Contents

Search for pair- and single-production of vector-like quarks in final states with at least one $Z$ boson decaying into a pair of electrons or muons in $pp$ collision data collected with the ATLAS detector at $\sqrt{s} = 13$ TeV

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Acknowledgements.bib \addbibresourceEXOT-2016-35-PAPER.bib \addbibresourceATLAS.bib \addbibresourceATLAS-errata.bib \addbibresourceCMS.bib \addbibresourceConfNotes.bib \addbibresourcePubNotes.bib \AtlasTitleSearch for pair- and single-production of vector-like quarks in final states with at least one boson decaying into a pair of electrons or muons in collision data collected with the ATLAS detector at \PreprintIdNumberCERN-EP-2018-145 \AtlasJournalPhys. Rev. D \AtlasAbstract A search for vector-like quarks is presented, which targets their decay into a boson and a third-generation Standard Model quark. In the case of a vector-like quark () with charge (), the decay searched for is (). Data for this analysis were taken during 2015 and 2016 with the ATLAS detector at the Large Hadron Collider and correspond to \lumi of collisions at . The final state used is characterized by the presence of a boson with high transverse momentum, which is reconstructed from a pair of opposite-sign same-flavor leptons, as well as -tagged jets. Pair- and single-production of vector-like quarks are both taken into account and are each searched for using optimized dileptonic exclusive and trileptonic inclusive event selections. In these selections, the high scalar sum of jet transverse momenta, the presence of high-transverse-momentum large-radius jets, as well as—in the case of the single-production selections—the presence of forward jets are used. No significant excess over the background-only hypothesis is found and exclusion limits at 95% confidence level allow masses of vector-like quarks of () and () in the singlet (doublet) model. In the case of 100% branching ratio for (), the limits are (). Limits at 95% confidence level are also set on the coupling to Standard Model quarks for given vector-like quark masses. \sisetuptable-align-uncertainty = true, group-digits = false

1 Introduction

In the Standard Model (SM), the electromagnetic and weak interactions arise from a gauge symmetry that is spontaneously broken by the Englert–Brout–Higgs mechanism. Measurements at collider experiments are so far consistent with its predictions. However, it is believed to be only a low-energy approximation of a more fundamental theory because several questions remain unanswered in the SM. For example, it cannot explain the matter–antimatter asymmetry in the universe and the origin of dark matter. When the SM is extrapolated to high energies, fine-tuning is required due to divergent corrections to the Higgs boson self-energy [Naturalness]. Solutions to this so-called “hierarchy problem” are proposed in several beyond-the-Standard Model (BSM) theories, which can be considered a first step towards a more fundamental theory of particle physics.

Since a large contribution to the fine-tuning originates from top-quark loop corrections, the hierarchy problem can be reduced in models predicting top-quark partners that mitigate the top quark’s contribution: while a scalar top-quark partner appears in supersymmetry as the bosonic superpartner of the top quark, fermionic top-quark partners appear in theories with a new broken global symmetry, in which the Higgs boson is interpreted as a pseudo Nambu–Goldstone boson [StrongEWSB], for example in Little Higgs [LittleHiggs, LittleHiggsRev] and Composite Higgs [CompHiggs1, CompHiggs2] models. In these models, the new symmetry corresponds to a new strong interaction, whose bound states include vector-like quarks (VLQ). These are color-triplet spin- fermions, but in contrast to the chiral SM quarks their left- and right-handed components have the same properties under transformations.

Only a limited set of possibilities exist for the quantum numbers of the VLQs if gauge invariance is required to be preserved [delAguila, delAguila:2000rc]. Their electric charge could be ( quark), ( quark), ( quark) or ( quark), where is the elementary charge, and they could appear in electroweak singlets, () or (), electroweak doublets, ( ), ( ), or ( ), or electroweak triplets, (  ) or (  ). This paper focuses solely on the search for and quarks, which could couple to SM quarks by mixing [VLQmixing]. Although couplings of VLQs to first- and second-generation SM quarks are not excluded [Atre:2008iu, Atre:2011ae], this paper searches for VLQs that couple exclusively to third-generation SM quarks. The couplings of and quarks can be described in terms of and  [Aguilar-Saavedra:2013qpa], where and are the mixing angles with the top quark and the -quark, respectively, or they can be described in terms of generalized couplings and of the or quark to third-generation SM quarks [Buchkremer:2013bha, Matsedonskyi:2014mna].

Search strategies for VLQs have been proposed [ContinoServant, JA_TP, TP_guide, Aguilar-Saavedra:2013qpa, Backovic:2015bca] that focus either on the search for VLQ pair production via the strong interaction or on single production via the electroweak interaction. The decay of and quarks can either happen via the charged current, i.e.  and ,1 or via flavor-changing neutral currents [delAguila2], i.e. , , , and . Decays including non-SM particles are not excluded [Chala:2017xgc], but are not considered in this paper, so that for and quarks the branching ratios (BR) to the three decay modes add up to unity. While the cross section for pair production is given by quantum chromodynamics, the single-production cross section explicitly depends on the coupling of the VLQ to SM quarks.

Pair-production channels Single-production channels
Dilepton with \ljet Dilepton with \ljets Trilepton Dilepton Trilepton
(PP 2 0-1J) (PP 2 2J) (PP 3) (SP 2) (SP 3)
Leptons
\btagged jets
\Ljets (top-tagged)
Forward jets
\ptll
Additional optimized kinematic requirements for each channel
Table 1: Overview of the requirements used in each channel to search for pair and single production of VLQs.

The ATLAS and CMS Collaborations have searched for pair production of and quarks that decay into third-generation quarks in collisions at  [Aad:2015kqa, Aad:2015gdg, Aad:2014efa, Aad:2015mba, Khachatryan:2015gza, Khachatryan:2015oba] in all three possible decay modes of each of the VLQs. Current searches at have used single-lepton final states to search for the decay with the boson decaying invisibly [Aaboud:2017qpr, Aaboud:2018xuw],  [Aaboud:2017zfn, Sirunyan:2017pks],  [Aaboud:2018xuw], and  [Aaboud:2017zfn, WtX], as well as general single-lepton final states with boosted and Higgs bosons [Sirunyan:2017usq]. The CMS Collaboration has also searched for pair production of and quarks in a combination of single-lepton final states, dilepton final states with the same electric charge and trilepton final states [Sirunyan:2018omb] at . These searches have set upper limits at 95% confidence level (CL) on the VLQ pair-production cross section, also interpreted as lower limits on the VLQ mass, , depending on the VLQ BRs assumed. The most stringent limits in the case of the and singlets are 1.20 \TeV [Sirunyan:2018omb] and 1.17 \TeV [WtX, Sirunyan:2018omb], respectively. In the case of 100% BRs of to and to , the most stringent limits are 1.30 \TeV [Sirunyan:2018omb] and 0.96 \TeV [Sirunyan:2018omb], respectively. The searches at are significantly more sensitive than the searches at due to the larger expected pair-production cross sections at the higher center-of-mass energy. This paper includes searches for pair-produced VLQ at in final states with more than one lepton which are particularly sensitive to the decays and .

At large , the cross section for the single production of VLQs may be larger than the pair-production cross section because of the larger available phase space, even though single production is mediated by the weak interaction. However, the comparison of single- and pair-production cross sections depends on the assumed coupling to the SM quarks. Single production was searched for at  [Aad:2015voa, Aad:2014efa, Aad:2016qpo] by the ATLAS and CMS Collaborations. At , the CMS Collaboration has searched for the decays  [Sirunyan:2017tfc],  [Sirunyan:2016ipo, Khachatryan:2016vph],  [Sirunyan:2017ynj, Sirunyan:2017ezy],  [Sirunyan:2018fjh], and  [Sirunyan:2017ezy]. In these searches, upper limits were set on the single-production cross section, which were also interpreted as upper limits on the coupling to SM quarks as a function of . Similarly to the case of pair production, the expected single-production cross sections are much larger at than at , so that the searches at the higher center-of-mass energy are more sensitive. Searches for single-VLQ production at were not performed before by the ATLAS Collaboration. As in the search for VLQ pair production, final states with more than one lepton are used, which are particularly sensitive to the decay .

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Figure 1: Sketches of the processes searched for in the pair-production channels in (a) dilepton final states with at most one \ljet (PP 2 0-1J), (b) dilepton final states with at least two \ljets (PP 2 2J), and (c) final states with at least three leptons (PP 3), and sketches of the processes searched for in the single-production channels in (d) the dilepton final state (SP 2), and (e) final states with at least three leptons (SP 3).

The analysis was performed with data collected in collisions at , searching for the pair production of and quarks and for the single production of quarks in final states with at least one boson. In the case of single production, the quark is hence expected to decay into . In the case of pair production, the search targets only one VLQ decay into a boson and a third-generation quark explicitly, so that it is particularly sensitive to all decays that include at least one boson in the final state, i.e. not only and , but also , , , and .

The overall analysis strategy is based on a search that was performed with data [Aad:2014efa], which exploited the leptonic boson decays and . Several improvements have been made, in particular adding new channels and optimizing the analysis for the higher and a larger dataset. Five analysis channels are defined; three for the search for and pair-production, and two for the search for single- production, as shown in \Tab1. An event preselection that is common to all channels is used, in which all events are required to include a boson candidate, reconstructed from two same-flavor leptons (, ) with opposite electric charge. The event selection in each channel was then optimized for a particular final state, as shown in \Fig1. First, the searches were split into pair- and single-production categories and then further into dilepton channels—requiring no lepton in addition to the leptons that are used to reconstruct the boson candidate—and trilepton channels, in which at least three leptons are required. Since the VLQs are assumed to decay into third-generation SM quarks, the presence of -tagged jets is exploited in order to discriminate the signal from SM background processes. Since the signal process includes high-energy hadronically decaying massive resonances, \ljets are used in the dilepton channels, further enhancing the sensitivity of the search. In the dilepton single-production channel, top-tagging is used in order to identify \ljets originating from the hadronic decays of high-energy top quarks. In both single-production channels, the presence of a forward jet from the -channel production is used to suppress the background. Due to the large expected values of , the transverse momentum2 of the boson, \ptll, is expected to be much larger in signal than in background events. More requirements, in particular on the event kinematics, were optimized in each channel, as discussed in \Sect5. In the following, the three pair-production channels are referred to as the dilepton channel with at most one \ljet (PP 2 0-1J), the dilepton channel with at least two \ljets (PP 2 2J), and the trilepton channel (PP 3). The two single-production channels are referred to as the dilepton channel (SP 2), and the trilepton channel (SP 3).

