Search for pair production of third-generation leptoquarks decaying into a bottom quark and a τ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau $$\end{document}-lepton with the ATLAS detector

A search for pair-produced scalar or vector leptoquarks decaying into a b-quark and a τ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau $$\end{document}-lepton is presented using the full LHC Run 2 (2015–2018) data sample of 139 fb-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-1}$$\end{document} collected with the ATLAS detector in proton–proton collisions at a centre-of-mass energy of s=13\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sqrt{s} =13$$\end{document} TeV. Events in which at least one τ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau $$\end{document}-lepton decays hadronically are considered, and multivariate discriminants are used to extract the signals. No significant deviations from the Standard Model expectation are observed and 95% confidence-level upper limits on the production cross-section are derived as a function of leptoquark mass and branching ratio B\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {B}$$\end{document} into a τ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau $$\end{document}-lepton and b-quark. For scalar leptoquarks, masses below 1460 GeV are excluded assuming B=100\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {B}=100$$\end{document}%, while for vector leptoquarks the corresponding limit is 1650 GeV (1910 GeV) in the minimal-coupling (Yang–Mills) scenario.


Introduction
Many extensions of the Standard Model (SM) of particle physics predict particles known as leptoquarks (LQs) [1][2][3][4][5][6][7].These particles provide a connection between the lepton and quark sectors, which are similar in structure in the SM.LQs can be scalar (spin-0) or vector (spin-1) bosons, and they carry colour and a fractional electric charge.They also have non-zero lepton and baryon numbers, and decay into quark-lepton pairs.They can mediate neutral currents, and therefore can potentially provide an explanation for hints of violations of lepton universality observed in flavour experiments [8][9][10][11][12][13][14].
LQs could be produced singly or in pairs in proton-proton ( ) collisions at the LHC, and this analysis targets pair-produced LQs that couple strongly to the third generation of quarks and leptons.Within the Buchmüller-Rückl-Wyler (BRW) model [15], which is the benchmark for scalar LQs in this analysis, it is assumed that these LQs can only interact within the same family via a Yukawa interaction.This interaction is described by two parameters, a model parameter  and a coupling parameter .In the benchmark models considered in this paper, the pair-production cross-section is independent of .This analysis also considers pair-production of vector LQs [16] corresponding to the  1 state in the BRW classification [15].The scenarios considered in this model differ by a dimensionless coupling constant , which is zero for the minimal-coupling scenario and one for the Yang-Mills scenario.For both scalar and vector LQs, the parameter  controls the decay into charged leptons.For these third generation LQs, results are generally given in terms of the branching ratio (B) and mass of the LQ ( LQ ).
ATLAS and CMS have published searches for LQs coupling to the first, second and third generations [17][18][19][20][21][22][23][24][25][26].Each generation of LQs is split into up-type and down-type LQs with different electric charges.For instance, for the third generation they are split into up-type LQs (LQ u 3 ), which decay into  or , and down-type LQs (LQ d  3 ), which decay into  or .Both types of LQs are currently excluded for masses below 1150 GeV for the BRW model, for all values of B.
This paper updates the ATLAS search for an up-type LQ pair decaying into  [18], shown in Figure 1, using the full Run 2 data sample and an updated analysis strategy, prioritising high LQ masses that are not yet excluded for the benchmark models considered.Analysis improvements include updated analysis-optimisation and background-estimation methods, as well as updates to several object identification algorithms.The analysis signature is two jets, at least one of which must be identified as containing a -hadron, and two -leptons.For the -leptons, the cases considered are where both decay hadronically or where one -lepton decays into a light lepton (electron or muon, ℓ) and neutrinos and the other decays hadronically.The mass range considered for the LQ is from 300 GeV to 2000 GeV.The extraction of the signals is performed through a simultaneous likelihood fit to multivariate discriminants.For the results, both scalar and vector LQs are considered, with the limits on vector LQs interpreted in the context of two scenarios, the Yang-Mills scenario and the minimal-coupling scenario [27].
The paper is structured as follows.After a brief description of the ATLAS detector, the data sample, simulated backgrounds and simulated signals are described.This is followed by a description of the event reconstruction, the object selection, the event selections for the signal regions, and the multivariate discriminants that are used in the final fit.The next sections include a description of the data-driven background estimation methods, the systematic uncertainties, and finally the statistical methods and results.
Figure 1: Pair production of a leptoquark (LQ) and its subsequent decay into a -quark and a -lepton.

ATLAS detector
The ATLAS detector [28] at the LHC is a multipurpose particle detector with a forward-backward symmetric cylindrical geometry and a near 4 coverage in solid angle. 1 The inner tracking detector consists of pixel and microstrip silicon detectors covering the pseudorapidity region || < 2.5, surrounded by a transition radiation tracker to enhance electron identification in the range of || < 2.0.An additional innermost pixel layer, the insertable B-layer [29,30], was added before Run 2 of the LHC.The inner detector (ID) is surrounded by a thin superconducting solenoid providing a 2 T axial magnetic field, and by a fine-granularity lead/liquid-argon (LAr) electromagnetic (EM) calorimeter covering || < 3.2.Hadronic calorimetry is provided by a steel/scintillator-tile calorimeter in the central pseudorapidity range (|| < 1.7).The endcap and forward regions are instrumented with LAr calorimeters for both the EM and hadronic energy measurements up to || = 4.9.The muon spectrometer (MS) surrounds the calorimeters and is based on three large superconducting air-core toroidal magnets with eight coils each.Three layers of high-precision tracking chambers provide coverage in the range of || < 2.7, while dedicated fast chambers allow triggering in the region || < 2.4.A two-level trigger system [31], consisting of a hardware-based first-level trigger followed by a software-based high-level trigger (HLT), is used to select events.An extensive software suite [32] is used in data simulation, in the reconstruction and analysis of real and simulated data, in detector operations, and in the trigger and data acquisition systems of the experiment.

