.For the signal and t t¯ , t t¯ H and t t¯ Z production the nominalsamples are compared with alternative samples, for whichthe individual matrix element generators were interfaced toHerwig[7.1.3] [114,115] (for t t¯ production), Herwig[7.0.4](for t t¯ H production) and Herwig[7.2.1] (for t t¯ Z production)instead of the respective versions of Pythia[8]. For t t¯W pro-duction, two alternative samples are generated. The matrixelement of both the samples is generated with Powheg-box[v2], which is interfaced toPythia[8] for one sample andto Herwig[7] for the other. The relative differences betweenthe two samples is determined for all bins in the analysis andapplied to the nominal Sherpa[2.2.10] t t¯W sample.The impact of the generator choice for t t¯W is evalu-ated using an alternative sample and is applied as system-atic uncertainties for both the normalisation and shape. Thisalternative sample is generated with up to one additional par-ton in the final state at NLO accuracy using Mgnlo[2.9.3],with different parton multiplicities being merged using theFxFx NLO matrix-element and parton-shower merging pre-scription [89] with a merging scale of 30 GeV. The eventsare interfaced with Pythia[8.245] using the A14 set of tunedparameters and the NNPDF[2.3lo] PDF set to simulate hadro-nisation and showering. The uncertainty is split into threecomponents: a shape uncertainty in each region, a regionmigration uncertainty and a global normalisation uncertainty.Uncertainties related to the choice of the renormalisationscale μr and the factorisation scale μf for the matrix-elementcalculations are evaluated by varying the scales indepen-dently by factors of 2 and 0.5, separately for V V productionand each of the top-quark production processes, includingproduction with an additional boson and the two signal pro-cesses. The scale variations are implemented as generatorweights in the nominal sample. The uncertainties are treatedas uncorrelated across individual processes.The uncertainty in matching the NLO matrix elementsto the parton shower when generating t t¯ events is evaluatedby comparing the nominal samples of simulated events tosamples with an alternative setting of the phardT parameter inthe matching code, using one instead of the default settingof zero. This parameter regulates the definition of the vetoedregion of the parton shower, which is needed to avoid overlapin the phase space filled by Powheg and Pythia. This esti-mate of the uncertainty follows the description in Ref. [116].The uncertainty in the choice of the hdamp parameter for thet t¯ event generation is estimated by using an additional t t¯sample produced with the hdamp parameter set to 3mt , whilekeeping all other generator settings the same as used for thenominal sample of events.Three uncertainties are defined for the modelling of theQ-misID template. The statistical uncertainty in the Q-misIDefficiencies obtained from the likelihood fit is taken intoaccount. An uncertainty in the selection of the Z -windowis calculated by redefining the Z -window with 3σ and 5σ ,where σ corresponds to the width of the fitted Breit–Wignerdistribution. The width of the Z -window is varied and theefficiencies are determined again, with the symmetrised dif-ference to the nominal values comprising the uncertainty,which is then propagated through the analysis. Finally, a non-closure uncertainty is implemented by applying the Q-misIDestimation method to a Z → ee MC sample and comparingthe resulting misidentification rates to the MC prediction.The symmetrised difference applied to the nominal Q-misIDrates constitutes the uncertainty.Uncertainties in the amount of initial-state radiation aredefined for the top-quark production processes t t¯ , t t¯ Z andt t¯ H . They are assessed by varying the eigentune Var3c ofthe A14 Pythia[8] tune consistent with the uncertainties of123Eur. Phys. J. C (2024) 84:757 Page 15 of 42 757 Fig. 6 Distributions of the most important NN input variable for thesignal regions a SR2Dec, b SR2Prod, c SR3Dec and d SR3Prod.The corrections from a background-only fit are applied. Only eventswith DNN < 0.5 were used in the fit and in the plots. The first bin con-tains all events below its lower boundary, while the last bin contains allevents falling above its upper boundary. The Others template containsvarious minor processes, which individually only have small contribu-tions. The total statistical and systematic uncertainty is indicated bythe hatched band. The dashed line depicts the sum of all backgroundprocesses prior to the fit. The last bin includes the overflow123 757 Page 16 of 42 Eur. Phys. J. C (2024) 84:757 Fig. 7 The DNN distributions in the a SR2Dec, b SR2Prod, cSR3Dec and d SR3Prod, obtained from the signal-plus-backgroundfit to data in the t Hc channel. The Others template contains variousminor processes, which individually only have small contributions. Thetotal statistical and systematic uncertainty is indicated by the hatchedband. The dotted line represents the distribution of the signal, scaled tothe number of background events. The dashed line depicts the sum ofall background processes prior to the fit123Eur. Phys. J. C (2024) 84:757 Page 17 of 42 757 Fig. 8 Summary plot of thefitted distributions in all controlregions obtained from thesignal-plus-background fit todata in the t Hc channel. The binboundaries for each region aredepicted by the parenthesisednumbers. The Others templatecontains various minorprocesses, which individuallyonly have small contributions.The total statistical andsystematic uncertainty isindicated by the hatched band.The dashed line depicts the sumof all background processesprior to the fitTable 6 The predicted and observed yields in all 2SS regions ofthe analysis from the signal-plus-background fit to signal and controlregions. The pre-fit predictions for the two signal components are pre-sented also, scaled to a cross-section equivalent to a branching ratioB(t → Hq) = 0.1 %. The Others template contains various minorprocesses, which individually only have small contributions. The uncer-tainties in non-signal MC yields reflect the sum in quadrature of all post-fit systematic and statistical uncertainties. The row labelled Post-fit BGshows the sum of all above background (BG) processes with post-fituncertainties, while the row labelled Pre-fit BG shows the total pre-fitbackground yield with the corresponding pre-fit uncertainties. Hyphenssignify that the corresponding process does not contribute to the givenregionProcess SR2Dec SR2Prod CR2HFe CR2HFμ CR2t t¯VHF-decay e 122 ± 27 113 ± 25 66 ± 13 – 2.9 ± 0.9HF-decay μ 201 ± 36 192 ± 35 0.1 ± 0.02 120 ± 22 5.6 ± 1.2Q-misID 204 ± 16 457 ± 35 2.4 ± 0.2 – 15.5 ± 1.4t t¯ H 132 ± 20 27 ± 5 0.6 ± 0.1 1.0 ± 0.2 51 ± 8t t¯W 512 ± 61 285 ± 42 4.8 ± 0.9 7.5 ± 1.4 216 ± 24t t¯ Z 210 ± 21 66 ± 9 1.5 ± 0.2 2.4 ± 0.4 70 ± 6V V 3+b/c 104 ± 20 192 ± 32 4.7 ± 1.0 6.6 ± 1.4 6.0 ± 1.2tW Z 23 ± 7 12 ± 4 0.11 ± 0.04 0.17 ± 0.06 3.6 ± 1.1t Zq 26 ± 8 63 ± 18 0.7 ± 0.2 1.1 ± 0.3 5.8 ± 1.7Others 340 ± 64 322 ± 46 36 ± 8 59 ± 20 79 ± 14Pre-fit BG 1845 ± 91 1585 ± 70 111 ± 11 210 ± 32 424 ± 22Post-fit BG 1874 ± 38 1729 ± 36 117 ± 10 198 ± 12 455 ± 17t t¯(t → Hu) 207 ± 22 181 ± 10 3.4 ± 0.3 5.4 ± 0.7 6.8 ± 0.6ug → Ht 31 ± 4 68 ± 2 1.2 ± 0.1 2.1 ± 0.2 1.1 ± 0.1t t¯(t → Hc) 196 ± 22 180 ± 10 3.5 ± 0.4 5.9 ± 0.7 13.4 ± 1.5cg → Ht 5 ± 1 11 ± 1 0.2 ± 0.1 0.4 ± 0.1 0.2 ± 0.1Data 1847 1723 116 193 443123 757 Page 18 of 42 Eur. Phys. J. C (2024) 84:757 Table 7 The predicted and observed yields in all 3 regions of theanalysis from the signal-plus-background fit to signal and controlregions. The pre-fit predictions for the two signal components are