2 The ATLAS detector

The ATLAS detector [PERF-2007-01] at the LHC covers nearly the entire solid angle around the collision point. It consists of an inner tracking detector surrounded by a thin superconducting solenoid, electromagnetic and hadronic calorimeters, and a muon spectrometer incorporating three large superconducting toroidal magnets.

The inner-detector system (ID) is immersed in a \SI2\tesla axial magnetic field and provides charged-particle tracking in the range . The high-granularity silicon pixel detector covers the vertex region and typically provides four measurements per track, the first hit being normally in the innermost layer, the insertable B-layer [ATLAS-TDR-19]. It is followed by the silicon microstrip tracker which usually provides four two-dimensional measurement points per track. These silicon detectors are complemented by the transition radiation tracker, which enables radially extended track reconstruction up to . The transition radiation tracker also provides electron identification information based on the fraction of hits (typically 30 in total) above a higher energy-deposit threshold corresponding to transition radiation.

The calorimeter system covers the pseudorapidity range . Within the region , electromagnetic calorimetry is provided by barrel and endcap high-granularity lead/liquid-argon (LAr) electromagnetic calorimeters, with an additional thin LAr presampler covering , to correct for energy loss in material upstream of the calorimeters. Hadronic calorimetry is provided by the steel/scintillator-tile calorimeter, segmented into three barrel structures within , and two copper/LAr hadronic endcap calorimeters. The solid angle coverage is completed with forward copper/LAr and tungsten/LAr calorimeter modules optimized for electromagnetic and hadronic measurements respectively.

The muon spectrometer (MS) comprises separate trigger and high-precision tracking chambers measuring the deflection of muons in a magnetic field generated by superconducting air-core toroidal magnets. The field integral of the toroidal magnets ranges between \num2.0 and \SI6.0\tesla\metre across most of the detector. A set of precision chambers covers the region with three layers of monitored drift tubes, complemented by cathode strip chambers in the forward region, where the background is highest. The muon trigger system covers the range with resistive plate chambers in the barrel, and thin gap chambers in the endcap regions.

A two-level trigger system is used in order to select interesting events [Aaboud:2016leb]. The first-level trigger is implemented in hardware and uses a subset of detector information to reduce the event rate to a design value of at most \SI100\kHz. This is followed by a software-based trigger which reduces the event rate to about \SI1\kHz.

3 Data and Monte Carlo samples

For this search, collision data collected with the ATLAS detector during 2015 and 2016 at were used, corresponding to an integrated luminosity of \lumi. Only events taken during stable beam conditions, and for which all relevant components of the detector were operational, are considered. Events are required to have a primary vertex with at least two tracks with a minimum \pt of 400 \MeV. If several such vertices exists, the vertex with the highest is chosen as the hard-scatter vertex [ATL-PHYS-PUB-2015-026]. Events are rejected if they satisfy the criteria [ATLAS-CONF-2015-029] designed to reject beam-induced background and backgrounds from cosmic-ray showers and calorimeter noise. Several single-lepton triggers with different \pt thresholds were used for electrons and muons depending on the data-taking period. For data collected in 2015, the thresholds are 24, 60 and 120 \GeV for electrons and 20 and 50 \GeV for muons, where lepton isolation requirements are applied to the lowest-\pt triggers to reduce their rate. For the highest-\pt electron trigger, the identification criteria are relaxed. For data-taking in 2016, the thresholds were raised slightly to 26, 60 and 140 \GeV for electrons and 26 and 50 \GeV for muons.

The main sources of background in this search are \zjets and \ttbar production in the case of the dilepton channels and diboson (, , ) and production in the case of the trilepton channels, where is dominated by \ttbar production with associated vector bosons (, or ) but also includes and production. Smaller sources of background are also considered,3 which include single-top and triboson production (, , , ). The background contribution from production was found to be negligible and is not considered in this search. For all background and signal processes, Monte Carlo (MC) samples were generated and the detector response was simulated in GEANT[Agostinelli:2002hh] with a full model of the ATLAS detector [SOFT-2010-01], unless stated otherwise. The simulations include the contributions from additional collisions in the same or an adjacent bunch crossing (pileup). Corrections for trigger and object-identification efficiencies, and for -tagging misidentification efficiencies, as well as for energy and momentum scales and resolutions of the objects were applied to the simulated samples, based on the differences observed between data and MC samples in reference processes. A summary of the background samples used in this paper is shown in \Tab2.

The \zjets process was simulated with \SHERPAV2.2.1 [Gleisberg:2008ta, Hoeche:2009rj, Gleisberg:2008fv, Schumann:2007mg] using the NNPDF3.0 [Ball:2014uwa] next-to-next-to-leading-order (NNLO) set of parton distribution functions (PDFs), and normalized to the NNLO cross section in QCD4 calculated with FEWZ [Anastasiou:2003ds] and the MSTW 2008 [Martin:2009iq, Martin:2009bu, Martin:2010db] NNLO PDF set. The \ttbar process was simulated with the POWHEG method [Nason:2004rx, Frixione:2007vw] implemented in \POWHEGBOXVv2 [Alioli:2010xd, Campbell:2014kua] using the NNPDF3.0 NNLO PDF set. \POWHEGBOXwas interfaced with \PYTHIAV[Sjostrand:2007gs] with the A14 set of tuned parameters [ATL-PHYS-PUB-2014-021] and the NNPDF2.3 LO PDF set [Ball:2012cx] for parton showering and hadronization. The parameter5 in \POWHEGBOXwas set to  [ATL-PHYS-PUB-2017-007], where . The sample was normalized to the NNLO cross section including resummation of next-to-next-to-leading logarithmic (NNLL) soft gluon terms with TOP++ [Czakon:2011xx, Czakon:2013goa, Beneke:2011mq, Cacciari:2011hy, Czakon:2012pz, Czakon:2012zr, Baernreuther:2012ws]. The PDF and uncertainties were calculated using the PDF4LHC prescription [Botje:2011sn] with the MSTW 2008 NNLO, CT10 NNLO [Lai:2010vv, Gao:2013xoa] and NNPDF2.3 5f FFN PDF sets, added in quadrature to the scale uncertainty. The diboson processes were simulated with \SHERPAV2.2.1 for up to one additional parton at next-to-leading order (NLO) and up to three additional partons at leading order (LO) using Comix [Gleisberg:2008fv] and OpenLoops [Cascioli:2011va], and merged with the \SHERPA parton shower [Schumann:2007mg] according to the ME+PS@NLO prescripton [Hoeche:2012yf]. The NNPDF3.0 NNLO PDF set was used and the samples were normalized to the NLO cross sections calculated with \SHERPA. The processes were simulated with \MGMCatNLO [Alwall:2014hca] using the NNPDF3.0 NLO PDF set. \MGMCatNLOwas interfaced with \PYTHIAV8 with the A14 set of tuned parameters and the NNPDF2.3 LO PDF set for parton showering and hadronization. The samples were normalized to the NLO cross section calculated with \MGMCatNLO. The single-top processes were simulated with \POWHEGBOXVv1 [Alioli:2009je, Re:2010bp] using the CT10 PDF set. \POWHEGBOXwas interfaced to \PYTHIAV[Sjostrand:2006za] with the Perugia 2012 [Skands:2010ak] set of tuned parameters and the CTEQ6L1 PDF set [Pumplin:2002vw]. The single-top samples were normalized to NLO cross sections with additional NNLL soft gluon terms [Kidonakis:2011wy, Kidonakis:2010tc, Kidonakis:2010ux]. The triboson processes were simulated using \SHERPAV2.1 using the CT10 PDF set, and normalized to the NLO cross sections calculated with \SHERPA. The and processes were simulated with \MADGRAPHV5 and \PYTHIAV8 using the NNPDF2.3 LO PDF set and the A14 set of tuned parameters, and were normalized to the NLO cross section calculated with \MGMCatNLO. Additional MC samples were generated for the evaluation of systematic uncertainties due to the choice of factorization and renormalization scales, generator, and parton shower program for the \zjets, \ttbar, and diboson background processes. These samples are described in \Sect6.

The pair production of VLQs was simulated at LO with \PROTOS [PROTOS] using the NNPDF2.3LO PDF set. \PROTOS was interfaced to \PYTHIAV8 with the A14 set of tuned parameters. Samples were produced for in the range of 500 to 1400 \GeV. Steps of 50 \GeV were used in the range from 700 to 1200 \GeV, and steps of 100 \GeV otherwise. The samples were generated in the singlet models for and quarks, but samples at of 700, 900 and 1200 \GeV were also generated in the ( ) doublet model in order to test kinematic differences between singlet and doublet models. In the singlet models, the BRs are independent of the mixing angles between VLQ and SM quarks for small values of the mixing angles and hence only a function of . With this assumption, for large , the BRs approach the relative proportions of 50:25:25 for the :: decay modes in the singlet model for the quark as well as for the quark. In the ( ) doublet and ( ) doublet models, the BRs approach the relative proportions of 50:50 for the : decays of the quark and quark, respectively. The same holds for the ( ) doublet model if the top quark mixes much more strongly with its VLQ partner than the bottom quark, a natural scenario for the SM Yukawa couplings [JA_TP]. However, kinematic differences may exist between the singlet and doublet models. The samples generated for the ( ) doublet were used to verify that such kinematic differences have a small impact on the analysis, and therefore the difference between the two cases is only a change in the BRs. Thus, the singlet model samples were also used for the doublet case, reweighting the yields for each decay mode to obtain the expected observables for any given BR. The pair-production cross sections were calculated with TOP++ at NNLO+NNLL using the MSTW 2008 NNLO PDF set.

The single production of quarks was simulated using \MADGRAPHV5 with the “VLQ” UFO model [UFO], which implements the Lagrangian described in Ref [Buchkremer:2013bha], using the NNPDF2.3 LO PDF set. \MADGRAPH was interfaced to \PYTHIAV8 with the A14 set of tuned parameters. Only the decay was considered. Samples were generated with a quark produced via and also via interactions. Since production via the interaction is suppressed due to the required top quark in the initial state, single-VLQ production refers to production via the interaction in the remainder of this paper, unless stated otherwise. Samples were generated for in the range from 700 to 2000 \GeV with a benchmark coupling of for the and interactions, respectively. Additional samples were generated with alternative values of and in order to study the effect of a varying -quark width on kinematic distributions.