Data and simulation samples
The data used in this search correspond to an integrated luminosity of 139 fb −1 of   collision data collected by the ATLAS detector between 2015 and 2018 at a centre-of-mass energy √  = 13 TeV.The uncertainty in the combined 2015-2018 integrated luminosity is 1.7% [33], obtained using the LUCID-2 detector [34] for the primary luminosity measurements.The presence of additional interactions in the same 1 ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the centre of the detector and the -axis along the beam pipe.The -axis points from the IP to the centre of the LHC ring, and the -axis points upwards.Cylindrical coordinates (, ) are used in the transverse plane,  being the azimuthal angle around the -axis.
The pseudorapidity is defined in terms of the polar angle  as  = − ln tan(/2).Angular distance is measured in units of or neighbouring bunch crossing, referred to as pile-up, is characterised by the average number of such interactions,  , which was 33.7 for the combined data sample.Only events recorded under stable beam conditions and for which all relevant detector subsystems were known to be in a good operating condition are used.
Dedicated Monte Carlo (MC) simulated samples are used to model SM processes and estimate the expected signal yields.All samples were passed through the full ATLAS detector simulation [35] based on G 4 [36], except for the signal samples that use a parameterised fast simulation of the calorimeter response [37] and G 4 for the other detector systems.The simulated events were reconstructed with the same algorithms as used for data.They contain a realistic modelling of pile-up interactions with pile-up profiles matching the ones of each data sample between 2015 and 2018, obtained by overlaying minimum-bias events simulated using the soft QCD processes of Pythia 8.186 [38] with the NNPDF2.3leading-order (LO) [39] set of parton distribution functions (PDFs) and the A3 [40] set of tuned parameters (tune).The MC samples are corrected to account for differences between simulation and data in terms of the pile-up, the energy and momentum scales, and the reconstruction and identification efficiencies of physics objects.
Simulated events with pair-produced up-type ( = + 2 3 ) scalar LQs were generated at next-to-leading order (NLO) in QCD with M G 5_ MC@NLO v2.6.0 [41], using the LQ model of Ref. [42], in which fixed-order NLO QCD calculations [43,44] are interfaced to P 8.230 [45] for the parton shower (PS) and hadronisation.Parton luminosities were provided by the five-flavour scheme NNPDF3.0NLO [46] PDF set with   = 0.118 and the underlying event (UE) was modelled with the A14 tune [47,48].The coupling parameter  was set to 0.3, resulting in a relative LQ width of approximately 0.2% and ensuring the LQs decay promptly.In all cases,  = 0.5 such that the couplings to charged leptons and neutrinos were equal and the decay products were interfaced to M S [49] to preserve spin correlations.Different values for B were then obtained by reweighting the simulated events according to the generator information about their decay following the procedure in Ref. [18].Signal cross-sections were obtained from the calculation of the pair production of scalar coloured particles, such as the hypothesised supersymmetric partner of the top quark, as these particles have the same production modes and their pair-production cross-section depends only on their mass.These processes were computed at approximate next-to-next-to-leading order (NNLO) in QCD with resummation of next-to-next-to-leading-logarithmic (NNLL) soft gluon terms [50][51][52][53].The cross-sections do not include contributions from -channel lepton exchange, which are neglected in Ref. [42] and may lead to corrections at the percent level [54].The nominal cross-section and its uncertainty were derived using the PDF4LHC15_mc PDF set, following the recommendations of Ref. [55].For LQ masses between 300 GeV and 2000 GeV, the cross-sections range from 10 pb to 0.01 fb.
Simulated events with pair-produced up-type vector LQs were generated at LO in QCD with M -G 5_ MC@NLO v2.6.0, using the LQ model of Ref. [16] and the NNPDF3.0NLO PDF set with   = 0.118.Decays of the LQs were performed with M S , while PS and hadronisation were simulated using P 8.244 with the A14 tune.The full model includes two additional vector states that are necessary to obtain a realistic extension of the SM, a colour singlet  and a colour octet  .However, these are not present in the M G model and hence do not contribute to the Feynman diagrams considered for pair production of vector leptoquarks.The samples were produced with a coupling strength   = 3.0, where   represents the overall coupling between the LQ and the fermion, motivated by a suppression of the production cross-section for the additional mediators in the ultraviolet completion of the model, which might otherwise be in tension with existing LHC limits.This choice of coupling results in a relative LQ width of around 10%.In all cases,  = 0.5 and the same reweighting as in the scalar LQ case is then used to probe different B values.As mentioned, the model introduces two different coupling scenarios the minimal-coupling scenario and the Yang-Mills scenario.In the latter case the LQ is a massive gauge boson and has additional couplings to the SM gauge bosons, resulting in enhanced cross-sections.Since no higher-order cross-sections are available for this model, the LO M G 5_ MC@NLO cross-sections were used and vary between 94 pb (340 pb) and 0.05 fb (0.61 fb) for LQ masses between 300 GeV and 2000 GeV in the minimal-coupling (Yang-Mills) case.Above 500 GeV, kinematic differences between the two scenarios are negligible.Scalar (vector) LQ samples were produced with LQ masses between 300 GeV to 2000 GeV, with a mass interval of 50 GeV in the range of 800-1600 GeV (1400-1600 GeV) and 100 GeV otherwise.
Table 1: The list of generators used for the simulation of the SM background processes.Information is given on the matrix element (ME) generator (including the perturbative QCD order), the PDF set, the parton shower (PS) and the underlying event (UE).The perturbative order (in QCD unless otherwise specified) of the cross-section used to normalise the different samples is also presented.( §) The  t −  interference was handled using the diagram removal scheme.( †) The cross-sections from S at NLO were used to normalise the ,  ,   and  t/ events.( ‡) The  →   process was normalised to the NNLO (QCD) + NLO( EW) cross-section for the   →   process [56][57][58][59][60][61] Background samples were simulated using different MC event generators depending on the process.All background processes are normalised to the most accurate available theoretical calculation of their respective cross-sections.The most relevant event generators, the accuracy of theoretical cross-sections, the UE parameter tunes, and the PDF sets used in simulating the SM background processes are summarised in Table 1.For all samples, except those generated using S , the E G v1.2.0 [86] program was used to simulate the properties of the -and -hadron decays.