pre-sented as well, scaled to a cross-section equivalent to a branching ratioB(t → Hq) = 0.1 %. The Others template contains various minor pro-cesses, which individually only have small contributions. The uncertain-ties in non-signal MC yields reflect the sum in quadrature of all post-fitsystematic and statistical uncertainties. The row labelled Post-fit BGshows the sum of all above background (BG) processes with post-fituncertainties, while the row labelled Pre-fit BG shows the total pre-fitbackground yield with the corresponding pre-fit uncertainties. Hyphenssignify that the corresponding process does not contribute to the givenregionProcess SR3Prod SR3Dec CR3t t¯W CR3t t¯ Z CR3HFe CR3HFμHF-decay e 38 ± 9 14 ± 3 1.3 ± 0.3 0.28 ± 0.09 53 ± 11 –HF-decay μ 63 ± 11 22 ± 4 1.6 ± 0.3 0.37 ± 0.08 0.2 ± 0.1 122 ± 19Q-misID – – – – – –t t¯ H 10 ± 2 47 ± 7 32 ± 5 6.7 ± 1.1 3.0 ± 0.5 5.2 ± 0.9t t¯W 77 ± 12 80 ± 10 98 ± 16 12.5 ± 1.6 5.8 ± 1.0 9.5 ± 1.4t t¯ Z 75 ± 11 438 ± 40 78 ± 7 261 ± 20 14.7 ± 1.8 28 ± 3V V 3+b/c 296 ± 49 215 ± 39 4.8 ± 0.9 27 ± 5 15 ± 3 30 ± 5tW Z 19 ± 6 57 ± 18 2.9 ± 0.9 16 ± 5 1.9 ± 0.6 3.6 ± 1.1t Zq 134 ± 38 69 ± 20 3.5 ± 1.0 35 ± 10 6.1 ± 1.8 12 ± 3Others 171 ± 32 119 ± 23 43 ± 7 11.7 ± 1.5 59 ± 8 48 ± 9Pre-fit BG 710 ± 48 941 ± 42 228 ± 17 312 ± 19 148 ± 11 248 ± 16Post-fit BG 882 ± 28 1061 ± 28 265 ± 14 371 ± 17 159 ± 10 258 ± 14t t¯(t → Hu) 26 ± 2 39 ± 3 1.2 ± 0.2 0.7 ± 0.1 4.6 ± 0.5 8.0 ± 0.8ug → Ht 14 ± 1 7 ± 1 0.4 ± 0.1 0.2 ± 0.1 1.2 ± 0.1 2.1 ± 0.2t t¯(t → Hc) 27 ± 2 37 ± 3 4.3 ± 0.4 1.5 ± 0.1 4.4 ± 0.5 7.8 ± 0.7cg → Ht 2 ± 1 1 ± 1 0.1 ± 0.1 0.1 ± 0.1 0.2 ± 0.1 0.4 ± 0.1Data 896 1046 268 381 159 263Table 8 Normalisation factors for various backgrounds determinedfrom the signal-plus-background fit to signal and control regions. Theresults for the t Hu fit and the t Hc fit are shownProcess t Hu fit t Hc fitHF-decay e 1.05 ± 0.24 1.02 ± 0.23HF-decay μ 0.94 ± 0.18 0.92 ± 0.18V V 3 + b/c 1.41 ± 0.23 1.37 ± 0.24t t¯W 1.15 ± 0.14 1.19 ± 0.14t t¯ Z 1.16 ± 0.11 1.17 ± 0.11the tune. An uncertainty in the final-state radiation is intro-duced by varying the renormalisation scale μr in the partonshower, at which the strong coupling constant αs is evaluated,by factors of 0.5 and 2.0.In all uncertainty evaluations mentioned above the alter-native samples or reweighted samples are normalised to thetotal cross-section of the nominal samples.Uncertainties in the PDFs are evaluated for the back-ground processes simulated using Powhegbox, meaningt t¯ , single-t and t t¯ H production, using the PDF4LHC15prescription with 30 eigenvectors [117]. Simulated eventsare reweighted to the central value and the eigenvectors ofthe combined PDF set. Systematically varied templates areTable 9 The expected 95 % upper limits on the branching ratio B(t →Hq) for the nominal and alternative fit configurations. One fit is per-formed in the full phase space considering only statistical uncertainties.Two other fits are performed using the full set of uncertainties in onlythe 2SS or 3 final states. The ±1 σ interval of the expected limit isindicated by the upper and lower indices. For the t Hu channel, theassumption of B(t → Hc) = 0 is made and vice versaFit configuration Expected 95 % CL upper limits / 10−4B(t → Hu) B(t → Hc)Nominal fit 3.0+1.2−0.8 3.8+1.5−1.1Statistical uncertainties only 2.6+1.1−0.7 3.3+1.2−1.02SS final state only 3.6+1.5−1.0 4.3+1.9−1.23 final state only 6.5+2.7−1.9 8.9+3.7−2.6Table 10 The observed (expected) 95 % upper limits on the branchingratio B(t → Hq) and the absolute value of the Wilson coefficient|Cuφ | under the assumption of a cutoff-scale of  = 1 TeV. For thet Hu channel, the assumption of B(t → Hc) = 0 is made and viceversaSignal Observed (expected) 95 % CL upper limitsB(t → Hq) |Cqt,tquφ |t Hu 2.8 (3.0) × 10−4 0.71 (0.73)t Hc 3.3 (3.8) × 10−4 0.76 (0.82)123Eur. Phys. J. C (2024) 84:757 Page 19 of 42 757 constructed by taking the differences between the samplesreweighted to the central value and those reweighted to theeigenvectors. In the likelihood fit, the PDF uncertainties aretreated as correlated across the top-quark production pro-cesses.The uncertainties due to the finite number of simulatedevents, also called the MC statistical uncertainty, is accountedfor by adding a nuisance parameter for each bin of the DNNdistributions and the distributions in the CRs, implementingthe Barlow–Beeston approach [118].9 Statistical analysisThe normalisation μ of the t Hu and t Hc signal couplingsis determined in binned profile maximum-likelihood fits.The fits are performed simultaneously in all signal and con-trol regions. In the signal regions, the respective DNN dis-tributions optimised for the considered signal coupling areused. For the CR2HFe and CR2HFμ only event yields areemployed in the fit, whereas for the CR3HFe and CR3HFμthe transverse momentum of the third-leading-pT lepton isfitted. In the CR2t t¯V , the distribution of the subleading-pTlepton’s transverse momentum is used, as it provides separa-tion between prompt and non-prompt leptons. The CR3t t¯Wand CR3t t¯ Z are incorporated into the fit with the distribu-tion of the transverse momentum of the leading-pT b-taggedjet. This distribution separates the t t¯ Z background fromremaining V V events in the CR3t t¯ Z and is also adopted inthe CR3t t¯W for reasons of consistency. In the fits, each ofthe signal processes are treated as maximally anti-correlated,implying that the presence of one signal automatically pre-cludes the presence of the other signal.The likelihood function is constructed as a product of Pois-son probability terms over all considered bins. The fittedevent yields in the bins depend on nuisance parameters θwhich include the effects of systematic uncertainties. Eachnuisance parameter, except those representing the MC statis-tical uncertainties, is constrained by a Gaussian distributionterm in the likelihood function. Some systematically varieddiscriminant distributions are smoothed and nuisance param-eters of systematic uncertainties with negligible impact onthe parameter of interest are entirely removed to reduce spu-rious effects in minimisation, improve convergence of thefit, and reduce the computing time. Normalisation and shapeeffects from a source of systematic uncertainty are treatedseparately in this removal process. Single-sided systematicvariations are turned into symmetric variations by taking thedifference between the nominal model and the alternativemodel and mirroring this difference in the opposite direc-tion. This is done for the event yield and for the event shape,where the distributions are subtracted from the nominal one.For most sources with two variations, their effects are madesymmetric by using the average deviation from the nominalprediction. Exceptions are the uncertainties in the JER, forwhich the asymmetric variations are kept because the under-lying effects are known to be asymmetric. Free-floating nor-malisation factors are assigned to the templates modellingthe HF-decay e and HF-decay μ background, as well as theV V 3+b/c, t t¯W , and t t¯ Z templates.The test statistic qμ is defined as the profile likelihoodratioqμ = −2 ln L(μ,ˆˆθ)L(μˆ, θˆ ) ,where μˆ and θˆ are the values of the parameters that max-imise the likelihood function and ˆˆθ are the values of thenuisance parameters that maximise the likelihood functionfor a given value of μ. The test statistic is evaluated with theRooFit package [119]. If the observed signal normalisation μis compatible with the background hypothesis, that is μ = 0,the test statistic qμ is used in the CLS method [120] to obtainexclusion limits on the signal normalisation. For a given sig-nal scenario, values of