The single-production cross sections were calculated [Matsedonskyi:2014mna] at NLO and in narrow-width approximation for , with the coupling defined in Ref. [Matsedonskyi:2014mna] and corresponding to up to numerical constants. In order to predict the cross section for different values of , they are multiplied by . It was shown in the context of this analysis that the chirality of the coupling has a negligible impact on the sensitivity of the analysis and hence is taken as the sum in quadrature of the left- and right-handed couplings and , i.e. . The cross section is additionally corrected for width effects calculated with \MADGRAPHV5, assuming that the ratio of NLO and LO cross sections remains approximately the same for a non-vanishing -quark width. The cross section is then multiplied by the BR to in the singlet model, which is % in the range of VLQ masses investigated in this analysis. The benchmark coupling of corresponds to a coupling of the quark to the boson, .

Generator Shower program PDF set (ME) Cross section
and tune
\zjets \SHERPAV2.2.1 \SHERPAV2.2.1 NNPDF3.0 NNLO NNLO
\ttbar \POWHEGBOXVv2 \PYTHIAV8, A14 NNPDF3.0 NNLO NNLO+NNLL
Diboson \SHERPAV2.2.1 \SHERPAV2.2.1 NNPDF3.0 NNLO NLO
(/) \MGMCatNLO \PYTHIAV8, A14 NNPDF3.0 NLO NLO
\MADGRAPHV5 \PYTHIAV8, A14 NNPDF2.3 LO NLO
\MADGRAPHV5 \PYTHIAV8, A14 NNPDF2.3 LO NLO
Single top \POWHEGBOXVv1 \PYTHIA8, CT10 NLO+NNLL
Perugia 2012
Triboson \SHERPAV2.1 \SHERPAV2.1 CT10 NLO
Table 2: List of background Monte Carlo samples used, giving information about the matrix-element generator, the parton shower program to which it is interfaced and its set of tuned parameters (“tune”, if applicable), the PDF sets used in the matrix element (ME), and the order in QCD of the cross-section calculation.

4 Object reconstruction

Reconstructed electrons, muons and jets are used. Jets are reconstructed with the anti- algorithm [Cacciari:2008gp] with a radius parameter of 0.4 (\sjets) and with a parameter of 1.0 (\ljets). A -tagging algorithm is applied to \sjets, and a top-tagging algorithm is applied to \ljets. Moreover, missing transverse momentum (\met) is used for the definition of one signal-enriched region and one background-enriched region. For electrons, muons and jets, an overlap-removal procedure based on their proximity in space is used, as described at the end of this section.

Electrons are reconstructed [ATLAS-CONF-2016-024] from energy clusters in the electromagnetic calorimeter with ID tracks matched to them. Their energy is calibrated [PERF-2013-05, ATL-PHYS-PUB-2016-015], and they are required to fulfill the “tight likelihood” identification criteria [ATLAS-CONF-2016-024]. Electrons are required to have a minimum transverse energy, \et, of at least 28 \GeV and to be within the fiducial region , excluding the barrel–endcap transition region, . Electron tracks must point to the primary vertex, which is ensured by requiring that the track’s impact parameter significance is smaller than 5, and that is smaller than 0.5 mm, where is the distance along the -axis between the primary vertex and the track’s point of closest approach. In order to suppress background from electrons originating from hadron decays and from hadrons that are misidentified as electrons, an isolation criterion is applied that requires the scalar sum of the \pt of the tracks which point to the primary vertex within a cone around the electron (but excluding its track) be less than 6% of its \et. A variable cone size [Rehermann:2010vq] of is used.

Muons are reconstructed [PERF-2015-10] from combined tracks in the MS and the ID. Their transverse momentum, \pt, is calibrated [PERF-2015-10], and they are required to fulfill the “medium” identification criteria [PERF-2015-10]. Muons must have a minimum \pt of 28 \GeV and they must be within the fiducial region . Muon tracks must point to the primary vertex, which is ensured by requiring that the track’s impact parameter significance is smaller than 3, and that is smaller than 0.5 mm. In order to suppress background from muons originating from hadron decays, an isolation criterion similar to that for electrons is applied: the scalar sum of the \pt of the tracks around the muon which point to the primary vertex, excluding the muon track, must be smaller than 6% of its \pt, using a variable cone size of .

\Sjets

are reconstructed from topological clusters of calorimeter cells [PERF-2014-07, ATL-PHYS-PUB-2015-036] with the anti- algorithm using FastJet [Cacciari:2011ma] with a radius parameter of 0.4. \Sjets are calibrated to the jet energy scale (JES) at particle level [PERF-2016-04] and are required to be within the fiducial volume . \Sjets with must have a minimum \pt of 25 \GeV and forward jets, , must have a minimum \pt of 35 \GeV to reduce contributions from pileup. For \sjets with and , pileup contributions are suppressed by the use of the jet vertex tagger [PERF-2014-03]. \Sjets within are \btagged using the MV2c10 algorithm [ATL-PHYS-PUB-2016-012], for which several basic -tagging-algorithms [PERF-2012-04] are combined in a boosted decision tree. The MV2c10 algorithm is used such that it provides a -tagging efficiency of for -jets,6 and a rejection factor of for -jets and for other light jets, based on simulated \ttbar events.

\Ljets

are also reconstructed from topological clusters with the anti- algorithm, but with a radius parameter of 1.0. In contrast to the \sjet calibration, the topological clusters that are used as inputs to the \ljet reconstruction take into account corrections for the calorimeter’s response to hadrons and other effects [Barillari:2009zza]. Contributions to \ljets from pileup and the underlying event are removed by applying trimming [Krohn:2009th] with parameters that were optimized for separating \ljets that originate from hadronic decays of high-energy massive resonances [PERF-2015-03, ATL-PHYS-PUB-2015-033, ATL-PHYS-PUB-2015-053] from those that originate from -quarks, light quarks or gluons. \Ljets are calibrated to the JES at particle level [PERF-2012-02]. They are required to have a minimum \pt of 200 \GeV and to be within the fiducial region . The mass of \ljets is calculated from a combination of calorimeter and tracking information [ATLAS-CONF-2016-035]. It is calibrated [ATLAS-CONF-2016-035] and required to be at least 50 \GeV, which suppresses contributions from -jets and light jets in favor of \ljets that originate from hadronic decays of high-energy bosons, bosons, Higgs bosons and top quarks. In the SP 2 channel (\Sect5.4), top-tagging is used to identify hadronic decays of high-energy top quarks. It is based on a combination [ATL-PHYS-PUB-2015-053] of the \ljet mass and the -subjettiness [Thaler:2010tr, Thaler:2011gf] ratio , calculated in the “winner-take-all” mode [Larkoski:2014uqa]. This top-tagger provides an efficiency of for hadronically decaying top quarks with a \pt of at least 200 \GeV with a varying background rejection of at that decreases to at , as estimated with simulated dijet events.

In order to avoid double-counting of tracks or energy deposits and in order to improve the identification of the different reconstructed objects, a sequential overlap-removal procedure is used. In the first step, electrons that share a track with a muon are removed. In the second step, any \sjet is removed that has a to an electron that is smaller than 0.2, and in the third step, electrons are removed if they are closer than 0.4 to any remaining \sjet. Finally, \sjets that have a to a muon are removed if they have at most two associated tracks with , otherwise the muon is removed. \Sjets and \ljets are not subject to an overlap-removal procedure, because the analysis strategies in all channels are designed such that the energy deposits in \ljets and \sjets are not counted twice, as explained in the following lines: in the trilepton channels, \ljets are not used (\Sect5.3 and 5.5); in the dilepton pair-production channels, \ljets are only used for the classification of events (\Sect5.1 and 5.2); in the dilepton single-production channel, \sjets are only used for the classification of events, but not for the calculation of the discriminating variable (\Sect5.4).

Missing transverse momentum is only used for the reduction of the contribution from \TTbar pair-production in one search region for single- production (\Sect5.4) and for the definition of one background-enriched region (\Sect5.2), and it is calculated from the vectorial sum of the transverse momenta of reconstructed and calibrated leptons and \sjets [Aaboud:2018tkc], with the overlap between these objects removed. The calculation also includes the contributions from tracks in the ID that are matched to the primary vertex but are not associated with any of the reconstructed objects.

5 Event selection and background control regions

Five different channels are analyzed, each searching for either pair production or single production of VLQs, as introduced in \Sect1 and visualized in \Fig1. In each channel, event-selection criteria were optimized for maximum sensitivity to benchmark processes by studying expected 95% CL exclusion limits. In the pair-production channels, the mass reach for and quarks in the singlet and doublet models was maximized. While the search focuses on the decay of one VLQ to a boson and a third-generation SM quark, a high sensitivity to all three - and -quark decay modes is ensured by choosing these benchmark models, because the second VLQ is not only allowed to decay into a boson, but also into a boson or a Higgs boson in association with a third-generation SM quark. In the single-production channels, the sensitivity to single--quark production via the exchange of a boson with was optimized.

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Figure 2: Distributions of the sum of all background processes (solid area) and of benchmark signal processes (lines), based on MC simulations after preselection and requiring : (a) the number of leptons, (b) the number of \btagged jets, (c) the number of \ljets, and (d) the number of forward jets. The signal processes shown are - and -quark pair production in the singlet model and single--quark production with a coupling of , each with a mass of . All distributions are normalized to unit area. The last bin contains the overflow.

A preselection common to the channels was used as the basis for these optimizations. This preselection requires the presence of a boson candidate that is constructed from two leptons with opposite-sign electric charge. In all events, at least two leptons of the same flavor with and with opposite-sign electric charge are required. Out of all such lepton pairs in an event, a boson candidate is defined by the pair with invariant mass closest to the mass of the boson. Events in which this invariant mass is larger than 400 \GeV are removed because they are very unlikely to occur in any of the considered signal processes. In addition, at least two \sjets with must be present. In the SP 2 channel, this last criterion is replaced by a requirement on the presence of at least one \ljet with and .

In \Fig2, normalized distributions after preselection are shown for the sum of all background processes, which are estimated from MC simulations, as well as for benchmark signal models for pair and single VLQ production. In \Fig2, the distribution of the number of leptons is shown. By selecting events with exactly two leptons, a high signal efficiency is achieved. In events with at least three leptons, however, the signal-to-background ratio is significantly improved. The searches for pair and single production are hence split into complementary dilepton and trilepton channels. The distribution of the number of \btagged jets is shown in \Fig2. A higher number of \btagged jets is characteristic of the signal processes, and at least one or two \btagged jets are required in the event selection, depending on the channel. The distribution of the number of \ljets is shown in \Fig2. Signal events show a higher number of \ljets than background events, which in signal mostly originate from the hadronic decays of boosted top quarks, bosons, bosons or Higgs bosons. The presence of \ljets is used in the dilepton channels to suppress backgrounds and hence improve the sensitivity to the signal. In order to achieve a high signal efficiency, in the pair production case, two complementary dilepton channels are defined, one for events with at most one \ljet and one for events with at least two \ljets. In the trilepton channels, \ljet requirements are not used because the presence of at least three leptons suppresses the backgrounds efficiently. In \Fig2, the forward-jet multiplicity is shown. The single-production process often features a forward jet from -channel production. The presence of a forward jet is hence used in the single-production searches to separate the signal from the background.

