CMSEXO23006 ; CERNEP2024095  
Review of searches for vectorlike quarks, vectorlike leptons, and heavy neutral leptons in protonproton collisions at $ \sqrt{s}= $ 13 TeV at the CMS experiment  
CMS Collaboration  
27 May 2024  
Submitted to Physics Reports  
Abstract: The LHC has provided an unprecedented amount of protonproton collision data, bringing forth exciting opportunities to address fundamental open questions in particle physics. These questions can potentially be answered by performing searches for very rare processes predicted by models that attempt to extend the standard model of particle physics. The data collected by the CMS experiment in 20152018 at a centerofmass energy of 13 TeV help to test the standard model at the highest precision ever and potentially discover new physics. An interesting opportunity is presented by the possibility of new fermions with masses ranging from the MeV to the TeV scale. Such new particles appear in many possible extensions of the standard model and are well motivated theoretically. They may explain the appearance of three generations of leptons and quarks, the mass hierarchy across the generations, and the nonzero neutrino masses. In this report, the status of searches targeting vectorlike quarks, vectorlike leptons, and heavy neutral leptons at the CMS experiment is discussed. A complete overview of final states is provided together with their complementarity and partial combination. The discovery potential for several of these searches at the HighLuminosity LHC is also discussed.  
Links: eprint arXiv:2405.17605 [hepex] (PDF) ; CDS record ; inSPIRE record ; CADI line (restricted) ; 
Figures  
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Figure 1:
Representative Feynman diagrams showing the production of VLQs (Q, left), VLLs (L, middle), and HNLs (N, right) in protonproton collisions. 
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Figure 1a:
Representative Feynman diagrams showing the production of VLQs (Q, left), VLLs (L, middle), and HNLs (N, right) in protonproton collisions. 
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Figure 1b:
Representative Feynman diagrams showing the production of VLQs (Q, left), VLLs (L, middle), and HNLs (N, right) in protonproton collisions. 
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Figure 1c:
Representative Feynman diagrams showing the production of VLQs (Q, left), VLLs (L, middle), and HNLs (N, right) in protonproton collisions. 
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Figure 2:
Examples of either four (left) or six (right) selection regions used in the ABCD background estimation method. The region for which both criteria are satisfied is the SR. Expanding beyond four regions provides at least one ``validation region'' (VR). 
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Figure 2a:
Examples of either four (left) or six (right) selection regions used in the ABCD background estimation method. The region for which both criteria are satisfied is the SR. Expanding beyond four regions provides at least one ``validation region'' (VR). 
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Figure 2b:
Examples of either four (left) or six (right) selection regions used in the ABCD background estimation method. The region for which both criteria are satisfied is the SR. Expanding beyond four regions provides at least one ``validation region'' (VR). 
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Figure 3:
Representative LO Feynman diagrams for pair production of VLQs via the strong interaction (upper row) and single production of VLQs via EW processes (lower left) or via new interactions (lower right). Here, Q stands for either VLQ flavor. 
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Figure 3a:
Representative LO Feynman diagrams for pair production of VLQs via the strong interaction (upper row) and single production of VLQs via EW processes (lower left) or via new interactions (lower right). Here, Q stands for either VLQ flavor. 
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Figure 3b:
Representative LO Feynman diagrams for pair production of VLQs via the strong interaction (upper row) and single production of VLQs via EW processes (lower left) or via new interactions (lower right). Here, Q stands for either VLQ flavor. 
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Figure 3c:
Representative LO Feynman diagrams for pair production of VLQs via the strong interaction (upper row) and single production of VLQs via EW processes (lower left) or via new interactions (lower right). Here, Q stands for either VLQ flavor. 
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Figure 3d:
Representative LO Feynman diagrams for pair production of VLQs via the strong interaction (upper row) and single production of VLQs via EW processes (lower left) or via new interactions (lower right). Here, Q stands for either VLQ flavor. 
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Figure 4:
Cross sections for the production of VLQs at $ \sqrt{s}= $ 13 TeV as a function of the VLQ mass. Pair production cross sections via the strong interaction are computed to NNLO, using the models and tools from Refs. [127,128,129] (left). Reduced cross section $ \hat{\sigma} $ for single production via the EW interaction is computed at LO in EW in the NWA using the models and tools from Refs. [130,128,117,131] (right). The shaded bands indicate PDF, renormalization scale, and factorization scale uncertainties associated with the predictions. 
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Figure 4a:
Cross sections for the production of VLQs at $ \sqrt{s}= $ 13 TeV as a function of the VLQ mass. Pair production cross sections via the strong interaction are computed to NNLO, using the models and tools from Refs. [127,128,129] (left). Reduced cross section $ \hat{\sigma} $ for single production via the EW interaction is computed at LO in EW in the NWA using the models and tools from Refs. [130,128,117,131] (right). The shaded bands indicate PDF, renormalization scale, and factorization scale uncertainties associated with the predictions. 
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Figure 4b:
Cross sections for the production of VLQs at $ \sqrt{s}= $ 13 TeV as a function of the VLQ mass. Pair production cross sections via the strong interaction are computed to NNLO, using the models and tools from Refs. [127,128,129] (left). Reduced cross section $ \hat{\sigma} $ for single production via the EW interaction is computed at LO in EW in the NWA using the models and tools from Refs. [130,128,117,131] (right). The shaded bands indicate PDF, renormalization scale, and factorization scale uncertainties associated with the predictions. 
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Figure 5:
Coupling factors for single VLQ production via the EW interaction in the narrowwidth approximation as a function of the VLQ mass, using the models and tools from Refs. [130,128,117,131]. Coupling factors in single production of T (upper left), B (upper right) in the singlet and doublet scenarios. Coupling factors in single production of $\mathrm{X}_{5/3}$ (lower left), $\mathrm{Y}_{4/3}$ (lower right) in doublet scenarios. 
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Figure 5a:
Coupling factors for single VLQ production via the EW interaction in the narrowwidth approximation as a function of the VLQ mass, using the models and tools from Refs. [130,128,117,131]. Coupling factors in single production of T (upper left), B (upper right) in the singlet and doublet scenarios. Coupling factors in single production of $\mathrm{X}_{5/3}$ (lower left), $\mathrm{Y}_{4/3}$ (lower right) in doublet scenarios. 
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Figure 5b:
Coupling factors for single VLQ production via the EW interaction in the narrowwidth approximation as a function of the VLQ mass, using the models and tools from Refs. [130,128,117,131]. Coupling factors in single production of T (upper left), B (upper right) in the singlet and doublet scenarios. Coupling factors in single production of $\mathrm{X}_{5/3}$ (lower left), $\mathrm{Y}_{4/3}$ (lower right) in doublet scenarios. 
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Figure 5c:
Coupling factors for single VLQ production via the EW interaction in the narrowwidth approximation as a function of the VLQ mass, using the models and tools from Refs. [130,128,117,131]. Coupling factors in single production of T (upper left), B (upper right) in the singlet and doublet scenarios. Coupling factors in single production of $\mathrm{X}_{5/3}$ (lower left), $\mathrm{Y}_{4/3}$ (lower right) in doublet scenarios. 
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Figure 5d:
Coupling factors for single VLQ production via the EW interaction in the narrowwidth approximation as a function of the VLQ mass, using the models and tools from Refs. [130,128,117,131]. Coupling factors in single production of T (upper left), B (upper right) in the singlet and doublet scenarios. Coupling factors in single production of $\mathrm{X}_{5/3}$ (lower left), $\mathrm{Y}_{4/3}$ (lower right) in doublet scenarios. 
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Figure 6:
Distributions of observables used to maximize the $ {\mathrm{X}_{5/3}} {\mathrm{X}_{5/3}} $ signal significance for the SSDL (left) and singlelepton (right) final states. The left figure shows the $ H_{\mathrm{T}}^{\text{lep}} $ distribution after the SS dilepton selection, Z boson and quarkonia lepton invariant mass vetoes, and the requirement of at least two smallradius jets in the event, for a combination of $ \mathrm{e}\mathrm{e} $, $ \mathrm{e}\mu $, and $ \mu\mu $ channels. The right figure shows the $ \mathrm{min} M(\ell,\mathrm{b}) $ distribution in events with $ \geq $1 ttagged jet, $ \geq $1 Wtagged jets, and $ \geq $2 btagged jets for the combined electron and muon samples in the SR. The distribution has variablesize bins such that the statistical uncertainty in each bin is less than 30%. The lower panel in each plot shows the difference between the observed and the predicted numbers of events divided by the total uncertainty. Figures taken from Ref. [142]. 
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Figure 6a:
Distributions of observables used to maximize the $ {\mathrm{X}_{5/3}} {\mathrm{X}_{5/3}} $ signal significance for the SSDL (left) and singlelepton (right) final states. The left figure shows the $ H_{\mathrm{T}}^{\text{lep}} $ distribution after the SS dilepton selection, Z boson and quarkonia lepton invariant mass vetoes, and the requirement of at least two smallradius jets in the event, for a combination of $ \mathrm{e}\mathrm{e} $, $ \mathrm{e}\mu $, and $ \mu\mu $ channels. The right figure shows the $ \mathrm{min} M(\ell,\mathrm{b}) $ distribution in events with $ \geq $1 ttagged jet, $ \geq $1 Wtagged jets, and $ \geq $2 btagged jets for the combined electron and muon samples in the SR. The distribution has variablesize bins such that the statistical uncertainty in each bin is less than 30%. The lower panel in each plot shows the difference between the observed and the predicted numbers of events divided by the total uncertainty. Figures taken from Ref. [142]. 
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Figure 6b:
Distributions of observables used to maximize the $ {\mathrm{X}_{5/3}} {\mathrm{X}_{5/3}} $ signal significance for the SSDL (left) and singlelepton (right) final states. The left figure shows the $ H_{\mathrm{T}}^{\text{lep}} $ distribution after the SS dilepton selection, Z boson and quarkonia lepton invariant mass vetoes, and the requirement of at least two smallradius jets in the event, for a combination of $ \mathrm{e}\mathrm{e} $, $ \mathrm{e}\mu $, and $ \mu\mu $ channels. The right figure shows the $ \mathrm{min} M(\ell,\mathrm{b}) $ distribution in events with $ \geq $1 ttagged jet, $ \geq $1 Wtagged jets, and $ \geq $2 btagged jets for the combined electron and muon samples in the SR. The distribution has variablesize bins such that the statistical uncertainty in each bin is less than 30%. The lower panel in each plot shows the difference between the observed and the predicted numbers of events divided by the total uncertainty. Figures taken from Ref. [142]. 
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Figure 7:
Expected and observed cross section upper limits at 95% CL for an LH (left) and RH (right) $\mathrm{X}_{5/3}$ as a function of its mass, after combining the SS dilepton and singlelepton final states. The theoretical uncertainty in the signal cross section is shown with a band around the theoretical prediction. Figures adapted from Ref. [142]. 
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Figure 7a:
Expected and observed cross section upper limits at 95% CL for an LH (left) and RH (right) $\mathrm{X}_{5/3}$ as a function of its mass, after combining the SS dilepton and singlelepton final states. The theoretical uncertainty in the signal cross section is shown with a band around the theoretical prediction. Figures adapted from Ref. [142]. 
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Figure 7b:
Expected and observed cross section upper limits at 95% CL for an LH (left) and RH (right) $\mathrm{X}_{5/3}$ as a function of its mass, after combining the SS dilepton and singlelepton final states. The theoretical uncertainty in the signal cross section is shown with a band around the theoretical prediction. Figures adapted from Ref. [142]. 
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Figure 8:
Distributions of $ H_{\mathrm{T}} $ in a combination of SRs in the NNbased approach, inclusive in $ \geq $1 t tags (left), and in the SR with two Wtagged and two btagged jets in the selectionbased approach (right). The lower panels show the ratio between observed data and the background estimate. Figures taken from Ref. [139]. 
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Figure 8a:
Distributions of $ H_{\mathrm{T}} $ in a combination of SRs in the NNbased approach, inclusive in $ \geq $1 t tags (left), and in the SR with two Wtagged and two btagged jets in the selectionbased approach (right). The lower panels show the ratio between observed data and the background estimate. Figures taken from Ref. [139]. 
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Figure 8b:
Distributions of $ H_{\mathrm{T}} $ in a combination of SRs in the NNbased approach, inclusive in $ \geq $1 t tags (left), and in the SR with two Wtagged and two btagged jets in the selectionbased approach (right). The lower panels show the ratio between observed data and the background estimate. Figures taken from Ref. [139]. 
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Figure 9:
Observed lower limits at 95% CL on the T quark mass as functions of the T quark branching fractions to $ \mathrm{t}\mathrm{H} $ and $ \mathrm{b}\mathrm{W} $, using the NNbased (left) and selectionbased (right) approaches. Figures adapted from Ref. [139]. 
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Figure 9a:
Observed lower limits at 95% CL on the T quark mass as functions of the T quark branching fractions to $ \mathrm{t}\mathrm{H} $ and $ \mathrm{b}\mathrm{W} $, using the NNbased (left) and selectionbased (right) approaches. Figures adapted from Ref. [139]. 
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Figure 9b:
Observed lower limits at 95% CL on the T quark mass as functions of the T quark branching fractions to $ \mathrm{t}\mathrm{H} $ and $ \mathrm{b}\mathrm{W} $, using the NNbased (left) and selectionbased (right) approaches. Figures adapted from Ref. [139]. 
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Figure 10:
Example singlelepton channel $ {\mathrm{T}} \overline{\mathrm{T}} $ NN output distributions of the T quark score in the inclusive SR (left) and the W+jets score in the CRs (right). The observed data are shown using black markers, predicted $ {\mathrm{T}} \overline{\mathrm{T}} $ signal with a T mass of 1.2 (1.5) TeV in the singlet scenario using solid (dashed) lines, and backgrounds using filled histograms. Statistical and systematic uncertainties in the background estimate before performing the fit to data are shown by the hatched region. The lower panels show the difference between the observed data and the background estimate as a multiple of the total uncertainty in both sources. The signal predictions in the left distribution have been scaled for visibility by the factor indicated in the figure. Figures taken from Ref. [140]. 
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Figure 10a:
Example singlelepton channel $ {\mathrm{T}} \overline{\mathrm{T}} $ NN output distributions of the T quark score in the inclusive SR (left) and the W+jets score in the CRs (right). The observed data are shown using black markers, predicted $ {\mathrm{T}} \overline{\mathrm{T}} $ signal with a T mass of 1.2 (1.5) TeV in the singlet scenario using solid (dashed) lines, and backgrounds using filled histograms. Statistical and systematic uncertainties in the background estimate before performing the fit to data are shown by the hatched region. The lower panels show the difference between the observed data and the background estimate as a multiple of the total uncertainty in both sources. The signal predictions in the left distribution have been scaled for visibility by the factor indicated in the figure. Figures taken from Ref. [140]. 
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Figure 10b:
Example singlelepton channel $ {\mathrm{T}} \overline{\mathrm{T}} $ NN output distributions of the T quark score in the inclusive SR (left) and the W+jets score in the CRs (right). The observed data are shown using black markers, predicted $ {\mathrm{T}} \overline{\mathrm{T}} $ signal with a T mass of 1.2 (1.5) TeV in the singlet scenario using solid (dashed) lines, and backgrounds using filled histograms. Statistical and systematic uncertainties in the background estimate before performing the fit to data are shown by the hatched region. The lower panels show the difference between the observed data and the background estimate as a multiple of the total uncertainty in both sources. The signal predictions in the left distribution have been scaled for visibility by the factor indicated in the figure. Figures taken from Ref. [140]. 
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Figure 11:
Template histograms of $ H_{\mathrm{T}}^{\text{lep}} $ in the $ \mu\mu $ category of the SS dilepton channel (left) and $ S_{\mathrm{T}} $ in the $ \mu\mu\mu $ category of the multilepton channel (right). The observed data from 20172018 (combined for illustration) are shown using black markers, the predicted $ {\mathrm{T}} \overline{\mathrm{T}} $ signal for a mass of 1.2 (1.5) TeV in the singlet scenario using solid (dashed) lines, and the postfit background estimates using filled histograms. Statistical and systematic uncertainties in the background estimate after performing the fit to the observed data are shown by the hatched region. The lower panels show the difference between the observed data and the background estimate as a multiple of the total uncertainty from both sources. Figures adapted from Ref. [140]. 
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Figure 11a:
Template histograms of $ H_{\mathrm{T}}^{\text{lep}} $ in the $ \mu\mu $ category of the SS dilepton channel (left) and $ S_{\mathrm{T}} $ in the $ \mu\mu\mu $ category of the multilepton channel (right). The observed data from 20172018 (combined for illustration) are shown using black markers, the predicted $ {\mathrm{T}} \overline{\mathrm{T}} $ signal for a mass of 1.2 (1.5) TeV in the singlet scenario using solid (dashed) lines, and the postfit background estimates using filled histograms. Statistical and systematic uncertainties in the background estimate after performing the fit to the observed data are shown by the hatched region. The lower panels show the difference between the observed data and the background estimate as a multiple of the total uncertainty from both sources. Figures adapted from Ref. [140]. 
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Figure 11b:
Template histograms of $ H_{\mathrm{T}}^{\text{lep}} $ in the $ \mu\mu $ category of the SS dilepton channel (left) and $ S_{\mathrm{T}} $ in the $ \mu\mu\mu $ category of the multilepton channel (right). The observed data from 20172018 (combined for illustration) are shown using black markers, the predicted $ {\mathrm{T}} \overline{\mathrm{T}} $ signal for a mass of 1.2 (1.5) TeV in the singlet scenario using solid (dashed) lines, and the postfit background estimates using filled histograms. Statistical and systematic uncertainties in the background estimate after performing the fit to the observed data are shown by the hatched region. The lower panels show the difference between the observed data and the background estimate as a multiple of the total uncertainty from both sources. Figures adapted from Ref. [140]. 
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Figure 12:
The 95% CL expected (left) and observed (right) lower mass limits on pairproduced T quark masses, from the combined fit to all channels, as functions of their branching fractions to Higgs and W bosons. Mass contours are shown with lines of various styles. Figures adapted from Ref. [140]. 
