A search for pair-produced scalar or vector leptoquarks decaying into a b-quark and a τ\documentclass[12pt]{minimal}
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\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}
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\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}
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\begin{document}$$\sqrt{s} =13$$\end{document} TeV. Events in which at least one τ\documentclass[12pt]{minimal}
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\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}
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\begin{document}$$\mathcal {B}$$\end{document} into a τ\documentclass[12pt]{minimal}
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\begin{document}$$\tau $$\end{document}-lepton and b-quark. For scalar leptoquarks, masses below 1460 GeV are excluded assuming B=100\documentclass[12pt]{minimal}
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\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.
publisher-imprint-nameSpringervolume-issue-count12issue-article-count89issue-toc-levels0issue-pricelist-year2023issue-copyright-holderEDP Sciences, Societa Italiana di Fisica (SIF) and Springer-Verlag GmbH, DE, part of Springer Natureissue-copyright-year2023article-contains-esmNoarticle-numbering-styleContentOnlyarticle-registration-date-year2023article-registration-date-month10article-registration-date-day5article-toc-levels0toc-levels0volume-typeRegularjournal-productNonStandardArchiveJournalnumbering-styleContentOnlyarticle-grants-typeOpenChoicemetadata-grantOpenAccessabstract-grantOpenAccessbodypdf-grantOpenAccessbodyhtml-grantOpenAccessbibliography-grantOpenAccessesm-grantOpenAccessonline-firstfalsepdf-file-referenceBodyRef/PDF/10052_2023_Article_12104.pdfpdf-typeTypesettarget-typeOnlinePDFissue-typeRegulararticle-typeOriginalPaperjournal-subject-primaryPhysicsjournal-subject-secondaryElementary Particles, Quantum Field Theoryjournal-subject-secondaryNuclear Physics, Heavy Ions, Hadronsjournal-subject-secondaryQuantum Field Theories, String Theoryjournal-subject-secondaryMeasurement Science and Instrumentationjournal-subject-secondaryAstronomy, Astrophysics and Cosmologyjournal-subject-secondaryNuclear Energyjournal-subject-collectionPhysics and Astronomyopen-accesstrue
D. Brucnko, A. Budagov, E. F. Torregrosa, V. Gratchev, M. Lokajicek, J. Olszowska, L. Perini, S. Y. Sivollokov: Deceased.
Introduction
Many extensions of the Standard Model (SM) of particle physics predict particles known as leptoquarks (LQs) [1–7]. 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 and charge currents, and therefore can potentially provide an explanation for hints of violations of lepton universality observed in flavour experiments [8–14].
This analysis searches for the pair-production of LQs that couple strongly to the third generation of quarks and leptons in proton–proton (pp) collisions at the LHC. 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 β\documentclass[12pt]{minimal}
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\begin{document}$$\beta $$\end{document} and a coupling parameter λ\documentclass[12pt]{minimal}
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\begin{document}$$\lambda $$\end{document}. In the BRW model, the pair-production cross-section is independent of λ\documentclass[12pt]{minimal}
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\begin{document}$$\lambda $$\end{document}. This analysis also considers pair-production of vector LQs [16, 17] corresponding to the U1\documentclass[12pt]{minimal}
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\begin{document}$$U_1$$\end{document} state in the BRW classification [15]. The scenarios considered in this model differ by a dimensionless coupling constant k, which is zero for the minimal-coupling scenario and one for the Yang–Mills scenario. For both scalar and vector LQs, the parameter β\documentclass[12pt]{minimal}
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\begin{document}$$\beta $$\end{document} controls the coupling to charged leptons. For third generation LQs, results are generally given in terms of the mass of the LQ (mLQ\documentclass[12pt]{minimal}
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\begin{document}$$m_{\text {LQ}}$$\end{document}) and its branching ratio (B\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {B}$$\end{document}), rather than β\documentclass[12pt]{minimal}
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\begin{document}$$\beta $$\end{document} as is the case for first- and second-generation LQs. This is because β\documentclass[12pt]{minimal}
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\begin{document}$$\beta $$\end{document} is not equal to B\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {B}$$\end{document} for third-generation LQs due to the sizable top-quark mass.