Event reconstruction and object definitions
The LQ signature of interest in this search gives rise to a set of reconstructed objects that consist primarily of -leptons, which may decay into light leptons or hadronically, and jets from the hadronisation of quarks, specifically -quarks.In addition, neutrinos produced in the decay of -leptons and the semileptonic decay of -hadrons contribute to the missing transverse momentum    miss T of the event.To be considered for analysis, events are required to have at least one   interaction vertex, reconstructed from two or more charged-particle tracks with  T > 500 MeV; the one with the highest summed  2 T of associated tracks is selected as the primary vertex.
Electron candidates are reconstructed by matching ID tracks to energy clusters in the EM calorimeter.They must satisfy  T > 7 GeV and lie in the range of || < 2.47, excluding the transition region between the barrel and endcap detectors (1.37 < || < 1.52).Electrons are further identified using a likelihood-based method, based on the track quality, the profile of the shower measured in the EM calorimeter and the consistency between the track and the energy cluster [87].Two identification criteria are used to select electrons in this analysis: 'veto electrons' are required to satisfy the 'loose' identification working point, while 'signal electrons' are required to satisfy the more stringent 'tight' working point.
Muon candidates are reconstructed from tracks in the MS, matched with compatible tracks in the ID where coverage allows; in regions where the MS is only partially instrumented (|| < 0.1) an energy deposit in the calorimeter compatible with a minimum-ionising particle is combined with a compatible ID track instead.They must satisfy  T > 7 GeV and lie in the range of || < 2.7.Muons are further identified based on the number of hits in the various ID subdetectors and MS stations, the compatibility between the measurements in the two detectors and the properties of the resulting track fit.Two identification criteria [88] are used to select muons: 'veto muons' must satisfy a 'loose' identification requirement, while the 'signal muons' are required to satisfy the 'medium' ('high- T ') working point if the  T is less than (greater than) 800 GeV.The more stringent high- T requirements remove around 20% of muons but improve the  T resolution by ≈ 30% above 1.5 TeV, significantly suppressing potential backgrounds [89].
To suppress misidentified leptons or those arising from hadron decays, all light-lepton candidates must satisfy an isolation criterion that limits the presence of tracks (calorimeter deposits) in a  T -dependent (fixed) radius cone.The resulting efficiency is above 99% for both electrons and muons in the signal regions.Finally, signal leptons must satisfy stricter requirements on their transverse momenta depending on the data-taking period, as detailed in Section 5.
Jets are reconstructed from topological energy clusters and charged-particle tracks, resulting from a particle-flow algorithm [90], using the anti-  algorithm with a radius parameter of  = 0.4 [91,92].They are required to satisfy  T > 20 GeV and lie in the range of || < 2.5.To suppress jets from pile-up, jets with  T < 60 GeV and || < 2.4 are required to originate from the primary vertex using a multivariate 'jet vertex tagger' [93].A multivariate algorithm based on a deep neural network, known as the 'DL1r tagger' [94][95][96], is used to identify jets containing -hadrons (-jets) based on the jet kinematics, the impact parameters of tracks associated with the jet and the reconstruction of displaced vertices.This analysis uses a working point with a 77% efficiency for true -jets and corresponding rejection factors for light-flavour jets, charm jets and -leptons, measured in simulated  t events, of 170, 5 and 21, respectively [97,98].
Hadronically decaying -lepton candidates are seeded by jets, which are required to have one or three associated tracks (referred to hereafter as 'one-prong' or 'three-prong' candidates, respectively) with a total charge of ±1 [99].The transverse momentum of the visible decay products ( had-vis ) must satisfy  T > 20 GeV and lie in the range of || < 2.47, excluding the transition region defined above.True  had-vis candidates are discriminated from quark-and gluon-initiated jets via a recurrent neural network (RNN) using calorimeter-and tracking-based variables as input and trained separately on one-and three-prong candidates [100].The 'loose' working point used has an efficiency of approximately 85% and 75% for oneand three-prong  had-vis respectively.A further boosted decision tree (BDT) is used to reject one-prong  had-vis candidates originating from electrons with an efficiency of about 95% [101].For the estimation of the background from jets misidentified as  had-vis (described in Section 6), anti- had-vis candidates are defined in the same way as above but are required to fail to satisfy the nominal loose RNN working point requirements and instead satisfy a looser requirement that has an efficiency of 99% for selecting true  had-vis candidates.
The    miss T (with magnitude  miss T ) is computed from the negative vectorial sum of the selected and calibrated objects described above, along with an extra track-based 'soft term' to account for the energy of particles originating from the primary vertex but not associated to any of the reconstructed objects [102,103].
To resolve ambiguities whereby the same detector signature may be reconstructed as more than one physics object, a sequential overlap-removal procedure is applied.First, electron candidates are discarded if they share a track with a more energetic electron or a muon identified in the MS; if the muon is identified in the calorimeter it is removed instead.Any  had-vis candidate within Δ = 0.2 of an electron or a muon (which must be reconstructed in the MS if the  had-vis  T is above 50 GeV) is then rejected.Jets are discarded if they lie within Δ = 0.2 of an electron or have fewer than three associated tracks and lie within the same distance of a muon.Electron or muon ( had-vis ) candidates within Δ = 0.4 (Δ = 0.2) of any remaining jet are then removed.Finally, ambiguities between anti- had-vis candidates and jets within Δ = 0.2 are resolved in favour of the jet if it is -tagged or the anti- had-vis otherwise.