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Figure 12a:
The 95% CL expected (left) and observed (right) lower mass limits on pairproduced T quark masses, from the combined fit to all channels, as functions of their branching fractions to Higgs and W bosons. Mass contours are shown with lines of various styles. Figures adapted from Ref. [140]. 
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Figure 12b:
The 95% CL expected (left) and observed (right) lower mass limits on pairproduced T quark masses, from the combined fit to all channels, as functions of their branching fractions to Higgs and W bosons. Mass contours are shown with lines of various styles. Figures adapted from Ref. [140]. 
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Figure 13:
Observed lower limit at 95% CL on B quark masses as a function of the branching fractions to $ \mathrm{b}\mathrm{H} $ and $ \mathrm{t}\mathrm{W} $, for the NNbased (left) and selectionbased (right) approaches of the search for $ {\mathrm{B}} \overline{\mathrm{B}} $ production in the allhadronic final state. Figures adapted from Ref. [139]. 
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Figure 13a:
Observed lower limit at 95% CL on B quark masses as a function of the branching fractions to $ \mathrm{b}\mathrm{H} $ and $ \mathrm{t}\mathrm{W} $, for the NNbased (left) and selectionbased (right) approaches of the search for $ {\mathrm{B}} \overline{\mathrm{B}} $ production in the allhadronic final state. Figures adapted from Ref. [139]. 
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Figure 13b:
Observed lower limit at 95% CL on B quark masses as a function of the branching fractions to $ \mathrm{b}\mathrm{H} $ and $ \mathrm{t}\mathrm{W} $, for the NNbased (left) and selectionbased (right) approaches of the search for $ {\mathrm{B}} \overline{\mathrm{B}} $ production in the allhadronic final state. Figures adapted from Ref. [139]. 
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Figure 14:
The 95% CL expected (left) and observed (right) lower mass limits on pairproduced B quark masses, from the combined fit to all channels, as functions of branching fractions to Higgs and W bosons. Mass contours are shown with lines of various styles. Figures adapted from Ref. [140]. 
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Figure 14a:
The 95% CL expected (left) and observed (right) lower mass limits on pairproduced B quark masses, from the combined fit to all channels, as functions of branching fractions to Higgs and W bosons. Mass contours are shown with lines of various styles. Figures adapted from Ref. [140]. 
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Figure 14b:
The 95% CL expected (left) and observed (right) lower mass limits on pairproduced B quark masses, from the combined fit to all channels, as functions of branching fractions to Higgs and W bosons. Mass contours are shown with lines of various styles. Figures adapted from Ref. [140]. 
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Figure 15:
Distributions of the reconstructed VLQ mass for expected background (blue histogram), signal plus background (colored lines), and observed data (black points) for events in the hadronic fourjet $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ category (left) and the leptonic fourjet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ category (right) in the search for $ {\mathrm{B}} \overline{\mathrm{B}} $ production. Five signal masses are shown: 1000 GeV (pink), 1200 GeV (red), 1400 GeV (orange), 1600 GeV (yellow), and 1800 GeV (green). The signal distributions are normalized to the number of events determined by the expected VLQ production cross section. The hatched regions indicate the total systematic uncertainty in the background estimate. The lower panels show the difference between the observed data and the background estimate as a multiple of the background estimate. Figures taken from Ref. [141]. 
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Figure 15a:
Distributions of the reconstructed VLQ mass for expected background (blue histogram), signal plus background (colored lines), and observed data (black points) for events in the hadronic fourjet $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ category (left) and the leptonic fourjet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ category (right) in the search for $ {\mathrm{B}} \overline{\mathrm{B}} $ production. Five signal masses are shown: 1000 GeV (pink), 1200 GeV (red), 1400 GeV (orange), 1600 GeV (yellow), and 1800 GeV (green). The signal distributions are normalized to the number of events determined by the expected VLQ production cross section. The hatched regions indicate the total systematic uncertainty in the background estimate. The lower panels show the difference between the observed data and the background estimate as a multiple of the background estimate. Figures taken from Ref. [141]. 
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Figure 15b:
Distributions of the reconstructed VLQ mass for expected background (blue histogram), signal plus background (colored lines), and observed data (black points) for events in the hadronic fourjet $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ category (left) and the leptonic fourjet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ category (right) in the search for $ {\mathrm{B}} \overline{\mathrm{B}} $ production. Five signal masses are shown: 1000 GeV (pink), 1200 GeV (red), 1400 GeV (orange), 1600 GeV (yellow), and 1800 GeV (green). The signal distributions are normalized to the number of events determined by the expected VLQ production cross section. The hatched regions indicate the total systematic uncertainty in the background estimate. The lower panels show the difference between the observed data and the background estimate as a multiple of the background estimate. Figures taken from Ref. [141]. 
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Figure 16:
Expected (left) and observed (right) lower limits on the B quark mass at 95% CL as a function of the branching fractions $ \mathcal{B}({\mathrm{B}} \to\mathrm{b}\mathrm{H}) $ and $ \mathcal{B}({\mathrm{B}} \to\mathrm{t}\mathrm{W}) $, with $ \mathcal{B}({\mathrm{B}} \to\mathrm{t}\mathrm{W})=1\mathcal{B}({\mathrm{B}} \to\mathrm{b}\mathrm{H})\mathcal{B}({\mathrm{B}} \to\mathrm{b}\mathrm{Z}) $. Results in the grey region, where the lower limit is less than 1.0 TeV, are omitted. Figures adapted from Ref. [141]. 
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Figure 16a:
Expected (left) and observed (right) lower limits on the B quark mass at 95% CL as a function of the branching fractions $ \mathcal{B}({\mathrm{B}} \to\mathrm{b}\mathrm{H}) $ and $ \mathcal{B}({\mathrm{B}} \to\mathrm{t}\mathrm{W}) $, with $ \mathcal{B}({\mathrm{B}} \to\mathrm{t}\mathrm{W})=1\mathcal{B}({\mathrm{B}} \to\mathrm{b}\mathrm{H})\mathcal{B}({\mathrm{B}} \to\mathrm{b}\mathrm{Z}) $. Results in the grey region, where the lower limit is less than 1.0 TeV, are omitted. Figures adapted from Ref. [141]. 
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Figure 16b:
Expected (left) and observed (right) lower limits on the B quark mass at 95% CL as a function of the branching fractions $ \mathcal{B}({\mathrm{B}} \to\mathrm{b}\mathrm{H}) $ and $ \mathcal{B}({\mathrm{B}} \to\mathrm{t}\mathrm{W}) $, with $ \mathcal{B}({\mathrm{B}} \to\mathrm{t}\mathrm{W})=1\mathcal{B}({\mathrm{B}} \to\mathrm{b}\mathrm{H})\mathcal{B}({\mathrm{B}} \to\mathrm{b}\mathrm{Z}) $. Results in the grey region, where the lower limit is less than 1.0 TeV, are omitted. Figures adapted from Ref. [141]. 
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Figure 17:
Distributions of the reconstructed T quark mass, $ m_{\mathrm{t}\mathrm{Z}} $ for the observed data, the background estimates, and the expected signal for the two categories where the singly produced T quark is reconstructed in the resolved topology for events with the Z boson decaying into muons and no forward jets (left) and at least one forward jet (right). The background composition is taken from simulation. The expected signal is shown for two benchmark values of the width, for a T quark produced in association with a b quark: NWA and 30% of the T quark mass. The lower panel in each plot shows the ratio of the observed data to the background estimation, with the hatched band representing the uncertainties in the background estimate. Figures taken from Ref. [143]. 
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Figure 17a:
Distributions of the reconstructed T quark mass, $ m_{\mathrm{t}\mathrm{Z}} $ for the observed data, the background estimates, and the expected signal for the two categories where the singly produced T quark is reconstructed in the resolved topology for events with the Z boson decaying into muons and no forward jets (left) and at least one forward jet (right). The background composition is taken from simulation. The expected signal is shown for two benchmark values of the width, for a T quark produced in association with a b quark: NWA and 30% of the T quark mass. The lower panel in each plot shows the ratio of the observed data to the background estimation, with the hatched band representing the uncertainties in the background estimate. Figures taken from Ref. [143]. 
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Figure 17b:
Distributions of the reconstructed T quark mass, $ m_{\mathrm{t}\mathrm{Z}} $ for the observed data, the background estimates, and the expected signal for the two categories where the singly produced T quark is reconstructed in the resolved topology for events with the Z boson decaying into muons and no forward jets (left) and at least one forward jet (right). The background composition is taken from simulation. The expected signal is shown for two benchmark values of the width, for a T quark produced in association with a b quark: NWA and 30% of the T quark mass. The lower panel in each plot shows the ratio of the observed data to the background estimation, with the hatched band representing the uncertainties in the background estimate. Figures taken from Ref. [143]. 
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Figure 18:
Observed and expected upper limits on the product of the cross section and branching fraction for singlet LH T quark (left) and doublet RH T quark production (right) in association with a b quark and a t quark, respectively, in the NWA hypothesis. The T quark decays to $ \mathrm{t}\mathrm{Z} $ with a branching fraction $ \mathcal{B}({\mathrm{T}} \to\mathrm{t}\mathrm{Z}) $ of 0.25 (0.5) for the left (right) figure. The red lines represent theoretical cross sections calculated at NLO in perturbative QCD, whereas the inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the backgroundonly hypothesis. Figures taken from Ref. [143]. 
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Figure 18a:
Observed and expected upper limits on the product of the cross section and branching fraction for singlet LH T quark (left) and doublet RH T quark production (right) in association with a b quark and a t quark, respectively, in the NWA hypothesis. The T quark decays to $ \mathrm{t}\mathrm{Z} $ with a branching fraction $ \mathcal{B}({\mathrm{T}} \to\mathrm{t}\mathrm{Z}) $ of 0.25 (0.5) for the left (right) figure. The red lines represent theoretical cross sections calculated at NLO in perturbative QCD, whereas the inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the backgroundonly hypothesis. Figures taken from Ref. [143]. 
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Figure 18b:
Observed and expected upper limits on the product of the cross section and branching fraction for singlet LH T quark (left) and doublet RH T quark production (right) in association with a b quark and a t quark, respectively, in the NWA hypothesis. The T quark decays to $ \mathrm{t}\mathrm{Z} $ with a branching fraction $ \mathcal{B}({\mathrm{T}} \to\mathrm{t}\mathrm{Z}) $ of 0.25 (0.5) for the left (right) figure. The red lines represent theoretical cross sections calculated at NLO in perturbative QCD, whereas the inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the backgroundonly hypothesis. Figures taken from Ref. [143]. 
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Figure 19:
Distributions from the 2018 data set of the transverse mass of the reconstructed top quark and $ {\vec p}_{\mathrm{T}}^{\kern1pt\text{miss}} $ system, for the selected events in the resolved categories, for events with no forward jet (left) and at least one forward jet (right). The distributions for the main background components have been determined in simulation with SFs extracted from CRs. All background processes and the respective uncertainties are derived from the fit to data, whereas the distributions of signal processes are represented according to the expectation before the fit. The lines show the signal predictions for three benchmark mass values (0.8, 1.2, and 1.6 TeV) for a T quark of a narrow width. Figures taken from Ref. [145]. 
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Figure 19a:
Distributions from the 2018 data set of the transverse mass of the reconstructed top quark and $ {\vec p}_{\mathrm{T}}^{\kern1pt\text{miss}} $ system, for the selected events in the resolved categories, for events with no forward jet (left) and at least one forward jet (right). The distributions for the main background components have been determined in simulation with SFs extracted from CRs. All background processes and the respective uncertainties are derived from the fit to data, whereas the distributions of signal processes are represented according to the expectation before the fit. The lines show the signal predictions for three benchmark mass values (0.8, 1.2, and 1.6 TeV) for a T quark of a narrow width. Figures taken from Ref. [145]. 
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Figure 19b:
Distributions from the 2018 data set of the transverse mass of the reconstructed top quark and $ {\vec p}_{\mathrm{T}}^{\kern1pt\text{miss}} $ system, for the selected events in the resolved categories, for events with no forward jet (left) and at least one forward jet (right). The distributions for the main background components have been determined in simulation with SFs extracted from CRs. All background processes and the respective uncertainties are derived from the fit to data, whereas the distributions of signal processes are represented according to the expectation before the fit. The lines show the signal predictions for three benchmark mass values (0.8, 1.2, and 1.6 TeV) for a T quark of a narrow width. Figures taken from Ref. [145]. 
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Figure 20:
Observed 95% CL upper limit on the product of the single production cross section for a singlet VLQ T quark and the $ {\mathrm{T}} \to\mathrm{t}\mathrm{Z} $ branching fraction, as a function of the T quark mass $ m_{{\mathrm{T}} } $ and width $ \Gamma $, for widths from 5 to 30% of the mass. A singlet T quark that is produced in association with a bottom quark is assumed. The solid red line indicates the boundary of the excluded region (on the hatched side) of theoretical cross sections multiplied by the T branching fraction. Figure taken from Ref. [145]. 
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Figure 21:
Backgroundonly postfit distributions of $ \widetilde{m}_{{\mathrm{T}} } $, the adjusted T mass sensitive observable defined in Ref. [144], of the observed data for the SR of the $ {\mathrm{T}} \to\mathrm{t}\mathrm{Z} $ (left) and $ {\mathrm{T}} \to\mathrm{t}\mathrm{H} $ (right) channels, respectively, for the highmass search. The dashed red histogram in each case represents an example signal for the $ \mathrm{t}\mathrm{Z}\mathrm{b}\mathrm{q} $ or $ \mathrm{t}\mathrm{H}\mathrm{b}\mathrm{q} $ process with a T quark mass of 1.2 TeV and a relative width of 30%. The lower panels of the plots display the ratio of observed data to the fitted background for each bin. The error bars on the data points correspond to the 68% CL Poisson intervals, whereas the light blue band in each ratio panel represents the relative uncertainties in the fitted background. Figures taken from Ref. [144]. 
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Figure 21a:
Backgroundonly postfit distributions of $ \widetilde{m}_{{\mathrm{T}} } $, the adjusted T mass sensitive observable defined in Ref. [144], of the observed data for the SR of the $ {\mathrm{T}} \to\mathrm{t}\mathrm{Z} $ (left) and $ {\mathrm{T}} \to\mathrm{t}\mathrm{H} $ (right) channels, respectively, for the highmass search. The dashed red histogram in each case represents an example signal for the $ \mathrm{t}\mathrm{Z}\mathrm{b}\mathrm{q} $ or $ \mathrm{t}\mathrm{H}\mathrm{b}\mathrm{q} $ process with a T quark mass of 1.2 TeV and a relative width of 30%. The lower panels of the plots display the ratio of observed data to the fitted background for each bin. The error bars on the data points correspond to the 68% CL Poisson intervals, whereas the light blue band in each ratio panel represents the relative uncertainties in the fitted background. Figures taken from Ref. [144]. 
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Figure 21b:
Backgroundonly postfit distributions of $ \widetilde{m}_{{\mathrm{T}} } $, the adjusted T mass sensitive observable defined in Ref. [144], of the observed data for the SR of the $ {\mathrm{T}} \to\mathrm{t}\mathrm{Z} $ (left) and $ {\mathrm{T}} \to\mathrm{t}\mathrm{H} $ (right) channels, respectively, for the highmass search. The dashed red histogram in each case represents an example signal for the $ \mathrm{t}\mathrm{Z}\mathrm{b}\mathrm{q} $ or $ \mathrm{t}\mathrm{H}\mathrm{b}\mathrm{q} $ process with a T quark mass of 1.2 TeV and a relative width of 30%. The lower panels of the plots display the ratio of observed data to the fitted background for each bin. The error bars on the data points correspond to the 68% CL Poisson intervals, whereas the light blue band in each ratio panel represents the relative uncertainties in the fitted background. Figures taken from Ref. [144]. 
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Figure 22:
Backgroundonly postfit fivejet invariant mass distributions for the SR for the lowmass (left) and highmass (right) selections. The shaded blue region represents the uncertainty in the fitted background estimate. The expected signal distributions (scaled for visibility) for a 700 GeV and a 900 GeV T quark are shown as red dashed lines for the low and highmass selections, respectively. Figures adapted from Ref. [147]. 
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Figure 22a:
Backgroundonly postfit fivejet invariant mass distributions for the SR for the lowmass (left) and highmass (right) selections. The shaded blue region represents the uncertainty in the fitted background estimate. The expected signal distributions (scaled for visibility) for a 700 GeV and a 900 GeV T quark are shown as red dashed lines for the low and highmass selections, respectively. Figures adapted from Ref. [147]. 
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Figure 22b:
Backgroundonly postfit fivejet invariant mass distributions for the SR for the lowmass (left) and highmass (right) selections. The shaded blue region represents the uncertainty in the fitted background estimate. The expected signal distributions (scaled for visibility) for a 700 GeV and a 900 GeV T quark are shown as red dashed lines for the low and highmass selections, respectively. Figures adapted from Ref. [147]. 
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Figure 23:
Observed and median expected upper limits at 95% CL on the cross sections for single T quark production associated with a b quark, for the sum of $ \mathrm{t}\mathrm{H}\mathrm{b}\mathrm{q} $ and $ \mathrm{t}\mathrm{Z}\mathrm{b}\mathrm{q} $ channels, as a function of the assumed values of the T quark mass. The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the backgroundonly hypothesis. The left figure corresponds to the analysis strategy described in Ref. [147], based on the fivejet invariant mass reconstruction of the T. The figure on the right corresponds to the analysis strategy in Ref. [144], which employs different reconstruction algorithms for the low and highmass searches. The vertical dashed lines represent the crossover point in sensitivity for the lowmass and highmass selections. Figures adapted from Refs. [147,144]. 