ATLAS and CMS have published searches for LQs coupling to the first, second and third generations [18–27]. 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 (LQ3u\documentclass[12pt]{minimal}
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\begin{document}$$\text {LQ}^{\text {u}}_{3}$$\end{document}), which decay into bτ\documentclass[12pt]{minimal}
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\begin{document}$$b\tau $$\end{document} or tν\documentclass[12pt]{minimal}
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\begin{document}$$t\nu $$\end{document}, and down-type LQs (LQ3d\documentclass[12pt]{minimal}
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\begin{document}$$\text {LQ}^{\text {d}}_{3}$$\end{document}), which decay into tτ\documentclass[12pt]{minimal}
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\begin{document}$$t\tau $$\end{document} or bν\documentclass[12pt]{minimal}
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\begin{document}$$b\nu $$\end{document}. Both types of LQs are currently excluded for masses below 1150 GeV\documentclass[12pt]{minimal}
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\begin{document}$$\text {GeV}$$\end{document} for the BRW model, for all values of B\documentclass[12pt]{minimal}
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This paper updates the ATLAS search for an up-type LQ pair decaying into bτ\documentclass[12pt]{minimal}
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\begin{document}$$b\tau $$\end{document} [19], shown in Fig. 1, using the full Run 2 data sample and an updated analysis strategy, prioritising high LQ masses that are not yet excluded in 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 b-hadron, and two τ\documentclass[12pt]{minimal}
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\begin{document}$$\tau $$\end{document}-leptons. For the τ\documentclass[12pt]{minimal}
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\begin{document}$$\tau $$\end{document}-leptons, the cases considered are where both decay hadronically or where one τ\documentclass[12pt]{minimal}
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\begin{document}$$\tau $$\end{document}-lepton decays into a light lepton (electron or muon, ℓ\documentclass[12pt]{minimal}
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\begin{document}$$\ell $$\end{document}) and neutrinos and the other decays hadronically. The mass range considered for the LQ is from 300 to 2000 GeV\documentclass[12pt]{minimal}
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\begin{document}$$\text {GeV}$$\end{document}. 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 [28].
Pair production of a leptoquark (LQ) and its subsequent decay into a b-quark and a τ\documentclass[12pt]{minimal}
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\begin{document}$$\tau $$\end{document}-lepton
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.
ATLAS detector
The ATLAS detector [29] at the LHC is a multipurpose particle detector with a forward–backward symmetric cylindrical geometry and a near 4π\documentclass[12pt]{minimal}
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\begin{document}$$4\pi $$\end{document} coverage in solid angle.1 The inner tracking detector consists of pixel and microstrip silicon detectors covering the pseudorapidity region |η|<2.5\documentclass[12pt]{minimal}
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\begin{document}$$|\eta | < 2.0$$\end{document}. An additional innermost pixel layer, the insertable B-layer [30, 31], 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 |η|<3.2\documentclass[12pt]{minimal}
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\begin{document}$$|\eta | < 3.2$$\end{document}. Hadronic calorimetry is provided by a steel/scintillator-tile calorimeter in the central pseudorapidity range (|η|<1.7\documentclass[12pt]{minimal}
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\begin{document}$$|\eta | < 1.7$$\end{document}). The endcap and forward regions are instrumented with LAr calorimeters for both the EM and hadronic energy measurements up to |η|=4.9\documentclass[12pt]{minimal}
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\begin{document}$$|\eta | = 4.9$$\end{document}. 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 |η|<2.7\documentclass[12pt]{minimal}
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\begin{document}$$|\eta | < 2.7$$\end{document}, while dedicated fast chambers allow triggering in the region |η|<2.4\documentclass[12pt]{minimal}
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\begin{document}$$|\eta | < 2.4$$\end{document}. A two-level trigger system [32], 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 [33] 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 139fb-1\documentclass[12pt]{minimal}
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\begin{document}$$139\,\hbox {fb}^{-1}$$\end{document} of pp collision data collected by the ATLAS detector between 2015 and 2018 at a centre-of-mass energy s=13\documentclass[12pt]{minimal}
