Search for new phenomena in $pp$ collisions in final states with tau leptons, $b$-jets, and missing transverse momentum with the ATLAS detector

A search for new phenomena in final states with hadronically decaying tau leptons, $b$-jets, and missing transverse momentum is presented. The analyzed dataset comprises $pp$~collision data at a center-of-mass energy of $\sqrt s = 13$ TeV with an integrated luminosity of 139/fb, delivered by the Large Hadron Collider and recorded with the ATLAS detector from 2015 to 2018. The observed data are compatible with the expected Standard Model background. The results are interpreted in simplified models for two different scenarios. The first model is based on supersymmetry and considers pair production of top squarks, each of which decays into a $b$-quark, a neutrino and a tau slepton. Each tau slepton in turn decays into a tau lepton and a nearly massless gravitino. Within this model, top-squark masses up to 1.4 TeV can be excluded at the 95% confidence level over a wide range of tau-slepton masses. The second model considers pair production of leptoquarks with decays into third-generation leptons and quarks. Depending on the branching fraction into charged leptons, leptoquarks with masses up to around 1.25 TeV can be excluded at the 95% confidence level for the case of scalar leptoquarks and up to 1.8 TeV (1.5 TeV) for vector leptoquarks in a Yang--Mills (minimal-coupling) scenario. In addition, model-independent upper limits are set on the cross section of processes beyond the Standard Model.

The results are interpreted in simplified models for two different scenarios. The first model is based on supersymmetry and considers pair production of top squarks, each of which decays into a -quark, a neutrino and a tau slepton. Each tau slepton in turn decays into a tau lepton and a nearly massless gravitino. Within this model, top-squark masses up to 1.4 TeV can be excluded at the 95% confidence level over a wide range of tau-slepton masses. The second model considers pair production of leptoquarks with decays into third-generation leptons and quarks. Depending on the branching fraction into charged leptons, leptoquarks with masses up to around 1.25 TeV can be excluded at the 95% confidence level for the case of scalar leptoquarks and up to 1.8 TeV (1.5 TeV) for vector leptoquarks in a Yang-Mills (minimal-coupling) scenario. In addition, model-independent upper limits are set on the cross section of processes beyond the Standard Model.