Event selection
The event selection targets a signature consisting of a pair of -leptons and a pair of -quarks.It splits the events into two orthogonal signal categories based on the -lepton decay mode: the  lep  had channel, which selects events with a light lepton, an oppositely charged  had-vis and one or two -jets, and the  had  had channel, which selects events with two opposite-charge  had-vis and one or two -jets.Multivariate techniques are used to search for a LQ-pair signal in the two signal regions (SRs).

Signal regions
Candidate events were recorded using a combination of single-lepton [104,105] and single- had-vis triggers [106].The single-lepton trigger used in the  lep  had channel required a reconstructed light lepton at the HLT, with a minimum  T threshold ranging from 24 to 26 GeV for electrons and a minimum  T threshold ranging from 20 to 25 GeV for the muons, depending on the data-taking period.Offline leptons are required to be geometrically matched to the corresponding trigger object and have a  T threshold 1-2 GeV above the HLT threshold in order to operate in the region where the trigger was fully efficient.The single- had-vis triggers used in the  had  had channel required a reconstructed HLT  had-vis with a period-dependent minimum  T threshold ranging between 80 GeV and 160 GeV.The corresponding  T -threshold for the offline  had-vis , which is again required to be geometrically matched to the trigger object, ranges between 100 GeV and 180 GeV, while the non-trigger-matched  had-vis is required to have  T > 20 GeV.
Following the trigger selection, the  lep  had category requires exactly one 'signal' light lepton and an oppositely charged  had-vis , while the  had  had category requires exactly two opposite-charge  had-vis and no 'veto' light leptons.Both categories require at least two jets, one or two of which must be -tagged, with  T > 45 (20) GeV for the leading (sub-leading) jet.
The invariant mass of the two -lepton decay products is an important variable with which to reject the +jets background.It is calculated using the missing mass calculator (MMC) [107], with the light lepton and the  had-vis (two  had-vis ) and the    miss T as input in the  lep  had ( had  had ) category, and it is required to satisfy  MMC   ∉ 40 − 150 GeV.Two further selections are applied to target the characteristic LQ signature while reducing the large multi-jet background.The scalar sum of the transverse momenta ( T ), calculated taking into account the light lepton,  had-vis , two leading jets and the  miss T , is a powerful discriminator.It is required to satisfy  T > 600 GeV, while the  miss T itself is required to exceed 100 GeV.
The full event selection is summarised in Table 2 and the resulting acceptance times efficiency is shown in Figure 2 as a function of  LQ .Since the analysis prioritises high mass LQs that have not yet been excluded in the benchmark models under consideration, it is not optimal for low LQ masses.

Multivariate signal extraction
Following the event selection, the LQ signal is extracted using a multivariate discriminant.To obtain near-optimal sensitivity and continuity over the full range of LQ masses considered, a parameterised neural network (PNN) [108], parameterised in terms of the generated LQ mass, is chosen.The PNN consists of three hidden layers, each with 32 nodes, implemented in Keras [109] with the Tensorflow [110] backend.
The PNN inputs consist of a combination of multiplicity, kinematic and angular quantities that discriminate between the signal and the dominant background.In the case of the  invariant mass, the most likely combination of the -lepton and a -jet2 is chosen based on a mass-pairing strategy that minimises the mass difference between the two resulting LQ candidates.The variables, which are similar for both the  lep  had and  had  had categories, are summarised in Table 3 and defined as follows: •  had-vis  0 T is the transverse momentum of the highest- T  had-vis ; •  T is the scalar sum of the transverse momenta defined above; •  −jets is the number of -jets; • (, jet) 0,1 are the larger (0) and smaller (1) of the two LQ masses obtained via the mass-pairing strategy ( had  had channel only); • (ℓ, jet) and ( had , jet) are the mass of the light-lepton or  had-vis , respectively, combined with its mass-paired -jet ( lep  had channel only); • Δ(ℓ, jet) (Δ( had , jet)) is the Δ between the light lepton (leading  had-vis ) and the mass-paired jet in the  lep  had ( had  had ) category; • Δ(ℓ,  miss T ) is the azimuthal opening angle between the lepton and the  miss T ( lep  had category only); •  miss T  centrality quantifies the transverse direction of the    miss T relative to the light lepton and  had-vis (two  had-vis ) in the  lep  had ( had  had ) category and is defined in Ref. [111].
A selection of representative input distributions, after the background corrections described in Section 6, are presented in Figures 3 and 4 for the  lep  had SR and the  had  had SR, respectively.While the relative importance of the variables varies with LQ mass, the  T and mass variables are generally the most performant.The resulting PNN score distributions, which peak at higher values for LQ signals than the background processes, are used as the final analysis discriminant.

𝜙 centrality
The PNNs are trained on all scalar LQ signal masses simultaneously against the main  t and single-top backgrounds, taking into account both the true and misidentified  had-vis components with the latter corrected as described in Section 6.The same PNN training is used for both vector LQ models since separate trainings were found to provide a negligible improvement in sensitivity.For the signals, the generated LQ mass is used as the parameterisation input in addition to the input variables described above, while in the case of the backgrounds a mock LQ mass is randomly assigned from the range of signal LQ masses such that the resulting training is independent of the mass.In all cases, the input variables are standardised by subtracting the median value and dividing by the interquartile range.The resulting PNN score distributions are used as the final analysis discriminants.