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\begin{document}$$\text {TeV}$$\end{document}. The uncertainty in the combined 2015–2018 integrated luminosity is 1.7% [34], obtained using the LUCID-2 detector [35] for the primary luminosity measurements. The presence of additional interactions in the same or neighbouring bunch crossing, referred to as pile-up, is characterised by the average number of such interactions, ⟨μ⟩\documentclass[12pt]{minimal}
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\begin{document}$$\langle \mu \rangle $$\end{document}, 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 [36] based on Geant4 [37], except for the signal samples that use a parameterised fast simulation of the calorimeter response [38] and Geant4 for the other detector systems. The simulated events were reconstructed with the same algorithms as used for data, and contain a realistic modelling of pile-up interactions. The pile-up profiles match those of each data sample between 2015 and 2018, and are obtained by overlaying minimum-bias events simulated using the soft QCD processes of Pythia 8.186 [39] with the NNPDF2.3 leading-order (LO) [40] set of parton distribution functions (PDFs) and the A3 [41] set of tuned parameters (tune). The MC samples are corrected to account for the 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 (Q=+23\documentclass[12pt]{minimal}
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\begin{document}$$Q = +\frac{2}{3}$$\end{document}) scalar LQs were generated at next-to-leading order (NLO) in QCD with MadGraph5_aMC@NLO v2.6.0 [42], using the LQ model of Ref. [43], in which fixed-order NLO QCD calculations [44, 45] are interfaced to Pythia 8.230 [46] for the parton shower (PS) and hadronisation. Parton luminosities were provided by the five-flavour scheme NNPDF3.0 NLO [47] PDF set with αs=0.118\documentclass[12pt]{minimal}
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\begin{document}$$\alpha _s = 0.118$$\end{document} and the underlying event (UE) was modelled with the A14 tune [48, 49]. The coupling parameter λ\documentclass[12pt]{minimal}
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\begin{document}$$\lambda $$\end{document} was set to 0.3, resulting in a relative LQ width of approximately 0.2% and ensuring the LQs decay promptly. In all cases, β=0.5\documentclass[12pt]{minimal}
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\begin{document}$$\beta = 0.5$$\end{document} such that the couplings to charged leptons and neutrinos were equal and the decay products were interfaced to MadSpin [50] to preserve spin correlations. Different values for B\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {B}$$\end{document} were then obtained by reweighting the simulated events according to the generator information about their decay following the procedure in Ref. [19]. 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 [51–54]. The cross-sections do not include contributions from t-channel lepton exchange, which are neglected in Ref. [43] and may lead to corrections at the percent level [55]. The nominal cross-section and its uncertainty were derived using the PDF4LHC15_mc PDF set, following the recommendations of Ref. [56]. For LQ masses between 300 GeV\documentclass[12pt]{minimal}
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\begin{document}$$\text {GeV}$$\end{document}, 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 MadGraph5_aMC@NLO v2.6.0, using the LQ model of Ref. [17] and the NNPDF3.0 NLO PDF set with αs=0.118\documentclass[12pt]{minimal}
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\begin{document}$$\alpha _s = 0.118$$\end{document}. Decays of the LQs were performed with MadSpin, while PS and hadronisation were simulated using Pythia8.244 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 Z′\documentclass[12pt]{minimal}
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\begin{document}$$G^{\prime }$$\end{document}. However, these are not present in the MadGraph 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 gU=3.0\documentclass[12pt]{minimal}
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\begin{document}$$g_U$$\end{document} 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, β=0.5\documentclass[12pt]{minimal}
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\begin{document}$$\beta = 0.5$$\end{document} and the same reweighting as in the scalar LQ case is then used to probe different B\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {B}$$\end{document} 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. B\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {B}$$\end{document} is assumed to be unaffected by these couplings since the corresponding decays are either forbidden or heavily suppressed. Since no higher-order cross-sections are available for this model, the LO MadGraph5_aMC@NLOcross-sections were used and vary between 94 pb (340 pb) and 0.05 fb (0.61 fb) for LQ masses between 300 GeV\documentclass[12pt]{minimal}
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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. (§)\documentclass[12pt]{minimal}
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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 Sherpa, the EvtGen v1.2.0 [87] program was used to simulate the properties of the b- and c-hadron decays.