Introduction
The Standard Model (SM) of particle physics has been verified to high precision. Despite its success, several observations have been made which have exposed the theory's shortcomings in various aspects and fostered new theoretical ideas. Supersymmetry (SUSY) [1][2][3][4][5][6][7] is a framework for models that extend the symmetries underlying the SM by introducing superpartners of the known bosons and fermions with the same quantum numbers but a spin difference of half a unit. These models can address the gauge hierarchy problem [8][9][10][11]. When conservation of -parity [12] is assumed, the lightest supersymmetric particle is stable and may provide a candidate particle for the cold dark matter component of the universe [13,14]. The introduction of supersymmetric partner particles can also modify the renormalization group equations in such a way that the coupling constants of the SM electromagnetic, weak and strong interactions meet at one point at some high energy scale as expected in a grand unified theory [15]. Another possible way to extend the SM is to embed the SM symmetry group in an overarching symmetry group, such as SU (5) [16] in grand unification, which gives rise to a new class of bosons that carry nonzero baryon and lepton quantum numbers and are charged under all SM gauge groups. These leptoquarks (LQ), which can be either scalar or vector bosons, appear in a variety of SM extensions [17][18][19][20][21] and would provide an explanation for the structural similarities of the quark and lepton sectors in the SM. Processes mediated by the exchange of leptoquarks can violate lepton-flavor universality and have been proposed as an explanation [22][23][24][25][26][27][28] for the deviations from the SM predictions seen by many experiments in measurements of -meson decays [29][30][31][32][33][34][35][36][37]. Contributions arising from leptoquarks with additional couplings to the muon could also bridge the gap [38,39] between the theoretical prediction for the anomalous magnetic moment of the muon ( − 2) within the SM and the experimentally measured value, which is higher by 4.2 [40].  Figure 1: Diagrams illustrating the production and decay of particles considered in the simplified models for the supersymmetric "stop-stau" scenario (left) and for scalar leptoquarks of charge + 2 3 (middle) and − 1 3 (right).
In this paper, a search for physics beyond that described in the Standard Model is conducted using events with final states with one or more hadronically decaying tau leptons, one or more -tagged jets and large missing transverse momentum. This is a signature that is sensitive to models in which the new particles preferentially decay into third-generation SM particles. Two benchmark signal models are studied. The first model considers the production of supersymmetric partner states of the third-generation SM particles, while the second model foresees scalar leptoquarks that decay into third-generation SM particles. An additional interpretation, for which the analysis was not explicitly optimized, is provided for vector leptoquarks that decay into third-generation SM particles. The full Run-2 dataset of proton-proton (pp) collisions recorded with the ATLAS detector at the Large Hadron Collider (LHC) is analyzed. This dataset corresponds to an integrated luminosity of 139 fb −1 , taken from 2015 through 2018, at a center-of-mass energy of √ = 13 TeV.
The investigated SUSY signal model is motivated by gauge-mediated SUSY breaking (GMSB) [41][42][43] and natural gauge mediation [44]. In this -parity-conserving scenario, only three SUSY particles are assumed to be sufficiently light to be relevant: the lighter scalar partner of the top quark˜(top squark or stop), the lighter scalar partner of the tau lepton˜(tau slepton or stau), and the spin-3/2 partner of the graviton, the gravitino˜. The top squark is assumed to be the lightest squark [45,46] and to be directly pair-produced through the strong interaction. The gravitino is assumed to be almost massless, making it the lightest SUSY particle (LSP) in this scenario. The search strategy is optimized using a simplified model [47][48][49] with this limited SUSY particle content, the model parameters being the scalar-fermion masses (˜) and (˜). The decay chain is illustrated in the left diagram of Figure 1: a three-body decay proceeding through an off-shell chargino˜→˜followed by˜→˜. This model is referred to as the "stop-stau" signal model in the following. When the LSP is the gravitino, direct decays of SUSY particles into the gravitino LSP (plus a SM particle) are very unlikely due to its weak coupling, except for the next-to-lightest supersymmetric particle, which in -parity-conserving scenarios has no other option than to decay into the gravitino LSP. Other SUSY models which instead assume the lightest neutralino˜0 1 to be the LSP are not studied here, as this would favor a high branching fraction of˜→˜0 1 ; this case has been studied elsewhere by the ATLAS Collaboration [50][51][52] and by the CMS Collaboration [53][54][55][56].
Previous searches by the ATLAS Collaboration for signals in this model used 20 fb −1 of √ = 8 TeV data taken in Run 1 [57] and 36.1 fb −1 of √ = 13 TeV data taken in Run 2 of the LHC [58]. No significant excess was observed in either of these searches, and thus limits were set on the masses of the top squark and tau slepton. These limits exclude top-squark masses of up to 1.16 TeV and tau-slepton masses of up to 1.0 TeV at the 95% confidence level. The CMS Collaboration has published a related search in a simplified model with pair production of top squarks, which are also assumed to decay via tau sleptons or tau sneutrinos, but where the LSP is the lightest neutralino˜0 1 instead of the gravitino [59]. This search is based on an integrated luminosity of 77.2 fb −1 and sets exclusion limits at the 95% confidence level on the top-squark mass of up to 1.1 TeV for a nearly massless neutralino.
The previous ATLAS Run-2 search in Ref. [58] made use of two event categories: events where one of the two tau leptons decays leptonically and the other hadronically were considered in addition to events where both tau leptons decay hadronically. While the branching fractions are almost the same for both categories, the leptonic decay of the tau lepton yields one neutrino more, which washes out the kinematic distributions and on average leads to a lower energy fraction carried by the lepton compared to the visible decay products from a hadronic tau-lepton decay. Taken together, the two effects significantly reduce the discriminative power of the selection requirements. As the sensitivity of the search is thus dominated by the category where both tau leptons decay hadronically, this paper considers only events with hadronically decaying tau leptons. These events are separated in two event categories (channels). One category selects events with at least two hadronically decaying tau leptons but no lighter leptons, at least one -jet and large missing transverse momentum miss T (di-tau channel). The other category selects events with exactly one hadronically decaying tau lepton, no electrons or muons, at least two -jets and large miss T (single-tau channel). The latter channel extends the sensitivity by covering the signal parameter space where the tau slepton is relatively light and one of the soft tau leptons easily escapes detection. Importantly, it also provides good sensitivity to events with pair-produced leptoquarks that decay into third-generation particles, which correspond to the second benchmark model. The second benchmark model used in the design of the analysis considers pair production of scalar leptoquarks. It assumes that these only couple to third-generation quark-lepton pairs, following the minimal Buchmüller-Rückl-Wyler (BRW) model [60]. In addition to the coupling to the third fermion generation that is probed in this analysis, leptoquarks would need to have cross-generational couplings in order to explain the anomalies observed in -meson decays. The search is carried out for both up-type scalar leptoquarks with fractional charge (LQ u 3 ) = + 2 3 and decays LQ u 3 → / , and down-type scalar leptoquarks with (LQ d 3 ) = − 1 3 and decays LQ d 3 → / . The production and decay of the leptoquarks are illustrated in Figure 1. The model parameters are the leptoquark mass (LQ u/d 3 ) and the branching fraction (LQ u/d 3 → ℓ) into a quark and a charged lepton. For a branching fraction (LQ u/d 3 → ℓ) ∼ 0.5, most of the decays of the pair of third-generation leptoquarks yield a final state with one tau lepton, two -jets and large miss T from the tau neutrino. This signature matches that of the single-tau channel, which presents unique coverage of leptoquark masses at (LQ u/d 3 → ℓ) ∼ 0.5, but also has good sensitivity to a wide range of smaller or larger branching fractions.
The scalar-LQ model is the same as was used in a previous ATLAS paper [61] detailing a search for third-generation leptoquarks based on 36.1 fb −1 of data taken at √ = 13 TeV. This earlier paper comprises a dedicated reoptimization of the ATLAS search for pair-produced Higgs bosons and four reinterpretations of ATLAS SUSY searches, one of which is the previous iteration of the stop-stau search [58]. Leptoquark masses below at least 0.8 TeV are excluded at intermediate values of the branching fraction (LQ u/d 3 → ℓ), with the lower limit increasing at both small and large (LQ u/d 3 → ℓ), e.g. to 0.96 (1.02) TeV at (LQ u/d 3 → ℓ) = 0 (1) for down-type (up-type) leptoquarks. Two recent ATLAS searches for top or bottom squark pair production have been reinterpreted in the same up-type or down-type leptoquark model, respectively [50,62]. Another recent dedicated ATLAS search for pair-produced leptoquarks combines several event categories which all require at least one hadronically decaying tau lepton plus at least one electron or muon [63] and are complementary to the final states considered in this paper. It targets the down-type leptoquark model and excludes leptoquark masses up to 1.43 TeV assuming (LQ u/d 3 → ℓ) = 1 and up to 1.22 TeV assuming (LQ u/d 3 → ℓ) = 0.5. The CMS Collaboration has published a search of the full Run-2 dataset for single or pair production of scalar or vector leptoquarks coupling to third-generation Table 1: Simulated background and signal samples with the corresponding matrix element and parton shower (PS) generators. Also, the cross-section order in s used to normalize the event yield and the parton distribution function (PDF) sets used in the generator and PS simulation are given.