Background modelling
The dominant background in the  had  had and  lep  had channels is top production, including  t and singletop-quark production.A subdominant background is  boson production in association with heavy-flavour quarks (, , ), termed  + HF hereafter.Both top production and  + HF are estimated from simulation to which data-driven corrections are applied.In the  had  had channel, multi-jet events form a non-negligible background that is estimated by using data-driven techniques.Small contributions to the background from all other processes are estimated by using simulated events.This section describes the background estimation methods used for top-quark-pair and single-top backgrounds, multi-jet backgrounds, and the  + HF background.The background is validated for  had  had and  lep  had events in a region with an inverted  T selection, as well as a region with a low PNN score and the signal region selection.In addition, the  had  had multi-jet estimate is validated in a region where the two  had-vis have the same electric charge.The potential signal contamination in all regions described in this section is negligible.
The process of estimating the backgrounds follows several steps.First, an overall shape correction is determined for the top background, as described in Section 6.1.1.Then, with this in place, a shape and normalisation correction is determined for the top backgrounds with jets misidentified as  had-vis , as described in Section 6.1.2.After applying these corrections, a prediction for the shape and normalisation of multi-jet backgrounds is determined for the  had  had channel in Section 6.2.Finally, with all relevant corrections in place, a normalisation factor is determined for the  + HF backgrounds, as described in Section 6.3.The resulting corrections are only weakly coupled due to the high purity of each control region, meaning that corrections for a specific background process do not significantly affect the overall background in control regions targeting other backgrounds.All of these corrections are applied in the final SR fit.

Top quark backgrounds
For top-quark-pair and single-top-quark production (top backgrounds), events are estimated separately based on whether the  had-vis candidate in the event is correctly identified (referred to as a true  had-vis ) or whether it is a quark-or gluon-initiated jet misidentified as a  had-vis (referred to as a fake  had-vis ).The small contributions from light leptons that are misidentified as  had-vis are considered together with the true  had-vis contribution.Events with a true  had-vis and a hadronic jet misidentified as a light lepton contribute negligibly to the  lep  had channel and are not considered.
These backgrounds are estimated in a multi-step data-driven process that is applied to simulated events.First, all top backgrounds are scaled by an  T -dependent reweighting factor (RF), and then simulated background events with misidentified  had-vis are further corrected by a scale factor (SF) that is binned in the  had-vis transverse momentum.

Overall reweighting of top backgrounds
The motivation for scaling the  t and single-top backgrounds arises from mismodelling of the data by simulation observed in control regions (CRs).It is seen that this effect becomes more pronounced for events with higher momentum top quarks, which is where this analysis is primarily focused.This mismodelling has also been observed in ATLAS measurements of the  t differential cross-section, where it is seen that the number of events is overestimated at high top-quark  T [112][113][114].
For this reason, a CR is defined to determine a binned shape and normalisation correction of the simulated top quark events to data.Events in this CR are required to have two -jets with  T greater than 45 and 20 GeV, exactly two light leptons with opposite charge,  miss T > 100 GeV, and a dilepton mass ( ℓℓ ) > 110 GeV.They are also required to have  ℓ > 250 GeV, where  ℓ = min(max(  0 ℓ 0 ,   1 ℓ 1 ), max(  0 ℓ 1 ,   1 ℓ 0 )), where the 0 and 1 indices refer to the leading and sub-leading -tagged jets and leptons in order of transverse momentum.This region is orthogonal to the SRs and is over 99% pure in  t events.
The RFs are derived by subtracting all non-top backgrounds, as estimated using simulation, from data.A ratio of the remaining events to the prediction of  t and single-top events in simulation is then calculated.This factor is binned in  T , with one bin up to 400 GeV, steps of 100 GeV from 400 to 1400 GeV, and then one bin for values greater than 1400 GeV.The values of the RFs decrease from 0.97 at low  T to approximately 0.62 in the highest  T bin.Even in the highest  T bin, the signal contamination remains at the percent level.The largest relative contribution of single-top events is also at high  T .This reweighting is applied in both the  lep  had and  had  had SRs for  t and single-top events with true and misidentified -leptons, as well as in all CRs.The uncertainty in this RF is taken from the statistical uncertainty in the factor, bin-by-bin in  T , and its impact on the shape and normalisation of the final PNN score distribution are considered.In addition, top background modelling uncertainties are propagated through the reweighting process, so that modified RFs are applied when evaluating such uncertainties in the final fit.

Top backgrounds with jets misidentified as 𝝉 had-vis
In addition to this overall RF, the estimation of top backgrounds with jets misidentified as  had-vis in the SRs is performed using simulated events with additional data-driven corrections.A fit is performed in a  lep  had -based CR to simultaneously correct the overall normalisation of true  had-vis and misidentified  had-vis events while deriving an SF to be applied to misidentified  had-vis events in the  lep  had and  had  had SRs.The RF for top backgrounds is applied to this CR before the fit.The SFs obtained are then applied in the SRs, in order to correct the  had-vis misidentification rate in simulation to that observed in data.
The CR has the same selection as the SR for the  lep  had channel, except that the  had-vis  T > 100 GeV requirement is removed and  T is required to be in a range of 400-600 GeV.This region is 97% pure in  t events, with a mixture of both correctly identified and misidentified  had-vis that varies with  had-vis  T .
The distribution used for this estimation is the transverse mass of the light lepton and missing transverse momentum, defined as  T (ℓ, The expected shapes for top backgrounds with true and misidentified  had-vis in this distribution differ significantly, making it possible to constrain the two background sources.The normalisation of the true and misidentified  had-vis background is allowed to vary freely, and SFs for the misidentified  had-vis background are determined in bins of  had-vis  T .All detector-related uncertainties and top background modelling uncertainties are included as nuisance parameters in the fit.An example fit in a single bin of  T is shown in Figure 5 for the (a)  had-vis and (b) anti- had-vis CRs.Depending on  had-vis  T , the SFs run from 0.90 in the lowest  T bin down to 0.56 in the highest  T bin.  Figure 5: Post-fit plots for true and misidentified  had-vis in (a) the  had-vis and (b) the anti- had-vis CRs, in a single  T bin ( had-vis  T >100 GeV).'Other' refers to the sum of minor backgrounds (vector boson + jets, diboson and Higgs boson).The lower panels show the ratios of the data to the sum of the predicted backgrounds.The hatched bands indicate the combined statistical and systematic uncertainty in the total background predictions.The dashed lines denote the total pre-fit backgrounds for comparison, while the last bins include the overflow.
For the estimation of top backgrounds with misidentified  had-vis , an uncertainty is considered that arises from the limited number of events and an additional uncertainty is defined by comparing the nominal SFs to SFs derived with a more inclusive  T selection ( T < 600 GeV).This last uncertainty is intended to address a possible  T -dependence in the mismodelling of top backgrounds.The difference between the central values for SFs measured with these two  T selections is taken as the  T -dependence uncertainty.