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Figure 23a:
Observed and median expected upper limits at 95% CL on the cross sections for single T quark production associated with a b quark, for the sum of $ \mathrm{t}\mathrm{H}\mathrm{b}\mathrm{q} $ and $ \mathrm{t}\mathrm{Z}\mathrm{b}\mathrm{q} $ channels, as a function of the assumed values of the T quark mass. The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the backgroundonly hypothesis. The left figure corresponds to the analysis strategy described in Ref. [147], based on the fivejet invariant mass reconstruction of the T. The figure on the right corresponds to the analysis strategy in Ref. [144], which employs different reconstruction algorithms for the low and highmass searches. The vertical dashed lines represent the crossover point in sensitivity for the lowmass and highmass selections. Figures adapted from Refs. [147,144]. 
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Figure 23b:
Observed and median expected upper limits at 95% CL on the cross sections for single T quark production associated with a b quark, for the sum of $ \mathrm{t}\mathrm{H}\mathrm{b}\mathrm{q} $ and $ \mathrm{t}\mathrm{Z}\mathrm{b}\mathrm{q} $ channels, as a function of the assumed values of the T quark mass. The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the backgroundonly hypothesis. The left figure corresponds to the analysis strategy described in Ref. [147], based on the fivejet invariant mass reconstruction of the T. The figure on the right corresponds to the analysis strategy in Ref. [144], which employs different reconstruction algorithms for the low and highmass searches. The vertical dashed lines represent the crossover point in sensitivity for the lowmass and highmass selections. Figures adapted from Refs. [147,144]. 
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Figure 24:
Observed and median expected upper limits at 95% CL on the cross sections for single T quark production associated with a b quark, for the sum of $ \mathrm{t}\mathrm{H}\mathrm{b}\mathrm{q} $ and $ \mathrm{t}\mathrm{Z}\mathrm{b}\mathrm{q} $ channels, as a function of the assumed values of the T quark mass. The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the backgroundonly hypothesis. The results are given for relative widths of $ \Gamma/m_{{\mathrm{T}} }= $ 10 (upper left), 20 (upper right), and 30% (lower). The vertical dashed lines represent the crossover point in sensitivity for the lowmass and highmass selections. Figures adapted from Ref. [144]. 
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Figure 24a:
Observed and median expected upper limits at 95% CL on the cross sections for single T quark production associated with a b quark, for the sum of $ \mathrm{t}\mathrm{H}\mathrm{b}\mathrm{q} $ and $ \mathrm{t}\mathrm{Z}\mathrm{b}\mathrm{q} $ channels, as a function of the assumed values of the T quark mass. The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the backgroundonly hypothesis. The results are given for relative widths of $ \Gamma/m_{{\mathrm{T}} }= $ 10 (upper left), 20 (upper right), and 30% (lower). The vertical dashed lines represent the crossover point in sensitivity for the lowmass and highmass selections. Figures adapted from Ref. [144]. 
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Figure 24b:
Observed and median expected upper limits at 95% CL on the cross sections for single T quark production associated with a b quark, for the sum of $ \mathrm{t}\mathrm{H}\mathrm{b}\mathrm{q} $ and $ \mathrm{t}\mathrm{Z}\mathrm{b}\mathrm{q} $ channels, as a function of the assumed values of the T quark mass. The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the backgroundonly hypothesis. The results are given for relative widths of $ \Gamma/m_{{\mathrm{T}} }= $ 10 (upper left), 20 (upper right), and 30% (lower). The vertical dashed lines represent the crossover point in sensitivity for the lowmass and highmass selections. Figures adapted from Ref. [144]. 
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Figure 24c:
Observed and median expected upper limits at 95% CL on the cross sections for single T quark production associated with a b quark, for the sum of $ \mathrm{t}\mathrm{H}\mathrm{b}\mathrm{q} $ and $ \mathrm{t}\mathrm{Z}\mathrm{b}\mathrm{q} $ channels, as a function of the assumed values of the T quark mass. The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the backgroundonly hypothesis. The results are given for relative widths of $ \Gamma/m_{{\mathrm{T}} }= $ 10 (upper left), 20 (upper right), and 30% (lower). The vertical dashed lines represent the crossover point in sensitivity for the lowmass and highmass selections. Figures adapted from Ref. [144]. 
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Figure 25:
Distributions of the observed data (black dots) and $ m_{\gamma\gamma} $ signalplusbackground model fits (red line) for a T quark signal with $ m_{{\mathrm{T}} } $ of 900 (left) and 1200 GeV (right), combining the leptonic and hadronic channels. The green (yellow) band represents the 68 (95)% CL interval in the background component of the fit. The peak in the background component shows the considered irreducible SM Higgs boson contribution ($ \mathrm{g}\mathrm{g}\mathrm{H} $, VBF, VH, $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{H} $, and $ \mathrm{t}\mathrm{H} $). Here, $ \hat{\mu} $ is the best fit value of the signal strength parameter $ \mu $, which is zero for the two $ m_{{\mathrm{T}} } $ values considered. The lower panel shows the residuals after the subtraction of the background component. Figures adapted from Ref. [146]. 
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Figure 25a:
Distributions of the observed data (black dots) and $ m_{\gamma\gamma} $ signalplusbackground model fits (red line) for a T quark signal with $ m_{{\mathrm{T}} } $ of 900 (left) and 1200 GeV (right), combining the leptonic and hadronic channels. The green (yellow) band represents the 68 (95)% CL interval in the background component of the fit. The peak in the background component shows the considered irreducible SM Higgs boson contribution ($ \mathrm{g}\mathrm{g}\mathrm{H} $, VBF, VH, $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{H} $, and $ \mathrm{t}\mathrm{H} $). Here, $ \hat{\mu} $ is the best fit value of the signal strength parameter $ \mu $, which is zero for the two $ m_{{\mathrm{T}} } $ values considered. The lower panel shows the residuals after the subtraction of the background component. Figures adapted from Ref. [146]. 
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Figure 25b:
Distributions of the observed data (black dots) and $ m_{\gamma\gamma} $ signalplusbackground model fits (red line) for a T quark signal with $ m_{{\mathrm{T}} } $ of 900 (left) and 1200 GeV (right), combining the leptonic and hadronic channels. The green (yellow) band represents the 68 (95)% CL interval in the background component of the fit. The peak in the background component shows the considered irreducible SM Higgs boson contribution ($ \mathrm{g}\mathrm{g}\mathrm{H} $, VBF, VH, $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{H} $, and $ \mathrm{t}\mathrm{H} $). Here, $ \hat{\mu} $ is the best fit value of the signal strength parameter $ \mu $, which is zero for the two $ m_{{\mathrm{T}} } $ values considered. The lower panel shows the residuals after the subtraction of the background component. Figures adapted from Ref. [146]. 
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Figure 26:
Expected (dotted black) and observed (solid black) upper limits at 95% CL on $ \sigma_{{\mathrm{T}} \mathrm{b}\mathrm{q}}\mathcal{B}({\mathrm{T}} \to\mathrm{t}\mathrm{H}) $ are displayed as a function of $ m_{{\mathrm{T}} } $, combining the leptonic and hadronic channels. The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the backgroundonly hypothesis. The theoretical cross sections for the singlet T production with representative $ \kappa_{{\mathrm{T}} } $ values fixed at 0.1, 0.15, 0.2, and 0.25 (for $ \Gamma/m_{{\mathrm{T}} } < $ 5%) are shown as red lines. Figure adapted from Ref. [146]. 
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Figure 27:
The distribution in the reconstructed B quark mass in events with one ttagged jet and a forward jet, where the SM background is obtained from a CR without a forward jet (left). The product of the observed upper limits on the cross section and $ \mathcal{B}({\mathrm{B}} \to\mathrm{t}\mathrm{W}) $ as a function of $ m_{\text{VLQ}} $ for different relative decay widths of the B quark (right), for single B quark production in association with a b quark. Figures taken from Ref. [150]. 
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Figure 27a:
The distribution in the reconstructed B quark mass in events with one ttagged jet and a forward jet, where the SM background is obtained from a CR without a forward jet (left). The product of the observed upper limits on the cross section and $ \mathcal{B}({\mathrm{B}} \to\mathrm{t}\mathrm{W}) $ as a function of $ m_{\text{VLQ}} $ for different relative decay widths of the B quark (right), for single B quark production in association with a b quark. Figures taken from Ref. [150]. 
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Figure 27b:
The distribution in the reconstructed B quark mass in events with one ttagged jet and a forward jet, where the SM background is obtained from a CR without a forward jet (left). The product of the observed upper limits on the cross section and $ \mathcal{B}({\mathrm{B}} \to\mathrm{t}\mathrm{W}) $ as a function of $ m_{\text{VLQ}} $ for different relative decay widths of the B quark (right), for single B quark production in association with a b quark. Figures taken from Ref. [150]. 
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Figure 28:
Upper limits on the product of the production cross section and branching fraction to $ \mathrm{t}\mathrm{W} $ of the $ \mathrm{b}\mathrm{b} $ (left) and $ \mathrm{b}\mathrm{t} $ (right) production modes at 95% CL. Colored lines show the expected limits from the $ \ell $+jets (dotted) and allhadronic (dashdotted) channels, where the latter start at B masses of 1.4 TeV. The observed and expected limits from the combination are shown as solid and dashed black lines, respectively. The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of the limits expected under the backgroundonly hypothesis. The theoretical cross sections are shown as the red and blue lines, where the uncertainties due to missing higher orders are depicted by shaded areas. Figures adapted from Ref. [152]. 
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Figure 28a:
Upper limits on the product of the production cross section and branching fraction to $ \mathrm{t}\mathrm{W} $ of the $ \mathrm{b}\mathrm{b} $ (left) and $ \mathrm{b}\mathrm{t} $ (right) production modes at 95% CL. Colored lines show the expected limits from the $ \ell $+jets (dotted) and allhadronic (dashdotted) channels, where the latter start at B masses of 1.4 TeV. The observed and expected limits from the combination are shown as solid and dashed black lines, respectively. The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of the limits expected under the backgroundonly hypothesis. The theoretical cross sections are shown as the red and blue lines, where the uncertainties due to missing higher orders are depicted by shaded areas. Figures adapted from Ref. [152]. 
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Figure 28b:
Upper limits on the product of the production cross section and branching fraction to $ \mathrm{t}\mathrm{W} $ of the $ \mathrm{b}\mathrm{b} $ (left) and $ \mathrm{b}\mathrm{t} $ (right) production modes at 95% CL. Colored lines show the expected limits from the $ \ell $+jets (dotted) and allhadronic (dashdotted) channels, where the latter start at B masses of 1.4 TeV. The observed and expected limits from the combination are shown as solid and dashed black lines, respectively. The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of the limits expected under the backgroundonly hypothesis. The theoretical cross sections are shown as the red and blue lines, where the uncertainties due to missing higher orders are depicted by shaded areas. Figures adapted from Ref. [152]. 
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Figure 29:
Observed and expected 95% CL upper limits on the product of the B quark production cross section and branching fraction to $ \mathrm{b}\mathrm{H} $, as a function of the signal mass, under the NWA. The results are shown for the combination of 0 and $ > $0 forwardjet categories. The continuous red curves correspond to the theoretical expectations for singlet and doublet models. Figure taken from Ref. [149]. 
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Figure 30:
Reconstructed $ m_{\mathrm{Z}^{'}} $ (left) and $ m_{{\mathrm{T}} } $ (right) distributions obtained in a search for $ \mathrm{p}\mathrm{p}\to\mathrm{Z}^{'}\to{\mathrm{T}} \overline{\mathrm{T}} $ in the allhadronic final state. The $ \mathrm{Z}^{'} $ boson is reconstructed using a t, a W, and a btagged jet, whereas the T quark is reconstructed using the latter two jets. The lower panels show the difference between the data and the estimated backgrounds divided by the sum in quadrature of the statistical uncertainties in data and backgrounds, and the systematic uncertainties in the estimated backgrounds. Figures adapted from Ref. [153]. 
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Figure 30a:
Reconstructed $ m_{\mathrm{Z}^{'}} $ (left) and $ m_{{\mathrm{T}} } $ (right) distributions obtained in a search for $ \mathrm{p}\mathrm{p}\to\mathrm{Z}^{'}\to{\mathrm{T}} \overline{\mathrm{T}} $ in the allhadronic final state. The $ \mathrm{Z}^{'} $ boson is reconstructed using a t, a W, and a btagged jet, whereas the T quark is reconstructed using the latter two jets. The lower panels show the difference between the data and the estimated backgrounds divided by the sum in quadrature of the statistical uncertainties in data and backgrounds, and the systematic uncertainties in the estimated backgrounds. Figures adapted from Ref. [153]. 
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Figure 30b:
Reconstructed $ m_{\mathrm{Z}^{'}} $ (left) and $ m_{{\mathrm{T}} } $ (right) distributions obtained in a search for $ \mathrm{p}\mathrm{p}\to\mathrm{Z}^{'}\to{\mathrm{T}} \overline{\mathrm{T}} $ in the allhadronic final state. The $ \mathrm{Z}^{'} $ boson is reconstructed using a t, a W, and a btagged jet, whereas the T quark is reconstructed using the latter two jets. The lower panels show the difference between the data and the estimated backgrounds divided by the sum in quadrature of the statistical uncertainties in data and backgrounds, and the systematic uncertainties in the estimated backgrounds. Figures adapted from Ref. [153]. 
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Figure 31:
Reconstructed $ m_{\mathrm{Z}^{'}} $ distributions obtained in a search for $ \mathrm{p}\mathrm{p}\to\mathrm{Z}^{'}\to{\mathrm{T}} \overline{\mathrm{T}} $ in the $ \ell $+jets final state, in events with a V and a ttagged jet (left) and in events with an Htagged jet (right). The lower panels show the ratio of the observed data to the background prediction. Figures adapted from Ref. [154]. 
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Figure 31a:
Reconstructed $ m_{\mathrm{Z}^{'}} $ distributions obtained in a search for $ \mathrm{p}\mathrm{p}\to\mathrm{Z}^{'}\to{\mathrm{T}} \overline{\mathrm{T}} $ in the $ \ell $+jets final state, in events with a V and a ttagged jet (left) and in events with an Htagged jet (right). The lower panels show the ratio of the observed data to the background prediction. Figures adapted from Ref. [154]. 
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Figure 31b:
Reconstructed $ m_{\mathrm{Z}^{'}} $ distributions obtained in a search for $ \mathrm{p}\mathrm{p}\to\mathrm{Z}^{'}\to{\mathrm{T}} \overline{\mathrm{T}} $ in the $ \ell $+jets final state, in events with a V and a ttagged jet (left) and in events with an Htagged jet (right). The lower panels show the ratio of the observed data to the background prediction. Figures adapted from Ref. [154]. 
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Figure 32:
Reconstructed $ \mathrm{W^{'}} $ boson mass distributions obtained in a search for $ \mathrm{p}\mathrm{p}\to\mathrm{W^{'}}\to{\mathrm{T}} \overline{\mathrm{b}}/{\mathrm{B}} \overline{\mathrm{t}} $ in the allhadronic final state, in events with a t, H and btagged jet (left). Upper limits at 95% CL on the product of the cross section and branching fraction for the production of a $ \mathrm{W^{'}} $ boson with decays to $ {\mathrm{T}} \overline{\mathrm{b}} $ and $ {\mathrm{B}} \overline{\mathrm{t}} $ (right). Figures adapted from Ref. [156]. 
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Figure 32a:
Reconstructed $ \mathrm{W^{'}} $ boson mass distributions obtained in a search for $ \mathrm{p}\mathrm{p}\to\mathrm{W^{'}}\to{\mathrm{T}} \overline{\mathrm{b}}/{\mathrm{B}} \overline{\mathrm{t}} $ in the allhadronic final state, in events with a t, H and btagged jet (left). Upper limits at 95% CL on the product of the cross section and branching fraction for the production of a $ \mathrm{W^{'}} $ boson with decays to $ {\mathrm{T}} \overline{\mathrm{b}} $ and $ {\mathrm{B}} \overline{\mathrm{t}} $ (right). Figures adapted from Ref. [156]. 
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Figure 32b:
Reconstructed $ \mathrm{W^{'}} $ boson mass distributions obtained in a search for $ \mathrm{p}\mathrm{p}\to\mathrm{W^{'}}\to{\mathrm{T}} \overline{\mathrm{b}}/{\mathrm{B}} \overline{\mathrm{t}} $ in the allhadronic final state, in events with a t, H and btagged jet (left). Upper limits at 95% CL on the product of the cross section and branching fraction for the production of a $ \mathrm{W^{'}} $ boson with decays to $ {\mathrm{T}} \overline{\mathrm{b}} $ and $ {\mathrm{B}} \overline{\mathrm{t}} $ (right). Figures adapted from Ref. [156]. 
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Figure 33:
Observed (solid lines) and expected (dashed lines) 95% CL upper limits on $ {\mathrm{B}} \overline{\mathrm{B}} $ production as a function of the B quark mass for the singlet (left) and doublet (right) branching fraction scenarios, from the combination of two searches for $ {\mathrm{B}} \overline{\mathrm{B}} $ production. Predicted cross sections are shown by the red line surrounded by a band representing energy scale and PDF uncertainties in the calculation. 
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Figure 33a:
Observed (solid lines) and expected (dashed lines) 95% CL upper limits on $ {\mathrm{B}} \overline{\mathrm{B}} $ production as a function of the B quark mass for the singlet (left) and doublet (right) branching fraction scenarios, from the combination of two searches for $ {\mathrm{B}} \overline{\mathrm{B}} $ production. Predicted cross sections are shown by the red line surrounded by a band representing energy scale and PDF uncertainties in the calculation. 
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Figure 33b:
Observed (solid lines) and expected (dashed lines) 95% CL upper limits on $ {\mathrm{B}} \overline{\mathrm{B}} $ production as a function of the B quark mass for the singlet (left) and doublet (right) branching fraction scenarios, from the combination of two searches for $ {\mathrm{B}} \overline{\mathrm{B}} $ production. Predicted cross sections are shown by the red line surrounded by a band representing energy scale and PDF uncertainties in the calculation. 