Data and simulated event samples
The dataset used in this analysis was collected with the ATLAS detector in proton-proton collisions provided by the LHC during its second run from 2015 to 2018. The data was taken at a center-of-mass energy of √ = 13 TeV with a minimum separation of 25 ns between consecutive crossings of proton bunches from the two beams. Events are selected with triggers on missing transverse momentum [75], and data-quality requirements are applied to ensure that all elements of the detectors were operational during data-taking [76]. The total integrated luminosity amounts to 139 fb −1 with an uncertainty of 1.7% [77], obtained using the LUCID-2 detector [78] for the primary luminosity measurements.
Monte Carlo (MC) simulation was used to generate samples of collision events, which model the expected kinematics of the investigated signal and SM background processes. Table 1 gives a detailed summary of the generation of the different MC samples used in the analysis. It lists the generators, the order of the cross-section computation, the parton distribution function (PDF) sets, and the sets of tuned parameters (tunes) for the parton shower. For background processes, the detector response was simulated [79] using the full modeling of the ATLAS detector in G 4 [80], while for the signal samples a faster variant of the simulation was used that relies on a parameterized response of the calorimeters [81]. Except for samples produced with S [82], which uses a dedicated parton-shower (PS) modeling and parameter tune developed by the S authors, the parton shower and hadronization simulation for all samples used the A14 tune [83], and the E G program [84] was used to model the decays of -and -hadrons in signal samples and background events. The effect of multiple concurrent interactions in the same and neighboring bunch crossings (pileup) was modeled by overlaying the hard-scattering events with simulated inelastic pp events generated with P 8.186 [85] using the NNPDF2.3 set of PDFs [86] and the A3 tune [87]. All simulated events are processed with the same trigger, reconstruction and identification algorithms as the data, and are weighted to match the observed distribution of the pileup in data. Dedicated correction factors are applied to simulation to account for differences in efficiencies and energy calibrations between recorded data and simulations. In this analysis, data-driven methods are applied that improve the modeling of the dominant SM background processes by normalizing their contributions to data. These are described in Section 6.
The production of top-quark pairs, with or without an associated Higgs boson, and of single top quarks in the -or -channel or associated with bosons was simulated with P B [88][89][90][91], while associated production of top-quark pairs and a vector boson = or , as well as top-quark production in other processes (later called "other top") giving smaller contributions (¯+ ,¯+ , , ,¯and¯¯), was simulated with M G 5_aMC@NLO [104]. The events were interfaced to P [92] to model the parton shower, hadronization, and underlying event, using the NNPDF2.3 set of PDFs [86]. The production of single vector boson ( + jets), diboson ( ) and triboson ( ) events was simulated with S using the NNPDF3.0 PDF set [94].
Stop-stau signal samples were produced for various values of˜and˜. The pair production of top squarks was simulated at leading order with up to two additional partons in M G 5_aMC@NLO. For the decays of the SUSY particles, the top squark and the tau slepton, M S [111] was used to preserve spin correlation and finite-width effects. Both decays are assumed to be prompt, i.e. the SUSY particles have a negligible lifetime. The subsequent decays as well as the hadronization were simulated in P . Cross sections are calculated including approximate next-to-next-to-leading-order (NNLO) supersymmetric quantum chromodynamics (QCD) corrections, with resummation of next-to-next-to-leading logarithmic (NNLL) soft gluon terms [107][108][109][110]. The matching of matrix element and parton shower was done with the CKKW-L prescription [112,113], with the matching scale set to one quarter of the top-squark mass.
Simulated events with pair production of up-or down-type scalar third-generation leptoquarks LQ u/d 3 were generated at next-to-leading order (NLO) in QCD with M G 5_aMC@NLO, using the LQ model of Ref. [114] that adds parton showers to previous fixed-order NLO QCD calculations [115,116], and the NNPDF3.0 parton distribution function set with s ( ) = 0.118. M S was used for the prompt decays of the leptoquarks into spin-entangled quark-lepton pairs of the third generation. Parton showering and hadronization were simulated in P with the NNPDF2.3 PDF set with s ( ) = 0.130. The couplings in the Yukawa-type interaction of the leptoquarks with the quark-lepton pair are determined by two parameters: a common coupling strength and an additional parameter , with the coupling to a quark and a charged lepton given by √ , and the coupling to a quark and a neutrino by √︁ 1 − . The branching fraction (LQ u/d 3 → ℓ) into a quark and a charged lepton is, except for kinematic effects arising from the mass differences of the decay products, equal to . The leptoquark signal samples were generated for various leptoquark masses (LQ u/d 3 ) and with a fixed parameter value of = 0.5, so that both decays of the leptoquarks, either into a quark and a neutrino or into a quark and a charged lepton, were possible. These events can be reweighted to arbitrary branching fractions (LQ u/d 3 → ℓ) to derive the interpretation of the analysis results in the plane of (LQ u/d 3 ) vs. (LQ u/d 3 → ℓ). The coupling parameter was set to 0.3, close to the numeric value of the electromagnetic coupling = √ 4 , resulting in a LQ u/d 3 width equal to about 0.2% of its mass [60,117]. The cross sections for direct top-squark pair production are used for LQ u/d 3 pair production, as both involve massive, scalar, color-charged particles and the production modes are the same. These cross sections do not include the lepton -channel contributions possible for LQ pair production, which are also neglected in Ref. [114] and may lead to corrections at the percent level [118].
Simulated events with pair production of third-generation vector leptoquarks LQ v 3 were generated at leading order in QCD with M G 5_aMC@NLO, using the LQ model of Ref.
[119], and the NNPDF3.0 parton distribution function set with s ( ) = 0.118. M S was used for the prompt decays of the leptoquarks, and parton showering and hadronization were simulated in P with the NNPDF2.3 PDF set with s ( ) = 0.130. The LQ v 3 in this model corresponds to the 1 state in the BRW classification [60] and carries an electric charge of (LQ v 3 ) = + 2 3 . The model includes two additional vector states that are needed to obtain a realistic extension of the SM, a color singlet and a color octet . However, the and do not appear in the Feynman diagrams considered for pair production of vector leptoquarks, as their interactions with the vector leptoquarks are not included in the model. All parameters are set to zero except for 33 L , such that only decays to left-chiral fermion fields are allowed, for which the coupling strength is set to = 3.0. The large value of is motivated by a suppression of the production cross section for additional mediators in a ultraviolet completion of the model, which might otherwise be in tension with LHC limits if these mediators are as light as needed to be consistent with the range of LQ masses considered here. As no higher-order computations of the cross sections are available for this vector-leptoquark model, the leading-order cross sections computed by the event generator are used. Two different scenarios are considered: the minimal-coupling scenario with =˜= 1, where the LQ couples to the SM gauge bosons purely through the covariant derivative, and the Yang-Mills scenario with =˜= 0, where the LQ is a massive gauge boson and has additional couplings to the SM gauge bosons [120]. The two scenarios differ mainly in the pair-production cross section, which is roughly five times as large in the Yang-Mills scenario at (LQ v 3 ) = 1.5 TeV as in the minimal-coupling scenario, which in turn is roughly four times as large as the pair-production cross section for the scalar LQ u/d 3 at the same mass.

