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CMS-EXO-23-006 ; CERN-EP-2024-095

Review of searches for vector-like quarks, vector-like leptons, and heavy neutral leptons in proton-proton collisions at $\sqrt{s}=$ 13 TeV at the CMS experiment

CMS Collaboration

27 May 2024

Physics Reports 1115 (2025) 570

Abstract: The LHC has provided an unprecedented amount of proton-proton 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 2015--2018 at a center-of-mass energy of 13 TeV can be used to test the standard model with high precision and potentially uncover evidence for new particles or interactions. An interesting possibility is the existence of new fermions with masses ranging from the MeVns to the TeVns scale. Such new particles appear in many possible extensions of the standard model and are well motivated theoretically. New fermions may explain the appearance of three generations of leptons and quarks, the mass hierarchy across these generations, and the nonzero neutrino masses. In this report, the results of searches targeting vector-like quarks, vector-like leptons, and heavy neutral leptons at the CMS experiment are summarized. The complementarity of current searches for each type of new fermion is discussed, and combinations of several searches for vector-like quarks are presented. The discovery potential for some of these searches at the High-Luminosity LHC is also discussed.

Links: e-print arXiv:2405.17605 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; Physics Briefing ; CADI line (restricted) ;

Figures
png pdf	Figure 1: Representative Feynman diagrams showing the production of VLQs (Q, left), VLLs (L, middle), and HNLs ($\mathrm{N}$, right) in proton-proton collisions.
png pdf	Figure 1-a: Representative Feynman diagrams showing the production of VLQs (Q, left), VLLs (L, middle), and HNLs ($\mathrm{N}$, right) in proton-proton collisions.
png pdf	Figure 1-b: Representative Feynman diagrams showing the production of VLQs (Q, left), VLLs (L, middle), and HNLs ($\mathrm{N}$, right) in proton-proton collisions.
png pdf	Figure 1-c: Representative Feynman diagrams showing the production of VLQs (Q, left), VLLs (L, middle), and HNLs ($\mathrm{N}$, right) in proton-proton collisions.
png pdf	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).
png	Figure 2-a: 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).
png	Figure 2-b: 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).
png pdf	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.
png pdf	Figure 3-a: 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.
png pdf	Figure 3-b: 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.
png pdf	Figure 3-c: 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.
png pdf	Figure 3-d: 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.
png pdf	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. [130,128,118,131] (right). The shaded bands indicate PDF, renormalization scale, and factorization scale uncertainties associated with the predictions.
png pdf	Figure 4-a: 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. [130,128,118,131] (right). The shaded bands indicate PDF, renormalization scale, and factorization scale uncertainties associated with the predictions.
png pdf	Figure 4-b: 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. [130,128,118,131] (right). The shaded bands indicate PDF, renormalization scale, and factorization scale uncertainties associated with the predictions.
png pdf	Figure 5: Coupling factors for single VLQ production via the EW interaction in the narrow-width approximation as a function of the VLQ mass, using the models and tools from Refs. [130,128,118,131]. Coupling factors in single production of T (upper left), B (upper right) in the singlet (solid lines) and doublet (dashed lines) scenarios. Coupling factors in single production of $\mathrm{X}_{5/3}$ (lower left), $\mathrm{Y}_{4/3}$ (lower right) in doublet scenarios.
png pdf	Figure 5-a: Coupling factors for single VLQ production via the EW interaction in the narrow-width approximation as a function of the VLQ mass, using the models and tools from Refs. [130,128,118,131]. Coupling factors in single production of T (upper left), B (upper right) in the singlet (solid lines) and doublet (dashed lines) scenarios. Coupling factors in single production of $\mathrm{X}_{5/3}$ (lower left), $\mathrm{Y}_{4/3}$ (lower right) in doublet scenarios.
png pdf	Figure 5-b: Coupling factors for single VLQ production via the EW interaction in the narrow-width approximation as a function of the VLQ mass, using the models and tools from Refs. [130,128,118,131]. Coupling factors in single production of T (upper left), B (upper right) in the singlet (solid lines) and doublet (dashed lines) scenarios. Coupling factors in single production of $\mathrm{X}_{5/3}$ (lower left), $\mathrm{Y}_{4/3}$ (lower right) in doublet scenarios.
png pdf	Figure 5-c: Coupling factors for single VLQ production via the EW interaction in the narrow-width approximation as a function of the VLQ mass, using the models and tools from Refs. [130,128,118,131]. Coupling factors in single production of T (upper left), B (upper right) in the singlet (solid lines) and doublet (dashed lines) scenarios. Coupling factors in single production of $\mathrm{X}_{5/3}$ (lower left), $\mathrm{Y}_{4/3}$ (lower right) in doublet scenarios.
png pdf	Figure 5-d: Coupling factors for single VLQ production via the EW interaction in the narrow-width approximation as a function of the VLQ mass, using the models and tools from Refs. [130,128,118,131]. Coupling factors in single production of T (upper left), B (upper right) in the singlet (solid lines) and doublet (dashed lines) scenarios. Coupling factors in single production of $\mathrm{X}_{5/3}$ (lower left), $\mathrm{Y}_{4/3}$ (lower right) in doublet scenarios.
png pdf	Figure 6: Distributions of observables used to maximize the ${\mathrm{X}_{5/3}} {\mathrm{X}_{5/3}}$ signal significance for the SSDL (left) and single-lepton (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 small-radius jets in the event, for a combination of $\mathrm{e}\mathrm{e}$, $\mathrm{e}\mu$, and $\mu\mu$ channels. The right figure shows the $\min M(\ell,\mathrm{b})$ distribution in events with $\geq$1 t-tagged jet, $\geq$1 W-tagged jets, and $\geq$2 b-tagged jets for the combined electron and muon samples in the SR. The distribution has variable-size 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. [143].
png pdf	Figure 6-a: Distributions of observables used to maximize the ${\mathrm{X}_{5/3}} {\mathrm{X}_{5/3}}$ signal significance for the SSDL (left) and single-lepton (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 small-radius jets in the event, for a combination of $\mathrm{e}\mathrm{e}$, $\mathrm{e}\mu$, and $\mu\mu$ channels. The right figure shows the $\min M(\ell,\mathrm{b})$ distribution in events with $\geq$1 t-tagged jet, $\geq$1 W-tagged jets, and $\geq$2 b-tagged jets for the combined electron and muon samples in the SR. The distribution has variable-size 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. [143].