The event selection criteria in the different channels are defined in Sections 5.15.5. In each channel, these signal regions (SR) are complemented by a set of control regions (CR), which are enriched in the main background processes. The CRs are used to check the modeling of the background and to improve the background prediction in the SRs by a combined fit of CRs and SRs (\Sect7). In the design of the CRs, not only a high purity of the respective background processes was aimed for, but also a large number of background events, as well as kinematic properties of the background events that resemble those of the events in the SRs. Each CR was checked to ensure that it was not sensitive to any signal process.

All SRs and CRs defined in the three pair-production channels (Sections 5.15.3) are orthogonal, so that the results in these channels can be combined (\Sect7). The same holds for all SRs and CRs in the single-production channels (Sections 5.45.5), which are also combined (\Sect7). Orthogonality is not ensured between pair- and single-production regions. However, single-production channels include requirements designed to suppress the pair-production signal in their SRs.

5.1 Search strategy: PP 2 0-1j

Two orthogonal channels are defined for the pair-production search in dilepton final states, one with at least two \ljets, described in \Sect5.2 (PP 2 2J), and one with at most one \ljet (PP 2 0-1J), described in this section. While in the PP 2 2J channel background processes are strongly suppressed, the signal efficiency is also reduced so that a complementary channel optimized for events with at most one \ljet provides additional sensitivity to the signal.

The definitions of the SRs in the PP 2 0-1J channel are summarized in \Tab3. Two SRs are defined, for which the preselection and the presence of exactly two leptons are required. The mass of the boson candidate, built from the two leptons, \mll, must be within a 10 \GeV window around the boson mass, . At least two \btagged jets must be present, which strongly reduces the background contribution from the production of a boson in association with light jets. The sensitivity of the channel is improved by defining two SRs, one for events without any \ljet and one for events with exactly one \ljet. Since in the signal process the boson is produced in the decay of a massive VLQ, the \pt of the boson candidate, \ptll, is on average much larger than in the background processes, so \ptll is required to be larger than 250 \GeV for both SRs. Moreover, the scalar sum of the transverse momenta of all \sjets in the event, \htj, is on average much larger for signal events than for background events, because the quarks from the decay chain of the massive VLQ result in high-\pt jets. Therefore, the \htj distribution is used in the statistical analysis (\Sect7) to search for an excess of data over the background prediction, with a signal expected to result in an excess for large values of \htj. In addition, a minimum \htj value of 800 \GeV is required for both SRs.

CR +jets CR 0-\ljet SR 1-\ljet SR
Preselection
leptons
and
\btagged jets
\ljet \ljets \ljet
Table 3: Definition of the control and signal regions for the PP 2 0-1J channel.

The main background processes are from +jets production containing two jets which originate from the hadronization of -quarks and \ttbar production with a dileptonic final state. The background from \ttbar production is strongly suppressed by requiring \mll to be close to \mz. In both main background processes, no hadronically decaying massive resonances are present, so that the SR with exactly one \ljet has a higher signal-to-background ratio than the SR without a \ljet. The contributions from all background processes are strongly reduced by the requirements on \ptll and \htj.

In order to validate the modeling of the main background processes, CRs are defined for the +jets and \ttbar processes. A summary of the CR definitions is given in \Tab3. The +jets CR is defined by the same criteria as the SRs, except for the \ljets and \htj criteria. Events with no \ljets and events with exactly one \ljet are considered together and \htj is required to be in the range 200–800 \GeV, ensuring that the CR is almost free of a potential signal. The resulting CR sample is expected to be +jets events. The \ttbar CR is defined by requiring the same preselection, lepton multiplicity, and \btagged-jet multiplicity criteria as in the SRs. However, the mass of the boson candidate, \mll, must be outside of a 10 \GeV window around the boson mass, \mz. In addition, \mll is required to be larger than 50 \GeV, because events with lower \mll do not stem mainly from \ttbar production, but from Drell–Yan production in association with jets. Also in the \ttbar CR, events without \ljets and events with exactly one \ljet are considered together. In contrast to the definition of the SRs, the \pt of the boson candidate is required to be less than 600 \GeV in order to ensure that the CR does not contain signal contributions from potential VLQ pair production with two leptons that do not stem from the decay of a boson, such as . Morever, the lower bound on \htj is lowered to 200 \GeV in order to increase the number of events in the CR and to test the modeling of the full \htj distribution. The resulting CR sample is expected to be \ttbar events.

5.2 Search strategy: PP 2 2j

In addition to the PP 2 0-1J channel, a second dilepton channel was optimized for events with at least two \ljets (PP 2 2J) in order to exploit the presence of highly boosted, hadronically decaying massive resonances in the signal processes. All such \ljets are required to have a \pt of at least 200 \GeV and a mass of at least 50 \GeV after trimming. Due to the mass requirement, hadronic decays of boosted top quarks, and of , , and Higgs bosons are efficiently selected and jets that originate from the hadronization of high-\pt light quarks, -quarks or gluons are suppressed.

The definition of the SR in the PP 2 2J channel is summarized in \Tab4. The same requirements as in the PP 2 0-1J channel are imposed: the preselection, the presence of exactly two leptons with \mll within a 10 \GeV window around \mz, and the presence of at least two \btagged jets. In addition, at least two \ljets are required in each event. Also in this channel, the large expected values for \ptll and \htj are exploited to discriminate the signal from the background processes. The optimized requirements are and . In order to search for an excess of data over the background prediction, the invariant mass of the boson candidate and the highest-\pt \btagged jet, , is used as a discriminating variable. In the search for \BBbar production, would show a resonant structure around if VLQs were present, because it often corresponds to the reconstructed mass of the VLQ. Also, in the search for \TTbar production, this variable shows very good discrimination between signal and background, with the signal resulting in larger values of than the background.

CR +jets CR SR
Preselection
leptons
and
\btagged jets
\ljets
or
Table 4: Definition of the control regions and the signal region for the PP 2 2J channel.

The main background processes are +jets production with two jets originating from the hadronization of -quarks, and \ttbar production in the dileptonic decay mode. As in the PP 2 0-1J channel, \ttbar production is strongly suppressed by requiring \mll to be close to the mass of the boson, and the contributions from all background processes are significantly reduced by the requirements on \ptll and \htj. The contributions from +jets production and dileptonic \ttbar decays are efficiently reduced by the presence of two \ljets, because no massive hadronically decaying resonance is present in these processes.

For the two main background processes, +jets and \ttbar production, CRs are defined. A summary of the CR definitions is given in \Tab4. Similarly to the \ttbar CR in the PP 2 0-1J channel, the definition of the \ttbar CR is based on the requirement that \mll must be outside a 10 \GeV window around \mz but must still fulfill . In order to suppress potential signal contributions in the CR, \ptll is required to be smaller than 600 \GeV. The requirement on \htj is removed, which increases the number of events in the CR. In addition, \met is required to be smaller than 200 \GeV, which reduces potential signal contributions from VLQ pair production with two leptons that do not stem from the decay of a boson, but for example from the decay of bosons from the VLQ decay chain. Moreover, the between the boson candidate and the highest-\pt \ljet is required to be smaller than 2.0 or larger than 2.8, which further reduces the contributions from a potential signal because in signal events the highest-\pt \ljet and the boson candidate are typically not back-to-back due to the presence of additional final-state particles. The resulting CR sample is expected to be \ttbar events. The CR for the +jets process is defined by the same criteria as in the SR, but the requirement on \htj is inverted in order to remove potential signal contributions, and the requirement on \ptll is removed in order to increase the number of events in the CR. The resulting CR sample is expected to be only +jets events, but also \ttbar events.

5.3 Search strategy: PP 3

The trilepton pair-production channel (PP 3) is sensitive to signal events in which at least one lepton appears in addition to the leptons from the boson decay that originates from or . Additional leptons can originate from the decay of the other VLQ, such as in or . In \TTbar production, an additional lepton can also originate from the decay itself, if the top quark decays into .

The definition of the SR is summarized in \Tab5. Events must pass the preselection, and they must have at least three leptons including a boson candidate with \mll within a 10 \GeV window around \mz. Only one \btagged jet is required, because background contributions are already strongly reduced by the requirement of at least one additional lepton. Relaxing the -tagging requirement compared to the dilepton channels improves the sensitivity to the signal processes because of the larger signal efficiency. As in the dilepton channels, a large transverse momentum of the boson candidate is required, . In order to search for an excess of data over the background prediction, the scalar sum of the \sjet and lepton transverse momenta, \htjl, is used. In contrast to the use of \htj in the PP 2 0-1J channel (\Sect5.1), the lepton transverse momenta are added to the discriminating variable \htjl, which exploits the \pt of all leptons in order to discriminate the signal from the background in addition to the use of \ptll, which is constructed from only two leptons.

Diboson CR CR SR
Preselection
leptons
= 0 \btagged jets \btagged jets
Table 5: Definition of the control regions and the signal region for the PP 3 channel.

The main background processes are diboson, in particular and , production, and production (dominated by production), which can both result in events with three leptons. The diboson background is strongly reduced by the -tagging requirement, so that only diboson events with additional -jets or mis-tagged light jets pass the event selection. Both main backgrounds are suppressed by the requirement on \ptll, because in background events boson candidates rarely have a large transverse momentum.

For the two main background processes, diboson and production, CRs are defined and summarized in \Tab5. The diboson CR is defined by the same criteria as the SR, except for the -tagging and \ptll requirements. No \btagged jets are allowed in the diboson CR, which reduces contributions from production and from a potential VLQ signal. The \ptll requirement is removed in order to further increase the number of diboson events in the CR. The resulting CR is expected to consist of diboson events, mainly from production. The CR is defined by inverting only the \ptll requirement, which removes contributions from a potential VLQ signal. The resulting CR sample is expected to consist mainly of and diboson events in similar proportions ( and , respectively).