Event reconstruction
All events are required to have at least one reconstructed interaction vertex with a minimum of two associated tracks with T > 500 MeV. In events with multiple vertices, the one with the highest sum of squared transverse momenta of associated tracks is chosen as the primary vertex [121]. Events that contain jets that do not satisfy the set of quality criteria described in Ref. [122] are rejected in order to reduce non-collision backgrounds and backgrounds induced by calorimeter noise. Jets are reconstructed from particle-flow objects [123] calibrated at the EM scale using the anti-algorithm with a radius parameter of = 0.4 [124,125]. Since both signal models predict the production of particles with large masses, only jets in the central region within | | < 2.8 are used. The jets are calibrated following the procedure described in Ref. [126] and are required to have T > 20 GeV. To suppress jets from pileup interactions, jet candidates with T < 60 GeV and | | < 2.4 are required to pass the Tight working point of the jet vertex tagger [127]. Selected jets that are likely to originate from the hadronization of a bottom quark are flagged as -jets if they lie within | | < 2.5 and are tagged by the DL1r algorithm, a multivariate discriminant based on various inputs such as track impact parameters and displaced secondary vertices [128, 129]. The -tagging algorithm uses a working point with an efficiency of 77%, with an approximate misidentification probability of 20% for jets arising from charm quarks, 6.7% for hadronically decaying -leptons, and 0.9% for light-flavor jets in simulated¯events.
Tau leptons which decay leptonically are not identified as such, but are instead reconstructed as a candidate for a prompt electron or muon. Therefore, in the context of reconstructed analysis objects, "tau lepton" will always refer to a hadronic tau lepton, i.e. a tau lepton that decays hadronically. The visible component of hadronically decaying tau leptons is reconstructed from anti-jets ( = 0.4) built from locally calibrated topological clusters [130], with a distance parameter = 0.4 and requiring T > 10 GeV and | | < 2.5 [131, 132]. The energy calibration applies a pileup subtraction and a correction to the detector response. Information from the tracking system improves the energy resolution at low T [132,133]. Tau-lepton candidates are required to have T > 20 GeV and lie outside the transition region 1.37 < | | < 1.52 between the barrel and endcap calorimeters. Furthermore, they must have either one or three charged tracks ("prongs") with a charge sum of ±1 in units of the elementary charge. A recurrent neural network algorithm [134] distinguishes hadronically decaying tau leptons from quark-and gluon-initiated jets by using a combination of high-level discriminating variables as well as tracking and calorimeter measurements. Its Medium working point is used to identify hadronic tau leptons, with efficiencies of 75% and 60% in simulated Drell-Yan events, and background-rejection factors of 35 and 240 in simulated dĳet events, for one-prong and three-prong decays, respectively. Electrons misidentified as hadronic tau-lepton candidates are rejected using a dedicated boosted decision tree algorithm. Reconstructed tau leptons in simulated events are called "real" tau leptons if they can be geometrically matched to a tau lepton in the MC "truth" record, otherwise they are referred to as "fake" tau leptons.
As described in Section 5, events with prompt electrons or muons are rejected in the analysis selections, so these only enter in the computation of missing transverse momentum and in the overlap-removal procedure, and are not considered otherwise. Electron candidates are reconstructed from energy deposits in the electromagnetic calorimeter that are matched to tracks in the inner detector (ID) [135,136]. They are required to have T > 10 GeV and | | < 2.47 and pass the LooseAndBLayer identification requirement. Muon candidates are reconstructed by combining information from the ID and the muon spectrometer [137]. They are required to have T > 10 GeV and | | < 2.7 and satisfy the Medium identification criteria. The absolute value of the longitudinal impact parameter 0 of each prompt electron or muon candidate is required to be less than 0.5 mm.
An overlap-removal procedure is applied to all selected objects to resolve ambiguities in the reconstruction in several consecutive steps. First, if two electrons share the same track, the electron with lower transverse momentum is discarded. Next, tau leptons overlapping with an electron or a muon within Δ < 0.2 are removed, where the angular distance is measured in units of Δ ≡ √︁ (Δ ) 2 + (Δ ) 2 with the rapidity instead of the pseudorapidity to account for cases where particle masses cannot be neglected. If an electron shares an ID track with a muon, the electron is discarded unless the muon is tagged as a minimum-ionizing particle in the calorimeter, in which case the muon is discarded. Jets within Δ = 0.2 of an electron are removed. In order to suppress electrons from semileptonic heavy-flavor decays, electrons within Δ = 0.4 of a jet are removed. Any jet with fewer than three associated tracks is discarded if a muon is within Δ = 0.2 of the jet or if a muon can be matched to a track associated with the jet. For the same reason as for electrons, muons within Δ = 0.4 of a jet are removed. Lastly, jets within Δ = 0.4 of a tau lepton are removed.
The missing transverse momentum E miss T is defined as the negative vector sum of the transverse momenta of all calibrated objects mentioned above, photons [136], and an additional soft term including all tracks associated with the primary vertex but not matched to any reconstructed object [138,139]. The magnitude of E miss T is denoted by miss T .

Event selection
The analysis covers two different channels: the single-tau channel and the di-tau channel. In both channels, object multiplicities and kinematic variables are used to define several different event selections (analysis regions). All of these event selections start from a common preselection described below. The preselections in the single-tau and di-tau channels are identical except for the number of tau leptons and -tagged jets.
The sets of events selected in the two channels are thus mutually exclusive and can therefore be statistically combined, as is done in the interpretation of the results.

Preselection
The preselection requirements for the two channels are summarized in Table 2. Events are selected using an miss T trigger [75]. In combination with the requirement of miss T > 250 GeV, this trigger is fully efficient in the phase space that the analysis targets. As no light leptons are expected from the benchmark signal models At least two jets At least two hadronic tau leptons Exactly one hadronic tau lepton At least one -tagged jet At least two -tagged jets when only hadronically decaying tau leptons are considered, events with light leptons are rejected. Events are required to have at least two jets, at least one (two) of which must be -tagged in the di-tau (single-tau) channel. Additionally, events in the di-tau channel are required to have at least two reconstructed tau leptons, whereas exactly one tau lepton is required in the single-tau channel. The tight miss T and -tagging requirements efficiently suppress multĳet events such that their contribution to the analysis regions is negligible. This was verified with dedicated data-driven estimates for both channels.