μ yielding CLS ≤ 0.05, where CLSis computed using the asymptotic approximation [121], areexcluded at ≥ 95 % CL. The obtained upper limits on the sig-nal strength μ are then transformed into limits on the respec-tive Wilson coefficient Cuφ and the corresponding branchingratio B(t → Hq) through their dimension-6 operators [60].10 ResultsThis section presents the results of the profile-likelihood fit.Prior to the full fit to extract the signal normalisation, abackground-only fit using only regions with little signal con-tribution is performed to check the modelling of NN inputvariables. Once the modelling is checked and validity of thefit model is established, the signal normalisation is deter-mined in a full fit to data using the entire phase space of theanalysis.10.1 Cross-checks on the modelling of the neural networkinput variablesBefore the application of the NNs to the full collision data,modelling of the input variables is checked in parts of thesignal regions. For this purpose, the events populating therespective signal regions up to a threshold value of DNN =0.5 are selected. The threshold of DNN = 0.5 is chosen tomaximise the available statistics while avoiding a signal con-tamination of more than 10 %. The full fit is performed withboth statistical and systematic uncertainties considered in allcontrol regions and the low-DNN signal regions. The correc-123 757 Page 20 of 42 Eur. Phys. J. C (2024) 84:757 tions made by the fit are then applied to the input variablesof the various NNs, using only events with DNN < 0.5, tocheck the variable modelling. The resulting distributions ofthe most important NN input variables in each signal regionare shown in Fig. 6. Overall, no discrepancies between thepost-fit distributions and data could be observed in any of theinput variables.10.2 Full fit to dataFigure 7 shows the DNN(t Hc) distributions in all four sig-nal regions after the fit. A summary plot of all 2SS and 3control regions is shown in Fig. 8. Overall, a good agree-ment between MC and data is observed. The event yieldsshown in Tables 6, 7 confirm this. The best fit value ofthe normalisation of the t Hu (t Hc) signal is found to beμt Hq = −0.03 ± 0.15(−0.08 ± 0.19). No pulls beyond 1σor strong constraints are observed for any of the nuisanceparameters. The observed post-fit values of all normalisa-tion factors and nuisance parameters are in agreement withthe background-only fit consistent with the statistical uncer-tainties, suggesting a good modelling of the most signal-sensitive DNN bins. The obtained normalisation factors forfree-floating background processes are listed in Table 8. Forthe HF-decay e and HF-decay μ processes they are com-patible with one. A 40 % increase can be observed for theV V 3+b/c template, owing to the poorer modelling of b-jetsby the shower generator. The normalisations of the t t¯W andt t¯ Z processes are increased by approximately 15 %, which iscompatible at a 1σ level. The increased normalisation of t t¯Wproduction is expected based on dedicated measurements ofthe process, while for t t¯ Z , the slightly higher normalisationcomes from the inclusion of events with low jet multiplicity.Studies on the process confirm that for higher values of Njetsthe normalisation is compatible with one.As the best fit value of the signal strength is compati-ble with μ = 0, upper limits are determined with the CLSmethod. In addition to the nominal limits of the analysis,expected limits are determined for a fit considering only sta-tistical uncertainties, as well as for fits in the 2SS and 3channels separately. A comparison of the expected upper lim-its on the branching ratio B(t → Hq) for each configurationis shown in Table 9. A degradation in the expected upperlimit of approximately 20 % can be observed for both thesignal processes when systematic uncertainties are included.This shows that the sensitivity of this analysis is primarilylimited by available statistics. When comparing the two finalstates with each other, a clear dominance of the 2SS finalstate can be observed. Including the 3 final states yields animprovement of 20 % in the t Hu channel and 13 % in thet Hc channel.The observed upper limits on the branching ratio B(t →Hq) together with a reinterpretation as limits on the absolutevalue of the Wilson coefficient |Cuφ | for the EFT dimension-6 operators can be found in Table 10. The signal does notinterfere with other SM processes, meaning that the signalnormalisation is proportional to |Cuφ |2 and limits can only beset on the coefficient’s absolute value. Additionally, owing tothe averaging of the left-handed and the right-handed signalcomponent, these limits are set on the average of the tworespective coefficients |Ctquφ | and |Cqtuφ |. The final observed(expected) upper limits on the branching ratio are B(t →Hu) < 2.8 (3.0) × 10−4 and B(t → Hc) < 3.3 (3.8) ×10−4 for a cutoff scale  = 1 TeV. The limits on the Wilsoncoefficients amount to |Cut,tuuφ | < 0.71 (0.73) and |Cct,tcuφ | <0.76 (0.82). Limits for each of the two signal couplings aredetermined with the assumption that the other signal couplingdo not contribute.Compared with a previous ATLAS search for t Hq FCNCcouplings in 2SS/ 3 final states using a partial Run 2 datasample of 36 fb−1 [32], a luminosity-adjusted improvementby a factor of two for the t Hc channel and three for thet Hu channel can be observed. This is determined by creat-ing an Asimov-data sample, scaling its luminosity to that ofthe previous analysis, and comparing the resulting expectedupper limits to the original analysis. This improvement pri-marily results from using improved analysis techniques suchas new methods for event reconstruction and a more thoroughmultivariate analysis, and more precise detector calibrations.The additional improvement in the t Hu channel is achievedbecause of the inclusion of the gq → Ht production processin the analysis. This process primarily plays a role in the t Huchannel because the up quark is a valence quark of the proton.11 Combination of results with other searchesThe reported results are combined with the correspondingATLAS searches that use H → τ+τ− decays with one ortwo hadronically decaying τ -leptons [33], and H → bb¯ [34]and H → γ γ [35] decays. For clarity, this analysis isreferred to as the H → V V ∗ channel in the following, asthe H → W W ∗/Z Z∗ decay modes are by far the most dom-inant ones contributing to 2SS and 3 final states. Orthogo-nality among all analyses is ensured by their respective eventselections. The H → τ+τ− and the H → V V ∗ analy-sis, specifically, are orthogonal to each other, because theH → τ+τ− analysis exclusively uses events with exactlyone or zero leptons. The combination is performed througha simultaneous profile-likelihood fit of all four analyses. Thecorrelations between the uncertainties in the different chan-nels are assessed. In each search, the dominant systematicuncertainties are different. In addition, the H → τ+τ−,H → γ γ and H → V V ∗ channels are dominated by thestatistical uncertainty in the data. Therefore, the combina-tion exhibits minimal sensitivity to possible correlations of123Eur. Phys. J. C (2024) 84:757 Page 21 of 42 757 Fig. 9 The 95 % CL upper limits on a B(t → Hu) assuming B(t →Hc) = 0 and b B(t → Hc) assuming B(t → Hu) = 0 for the individ-ual searches and their combination. The observed limits (solid lines) arecompared with the expected (median) limits under the background-onlyhypothesis (dotted lines). The surrounding shaded bands correspond tothe 68 % and 95 % CL intervals around the expected limits, denoted by±1σ and ±2σ , respectively. The H → V V ∗ also includes events fromleptonic H → τ+τ− decaysuncertainties