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\begin{document}$$1.37< | \eta | < 1.52$$\end{document}). 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 [88]. Two identification criteria are used to select electrons in this analysis: ‘veto electrons’2 are required to satisfy the ‘loose’ identification working point, while ‘signal electrons’ are required to satisfy the more stringent ‘tight’ working point.
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\begin{document}$$|\eta | < 2.7$$\end{document}. 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 [89] are used to select muons: ‘veto muons’ (See footnote 2) must satisfy a ‘loose’ identification requirement, while the ‘signal muons’ are required to satisfy the ‘medium’ (‘high-pT\documentclass[12pt]{minimal}
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Summary of the event selections for the τlepτhad\documentclass[12pt]{minimal}
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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 τhad-vis\documentclass[12pt]{minimal}
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\begin{document}$$\Delta R = 0.2$$\end{document}) of any remaining jet are then removed. Finally, ambiguities between anti-τhad-vis\documentclass[12pt]{minimal}
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\begin{document}$$\tau _{\text {had-vis}} $$\end{document} otherwise.
Event selection
The event selection targets a signature consisting of a pair of τ\documentclass[12pt]{minimal}
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\begin{document}$$\tau _{\text {had-vis}}$$\end{document} and one or two b-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-light-lepton [105, 106] and single-τhad-vis\documentclass[12pt]{minimal}
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Following the trigger selection, the τlepτhad\documentclass[12pt]{minimal}
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The invariant mass of the two τ\documentclass[12pt]{minimal}
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\begin{document}$$m_{\text {LQ}}$$\end{document}. 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) [109], parameterised in terms of the generated LQ mass, is chosen. The PNN consists of three hidden layers, each with 32 nodes, implemented in Keras [110] with the Tensorflow [111] backend.
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sT\documentclass[12pt]{minimal}
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\begin{document}$$\tau _{\text {had-vis}}$$\end{document}, respectively, combined with its mass-paired b-jet (τlepτhad\documentclass[12pt]{minimal}
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\begin{document}$$\tau _{\text {had-vis}}$$\end{document}) in the τlepτhad\documentclass[12pt]{minimal}
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\begin{document}$$\tau _{\text {lep}}\tau _{\text {had}}$$\end{document} (τhadτhad\documentclass[12pt]{minimal}
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\begin{document}$$\tau _{\text {had}}\tau _{\text {had}}$$\end{document}) category and is defined in Ref. [112].
A selection of representative input distributions, after the background corrections described in Sect. 6, are presented in Figures 3 and 4 for the τlepτhad\documentclass[12pt]{minimal}
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\begin{document}$$\tau _{\text {had}}\tau _{\text {had}}$$\end{document} SR, respectively. While the relative importance of the variables varies with LQ mass, the sT\documentclass[12pt]{minimal}
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\begin{document}$$s_{\text {T}}$$\end{document} and mass variables are generally the most performant.