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Figure 34:
Expected (left) and observed (right) lower limits on the B quark mass at 95% CL from the combination of two searches for $ {\mathrm{B}} \overline{\mathrm{B}} $ production. The limits are shown as a function of the branching fractions $ \mathcal{B}({\mathrm{B}} \to\mathrm{b}\mathrm{H}) $ and $ \mathcal{B}({\mathrm{B}} \to\mathrm{t}\mathrm{W}) $, with $ \mathcal{B}({\mathrm{B}} \to\mathrm{t}\mathrm{W})=1\mathcal{B}({\mathrm{B}} \to\mathrm{b}\mathrm{H})\mathcal{B}({\mathrm{B}} \to\mathrm{b}\mathrm{Z}) $. 
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Figure 34a:
Expected (left) and observed (right) lower limits on the B quark mass at 95% CL from the combination of two searches for $ {\mathrm{B}} \overline{\mathrm{B}} $ production. The limits are shown as a function of the branching fractions $ \mathcal{B}({\mathrm{B}} \to\mathrm{b}\mathrm{H}) $ and $ \mathcal{B}({\mathrm{B}} \to\mathrm{t}\mathrm{W}) $, with $ \mathcal{B}({\mathrm{B}} \to\mathrm{t}\mathrm{W})=1\mathcal{B}({\mathrm{B}} \to\mathrm{b}\mathrm{H})\mathcal{B}({\mathrm{B}} \to\mathrm{b}\mathrm{Z}) $. 
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Figure 34b:
Expected (left) and observed (right) lower limits on the B quark mass at 95% CL from the combination of two searches for $ {\mathrm{B}} \overline{\mathrm{B}} $ production. The limits are shown as a function of the branching fractions $ \mathcal{B}({\mathrm{B}} \to\mathrm{b}\mathrm{H}) $ and $ \mathcal{B}({\mathrm{B}} \to\mathrm{t}\mathrm{W}) $, with $ \mathcal{B}({\mathrm{B}} \to\mathrm{t}\mathrm{W})=1\mathcal{B}({\mathrm{B}} \to\mathrm{b}\mathrm{H})\mathcal{B}({\mathrm{B}} \to\mathrm{b}\mathrm{Z}) $. 
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Figure 35:
Observed and expected 95% CL upper limits on the production cross section of a single T quark in association with a b quark in a singlet scenario, versus the T quark mass. Theoretical predictions for relative widths of 1 and 5% of the mass are shown as red solid line and red dashed line, respectively. 
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Figure 36:
Expected (left) and observed (right) 95% CL upper limits on the product of the singleproduction cross section and the $ {\mathrm{T}} \to\mathrm{t}\mathrm{Z}/\mathrm{H} $ branching fraction for a singlet T quark, as a function of the T quark mass $ m_{{\mathrm{T}} } $ and width $ \Gamma $, for relative widths from 1 to 30% of the mass. A singlet T quark that is produced in association with a b quark is assumed. The solid red line indicates the boundary of the excluded region (hatched area) of theoretical cross sections. 
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Figure 36a:
Expected (left) and observed (right) 95% CL upper limits on the product of the singleproduction cross section and the $ {\mathrm{T}} \to\mathrm{t}\mathrm{Z}/\mathrm{H} $ branching fraction for a singlet T quark, as a function of the T quark mass $ m_{{\mathrm{T}} } $ and width $ \Gamma $, for relative widths from 1 to 30% of the mass. A singlet T quark that is produced in association with a b quark is assumed. The solid red line indicates the boundary of the excluded region (hatched area) of theoretical cross sections. 
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Figure 36b:
Expected (left) and observed (right) 95% CL upper limits on the product of the singleproduction cross section and the $ {\mathrm{T}} \to\mathrm{t}\mathrm{Z}/\mathrm{H} $ branching fraction for a singlet T quark, as a function of the T quark mass $ m_{{\mathrm{T}} } $ and width $ \Gamma $, for relative widths from 1 to 30% of the mass. A singlet T quark that is produced in association with a b quark is assumed. The solid red line indicates the boundary of the excluded region (hatched area) of theoretical cross sections. 
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Figure 37:
Observed and expected 95% CL upper limits on the production cross section of a pair of vectorlike T quarks decaying to $ \mathrm{t}\mathrm{Z} $ (upper left), $ \mathrm{t}\mathrm{H} $ (upper right), and $ \mathrm{b}\mathrm{W} $ (lower), as a function of the T quark mass, obtained by different analyses: 0$ \ell $+jets (NN, selectionbased) [139], and $ \geq $1$ \ell $+jets [140]. A theory prediction at NNLO in perturbative QCD of the pair production cross section in the NWA is superimposed. 
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Figure 37a:
Observed and expected 95% CL upper limits on the production cross section of a pair of vectorlike T quarks decaying to $ \mathrm{t}\mathrm{Z} $ (upper left), $ \mathrm{t}\mathrm{H} $ (upper right), and $ \mathrm{b}\mathrm{W} $ (lower), as a function of the T quark mass, obtained by different analyses: 0$ \ell $+jets (NN, selectionbased) [139], and $ \geq $1$ \ell $+jets [140]. A theory prediction at NNLO in perturbative QCD of the pair production cross section in the NWA is superimposed. 
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Figure 37b:
Observed and expected 95% CL upper limits on the production cross section of a pair of vectorlike T quarks decaying to $ \mathrm{t}\mathrm{Z} $ (upper left), $ \mathrm{t}\mathrm{H} $ (upper right), and $ \mathrm{b}\mathrm{W} $ (lower), as a function of the T quark mass, obtained by different analyses: 0$ \ell $+jets (NN, selectionbased) [139], and $ \geq $1$ \ell $+jets [140]. A theory prediction at NNLO in perturbative QCD of the pair production cross section in the NWA is superimposed. 
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Figure 37c:
Observed and expected 95% CL upper limits on the production cross section of a pair of vectorlike T quarks decaying to $ \mathrm{t}\mathrm{Z} $ (upper left), $ \mathrm{t}\mathrm{H} $ (upper right), and $ \mathrm{b}\mathrm{W} $ (lower), as a function of the T quark mass, obtained by different analyses: 0$ \ell $+jets (NN, selectionbased) [139], and $ \geq $1$ \ell $+jets [140]. A theory prediction at NNLO in perturbative QCD of the pair production cross section in the NWA is superimposed. 
png pdf 
Figure 38:
Observed and expected 95% CL upper limits on the production cross section of a pair of vectorlike B quarks decaying to $ \mathrm{b}\mathrm{Z} $ (upper left), $ \mathrm{b}\mathrm{H} $ (upper right), and $ \mathrm{t}\mathrm{W} $ (lower), as a function of the B quark mass, obtained by different analyses: 0$ \ell $+jets (NN) [139], 0$ \ell $+jets [158], $ \geq $1$ \ell $+jets [140], 0$\ell$/2$ \ell $+jets [141], and the $ {\mathrm{B}} \overline{\mathrm{B}} $ combination of Section 6.5.1. A theory prediction at NNLO in perturbative QCD of the pair production cross section in the NWA is superimposed. 
png pdf 
Figure 38a:
Observed and expected 95% CL upper limits on the production cross section of a pair of vectorlike B quarks decaying to $ \mathrm{b}\mathrm{Z} $ (upper left), $ \mathrm{b}\mathrm{H} $ (upper right), and $ \mathrm{t}\mathrm{W} $ (lower), as a function of the B quark mass, obtained by different analyses: 0$ \ell $+jets (NN) [139], 0$ \ell $+jets [158], $ \geq $1$ \ell $+jets [140], 0$\ell$/2$ \ell $+jets [141], and the $ {\mathrm{B}} \overline{\mathrm{B}} $ combination of Section 6.5.1. A theory prediction at NNLO in perturbative QCD of the pair production cross section in the NWA is superimposed. 
png pdf 
Figure 38b:
Observed and expected 95% CL upper limits on the production cross section of a pair of vectorlike B quarks decaying to $ \mathrm{b}\mathrm{Z} $ (upper left), $ \mathrm{b}\mathrm{H} $ (upper right), and $ \mathrm{t}\mathrm{W} $ (lower), as a function of the B quark mass, obtained by different analyses: 0$ \ell $+jets (NN) [139], 0$ \ell $+jets [158], $ \geq $1$ \ell $+jets [140], 0$\ell$/2$ \ell $+jets [141], and the $ {\mathrm{B}} \overline{\mathrm{B}} $ combination of Section 6.5.1. A theory prediction at NNLO in perturbative QCD of the pair production cross section in the NWA is superimposed. 
png pdf 
Figure 38c:
Observed and expected 95% CL upper limits on the production cross section of a pair of vectorlike B quarks decaying to $ \mathrm{b}\mathrm{Z} $ (upper left), $ \mathrm{b}\mathrm{H} $ (upper right), and $ \mathrm{t}\mathrm{W} $ (lower), as a function of the B quark mass, obtained by different analyses: 0$ \ell $+jets (NN) [139], 0$ \ell $+jets [158], $ \geq $1$ \ell $+jets [140], 0$\ell$/2$ \ell $+jets [141], and the $ {\mathrm{B}} \overline{\mathrm{B}} $ combination of Section 6.5.1. A theory prediction at NNLO in perturbative QCD of the pair production cross section in the NWA is superimposed. 
png pdf 
Figure 39:
Observed and expected 95% CL upper limits on the production cross section of a pair of vectorlike T or B quarks, as functions of their mass, obtained by different analyses: 0$ \ell $+jets [158], $ \geq $1$ \ell $+jets [140], 0$\ell$/2$ \ell $+jets [141], and the $ {\mathrm{B}} \overline{\mathrm{B}} $ combination. A theory prediction at NNLO in perturbative QCD of the pair production cross section in the NWA is superimposed. Branching fractions of a singlet (upper and lower left panel) and doublet (upper and lower right panel) are assumed. 
png pdf 
Figure 39a:
Observed and expected 95% CL upper limits on the production cross section of a pair of vectorlike T or B quarks, as functions of their mass, obtained by different analyses: 0$ \ell $+jets [158], $ \geq $1$ \ell $+jets [140], 0$\ell$/2$ \ell $+jets [141], and the $ {\mathrm{B}} \overline{\mathrm{B}} $ combination. A theory prediction at NNLO in perturbative QCD of the pair production cross section in the NWA is superimposed. Branching fractions of a singlet (upper and lower left panel) and doublet (upper and lower right panel) are assumed. 
png pdf 
Figure 39b:
Observed and expected 95% CL upper limits on the production cross section of a pair of vectorlike T or B quarks, as functions of their mass, obtained by different analyses: 0$ \ell $+jets [158], $ \geq $1$ \ell $+jets [140], 0$\ell$/2$ \ell $+jets [141], and the $ {\mathrm{B}} \overline{\mathrm{B}} $ combination. A theory prediction at NNLO in perturbative QCD of the pair production cross section in the NWA is superimposed. Branching fractions of a singlet (upper and lower left panel) and doublet (upper and lower right panel) are assumed. 
png pdf 
Figure 39c:
Observed and expected 95% CL upper limits on the production cross section of a pair of vectorlike T or B quarks, as functions of their mass, obtained by different analyses: 0$ \ell $+jets [158], $ \geq $1$ \ell $+jets [140], 0$\ell$/2$ \ell $+jets [141], and the $ {\mathrm{B}} \overline{\mathrm{B}} $ combination. A theory prediction at NNLO in perturbative QCD of the pair production cross section in the NWA is superimposed. Branching fractions of a singlet (upper and lower left panel) and doublet (upper and lower right panel) are assumed. 
png pdf 
Figure 40:
Observed and expected 95% CL upper limits on the production cross section of a single T quark in association with a b quark (upper) or a t quark (lower row) in a singlet (upper and lower left) and doublet (lower right) scenario, versus the T quark mass, obtained by different analyses: $ {\mathrm{T}} \to\mathrm{b}\mathrm{W}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\nu/\mathrm{b}\ell\nu\,\mathrm{q}\mathrm{q} $ [148], $ {\mathrm{T}} \to\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\ell $ [143], $ {\mathrm{T}} \to\mathrm{t}\mathrm{H}+\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\mathrm{b}\mathrm{b} $ (mergedjet) [144], $ {\mathrm{T}} \to\mathrm{t}\mathrm{H}\to\mathrm{b}\ell\nu/\mathrm{b}\mathrm{q}\mathrm{q}\,\gamma\gamma $ [146], $ {\mathrm{T}} \to\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\nu\nu $ [145], $ {\mathrm{T}} \to\mathrm{t}\mathrm{H}+\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\mathrm{b}\mathrm{b} $ [147], and the single T quark combination of Section 6.5.2. Only the three analyses using the full Run2 data set are included in the single T quark combination. Two theory predictions at LO in perturbative QCD are superimposed, corresponding to different VLQ widths. 
png pdf 
Figure 40a:
Observed and expected 95% CL upper limits on the production cross section of a single T quark in association with a b quark (upper) or a t quark (lower row) in a singlet (upper and lower left) and doublet (lower right) scenario, versus the T quark mass, obtained by different analyses: $ {\mathrm{T}} \to\mathrm{b}\mathrm{W}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\nu/\mathrm{b}\ell\nu\,\mathrm{q}\mathrm{q} $ [148], $ {\mathrm{T}} \to\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\ell $ [143], $ {\mathrm{T}} \to\mathrm{t}\mathrm{H}+\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\mathrm{b}\mathrm{b} $ (mergedjet) [144], $ {\mathrm{T}} \to\mathrm{t}\mathrm{H}\to\mathrm{b}\ell\nu/\mathrm{b}\mathrm{q}\mathrm{q}\,\gamma\gamma $ [146], $ {\mathrm{T}} \to\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\nu\nu $ [145], $ {\mathrm{T}} \to\mathrm{t}\mathrm{H}+\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\mathrm{b}\mathrm{b} $ [147], and the single T quark combination of Section 6.5.2. Only the three analyses using the full Run2 data set are included in the single T quark combination. Two theory predictions at LO in perturbative QCD are superimposed, corresponding to different VLQ widths. 
png pdf 
Figure 40b:
Observed and expected 95% CL upper limits on the production cross section of a single T quark in association with a b quark (upper) or a t quark (lower row) in a singlet (upper and lower left) and doublet (lower right) scenario, versus the T quark mass, obtained by different analyses: $ {\mathrm{T}} \to\mathrm{b}\mathrm{W}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\nu/\mathrm{b}\ell\nu\,\mathrm{q}\mathrm{q} $ [148], $ {\mathrm{T}} \to\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\ell $ [143], $ {\mathrm{T}} \to\mathrm{t}\mathrm{H}+\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\mathrm{b}\mathrm{b} $ (mergedjet) [144], $ {\mathrm{T}} \to\mathrm{t}\mathrm{H}\to\mathrm{b}\ell\nu/\mathrm{b}\mathrm{q}\mathrm{q}\,\gamma\gamma $ [146], $ {\mathrm{T}} \to\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\nu\nu $ [145], $ {\mathrm{T}} \to\mathrm{t}\mathrm{H}+\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\mathrm{b}\mathrm{b} $ [147], and the single T quark combination of Section 6.5.2. Only the three analyses using the full Run2 data set are included in the single T quark combination. Two theory predictions at LO in perturbative QCD are superimposed, corresponding to different VLQ widths. 
png pdf 
Figure 40c:
Observed and expected 95% CL upper limits on the production cross section of a single T quark in association with a b quark (upper) or a t quark (lower row) in a singlet (upper and lower left) and doublet (lower right) scenario, versus the T quark mass, obtained by different analyses: $ {\mathrm{T}} \to\mathrm{b}\mathrm{W}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\nu/\mathrm{b}\ell\nu\,\mathrm{q}\mathrm{q} $ [148], $ {\mathrm{T}} \to\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\ell $ [143], $ {\mathrm{T}} \to\mathrm{t}\mathrm{H}+\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\mathrm{b}\mathrm{b} $ (mergedjet) [144], $ {\mathrm{T}} \to\mathrm{t}\mathrm{H}\to\mathrm{b}\ell\nu/\mathrm{b}\mathrm{q}\mathrm{q}\,\gamma\gamma $ [146], $ {\mathrm{T}} \to\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\nu\nu $ [145], $ {\mathrm{T}} \to\mathrm{t}\mathrm{H}+\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\mathrm{b}\mathrm{b} $ [147], and the single T quark combination of Section 6.5.2. Only the three analyses using the full Run2 data set are included in the single T quark combination. Two theory predictions at LO in perturbative QCD are superimposed, corresponding to different VLQ widths. 
png pdf 
Figure 41:
Observed and expected 95% CL upper limits on the production cross section of a single B quark in association with a b quark (upper row) or a t quark (lower) in a singlet (upper left and lower) and doublet (upper right) scenario, versus the B quark mass, obtained by different analyses: $ {\mathrm{B}} \to\mathrm{t}\mathrm{W}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\nu/\mathrm{q}\mathrm{q} $ [152], $ {\mathrm{B}} \to\mathrm{t}\mathrm{W}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\nu/\mathrm{b}\ell\nu\,\mathrm{q}\mathrm{q} $ [150], and $ {\mathrm{B}} \to\mathrm{b}\mathrm{H}\to\mathrm{b}\,\mathrm{b}\mathrm{b} $ [149]. Two theory predictions at LO in perturbative QCD are superimposed, corresponding to different VLQ widths. 
png pdf 
Figure 41a:
Observed and expected 95% CL upper limits on the production cross section of a single B quark in association with a b quark (upper row) or a t quark (lower) in a singlet (upper left and lower) and doublet (upper right) scenario, versus the B quark mass, obtained by different analyses: $ {\mathrm{B}} \to\mathrm{t}\mathrm{W}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\nu/\mathrm{q}\mathrm{q} $ [152], $ {\mathrm{B}} \to\mathrm{t}\mathrm{W}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\nu/\mathrm{b}\ell\nu\,\mathrm{q}\mathrm{q} $ [150], and $ {\mathrm{B}} \to\mathrm{b}\mathrm{H}\to\mathrm{b}\,\mathrm{b}\mathrm{b} $ [149]. Two theory predictions at LO in perturbative QCD are superimposed, corresponding to different VLQ widths. 