across channels. Specifically, uncertainties per-taining to luminosity, pile-up modelling, and jet energy scaleand resolution are correlated among the four channels. Theuncertainties related to b-tagging are correlated between theH → τ+τ−, the H → bb¯ and the H → V V ∗ analy-ses, but uncorrelated with the H → γ γ analysis, whichuses a simplified b-tagging scheme. The remaining uncer-tainties (mostly from experimental sources, and signal andbackground modelling) are taken as uncorrelated. Some ofthe sources of systematic uncertainties (especially related toelectron and muon identification and signal modelling) arecommon to the three search channels, but are treated as uncor-related due to slight differences in their treatment by individ-ual analyses. The combined p-value for the t Hu fit is 0.134,while that for the t Hc fit it is 0.117, showing an overall goodagreement among the four analyses.The observed (expected) 95 % CL combined upper limitson the branching ratios are B(t → Hu) < 2.6 (1.8) × 10−4and B(t → Hc) < 3.4 (2.3) × 10−4. For the t Hc couplingthe observed limit is larger than that of the individual H →V V ∗ analysis, because of the strong upward-fluctuation inthe H → τ+τ− analysis. A summary of the upper limits onthe branching ratios from the individual searches, and theircombination, is given in Fig. 9. In the EFT framework, thelimits observed for the respective branching ratios translateto a limit on the Wilson coefficients of the t Hu dimension-6 operators of |Cut,tuuφ | < 0.68(0.56) at 95 % CL, assumingCct,tcuφ = 0, and for a mass scale  = 1 TeV. The analogouslimit on the Wilson coefficient of the t Hc dimension-6 oper-ator amounts to |Cct,tcuφ | < 0.78(0.64) assuming Cut,tuuφ = 0.12 ConclusionA search is reported for FCNC couplings between the topquark, the Higgs boson and a second up-type quark in finalstates containing either two leptons of the same charge orthree leptons. This search uses 140 fb−1 of proton–protoncollision data collected with the ATLAS detector at the LHCbetween 2015 and 2018. The FCNC processes are consideredin t t¯ production where either the top quark or the top anti-quark decays via t → Hq, and in the production of a singletop quark with a Higgs boson via the q → t H FCNC process.The results are compatible with the SM and no evidence ofFCNC couplings is observed. Upper limits at 95 % CL are seton the branching ratio B(t → Hq). The observed (expected)upper limits on the branching ratio are B(t → Hu) <2.8 (3.0) × 10−4 and B(t → Hc) < 3.3 (3.8) × 10−4. Theyare reinterpreted as limits on the average of the Wilson coef-ficients for the left-handed and the right-handed dimension-6 operators modelling the effective t Hq couplings with anew physics scale at  = 1 TeV. These limits amount to|Cut,tuuφ | < 0.71 (0.73) and |Cct,tcuφ | < 0.76 (0.82). Theseare the most stringent upper limits reported by any anal-ysis searching for t Hq FCNC couplings with the ATLASdetector. They are also lower than any other search for thesecouplings in 2SS and 3 final states.The results are combined with three other searches fort Hq FCNC couplings with the ATLAS detector. The com-bined observed (expected) limits set by all four analyses,considering correlations between the individual searches,are B(t → Hu) < 2.6 (1.8) × 10−4 and B(t → Hc) <3.4 (2.3) × 10−4 on the branching ratios, and |Cut,tuuφ | <123 757 Page 22 of 42 Eur. Phys. J. C (2024) 84:757 0.68(0.56) and |Cct,tcuφ | < 0.78(0.64) on the dimension-6Wilson coefficients.Acknowledgements We thank CERN for the very successful oper-ation of the LHC and its injectors, as well as the support staff atCERN and at our institutions worldwide without whom ATLAS couldnot be operated efficiently.The crucial computing support from allWLCG partners is acknowledged gratefully, in particular from CERN,the ATLAS Tier-1 facilities at TRIUMF/SFU (Canada), NDGF (Den-mark, Norway, Sweden), CC-IN2P3 (France), KIT/GridKA (Germany),INFN-CNAF (Italy), NL-T1 (Netherlands), PIC (Spain), RAL (UK)and BNL (USA), the Tier-2 facilities worldwide and large non-WLCGresource providers. Major contributors of computing resources are listedin Ref. [122]. We gratefully acknowledge the support of ANPCyT,Argentina; YerPhI, Armenia; ARC, Australia; BMWFW and FWF, Aus-tria; ANAS, Azerbaijan; CNPq and FAPESP, Brazil; NSERC, NRCand CFI, Canada; CERN; ANID, Chile; CAS, MOST and NSFC,China; Minciencias, Colombia; MEYS CR, Czech Republic; DNRFand DNSRC, Denmark; IN2P3-CNRS and CEA-DRF/IRFU, France;SRNSFG, Georgia; 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, Nether-lands; RCN, Norway; MEiN, Poland; FCT, Portugal; MNE/IFA, Roma-nia; MESTD, Serbia; MSSR, Slovakia; ARRS and MIZŠ, Slove-nia; DSI/NRF, South Africa; MICINN, Spain; SRC and WallenbergFoundation, Sweden; SERI, SNSF and Cantons of Bern and Geneva,Switzerland; MOST, Taipei; TENMAK, Türkiye; STFC, United King-dom; DOE and NSF, USA. Individual groups and members havereceived support from BCKDF, CANARIE, CRC and DRAC, Canada;CERN-CZ, PRIMUS 21/SCI/017 and UNCE SCI/013, Czech Repub-lic; COST, ERC, ERDF, Horizon 2020, ICSC-NextGenerationEU andMarie Skłodowska-Curie Actions, European Union; Investissementsd’Avenir Labex, Investissements d’Avenir Idex and ANR, France; DFGand AvH Foundation, Germany; Herakleitos, Thales and Aristeia pro-grammes co-financed by EU-ESF and the Greek NSRF, Greece; BSF-NSF and MINERVA, Israel; Norwegian Financial Mechanism 2014-2021, Norway; NCN and NAWA, Poland; La Caixa Banking Founda-tion, CERCA Programme Generalitat de Catalunya and PROMETEOand GenT Programmes Generalitat Valenciana, Spain; Göran Gustafs-sons Stiftelse, Sweden; The Royal Society and Leverhulme Trust, UK.In addition, individual members wish to acknowledge support fromCERN: European Organization for Nuclear Research (CERN PJAS);Chile: Agencia Nacional de Investigación y Desarrollo (FONDECYT1190886, FONDECYT 1210400, FONDECYT 1230812, FONDE-CYT 1230987); China: National Natural Science Foundation of China(NSFC-12175119, NSFC 12275265, NSFC-12075060); Czech Repub-lic: PRIMUS Research Programme (PRIMUS/21/SCI/017); EuropeanUnion: European Research Council (ERC-948254, ERC 101089007),Horizon 2020 Framework Programme (MUCCA-CHIST-ERA-19-XAI-00), European Union, Future Artificial Intelligence Research(FAIR-NextGenerationEU PE00000013), Italian Center for High Per-formance Computing, Big Data and Quantum Computing (ICSC,NextGenerationEU); France: Agence Nationale de la Recherche (ANR-20-CE31-0013, ANR-21-CE31-0013, ANR-21-CE31-0022), Investisse-ments d’Avenir Labex (ANR-11-LABX-0012); Germany: Baden-Württemberg Stiftung (BW Stiftung-Postdoc Eliteprogramme), DeutscheForschungsgemeinschaft (DFG-469666862, DFG-CR 312/5-2); Italy:Istituto Nazionale di Fisica Nucleare (ICSC, NextGenerationEU);Japan: Japan Society for the Promotion of Science (JSPS KAK-ENHI JP21H05085, JSPS KAKENHI JP22H01227, JSPS KAK-ENHI JP22H04944, JSPS KAKENHI JP22KK0227); Netherlands:Netherlands Organisation for Scientific Research (NWO Veni 2020-VI.Veni.202.179); Norway: Research Council of Norway (RCN-314472); Poland: Polish National Agency for Academic Exchange(PPN/PPO/2020/1/00002/U/00001), Polish National Science Centre(NCN 2021/42/E/ST2/00350, NCN OPUS nr 2022/47/B/ST2/03059,NCN UMO-2019/34/E/ST2/00393, UMO-2020/37/B/ST2/01043, UMO-2021/40/C/ST2/00187, UMO-2022/47/O/ST2/00148); Slovenia: Slove-nian Research Agency (ARIS grant J1-3010); Spain: BBVA Foun-dation (LEO22-1-603), Generalitat Valenciana (Artemisa, FEDER,IDIFEDER/2018/048), Ministry of Science and Innovation (MCINand NextGenEU-PCI2022-135018-2, MICIN and FEDER-PID2021-125273NB, RYC2019-028510-I, RYC2020-030254-I, RYC2021-031273-I, RYC2022-038164-I), PROMETEO and GenT Programmes General-itat Valenciana (CIDEGENT/2019/023, CIDEGENT/2019/027); Swe-den: Swedish Research Council (VR 2018-00482, VR 2022-03845, VR2022-04683, VR grant 2021-03651), Knut and Alice Wallenberg Foun-dation (KAW 2017.0100, KAW 2018.0157, KAW 2018.0458, KAW2019.0447, KAW 2022.0358); Switzerland: Swiss National ScienceFoundation (SNSF-PCEFP2_194658); UK: Leverhulme Trust (Lever-hulme Trust RPG-2020-004), Royal Society (NIF-R1-231091); UnitedStates of America: Neubauer Family Foundation.Data Availability Statement This manuscript has no associated data.