Signal regions
Dedicated signal-enriched regions are defined for each channel, having been optimized individually by maximizing the estimated discovery significance [140] for benchmark signal models close to the previous exclusion contours. The selection requirements for the signal regions are explained in the following, and a summary is included in the overview of the analysis regions in Table 3 for the di-tau channel and Table 4 for the single-tau channel. The signal region (SR) in the di-tau channel targets stop-stau signal models with a low to modest mass difference between the top squark and the tau slepton. This SR is not used for the leptoquark models, as the final states for that model at = 0.5 have only one tau lepton on average. The case of = 1.0, which would yield two tau leptons, is not within the scope of this paper, and the requirements on miss T and that no leptons be present in the final state strongly reduce the sensitivity to this scenario. The single-tau channel employs two signal regions: a one-bin SR for the model-independent fit, and a multi-bin SR for the model-dependent fit, as is discussed in Section 8. Each of the two signal regions in this channel is optimized simultaneously for the scalar-leptoquark signal models and the stop-stau signal models that have a large mass difference between the top squark and the tau slepton.

Di-tau channel
The most discriminating variable in the di-tau channel is the "stransverse" mass variable [141,142], which by itself already provides good separation between the signal and the background. The stransverse mass T2 is a generalization of the transverse mass T , which is computed as 2 from the transverse momentum of some given particle and the missing transverse momentum. It generalizes the transverse mass for symmetric event topologies where two identical particles each decay into a visible and an invisible product. In this case the individual transverse momenta of the invisible particles can no longer be directly approximated by the measured missing transverse momentum, as the information about their individual contributions to the missing transverse momentum is lost. Using subscripts to refer to the physics objects reconstructed in a collision event in order of decreasing transverse momentum, for the two leading tau leptons, i.e. the two tau leptons with the largest ( 1 ) and second-largest ( 2 ) transverse momentum, T2 ( 1 , 2 ) is computed as where and refer to two invisible particles assumed to be produced with transverse momentum q , T . The minimum is taken over all possible assignments to q , T that sum to the measured E miss T . The masses of the invisible particles are free parameters and are set to zero. For the dominant top-quark-related backgrounds, the T2 ( 1 , 2 ) distribution features an endpoint near the -boson mass. By placing a lower bound at 70 GeV most of this background can be removed, while efficiently selecting stop-stau signal events, for which the T2 ( 1 , 2 ) distribution exhibits a tail towards much higher values. The sensitivity is further enhanced by raising the lower bound on miss T to 280 GeV and requiring the two leading tau leptons to carry electric charges with opposite signs, a criterion later denoted by ( 1 , 2 ) = 1.

Single-tau channel
Both signal regions in the single-tau channel have a lower bound on miss T at 280 GeV and on the sum of the transverse masses of the -jets, , at 700 GeV. In this expression and the following, T ( ) for a given particle should be read as T ( ) ≡ T (p T , E miss T ). The one-bin SR requires T ( ) > 300 GeV and T > 800 GeV, where T is defined as the scalar sum of the transverse momenta of the tau lepton and the two leading jets, T = T ( ) + T (jet 1 ) + T (jet 2 ). While both the stop-stau and LQ u/d 3 signals show fairly similar behavior in most kinematic variables, their T ( ) distributions differ. This is due to the large mass difference in the stop-stau target scenario, so that the tau leptons are softer than those produced in the LQ u/d 3 decay. To account for the different shapes of the transverse momentum distributions of the tau leptons, the second SR is defined with three bins in T ( ). The first two T ( ) bins cover 50 to 100 GeV and 100 to 200 GeV, and the last bin all values beyond 200 GeV. To reduce the statistical uncertainty in the three T ( ) bins, two selection requirements are loosened relative to the one-bin SR: the minimum T ( ) requirement is lowered to 150 GeV, and the minimum T requirement to 600 GeV. As the one-bin SR is a subset of the multi-bin SR, they cannot be combined in the statistical interpretation of the results discussed in Section 8. A multi-bin SR based on T instead of T ( ) was also tested, but was found to have lower sensitivity.

Background estimation
The background in the signal regions is dominated by¯and single-top production, which can yield events with a final state similar to the signal processes. Dedicated control regions are defined for these background processes. Top-quark production can contribute to the background in different ways. Events withp roduction, where both bosons arising from the top-quark decay into a hadronic tau lepton, have two real tau leptons. This process, denoted by¯(2 real ), contributes to the di-tau channel if both hadronic tau leptons are correctly identified. If instead only one of the bosons from the¯system gives a hadronic tau lepton which is correctly identified, and the second boson decays hadronically, the resulting jet from the second -boson decay can be misidentified as a tau lepton, and such an event can then still satisfy the di-tau channel selection criteria. While the misidentification probability is of the order of a few percent, the larger branching fraction of hadronic decays and the less pronounced endpoint in the T2 ( 1 , 2 ) Table 3: Definitions of the¯control and validation regions and the signal region in the di-tau channel. A dash signifies that no requirement on the given variable is applied, while brackets indicate an allowed range for the variable. These requirements extend those of the di-tau preselection from Table 2.
GeV distribution for¯events with one real and one fake tau lepton still leads to a significant contribution in the di-tau channel. This type of event can also enter the single-tau channel selection, if the jet from the second boson is not misidentified as a tau lepton. Di-tau¯events in which only one of the two identified tau leptons is real, and single-tau¯events with one real tau lepton, are referred to as¯(1 real ) events. Lastly, fully hadronic¯decays, without any real tau leptons that pass the selections in either the single-tau or di-tau channel, are referred to as¯-fake events. Due to their different kinematics, the simulated¯events are separated into these three event types,¯(2 real ),¯(1 real ), and¯-fake, and treated as separate background components in the following.
Subdominant contributions to the SM background arise from singly produced vector bosons ( + jets and + jets events) and production of vector bosons in association with top-quark pairs (¯+ ). In addition, multiboson production,¯production in association with a Higgs boson (¯+ ) and other top-related processes yield small contributions. These subdominant processes are normalized according to the theory cross-section predictions and the integrated luminosity measured in data.
The normalization factors for the MC predictions for¯and single-top production are extracted in a simultaneous binned maximum-likelihood fit to the observed data in the control regions (CRs). This fit, where no signal contributions are included, is referred to as the background-only fit. The CRs are designed to be enriched in a given background process and to be kinematically as similar to the SRs as possible, while maintaining sufficient purity and a high enough event yield with negligible contamination from signal. In addition to the data yields in the CRs, the expected yields and statistical and systematic uncertainties from MC simulation, described in Section 7, are input to the background-only fit. The yields obtained from the background-only fit can then be extrapolated to dedicated validation regions (VRs) to assess the accuracy of the background estimate. All CR, VR and SR selections are mutually exclusive so that they are statistically independent as required for the fit. The CR and VR selections are introduced in Sections 6.1 and 6.2 for the di-tau and single-tau channel, respectively. In addition to the background-only fit, model-dependent and model-independent fit setups [143] which include the signal regions are used for the interpretation of the results as further detailed in Section 8. Table 3 summarizes the selections that define the control, validation and signal regions in the di-tau channel. One control region and one validation region are defined in this channel for each of the¯(2 real ) and( 1 real ) processes. Their location in the phase-space spanned by T2 ( 1 , 2 ), T ( 1 ), and ( 1 , 2 ) is  Table 3.