png pdf	Figure 6-b: Distributions of observables used to maximize the ${\mathrm{X}_{5/3}} {\mathrm{X}_{5/3}}$ signal significance for the SSDL (left) and single-lepton (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 small-radius jets in the event, for a combination of $\mathrm{e}\mathrm{e}$, $\mathrm{e}\mu$, and $\mu\mu$ channels. The right figure shows the $\min M(\ell,\mathrm{b})$ distribution in events with $\geq$1 t-tagged jet, $\geq$1 W-tagged jets, and $\geq$2 b-tagged jets for the combined electron and muon samples in the SR. The distribution has variable-size 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. [143].
png pdf	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 single-lepton final states. The theoretical uncertainty in the signal cross section is shown with a band around the theoretical prediction. Figures adapted from Ref. [143].
png pdf	Figure 7-a: 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 single-lepton final states. The theoretical uncertainty in the signal cross section is shown with a band around the theoretical prediction. Figures adapted from Ref. [143].
png pdf	Figure 7-b: 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 single-lepton final states. The theoretical uncertainty in the signal cross section is shown with a band around the theoretical prediction. Figures adapted from Ref. [143].
png pdf	Figure 8: Distributions of $H_{\mathrm{T}}$ in a combination of SRs in the NN-based approach, inclusive in $\geq$1 t tags (left), and in the SR with two W-tagged and two b-tagged jets in the selection-based approach (right). The lower panels show the ratio between observed data and the background estimate. Figures taken from Ref. [140].
png pdf	Figure 8-a: Distributions of $H_{\mathrm{T}}$ in a combination of SRs in the NN-based approach, inclusive in $\geq$1 t tags (left), and in the SR with two W-tagged and two b-tagged jets in the selection-based approach (right). The lower panels show the ratio between observed data and the background estimate. Figures taken from Ref. [140].
png pdf	Figure 8-b: Distributions of $H_{\mathrm{T}}$ in a combination of SRs in the NN-based approach, inclusive in $\geq$1 t tags (left), and in the SR with two W-tagged and two b-tagged jets in the selection-based approach (right). The lower panels show the ratio between observed data and the background estimate. Figures taken from Ref. [140].
png pdf	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 NN-based (left) and selection-based (right) approaches. Figures adapted from Ref. [140].
png pdf	Figure 9-a: 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 NN-based (left) and selection-based (right) approaches. Figures adapted from Ref. [140].
png pdf	Figure 9-b: 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 NN-based (left) and selection-based (right) approaches. Figures adapted from Ref. [140].
png pdf	Figure 10: Example single-lepton 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 ${\mathrm{T}} \overline{\mathrm{T}}$ signals 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. [141].
png pdf	Figure 10-a: Example single-lepton 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 ${\mathrm{T}} \overline{\mathrm{T}}$ signals 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. [141].
png pdf	Figure 10-b: Example single-lepton 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 ${\mathrm{T}} \overline{\mathrm{T}}$ signals 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. [141].
png pdf	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 2017--2018 (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. [141].
png pdf	Figure 11-a: 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 2017--2018 (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. [141].
png pdf	Figure 11-b: 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 2017--2018 (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. [141].
png pdf	Figure 12: The 95% CL expected (left) and observed (right) lower mass limits on pair-produced T quark masses, from the combined fit to the three leptonic 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. [141].
png pdf	Figure 12-a: The 95% CL expected (left) and observed (right) lower mass limits on pair-produced T quark masses, from the combined fit to the three leptonic 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. [141].
png pdf	Figure 12-b: The 95% CL expected (left) and observed (right) lower mass limits on pair-produced T quark masses, from the combined fit to the three leptonic 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. [141].
png pdf	Figure 13: The 95% CL expected (left) and observed (right) lower mass limits on pair-produced B quark masses, from the combined fit to the three leptonic channels, as functions of branching fractions to Higgs and W bosons. Mass contours are shown with lines of various styles. Figures adapted from Ref. [141].
png pdf	Figure 13-a: The 95% CL expected (left) and observed (right) lower mass limits on pair-produced B quark masses, from the combined fit to the three leptonic channels, as functions of branching fractions to Higgs and W bosons. Mass contours are shown with lines of various styles. Figures adapted from Ref. [141].
png pdf	Figure 13-b: The 95% CL expected (left) and observed (right) lower mass limits on pair-produced B quark masses, from the combined fit to the three leptonic channels, as functions of branching fractions to Higgs and W bosons. Mass contours are shown with lines of various styles. Figures adapted from Ref. [141].
png pdf	Figure 14: 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 NN-based (left) and selection-based (right) approaches of the search for ${\mathrm{B}} \overline{\mathrm{B}}$ production in the all-hadronic final state. Figures adapted from Ref. [140].
png pdf	Figure 14-a: 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 NN-based (left) and selection-based (right) approaches of the search for ${\mathrm{B}} \overline{\mathrm{B}}$ production in the all-hadronic final state. Figures adapted from Ref. [140].
png pdf	Figure 14-b: 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 NN-based (left) and selection-based (right) approaches of the search for ${\mathrm{B}} \overline{\mathrm{B}}$ production in the all-hadronic final state. Figures adapted from Ref. [140].
png pdf	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 four-jet $\mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z}$ category (left) and the leptonic four-jet $\mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z}$ 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. [142].
png pdf	Figure 15-a: 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 four-jet $\mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z}$ category (left) and the leptonic four-jet $\mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z}$ 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. [142].
png pdf	Figure 15-b: 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 four-jet $\mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z}$ category (left) and the leptonic four-jet $\mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z}$ 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. [142].
png pdf	Figure 16: Expected (left) and observed (right) lower limits on the B quark mass at 95% CL from the combination of the full Run 2 hadronic and OS dilepton channels, 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. [142].
png pdf	Figure 16-a: Expected (left) and observed (right) lower limits on the B quark mass at 95% CL from the combination of the full Run 2 hadronic and OS dilepton channels, 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. [142].
png pdf	Figure 16-b: Expected (left) and observed (right) lower limits on the B quark mass at 95% CL from the combination of the full Run 2 hadronic and OS dilepton channels, 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. [142].
png pdf	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. [144].
png pdf	Figure 17-a: 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. [144].
png pdf	Figure 17-b: 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. [144].