[Author’s comment: “All ATLAS scientific output is published in jour-nals, and preliminary results are made available in Conference Notes.All are openly available, without restriction on use by external partiesbeyond copyright law and the standard conditions agreed by CERN.Data associated with journal publications are also made available: tablesand data from plots (e.g. cross section values, likelihood profiles, selec-tion efficiencies, cross section limits, ...) are stored in appropriate repos-itories such as HEPDATA (http://hepdata.cedar.ac.uk/). ATLAS alsostrives to make additional material related to the paper available thatallows a reinterpretation of the data in the context of new theoreti-cal models. For example, an extended encapsulation of the analysis isoften provided for measurements in the framework of RIVET (http://rivet.hepforge.org/).” This information is taken from the ATLAS DataAccess Policy, which is a public document that can be downloaded fromhttp://opendata.cern.ch/record/413 [opendata.cern.ch].]Code Availability Statement This manuscript has no associatedcode/software. [Author’s comment: Code/Software sharing not applica-ble to this article as no code/software was generated or analysed duringthe current study.]Open Access This article is licensed under a Creative Commons Attri-bution 4.0 International License, which permits use, sharing, adaptation,distribution and reproduction in any medium or format, as long as yougive appropriate credit to the original author(s) and the source, pro-vide a link to the Creative Commons licence, and indicate if changeswere made. The images or other third party material in this articleare included in the article’s Creative Commons licence, unless indi-cated otherwise in a credit line to the material. If material is notincluded in the article’s Creative Commons licence and your intendeduse is not permitted by statutory regulation or exceeds the permit-ted use, you will need to obtain permission directly from the copy-right holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.Funded by SCOAP3.AppendixTables 11, 12, 13, 14 list the input variables to the NNsused in the four signal regions, approximately ordered bythe increase in significance provided by each variable. Theexact order differs among the two signal processes.123Eur. Phys. J. C (2024) 84:757 Page 23 of 42 757 Table 11 List of input variables to the NN in the SR3Prod, approximately ordered by the increase in significance provided by each variable. Theexact order differs among the two signal processesVariable Descriptionm(OS, SS,1) Invariant mass of the opposite-charge and the subleading-pT same-charge leptonm(OS, SS,0) Invariant mass of the opposite-charge and the leading-pT same-charge leptonm(t , bt ) Invariant mass of the b-tagged jet and the lepton assigned to the top-quark decayNjets Number of jetsHT (jets) Scalar sum of the pT of all jetsm(tSM, H) Invariant mass of the RJR top quark decaying via t → W b and the Higgs boson R(SS,0, SS,1) Angular separation between the leading and subleading-pT same-charge leptonm(H,0, H,1) Invariant mass of the two leptons assigned to the Higgs-boson decaym(b-jet, SS,0) Invariant mass of the b-tagged jet and the leading-pT same-charge lepton R(t , bt ) Angular separation between the b-tagged jet and the lepton assigned to the top-quark decaypT(tSM) Transverse momentum of the RJR top quark decaying via t → W bpT(b-jet) Transverse momentum of the b-tagged jetη(SS,1) Pseudorapidity of the subleading-pT same-charge leptonpT(SS,1) Transverse momentum of the subleading-pT same-charge leptonm(H, SS,1) Invariant mass of the RJR Higgs boson and the subleading-pT same-charge lepton R(tSM, OS) Angular separation between the RJR top quark decaying via t → W b and the opposite-charge lepton R(H, OS) Angular separation between the RJR Higgs boson and the opposite-charge lepton R(OS,SS,1 ) Angular separation between the opposite-charge and the subleading-pT same-charge leptonTable 12 List of input variables to the NN in the SR3Dec, approximately ordered by the increase in significance provided by each variable. Theexact order differs among the two signal processes. Variables labelled NICE were reconstructed with a fulfilled NICE Reco conditionVariable Descriptionm(OS, SS,1) Invariant mass of the opposite-charge and the subleading-pT same-charge leptonm(OS, SS,0) Invariant mass of the opposite-charge and the leading-pT same-charge leptonNICE m(t , bt ) Invariant mass of the b-tagged jet and the lepton assigned to the top-quark decay with a fulfilled NICE Reco conditionHT (jets) Scalar sum of the pT of all jetsm(b-jet, SS,0) Invariant mass of the b-tagged jet and the leading-pT same-charge leptonm(tSM, H) Invariant mass of the RJR top quark decaying via t → W b and the RJR Higgs bosonm(H,0, H,1) Invariant mass of the two leptons assigned to the Higgs-boson decaym(H, SS,1) Invariant mass of the RJR Higgs boson and the subleading-pT same-charge lepton R(b-jet, tSM) Angular separation between the b-tagged jet and the RJR top quark decaying via t → W bm(0, tSM) Invariant mass of the leading-pT lepton and the RJR top quark decaying via t → W bpT(tSM) Transverse momentum of the RJR top quark decaying via t → W bm(tSM, SS,1) Invariant mass of the RJR top quark decaying via t → W b and the subleading-pT same-charge lepton R(OS, SS,0) Angular separation between the opposite-charge and the leading-pT same-charge leptonpT(OS) Transverse momentum of the opposite-charge leptonm(b-jet, OS) Invariant mass of the b-tagged jet and the opposite-charge leptonm(b-jet, H) Invariant mass of the b-tagged jet and the RJR Higgs bosonpT(2) Transverse momentum of the third-leading-pT leptonη(0) Pseudorapidity of the leading-pT leptonm(Wt ) Mass of the RJR W boson from the top-quark decaym(t , bt ) Invariant mass of the b-tagged jet and the lepton assigned to the top-quark decay123 757 Page 24 of 42 Eur. Phys. J. C (2024) 84:757 Table 13 List of input variables to the NN in the SR2Prod, approximately ordered by the increase in significance provided by each variable. Theexact order differs among the various signal processesVariable Descriptionm(1, H) Invariant mass of the subleading-pT lepton and the RJR Higgs bosonNjets Number of jetsm(b-jet, tSM) Invariant mass of the b-tagged jet and the RJR top quark decaying via t → W bm(H, b-jet) Invariant mass of the RJR Higgs boson and the b-tagged jetpT(Whad) Transverse momentum of the hadronically decaying RJR W boson R(1, H) Angular separation between the subleading-pT lepton and the RJR Higgs bosonm(Whad) Mass of the hadronically decaying RJR W bosonpT(1) Transverse momentum of the subleading-pT leptonη(1) Pseudorapidity of the subleading-pT lepton R(H, Wt ) Angular separation between the RJR Higgs boson and the RJR W boson from the top-quark decay R(0, 1) Angular separation between leading and subleading-pT leptonm(1, b-jet) Invariant mass of the subleading-pT lepton and the b-tagged jetη(b-jet) Pseudorapidity of the b-tagged jet R(0, tSM) Angular separation between the leading-pT lepton and the RJR top quark decaying via t → W bEmissT Missing transverse momentumfl.