png pdf 
Figure 41b:
Observed and expected 95% CL upper limits on the production cross section of a single B quark in association with a b quark (upper row) or a t quark (lower) in a singlet (upper left and lower) and doublet (upper right) scenario, versus the B quark mass, obtained by different analyses: $ {\mathrm{B}} \to\mathrm{t}\mathrm{W}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\nu/\mathrm{q}\mathrm{q} $ [152], $ {\mathrm{B}} \to\mathrm{t}\mathrm{W}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\nu/\mathrm{b}\ell\nu\,\mathrm{q}\mathrm{q} $ [150], and $ {\mathrm{B}} \to\mathrm{b}\mathrm{H}\to\mathrm{b}\,\mathrm{b}\mathrm{b} $ [149]. Two theory predictions at LO in perturbative QCD are superimposed, corresponding to different VLQ widths. 
png pdf 
Figure 41c:
Observed and expected 95% CL upper limits on the production cross section of a single B quark in association with a b quark (upper row) or a t quark (lower) in a singlet (upper left and lower) and doublet (upper right) scenario, versus the B quark mass, obtained by different analyses: $ {\mathrm{B}} \to\mathrm{t}\mathrm{W}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\nu/\mathrm{q}\mathrm{q} $ [152], $ {\mathrm{B}} \to\mathrm{t}\mathrm{W}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\nu/\mathrm{b}\ell\nu\,\mathrm{q}\mathrm{q} $ [150], and $ {\mathrm{B}} \to\mathrm{b}\mathrm{H}\to\mathrm{b}\,\mathrm{b}\mathrm{b} $ [149]. Two theory predictions at LO in perturbative QCD are superimposed, corresponding to different VLQ widths. 
png pdf 
Figure 42:
Observed and expected 95% CL upper limits on the coupling strength $ \kappa $ for single T quark production in a singlet (upper) and doublet (lower) scenarios as functions of the T quark mass, obtained by different analyses: $ {\mathrm{T}} \to\mathrm{t}\mathrm{H}+\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\mathrm{b}\mathrm{b} $ (mergedjet) [144], $ {\mathrm{T}} \to\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\ell $ [143], $ {\mathrm{T}} \to\mathrm{b}\mathrm{W}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\nu/\mathrm{b}\ell\nu\,\mathrm{q}\mathrm{q} $ [148], $ {\mathrm{T}} \to\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\ell $ [143], $ {\mathrm{T}} \to\mathrm{t}\mathrm{H}\to\mathrm{b}\ell\nu/\mathrm{b}\mathrm{q}\mathrm{q}\,\gamma\gamma $ [146], $ {\mathrm{T}} \to\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\nu\nu $ [145], $ {\mathrm{T}} \to\mathrm{t}\mathrm{H}+\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\mathrm{b}\mathrm{b} $ [147], and the single T quark combination of Section 6.5.2. Only the three analyses using the full Run2 data set are included in the single T quark combination. Two theory predictions at LO in perturbative QCD are superimposed, corresponding to different VLQ widths. 
png pdf 
Figure 42a:
Observed and expected 95% CL upper limits on the coupling strength $ \kappa $ for single T quark production in a singlet (upper) and doublet (lower) scenarios as functions of the T quark mass, obtained by different analyses: $ {\mathrm{T}} \to\mathrm{t}\mathrm{H}+\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\mathrm{b}\mathrm{b} $ (mergedjet) [144], $ {\mathrm{T}} \to\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\ell $ [143], $ {\mathrm{T}} \to\mathrm{b}\mathrm{W}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\nu/\mathrm{b}\ell\nu\,\mathrm{q}\mathrm{q} $ [148], $ {\mathrm{T}} \to\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\ell $ [143], $ {\mathrm{T}} \to\mathrm{t}\mathrm{H}\to\mathrm{b}\ell\nu/\mathrm{b}\mathrm{q}\mathrm{q}\,\gamma\gamma $ [146], $ {\mathrm{T}} \to\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\nu\nu $ [145], $ {\mathrm{T}} \to\mathrm{t}\mathrm{H}+\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\mathrm{b}\mathrm{b} $ [147], and the single T quark combination of Section 6.5.2. Only the three analyses using the full Run2 data set are included in the single T quark combination. Two theory predictions at LO in perturbative QCD are superimposed, corresponding to different VLQ widths. 
png pdf 
Figure 42b:
Observed and expected 95% CL upper limits on the coupling strength $ \kappa $ for single T quark production in a singlet (upper) and doublet (lower) scenarios as functions of the T quark mass, obtained by different analyses: $ {\mathrm{T}} \to\mathrm{t}\mathrm{H}+\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\mathrm{b}\mathrm{b} $ (mergedjet) [144], $ {\mathrm{T}} \to\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\ell $ [143], $ {\mathrm{T}} \to\mathrm{b}\mathrm{W}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\nu/\mathrm{b}\ell\nu\,\mathrm{q}\mathrm{q} $ [148], $ {\mathrm{T}} \to\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\ell $ [143], $ {\mathrm{T}} \to\mathrm{t}\mathrm{H}\to\mathrm{b}\ell\nu/\mathrm{b}\mathrm{q}\mathrm{q}\,\gamma\gamma $ [146], $ {\mathrm{T}} \to\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\nu\nu $ [145], $ {\mathrm{T}} \to\mathrm{t}\mathrm{H}+\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\mathrm{b}\mathrm{b} $ [147], and the single T quark combination of Section 6.5.2. Only the three analyses using the full Run2 data set are included in the single T quark combination. Two theory predictions at LO in perturbative QCD are superimposed, corresponding to different VLQ widths. 
png pdf 
Figure 43:
Observed and expected 95% CL upper limits on the coupling strength $ \kappa $ for single B quark production in a singlet (upper) and doublet (lower) scenarios as functions of the B quark mass, obtained by different analyses: $ {\mathrm{B}} \to\mathrm{t}\mathrm{W}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\nu/\mathrm{q}\mathrm{q} $ [152], $ {\mathrm{B}} \to\mathrm{b}\mathrm{H}\to\mathrm{b}\,\mathrm{b}\mathrm{b} $ [149], and $ {\mathrm{B}} \to\mathrm{t}\mathrm{W}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\nu/\mathrm{b}\ell\nu\,\mathrm{q}\mathrm{q} $ [150]. Two theory predictions at LO in perturbative QCD are superimposed, corresponding to different VLQ widths. 
png pdf 
Figure 43a:
Observed and expected 95% CL upper limits on the coupling strength $ \kappa $ for single B quark production in a singlet (upper) and doublet (lower) scenarios as functions of the B quark mass, obtained by different analyses: $ {\mathrm{B}} \to\mathrm{t}\mathrm{W}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\nu/\mathrm{q}\mathrm{q} $ [152], $ {\mathrm{B}} \to\mathrm{b}\mathrm{H}\to\mathrm{b}\,\mathrm{b}\mathrm{b} $ [149], and $ {\mathrm{B}} \to\mathrm{t}\mathrm{W}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\nu/\mathrm{b}\ell\nu\,\mathrm{q}\mathrm{q} $ [150]. Two theory predictions at LO in perturbative QCD are superimposed, corresponding to different VLQ widths. 
png pdf 
Figure 43b:
Observed and expected 95% CL upper limits on the coupling strength $ \kappa $ for single B quark production in a singlet (upper) and doublet (lower) scenarios as functions of the B quark mass, obtained by different analyses: $ {\mathrm{B}} \to\mathrm{t}\mathrm{W}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\nu/\mathrm{q}\mathrm{q} $ [152], $ {\mathrm{B}} \to\mathrm{b}\mathrm{H}\to\mathrm{b}\,\mathrm{b}\mathrm{b} $ [149], and $ {\mathrm{B}} \to\mathrm{t}\mathrm{W}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\nu/\mathrm{b}\ell\nu\,\mathrm{q}\mathrm{q} $ [150]. Two theory predictions at LO in perturbative QCD are superimposed, corresponding to different VLQ widths. 
png pdf 
Figure 44:
Observed and expected 95% CL upper limits on the coupling strength $ \kappa $ for single $\mathrm{X}_{5/3}$ (left) and $\mathrm{Y}_{4/3}$ (right) production as functions of the VLQ mass, obtained by different analyses: $ {\mathrm{X}_{5/3}} \to\mathrm{t}\mathrm{W}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\nu/\mathrm{q}\mathrm{q} $ [152], $ {\mathrm{X}_{5/3}} \to\mathrm{t}\mathrm{W}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\nu/\mathrm{b}\ell\nu\,\mathrm{q}\mathrm{q} $ [150], and $ {\mathrm{Y}_{4/3}} \to\mathrm{b}\mathrm{W}\to\mathrm{b}\,\ell\nu $ [148]. 
png pdf 
Figure 44a:
Observed and expected 95% CL upper limits on the coupling strength $ \kappa $ for single $\mathrm{X}_{5/3}$ (left) and $\mathrm{Y}_{4/3}$ (right) production as functions of the VLQ mass, obtained by different analyses: $ {\mathrm{X}_{5/3}} \to\mathrm{t}\mathrm{W}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\nu/\mathrm{q}\mathrm{q} $ [152], $ {\mathrm{X}_{5/3}} \to\mathrm{t}\mathrm{W}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\nu/\mathrm{b}\ell\nu\,\mathrm{q}\mathrm{q} $ [150], and $ {\mathrm{Y}_{4/3}} \to\mathrm{b}\mathrm{W}\to\mathrm{b}\,\ell\nu $ [148]. 
png pdf 
Figure 44b:
Observed and expected 95% CL upper limits on the coupling strength $ \kappa $ for single $\mathrm{X}_{5/3}$ (left) and $\mathrm{Y}_{4/3}$ (right) production as functions of the VLQ mass, obtained by different analyses: $ {\mathrm{X}_{5/3}} \to\mathrm{t}\mathrm{W}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\nu/\mathrm{q}\mathrm{q} $ [152], $ {\mathrm{X}_{5/3}} \to\mathrm{t}\mathrm{W}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\nu/\mathrm{b}\ell\nu\,\mathrm{q}\mathrm{q} $ [150], and $ {\mathrm{Y}_{4/3}} \to\mathrm{b}\mathrm{W}\to\mathrm{b}\,\ell\nu $ [148]. 
png pdf 
Figure 45:
Distributions of the $ S_{\mathrm{T}} $ observable for signal and background processes (left), with signal distributions scaled by factors of 20, 2000, and 200\,000, depending on the T quark mass, and expected upper limits at 95% CL on the $ {\mathrm{T}} \overline{\mathrm{T}} $ production cross section (right). The inner (green) and the outer (yellow) bands indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the backgroundonly hypothesis. Figures adapted from Ref. [169]. 
png pdf 
Figure 45a:
Distributions of the $ S_{\mathrm{T}} $ observable for signal and background processes (left), with signal distributions scaled by factors of 20, 2000, and 200\,000, depending on the T quark mass, and expected upper limits at 95% CL on the $ {\mathrm{T}} \overline{\mathrm{T}} $ production cross section (right). The inner (green) and the outer (yellow) bands indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the backgroundonly hypothesis. Figures adapted from Ref. [169]. 
png pdf 
Figure 45b:
Distributions of the $ S_{\mathrm{T}} $ observable for signal and background processes (left), with signal distributions scaled by factors of 20, 2000, and 200\,000, depending on the T quark mass, and expected upper limits at 95% CL on the $ {\mathrm{T}} \overline{\mathrm{T}} $ production cross section (right). The inner (green) and the outer (yellow) bands indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the backgroundonly hypothesis. Figures adapted from Ref. [169]. 
png pdf 
Figure 46:
Expected significances for T quark pair production as a function of the integrated luminosity at the HLLHC, assuming equal branching fractions for $ {\mathrm{T}} \to\mathrm{b}\mathrm{W} $, $ \mathrm{t}\mathrm{Z} $, $ \mathrm{t}\mathrm{H} $ decays (left). Discovery potential at three and five standard deviations for T quark pairs, as a function of the T quark mass and the integrated luminosity (right). Figures adapted from Ref. [169]. 
png pdf 
Figure 46a:
Expected significances for T quark pair production as a function of the integrated luminosity at the HLLHC, assuming equal branching fractions for $ {\mathrm{T}} \to\mathrm{b}\mathrm{W} $, $ \mathrm{t}\mathrm{Z} $, $ \mathrm{t}\mathrm{H} $ decays (left). Discovery potential at three and five standard deviations for T quark pairs, as a function of the T quark mass and the integrated luminosity (right). Figures adapted from Ref. [169]. 
png pdf 
Figure 46b:
Expected significances for T quark pair production as a function of the integrated luminosity at the HLLHC, assuming equal branching fractions for $ {\mathrm{T}} \to\mathrm{b}\mathrm{W} $, $ \mathrm{t}\mathrm{Z} $, $ \mathrm{t}\mathrm{H} $ decays (left). Discovery potential at three and five standard deviations for T quark pairs, as a function of the T quark mass and the integrated luminosity (right). Figures adapted from Ref. [169]. 
png pdf 
Figure 47:
Example processes illustrating production and decay of doublet (left) and singlet (right) VLL pairs at the LHC that result in multilepton final states. 
png pdf 
Figure 47a:
Example processes illustrating production and decay of doublet (left) and singlet (right) VLL pairs at the LHC that result in multilepton final states. 
png pdf 
Figure 47b:
Example processes illustrating production and decay of doublet (left) and singlet (right) VLL pairs at the LHC that result in multilepton final states. 
png pdf 
Figure 48:
Example diagrams showing $ s $channel EW production of VLL pairs through SM bosons, as expected at the LHC (left two diagrams). In these diagrams, L represents either the neutral VLL, N, or the charged VLL, E. The VLL decays are mediated by a vector leptoquark U (right two diagrams). In the 4321 model, these decays are primarily to thirdgeneration leptons and quarks. 
png pdf 
Figure 48a:
Example diagrams showing $ s $channel EW production of VLL pairs through SM bosons, as expected at the LHC (left two diagrams). In these diagrams, L represents either the neutral VLL, N, or the charged VLL, E. The VLL decays are mediated by a vector leptoquark U (right two diagrams). In the 4321 model, these decays are primarily to thirdgeneration leptons and quarks. 
png pdf 
Figure 48b:
Example diagrams showing $ s $channel EW production of VLL pairs through SM bosons, as expected at the LHC (left two diagrams). In these diagrams, L represents either the neutral VLL, N, or the charged VLL, E. The VLL decays are mediated by a vector leptoquark U (right two diagrams). In the 4321 model, these decays are primarily to thirdgeneration leptons and quarks. 
png pdf 
Figure 48c:
Example diagrams showing $ s $channel EW production of VLL pairs through SM bosons, as expected at the LHC (left two diagrams). In these diagrams, L represents either the neutral VLL, N, or the charged VLL, E. The VLL decays are mediated by a vector leptoquark U (right two diagrams). In the 4321 model, these decays are primarily to thirdgeneration leptons and quarks. 
png pdf 
Figure 48d:
Example diagrams showing $ s $channel EW production of VLL pairs through SM bosons, as expected at the LHC (left two diagrams). In these diagrams, L represents either the neutral VLL, N, or the charged VLL, E. The VLL decays are mediated by a vector leptoquark U (right two diagrams). In the 4321 model, these decays are primarily to thirdgeneration leptons and quarks. 
png pdf 
Figure 49:
The $ L_{\mathrm{T}} $ distribution in 3$\mathrm{e}/\mu$, 2$\mathrm{e}/\mu $1$ \tau_{\mathrm{h}}$, and 1$\mathrm{e}/\mu $2$ \tau_{\mathrm{h}}$ events (left), and the invariant mass distribution of the OS differentflavor ($ m_{\text{OSDF}} $) light lepton and tau lepton pair in 2$\mathrm{e}/\mu $1$ \tau_{\mathrm{h}}$ and 1$\mathrm{e}/\mu $2$ \tau_{\mathrm{h}}$ events (right). The rightmost bin contains the overflow events. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the quadratic sum of statistical and systematic uncertainties in the SM background prediction. The expected SM background distributions and the uncertainties are shown after fitting the data under the backgroundonly hypothesis. For illustration, an example signal hypothesis for the production of the vectorlike tau lepton in the doublet scenario with a mass of 1 TeV, before the fit, is overlaid. Figures adapted from Ref. [202]. 
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Figure 49a:
The $ L_{\mathrm{T}} $ distribution in 3$\mathrm{e}/\mu$, 2$\mathrm{e}/\mu $1$ \tau_{\mathrm{h}}$, and 1$\mathrm{e}/\mu $2$ \tau_{\mathrm{h}}$ events (left), and the invariant mass distribution of the OS differentflavor ($ m_{\text{OSDF}} $) light lepton and tau lepton pair in 2$\mathrm{e}/\mu $1$ \tau_{\mathrm{h}}$ and 1$\mathrm{e}/\mu $2$ \tau_{\mathrm{h}}$ events (right). The rightmost bin contains the overflow events. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the quadratic sum of statistical and systematic uncertainties in the SM background prediction. The expected SM background distributions and the uncertainties are shown after fitting the data under the backgroundonly hypothesis. For illustration, an example signal hypothesis for the production of the vectorlike tau lepton in the doublet scenario with a mass of 1 TeV, before the fit, is overlaid. Figures adapted from Ref. [202]. 
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Figure 49b:
The $ L_{\mathrm{T}} $ distribution in 3$\mathrm{e}/\mu$, 2$\mathrm{e}/\mu $1$ \tau_{\mathrm{h}}$, and 1$\mathrm{e}/\mu $2$ \tau_{\mathrm{h}}$ events (left), and the invariant mass distribution of the OS differentflavor ($ m_{\text{OSDF}} $) light lepton and tau lepton pair in 2$\mathrm{e}/\mu $1$ \tau_{\mathrm{h}}$ and 1$\mathrm{e}/\mu $2$ \tau_{\mathrm{h}}$ events (right). The rightmost bin contains the overflow events. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the quadratic sum of statistical and systematic uncertainties in the SM background prediction. The expected SM background distributions and the uncertainties are shown after fitting the data under the backgroundonly hypothesis. For illustration, an example signal hypothesis for the production of the vectorlike tau lepton in the doublet scenario with a mass of 1 TeV, before the fit, is overlaid. Figures adapted from Ref. [202]. 