png pdf	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 background-only hypothesis. Figures taken from Ref. [144].
png pdf	Figure 18-a: 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 background-only hypothesis. Figures taken from Ref. [144].
png pdf	Figure 18-b: 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 background-only hypothesis. Figures taken from Ref. [144].
png pdf	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. [146].
png pdf	Figure 19-a: 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. [146].
png pdf	Figure 19-b: 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. [146].
png pdf	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. [146].
png pdf	Figure 21: Background-only postfit distributions of $\widetilde{m}_{{\mathrm{T}} }$, the adjusted T mass sensitive observable defined in Ref. [145], 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 high-mass 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. [145].
png pdf	Figure 21-a: Background-only postfit distributions of $\widetilde{m}_{{\mathrm{T}} }$, the adjusted T mass sensitive observable defined in Ref. [145], 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 high-mass 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. [145].
png pdf	Figure 21-b: Background-only postfit distributions of $\widetilde{m}_{{\mathrm{T}} }$, the adjusted T mass sensitive observable defined in Ref. [145], 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 high-mass 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. [145].
png pdf	Figure 22: Background-only postfit five-jet invariant mass distributions for the SR for the low-mass (left) and high-mass (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 high-mass selections, respectively. Figures adapted from Ref. [148].
png pdf	Figure 22-a: Background-only postfit five-jet invariant mass distributions for the SR for the low-mass (left) and high-mass (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 high-mass selections, respectively. Figures adapted from Ref. [148].
png pdf	Figure 22-b: Background-only postfit five-jet invariant mass distributions for the SR for the low-mass (left) and high-mass (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 high-mass selections, respectively. Figures adapted from Ref. [148].
png pdf	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 background-only hypothesis. The left figure corresponds to the analysis strategy described in Ref. [148], based on the five-jet invariant mass reconstruction of the T. The figure on the right corresponds to the analysis strategy in Ref. [145], which employs different reconstruction algorithms for the low- and high-mass searches. The vertical dashed lines represent the crossover point in sensitivity for the low-mass and high-mass selections. Figures adapted from Refs. [148,145].
png pdf	Figure 23-a: 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 background-only hypothesis. The left figure corresponds to the analysis strategy described in Ref. [148], based on the five-jet invariant mass reconstruction of the T. The figure on the right corresponds to the analysis strategy in Ref. [145], which employs different reconstruction algorithms for the low- and high-mass searches. The vertical dashed lines represent the crossover point in sensitivity for the low-mass and high-mass selections. Figures adapted from Refs. [148,145].
png pdf	Figure 23-b: 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 background-only hypothesis. The left figure corresponds to the analysis strategy described in Ref. [148], based on the five-jet invariant mass reconstruction of the T. The figure on the right corresponds to the analysis strategy in Ref. [145], which employs different reconstruction algorithms for the low- and high-mass searches. The vertical dashed lines represent the crossover point in sensitivity for the low-mass and high-mass selections. Figures adapted from Refs. [148,145].
png pdf	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 background-only 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 low-mass and high-mass selections. Figures adapted from Ref. [145].
png pdf	Figure 24-a: 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 background-only 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 low-mass and high-mass selections. Figures adapted from Ref. [145].
png pdf	Figure 24-b: 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 background-only 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 low-mass and high-mass selections. Figures adapted from Ref. [145].
png pdf	Figure 24-c: 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 background-only 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 low-mass and high-mass selections. Figures adapted from Ref. [145].
png pdf	Figure 25: Distributions of the observed data (black dots) and $m_{\gamma\gamma}$ signal-plus-background 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. [147].
png pdf	Figure 25-a: Distributions of the observed data (black dots) and $m_{\gamma\gamma}$ signal-plus-background 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. [147].
png pdf	Figure 25-b: Distributions of the observed data (black dots) and $m_{\gamma\gamma}$ signal-plus-background 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. [147].
png pdf	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 background-only 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. [147].
png pdf	Figure 27: The distribution in the reconstructed B quark mass in events with one t-tagged 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. [151].
png pdf	Figure 27-a: The distribution in the reconstructed B quark mass in events with one t-tagged 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. [151].
png pdf	Figure 27-b: The distribution in the reconstructed B quark mass in events with one t-tagged 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. [151].
png pdf	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 all-hadronic (dash-dotted) 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 background-only 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. [153].
png pdf	Figure 28-a: 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 all-hadronic (dash-dotted) 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 background-only 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. [153].
png pdf	Figure 28-b: 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 all-hadronic (dash-dotted) 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 background-only 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. [153].
png pdf	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 forward-jet categories. The continuous red curves correspond to the theoretical expectations for singlet and doublet models. Figure taken from Ref. [150].
png pdf	Figure 30: Reconstructed $m_{\mathrm{Z}^{'}}$ (left) and $m_{{\mathrm{T}} }$ (right) distributions obtained in a search for $\mathrm{p}\mathrm{p}\to\mathrm{Z}^{'}\to{\mathrm{T}} {\overline{T}}$ in the all-hadronic final state. The $\mathrm{Z}^{'}$ boson is reconstructed using a t-, a W-, and a b-tagged 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. [154].
png pdf	Figure 30-a: Reconstructed $m_{\mathrm{Z}^{'}}$ (left) and $m_{{\mathrm{T}} }$ (right) distributions obtained in a search for $\mathrm{p}\mathrm{p}\to\mathrm{Z}^{'}\to{\mathrm{T}} {\overline{T}}$ in the all-hadronic final state. The $\mathrm{Z}^{'}$ boson is reconstructed using a t-, a W-, and a b-tagged 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. [154].
png pdf	Figure 30-b: Reconstructed $m_{\mathrm{Z}^{'}}$ (left) and $m_{{\mathrm{T}} }$ (right) distributions obtained in a search for $\mathrm{p}\mathrm{p}\to\mathrm{Z}^{'}\to{\mathrm{T}} {\overline{T}}$ in the all-hadronic final state. The $\mathrm{Z}^{'}$ boson is reconstructed using a t-, a W-, and a b-tagged 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. [154].
png pdf	Figure 31: Reconstructed $m_{\mathrm{Z}^{'}}$ distributions obtained in a search for $\mathrm{p}\mathrm{p}\to\mathrm{Z}^{'}\to{\mathrm{T}} {\overline{T}}$ in the $\ell$+jets final state, in events with a V- and a t-tagged jet (left) and in events with an H-tagged jet (right). The lower panels show the ratio of the observed data to the background prediction. Figures adapted from Ref. [155].