(0) Flavour of the leading-pT leptonη(0) Pseudorapidity of the leading-pT leptonpT(0) Transverse momentum of the leading-pT lepton R(1, tSM) Angular separation between the subleading-pT lepton and the RJR top quark decaying via t → W bm(H, Wt ) Invariant mass of the RJR Higgs boson and the RJR W boson from the top-quark decay R(1, Wt ) Angular separation between the subleading-pT lepton and the RJR W boson from the top-quark decaym(0, H) Invariant mass of the leading-pT lepton and the RJR Higgs bosonpT(b-jet) Transverse momentum of the b-tagged jetTable 14 List of input variables to the NN in the SR2Dec, approximately ordered by the increase in significance provided by each variable. Theexact order differs among the various signal processesVariable DescriptionHT (jets) Scalar sum of the pT of all jetsm(0, b-jet) Invariant mass of the leading-pT lepton and the b-tagged jet R(1, H) Angular separation between the subleading-pT lepton and the RJR Higgs bosonpT(1) Transverse momentum of the subleading-pT leptonm(jetsmin R) Invariant mass of the two non-b-tagged jets with the smallest Rm(tSM, l-jet0) Invariant mass of the RJR top quark decaying via t → W b and the leading-pT non-b-tagged jetη(1) Pseudorapidity of the subleading-pT lepton R(0, l-jet1) Angular separation between the leading-pT lepton and the subleading-pT non-b-tagged jetm(1, l-jet0) Invariant mass of the subleading-pT lepton and the leading-pT non-b-tagged jetm(0, l-jet0) Invariant mass of the leading-pT lepton and the leading-pT non-b-tagged jet R(0, l-jet2) Angular separation between the leading-pT lepton and the third-leading-pT non-b-tagged jet R(1, l-jet2) Angular separation between the subleading-pT lepton and the third-leading-pT non-b-tagged jetm(tFCNC, l-jet0) Invariant mass of the RJR top quark decaying via t → Hqand the leading-pT non-b-tagged jetm(1, l-jet1) Invariant mass of the subleading-pT lepton and the subleading-pT non-b-tagged jetm(1, tFCNC) Invariant mass of the subleading-pT lepton and the RJR top quark decaying via t → Hqm(Wt , Whad) Invariant mass of the RJR W boson from the top-quark decay and the hadronically decaying RJR W boson R(0, l-jet0) Angular separation between the leading-pT lepton and the leading-pT non-b-tagged jet123Eur. 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Zwalinski361 Department of Physics, University of Adelaide, Adelaide, Australia2 Department of Physics, University of Alberta, Edmonton, AB, Canada3 (a)Department of Physics, Ankara University, Ankara, Türkiye; (b)Division of Physics, TOBB University of Economicsand Technology, Ankara, Türkiye4 LAPP, Université Savoie Mont Blanc, CNRS/IN2P3, Annecy, France5 APC, Université Paris Cité, CNRS/IN2P3, Paris, France6 High Energy Physics Division, Argonne National Laboratory, Argonne, IL, USA7 Department of Physics, University of Arizona, Tucson, AZ, USA8 Department of Physics, University of Texas at Arlington, Arlington, TX, USA9 Physics Department, National and Kapodistrian University of Athens, Athens, Greece10 Physics Department, National Technical University of Athens, Zografou, Greece11 Department of Physics, University of Texas at Austin, Austin, TX, USA12 Institute of Physics, Azerbaijan Academy of Sciences, Baku, Azerbaijan13 Institut de Física d’Altes Energies (IFAE), Barcelona Institute of Science and Technology, Barcelona, Spain14 (a)Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China; (b)Physics Department, TsinghuaUniversity, Beijing, China; (c)Department of Physics, Nanjing University, Nanjing, China; (d)School of Science,123 757 Page 38 of 42 Eur. Phys. J. C (2024) 84:757 Shenzhen Campus of Sun Yat-sen University, Shenzhen, China; (e)University of Chinese Academy of Science (UCAS),Beijing, China15 Institute of Physics, University of Belgrade, Belgrade, Serbia16 Department for Physics and Technology, University of Bergen, Bergen, Norway17 (a)Physics Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA; (b)University of California, Berkeley,CA, USA18 Institut für Physik, Humboldt Universität zu Berlin, Berlin, Germany19 Albert Einstein Center for Fundamental Physics and Laboratory for High Energy Physics, University of Bern, Bern,Switzerland20 School of Physics and Astronomy, University of Birmingham, Birmingham, UK21 (a)Department of Physics, Bogazici University, Istanbul, Türkiye; (b)Department of Physics Engineering, GaziantepUniversity, Gaziantep, Türkiye; (c)Department of Physics, Istanbul University, Istanbul, Türkiye22 (a)Facultad de Ciencias y Centro de Investigaciónes, Universidad Antonio Nariño, Bogotá, Colombia; (b)Departamentode Física, Universidad Nacional de Colombia, Bogotá, Colombia23 (a)Dipartimento di Fisica e Astronomia A. Righi, Università di Bologna, Bologna, Italy; (b)INFN Sezione di Bologna,Bologna, Italy24 Physikalisches Institut, Universität Bonn, Bonn, Germany25 Department of Physics, Boston University, Boston, MA, USA26 Department of Physics, Brandeis University, Waltham, MA, USA27 (a)Transilvania University of Brasov, Brasov, Romania; (b)Horia Hulubei National Institute of Physics and NuclearEngineering, Bucharest, Romania; (c)Department of Physics, Alexandru Ioan Cuza University of Iasi, Iasi, Romania; (d)Physics Department, National Institute for Research and Development of Isotopic and Molecular Technologies,Cluj-Napoca, Romania; (e)National University of Science and Technology Politechnica, Bucharest, Romania; (f)WestUniversity in Timisoara, Timisoara, Romania; (g)Faculty of Physics, University of Bucharest, Bucharest, Romania28 (a)Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovak Republic; (b)Department ofSubnuclear Physics, Institute of Experimental Physics of the Slovak Academy of Sciences, Kosice, Slovak Republic29 Physics Department, Brookhaven National Laboratory, Upton, NY, USA30 Instituto de Física de Buenos Aires (IFIBA), Departamento de Física, y CONICET, Facultad de Ciencias Exactas yNaturales, Universidad de Buenos Aires, Buenos Aires, Argentina31 California State University, Los Angeles, CA, USA32 Cavendish Laboratory, University of Cambridge, Cambridge, UK33 (a)Department of Physics, University of Cape Town, Cape Town, South Africa; (b)iThemba Labs, Western Cape, SouthAfrica; (c)Department of Mechanical Engineering Science, University of Johannesburg, Johannesburg, SouthAfrica; (d)National Institute of Physics, University of the Philippines, Diliman, Philippines; (e)Department of Physics,University of South Africa, Pretoria, South Africa; (f)University of Zululand, KwaDlangezwa, South Africa; (g)School ofPhysics, University of the Witwatersrand, Johannesburg, South Africa34 Department of Physics, Carleton University, Ottawa, ON, Canada35 (a)Faculté des Sciences Ain Chock, Réseau Universitaire de Physique des Hautes Energies-Université Hassan II,Casablanca, Morocco; (b)Faculté des Sciences, Université Ibn-Tofail, Kénitra, Morocco; (c)Faculté des SciencesSemlalia, Université Cadi Ayyad, LPHEA-Marrakech, Morocco; (d)LPMR, Faculté des Sciences, Université MohamedPremier, Oujda, Morocco; (e)Faculté des sciences, Université Mohammed V, Rabat, Morocco; (f)Institute of AppliedPhysics, Mohammed VI Polytechnic University, Ben Guerir, Morocco36 CERN, Geneva, Switzerland37 Affiliated with an Institute Covered by a Cooperation Agreement with CERN, Geneva, Switzerland38 Affiliated with an International Laboratory Covered by a Cooperation Agreement with CERN, Geneva, Switzerland39 Enrico Fermi Institute, University of Chicago, Chicago, IL, USA40 LPC, Université Clermont Auvergne, CNRS/IN2P3, Clermont-Ferrand, France41 Nevis Laboratory, Columbia University, Irvington, NY, USA42 Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark43 (a)Dipartimento di Fisica, Università della Calabria, Rende, Italy; (b)INFN Gruppo Collegato di Cosenza, LaboratoriNazionali di Frascati, Frascati, Italy44 Physics Department, Southern Methodist University, Dallas, TX, USA45 Physics Department, University of Texas at Dallas, Richardson, TX, USA123Eur. Phys. J. C (2024) 84:757 Page 39 of 42 757 46 National Centre for Scientific Research “Demokritos”, Agia Paraskevi, Greece47 (a)Department of Physics, Stockholm University, Stockholm, Sweden; (b)Oskar Klein Centre, Stockholm, Sweden48 Deutsches Elektronen-Synchrotron DESY, Hamburg and Zeuthen, Germany49 Fakultät Physik , Technische Universität Dortmund, Dortmund, Germany50 Institut für Kern- und Teilchenphysik, Technische Universität Dresden, Dresden, Germany51 Department of Physics, Duke University, Durham, NC, USA52 SUPA-School of Physics and Astronomy, University of Edinburgh, Edinburgh, UK53 INFN e Laboratori Nazionali di Frascati, Frascati, Italy54 Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Freiburg, Germany55 II. Physikalisches Institut, Georg-August-Universität Göttingen, Göttingen, Germany56 Département de Physique Nucléaire et Corpusculaire, Université de Genève, Genève, Switzerland57 (a)Dipartimento di Fisica, Università di Genova, Genova, Italy; (b)INFN Sezione di Genova, Genova, Italy58 II. Physikalisches Institut, Justus-Liebig-Universität Giessen, Giessen, Germany59 SUPA-School of Physics and Astronomy, University of Glasgow, Glasgow, UK60 LPSC, Université Grenoble Alpes, CNRS/IN2P3, Grenoble INP, Grenoble, France61 Laboratory for Particle Physics and Cosmology, Harvard University, Cambridge, MA, USA62 (a)Department of Modern Physics and State Key Laboratory of Particle Detection and Electronics, University of Scienceand Technology of China, Hefei, China; (b)Institute of Frontier and Interdisciplinary Science and Key Laboratory ofParticle Physics and Particle Irradiation (MOE), Shandong University, Qingdao, China; (c)School of Physics andAstronomy, Shanghai Jiao Tong University, Key Laboratory for Particle Astrophysics and Cosmology (MOE), SKLPPC,Shanghai, China; (d)Tsung-Dao Lee Institute, Shanghai, China; (e)School of Physics and Microelectronics, ZhengzhouUniversity, China63 (a)Kirchhoff-Institut für Physik, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany; (b)Physikalisches Institut,Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany64 (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 KongUniversity of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China65 Department of Physics, National Tsing Hua University, Hsinchu, Taiwan66 IJCLab, Université Paris-Saclay, CNRS/IN2P3, 91405 Orsay, France67 Centro Nacional de Microelectrónica (IMB-CNM-CSIC), Barcelona, Spain68 Department of Physics, Indiana University, Bloomington, IN, USA69 (a)INFN Gruppo Collegato di Udine, Sezione di Trieste, Udine, Italy; (b)ICTP, Trieste, Italy; (c)Dipartimento Politecnicodi Ingegneria e Architettura, Università di Udine, Udine, Italy70 (a)INFN Sezione di Lecce, Lecce, Italy; (b)Dipartimento di Matematica e Fisica, Università del Salento, Lecce, Italy71 (a)INFN Sezione di Milano, Milan, Italy; (b)Dipartimento di Fisica, Università di Milano, Milan, Italy72 (a)INFN Sezione di Napoli, Naples, Italy; (b)Dipartimento di Fisica, Università di Napoli, Naples, Italy73 (a)INFN Sezione di Pavia, Pavia, Italy; (b)Dipartimento di Fisica, Università di Pavia, Pavia, Italy74 (a)INFN Sezione di Pisa, Pisa, Italy; (b)Dipartimento di Fisica E. Fermi, Università di Pisa, Pisa, Italy75 (a)INFN Sezione di Roma, Rome, Italy; (b)Dipartimento di Fisica, Sapienza Università di Roma, Rome, Italy76 (a)INFN Sezione di Roma Tor Vergata, Rome, Italy; (b)Dipartimento di Fisica, Università di Roma Tor Vergata, Rome,Italy77 (a)INFN Sezione di Roma Tre, Rome, Italy; (b)Dipartimento di Matematica e Fisica, Università Roma Tre, Rome, Italy78 (a)INFN-TIFPA, Povo, Italy; (b)Università degli Studi di Trento, Trento, Italy79 Department of Astro and Particle Physics, Universität Innsbruck, Innsbruck, Austria80 University of Iowa, Iowa City, IA, USA81 Department of Physics and Astronomy, Iowa State University, Ames, IA, USA82 Istinye University, Sariyer, Istanbul, Türkiye83 (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 deSão Paulo, São Paulo, Brazil; (d)Rio de Janeiro State University, Rio de Janeiro, Brazil; (e)Federal University of Bahia,Bahia, Brazil84 KEK, High Energy Accelerator Research Organization, Tsukuba, Japan85 Graduate School of Science, Kobe University, Kobe, Japan123 757 Page 40 of 42 Eur. Phys. J. C (2024) 84:757 86 (a)AGH University of Krakow, Faculty of Physics and Applied Computer Science, Krakow, Poland; (b)MarianSmoluchowski Institute of Physics, Jagiellonian University, Krakow, Poland87 Institute of Nuclear Physics Polish Academy of Sciences, Krakow, Poland88 Faculty of Science, Kyoto University, Kyoto, Japan89 Research Center for Advanced Particle Physics and Department of Physics, Kyushu University, Fukuoka , Japan90 L2IT, Université de Toulouse, CNRS/IN2P3, UPS, Toulouse, France91 Instituto de Física La Plata, Universidad Nacional de La Plata and CONICET, La Plata, Argentina92 Physics Department, Lancaster University, Lancaster, UK93 Oliver Lodge Laboratory, University of Liverpool, Liverpool, UK94 Department of Experimental Particle Physics, Jožef Stefan Institute and Department of Physics, University of Ljubljana,Ljubljana, Slovenia95 School of Physics and Astronomy, Queen Mary University of London, London, UK96 Department of Physics, Royal Holloway University of London, Egham, UK97 Department of Physics and Astronomy, University College London, London, UK98 Louisiana Tech University, Ruston, LA, USA99 Fysiska institutionen, Lunds universitet, Lund, Sweden100 Departamento de Física Teorica C-15 and CIAFF, Universidad Autónoma de Madrid, Madrid, Spain101 Institut für Physik, Universität Mainz, Mainz, Germany102 School of Physics and Astronomy, University of Manchester, Manchester, UK103 CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France104 Department of Physics, University of Massachusetts, Amherst, MA, USA105 Department of Physics, McGill University, Montreal, QC, Canada106 School of Physics, University of Melbourne, Victoria, Australia107 Department of Physics, University of Michigan, Ann Arbor, MI, USA108 Department of Physics and Astronomy, Michigan State University, East Lansing, MI, USA109 Group of Particle Physics, University of Montreal, Montreal, QC, Canada110 Fakultät für Physik, Ludwig-Maximilians-Universität München, Munich, Germany111 Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), Munich, Germany112 Graduate School of Science and Kobayashi-Maskawa Institute, Nagoya University, Nagoya, Japan113 Department of Physics and Astronomy, University of New Mexico, Albuquerque, NM, USA114 Institute for Mathematics, Astrophysics and Particle Physics, Radboud University/Nikhef, Nijmegen, The Netherlands115 Nikhef National Institute for Subatomic Physics and University of Amsterdam, Amsterdam, The Netherlands116 Department of Physics, Northern Illinois University, DeKalb, IL, USA117 (a)New York University Abu Dhabi, Abu Dhabi, United Arab Emirates; (b)United Arab Emirates University, Al Ain,United Arab Emirates118 Department of Physics, New York University, New York, NY, USA119 Ochanomizu University, Otsuka, Bunkyo-ku, Tokyo, Japan120 Ohio State University, Columbus, OH, USA121 Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma, Norman, OK, USA122 Department of Physics, Oklahoma State University, Stillwater, OK, USA123 Joint Laboratory of Optics, Palacký