5.4 Search strategy: SP 2

The production of a single quark results in a signature with fewer high-\pt objects than in \TTbar production. As a result it is more difficult to separate it from the background. However, a forward-jet from the -channel production is often present, which can be exploited to strongly reduce the contributions from background processes. The final state from the decay of a single with a leptonic boson decay consists of the two leptons from the boson, a forward jet and the decay products of the top quark. While the leptonic top-quark decay, , is used in the trilepton single-production channel (SP 3), described in \Sect5.5, the hadronic decay, , is used in the dilepton channel (SP 2), described in this section.

The definition of the SR is summarized in \Tab6. Events are required to pass the preselection with the minimum requirement of two \sjets replaced by the presence of at least one \ljet. Events must have exactly two leptons that form a boson candidate with an invariant mass within a 10 \GeV window around \mz. In this channel, a minimum \pt of the boson candidate is also required, . At least one \btagged jet is required in the event. Although a second -quark from gluon splitting (\Fig1) is present in the signal, only in a fraction of signal events is a second \btagged jet found within the acceptance of the ID. The hadronically decaying top quark originating from the -quark decay often has such a large \pt that the top-quark decay products are contained within one \ljet. Top-tagging is used to discriminate \ljets from hadronic top-quark decays in single--quark production from the main background process, +jets production, which can only fulfill this requirement if a quark or gluon jet is falsely top-tagged (mis-tags). At least one forward jet is required in each event, which is a characteristic property of single--quark production. In order to search for an excess of data over the background prediction, the invariant mass of the boson candidate and the highest-\pt top-tagged \ljet, , is used, which, if VLQs were present, would show a resonant structure around . In order to facilitate the interpretation of the search for single--quark production, the potential signal contribution from \TTbar production is reduced by requiring . This requirement has an efficiency of for \TTbar pair-production in the singlet model in the mass range 800–1400 \GeV, while maintaining an efficiency of 90–95% for single--quark production with across the whole mass range studied.

0-\btagged-jet CR -\btagged-jet CR SR
Preselection with \ljet
leptons
\btagged jets \btagged jets
loose-not-tight top-tagged \ljet top-tagged \ljet
forward jet
Table 6: Definition of the control regions and the signal region for the SP 2 channel.

The main background process is +jets production, which mainly passes the event selection in the SR if it contains jets that originate from the hadronization of -quarks. The boson is mostly produced with low values of \pt, so that the \ptll requirement strongly reduces this background. In addition, the requirement of at least one top-tagged \ljet efficiently suppresses the contribution from +jets production, because it does not contain top quarks and can only fulfill the top-tagging requirement through mis-tags. Similarly, the requirement of at least one forward jet reduces the +jets background, because forward jets are not characteristic for the main production mode of this process.

For the +jets production background, two CRs are defined. One CR, called 0-\btagged-jet CR, requires that no \btagged jets be present, allowing to correct the modeling of +jets production in a region that is kinematically close to the SR. In a second CR, called -\btagged-jet CR, the modeling of +jets production in association with \btagged jets is controlled. If good data-MC agreement is observed in both CRs consistently, this provides confidence in the overall modeling of +jets production. A summary of the CR definitions is given in \Tab6. Both CRs are based on the SR with changes to the top-tagging, -tagging and forward-jet requirements. For both CRs, the top-tagging requirement is changed, so that there must be at least one \ljet that fails the top-tagging requirements on but fulfills the top-tagging requirements on the \ljet mass. Out of these \ljets, called “loose-not-tight top-tagged”, the \ljet with the largest \pt is used in the calculation of in the CRs. The change in the top-tagging requirement enriches the CRs in +jets production in comparison with a potential signal contribution. In both CRs, the forward-jet requirement is removed, which increases the number of events in the CRs. Finally, in the 0-\btagged-jet CR, no \btagged jet is allowed, while in the -\btagged-jet CR the same -tagging requirement as in the SR is used. The resulting samples in the CRs are expected to be and +jets events, respectively, and to contain a negligible amount of a potential single--quark signal. As the CRs do not contain requirements on the number of forward jets and make use of a modified top-tagging requirement (loose-not-tight), the modeling of the +jets background was cross-checked in another region with no \btagged jets, but requiring the presence of at least one forward jet and using the nominal top-tagging algorithm. The modeling of the distributions of kinematic properties was found to be consistent between the CRs and the cross-check region and a small difference observed between the overall numbers of events was assigned as a systematic uncertainty (\Sect6).

5.5 Search strategy: SP 3

The search for single- production in the trilepton channel (SP 3) is sensitive to the decay , featuring an additional lepton from the top-quark decay. It is hence complementary to the SP 2 channel (\Sect5.4).

The definition of the SR is summarized in \Tab7. Events must pass the preselection, and they must have at least three leptons including a boson candidate with \mll within a 10 \GeV window around \mz. In this channel, a minimum \pt of the boson candidate is also required, . As in the SP 2 channel (\Sect5.4), at least one \btagged-jet and at least one forward jet are required. In order to suppress background contributions in which leptons have lower \pt on average than in the signal, the transverse momentum of the highest-\pt lepton in each event, , must be larger than 200 \GeV. As in the SP 2 channel, the potential signal contribution from \TTbar production is reduced in the search for single--quark production. In the SP 3 channel, this is achieved by requiring that \htj multiplied by the number of \sjets in the event is smaller than 6 \TeV. This requirement has an efficiency of 50–30% for \TTbar pair-production in the singlet model in the mass range 800–1400 \GeV, while maintaining an efficiency of for single--quark production with across the whole mass range studied. In order to search for an excess of data over the background prediction, \htjl is used, as in the PP 3 channel (\Sect5.3).

Diboson CR CR SR
Preselection
3 leptons
= 0 \btagged jets \btagged jets
forward jets forward jets
< 6 \TeV
Table 7: Definition of the control regions and the signal region for the SP 3 channel.

The main background processes are diboson production with additional -quarks and production (dominated by production). The contributions of these backgrounds are strongly reduced by the requirements on \ptll and , as well as by requiring at least one forward jet, because forward jets are not characteristic for these processes.

For the two main background processes, diboson and production, two CRs are defined and summarized in \Tab7. The diboson CR is defined following the criteria in the SR, but the requirements on \ptll, and the presence of at least one forward jet are removed in order to increase the number of events in the CR. In addition, no \btagged jet is allowed in the diboson CR. The resulting CR sample is expected to be diboson events and to contain a negligible number of potential signal events. The CR is based on the SR by inverting the requirement on and by requiring that no forward jet is present. These changes remove potential signal contributions. In addition, the requirement on \ptll is removed in order to increase the number of events in the CR. The resulting CR sample is expected to consist mainly of and diboson events in similar proportions ( and , respectively).

6 Systematic uncertainties

Systematic uncertainties are divided into experimental uncertainties, mostly related to the uncertainty in the modeling of the detector response in the simulation, and theoretical uncertainties, related to the theoretical modeling of the background processes in the MC simulation. Experimental uncertainties on the signal efficiencies and the signal shape of the discriminating variables are also taken into account.

Systematic uncertainties are evaluated by varying each source by of its uncertainty. As a result, the predicted background and signal event yields in the different CRs and SRs can vary as well as the predicted shapes of the discriminating variables in these regions. For some sources only one systematic variation is defined. In such cases, the effect on the yields and shapes are symmetrized in order to construct the corresponding variation in the other direction.

The uncertainty in the integrated luminosity of the analyzed dataset is 2.1%. It is derived following a methodology similar to that in Ref. [DAPR-2013-01] from a calibration of the luminosity scale using beam-separation scans in August 2015 and May 2016.

Uncertainties in electron and muon trigger, reconstruction and identification efficiencies are derived from data using decays [ATLAS-CONF-2016-024] and decays [PERF-2015-10]. Uncertainties in the electron (muon) energy (momentum) calibration and resolution are also derived using events [ATL-PHYS-PUB-2016-015, PERF-2015-10].

Uncertainties in the \sjet energy scale are evaluated from MC simulations and from data using multijet, +jets, and +jets events [PERF-2016-04]. Additional \sjet uncertainties arise from the jet energy resolution [ATL-PHYS-PUB-2015-015], which are also derived from multijet, +jets and +jets events and from the jet vertex tagger.

Uncertainties in the -tagging efficiency of \sjets are derived from data [PERF-2012-04] for -jets, -jets, and other light jets. For the derivation of the -tagging efficiency and its uncertainty for -jets, dileptonic \ttbar events are used [Aaboud:2018xwy]. Additional uncertainties are derived using MC simulations for the extrapolation of this efficiency beyond the kinematic reach of the calibration.

Uncertainties in the \ljet energy scale, mass and -subjettiness ratio are derived from a comparison of the calorimeter-to-track-jet ratio in data and MC simulations [PERF-2012-02, ATLAS-CONF-2017-063]. While the uncertainty in the mass is taken to be correlated with the uncertainty in the energy scale, the uncertainty is taken to be uncorrelated with these two. The uncertainty in the resolutions of the \ljet energy, mass and is estimated by comparing the prediction from the nominal MC simulations with simulations where the resolution is 20% poorer.

The electron, muon and \sjet uncertainties are propagated to the calculation of the \met. Additional uncertainties are assigned to contributions to the \met calculation that arise from tracks which are matched to the primary vertex and not associated with any object [Aaboud:2018tkc].

All MC distributions are reweighted so that the distribution of the average number of interactions per bunch crossing corresponds to the distribution in data. In order to assess the associated systematic uncertainty, the reweighting is varied within its uncertainty.

A 5% uncertainty is assigned to the cross section for \zjets production [ATL-PHYS-PUB-2016-002]. Additional uncertainties in the selection efficiency and in the shape of the final discriminant due to the theoretical modeling of the \zjets process are evaluated by comparing the nominal \SHERPA sample with alternative samples, normalized to the same cross section. An uncertainty due to the choice of generator and parton shower is assigned by comparing the nominal sample with a sample generated with \MGMCatNLO and the NNPDF3.0 NLO PDF set, and showered with \PYTHIAV8 and using the A14 set of tuned parameters with the NNPDF2.3 LO PDF set. An uncertainty due to the scale choice is evaluated by varying the renormalization and factorization scales in the nominal sample independently by factors of 2 and 0.5. The assigned uncertainty is based on the largest deviations from the nominal sample observed. An uncertainty due to the choice of PDF set is evaluated by comparing the nominal \SHERPA sample using the NNPDF3.0 NLO PDF set with samples using the MMHT2014 NNLO [Harland-Lang:2014zoa] and CT14 NNLO PDF sets [Dulat:2015mca]. The largest observed deviations from the nominal sample are used to assign the uncertainty.