png pdf	Figure 31-a: Reconstructed $m_{\mathrm{Z}^{'}}$ distributions obtained in a search for $\mathrm{p}\mathrm{p}\to\mathrm{Z}^{'}\to{\mathrm{T}} {\overline{T}}$ in the $\ell$+jets final state, in events with a V- and a t-tagged jet (left) and in events with an H-tagged jet (right). The lower panels show the ratio of the observed data to the background prediction. Figures adapted from Ref. [155].
png pdf	Figure 31-b: Reconstructed $m_{\mathrm{Z}^{'}}$ distributions obtained in a search for $\mathrm{p}\mathrm{p}\to\mathrm{Z}^{'}\to{\mathrm{T}} {\overline{T}}$ in the $\ell$+jets final state, in events with a V- and a t-tagged jet (left) and in events with an H-tagged jet (right). The lower panels show the ratio of the observed data to the background prediction. Figures adapted from Ref. [155].
png pdf	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 all-hadronic final state, in events with a t-, H- and b-tagged 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. [157].
png pdf	Figure 32-a: 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 all-hadronic final state, in events with a t-, H- and b-tagged 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. [157].
png pdf	Figure 32-b: 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 all-hadronic final state, in events with a t-, H- and b-tagged 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. [157].
png pdf	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.
png pdf	Figure 33-a: 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.
png pdf	Figure 33-b: 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.
png pdf	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 $\mathcal{B}({\mathrm{B}} \to\mathrm{t}\mathrm{W})=1-\mathcal{B}({\mathrm{B}} \to\mathrm{b}\mathrm{H})-\mathcal{B}({\mathrm{B}} \to\mathrm{b}\mathrm{Z})$.
png pdf	Figure 34-a: 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 $\mathcal{B}({\mathrm{B}} \to\mathrm{t}\mathrm{W})=1-\mathcal{B}({\mathrm{B}} \to\mathrm{b}\mathrm{H})-\mathcal{B}({\mathrm{B}} \to\mathrm{b}\mathrm{Z})$.
png pdf	Figure 34-b: 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 $\mathcal{B}({\mathrm{B}} \to\mathrm{t}\mathrm{W})=1-\mathcal{B}({\mathrm{B}} \to\mathrm{b}\mathrm{H})-\mathcal{B}({\mathrm{B}} \to\mathrm{b}\mathrm{Z})$.
png pdf	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.
png pdf	Figure 36: Expected (left) and observed (right) 95% CL upper limits on the product of the single-production 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.
png pdf	Figure 36-a: Expected (left) and observed (right) 95% CL upper limits on the product of the single-production 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.
png pdf	Figure 36-b: Expected (left) and observed (right) 95% CL upper limits on the product of the single-production 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.
png pdf	Figure 37: Observed and expected 95% CL upper limits on the production cross section of a pair of vector-like 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, selection-based) [140], and $\geq$1$\ell$+jets [141]. A theory prediction at NNLO in perturbative QCD of the pair production cross section in the NWA is superimposed. Searches using data corresponding to an integrated luminosity of 36 fb$^{-1}$, rather than the full Run 2 integrated luminosity of 138 fb$^{-1}$, are indicated with a spade symbol in the legend.
png pdf	Figure 37-a: Observed and expected 95% CL upper limits on the production cross section of a pair of vector-like 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, selection-based) [140], and $\geq$1$\ell$+jets [141]. A theory prediction at NNLO in perturbative QCD of the pair production cross section in the NWA is superimposed. Searches using data corresponding to an integrated luminosity of 36 fb$^{-1}$, rather than the full Run 2 integrated luminosity of 138 fb$^{-1}$, are indicated with a spade symbol in the legend.
png pdf	Figure 37-b: Observed and expected 95% CL upper limits on the production cross section of a pair of vector-like 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, selection-based) [140], and $\geq$1$\ell$+jets [141]. A theory prediction at NNLO in perturbative QCD of the pair production cross section in the NWA is superimposed. Searches using data corresponding to an integrated luminosity of 36 fb$^{-1}$, rather than the full Run 2 integrated luminosity of 138 fb$^{-1}$, are indicated with a spade symbol in the legend.
png pdf	Figure 37-c: Observed and expected 95% CL upper limits on the production cross section of a pair of vector-like 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, selection-based) [140], and $\geq$1$\ell$+jets [141]. A theory prediction at NNLO in perturbative QCD of the pair production cross section in the NWA is superimposed. Searches using data corresponding to an integrated luminosity of 36 fb$^{-1}$, rather than the full Run 2 integrated luminosity of 138 fb$^{-1}$, are indicated with a spade symbol in the legend.
png pdf	Figure 38: Observed and expected 95% CL upper limits on the production cross section of a pair of vector-like 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) [140], 0$\ell$+jets [159], $\geq$1$\ell$+jets [141], 0\ell/2$\ell$+jets [142], 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. Searches using data corresponding to an integrated luminosity of 36 fb$^{-1}$, rather than the full Run 2 integrated luminosity of 138 fb$^{-1}$, are indicated with a spade symbol in the legend.
png pdf	Figure 38-a: Observed and expected 95% CL upper limits on the production cross section of a pair of vector-like 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) [140], 0$\ell$+jets [159], $\geq$1$\ell$+jets [141], 0\ell/2$\ell$+jets [142], 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. Searches using data corresponding to an integrated luminosity of 36 fb$^{-1}$, rather than the full Run 2 integrated luminosity of 138 fb$^{-1}$, are indicated with a spade symbol in the legend.
png pdf	Figure 38-b: Observed and expected 95% CL upper limits on the production cross section of a pair of vector-like 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) [140], 0$\ell$+jets [159], $\geq$1$\ell$+jets [141], 0\ell/2$\ell$+jets [142], 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. Searches using data corresponding to an integrated luminosity of 36 fb$^{-1}$, rather than the full Run 2 integrated luminosity of 138 fb$^{-1}$, are indicated with a spade symbol in the legend.
png pdf	Figure 38-c: Observed and expected 95% CL upper limits on the production cross section of a pair of vector-like 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) [140], 0$\ell$+jets [159], $\geq$1$\ell$+jets [141], 0\ell/2$\ell$+jets [142], 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. Searches using data corresponding to an integrated luminosity of 36 fb$^{-1}$, rather than the full Run 2 integrated luminosity of 138 fb$^{-1}$, are indicated with a spade symbol in the legend.