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Figure 50:
The VLLH BDT regions for the fourlepton channels for the full Run2 data set. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the quadratic sum of statistical and systematic uncertainties in the SM background prediction. The expected SM background distributions and the uncertainties are shown after fitting the data under the backgroundonly hypothesis. For illustration, an example signal hypothesis for the production of the vectorlike tau lepton in the doublet scenario for a VLL mass of 900 GeV, before the fit, is overlaid. Figure adapted from Ref. [202]. 
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Figure 51:
Observed and expected upper limits at 95% CL on the production cross section for the vectorlike tau leptons in the doublet model (left) and singlet model (right). For the doublet vectorlike lepton model, to the left of the vertical dashed gray line, the limits are shown from the modelindependent scheme, while to the right the limits are shown from the model dependent BDT regions. For the singlet vectorlike lepton model, the limit is shown from the modelindependent scheme for all masses. Figures adapted from Ref. [202]. 
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Figure 51a:
Observed and expected upper limits at 95% CL on the production cross section for the vectorlike tau leptons in the doublet model (left) and singlet model (right). For the doublet vectorlike lepton model, to the left of the vertical dashed gray line, the limits are shown from the modelindependent scheme, while to the right the limits are shown from the model dependent BDT regions. For the singlet vectorlike lepton model, the limit is shown from the modelindependent scheme for all masses. Figures adapted from Ref. [202]. 
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Figure 51b:
Observed and expected upper limits at 95% CL on the production cross section for the vectorlike tau leptons in the doublet model (left) and singlet model (right). For the doublet vectorlike lepton model, to the left of the vertical dashed gray line, the limits are shown from the modelindependent scheme, while to the right the limits are shown from the model dependent BDT regions. For the singlet vectorlike lepton model, the limit is shown from the modelindependent scheme for all masses. Figures adapted from Ref. [202]. 
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Figure 52:
Postfit distributions for the 2018 data set in the 1$ \tau_\mathrm{h} $ (left) and 2$ \tau_\mathrm{h} $ (right) channels. The upper row shows the backgroundonly fit and the lower row shows the fit including the signal. Not shown here, but included in the fit, are the 2017 data and the 0$ \tau_\mathrm{h} $ channel. Figures taken from Ref. [203]. 
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Figure 52a:
Postfit distributions for the 2018 data set in the 1$ \tau_\mathrm{h} $ (left) and 2$ \tau_\mathrm{h} $ (right) channels. The upper row shows the backgroundonly fit and the lower row shows the fit including the signal. Not shown here, but included in the fit, are the 2017 data and the 0$ \tau_\mathrm{h} $ channel. Figures taken from Ref. [203]. 
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Figure 52b:
Postfit distributions for the 2018 data set in the 1$ \tau_\mathrm{h} $ (left) and 2$ \tau_\mathrm{h} $ (right) channels. The upper row shows the backgroundonly fit and the lower row shows the fit including the signal. Not shown here, but included in the fit, are the 2017 data and the 0$ \tau_\mathrm{h} $ channel. Figures taken from Ref. [203]. 
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Figure 52c:
Postfit distributions for the 2018 data set in the 1$ \tau_\mathrm{h} $ (left) and 2$ \tau_\mathrm{h} $ (right) channels. The upper row shows the backgroundonly fit and the lower row shows the fit including the signal. Not shown here, but included in the fit, are the 2017 data and the 0$ \tau_\mathrm{h} $ channel. Figures taken from Ref. [203]. 
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Figure 52d:
Postfit distributions for the 2018 data set in the 1$ \tau_\mathrm{h} $ (left) and 2$ \tau_\mathrm{h} $ (right) channels. The upper row shows the backgroundonly fit and the lower row shows the fit including the signal. Not shown here, but included in the fit, are the 2017 data and the 0$ \tau_\mathrm{h} $ channel. Figures taken from Ref. [203]. 
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Figure 53:
Expected and observed 95% CL upper limits on the product of the VLL pair production cross section and the branching fraction to thirdgeneration quarks and leptons, combining the 2017 and 2018 data and all $ \tau_\mathrm{h} $ multiplicity channels. The theoretical prediction in the 4321 model for EW production of VLLs is also shown. Figure adapted from Ref. [203]. 
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Figure 54:
Expected HLLHC exclusion limits for vectorlike electrons (upper row), muons (middle row), and tau leptons (lower row) in the doublet model (left) and the singlet model (right). For both models, limits are calculated using $ L_{\mathrm{T}}+p_{\mathrm{T}}^\text{miss} $ from the model independent SRs for all masses. 
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Figure 54a:
Expected HLLHC exclusion limits for vectorlike electrons (upper row), muons (middle row), and tau leptons (lower row) in the doublet model (left) and the singlet model (right). For both models, limits are calculated using $ L_{\mathrm{T}}+p_{\mathrm{T}}^\text{miss} $ from the model independent SRs for all masses. 
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Figure 54b:
Expected HLLHC exclusion limits for vectorlike electrons (upper row), muons (middle row), and tau leptons (lower row) in the doublet model (left) and the singlet model (right). For both models, limits are calculated using $ L_{\mathrm{T}}+p_{\mathrm{T}}^\text{miss} $ from the model independent SRs for all masses. 
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Figure 54c:
Expected HLLHC exclusion limits for vectorlike electrons (upper row), muons (middle row), and tau leptons (lower row) in the doublet model (left) and the singlet model (right). For both models, limits are calculated using $ L_{\mathrm{T}}+p_{\mathrm{T}}^\text{miss} $ from the model independent SRs for all masses. 
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Figure 54d:
Expected HLLHC exclusion limits for vectorlike electrons (upper row), muons (middle row), and tau leptons (lower row) in the doublet model (left) and the singlet model (right). For both models, limits are calculated using $ L_{\mathrm{T}}+p_{\mathrm{T}}^\text{miss} $ from the model independent SRs for all masses. 
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Figure 54e:
Expected HLLHC exclusion limits for vectorlike electrons (upper row), muons (middle row), and tau leptons (lower row) in the doublet model (left) and the singlet model (right). For both models, limits are calculated using $ L_{\mathrm{T}}+p_{\mathrm{T}}^\text{miss} $ from the model independent SRs for all masses. 
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Figure 54f:
Expected HLLHC exclusion limits for vectorlike electrons (upper row), muons (middle row), and tau leptons (lower row) in the doublet model (left) and the singlet model (right). For both models, limits are calculated using $ L_{\mathrm{T}}+p_{\mathrm{T}}^\text{miss} $ from the model independent SRs for all masses. 
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Figure 55:
Representative Feynman diagram of a Majorana HNL, labeled as N, produced through the decay of a W or Z boson. 
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Figure 56:
Representative Feynman diagram of a Majorana HNL, labeled as N, produced through the $ \mathrm{W}\gamma $ fusion process and with two charged leptons and jets in the final state. 
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Figure 57:
Representative Feynman diagram showing the semileptonic decay of a $ {\mathrm{B}} $ meson into the primary lepton ($\ell_{\mathrm{P}}$), a hadronic system ($ \mathrm{X} $), and a neutrino, which contains the admixture of an HNL. The HNL propagates and decays weakly into a charged lepton $\ell^{\pm}$ and a charged pion $ \pi^{\mp} $. 
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Figure 58:
Example Feynman diagrams of VBF processes with heavy Majorana neutrino production (left) and processes mediated by the Weinberg operator (right). 
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Figure 58a:
Example Feynman diagrams of VBF processes with heavy Majorana neutrino production (left) and processes mediated by the Weinberg operator (right). 
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Figure 58b:
Example Feynman diagrams of VBF processes with heavy Majorana neutrino production (left) and processes mediated by the Weinberg operator (right). 
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Figure 59:
Example Feynman diagrams illustrating production and decay of $Type III$ seesaw heavy lepton $ \Sigma $ pairs at the LHC that may result in multilepton final states. 
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Figure 59a:
Example Feynman diagrams illustrating production and decay of $Type III$ seesaw heavy lepton $ \Sigma $ pairs at the LHC that may result in multilepton final states. 
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Figure 59b:
Example Feynman diagrams illustrating production and decay of $Type III$ seesaw heavy lepton $ \Sigma $ pairs at the LHC that may result in multilepton final states. 
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Figure 60:
Representative Feynman diagrams for the production of a heavy Majorana neutrino, labeled as $\ell$, via the decay of a $ \mathrm{W_R} $ (left) and $ \mathrm{Z}^{'} $ boson (right). 
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Figure 60a:
Representative Feynman diagrams for the production of a heavy Majorana neutrino, labeled as $\ell$, via the decay of a $ \mathrm{W_R} $ (left) and $ \mathrm{Z}^{'} $ boson (right). 
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Figure 60b:
Representative Feynman diagrams for the production of a heavy Majorana neutrino, labeled as $\ell$, via the decay of a $ \mathrm{W_R} $ (left) and $ \mathrm{Z}^{'} $ boson (right). 
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Figure 61:
The fermion interaction as a sum of gauge (center) and contact (right) interaction contributions. 
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Figure 62:
Example diagrams for the decay of a heavy composite Majorana neutrino to $ \ell\mathrm{q}{\bar{\mathrm{q}}{\prime}} $. 
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Figure 63:
Expected (observed) upper limits at 95% CL shown with a dashed (solid) black line, derived on heavy neutrino mixing matrix elements $ V_{\mathrm{eN}}^{2} $, $ V_{\mu\mathrm{N}}^{2} $, and $ V_{\mathrm{eN}}V_{\mu\mathrm{N}}^\ast^2/(V_{\mathrm{eN}}^{2}+V_{\mu\mathrm{N}}^{2}) $ as functions of the HNL mass. The dashed cyan line shows constraints from EW precision observables (EWPO) [248]. The upper limits from other direct searches at the DELPHI experiment [249], the L3 experiment [250,251], and the ATLAS experiment [252] are superimposed. Also shown are the upper limits from the CMS experiment at $ \sqrt{s}= $ 8 TeV using the 2012 data set [247] with a solid red line, and the search in the trilepton final state [253] based on the same 2016 data set as used in this analysis with a dashed red line. Figures adapted from Ref. [246]. 
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Figure 63a:
Expected (observed) upper limits at 95% CL shown with a dashed (solid) black line, derived on heavy neutrino mixing matrix elements $ V_{\mathrm{eN}}^{2} $, $ V_{\mu\mathrm{N}}^{2} $, and $ V_{\mathrm{eN}}V_{\mu\mathrm{N}}^\ast^2/(V_{\mathrm{eN}}^{2}+V_{\mu\mathrm{N}}^{2}) $ as functions of the HNL mass. The dashed cyan line shows constraints from EW precision observables (EWPO) [248]. The upper limits from other direct searches at the DELPHI experiment [249], the L3 experiment [250,251], and the ATLAS experiment [252] are superimposed. Also shown are the upper limits from the CMS experiment at $ \sqrt{s}= $ 8 TeV using the 2012 data set [247] with a solid red line, and the search in the trilepton final state [253] based on the same 2016 data set as used in this analysis with a dashed red line. Figures adapted from Ref. [246]. 
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Figure 63b:
Expected (observed) upper limits at 95% CL shown with a dashed (solid) black line, derived on heavy neutrino mixing matrix elements $ V_{\mathrm{eN}}^{2} $, $ V_{\mu\mathrm{N}}^{2} $, and $ V_{\mathrm{eN}}V_{\mu\mathrm{N}}^\ast^2/(V_{\mathrm{eN}}^{2}+V_{\mu\mathrm{N}}^{2}) $ as functions of the HNL mass. The dashed cyan line shows constraints from EW precision observables (EWPO) [248]. The upper limits from other direct searches at the DELPHI experiment [249], the L3 experiment [250,251], and the ATLAS experiment [252] are superimposed. Also shown are the upper limits from the CMS experiment at $ \sqrt{s}= $ 8 TeV using the 2012 data set [247] with a solid red line, and the search in the trilepton final state [253] based on the same 2016 data set as used in this analysis with a dashed red line. Figures adapted from Ref. [246]. 
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Figure 63c:
Expected (observed) upper limits at 95% CL shown with a dashed (solid) black line, derived on heavy neutrino mixing matrix elements $ V_{\mathrm{eN}}^{2} $, $ V_{\mu\mathrm{N}}^{2} $, and $ V_{\mathrm{eN}}V_{\mu\mathrm{N}}^\ast^2/(V_{\mathrm{eN}}^{2}+V_{\mu\mathrm{N}}^{2}) $ as functions of the HNL mass. The dashed cyan line shows constraints from EW precision observables (EWPO) [248]. The upper limits from other direct searches at the DELPHI experiment [249], the L3 experiment [250,251], and the ATLAS experiment [252] are superimposed. Also shown are the upper limits from the CMS experiment at $ \sqrt{s}= $ 8 TeV using the 2012 data set [247] with a solid red line, and the search in the trilepton final state [253] based on the same 2016 data set as used in this analysis with a dashed red line. Figures adapted from Ref. [246]. 
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Figure 64:
Expected (observed) upper limits at 95% CL derived on heavy neutrino mixing parameters $ V_{\mathrm{eN}}^{2} $, $ V_{\mu\mathrm{N}}^{2} $, and \mixparsq$ \tau \mathrm{N} $ as functions of the HNL mass $ m_{\mathrm{N}} $. No exclusion limit is evaluated for the range 75 $ < m_{\mathrm{N}} < $ 85 GeV, where HNL production through W boson decays has a resonance and the analysis strategy changes from using the low or highmass region. The area above the solid (dashed) black curve indicates the observed (expected) exclusion region. The upper limits from other direct searches at the DELPHI experiment [249] and the CMS experiment [253,255,256,257] are superimposed. Figures taken from Ref. [254]. 
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Figure 64a:
Expected (observed) upper limits at 95% CL derived on heavy neutrino mixing parameters $ V_{\mathrm{eN}}^{2} $, $ V_{\mu\mathrm{N}}^{2} $, and \mixparsq$ \tau \mathrm{N} $ as functions of the HNL mass $ m_{\mathrm{N}} $. No exclusion limit is evaluated for the range 75 $ < m_{\mathrm{N}} < $ 85 GeV, where HNL production through W boson decays has a resonance and the analysis strategy changes from using the low or highmass region. The area above the solid (dashed) black curve indicates the observed (expected) exclusion region. The upper limits from other direct searches at the DELPHI experiment [249] and the CMS experiment [253,255,256,257] are superimposed. Figures taken from Ref. [254]. 
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Figure 64b:
Expected (observed) upper limits at 95% CL derived on heavy neutrino mixing parameters $ V_{\mathrm{eN}}^{2} $, $ V_{\mu\mathrm{N}}^{2} $, and \mixparsq$ \tau \mathrm{N} $ as functions of the HNL mass $ m_{\mathrm{N}} $. No exclusion limit is evaluated for the range 75 $ < m_{\mathrm{N}} < $ 85 GeV, where HNL production through W boson decays has a resonance and the analysis strategy changes from using the low or highmass region. The area above the solid (dashed) black curve indicates the observed (expected) exclusion region. The upper limits from other direct searches at the DELPHI experiment [249] and the CMS experiment [253,255,256,257] are superimposed. Figures taken from Ref. [254]. 
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Figure 64c:
Expected (observed) upper limits at 95% CL derived on heavy neutrino mixing parameters $ V_{\mathrm{eN}}^{2} $, $ V_{\mu\mathrm{N}}^{2} $, and \mixparsq$ \tau \mathrm{N} $ as functions of the HNL mass $ m_{\mathrm{N}} $. No exclusion limit is evaluated for the range 75 $ < m_{\mathrm{N}} < $ 85 GeV, where HNL production through W boson decays has a resonance and the analysis strategy changes from using the low or highmass region. The area above the solid (dashed) black curve indicates the observed (expected) exclusion region. The upper limits from other direct searches at the DELPHI experiment [249] and the CMS experiment [253,255,256,257] are superimposed. Figures taken from Ref. [254]. 
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Figure 65:
Upper limits on $ V_{\mu\mathrm{N}}^{2} $ at 95% CL as a function of $ m_{\mathrm{N}} $. The black dashed curve shows the median expected upper limit, while the inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the backgroundonly hypothesis. The solid black curve is the observed upper limit [256]. The red dashed curve displays the observed upper limits from Ref. [253], while the blue dashed curve shows the observed upper limits from Ref. [246]. Figure adapted from Ref. [256]. 
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Figure 66:
Expected and observed background yields in 48 categories for resolved (left) and boosted (right) events. Two benchmark HNL scenarios are overlaid with masses of 4.5 and 10 GeV, and proper decay lengths of $ c\tau_{\mathrm{N}}= $ 100 and 1 mm, respectively. The $ d_{xy}^{\text{sig}} $ quantity is the significance of the impact parameter of the second lepton track. Figures taken from Ref. [257]. 
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Figure 66a:
Expected and observed background yields in 48 categories for resolved (left) and boosted (right) events. Two benchmark HNL scenarios are overlaid with masses of 4.5 and 10 GeV, and proper decay lengths of $ c\tau_{\mathrm{N}}= $ 100 and 1 mm, respectively. The $ d_{xy}^{\text{sig}} $ quantity is the significance of the impact parameter of the second lepton track. Figures taken from Ref. [257]. 
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Figure 66b:
Expected and observed background yields in 48 categories for resolved (left) and boosted (right) events. Two benchmark HNL scenarios are overlaid with masses of 4.5 and 10 GeV, and proper decay lengths of $ c\tau_{\mathrm{N}}= $ 100 and 1 mm, respectively. The $ d_{xy}^{\text{sig}} $ quantity is the significance of the impact parameter of the second lepton track. Figures taken from Ref. [257]. 