Multi-jet backgrounds with jets misidentified as 𝝉 had-vis
For the  had  had channel, multi-jet processes can contribute to the SR at non-negligible levels.For this reason, the  had  had channel uses a data-driven fake-factor (FF) method to estimate this background.These FFs are measured in a CR with the same selection as the  had  had SR, except that the two  had-vis candidates have the same charge and the  miss T requirement is loosened to 80 GeV.The FF is defined as the ratio of events where both  had-vis are loose to the number of events where one  had-vis is loose and the other is an anti- had-vis .These FFs are derived as a function of transverse momentum and the number of charged-particle tracks of the  had-vis candidate.The FFs are measured from data after subtracting all predicted non-multi-jet background contributions.The FFs range between approximately zero and 0.25.
The non-multi-jet background contributions that are subtracted, however, suffer from the same mismodelling issues described in the previous two sections.The top backgrounds are therefore corrected by the RFs and SFs derived as described in Section 6.1.1 and Section 6.1.2,respectively.Since the SFs are anticipated to be different for  had-vis and anti- had-vis , dedicated SFs are measured for this data-driven estimation.Specifically, the anti- had-vis region uses SFs that are derived in a CR as described in Section 6.1.2,except that the  had-vis identification requirement is changed to that of an anti- had-vis .An example fit in a single bin of  T is shown in Figure 5 for the anti- had-vis CR.Depending on  had-vis  T , these SFs vary between 0.77 and 0.95.
To construct the background estimate, FFs are applied to a region with the  had  had SR selection, except that the  had-vis identification requirement is changed to that of an anti- had-vis .This provides both a shape and a normalisation for the multi-jet contribution in the PNN score distribution.
For the estimation of multi-jet backgrounds in  had  had , uncertainties are considered due to the statistical uncertainty of the SFs, and to the uncertainty in the subtraction of different backgrounds using simulation.Top events with a correctly identified  had-vis , top events with a misidentified  had-vis , and other small backgrounds are considered separately.The top events are varied by the overall uncertainty defined by the procedure to determine the modelling uncertainties, but evaluated in the anti- had-vis region.Other backgrounds are varied by 30%.In addition, a 20% overall uncertainty in the estimate is applied based on checks of the method in validation regions.The total uncertainty in the multi-jet background is −64% to +61%.

𝒁 + HF background
The normalisation of the  + HF background, which is a relatively small contribution in the SRs, is observed to be in disagreement with the NLO cross-section in S (e.g.Ref. [115]).It is therefore determined from data using a  + HF CR that targets events containing a  boson decaying into a light-lepton pair and produced in association with two heavy-flavour jets.The composition of this control region is approximately 60%  + HF events and 40%  t events, with less than 1% arising from backgrounds with misidentified  had-vis .Since the contribution from backgrounds with misidentified  had-vis is negligible, only the RF for the  t shape is included in this CR.Data for the CR was recorded using a combination of the single-lepton triggers described above and additional dilepton triggers requiring pairs of same-flavour leptons.At the analysis level exactly two oppositely-charged same-flavour leptons, passing the 'veto' quality requirements and  T thresholds based on the corresponding trigger thresholds, are required.The invariant mass of the resulting lepton pair  ℓℓ is required to lie between 75 GeV and 110 GeV.In addition, exactly two -jets with  T > 20 GeV are required and their invariant mass   is required to be less than 40 GeV or greater than 150 GeV to avoid the Higgs boson mass peak.The RFs for top backgrounds derived in Section 6.1.1 are then applied.
A fit to the  ℓℓ distribution is performed to discriminate between the  + HF and top backgrounds, with the normalisation of both processes allowed to vary freely and all systematic uncertainties described in Section 7 included.The resulting  + HF normalisation factor is 1.36 ± 0.11 and is used to correct the  + HF background entering into the final fit (described in Section 8), which is allowed to vary within the associated uncertainty.