png pdf	Figure 39: Observed and expected 95% CL upper limits on the production cross section of a pair of vector-like T or B quarks, as functions of their mass, obtained by different analyses: 0$\ell$+jets [159], $\geq$1$\ell$+jets [141], 0\ell/2$\ell$+jets [142], 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 39-a: Observed and expected 95% CL upper limits on the production cross section of a pair of vector-like T or B quarks, as functions of their mass, obtained by different analyses: 0$\ell$+jets [159], $\geq$1$\ell$+jets [141], 0\ell/2$\ell$+jets [142], 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 39-b: Observed and expected 95% CL upper limits on the production cross section of a pair of vector-like T or B quarks, as functions of their mass, obtained by different analyses: 0$\ell$+jets [159], $\geq$1$\ell$+jets [141], 0\ell/2$\ell$+jets [142], 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 39-c: Observed and expected 95% CL upper limits on the production cross section of a pair of vector-like T or B quarks, as functions of their mass, obtained by different analyses: 0$\ell$+jets [159], $\geq$1$\ell$+jets [141], 0\ell/2$\ell$+jets [142], 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: ${\mathrm{T}} \to\mathrm{b}\mathrm{W}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\nu/\mathrm{b}\ell\nu\,\mathrm{q}\mathrm{q}$ [149], ${\mathrm{T}} \to\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\ell$ [144], ${\mathrm{T}} \to\mathrm{t}\mathrm{H}+\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\mathrm{b}\mathrm{b}$ (merged-jet) [145], ${\mathrm{T}} \to\mathrm{t}\mathrm{H}\to\mathrm{b}\ell\nu/\mathrm{b}\mathrm{q}\mathrm{q}\,\gamma\gamma$ [147], ${\mathrm{T}} \to\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\nu\nu$ [146], ${\mathrm{T}} \to\mathrm{t}\mathrm{H}+\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\mathrm{b}\mathrm{b}$ [148], and the single T quark combination of Section 6.5.2. Only the three analyses using the full Run 2 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. Searches using data corresponding to an integrated luminosity of 2.3 fb$^{-1}$ and 36 fb$^{-1}$, rather than the full Run 2 integrated luminosity of 138 fb$^{-1}$, are indicated with a heart and spade symbol, respectively, in the legend.
png pdf	Figure 40-a: 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: ${\mathrm{T}} \to\mathrm{b}\mathrm{W}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\nu/\mathrm{b}\ell\nu\,\mathrm{q}\mathrm{q}$ [149], ${\mathrm{T}} \to\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\ell$ [144], ${\mathrm{T}} \to\mathrm{t}\mathrm{H}+\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\mathrm{b}\mathrm{b}$ (merged-jet) [145], ${\mathrm{T}} \to\mathrm{t}\mathrm{H}\to\mathrm{b}\ell\nu/\mathrm{b}\mathrm{q}\mathrm{q}\,\gamma\gamma$ [147], ${\mathrm{T}} \to\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\nu\nu$ [146], ${\mathrm{T}} \to\mathrm{t}\mathrm{H}+\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\mathrm{b}\mathrm{b}$ [148], and the single T quark combination of Section 6.5.2. Only the three analyses using the full Run 2 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. Searches using data corresponding to an integrated luminosity of 2.3 fb$^{-1}$ and 36 fb$^{-1}$, rather than the full Run 2 integrated luminosity of 138 fb$^{-1}$, are indicated with a heart and spade symbol, respectively, in the legend.
png pdf	Figure 40-b: 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: ${\mathrm{T}} \to\mathrm{b}\mathrm{W}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\nu/\mathrm{b}\ell\nu\,\mathrm{q}\mathrm{q}$ [149], ${\mathrm{T}} \to\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\ell$ [144], ${\mathrm{T}} \to\mathrm{t}\mathrm{H}+\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\mathrm{b}\mathrm{b}$ (merged-jet) [145], ${\mathrm{T}} \to\mathrm{t}\mathrm{H}\to\mathrm{b}\ell\nu/\mathrm{b}\mathrm{q}\mathrm{q}\,\gamma\gamma$ [147], ${\mathrm{T}} \to\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\nu\nu$ [146], ${\mathrm{T}} \to\mathrm{t}\mathrm{H}+\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\mathrm{b}\mathrm{b}$ [148], and the single T quark combination of Section 6.5.2. Only the three analyses using the full Run 2 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. Searches using data corresponding to an integrated luminosity of 2.3 fb$^{-1}$ and 36 fb$^{-1}$, rather than the full Run 2 integrated luminosity of 138 fb$^{-1}$, are indicated with a heart and spade symbol, respectively, in the legend.
png pdf	Figure 40-c: 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: ${\mathrm{T}} \to\mathrm{b}\mathrm{W}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\nu/\mathrm{b}\ell\nu\,\mathrm{q}\mathrm{q}$ [149], ${\mathrm{T}} \to\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\ell$ [144], ${\mathrm{T}} \to\mathrm{t}\mathrm{H}+\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\mathrm{b}\mathrm{b}$ (merged-jet) [145], ${\mathrm{T}} \to\mathrm{t}\mathrm{H}\to\mathrm{b}\ell\nu/\mathrm{b}\mathrm{q}\mathrm{q}\,\gamma\gamma$ [147], ${\mathrm{T}} \to\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\nu\nu$ [146], ${\mathrm{T}} \to\mathrm{t}\mathrm{H}+\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\mathrm{b}\mathrm{b}$ [148], and the single T quark combination of Section 6.5.2. Only the three analyses using the full Run 2 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. Searches using data corresponding to an integrated luminosity of 2.3 fb$^{-1}$ and 36 fb$^{-1}$, rather than the full Run 2 integrated luminosity of 138 fb$^{-1}$, are indicated with a heart and spade symbol, respectively, in the legend.