Di-tau channel
illustrated in Figure 2. The CRs and VRs sit in the T2 ( 1 , 2 ) sideband below 70 GeV, above which the SR is located, and are separated at 35 GeV.
Top-quark pair-production events in which only one of the bosons decays leptonically, with one real tau lepton and one fake tau lepton, feature an endpoint in the T distribution of the real tau lepton near the mass. The reason is that the dominant source of miss T is the tau neutrino from the decay. By contrast, for¯events with two real tau leptons, two tau neutrinos contribute to the miss T and there is no distinct endpoint in T . This difference in the shapes of the T distributions is exploited in the selection of( 2 real ) and¯(1 real ) events. In the majority of¯(1 real ) events in the di-tau channel, the real tau lepton corresponds to the leading reconstructed tau lepton. A requirement on T ( 1 ) at 50 (70) GeV is thus used to separate the¯(2 real ) CR (VR) from the¯(1 real ) CR (VR). By requiring the leading and subleading tau lepton in the¯(2 real ) CR and VR selections to carry electric charges of opposite sign, ( 1 , 2 ) = 1, the purity is further increased. In addition, a lower bound on the invariant mass of the two tau leptons computed from the visible decay products, vis ( 1 , 2 ), at 50 GeV is applied to reduce the contribution from + jets events.

Single-tau channel
For the two dominant processes in the single-tau channel,¯production with one real tau lepton and single-top production, again two pairs of control and validation regions are defined. The definitions are illustrated in Figure 4 and summarized in Table 4. In contrast to the di-tau CRs and VRs, the larger available number of events in the single-tau channel allows the lower bound on miss T used in the CR and VR selections to be the same as for the SR. The¯(1 real ) control and validation regions in the single-tau channel are placed in the T ( 1,2 ) sideband between 600 and 700 GeV. The control region is located in the T window from 500 to 600 GeV, and the validation region covers the range above 600 GeV. The normalization of the¯(1 real ) process is obtained from a simultaneous fit of both control regions for this process, one from each channel. The CR and VR for the single-top background sit in the T ( ) window from 0 to 50 GeV and 50 to 150 GeV, respectively. Additionally, lower bounds on T ( 1,2 ) at 800 GeV and on T ( ) at 80 GeV increase the purity of both the single-top CR and VR. Events from¯(1 real ) are less likely to fulfill the T ( ) requirement, which favors high-energy decay products. They also tend  Table 4. Table 4: Definitions of the¯(1 real ) and single-top control and validation regions and the signal region in the single-tau channel. A dash signifies that no requirement on the given variable is applied, while brackets indicate an allowed range for the variable. In the last column, parentheses enclose the values and ranges used for the multi-bin SR. The binning in T ( ) of the multi-bin SR, abbreviated with "binned", is [50,100], [100,200], and > 200 GeV. These requirements extend those of the single-tau preselection from Table 2  to have lower T ( 1,2 ), as the transverse mass computed for the sub-leading -jet has a quite distinct endpoint near the top-quark mass. Figure 5 shows the distribution of T and T ( ) in the¯(1 real ) CR and VR and in the single-top CR and VR of the single-tau channel. The predictions for the top-quark backgrounds are scaled with the normalization factors obtained from the background-only fit. These are consistent with one for thē (2 real ) and¯(1 real ) backgrounds, but much smaller than one for the single-top background as discussed further in Section 8. Therefore, the contribution of scaled single-top events to the single-top CR and VR in the figure is very low, whereas it is 43% before applying the normalization factors. From the plots it can be seen that the background model describes the data very well.

Systematic uncertainties
The expected yields for signal and background processes are subject to experimental and theoretical systematic uncertainties. These uncertainties are implemented as variations which are parameterized as functions of nuisance parameters with Gaussian probability densities in the likelihood fits.
Experimental uncertainties comprise systematic uncertainties in the reconstruction, identification, calibration and corrections performed for the physics objects used in the analysis. Energy resolution and calibration uncertainties apply to all objects. For tau leptons, additional experimental systematic uncertainties arise from the reconstruction and identification efficiencies. Since events with prompt electrons and muons are rejected at preselection level, the related uncertainties in the reconstruction and identification are negligible in the analysis regions. For jets, additional uncertainties from the pileup subtraction, pseudorapidity intercalibration, flavor composition, and punch-through effects, as well as uncertainties in the flavor-tagging and jet-vertex tagging efficiencies, are considered. Systematic uncertainties affecting the energy or momentum of calibrated objects are propagated to the miss T calculation, and an additional uncertainty due to the contribution of the soft-track term is considered. To test the robustness of the analysis against a potential mismodeling of events with two fake tau leptons, it was verified that an additional uncertainty of 100% in the¯-fake background leads to a negligible decrease in the exclusion reach for the stop-stau signal model. Common sources of experimental uncertainty are assumed to be correlated across all regions and between the background processes and the signal.
Uncertainties in the renormalization and factorization scales are considered for all major background processes by separately varying the scales r and f up and down by a factor of two. Additionally, PDF and s uncertainties are considered by following the PDF4LHC15 prescription [144]. The PDF uncertainty is evaluated as the root mean square of a set of 100 variations, and the effect of the s uncertainty is derived by taking the average difference between the up and down variations. Additional initial-state and final-state radiation uncertainties are considered for the¯and single-top processes by varying generator settings, such as the simultaneous r and f variation and eigenvariations of the A14 tune [83]. Furthermore, theoretical uncertainties due to the hard-scatter and parton-shower simulation are estimated by comparing the corresponding nominal yields against those predicted with alternative generators, i.e. P versus aMC@NLO and P 8 versus H 7, respectively. The impact of the interference between the single-top and¯production processes is estimated by comparing samples produced with the nominal diagram-removal scheme with alternative samples generated with the diagram-subtraction scheme [145]. For + jets, additional uncertainties related to the resummation and CKKW matching scales [146,147] are considered. Uncertainties in the cross section and in the integrated luminosity of the data are applied for all simulated processes except for¯with one or two real tau leptons and single top-quark production, which are normalized to data. The theoretical systematic uncertainties are assumed to be correlated across analysis regions and uncorrelated between all simulated processes. Table 5 summarizes the total systematic uncertainties in the background expectation in the signal regions.
In the di-tau SR the largest sources of experimental uncertainty are the uncertainties in the jet energy resolution, whereas hard-scatter and parton-shower uncertainties dominate the uncertainty in the theoretical modeling. For the one-bin and multi-bin SRs in the single-tau channel, the theoretical uncertainties inē vent final-state radiation and in interference between the¯and processes take the leading role.
For the theoretical uncertainties in the signal acceptance an estimate of 20% is used, which is derived from a study of the impact of varying the renormalization and factorization scales, the radiation and merging scales, the PDF, and the s value for several stop-stau, LQ u/d 3 , and LQ v 3 signal points. Uncertainties in the signal production cross section are considered separately in the interpretation of the results discussed in Section 8.