The uncertainty in the cross section for \ttbar production is assigned as / [ATL-PHYS-PUB-2016-004]. Also for \ttbar production, additional uncertainties in the selection efficiency and in the shape of the final discriminant are assigned by comparing the nominal sample with alternative MC samples. An uncertainty due to the choice of generator is evaluated from a comparison of the nominal \POWHEGBOX sample with a sample generated with \MGMCatNLO with the NNPDF3.0 NLO PDF set, and showered with \PYTHIAV8 using the A14 set of tuned parameters and the NNPDF2.3 LO PDF set. An uncertainty due to the choice of shower model is assigned by comparing the nominal sample, showered by \PYTHIAV8, with an alternative sample showered by \HERWIGV[Bahr:2008pv, Bellm:2015jjp] with the H7-UE-MMHT set of tuned parameters and the MMHT PDF set. The uncertainties due to the choice of renormalization and factorization scales are evaluated by independently varying the scales by factors of 2 and 0.5. The largest differences observed are assigned as the systematic uncertainty for these two scales. An uncertainty due to the choice of PDF set is evaluated by comparing the nominal sample with samples generated with the MMHT2014 NLO and CT14 NLO PDF sets. The largest observed deviations from the nominal sample are used to assign the uncertainty.

An uncertainty of 6% is assigned to the cross section for diboson production [ATL-PHYS-PUB-2016-002]. As with the \zjets and \ttbar processes, alternative MC samples are used to assess additional uncertainties in the selection efficiency and in the shape of the final discriminant of the diboson processes. In order to assess the uncertainty due to the choice of renormalization and factorization scales, the nominal \SHERPA samples are compared with alternative samples with the scales varied independently by factors of 2 and 0.5 and the largest observed differences are assigned as the uncertainty. An uncertainty due to the choice of PDF set is assessed by comparing the nominal samples, generated with the NNPDF3.0 NNLO PDF set, with samples generated with the MMHT2014 NNLO and CT14 NNLO PDF sets. The largest deviations are used to assign the uncertainty.

For the processes, uncertainties of / are assigned for the production cross section and of / for the production cross section [ATL-PHYS-PUB-2016-005]. For the assessment of additional uncertainties in the selection efficiency and in the shape of the final discriminant of the processes, the nominal samples are compared with alternative MC samples. An uncertainty due to the choice of generator is assigned by comparing the nominal sample with a sample generated with \SHERPAV2.2 and the NNPDF3.0 NLO PDF set. For these samples, a fast simulation of the ATLAS detector [SOFT-2010-01] was used, which relies on a parameterization of the calorimeter response [ATL-PHYS-PUB-2010-013]. The nominal sample was additionally produced with the fast simulation configuration and the relative differences observed in the comparison with the samples with varied scales are assigned as the systematic uncertainty. An uncertainty due to the parton shower is assigned by comparing the nominal sample with samples with a varied amount of initial-state radiation. These alternative samples were produced with fast detector simulation and the procedure to assign a systematic uncertainty is again based on the relative difference observed in comparison with the nominal sample obtained with fast detector simulation.

Backgrounds due to misidentified electrons and muons play a minor role in this analysis, because such leptons typically have low transverse momentum and are hence strongly suppressed by the SR requirements, in particular by the lower thresholds for \ptll in the different channels. However, in the \ttbar CRs in the PP 2 0-1J and PP 2 2J channels and in the \zjets CR in the PP 2 2J channel, low-\ptll events are included. Similarly, +jets and \ttbar events could contribute to the CRs and SRs in the PP 3 and SP 3 channels due to misidentified leptons. The maximum observed difference between data and MC simulations in the lepton \pt spectra in the CRs is 25%. This is assigned as an uncertainty to +jets and \ttbar events in the trilepton channels and to \ttbar events with in the PP 2 0-1J and PP 2 2J channels.

No -tagged jet are allowed in the diboson CRs for the PP 3 and SP 3 channels (\Sect5.3 and \Sect5.5). While this requirement ensures a high purity in diboson processes, it differs from the requirements in the SRs. An uncertainty of 50% is assigned to the production of diboson events in association with -quarks, motivated by the precision of measurements of - and -boson production in association with -quarks [STDM-2012-11, STDM-2012-15].

In order to ensure a large number of events in the CRs for the dilepton single-production search, the SR forward-jet requirement is removed (\Sect5.4). A cross-check was performed in a region that only differs from the SR by a veto on -tagged jets. While the modeling of the shapes of kinematic variables in this region is satisfactory, the 11% difference in the overall number of events between data and background expectation is assigned as an additional uncertainty in the SR due to the forward-jet requirement.

The uncertainties on the reconstructed objects and the luminosity also affect the predictions for VLQ pair and single production. No further uncertainties on the signal processes were considered. As discussed in \Sect3, the MC samples for VLQ pair production were generated in the singlet model and alternative BR hypotheses for and quarks are obtained by reweighting the singlet BRs to the alternative BRs. This procedure is validated by comparing kinematic distributions of the nominal VLQ pair production samples with alternative samples that were generated in the ( ) doublet model. After reweighting both to the same BRs, no large differences were observed between these samples. Hence, the reweighting procedure is considered validated and no systematic uncertainty is assigned.

7 Results

In each channel, a binned likelihood fit is performed to the discriminating variable. Control and signal regions are fit simultaneously and systematic uncertainties are included in the fit as a set of nuisance parameters (NP), . The likelihood function consists of Poisson probabilities for each bin in the discriminating variable in each region, and a Gaussian or log-normal distribution for each NP. In the likelihood fit, the signal cross section is parameterized by multiplying the predicted cross section with a correction factor , called the signal-strength factor, which is a free parameter of the fit. In a background-only fit , and hence , is set to zero. For the combined control and signal region fit the modeling of the main background processes was adjusted during the fit via changes in the NPs, so that the background prediction in the signal regions is improved. The binning of the discriminating variable in the different channels was chosen in order to retain as much shape information about the distribution as possible given the number of background MC events in each bin.

The effect of each single source of systematic uncertainty is treated as correlated across all regions and processes with two exceptions. For the uncertainties associated with misidentified leptons, separate NPs are defined for the different CRs and SRs in each channel; for the uncertainties related to the choice of MC generator and hadronization model, separate NPs are defined for each channel. Different sources of systematic uncertainty are treated as uncorrelated with each other, except for the case of the \ljet scale uncertainties affecting the \pt and mass, which are treated as 100% correlated. In addition to the systematic uncertainties discussed in \Sect6, an additional NP is added for each bin in the discriminating variable in each region due to the statistical uncertainty of the MC samples.

7.1 Results: PP 2 0-1j

The observed number of events in the SRs and CRs and the expected number of events for the different background contributions are shown in \Tab9 for the PP 2 0-1J channel. Also shown is the expected number of events for \BBbar and \TTbar production in the singlet model for . The signal efficiencies for these benchmarks are 0.060% (0.013%) for \BBbar (\TTbar) in the 0-\ljet SR and 0.33% (0.16%) in the 1-\ljet SR, and include the branching ratios of the VLQ as well as of its decay products, including the decay .

CR +jets CR 0-\ljet SR 1-\ljet SR
Singlet \BBbar(900 GeV) \num16.2 \num1.0 \num2.29 \num0.31 \num1.94 \num0.27 \num10.6 \num0.8
Singlet \TTbar(900 GeV) \num14.9 \num0.9 \num1.81 \num0.21 \num0.43 \num0.09 \num5.1 \num0.4
+jets \num1090 \num310 \num630 \num190 \num21 \num9 \num43 \num21
\num30000 \num8000 \num8 \num4 \num2 \num5 \num2 \num5
Single top \num640 \num60 \num5.3 \num0.6 \num0.40 \num0.23 \num0.71 \num0.24
\num199 \num26 \num37 \num7 \num0.55 \num0.23 \num4.6 \num1.4
Diboson \num44 \num16 \num37 \num12 \num0.9 \num0.4 \num3.1 \num1.9
Total Bkg. \num32000 \num8000 \num710 \num190 \num24 \num9 \num54 \num21
Data \num32216 \num699 \num35 \num51
Data/Bkg. 1.00 0.26 0.98 0.26 1.4 0.6 1.0 0.4
Table 9: Observed number of events in data and post-fit expected number of background events in the control and signal regions for the PP 2 0-1J channel, i.e. after the fit to the data \htj distributions under the background-only hypothesis. The uncertainty in the expected number of events is the full uncertainty from the fit, from which the uncertainty in the ratio of the observed and expected numbers of events is calculated.
CR +jets CR 0-\ljet SR 1-\ljet SR
+jets \num1100 \num100 \num622 \num34 \num21.6 \num2.6 \num43 \num4
\num30200 \num600 \num8.7 \num3.0 \num3.1 \num2.3 \num2.4 \num2.0
Single top \num630 \num50 \num5.2 \num0.6 \num0.40 \num0.23 \num0.72 \num0.20
\num197 \num22 \num36 \num6 \num0.60 \num0.26 \num4.5 \num1.2
Diboson \num44 \num6 \num37 \num4 \num0.87 \num0.24 \num3.1 \num0.7
Total Bkg. \num32100 \num700 \num709 \num33 \num26.5 \num3.2 \num54 \num4
Data \num32216 \num699 \num35 \num51
Data/Bkg. 1.003 0.020 0.99 0.05 1.32 0.16 0.95 0.08
Table 8: Observed number of events in data and pre-fit expected number of signal and background events in the control and signal regions for the PP 2 0-1J channel, i.e. before the fit to data. For the signal, the expected number of events for the \BBbar and \TTbar benchmark processes with is shown for the singlet model. Statistical uncertainties from the limited size of MC samples and systematic uncertainties are added in quadrature. The uncertainty in the ratio of the observed and expected numbers of events contains the statistical uncertainty of the prediction from Poisson fluctuations.

A fit of the background prediction to the \htj distributions in data was performed. The post-fit yields are shown in \Tab9. The uncertainty in the background prediction is significantly reduced in all regions compared to the pre-fit value (\Tab9). The overall +jets (\ttbar) normalization is adjusted by a factor of \normfzjetszjcrtwolr (\normfttbarttcrtwolr) in the +jets (\ttbar) CR. The ratios of the post-fit and pre-fit background yields are consistent with unity in all regions.

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Figure 3: Comparison of the distribution of the transverse momentum of the boson candidate, \ptll, between data and the background prediction in (a) the \ttbar control region, (b) the +jets control region, (c) the 0-\ljet-signal region, and (d) the 1-\ljet-signal region of the pair-production (PP) 2 0-1J channel. The background prediction is shown post-fit, i.e. after the fit to the data \htj distributions under the background-only hypothesis. The last bin contains the overflow. An upward pointing triangle in the ratio plot indicates that the value of the ratio is beyond scale. An example distribution for a \BBbar signal in the singlet model with is overlaid. For better visibility, it is multiplied by a factor of five. The data are compatible with the background-only hypothesis.