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: ${\mathrm{B}} \to\mathrm{t}\mathrm{W}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\nu/\mathrm{q}\mathrm{q}$ [153], ${\mathrm{B}} \to\mathrm{t}\mathrm{W}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\nu/\mathrm{b}\ell\nu\,\mathrm{q}\mathrm{q}$ [151], and ${\mathrm{B}} \to\mathrm{b}\mathrm{H}\to\mathrm{b}\,\mathrm{b}\mathrm{b}$ [150]. Two theory predictions at LO in perturbative QCD are superimposed, corresponding to different VLQ widths. Searches using data corresponding to an integrated luminosity of 36 fb$^{-1}$, rather than the full Run 2 integrated luminosity of 138 fb$^{-1}$, are indicated with a spade symbol in the legend.
png pdf	Figure 41-a: 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: ${\mathrm{B}} \to\mathrm{t}\mathrm{W}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\nu/\mathrm{q}\mathrm{q}$ [153], ${\mathrm{B}} \to\mathrm{t}\mathrm{W}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\nu/\mathrm{b}\ell\nu\,\mathrm{q}\mathrm{q}$ [151], and ${\mathrm{B}} \to\mathrm{b}\mathrm{H}\to\mathrm{b}\,\mathrm{b}\mathrm{b}$ [150]. Two theory predictions at LO in perturbative QCD are superimposed, corresponding to different VLQ widths. Searches using data corresponding to an integrated luminosity of 36 fb$^{-1}$, rather than the full Run 2 integrated luminosity of 138 fb$^{-1}$, are indicated with a spade symbol in the legend.
png pdf	Figure 41-b: 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: ${\mathrm{B}} \to\mathrm{t}\mathrm{W}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\nu/\mathrm{q}\mathrm{q}$ [153], ${\mathrm{B}} \to\mathrm{t}\mathrm{W}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\nu/\mathrm{b}\ell\nu\,\mathrm{q}\mathrm{q}$ [151], and ${\mathrm{B}} \to\mathrm{b}\mathrm{H}\to\mathrm{b}\,\mathrm{b}\mathrm{b}$ [150]. Two theory predictions at LO in perturbative QCD are superimposed, corresponding to different VLQ widths. Searches using data corresponding to an integrated luminosity of 36 fb$^{-1}$, rather than the full Run 2 integrated luminosity of 138 fb$^{-1}$, are indicated with a spade symbol in the legend.
png pdf	Figure 41-c: 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: ${\mathrm{B}} \to\mathrm{t}\mathrm{W}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\nu/\mathrm{q}\mathrm{q}$ [153], ${\mathrm{B}} \to\mathrm{t}\mathrm{W}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\nu/\mathrm{b}\ell\nu\,\mathrm{q}\mathrm{q}$ [151], and ${\mathrm{B}} \to\mathrm{b}\mathrm{H}\to\mathrm{b}\,\mathrm{b}\mathrm{b}$ [150]. Two theory predictions at LO in perturbative QCD are superimposed, corresponding to different VLQ widths. Searches using data corresponding to an integrated luminosity of 36 fb$^{-1}$, rather than the full Run 2 integrated luminosity of 138 fb$^{-1}$, are indicated with a spade symbol in the legend.
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: ${\mathrm{T}} \to\mathrm{t}\mathrm{H}+\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\mathrm{b}\mathrm{b}$ (merged-jet) [145], ${\mathrm{T}} \to\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\ell$ [144], ${\mathrm{T}} \to\mathrm{b}\mathrm{W}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\nu/\mathrm{b}\ell\nu\,\mathrm{q}\mathrm{q}$ [149], ${\mathrm{T}} \to\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\ell$ [144], ${\mathrm{T}} \to\mathrm{t}\mathrm{H}\to\mathrm{b}\ell\nu/\mathrm{b}\mathrm{q}\mathrm{q}\,\gamma\gamma$ [147], ${\mathrm{T}} \to\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\nu\nu$ [146], ${\mathrm{T}} \to\mathrm{t}\mathrm{H}+\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\mathrm{b}\mathrm{b}$ [148], and the single T quark combination of Section 6.5.2. Only the three analyses using the full Run 2 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. Searches using data corresponding to an integrated luminosity of 2.3 fb$^{-1}$ and 36 fb$^{-1}$, rather than the full Run 2 integrated luminosity of 138 fb$^{-1}$, are indicated with a heart and spade symbol, respectively, in the legend.
png pdf	Figure 42-a: 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: ${\mathrm{T}} \to\mathrm{t}\mathrm{H}+\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\mathrm{b}\mathrm{b}$ (merged-jet) [145], ${\mathrm{T}} \to\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\ell$ [144], ${\mathrm{T}} \to\mathrm{b}\mathrm{W}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\nu/\mathrm{b}\ell\nu\,\mathrm{q}\mathrm{q}$ [149], ${\mathrm{T}} \to\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\ell$ [144], ${\mathrm{T}} \to\mathrm{t}\mathrm{H}\to\mathrm{b}\ell\nu/\mathrm{b}\mathrm{q}\mathrm{q}\,\gamma\gamma$ [147], ${\mathrm{T}} \to\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\nu\nu$ [146], ${\mathrm{T}} \to\mathrm{t}\mathrm{H}+\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\mathrm{b}\mathrm{b}$ [148], and the single T quark combination of Section 6.5.2. Only the three analyses using the full Run 2 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. Searches using data corresponding to an integrated luminosity of 2.3 fb$^{-1}$ and 36 fb$^{-1}$, rather than the full Run 2 integrated luminosity of 138 fb$^{-1}$, are indicated with a heart and spade symbol, respectively, in the legend.
png pdf	Figure 42-b: 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: ${\mathrm{T}} \to\mathrm{t}\mathrm{H}+\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\mathrm{b}\mathrm{b}$ (merged-jet) [145], ${\mathrm{T}} \to\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\ell$ [144], ${\mathrm{T}} \to\mathrm{b}\mathrm{W}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\nu/\mathrm{b}\ell\nu\,\mathrm{q}\mathrm{q}$ [149], ${\mathrm{T}} \to\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\ell$ [144], ${\mathrm{T}} \to\mathrm{t}\mathrm{H}\to\mathrm{b}\ell\nu/\mathrm{b}\mathrm{q}\mathrm{q}\,\gamma\gamma$ [147], ${\mathrm{T}} \to\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\nu\nu$ [146], ${\mathrm{T}} \to\mathrm{t}\mathrm{H}+\mathrm{t}\mathrm{Z}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\mathrm{b}\mathrm{b}$ [148], and the single T quark combination of Section 6.5.2. Only the three analyses using the full Run 2 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. Searches using data corresponding to an integrated luminosity of 2.3 fb$^{-1}$ and 36 fb$^{-1}$, rather than the full Run 2 integrated luminosity of 138 fb$^{-1}$, are indicated with a heart and spade symbol, respectively, in the legend.