Systematic uncertainties
The systematic uncertainties considered include detector-related uncertainties, modelling and theoretical uncertainties, and uncertainties derived for the data-driven background estimates, the latter of which have already been described in Section 6. Uncertainties are evaluated by shifting the central value upward or downward by one standard deviation, and then propagating the differences to the PNN score distributions that are used in the final fit.
Detector-related uncertainties are defined as uncertainties relating to the detector response, object reconstruction and object identification.There are systematic uncertainties associated with each of the reconstructed objects considered, as well as the  miss T .For light leptons,  had-vis , and jets, uncertainties are considered for energy scale and resolution, reconstruction and identification, while uncertainties in isolation are also considered for light leptons.For the  lep  had and  had  had channel, uncertainties associated with the lepton and  had-vis trigger efficiencies, respectively, are considered.For -jets, additional uncertainties are considered for the efficiency of (mis)tagging -jets, -jets, and light-quark-initiated jets.Uncertainties related to energy scale and resolution, and the inclusion of soft terms, are considered for the  miss T .Finally, there is also an uncertainty associated with shape and normalisation components that arises from uncertainties in the simulation of pile-up collisions.
Theoretical and modelling uncertainties include uncertainties in the cross-section calculations of background processes, which have only a normalisation component, and uncertainties in the acceptance of each process, for which normalisation and shape components are taken into account.For top backgrounds, relative acceptance uncertainties are also defined to take into account normalisation differences for  lep  had and  had  had SRs.
For  t processes, shape and normalisation uncertainties are considered that arise from changing the matrix element and parton shower simulation software, and from varying the initial and final state radiation, PDF, and   .The matrix element uncertainty is determined by comparing the P +P 8 sample with an MC@NLO+P 8 sample.The parton shower uncertainty is determined by comparing the P +P 8 sample with a P +H 7 [116,117] sample.The other modelling uncertainties are evaluated using internal weights in the nominal  t sample.
For single-top processes, acceptance uncertainties with shape and normalisation components are considered.Uncertainties are considered from changing the matrix element, parton shower, and impacts of diagram interference.In addition, variations of initial-and final-state radiation and PDFs are considered.The matrix element uncertainty is determined by comparing the P +P 8 sample with an MC@NLO+P 8 sample.The parton shower uncertainty is determined by comparing the P +P 8 sample with a P +H 7 sample.The diagram interference uncertainty is evaluated by comparing the nominal single top samples, which use a diagram removal scheme, with alternative samples that utilise a diagram subtraction scheme [118].The other modelling uncertainties are evaluated using internal weights in the nominal single-top samples.
All  t and single-top modelling uncertainties are also propagated through the top reweighting procedure, such that there is an uncertainty in the RF corresponding to each modelling uncertainty.
For +jets processes, uncertainties due to the choice of generator are evaluated by comparing the nominal S simulated samples with alternative samples simulated by M G with LO-accurate matrix elements that contain up to four final-state partons, using P for parton showering.In addition, uncertainties are considered by taking an envelope of variations in the renormalisation and factorisation scales and PDF values using internal weights in the simulated S sample.For this process specifically, uncertainties are also included based on varying the matrix element matching scale and the resummation scale for soft-gluon emission.All of these uncertainties are included in the  + HF fit described in Section 6.3, and their sum in quadrature, taking relative acceptance uncertainties into account, is considered as the uncertainty in the SRs for the final fit.
For signal samples, uncertainties arising from variations of scale, initial-state radiation, PDF, and   are considered, using alternative weights internal to the signal samples.Differences in shape are observed to be negligibly small in the PNN score distributions, so only variations in normalisation are included for the final fit.
The relative impact of the different sources of uncertainty on the analysis varies depending on the LQ model considered and the mass probed.Generally, the largest impact comes from the statistical uncertainties, which increase with  LQ .In the scalar LQ case, for example, the statistical impact on the limit ranges from 60% at the lowest  LQ evaluated to 80% above 1000 GeV.The main systematic uncertainties come from the  t and single-top-quark modelling uncertainties, including their interference, and normalisation.There is also a significant effect from the signal acceptance uncertainties, which increases with  LQ , particularly for the vector LQ models.

Statistical interpretation and results
The data are compared with the expectation, including the background modelling corrections outlined in Section 6, by performing simultaneous binned maximum-likelihood fits to the PNN score distributions, separately for each LQ hypothesis, in the  lep  had and  had  had SRs.For each hypothesis, the binning of the PNN score distributions is chosen separately to maximise the expected sensitivity, while ensuring sufficient background events in the signal-enhanced PNN bins and preserving the stability of the fit.In addition to the relative signal-strength modifier, , the top normalisation is free to float in the fit and is constrained by the background-enhanced PNN bins.
The statistical and systematic uncertainties affecting the signal and background model, described in Section 7, are represented by deviations from the nominal model scaled by Gaussian-or Poisson-constrained nuisance parameters that are profiled in the fit.Common sources of systematic uncertainty are correlated across the SRs.
The resulting event yields in the  lep  had and  had  had SRs, based on a background-only fit to the data, are presented in Table 4. Corresponding post-fit PNN score distributions for representative LQ signals at masses of 500 GeV, 1.1 TeV and 1.4 TeV are shown in Figure 6 (Figure 7) for the  lep  had ( had  had ) SR.At high values of the PNN score, top backgrounds dominate in the  lep  had channel, while the  had  had background consists of a roughly even mixture of all background sources.Overall, good agreement with the SM background expectation is observed in all cases, although there is a slight deficit of data relative to the background prediction in the highest PNN score bin for the  had  had channel.
Table 4: Post-fit yields for background events, determined from a background-only fit, compared with the observed number of data events in the  lep  had and  had  had SRs.'Fake  had (top)' refers to top backgrounds where a jet is misidentified as the  had-vis of the event, and 'Other' refers to the sum of minor backgrounds (vector boson + jets, diboson and Higgs boson).The total background is not identical to the sum of the individual components since the latter are rounded for presentation, while the sum is calculated with the full precision before being subsequently rounded.Systematic uncertainties are included.Due to the large correlations, individual uncertainties can be significantly larger than the total uncertainty.Since no significant excess is observed, upper limits on the scalar and vector LQ pair production crosssections for each mass hypothesis are computed based on the modified frequentist CL s method [119], using a profile likelihood test statistic [120] under the asymptotic approximation.The resulting observed and expected limits, assuming B = 1, as a function of  LQ at 95% confidence level (CL) are shown in Figure 8 for all LQ models.The expected contributions of the  lep  had and  had  had channels are approximately equal at high  LQ , while the  had  had is up to a factor of two more sensitive at low  LQ .The improvement in the observed limit compared with the expectation is driven by the data deficit in the highest  had  had PNN score bin mentioned above and is larger at high  LQ since the signal becomes more localised at high PNN score as  LQ increases.The theoretical prediction for the cross-section of scalar or vector LQ pair production is indicated by the solid line along with its uncertainties.The corresponding expected and observed 95% CL lower limits on the LQ mass for the three different   LQ models are summarised in Table 5, providing an improvement in mass reach for a scalar LQ of more than 450 GeV compared with the previous 36 fb −1 result in this channel [18].They extend the full Run 2 ATLAS reach for third-generation up-type LQs by around 200 GeV in all three models compared with the search in the  →  decay mode [26].
The results are also expressed as upper limits on the branching ratio to charged leptons as a function of  LQ for each LQ model in Figure 9.For all models investigated, constraints on the LQ mass are reduced by no more than 15% going from B = 1 to B = 0.5, while scalar LQ masses up to around 850 GeV are excluded for couplings into charged leptons as low as 0.1; the corresponding B = 0.1 exclusion for vector LQ is around 1100 GeV (1300 GeV) in the minimal-coupling (Yang-Mills) scenario.(c) Figure 9: The observed (solid line) and expected (dashed line) 95% CL upper limits on the branching ratio into charged leptons as a function of  LQ for (a) the scalar LQ case, (b) the vector LQ case in the minimal-coupling scenario, (c) vector LQs in the Yang-Mills scenario.The observed exclusion region is above the solid line, with the theoretical uncertainty in the model indicated by the dotted lines around this.The expected limit is indicated by the dashed line and the surrounding shaded bands correspond to the ±1 and ±2 standard deviation (±1, ±2) uncertainty in the expected limit.No limits are presented for B < 0.1 due to the lack of expected signal events in this final state.