Results
The predictions of the event yields from SM background processes obtained from the background-only fit to the control regions, as described in Section 6, and the observed data are shown in Table 6 for the Table 6: Observed event yields in data ("Observed") and expected event yields for SM background processes obtained from the background-only fit ("Total bkg." and rows below) in the signal regions of the di-tau and single-tau channels. The quoted uncertainties include both the statistical and systematic uncertainties and are truncated at zero yield. By construction, no¯(2 real ) events can pass the selections in the single-tau channel. Since the individual uncertainties are correlated, they do not sum in quadrature to equal the total background uncertainty.

Di-tau channel
Single-tau channel −0.16 for single-top production. The normalization factor for single-top production is significantly smaller than one and strongly depends on how the interference between single-top production at next-to-leading order and leading-order production is handled [145,148,149]. The value 0.18 is obtained from the samples generated with the nominal diagram-removal scheme. The alternative diagram-subtraction scheme gives a normalization factor larger than one with very large uncertainties due to the much smaller yields and thus insufficient purity in the control region. The difference between the CR yields can be attributed to the much softer -jet distribution for the diagram-subtraction scheme. However, the distribution shape of T ( 1 ), the variable used in the extrapolation from the control region to the signal region in the single-tau channel, agrees very well between the two schemes, giving confidence in the validity of the extrapolation. Furthermore, the predicted yields in the signal regions after the fit do not differ significantly between the two interference schemes, and the difference is taken into account as a systematic uncertainty.
No significant excess of data events above the SM expectation is observed in any of the signal regions. The largest excursions from the expected yields are a deficit with a significance of 1.0 in the signal region of the di-tau channel and an excess with a significance of 1.3 in the one-bin signal region of the single-tau channel, computed with the approximate formulae from Ref. [140]. The excess is not present, however,   in the binned signal region of the single-tau channel. Figure 6 compares the observed data yields with the expected backgrounds for all event selections of the analysis. The entries in the rightmost column of the plot are the sum of the three bins of the multi-bin signal region in the single-tau channel, labeled "SR (multi-bin)". Figure 7 shows distributions of several kinematic variables for the expected SM background, and compares them with the distributions expected for several benchmark signal models and the observed data in the di-tau and single-tau signal regions.
In the absence of a significant excess, the analysis results are interpreted in terms of exclusion limits on the parameters of the stop-stau and leptoquark signal models. The limits are derived from a model-dependent fit, which includes the relevant signal regions in addition to the control regions, and signal contributions are taken into account in all analysis regions. The signal contamination of the control and validation regions does not exceed 10% (12%) for model parameters that were not excluded by previous searches for the stop-stau (scalar leptoquark) signal. As there are no previous results for the vector-leptoquark model, the low (LQ v 3 ) range is included in the interpretation, where sizable signal contributions to the control and validation regions can be present, exceeding 10% below 1100 (900) GeV for the Yang-Mills (minimal-coupling) scenario. However, as any signal contamination of the control regions is accounted for in the model-dependent fit, and none of the normalization factors are found to be larger than one, the signal contamination is not expected to weaken the interpretation for these cases either. Whether the signal-plus-background hypothesis is compatible with the observed event yields is assessed using the CL s prescription [152], for which the -values are computed with asymptotic formulae obtained for a profile-likelihood ratio as the test statistic [140]. The validity of the asymptotic formulae has been checked through a comparison with the results from pseudoexperiments in the case of the model-independent limits. The likelihood is the product of Poisson terms modeling the joint probability of the event yields for all analysis regions considered in the fit and Gaussian probability terms that constrain the nuisance parameters related to the systematic uncertainties. Figure 8 shows the expected and observed exclusion contours at the 95% confidence level for the stop-stau signal computed from the model-dependent fit that includes both the di-tau and single-tau multi-bin SR. All systematic uncertainties are included in the fit with the exception of the signal cross-section uncertainty, for which a separate band around the observed limit contour is drawn instead. The expected exclusion reach of the analysis extends to top-squark masses around 1.35 TeV over a wide range of tau-slepton masses, and to tau-slepton masses around 1.15 TeV. With decreasing tau-slepton mass, most noticeably below 400 GeV, the exclusion reach in top-squark mass becomes lower, because the fraction of miss T that is due to the neutrinos from the top-squark decay increases, and thus the discrimination power of T2 is reduced. The observed exclusion reach slightly exceeds the expected exclusion reach, as the sensitivity to the stop-stau signal model for tau-slepton masses larger than 200 GeV is dominated by the di-tau SR with an observed deficit. Top-squark masses of up to 1.4 TeV and tau-slepton masses of up to 1.2 TeV are excluded at the 95% confidence level in this specific model. These are the strongest mass limits for these two supersymmetric particles in a simplified model from Run 2 of the LHC to date. They extend significantly beyond the limits from the previous ATLAS analysis, which are shown in the plot for comparison. The gain in sensitivity is partly due to the larger dataset used in the analysis, but also due to improved reconstruction and identification algorithms for tau leptons and -jets, and an improved signal-region strategy with reoptimized selection requirements and the added single-tau signal region targeting low tau-slepton masses.
Exclusion limits for the scalar-leptoquark signal are shown in the two plots in Figure 9, where the upper plot considers pair production of up-type leptoquarks LQ u 3 and the bottom plot pair production of down-type leptoquarks LQ d 3 . To derive these exclusion limits, the model-dependent fit includes, besides the four CRs, only the single-tau multi-bin SR. The di-tau SR has not been optimized for the leptoquark models, as final states with two tau leptons are covered by a previous search [63]. It has been checked that as a consequence this SR does not significantly contribute to the exclusion sensitivity, and it is thus not included in the interpretation for the leptoquark models. For both types of scalar leptoquarks, the expected and observed exclusion contours extend to masses around 1.25 TeV at the 95% confidence level for intermediate values of the branching fraction (LQ u/d 3 → ℓ). When (LQ u/d 3 → ℓ) approaches zero or one, the fraction of events with exactly one tau lepton decreases accordingly, leading to a reduction of the signal acceptance and thus a lower mass reach. At (LQ u/d 3 → ℓ) = 0 the leptoquark decays do not directly produce any tau leptons. The signal events only pass the signal-region selection if a top quark from an up-type leptoquark decay produces a tau lepton or if a fake tau lepton is present in the event. This leads to a large decrease in mass reach. The reduction of the probability of signal events to pass the SR selection when approaching (LQ u/d 3 → ℓ) = 0 is compensated by the cross section. For (LQ) = 750 GeV, corresponding to the mass reach at (LQ u/d 3 → ℓ) = 0, the cross section is larger by a factor of about 40 compared to the cross section at (LQ) = 1250 GeV, corresponding to the excluded LQ mass at (LQ u/d 3 → ℓ) = 0.5. The exclusion contours from the interpretation of the analysis results for the vector-leptoquark models are shown in the two plots in Figure 10. As in the scalar-leptoquark case, the model-dependent fit includes, besides the four CRs, only the single-tau multi-bin SR. For intermediate values of the branching fraction (LQ v 3 → ), the expected and observed exclusion contours at the 95% confidence level extend to masses around 1.5 TeV in the minimal-coupling scenario and to masses around 1.8 TeV in the Yang-Mills scenario.  Figure 9: Expected and observed exclusion contours at the 95% confidence level (CL) for the third-generation scalar-leptoquark signal model, as a function of the mass (LQ u/d 3 ) and the branching fraction (LQ u/d 3 → ℓ) into a quark and a charged lepton. The top plot shows the exclusion contour for up-type leptoquarks LQ u 3 with charge + 2 3 , the bottom plot the exclusion contour for down-type leptoquarks LQ d 3 with charge − 1 3 . The limits are derived from the binned single-tau signal region. Shown in gray for comparison are the observed exclusion-limit contours from the previous ATLAS publication that targets the same leptoquark models but is based on a subset of the Run-2 data [61]. In that publication, five different analyses were considered that target not only the final state studied here but also the final states that correspond to a branching fraction (LQ u/d 3 → ℓ) of 0 or 1, leading to the concave shapes of the gray exclusion contours.   ) shows the upper limit at the 95% CL on the number of signal events, given the expected number (and ±1 excursions of the expectation) of background events. The last two columns indicate the confidence level observed for the background-only hypothesis (CL b ), the discovery -value ( ( = 0)) and the significance ( ). In the di-tau SR, where fewer events are observed than predicted by the fitted background estimate, the -value is capped at 0.5. As expected, the shape of the contours as a function of (LQ v 3 → ) is very similar to that for the scalar-leptoquark models, and the larger cross sections for the pair production of vector leptoquarks leads to a larger mass reach.