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: ${\mathrm{B}} \to\mathrm{t}\mathrm{W}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\nu/\mathrm{q}\mathrm{q}$ [153], ${\mathrm{B}} \to\mathrm{b}\mathrm{H}\to\mathrm{b}\,\mathrm{b}\mathrm{b}$ [150], and ${\mathrm{B}} \to\mathrm{t}\mathrm{W}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\nu/\mathrm{b}\ell\nu\,\mathrm{q}\mathrm{q}$ [151]. Two theory predictions at LO in perturbative QCD are superimposed, corresponding to different VLQ widths. Searches using data corresponding to an integrated luminosity of 36 fb$^{-1}$, rather than the full Run 2 integrated luminosity of 138 fb$^{-1}$, are indicated with a spade symbol in the legend.
png pdf	Figure 43-a: 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: ${\mathrm{B}} \to\mathrm{t}\mathrm{W}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\nu/\mathrm{q}\mathrm{q}$ [153], ${\mathrm{B}} \to\mathrm{b}\mathrm{H}\to\mathrm{b}\,\mathrm{b}\mathrm{b}$ [150], and ${\mathrm{B}} \to\mathrm{t}\mathrm{W}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\nu/\mathrm{b}\ell\nu\,\mathrm{q}\mathrm{q}$ [151]. Two theory predictions at LO in perturbative QCD are superimposed, corresponding to different VLQ widths. Searches using data corresponding to an integrated luminosity of 36 fb$^{-1}$, rather than the full Run 2 integrated luminosity of 138 fb$^{-1}$, are indicated with a spade symbol in the legend.
png pdf	Figure 43-b: 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: ${\mathrm{B}} \to\mathrm{t}\mathrm{W}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\nu/\mathrm{q}\mathrm{q}$ [153], ${\mathrm{B}} \to\mathrm{b}\mathrm{H}\to\mathrm{b}\,\mathrm{b}\mathrm{b}$ [150], and ${\mathrm{B}} \to\mathrm{t}\mathrm{W}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\nu/\mathrm{b}\ell\nu\,\mathrm{q}\mathrm{q}$ [151]. Two theory predictions at LO in perturbative QCD are superimposed, corresponding to different VLQ widths. Searches using data corresponding to an integrated luminosity of 36 fb$^{-1}$, rather than the full Run 2 integrated luminosity of 138 fb$^{-1}$, are indicated with a spade symbol in the legend.
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: ${\mathrm{X}_{5/3}} \to\mathrm{t}\mathrm{W}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\nu/\mathrm{q}\mathrm{q}$ [153], ${\mathrm{X}_{5/3}} \to\mathrm{t}\mathrm{W}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\nu/\mathrm{b}\ell\nu\,\mathrm{q}\mathrm{q}$ [151], and ${\mathrm{Y}_{4/3}} \to\mathrm{b}\mathrm{W}\to\mathrm{b}\,\ell\nu$ [149]. Searches using data corresponding to an integrated luminosity of 2.3 fb$^{-1}$ and 36 fb$^{-1}$, rather than the full Run-s2 integrated luminosity of 138 fb$^{-1}$, are indicated with a heart and spade symbol, respectively, in the legend.
png pdf	Figure 44-a: 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: ${\mathrm{X}_{5/3}} \to\mathrm{t}\mathrm{W}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\nu/\mathrm{q}\mathrm{q}$ [153], ${\mathrm{X}_{5/3}} \to\mathrm{t}\mathrm{W}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\nu/\mathrm{b}\ell\nu\,\mathrm{q}\mathrm{q}$ [151], and ${\mathrm{Y}_{4/3}} \to\mathrm{b}\mathrm{W}\to\mathrm{b}\,\ell\nu$ [149]. Searches using data corresponding to an integrated luminosity of 2.3 fb$^{-1}$ and 36 fb$^{-1}$, rather than the full Run-s2 integrated luminosity of 138 fb$^{-1}$, are indicated with a heart and spade symbol, respectively, in the legend.
png pdf	Figure 44-b: 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: ${\mathrm{X}_{5/3}} \to\mathrm{t}\mathrm{W}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\nu/\mathrm{q}\mathrm{q}$ [153], ${\mathrm{X}_{5/3}} \to\mathrm{t}\mathrm{W}\to\mathrm{b}\mathrm{q}\mathrm{q}\,\ell\nu/\mathrm{b}\ell\nu\,\mathrm{q}\mathrm{q}$ [151], and ${\mathrm{Y}_{4/3}} \to\mathrm{b}\mathrm{W}\to\mathrm{b}\,\ell\nu$ [149]. Searches using data corresponding to an integrated luminosity of 2.3 fb$^{-1}$ and 36 fb$^{-1}$, rather than the full Run-s2 integrated luminosity of 138 fb$^{-1}$, are indicated with a heart and spade symbol, respectively, in the legend.
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 background-only hypothesis. Figures adapted from Ref. [170].
png pdf	Figure 45-a: 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 background-only hypothesis. Figures adapted from Ref. [170].
png pdf	Figure 45-b: 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 background-only hypothesis. Figures adapted from Ref. [170].
png pdf	Figure 46: Expected significances for T quark pair production as a function of the integrated luminosity at the HL-LHC, 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. [170].
png pdf	Figure 46-a: Expected significances for T quark pair production as a function of the integrated luminosity at the HL-LHC, 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. [170].
png pdf	Figure 46-b: Expected significances for T quark pair production as a function of the integrated luminosity at the HL-LHC, 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. [170].