Conclusion
A search for pair-produced scalar or vector leptoquarks decaying into a -quark and a -lepton is presented.The analysis exploits the full data sample recorded with the ATLAS detector in Run 2 of the LHC, corresponding to 139 fb −1 of proton-proton collisions at √  = 13 TeV.No significant deviations from the Standard Model expectation are observed and upper limits on the production cross-section are derived as a function of LQ mass and branching ratio into a charged lepton.Scalar LQs with masses below 1490 GeV are excluded assuming a 100% branching ratio, while for vector LQs the corresponding limit is 1690 GeV (1960 GeV) in the minimal-coupling (Yang-Mills) scenario.For branching ratios as low as 10%, scalar LQ masses below around 850 GeV are excluded; the corresponding mass limits for vector LQs are 1100 GeV (1300 GeV) in the minimal-coupling (Yang-Mills) scenario.These results significantly improve the sensitivity compared to previous ATLAS LQ searches, extending the mass reach for third-generation up-type LQs by more than 200 GeV in all models and surpassing the previous ATLAS search in this final state by more than 450 GeV for scalar LQs.In addition to the increased luminosity, this is due to upgraded hadronic -lepton and -jet identification, improved multivariate techniques and better background estimation methods.

Figure 2 :
Figure 2: The expected acceptance times efficiency for the scalar and vector LQs, with both the minimal-coupling and the Yang-Mills scenarios, at  = 0.5 as a function of  LQ in the (a)  lep  had and (b)  had  had channels.The values include the leptonic and hadronic branching ratios of the tau lepton.

Figure 3 :
Figure 3: Signal (solid lines), post-fit background (filled histograms) and data (dots with error bars) distributions of representative PNN input variables in the  lep  had SR: (a) Δ(ℓ, jet), (b), ( had , jet) and (c)  T .The normalisation and shape of the backgrounds are determined from the background-only likelihood fit to data and the ratios of the data to the sum of the predicted backgrounds are shown in the lower panels.'Other' refers to the sum of minor backgrounds (vector boson + jets, diboson and Higgs boson).The hatched band indicates the combined statistical and systematic uncertainty in the total background prediction.The expected signal for a 1.4 TeV scalar LQ, scaled by the indicated factor for visibility, is overlaid.The last bin includes the overflow.

Figure 4 :
Figure 4: Signal (solid lines), post-fit background (filled histograms) and data (dots with error bars) distributions of representative PNN input variables in the  had  had SR: (a) Δ( 0 had , jet) where  0 had is the leading -lepton, (b) the larger of the two -jet mass combinations ( had , jet) 0 and (c)  T .The normalisation and shape of the backgrounds are determined from the background-only likelihood fit to data and the ratios of the data to the sum of the predicted backgrounds are shown in the lower panels.'Other' refers to the sum of minor backgrounds (vector boson + jets, diboson and Higgs boson).The hatched band indicates the combined statistical and systematic uncertainty in the total background prediction.The expected signal for a 1.4 TeV scalar LQ, scaled by the indicated factor for visibility, is overlaid.The last bin includes the overflow.

Figure 6 :
Figure 6: The PNN score distributions in the  lep  had SR for (a)  LQ = 500 GeV, (b)  LQ = 1.1 TeV, (c)  LQ = 1.4 TeV.The normalisation and shape of the backgrounds are determined from the background-only likelihood fit to data and the ratios of the data to the sum of the backgrounds are shown in the lower panels.'Other' refers to the sum of minor backgrounds (vector boson + jets, diboson and Higgs boson).The hatched bands indicate the combined statistical and systematic uncertainty in the total background predictions.The expected signals for scalar LQs with the corresponding masses, scaled by the indicated factors for visibility, are overlaid.Since the PNN score itself is not a physical quantity, it is represented solely by the bin number.

Figure 7 :Figure 8 :
Figure 7: The PNN score distributions in the  had  had SR for (a)  LQ = 500 GeV, (b)  LQ = 1.1 TeV, (c)  LQ = 1.4 TeV.The normalisation and shape of the backgrounds are determined from the background-only likelihood fit to data and the ratios of the data to the sum of the backgrounds are shown in the lower panels.'Other' refers to the sum of minor backgrounds (vector boson + jets, diboson and Higgs boson).The hatched bands indicate the combined statistical and systematic uncertainty in the total background predictions.The expected signals for scalar LQs with the corresponding masses, scaled by the indicated factors for visibility, are overlaid.Since the PNN score itself is not a physical quantity, it is represented solely by the bin number.
, after subtracting the  →   contribution.

Table 2 :
Summary of the event selections for the  lep  had and  had  had categories.Where two objects are required, the thresholds on the sub-leading object are given in parenthesis.Where the selection depends on data-taking period, the different possible threshold values are separated by commas.

Table 3 :
Summary of variables used as inputs to the PNN in the  lep  had and  had  had categories.The variables are defined in the text.Variable lep  had channel  had  had channel lep  had channel  had  had channel

Table 5 :
Observed and expected lower limits on the LQ mass at 95% CL for the three different LQ models, assuming B = 1.