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Figure 4: Comparison of the distribution of the scalar sum of \sjet transverse momenta, \htj, between data and the background prediction in (a) the \ttbar control region, (b) the +jets control region, (c) the 0-\ljet-signal region, and (d) the 1-\ljet-signal region of the pair-production (PP) 2 0-1J channel. The background prediction is shown post-fit, i.e. after the fit to the data \htj distributions under the background-only hypothesis. The last bin contains the overflow. An upward pointing triangle in the ratio plot indicates that the value of the ratio is beyond scale. An example distribution for a \BBbar signal in the singlet model with is overlaid. For better visibility, it is multiplied by a factor of five. The data are compatible with the background-only hypothesis.

The modeling of the main backgrounds was validated by comparing the distributions of kinematic variables and object multiplicities between data and background prediction in each respective CR. As an example, the \ptll distribution is shown in \Fig3 in the two CRs and the two SRs. The background prediction is shown after the fit to the \htj distribution. In \Fig4, the \htj distribution is shown in the CRs and SRs for data and the background prediction after the fit. The VLQ pair-production signal would be expected to result in an excess of data over the background prediction at large values of \htj, as shown in \Fig4 and \Fig4. Good agreement between data and the background prediction is observed in both kinematic variables in the CRs, validating the background prediction.

7.2 Results: PP 2 2j

The observed and expected yields in the SR and the CRs and the expected number of events for the different background contributions are shown in \Tab11 for the PP 2 2J channel. Also shown is the expected number of events for \BBbar and \TTbar production in the singlet model for . The signal efficiency in the SR for these benchmarks is 0.28% for both \BBbar and \TTbarproduction, and includes the branching ratios of the VLQ as well as of its decay products, including the decay .

CR +jets CR SR
Singlet \BBbar(900 GeV) \num3.00 \num0.34 \num2.65 \num0.28 \num9.2 \num0.6
Singlet \TTbar(900 GeV) \num2.25 \num0.17 \num3.9 \num0.4 \num9.2 \num0.6
+jets \num11 \num5 \num66 \num22 \num8 \num4
\num80 \num70 \num18 \num14 \num2.0 \num3.4
Single top \num1.5 \num0.8 \num0.61 \num0.34 \num0.010 \num0.010
\num4.3 \num0.9 \num14.4 \num2.9 \num1.3 \num0.4
Diboson \num0.74 \num0.20 \num4.1 \num1.0 \num0.9 \num0.4
Total Bkg. \num100 \num70 \num103 \num26 \num12 \num5
Data \num112 \num100 \num9
Data/Bkg. 1.2 0.8 0.98 0.26 0.7 0.4
Table 11: Observed number of events in data and post-fit expected number of background events in the control regions and the signal region for the PP 2 2J channel, i.e. after the fit to the data distributions under the background-only hypothesis. The uncertainty in the expected number of events is the full uncertainty from the fit, from which the uncertainty in the ratio of the observed and expected numbers of events is calculated.
CR +jets CR SR
+jets \num9.0 \num2.3 \num60 \num10 \num6.5 \num2.2
\num95 \num12 \num20 \num6 \num2.2 \num1.5
Single top \num1.5 \num0.6 \num0.63 \num0.28 \num0.016 \num0.011
\num4.5 \num0.8 \num14.7 \num2.7 \num1.3 \num0.4
Diboson \num0.74 \num0.20 \num4.2 \num0.8 \num0.9 \num0.4
Total Bkg. \num111 \num12 \num100 \num10 \num10.9 \num2.7
Data \num112 \num100 \num9
Data/Bkg. 1.01 0.11 1.00 0.10 0.83 0.21
Table 10: Observed number of events in data and pre-fit expected number of signal and background events in the control regions and the signal region for the PP 2 2J channel, i.e. before the fit to data. For the signal, the expected number of events for the \BBbar and \TTbar benchmark processes with is shown for the singlet model. Statistical uncertainties from the limited size of MC samples and systematic uncertainties are added in quadrature. The uncertainty in the ratio of the observed and expected numbers of events contains the statistical uncertainty of the prediction from Poisson fluctuations.

A fit of the background prediction to the distributions in data was performed. The post-fit yields are shown in \Tab11. The uncertainty in the background prediction was significantly reduced in all regions compared to the pre-fit value (\Tab11). The overall +jets (\ttbar) normalization was adjusted by a factor of \normfzjetszjcrtwolb (\normfttbarttcrtwolb) in the +jets (\ttbar) CR. The ratios of the post-fit and pre-fit background yields are consistent with unity in all regions.

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Figure 5: Comparison of the distribution of the scalar sum of \sjet transverse momenta, \htj, between data and the background prediction in (a) the \ttbar control region, (b) the +jets control region, and (c) the signal region of the pair-production (PP) 2 2J channel. The background prediction is shown post-fit, i.e. after the fit to the data distributions under the background-only hypothesis. The last bin contains the overflow. An upward or downward pointing triangle in the ratio plot indicates that the value of the ratio is beyond scale. An example distribution for a \BBbar signal in the singlet model with is overlaid. The data are compatible with the background-only hypothesis.

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Figure 6: Comparison of the distribution of the invariant mass of the boson candidate and the highest-\pt \btagged jet, , between data and the background prediction in (a) the \ttbar control region, (b) the +jets control region, and (c) the signal region of the pair-production (PP) 2 2J channel. The background prediction is shown post-fit, i.e. after the fit to the data distributions under the background-only hypothesis. The last bin contains the overflow. An upward or downward pointing triangle in the ratio plot indicates that the value of the ratio is beyond scale. An example distribution for a \BBbar signal in the singlet model with is overlaid. The data are compatible with the background-only hypothesis.

The modeling of the main backgrounds was validated by comparing the distributions of kinematic variables and object multiplicities between data and background prediction in the respective CR. As an example, the \htj distribution is shown in \Fig5 in the two CRs and in the SR. The background prediction is shown after the fit to the distribution. In \Fig6, the distribution is shown in the CRs and SR for data and the background prediction after the fit. The VLQ pair-production signal would be expected to result in an excess of data over the background prediction at large values of , as shown in \Fig6. Good agreement between data and the background prediction is apparent in kinematic variables in the CRs, validating the background prediction.

7.3 Results: PP 3

The observed number of events in the SR and the CRs and the expected number of events for the different background contributions are shown in \Tab13 for the PP 3 channel. Also shown is the expected number of events for \BBbar and \TTbar production in the singlet model for . The signal efficiency in the SR for these benchmarks is 0.31% for \BBbarand 0.44% for \TTbarproduction, and includes the branching ratios of the VLQ as well as of its decay products, including the decay .

Diboson CR CR SR
Singlet \BBbar(900 GeV) \num1.57 \num0.31 \num1.26 \num0.15 \num10.1 \num0.6
Singlet \TTbar(900 GeV) \num1.60 \num0.30 \num1.64 \num0.14 \num14.2 \num0.7
+jets \num50 \num80 \num11 \num5 \num1.8 \num2.8
\num7 \num29 \num14 \num13 \num0.7 \num1.5
Single top \num7.2 \num2.0 \num26 \num7 \num4.2 \num1.1
\num23 \num4 \num111 \num15 \num47 \num6
Diboson \num1130 \num280 \num120 \num60 \num30 \num14
Triboson \num5.5 \num0.5 \num0.43 \num0.08 \num0.19 \num0.04
Total Bkg. \num1220 \num290 \num290 \num60 \num84 \num15
Data \num1150 \num320 \num93
Data/Bkg. 0.94 0.23 1.12 0.24 1.11 0.24
Table 13: Observed number of events in data and post-fit expected number of background events in the control regions and the signal region for the PP 3 channel, i.e. after the fit to the data \htjl distributions under the background-only hypothesis. The uncertainty in the expected number of events is the full uncertainty from the fit, from which the uncertainty in the ratio of the observed and expected numbers of events is calculated.
Diboson CR CR SR
+jets \num60 \num60 \num12 \num5 \num2.1 \num2.1
\num5 \num11 \num18 \num8 \num0.4 \num1.2
Single top \num6.9 \num2.0 \num29 \num6 \num4.3 \num1.1
\num23 \num4 \num117 \num14 \num49 \num6
Diboson \num1060 \num70 \num137 \num29 \num34 \num7
Triboson \num5.4 \num0.4 \num0.43 \num0.07 \num0.19 \num0.04
Total Bkg. \num1160 \num40 \num313 \num21 \num90 \num6
Data \num1150 \num320 \num93
Data/Bkg. 1.00 0.04 1.02 0.07 1.03 0.07
Table 12: Observed number of events in data and pre-fit expected number of signal and background events in the control regions and the signal region for the PP 3 channel, i.e. before the fit to data. For the signal, the expected number of events for the \BBbar and \TTbar benchmark processes with is shown for the singlet model. Statistical uncertainties from the limited size of MC samples and systematic uncertainties are added in quadrature. The uncertainty in the ratio of the observed and expected numbers of events contains the statistical uncertainty of the prediction from Poisson fluctuations.

A fit of the background prediction to the \htjl distributions in data was performed and the post-fit yields are shown in \Tab13. The uncertainty in the background prediction was significantly reduced in all regions compared to the pre-fit value (\Tab13). The overall diboson () normalization is adjusted by a factor of \normfdibosonvvcrtril (\normfttvttvcrtril) in the diboson () CR. The ratios of the post-fit and pre-fit background yields are consistent with unity in all regions.

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Figure 7: Comparison of the distribution of the transverse momentum of the highest-\pt lepton (leading lepton), , between data and the background prediction in (a) the diboson control region, (b) the control region, and (c) the signal region of the pair-production (PP) 3 channel. The background prediction is shown post-fit, i.e. after the fit to the data \htjl distributions under the background-only hypothesis. The last bin contains the overflow. An example distribution for a \BBbar signal in the singlet model with is overlaid. For better visibility, it is multiplied by a factor of five. The data are compatible with the background-only hypothesis.

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Figure 8: Comparison of the distribution of the scalar sum of \sjet and lepton transverse momenta, \htjl, between data and the background prediction in (a) the diboson control region, (b) the control region, and (c) the signal region of the pair-production (PP) 3 channel. The background prediction is shown post-fit, i.e. after the fit to the data \htjl distributions under the background-only hypothesis. The last bin contains the overflow. An upward pointing triangle in the ratio plot indicates that the value of the ratio is beyond scale. An example distribution for a \BBbar signal in the singlet model with is overlaid. For better visibility, it is multiplied by a factor of five. The data are compatible with the background-only hypothesis.