Summary of variables used as inputs to the PNN in the τlepτhad\documentclass[12pt]{minimal}
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\begin{document}$$\tau _{\text {had}}\tau _{\text {had}}$$\end{document} categories. The variables are defined in the text
Signal (solid lines), post-fit background (filled histograms) and data (dots with statistical error bars) distributions of representative PNN input variables in the τlepτhad\documentclass[12pt]{minimal}
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\begin{document}$$s_{\text {T}}$$\end{document}. 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\documentclass[12pt]{minimal}
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\begin{document}$$\text {TeV}$$\end{document} scalar LQ, scaled by the indicated factor for visibility, is overlaid. The last bin includes the overflow
Signal (solid lines), post-fit background (filled histograms) and data (dots with statistical error bars) distributions of representative PNN input variables in the τhadτhad\documentclass[12pt]{minimal}
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\begin{document}$$\text {TeV}$$\end{document} scalar LQ, scaled by the indicated factor for visibility, is overlaid. The last bin includes the overflow
The PNNs are trained on all scalar LQ signal masses simultaneously against the main tt¯\documentclass[12pt]{minimal}
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\begin{document}$$\tau _{\text {had-vis}}$$\end{document} components with the latter corrected as described in Sect. 6. The same PNN training is used for both vector LQ models since separate trainings are 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. Comparing the output between the training dataset and an independent testing dataset showed no sign of overtraining. The resulting PNN score distributions, which peak at higher values for LQ signals than for the background processes, are used as the final analysis discriminants.
Background modelling
The dominant background in the τhadτhad\documentclass[12pt]{minimal}
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\begin{document}$$s_{\text {T}}$$\end{document} selection, as well as a region with a low PNN score and the signal region selection. In addition, the τhadτhad\documentclass[12pt]{minimal}
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\begin{document}$$\tau _{\text {had-vis}} $$\end{document} 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 Sect. 6.1.1. Then, with this in place, a shape and normalisation correction is determined for the top backgrounds with jets misidentified as τhad-vis\documentclass[12pt]{minimal}
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Top quark backgrounds
For top-quark-pair and single-top-quark production (top backgrounds), events are estimated separately based on whether the τhad-vis\documentclass[12pt]{minimal}
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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 sT\documentclass[12pt]{minimal}
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The motivation for scaling the tt¯\documentclass[12pt]{minimal}
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\begin{document}$$s_{\text {T}}$$\end{document} bin, the signal contamination remains at the percent level. The largest relative contribution of single-top events is also at high sT\documentclass[12pt]{minimal}
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\begin{document}$$\tau $$\end{document}-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 sT\documentclass[12pt]{minimal}
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\begin{document}$$s_{\text {T}}$$\end{document}, 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 <inline-formula id="IEq389"><alternatives><mml:math><mml:msub><mml:mi>τ</mml:mi><mml:mtext>had-vis</mml:mtext></mml:msub></mml:math><tex-math id="IEq389_TeX">\documentclass[12pt]{minimal}
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In addition to this overall RF, the estimation of top backgrounds with jets misidentified as τhad-vis\documentclass[12pt]{minimal}
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\begin{document}$$\tau _{\text {had-vis}} $$\end{document} in the SRs is performed using simulated events with additional data-driven corrections. A fit is performed in a τlepτhad\documentclass[12pt]{minimal}
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\begin{document}$$\tau _{\text {had-vis}} $$\end{document} misidentification rate in simulation to that observed in data.
The CR has the same selection as the SR for the τlepτhad\documentclass[12pt]{minimal}
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\begin{document}$$\text {GeV}$$\end{document} requirement is removed and sT\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}} $$\end{document}.