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Figure 67:
Observed 95% CL lower limits on the mass (left) and the proper lifetime (right) for Majorana HNL production with $ c\tau_{\mathrm{N}}= $ 1 mm and $ m_{\mathrm{N}}= $ 4.5 GeV, respectively, as functions of the relative coupling strengths to electrons ($ f_{\mathrm{e}} $), muons ($ f_{\mu} $), and tau leptons ($ f_{\tau} $). Figures adapted from Ref. [257]. 
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Figure 67a:
Observed 95% CL lower limits on the mass (left) and the proper lifetime (right) for Majorana HNL production with $ c\tau_{\mathrm{N}}= $ 1 mm and $ m_{\mathrm{N}}= $ 4.5 GeV, respectively, as functions of the relative coupling strengths to electrons ($ f_{\mathrm{e}} $), muons ($ f_{\mu} $), and tau leptons ($ f_{\tau} $). Figures adapted from Ref. [257]. 
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Figure 67b:
Observed 95% CL lower limits on the mass (left) and the proper lifetime (right) for Majorana HNL production with $ c\tau_{\mathrm{N}}= $ 1 mm and $ m_{\mathrm{N}}= $ 4.5 GeV, respectively, as functions of the relative coupling strengths to electrons ($ f_{\mathrm{e}} $), muons ($ f_{\mu} $), and tau leptons ($ f_{\tau} $). Figures adapted from Ref. [257]. 
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Figure 68:
Comparison between the number of observed events in data and the background predictions (filled histograms) in the SR for $ \mathrm{e}\mathrm{e}\mathrm{X} $ (upper) and $ \mu\mu\mathrm{X} $ (lower) final states. The hatched band indicates the total systematic and statistical uncertainty in the background prediction. The lower panels indicate the ratio between the observed data and the prediction, where missing points indicate that the ratio lies outside the axis range. Predictions for signal events are shown for several benchmark hypotheses for Majorana HNL production: $ m_{\mathrm{N}}= $ 2 GeV and $ V_{\ell\mathrm{N}}^{2}=$ 0.8 $\times$ 10$^{4} $ (HNL2), $ m_{\mathrm{N}}= $ 6 GeV and $ V_{\ell\mathrm{N}}^{2}= $ 1.3 $\times$ 10$^{6} $ (HNL6), $ m_{\mathrm{N}}= $ 12 GeV and $ V_{\ell\mathrm{N}}^{2}=$ 1.0 $\times$ 10$^{6} $ (HNL12). Small contributions from background processes that are estimated from simulation are collectively referred to as ``Other''. Figures taken from Ref. [255]. 
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Figure 68a:
Comparison between the number of observed events in data and the background predictions (filled histograms) in the SR for $ \mathrm{e}\mathrm{e}\mathrm{X} $ (upper) and $ \mu\mu\mathrm{X} $ (lower) final states. The hatched band indicates the total systematic and statistical uncertainty in the background prediction. The lower panels indicate the ratio between the observed data and the prediction, where missing points indicate that the ratio lies outside the axis range. Predictions for signal events are shown for several benchmark hypotheses for Majorana HNL production: $ m_{\mathrm{N}}= $ 2 GeV and $ V_{\ell\mathrm{N}}^{2}=$ 0.8 $\times$ 10$^{4} $ (HNL2), $ m_{\mathrm{N}}= $ 6 GeV and $ V_{\ell\mathrm{N}}^{2}= $ 1.3 $\times$ 10$^{6} $ (HNL6), $ m_{\mathrm{N}}= $ 12 GeV and $ V_{\ell\mathrm{N}}^{2}=$ 1.0 $\times$ 10$^{6} $ (HNL12). Small contributions from background processes that are estimated from simulation are collectively referred to as ``Other''. Figures taken from Ref. [255]. 
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Figure 68b:
Comparison between the number of observed events in data and the background predictions (filled histograms) in the SR for $ \mathrm{e}\mathrm{e}\mathrm{X} $ (upper) and $ \mu\mu\mathrm{X} $ (lower) final states. The hatched band indicates the total systematic and statistical uncertainty in the background prediction. The lower panels indicate the ratio between the observed data and the prediction, where missing points indicate that the ratio lies outside the axis range. Predictions for signal events are shown for several benchmark hypotheses for Majorana HNL production: $ m_{\mathrm{N}}= $ 2 GeV and $ V_{\ell\mathrm{N}}^{2}=$ 0.8 $\times$ 10$^{4} $ (HNL2), $ m_{\mathrm{N}}= $ 6 GeV and $ V_{\ell\mathrm{N}}^{2}= $ 1.3 $\times$ 10$^{6} $ (HNL6), $ m_{\mathrm{N}}= $ 12 GeV and $ V_{\ell\mathrm{N}}^{2}=$ 1.0 $\times$ 10$^{6} $ (HNL12). Small contributions from background processes that are estimated from simulation are collectively referred to as ``Other''. Figures taken from Ref. [255]. 
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Figure 69:
The limits at 95% CL on $ V_{\mathrm{eN}}^{2} $ (left) and $ V_{\mu\mathrm{N}}^{2} $ (right) as functions of $ m_{\mathrm{N}} $ for a Majorana (upper) or Dirac (lower) HNL. The area inside the solid (dashed) black curve indicates the observed (expected) exclusion region. Results from the DELPHI [249] and the CMS [253,246] Collaborations are shown for reference. Figures adapted from Ref. [255]. 
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Figure 69a:
The limits at 95% CL on $ V_{\mathrm{eN}}^{2} $ (left) and $ V_{\mu\mathrm{N}}^{2} $ (right) as functions of $ m_{\mathrm{N}} $ for a Majorana (upper) or Dirac (lower) HNL. The area inside the solid (dashed) black curve indicates the observed (expected) exclusion region. Results from the DELPHI [249] and the CMS [253,246] Collaborations are shown for reference. Figures adapted from Ref. [255]. 
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Figure 69b:
The limits at 95% CL on $ V_{\mathrm{eN}}^{2} $ (left) and $ V_{\mu\mathrm{N}}^{2} $ (right) as functions of $ m_{\mathrm{N}} $ for a Majorana (upper) or Dirac (lower) HNL. The area inside the solid (dashed) black curve indicates the observed (expected) exclusion region. Results from the DELPHI [249] and the CMS [253,246] Collaborations are shown for reference. Figures adapted from Ref. [255]. 
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Figure 69c:
The limits at 95% CL on $ V_{\mathrm{eN}}^{2} $ (left) and $ V_{\mu\mathrm{N}}^{2} $ (right) as functions of $ m_{\mathrm{N}} $ for a Majorana (upper) or Dirac (lower) HNL. The area inside the solid (dashed) black curve indicates the observed (expected) exclusion region. Results from the DELPHI [249] and the CMS [253,246] Collaborations are shown for reference. Figures adapted from Ref. [255]. 
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Figure 69d:
The limits at 95% CL on $ V_{\mathrm{eN}}^{2} $ (left) and $ V_{\mu\mathrm{N}}^{2} $ (right) as functions of $ m_{\mathrm{N}} $ for a Majorana (upper) or Dirac (lower) HNL. The area inside the solid (dashed) black curve indicates the observed (expected) exclusion region. Results from the DELPHI [249] and the CMS [253,246] Collaborations are shown for reference. Figures adapted from Ref. [255]. 
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Figure 70:
Expected and observed number of events in the SR of different event categories. Signal yields of a Majorana HNL with a mass of 2 GeV and with a proper decay length of 1 m are overlaid on top of the expected background estimated using the ABCD method. Figure taken from Ref. [265]. 
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Figure 71:
Expected and observed upper limits at 95% CL on Majorana HNL production as functions of the HNL mass ($ m_{\mathrm{N}} $) and mixing amplitudes, for pure electron mixing (upper left), pure muon mixing (upper right), and pure tau neutrino mixing (lower). The limits in the tau neutrino mixing scenario are obtained by combining the results from the electron and muon decay channels of the tau lepton. Figures adapted from Ref. [265]. 
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Figure 71a:
Expected and observed upper limits at 95% CL on Majorana HNL production as functions of the HNL mass ($ m_{\mathrm{N}} $) and mixing amplitudes, for pure electron mixing (upper left), pure muon mixing (upper right), and pure tau neutrino mixing (lower). The limits in the tau neutrino mixing scenario are obtained by combining the results from the electron and muon decay channels of the tau lepton. Figures adapted from Ref. [265]. 
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Figure 71b:
Expected and observed upper limits at 95% CL on Majorana HNL production as functions of the HNL mass ($ m_{\mathrm{N}} $) and mixing amplitudes, for pure electron mixing (upper left), pure muon mixing (upper right), and pure tau neutrino mixing (lower). The limits in the tau neutrino mixing scenario are obtained by combining the results from the electron and muon decay channels of the tau lepton. Figures adapted from Ref. [265]. 
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Figure 71c:
Expected and observed upper limits at 95% CL on Majorana HNL production as functions of the HNL mass ($ m_{\mathrm{N}} $) and mixing amplitudes, for pure electron mixing (upper left), pure muon mixing (upper right), and pure tau neutrino mixing (lower). The limits in the tau neutrino mixing scenario are obtained by combining the results from the electron and muon decay channels of the tau lepton. Figures adapted from Ref. [265]. 
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Figure 72:
Expected and observed limits at 95% CL on \mixparsqN as functions of $ m_{\mathrm{N}} $, in the Majorana (left column) and Dirac (right column) scenarios. The limits are shown for the mixing scenarios $ (r_{\mathrm{e}},r_{\mu},r_{\tau})=(0,1,0) $ (upper row) and $ (r_{\mathrm{e}},r_{\mu},r_{\tau})=(1/3,1/3,1/3) $ (lower row). Results from the CMS [255,265,257], ATLAS [260], LHCb [271], and Belle [272] Collaborations are superimposed for comparison. The mass range with no results shown corresponds to a vetoed region around the $ \mathrm{D^0} $ mass. Figures taken from Ref. [211]. 
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Figure 72a:
Expected and observed limits at 95% CL on \mixparsqN as functions of $ m_{\mathrm{N}} $, in the Majorana (left column) and Dirac (right column) scenarios. The limits are shown for the mixing scenarios $ (r_{\mathrm{e}},r_{\mu},r_{\tau})=(0,1,0) $ (upper row) and $ (r_{\mathrm{e}},r_{\mu},r_{\tau})=(1/3,1/3,1/3) $ (lower row). Results from the CMS [255,265,257], ATLAS [260], LHCb [271], and Belle [272] Collaborations are superimposed for comparison. The mass range with no results shown corresponds to a vetoed region around the $ \mathrm{D^0} $ mass. Figures taken from Ref. [211]. 
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Figure 72b:
Expected and observed limits at 95% CL on \mixparsqN as functions of $ m_{\mathrm{N}} $, in the Majorana (left column) and Dirac (right column) scenarios. The limits are shown for the mixing scenarios $ (r_{\mathrm{e}},r_{\mu},r_{\tau})=(0,1,0) $ (upper row) and $ (r_{\mathrm{e}},r_{\mu},r_{\tau})=(1/3,1/3,1/3) $ (lower row). Results from the CMS [255,265,257], ATLAS [260], LHCb [271], and Belle [272] Collaborations are superimposed for comparison. The mass range with no results shown corresponds to a vetoed region around the $ \mathrm{D^0} $ mass. Figures taken from Ref. [211]. 
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Figure 72c:
Expected and observed limits at 95% CL on \mixparsqN as functions of $ m_{\mathrm{N}} $, in the Majorana (left column) and Dirac (right column) scenarios. The limits are shown for the mixing scenarios $ (r_{\mathrm{e}},r_{\mu},r_{\tau})=(0,1,0) $ (upper row) and $ (r_{\mathrm{e}},r_{\mu},r_{\tau})=(1/3,1/3,1/3) $ (lower row). Results from the CMS [255,265,257], ATLAS [260], LHCb [271], and Belle [272] Collaborations are superimposed for comparison. The mass range with no results shown corresponds to a vetoed region around the $ \mathrm{D^0} $ mass. Figures taken from Ref. [211]. 
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Figure 72d:
Expected and observed limits at 95% CL on \mixparsqN as functions of $ m_{\mathrm{N}} $, in the Majorana (left column) and Dirac (right column) scenarios. The limits are shown for the mixing scenarios $ (r_{\mathrm{e}},r_{\mu},r_{\tau})=(0,1,0) $ (upper row) and $ (r_{\mathrm{e}},r_{\mu},r_{\tau})=(1/3,1/3,1/3) $ (lower row). Results from the CMS [255,265,257], ATLAS [260], LHCb [271], and Belle [272] Collaborations are superimposed for comparison. The mass range with no results shown corresponds to a vetoed region around the $ \mathrm{D^0} $ mass. Figures taken from Ref. [211]. 
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Figure 73:
Observed limits at 95% CL on $ c\tau_{\mathrm{N}} $ as a function of the mixing ratios $ (r_{\mathrm{e}},r_{\mu},r_{\tau}) $ for $ m_{\mathrm{N}}= $ 1 GeV in the Majorana (left) and Dirac (right) scenarios. The red crosses indicate that there is no exclusion found for that point. The orientation of the value markers on each axis identifies the associated internal lines on the plot. Figures taken from Ref. [211]. 
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Figure 73a:
Observed limits at 95% CL on $ c\tau_{\mathrm{N}} $ as a function of the mixing ratios $ (r_{\mathrm{e}},r_{\mu},r_{\tau}) $ for $ m_{\mathrm{N}}= $ 1 GeV in the Majorana (left) and Dirac (right) scenarios. The red crosses indicate that there is no exclusion found for that point. The orientation of the value markers on each axis identifies the associated internal lines on the plot. Figures taken from Ref. [211]. 
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Figure 73b:
Observed limits at 95% CL on $ c\tau_{\mathrm{N}} $ as a function of the mixing ratios $ (r_{\mathrm{e}},r_{\mu},r_{\tau}) $ for $ m_{\mathrm{N}}= $ 1 GeV in the Majorana (left) and Dirac (right) scenarios. The red crosses indicate that there is no exclusion found for that point. The orientation of the value markers on each axis identifies the associated internal lines on the plot. Figures taken from Ref. [211]. 
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Figure 74:
Summary of searches at the CMS experiment for longlived HNLs in the $Type I$ seesaw model. The observed limits at 95% CL on the mixing parameter $  V_{\ell\mathrm{N}} ^{2} $ as a function of the HNL mass $ m_{\mathrm{N}} $ are shown, for Majorana and Dirac HNLs (upper and lower row, respectively), and in the muon and electron channel (left and right column, respectively). 
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Figure 74a:
Summary of searches at the CMS experiment for longlived HNLs in the $Type I$ seesaw model. The observed limits at 95% CL on the mixing parameter $  V_{\ell\mathrm{N}} ^{2} $ as a function of the HNL mass $ m_{\mathrm{N}} $ are shown, for Majorana and Dirac HNLs (upper and lower row, respectively), and in the muon and electron channel (left and right column, respectively). 
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Figure 74b:
Summary of searches at the CMS experiment for longlived HNLs in the $Type I$ seesaw model. The observed limits at 95% CL on the mixing parameter $  V_{\ell\mathrm{N}} ^{2} $ as a function of the HNL mass $ m_{\mathrm{N}} $ are shown, for Majorana and Dirac HNLs (upper and lower row, respectively), and in the muon and electron channel (left and right column, respectively). 
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Figure 74c:
Summary of searches at the CMS experiment for longlived HNLs in the $Type I$ seesaw model. The observed limits at 95% CL on the mixing parameter $  V_{\ell\mathrm{N}} ^{2} $ as a function of the HNL mass $ m_{\mathrm{N}} $ are shown, for Majorana and Dirac HNLs (upper and lower row, respectively), and in the muon and electron channel (left and right column, respectively). 
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Figure 74d:
Summary of searches at the CMS experiment for longlived HNLs in the $Type I$ seesaw model. The observed limits at 95% CL on the mixing parameter $  V_{\ell\mathrm{N}} ^{2} $ as a function of the HNL mass $ m_{\mathrm{N}} $ are shown, for Majorana and Dirac HNLs (upper and lower row, respectively), and in the muon and electron channel (left and right column, respectively). 
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Figure 75:
Observed and expected upper limits at 95% CL on the production cross section for $Type III$ seesaw HNLs in the flavordemocratic scenario using the modelindependent schemes and the BDT regions. To the left of the vertical dashed gray line, the limits are shown from the modelindependent SR, and to the right the limits are shown obtained using the BDT regions. Figure adapted from Ref. [202]. 
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Figure 76:
Expected (left) and observed (right) lower limits at 95% CL on the mass of $Type III$ seesaw HNLs in the plane defined by $ \mathcal{B}_{\mathrm{e}} $ and $ \mathcal{B}_{\tau} $, with the constraint that $ \mathcal{B}_{\mathrm{e}}+\mathcal{B}_{\mu}+\mathcal{B}_{\tau}= $ 1. For $ \mathcal{B}_{\tau}\geq $ 0.9, these limits are obtained using the high mass BDT trained assuming $ \mathcal{B}_{\tau}= $ 1, and for the other decay branching fraction combinations, the limits use the $ \mathcal{B}_{\mathrm{e}}=\mathcal{B}_{\mu}=\mathcal{B}_{\tau} $ BDT. Figures adapted from Ref. [202]. 
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Figure 76a:
Expected (left) and observed (right) lower limits at 95% CL on the mass of $Type III$ seesaw HNLs in the plane defined by $ \mathcal{B}_{\mathrm{e}} $ and $ \mathcal{B}_{\tau} $, with the constraint that $ \mathcal{B}_{\mathrm{e}}+\mathcal{B}_{\mu}+\mathcal{B}_{\tau}= $ 1. For $ \mathcal{B}_{\tau}\geq $ 0.9, these limits are obtained using the high mass BDT trained assuming $ \mathcal{B}_{\tau}= $ 1, and for the other decay branching fraction combinations, the limits use the $ \mathcal{B}_{\mathrm{e}}=\mathcal{B}_{\mu}=\mathcal{B}_{\tau} $ BDT. Figures adapted from Ref. [202]. 