University, Olomouc, Czech Republic124 Institute for Fundamental Science, University of Oregon, Eugene, OR, USA125 Graduate School of Science, Osaka University, Osaka, Japan126 Department of Physics, University of Oslo, Oslo, Norway127 Department of Physics, Oxford University, Oxford, UK128 LPNHE, Sorbonne Université, Université Paris Cité, CNRS/IN2P3, Paris, France129 Department of Physics, University of Pennsylvania, Philadelphia, PA, USA130 Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA, USA131 (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,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)Departamento de Física, Instituto Superior Técnico, Universidade de Lisboa, Lisbon, Portugal123Eur. Phys. J. C (2024) 84:757 Page 41 of 42 757 132 Institute of Physics of the Czech Academy of Sciences, Prague, Czech Republic133 Czech Technical University in Prague, Prague, Czech Republic134 Charles University, Faculty of Mathematics and Physics, Prague, Czech Republic135 Particle Physics Department, Rutherford Appleton Laboratory, Didcot, UK136 IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette, France137 Santa Cruz Institute for Particle Physics, University of California Santa Cruz, Santa Cruz, CA, USA138 (a)Departamento de Física, Pontificia Universidad Católica de Chile, Santiago, Chile; (b)Millennium Institute forSubatomic Physics at High Energy Frontier (SAPHIR), Santiago, Chile; (c)Instituto de Investigación Multidisciplinarioen Ciencia y Tecnología y Departamento de Física, Universidad de La Serena, La Serena, Chile; (d)Department ofPhysics, Universidad Andres Bello, Santiago, Chile; (e)Instituto de Alta Investigación, Universidad de Tarapacá, Arica,Chile; (f)Departamento de Física, Universidad Técnica Federico Santa María, Valparaíso, Chile139 Department of Physics, University of Washington, Seattle, WA, USA140 Department of Physics and Astronomy, University of Sheffield, Sheffield, UK141 Department of Physics, Shinshu University, Nagano, Japan142 Department Physik, Universität Siegen, Siegen, Germany143 Department of Physics, Simon Fraser University, Burnaby, BC, Canada144 SLAC National Accelerator Laboratory, Stanford, CA, USA145 Department of Physics, Royal Institute of Technology, Stockholm, Sweden146 Departments of Physics and Astronomy, Stony Brook University, Stony Brook, NY, USA147 Department of Physics and Astronomy, University of Sussex, Brighton, UK148 School of Physics, University of Sydney, Sydney, Australia149 Institute of Physics, Academia Sinica, Taipei, Taiwan150 (a)E. Andronikashvili Institute of Physics, Iv. Javakhishvili Tbilisi State University, Tbilisi, Georgia; (b)High EnergyPhysics Institute, Tbilisi State University, Tbilisi, Georgia; (c)University of Georgia, Tbilisi, Georgia151 Department of Physics, Technion, Israel Institute of Technology, Haifa, Israel152 Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv, Israel153 Department of Physics, Aristotle University of Thessaloniki, Thessaloniki, Greece154 International Center for Elementary Particle Physics and Department of Physics, University of Tokyo, Tokyo, Japan155 Department of Physics, Tokyo Institute of Technology, Tokyo, Japan156 Department of Physics, University of Toronto, Toronto, ON, Canada157 (a)TRIUMF, Vancouver, BC, Canada; (b)Department of Physics and Astronomy, York University, Toronto, ON, Canada158 Division of Physics and Tomonaga Center for the History of the Universe, Faculty of Pure and Applied Sciences,University of Tsukuba, Tsukuba, Japan159 Department of Physics and Astronomy, Tufts University, Medford, MA, USA160 Department of Physics and Astronomy, University of California Irvine, Irvine, CA, USA161 University of Sharjah, Sharjah, United Arab Emirates162 Department of Physics and Astronomy, University of Uppsala, Uppsala, Sweden163 Department of Physics, University of Illinois, Urbana, IL, USA164 Instituto de Física Corpuscular (IFIC), Centro Mixto Universidad de Valencia-CSIC, Valencia, Spain165 Department of Physics, University of British Columbia, Vancouver, BC, Canada166 Department of Physics and Astronomy, University of Victoria, Victoria, BC, Canada167 Fakultät für Physik und Astronomie, Julius-Maximilians-Universität Würzburg, Würzburg, Germany168 Department of Physics, University of Warwick, Coventry, UK169 Waseda University, Tokyo, Japan170 Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot, Israel171 Department of Physics, University of Wisconsin, Madison, WI, USA172 Fakultät für Mathematik und Naturwissenschaften, Fachgruppe Physik, Bergische Universität Wuppertal, Wuppertal,Germany173 Department of Physics, Yale University, New Haven, CT, USAa Also Affiliated with an Institute Covered by a Cooperation Agreement with CERN, Geneva, Switzerlandb Also at An-Najah National University, Nablus, Palestinec Also at Borough of Manhattan Community College, City University of New York, New York, NY, USA123 757 Page 42 of 42 Eur. Phys. J. C (2024) 84:757 d Also at Center for High Energy Physics, Peking University, Beijing, Chinae Also at Center for Interdisciplinary Research and Innovation (CIRI-AUTH), Thessaloniki, Greecef Also at Centro Studi e Ricerche Enrico Fermi, Rome, Italyg Also at CERN, Geneva, Switzerlandh Also at Département de Physique Nucléaire et Corpusculaire, Université de Genève, Geneva, Switzerlandi Also at Departament de Fisica de la Universitat Autonoma de Barcelona, Barcelona, Spainj Also at Department of Financial and Management Engineering, University of the Aegean, Chios, Greecek Also at Department of Physics, California State University, Sacramento, USAl Also at Department of Physics, King’s College London, London, UKm Also at Department of Physics, Stanford University, Stanford, CA, USAn Also at Department of Physics, Stellenbosch University, Stellenbosch, South Africao Also at Department of Physics, University of Fribourg, Fribourg, Switzerlandp Also at Department of Physics, University of Thessaly, Thessaly, Greeceq Also at Department of Physics, Westmont College, Santa Barbara, USAr Also at Hellenic Open University, Patras, Greeces Also at Institucio Catalana de Recerca i Estudis Avancats, ICREA, Barcelona, Spaint Also at Institut für Experimentalphysik, Universität Hamburg, Hamburg, Germanyu Also at Institute for Nuclear Research and Nuclear Energy (INRNE) of the Bulgarian Academy of Sciences, Sofia,Bulgariav Also at Institute of Applied Physics, Mohammed VI Polytechnic University, Ben Guerir, Moroccow Also at Institute of Particle Physics (IPP), Toronto, Canadax Also at Institute of Physics and Technology, Mongolian Academy of Sciences, Ulaanbaatar, Mongoliay Also at Institute of Physics, Azerbaijan Academy of Sciences, Baku, Azerbaijanz Also at Institute of Theoretical Physics, Ilia State University, Tbilisi, Georgiaaa Also at Lawrence Livermore National Laboratory, Livermore, USAab Also at National Institute of Physics, University of the Philippines, Diliman, Philippinesac Also at Technical University of Munich, Munich, Germanyad Also at The Collaborative Innovation Center of Quantum Matter (CICQM), Beijing, Chinaae Also at TRIUMF, Vancouver, BC, Canadaaf Also at Università di Napoli Parthenope, Naples, Italyag Also at Department of Physics, University of Colorado Boulder, Boulder, CO, USAah Also at Washington College, Chestertown, MD, USAai Also at Physics Department, Yeditepe University, Istanbul, Türkiye∗ Deceased123
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Search for flavour-changing neutral-current couplings between the top quark and the Higgs boson in multi-lepton final states in 13 TeV pp collisions with the ATLAS detector
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