The distribution used for this estimation is the transverse mass of the light lepton and missing transverse momentum, defined as mT(ℓ,ETmiss)=\documentclass[12pt]{minimal}
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\begin{document}$$\sqrt{(E_{\text {T}}^{\text {miss}} + p_{\text {T},\ell })^2 - (E_{\text {T},x}^{\text {miss}} + p_{x,\ell })^2 - (E_{\text {T},y}^{\text {miss}} + p_{y,\ell })^2 }$$\end{document}. The expected shapes for top backgrounds with true and misidentified τhad-vis\documentclass[12pt]{minimal}
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\begin{document}$$\tau _{\text {had-vis}} $$\end{document} in this distribution differ significantly, making it possible to constrain the two background sources. The normalisation of the true and misidentified τhad-vis\documentclass[12pt]{minimal}
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\begin{document}$$\text {GeV}$$\end{document}). ‘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
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For the τhadτhad\documentclass[12pt]{minimal}
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\begin{document}$$\tau _{\text {had-vis}} $$\end{document}. These FFs are derived as a function of transverse momentum and the number of charged-particle tracks of the τhad-vis\documentclass[12pt]{minimal}
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\begin{document}$$\tau _{\text {had-vis}} $$\end{document} 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 Sects. 6.1.1 and 6.1.2, respectively. Since the SFs are anticipated to be different for fake τhad-vis\documentclass[12pt]{minimal}
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\begin{document}$$\tau _{\text {had-vis}} $$\end{document} requirements, dedicated SFs are measured for this data-driven estimation. Specifically, the anti-τhad-vis\documentclass[12pt]{minimal}
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\begin{document}$$\tau _{\text {had-vis}} $$\end{document} region uses SFs that are derived in a CR as described in Sect. 6.1.2, except that the τhad-vis\documentclass[12pt]{minimal}
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\begin{document}$$\tau _{\text {had-vis}} $$\end{document}. An example fit in a single bin of pT\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}} $$\end{document}, these SFs vary between 0.77 and 0.95.
To construct the background estimate, FFs are applied to a region with the τhadτhad\documentclass[12pt]{minimal}
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\begin{document}$$\tau _{\text {had-vis}} $$\end{document}. This provides both a shape and a normalisation for the multi-jet contribution in the PNN score distribution.
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\begin{document}$$\text {GeV}$$\end{document}). ‘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
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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 pT\documentclass[12pt]{minimal}
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\begin{document}$$Z+\text {HF}$$\end{document} background entering into the final fit (described in Sect. 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 Sect. 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.
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\begin{document}$$\tau _{\text {had-vis}} $$\end{document} trigger efficiencies, respectively, are considered. For b-jets, additional uncertainties are considered for the efficiency of (mis)tagging b-jets, c-jets, and light-quark-initiated jets. Uncertainties related to energy scale and resolution, and the inclusion of soft terms, are considered for the ETmiss\documentclass[12pt]{minimal}
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\begin{document}$$m_{\text {LQ}}= 1.4$$\end{document}TeV\documentclass[12pt]{minimal}
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\begin{document}$$\text {TeV}$$\end{document}. 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
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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 mLQ\documentclass[12pt]{minimal}
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\begin{document}$$m_{\text {LQ}}$$\end{document}. In the scalar LQ case, for example, the statistical impact on the limit ranges from 60% at the lowest mLQ\documentclass[12pt]{minimal}
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The observed (solid line) and expected (dashed line) 95% CL upper limits on the LQ pair production cross-sections assuming B=1\documentclass[12pt]{minimal}
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\begin{document}$$\pm 1 \sigma , \pm 2 \sigma $$\end{document}) uncertainty in the expected limit. The theoretical prediction in each model, along with its uncertainty, is shown by the lines with the hatched bands
Statistical interpretation and results
The data are compared with the expectation, including the background modelling corrections outlined in Sect. 6, by performing simultaneous binned maximum-likelihood fits to the PNN score distributions, separately for each LQ hypothesis, in the τlepτhad\documentclass[12pt]{minimal}
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The statistical and systematic uncertainties affecting the signal and background model, described in Sect. 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.