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Figure 76b:
Expected (left) and observed (right) lower limits at 95% CL on the mass of $Type III$ seesaw HNLs in the plane defined by $ \mathcal{B}_{\mathrm{e}} $ and $ \mathcal{B}_{\tau} $, with the constraint that $ \mathcal{B}_{\mathrm{e}}+\mathcal{B}_{\mu}+\mathcal{B}_{\tau}= $ 1. For $ \mathcal{B}_{\tau}\geq $ 0.9, these limits are obtained using the high mass BDT trained assuming $ \mathcal{B}_{\tau}= $ 1, and for the other decay branching fraction combinations, the limits use the $ \mathcal{B}_{\mathrm{e}}=\mathcal{B}_{\mu}=\mathcal{B}_{\tau} $ BDT. Figures adapted from Ref. [202]. 
png pdf 
Figure 77:
The observed upper limits at 95% CL on the product of the production cross section and the branching fraction of a righthanded $ \mathrm{W_R} $ boson divided by the theory expectation for a coupling constant $ g_{\text{R}} $ equal to the SM coupling of the $ \mathrm{W_R} $ boson ($ g_{\text{L}} $), for the electron channel (left) and muon channel (right). The observed exclusion regions are shown for the resolved (solid green), boosted (solid blue), and combined (solid black) channels, together with the expected exclusion region for the combined result (dotted black). The dashdotted lines represent the 68% coverage of the boundaries of the expected exclusion regions. The observed exclusion regions obtained in the previous search performed by the CMS Collaboration [279] are bounded by the magenta lines. The biggest improvement may be seen in the $ m_{\mathrm{N}} < $ 0.5 TeV region, where the new boosted category greatly improves the sensitivity with respect to the previous result. Figures adapted from Ref. [276]. 
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Figure 77a:
The observed upper limits at 95% CL on the product of the production cross section and the branching fraction of a righthanded $ \mathrm{W_R} $ boson divided by the theory expectation for a coupling constant $ g_{\text{R}} $ equal to the SM coupling of the $ \mathrm{W_R} $ boson ($ g_{\text{L}} $), for the electron channel (left) and muon channel (right). The observed exclusion regions are shown for the resolved (solid green), boosted (solid blue), and combined (solid black) channels, together with the expected exclusion region for the combined result (dotted black). The dashdotted lines represent the 68% coverage of the boundaries of the expected exclusion regions. The observed exclusion regions obtained in the previous search performed by the CMS Collaboration [279] are bounded by the magenta lines. The biggest improvement may be seen in the $ m_{\mathrm{N}} < $ 0.5 TeV region, where the new boosted category greatly improves the sensitivity with respect to the previous result. Figures adapted from Ref. [276]. 
png pdf 
Figure 77b:
The observed upper limits at 95% CL on the product of the production cross section and the branching fraction of a righthanded $ \mathrm{W_R} $ boson divided by the theory expectation for a coupling constant $ g_{\text{R}} $ equal to the SM coupling of the $ \mathrm{W_R} $ boson ($ g_{\text{L}} $), for the electron channel (left) and muon channel (right). The observed exclusion regions are shown for the resolved (solid green), boosted (solid blue), and combined (solid black) channels, together with the expected exclusion region for the combined result (dotted black). The dashdotted lines represent the 68% coverage of the boundaries of the expected exclusion regions. The observed exclusion regions obtained in the previous search performed by the CMS Collaboration [279] are bounded by the magenta lines. The biggest improvement may be seen in the $ m_{\mathrm{N}} < $ 0.5 TeV region, where the new boosted category greatly improves the sensitivity with respect to the previous result. Figures adapted from Ref. [276]. 
png pdf 
Figure 78:
Observed and expected limits at 95% CL on the product of cross section and branching fraction, obtained from the combination of the $ \mathrm{e}\tau_\mathrm{h} $ and $ \mu\tau_\mathrm{h} $ channels (left), and the observed and expected upper limits at 95% CL on the production cross section as functions of the mass $ m_{\mathrm{W_R}} $ of the $ \mathrm{W_R} $ boson and the mass $ m_{{{\mathrm{N}}{\tau}} } $ of the HNL (right). The inner (green) band and the outer (yellow) band in the left figure indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the backgroundonly hypothesis. The dashed dark blue curve in the left figure represents the theoretical prediction for the product of the $ \mathrm{W_R} $ boson production cross section and the branching fraction for decay to a $ \tau $ lepton and RH neutrino, assuming the mass of the RH neutrino to be half the mass of the $ \mathrm{W_R} $ boson [282]. Figures taken from Ref. [280]. 
png 
Figure 78a:
Observed and expected limits at 95% CL on the product of cross section and branching fraction, obtained from the combination of the $ \mathrm{e}\tau_\mathrm{h} $ and $ \mu\tau_\mathrm{h} $ channels (left), and the observed and expected upper limits at 95% CL on the production cross section as functions of the mass $ m_{\mathrm{W_R}} $ of the $ \mathrm{W_R} $ boson and the mass $ m_{{{\mathrm{N}}{\tau}} } $ of the HNL (right). The inner (green) band and the outer (yellow) band in the left figure indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the backgroundonly hypothesis. The dashed dark blue curve in the left figure represents the theoretical prediction for the product of the $ \mathrm{W_R} $ boson production cross section and the branching fraction for decay to a $ \tau $ lepton and RH neutrino, assuming the mass of the RH neutrino to be half the mass of the $ \mathrm{W_R} $ boson [282]. Figures taken from Ref. [280]. 
png 
Figure 78b:
Observed and expected limits at 95% CL on the product of cross section and branching fraction, obtained from the combination of the $ \mathrm{e}\tau_\mathrm{h} $ and $ \mu\tau_\mathrm{h} $ channels (left), and the observed and expected upper limits at 95% CL on the production cross section as functions of the mass $ m_{\mathrm{W_R}} $ of the $ \mathrm{W_R} $ boson and the mass $ m_{{{\mathrm{N}}{\tau}} } $ of the HNL (right). The inner (green) band and the outer (yellow) band in the left figure indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the backgroundonly hypothesis. The dashed dark blue curve in the left figure represents the theoretical prediction for the product of the $ \mathrm{W_R} $ boson production cross section and the branching fraction for decay to a $ \tau $ lepton and RH neutrino, assuming the mass of the RH neutrino to be half the mass of the $ \mathrm{W_R} $ boson [282]. Figures taken from Ref. [280]. 
png pdf 
Figure 79:
Upper limits at 95% CL on the product of the cross section and the branching fraction for the production of $ \mathrm{W_R} $ bosons decaying to $ \mathrm{N}_{\tau} $ as function of the $ \mathrm{W_R} $ boson mass (left). The observed (expected) limit is shown as solid (dashed) black lines, and the inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the backgroundonly hypothesis. The theoretical cross section is indicated by the solid blue line. Expected and observed limits at 95% CL on the product of the cross section and the branching fraction for $ \mathrm{W_R}\to{{\mathrm{N}}_{\tau}} \tau $ as a function of $ m_{\mathrm{W_R}} $ and $ m_{{{\mathrm{N}}_{\tau}} }/m_{\mathrm{W_R}} $ (right). Figures taken from Ref. [281]. 
png 
Figure 79a:
Upper limits at 95% CL on the product of the cross section and the branching fraction for the production of $ \mathrm{W_R} $ bosons decaying to $ \mathrm{N}_{\tau} $ as function of the $ \mathrm{W_R} $ boson mass (left). The observed (expected) limit is shown as solid (dashed) black lines, and the inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the backgroundonly hypothesis. The theoretical cross section is indicated by the solid blue line. Expected and observed limits at 95% CL on the product of the cross section and the branching fraction for $ \mathrm{W_R}\to{{\mathrm{N}}_{\tau}} \tau $ as a function of $ m_{\mathrm{W_R}} $ and $ m_{{{\mathrm{N}}_{\tau}} }/m_{\mathrm{W_R}} $ (right). Figures taken from Ref. [281]. 
png 
Figure 79b:
Upper limits at 95% CL on the product of the cross section and the branching fraction for the production of $ \mathrm{W_R} $ bosons decaying to $ \mathrm{N}_{\tau} $ as function of the $ \mathrm{W_R} $ boson mass (left). The observed (expected) limit is shown as solid (dashed) black lines, and the inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the backgroundonly hypothesis. The theoretical cross section is indicated by the solid blue line. Expected and observed limits at 95% CL on the product of the cross section and the branching fraction for $ \mathrm{W_R}\to{{\mathrm{N}}_{\tau}} \tau $ as a function of $ m_{\mathrm{W_R}} $ and $ m_{{{\mathrm{N}}_{\tau}} }/m_{\mathrm{W_R}} $ (right). Figures taken from Ref. [281]. 
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Figure 80:
The observed and expected exclusion limits in the $ m_{\mathrm{N}} $$ m_{\mathrm{Z}^{'}} $ parameter space, in the dielectron channel (left) and the dimuon channel (right). Figures adapted from Ref. [284]. 
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Figure 80a:
The observed and expected exclusion limits in the $ m_{\mathrm{N}} $$ m_{\mathrm{Z}^{'}} $ parameter space, in the dielectron channel (left) and the dimuon channel (right). Figures adapted from Ref. [284]. 
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Figure 80b:
The observed and expected exclusion limits in the $ m_{\mathrm{N}} $$ m_{\mathrm{Z}^{'}} $ parameter space, in the dielectron channel (left) and the dimuon channel (right). Figures adapted from Ref. [284]. 
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Figure 81:
Summary of searches at the CMS experiment for Majorana HNLs in the context of the LRSM model. The observed limits at 95% CL in the twodimensional $ m_{\mathrm{N}} $$ m_{\mathrm{V}} $ plane are shown in the electron and muon channel (left and right, respectively). 
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Figure 81a:
Summary of searches at the CMS experiment for Majorana HNLs in the context of the LRSM model. The observed limits at 95% CL in the twodimensional $ m_{\mathrm{N}} $$ m_{\mathrm{V}} $ plane are shown in the electron and muon channel (left and right, respectively). 
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Figure 81b:
Summary of searches at the CMS experiment for Majorana HNLs in the context of the LRSM model. The observed limits at 95% CL in the twodimensional $ m_{\mathrm{N}} $$ m_{\mathrm{V}} $ plane are shown in the electron and muon channel (left and right, respectively). 
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Figure 82:
Expected (dashed black) and observed (blue solid) exclusion limits for the $ \mathrm{e}\mathrm{e}\mathrm{q}{\bar{\mathrm{q}}{\prime}} $ (left) and $ \mu\mu\mathrm{q}{\bar{\mathrm{q}}{\prime}} $ (right) channels in the search for heavy composite Majorana neutrinos. The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the backgroundonly hypothesis. Figures taken from Ref. [285]. 
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Figure 82a:
Expected (dashed black) and observed (blue solid) exclusion limits for the $ \mathrm{e}\mathrm{e}\mathrm{q}{\bar{\mathrm{q}}{\prime}} $ (left) and $ \mu\mu\mathrm{q}{\bar{\mathrm{q}}{\prime}} $ (right) channels in the search for heavy composite Majorana neutrinos. The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the backgroundonly hypothesis. Figures taken from Ref. [285]. 
png pdf 
Figure 82b:
Expected (dashed black) and observed (blue solid) exclusion limits for the $ \mathrm{e}\mathrm{e}\mathrm{q}{\bar{\mathrm{q}}{\prime}} $ (left) and $ \mu\mu\mathrm{q}{\bar{\mathrm{q}}{\prime}} $ (right) channels in the search for heavy composite Majorana neutrinos. The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the backgroundonly hypothesis. Figures taken from Ref. [285]. 
png pdf 
Figure 83:
Expected (dashed black) and observed (blue solid) exclusion limits for the $ \mathrm{e}\mathrm{e}\mathrm{q}{\bar{\mathrm{q}}{\prime}} $ (left) and $ \mu\mu\mathrm{q}{\bar{\mathrm{q}}{\prime}} $ (right) channel in the twodimensional plane $ m_{{{\mathrm{N}}_{\ell}} } $$ \Lambda $. The solid violet lines represent the fraction of simulated events that satisfy the unitarity condition in the EFT approximation [287] with the various percentages considered. The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the backgroundonly hypothesis. Figures taken from Ref. [285]. 
png pdf 
Figure 83a:
Expected (dashed black) and observed (blue solid) exclusion limits for the $ \mathrm{e}\mathrm{e}\mathrm{q}{\bar{\mathrm{q}}{\prime}} $ (left) and $ \mu\mu\mathrm{q}{\bar{\mathrm{q}}{\prime}} $ (right) channel in the twodimensional plane $ m_{{{\mathrm{N}}_{\ell}} } $$ \Lambda $. The solid violet lines represent the fraction of simulated events that satisfy the unitarity condition in the EFT approximation [287] with the various percentages considered. The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the backgroundonly hypothesis. Figures taken from Ref. [285]. 
png pdf 
Figure 83b:
Expected (dashed black) and observed (blue solid) exclusion limits for the $ \mathrm{e}\mathrm{e}\mathrm{q}{\bar{\mathrm{q}}{\prime}} $ (left) and $ \mu\mu\mathrm{q}{\bar{\mathrm{q}}{\prime}} $ (right) channel in the twodimensional plane $ m_{{{\mathrm{N}}_{\ell}} } $$ \Lambda $. The solid violet lines represent the fraction of simulated events that satisfy the unitarity condition in the EFT approximation [287] with the various percentages considered. The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the backgroundonly hypothesis. Figures taken from Ref. [285]. 
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Figure 84:
Coverage in the ($ p_{\mathrm{T}} $, $ d_0 $) plane for displaced leptons with the 2016 and 2018 triggers, and the new Run3 triggers, indicated in light blue, dark blue, and red, respectively [288]. Here, $ d_0 $ is the impact parameter of the charged lepton track with respect to the PV in the transverse plane. 
Tables  
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Table 1:
List of VLQ searches performed by the CMS experiment grouped by production mode. In this table, $\ell$ denotes an electron or a muon. Additional jets in the final state are not explicitly listed in the table. The 0$\ell$ channels correspond to the allhadronic final state. For the 2$\ell$ channels, it is indicated whether the leptons have oppositesign (OS) or samesign (SS) charges. For single VLQ searches, the channels are indicated through the decay products of the W, Z, and Higgs bosons, and t quarks. 
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Table 2:
Summary of event selection criteria for the primary CRs and SRs in the three leptonic search channels. The phrase ``max MLP'' refers to the largest score from the singlelepton multilayer perceptron network. Table taken from Ref. [nonenonenone]. 
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Table 3:
Summary of channels considered for each category and jet multiplicity in the search for $ {\mathrm{B}} \overline{\mathrm{B}} $ production that specifically targets $ {\mathrm{B}} \to\mathrm{b}\mathrm{Z} $ and $ {\mathrm{B}} \to\mathrm{b}\mathrm{H} $ decays. Table adapted from Ref. [141]. 
Summary 
In this report, the physics program of the CMS experiment has been summarized for searches for physics beyond the standard model (SM) in the context of models that introduce vectorlike quarks (VLQs), vectorlike leptons (VLLs), and heavy neutral leptons (HNLs). Each of these three model classes provides a complementary perspective on the origin of mass of fundamental particles. The VLQs extend the SM with nonchiral partners of SM quarks, and the searches focus on VLQs that couple to the thirdgeneration quarks. The VLLs, introduced in a class of models that can be particularly sensitive to leptonic anomalies, correspond to an analogous extension of the leptonic sector of the SM. These searches target chargedlepton partners. The HNLs provide yet another perspective on the interplay between chirality and neutrino massgenerating mechanisms, and produce distinct prompt and displaced signatures in the detector. These searches probe unexplored areas of parameter space in several models beyond the SM, using Run2 protonproton collision data sets collected by the CMS detector during the years 2015 to 2018 corresponding to an integrated luminosity of up to 138 fb$ ^{1} $. Two new statistical combinations of searches for VLQs have been performed. Pair production of B quarks with mass below 1.49 TeV is excluded at 95% confidence level for any thirdgeneration decay of the B quark. Single production of T quarks in the narrowwidth approximation is excluded at 95% confidence level for T quark masses below 1.20 TeV. No evidence for physics beyond the SM has been observed, and stringent exclusion limits on new fermion masses and couplings have been placed. One search for VLLs, detailed in Section 8.3, shows a modest excess of the observed data over the backgroundonly prediction that requires further investigation using more data. No VLQ and HNL searches report excesses. Using projections in the context of the future HighLuminosity LHC (HLLHC) and the corresponding upgrades to the CMS detector, an increased discovery reach of new fermions well into the TeVns energy domain is expected. Although the environment of the HLLHC with many simultaneous collisions will present new challenges for particle reconstruction and identification, searches for new fermions will benefit from the increased collision energy, unprecedented integrated luminosity, and the planned detector upgrades. Many of the searches presented in this report rely on identifying jets from the decays of massive SM particles, or feature highpseudorapidity jets from $ t $channel or vector boson fusion production modes. The expansion of the tracker volume and significant upgrades of the endcap calorimeter and muon detectors will provide improved jet reconstruction and identification at high pseudorapidity in the HLLHC era. There are still unexplored regions of parameter space in various models beyond the SM involving VLQs, VLLs, and HNLs within reach of the LHC, that can yield a first glimpse of new physics in the near or longer term. This includes considering nonminimal VLQ extensions such as decays of VLQs to scalar or pseudoscalar bosons, exploring VLQ production modes such as electroweak pair production, and expanding the searches for VLQs assuming a finite decay width. Manifestations of VLLs in other models and final states than currently probed may also be considered, involving final states with muon detector shower signatures, final states with highly Lorentzboosted decay products, or vector boson fusion modes of VLL pair production. Future runs of the LHC will bring great opportunities to explore new model phase spaces, detector upgrades will provide improved particle reconstruction, and continued efforts in innovating analysis techniques will further enhance the potential to discover new physics. 
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