The modeling of the main backgrounds was validated by comparing the distributions of kinematic variables and object multiplicities between data and background prediction in the respective CR. As an example, the distribution of the \pt of the highest-\pt lepton, , in the event is shown in \Fig7 in the two CRs and in the SR. The background prediction is shown after the fit to the \htjl distribution. In \Fig8, the \htjl distribution is shown in the CRs and SR for data and the background prediction after the fit. The VLQ pair-production signal would be expected to result in an excess of data over the background prediction at large values of \htjl, as shown in \Fig8. Good agreement between data and the background prediction is observed in both kinematic variables in the CRs, validating the background prediction.

7.4 Results: SP 2

The observed number of events in the SR and the CRs and the expected number of events for the different background contributions are shown in \Tab15 for the SP 2 channel. Also shown is the expected number of events for single- production for and . The signal efficiency in the SR is for decays produced via a coupling, and includes the branching ratios of the VLQ as well as of its decay products, including the decay .

0-\btagged-jet CR -\btagged-jet CR SR
Single- (900 GeV, ) \num2.6 \num0.4 \num13.7 \num1.0 \num27.4 \num3.4
+jets \num2300 \num800 \num520 \num130 \num130 \num50
\num0.8 \num0.7 \num3.4 \num1.7 \num0.9 \num0.9
Single top \num0.64 \num0.18 \num1.78 \num0.22 \num2.5 \num0.4
\num1.22 \num0.23 \num8.5 \num1.2 \num7.3 \num1.3
Diboson \num100 \num140 \num30 \num50 \num9 \num12
Triboson \num0.039 \num0.014 \num0.005 \num0.013
Total Bkg. \num2400 \num800 \num570 \num120 \num150 \num50
Data \num2350 \num495 \num124
Data/Bkg. 0.96 0.31 0.87 0.19 0.81 0.27
Table 15: Observed number of events in data and post-fit expected number of background events in the control regions and the signal region for the SP 2 channel, i.e. after the fit to the data distributions under the background-only hypothesis. The uncertainty in the expected number of events is the full uncertainty from the fit, from which the uncertainty in the ratio of the observed and expected numbers of events is calculated.
0-\btagged-jet CR -\btagged-jet CR SR
+jets \num2300 \num100 \num480 \num40 \num113 \num13
\num0.8 \num0.7 \num3.8 \num1.6 \num1.0 \num0.9
Single top \num0.63 \num0.18 \num1.77 \num0.22 \num2.33 \num0.28
\num1.27 \num0.23 \num8.3 \num1.1 \num6.8 \num1.0
Diboson \num40 \num100 \num12 \num34 \num4 \num8
Triboson \num0.038 \num0.014 \num0.005 \num0.013
Total Bkg. \num2400 \num100 \num509 \num34 \num127 \num15
Data \num2350 \num495 \num124
Data/Bkg. 1.00 0.04 0.97 0.06 0.98 0.11
Table 14: Observed number of events in data and pre-fit expected number of signal and background events in the control regions and the signal region for the SP 2 channel, i.e. before the fit to data. For the signal, the expected number of events for the single--quark benchmark process with and is shown. Statistical uncertainties from the limited size of MC samples and systematic uncertainties are added in quadrature. The uncertainty in the ratio of the observed and expected numbers of events contains the statistical uncertainty of the prediction from Poisson fluctuations.

A fit of the background prediction to the distributions in data was performed and the post-fit yields are shown in \Tab15. The uncertainty in the background prediction was significantly reduced in all regions compared to the pre-fit value (\Tab15). The overall +jets normalization was adjusted by factors of \normfzjetsnotnobcrtwols and \normfzjetsnotbcrtwols in the 0-\btagged-jet CR and the -\btagged-jet CR, respectively. The ratios of the post-fit and pre-fit background yields are consistent with unity in all regions. The ratio for +jets production in the SR is \normfzjetssrtwols, which is consistent with unity within at most.

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Figure 9: Comparison of the distribution of the transverse momentum of the highest-\pt top-tagged \ljet between data and the background prediction in (a) the 0-\btagged-jet control region, (b) the -\btagged-jet control region, and (c) the signal region of the single-production (SP) 2 channel. The background prediction is shown post-fit, i.e. after the fit to the data distributions under the background-only hypothesis. The last bin contains the overflow. An upward pointing triangle in the ratio plot indicates that the value of the ratio is beyond scale. An example distribution for a single--quark signal with and is overlaid. For better visibility, it is multiplied by a factor of three. The data are compatible with the background-only hypothesis.

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Figure 10: Comparison of the distribution of the invariant mass of the boson candidate and the highest-\pt top-tagged \ljet, , between data and the background prediction in (a) the 0-\btagged-jet control region, (b) the -\btagged-jet control region, and (c) the signal region of the single-production (SP) 2 channel. The background prediction is shown post-fit, i.e. after the fit to the data distributions under the background-only hypothesis. The last bin contains the overflow. An upward pointing triangle in the ratio plot indicates that the value of the ratio is beyond scale. An example distribution for a single--quark signal with and is overlaid. For better visibility, it is multiplied by a factor of three. The data are compatible with the background-only hypothesis.

The modeling of the main background was validated by comparing the distributions of kinematic variables and object multiplicities between data and background prediction in the two CRs. As an example, the \pt distribution of the highest-\pt top-tagged \ljet in the event is shown in \Fig9 in the two CRs and the SR. The background prediction is shown after the fit to the distribution. Contributions from VLQ single production would be expected at high values of the \ljet \pt. In \Fig10, the distribution is shown in the CRs and SR for data and the background prediction after the fit. The VLQ single-production signal would be expected to result in an excess of data over the background prediction in the distribution, as shown in \Fig10. Good agreement between data and the background prediction is observed in both kinematic variables in the CRs, validating the background prediction.

7.5 Results: SP 3

The observed number of events in the SR and the CRs and the expected number of events for the different background contributions are shown in \Tab17 for the SP 3 channel. Also shown is the expected number of events for single--quark production for and . Due to a low number of MC events for the single--quark signal in the SP 3 channel, in this channel the signal efficiency was interpolated as a function of with a third-order polynomial describing the efficiencies estimated from MC simulations within the uncertainties. The resulting signal efficiency in the SR is for decays produced via a coupling, and includes the branching ratios of the VLQ as well as of its decay products, including the decay .

Diboson CR CR SR
Single- (900 GeV, ) \num3.3 \num0.5 \num1.78 \num0.22 \num7.9 \num0.6
+jets \num52 \num29 \num9 \num6 \num0.16 \num0.10
\num7.1 \num1.6 \num12.0 \num2.7
Single top \num6.9 \num0.9 \num18.9 \num0.9 \num0.64 \num0.11
\num22 \num4 \num98 \num15 \num5.6 \num0.9
Diboson \num1120 \num260 \num110 \num50 \num3.1 \num1.4
Triboson \num5.9 \num0.4 \num0.46 \num0.06 \num0.026 \num0.007
Total Bkg. \num1210 \num260 \num250 \num50 \num9.5 \num2.0
Data \num1145 \num279 \num14
Data/Bkg. 0.94 0.20 1.13 0.24 1.5 0.6
Table 17: Observed number of events in data and post-fit expected number of background events in the control regions and the signal region for the SP 3 channel, i.e. after the fit to the data \htjl distributions under the background-only hypothesis. The uncertainty in the expected number of events is the full uncertainty from the fit, from which the uncertainty in the ratio of the observed and expected numbers of events is calculated.
Diboson CR CR SR
+jets \num55 \num27 \num11 \num6 \num0.17 \num0.11
\num7.3 \num3.4 \num15 \num6
Single top \num7.0 \num3.3 \num20 \num10 \num0.68 \num0.34
\num22 \num4 \num110 \num14 \num6.2 \num0.8
Diboson \num1060 \num50 \num116 \num25 \num3.2 \num0.7
Triboson \num6.0 \num2.5 \num0.50 \num0.17 \num0.031 \num0.014
Total Bkg. \num1160 \num40 \num280 \num20 \num10.2 \num1.1
Data \num1145 \num279 \num14
Data/Bkg. 0.99 0.04 1.01 0.07 1.37 0.14
Table 16: Observed number of events in data and pre-fit expected number of signal and background events in the control regions and the signal region for the SP 3 channel, i.e. before the fit to data. For the signal, the expected number of events for the single--quark benchmark process with and is shown. Statistical uncertainties from the limited size of MC samples and systematic uncertainties are added in quadrature. The uncertainty in the ratio of the observed and expected numbers of events contains the statistical uncertainty of the prediction from Poisson fluctuations.

A fit of the background prediction to the \htjl distributions in data was performed. The post-fit yields are shown in \Tab17. The uncertainty in the background prediction was significantly reduced in all regions compared to the pre-fit value (\Tab17). The overall diboson () normalization was adjusted by a factor of \normfdibosonvvcrtrils (\normfttvttvcrtrils) in the diboson () CR. The ratios of the post-fit and pre-fit background yields are consistent with unity in all regions.

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Figure 11: Comparison of the transverse momentum of the boson candidate, \ptll, between data and the background prediction in (a) the diboson control region, (b) the control region, and (c) the signal region of the single-production (SP) 3 channel. The background prediction is shown post-fit, i.e. after the fit to the data \htjl distributions under the background-only hypothesis. The last bin contains the overflow. An upward pointing triangle in the ratio plot indicates that the value of the ratio is beyond scale. An example distribution for a single--quark signal with and is overlaid. The data are compatible with the background-only hypothesis.

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Figure 12: Comparison of the distribution of the scalar sum of \sjet and lepton transverse momenta, \htjl, between data and the background prediction in (a) the diboson control region, (b) the control region, and (c) the signal region of the single-production (SP) 3 channel. The background prediction is shown post-fit, i.e. after the fit to the data \htjl distributions under the background-only hypothesis. The last bin contains the overflow. An upward pointing triangle in the ratio plot indicates that the value of the ratio is beyond scale. An example distribution for a single--quark signal with and is overlaid. The data are compatible with the background-only hypothesis.

The modeling of the main backgrounds was validated by comparing the distributions of kinematic variables and object multiplicities between data and background prediction in the respective CR. As an example, the \ptll distribution is shown in \Fig11 in the two CRs and in the SR. The background prediction is shown after the fit to the \htjl distribution. Contributions from VLQ single production would be expected at high values of \ptll. In \Fig12, the \htjl distribution is shown in the CRs and SR for data and the background prediction after the fit. For large values of