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Observed and expected lower limits on the LQ mass at 95% CL for the three different LQ models, assuming B=1\documentclass[12pt]{minimal}
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\begin{document}$$m_{\text {LQ}}$$\end{document} 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\documentclass[12pt]{minimal}
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Conclusion
A search for pair-produced scalar or vector leptoquarks decaying into a b-quark and a τ\documentclass[12pt]{minimal}
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Acknowledgements
We thank CERN for the very successful operation of the LHC, as well as the support staff from our institutions without whom ATLAS could not be operated efficiently. We acknowledge the support of ANPCyT, Argentina; YerPhI, Armenia; ARC, Australia; BMWFW and FWF, Austria; ANAS, Azerbaijan; CNPq and FAPESP, Brazil; NSERC, NRC and CFI, Canada; CERN; ANID, Chile; CAS, MOST and NSFC, China; Minciencias, Colombia; MEYS CR, Czech Republic; DNRF and DNSRC, Denmark; IN2P3-CNRS and CEA-DRF/IRFU, France; SRNSFG, Georgia; BMBF, HGF and MPG, Germany; GSRI, Greece; RGC and Hong Kong SAR, China; ISF and Benoziyo Center, Israel; INFN, Italy; MEXT and JSPS, Japan; CNRST, Morocco; NWO, Netherlands; RCN, Norway; MEiN, Poland; FCT, Portugal; MNE/IFA, Romania; MESTD, Serbia; MSSR, Slovakia; ARRS and MIZŠ, Slovenia; DSI/NRF, South Africa; MICINN, Spain; SRC and Wallenberg Foundation, Sweden; SERI, SNSF and Cantons of Bern and Geneva, Switzerland; MOST, Taiwan; TENMAK, Türkiye; STFC, United Kingdom; DOE and NSF, United States of America. In addition, individual groups and members have received support from BCKDF, CANARIE, Compute Canada and CRC, Canada; PRIMUS 21/SCI/017 and UNCE SCI/013, Czech Republic; COST, ERC, ERDF, Horizon 2020 and Marie Skłodowska-Curie Actions, European Union; Investissements d’Avenir Labex, Investissements d’Avenir Idex and ANR, France; DFG and AvH Foundation, Germany; Herakleitos, Thales and Aristeia programmes co-financed by EU-ESF and the Greek NSRF, Greece; BSF-NSF and MINERVA, Israel; Norwegian Financial Mechanism 2014-2021, Norway; NCN and NAWA, Poland; La Caixa Banking Foundation, CERCA Programme Generalitat de Catalunya and PROMETEO and GenT Programmes Generalitat Valenciana, Spain; Göran Gustafssons Stiftelse, Sweden; The Royal Society and Leverhulme Trust, United Kingdom. The crucial computing support from all WLCG partners is acknowledged gratefully, in particular from CERN, the ATLAS Tier-1 facilities at TRIUMF (Canada), NDGF (Denmark, Norway, Sweden), CC-IN2P3 (France), KIT/GridKA (Germany), INFN-CNAF (Italy), NL-T1 (Netherlands), PIC (Spain), ASGC (Taiwan), RAL (UK) and BNL (USA), the Tier-2 facilities worldwide and large non-WLCG resource providers. Major contributors of computing resources are listed in Ref. [122].
Data Availability Statement
This manuscript has no associated data or the data will not be deposited. [Authors’ comment: “All ATLAS scientific output is published in journals, and preliminary results are made available in Conference Notes. All are openly available, without restriction on use by external parties beyond copyright law and the standard conditions agreed by CERN. Data associated with journal publications are also made available: tables and data from plots (e.g. cross section values, likelihood profiles, selection efficiencies, cross section limits, ...) are stored in appropriate repositories such as HEPDATA (http://hepdata.cedar.ac.uk/). ATLAS also strives to make additional material related to the paper available that allows a reinterpretation of the data in the context of new theoretical models. For example, an extended encapsulation of the analysis is often provided for measurements in the framework of RIVET (http://rivet.hepforge.org/).” This information is taken from the ATLAS Data Access Policy, which is a public document that can be downloaded from http://opendata.cern.ch/record/413 [opendata.cern.ch].]
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\begin{document}$$\Delta R \equiv \sqrt{(\Delta \eta )^{2} + (\Delta \phi )^{2}}$$\end{document}.
‘Veto’ leptons are used to reject events with additional leptons as discussed in Sect. 5.1
The rejection factor is defined as the reciprocal of the efficiency to mistag a jet not containing B-hadrons as a b-jet.
In the case of only one b-jet, the highest-pT\documentclass[12pt]{minimal}
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\begin{document}$$p_{\text {T}}$$\end{document} non-b-jet is taken as the second jet.