Analysis
In addition to the model-dependent interpretations for the signal models shown above, model-independent statements about the presence of physics that is not included in the background expectation for SM processes can also be derived from the analysis results. The model-independent fit is performed for each of the one-bin SRs of the two analysis channels separately. As no specific model is assumed, the contamination of the CRs by a potential signal is neglected, and a generic signal of variable strength is included in the SR. Table 7 states the observed and expected upper limits, 95 obs and 95 exp , on the number of signal events at the 95% confidence level based on the CL s prescription, where the test statistic is evaluated using pseudoexperiments. These upper limits are also expressed as upper limits on the visible signal cross section 95 obs , which is defined as the product of acceptance , reconstruction efficiency and signal cross section . The table also reports the CL b value, i.e. the confidence level observed for the background-only hypothesis, the discovery -value, defined as the probability to find the observed number of events or more under the background-only hypothesis, and the equivalent significance for each of the two channels.

Conclusion
In this paper, a search for new phenomena in final states with hadronically decaying tau leptons, -jets and large missing transverse momentum is presented. This signature provides sensitivity to models in which the new particles preferentially decay into third-generation Standard Model particles. The analysis exploits the full dataset 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 excess of events is observed over the Standard Model expectation. The results are thus interpreted in terms of exclusion limits at 95% confidence level for two simplified models with pair production of supersymmetric top squarks or leptoquarks which are assumed to only decay into third-generation fermions. In the case of the supersymmetric model, masses up to 1.4 TeV are excluded for top squarks decaying via tau sleptons into nearly massless gravitinos across a wide range of tau-slepton masses. For both up-type and down-type scalar leptoquarks, masses up to about 1.25 TeV can be excluded. For vector leptoquarks with minimal couplings, masses up to about 1.5 TeV can be excluded, and up to about 1.8 TeV for vector leptoquarks with additional couplings to gauge bosons. The larger dataset, updated reconstruction and identifications algorithms for tau leptons and -jets, and optimized analysis strategy yield significantly better sensitivity than in earlier LHC studies. Based on the considered benchmark models, the search yields the strongest mass limits to date on pair-produced top squarks and on pair-produced third-generation scalar and vector leptoquarks at intermediate values of the branching fraction into a quark and a charged lepton.     [73] ATLAS Collaboration, Operation of the ATLAS trigger system in Run  [120] J. Blümlein, E. Boos, and A. Kryukov, Leptoquark pair production in hadronic interactions, Z. Phys. C 76 (1997) 137, arXiv: hep-ph/9610408.