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 47-a: 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 47-b: 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 third-generation leptons and quarks.
png pdf	Figure 48-a: 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 third-generation leptons and quarks.
png pdf	Figure 48-b: 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 third-generation leptons and quarks.
png pdf	Figure 48-c: 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 third-generation leptons and quarks.
png pdf	Figure 48-d: 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 third-generation leptons and quarks.
png pdf	Figure 49: The $L_{\mathrm{T}}$ distribution in 3$\mkern1mu\mathrm{e}\mkern-2mu/\mkern-3mu\mu$, 2 $\mkern1mu\mathrm{e}\mkern-2mu/\mkern-3mu\mu1\tau_\mathrm{h}$, and 1 $\mkern1mu\mathrm{e}\mkern-2mu/\mkern-3mu\mu2\tau_\mathrm{h}$ events (left), and the invariant mass distribution of the OS different-flavor ($m_{\text{OSDF}}$) light lepton and tau lepton pair in 2 $\mkern1mu\mathrm{e}\mkern-2mu/\mkern-3mu\mu1\tau_\mathrm{h}$ and 1 $\mkern1mu\mathrm{e}\mkern-2mu/\mkern-3mu\mu2\tau_\mathrm{h}$ 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 background-only hypothesis. For illustration, an example signal hypothesis for the production of vector-like leptons coupled to third-generation SM leptons in the doublet scenario for a VLL mass of 1 TeV, before the fit, is overlaid. The signal yield is scaled by a factor of 10 for visualization purposes. Figures adapted from Ref. [204].
png pdf	Figure 49-a: The $L_{\mathrm{T}}$ distribution in 3$\mkern1mu\mathrm{e}\mkern-2mu/\mkern-3mu\mu$, 2 $\mkern1mu\mathrm{e}\mkern-2mu/\mkern-3mu\mu1\tau_\mathrm{h}$, and 1 $\mkern1mu\mathrm{e}\mkern-2mu/\mkern-3mu\mu2\tau_\mathrm{h}$ events (left), and the invariant mass distribution of the OS different-flavor ($m_{\text{OSDF}}$) light lepton and tau lepton pair in 2 $\mkern1mu\mathrm{e}\mkern-2mu/\mkern-3mu\mu1\tau_\mathrm{h}$ and 1 $\mkern1mu\mathrm{e}\mkern-2mu/\mkern-3mu\mu2\tau_\mathrm{h}$ 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 background-only hypothesis. For illustration, an example signal hypothesis for the production of vector-like leptons coupled to third-generation SM leptons in the doublet scenario for a VLL mass of 1 TeV, before the fit, is overlaid. The signal yield is scaled by a factor of 10 for visualization purposes. Figures adapted from Ref. [204].
png pdf	Figure 49-b: The $L_{\mathrm{T}}$ distribution in 3$\mkern1mu\mathrm{e}\mkern-2mu/\mkern-3mu\mu$, 2 $\mkern1mu\mathrm{e}\mkern-2mu/\mkern-3mu\mu1\tau_\mathrm{h}$, and 1 $\mkern1mu\mathrm{e}\mkern-2mu/\mkern-3mu\mu2\tau_\mathrm{h}$ events (left), and the invariant mass distribution of the OS different-flavor ($m_{\text{OSDF}}$) light lepton and tau lepton pair in 2 $\mkern1mu\mathrm{e}\mkern-2mu/\mkern-3mu\mu1\tau_\mathrm{h}$ and 1 $\mkern1mu\mathrm{e}\mkern-2mu/\mkern-3mu\mu2\tau_\mathrm{h}$ 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 background-only hypothesis. For illustration, an example signal hypothesis for the production of vector-like leptons coupled to third-generation SM leptons in the doublet scenario for a VLL mass of 1 TeV, before the fit, is overlaid. The signal yield is scaled by a factor of 10 for visualization purposes. Figures adapted from Ref. [204].
png pdf	Figure 50: The \textitVLL-H BDT regions for the four-lepton channels for the full Run 2 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 background-only hypothesis. For illustration, an example signal hypothesis for the production of the vector-like leptons coupled to the third generation SM leptons in the doublet scenario for a VLL mass of 900 GeV, before the fit, is overlaid. The signal yield is scaled by a factor of 10 for visualization purposes. Figure adapted from Ref. [204].
png pdf	Figure 51: Observed and expected upper limits at 95% CL on the production cross section for the vector-like leptons coupled to third-generation SM leptons in the doublet model (left) and singlet model (right). For the doublet vector-like lepton model, to the left of the vertical dashed gray line, the limits are shown from the model-independent scheme, while to the right the limits are shown from the model dependent BDT regions. For the singlet vector-like lepton model, the limit is shown from the model-independent scheme for all masses. Figures adapted from Ref. [204].
png pdf	Figure 51-a: Observed and expected upper limits at 95% CL on the production cross section for the vector-like leptons coupled to third-generation SM leptons in the doublet model (left) and singlet model (right). For the doublet vector-like lepton model, to the left of the vertical dashed gray line, the limits are shown from the model-independent scheme, while to the right the limits are shown from the model dependent BDT regions. For the singlet vector-like lepton model, the limit is shown from the model-independent scheme for all masses. Figures adapted from Ref. [204].
png pdf	Figure 51-b: Observed and expected upper limits at 95% CL on the production cross section for the vector-like leptons coupled to third-generation SM leptons in the doublet model (left) and singlet model (right). For the doublet vector-like lepton model, to the left of the vertical dashed gray line, the limits are shown from the model-independent scheme, while to the right the limits are shown from the model dependent BDT regions. For the singlet vector-like lepton model, the limit is shown from the model-independent scheme for all masses. Figures adapted from Ref. [204].
png pdf	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 background-only 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. [205].
png pdf	Figure 52-a: 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 background-only 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. [205].
png pdf	Figure 52-b: 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 background-only 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. [205].
png pdf	Figure 52-c: 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 background-only 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. [205].
png pdf	Figure 52-d: 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 background-only 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. [205].
png pdf	Figure 53: Expected and observed 95% CL upper limits on the product of the VLL pair production cross section and the branching fraction to third-generation 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. [205].
png pdf	Figure 54: Expected HL-LHC exclusion limits for vector-like leptons coupled to first-generation (upper row), second-generation (middle row), and third-generation SM 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.
png pdf	Figure 54-a: Expected HL-LHC exclusion limits for vector-like leptons coupled to first-generation (upper row), second-generation (middle row), and third-generation SM 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.
png pdf	Figure 54-b: Expected HL-LHC exclusion limits for vector-like leptons coupled to first-generation (upper row), second-generation (middle row), and third-generation SM 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.
png pdf	Figure 54-c: Expected HL-LHC exclusion limits for vector-like leptons coupled to first-generation (upper row), second-generation (middle row), and third-generation SM 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.
png pdf	Figure 54-d: Expected HL-LHC exclusion limits for vector-like leptons coupled to first-generation (upper row), second-generation (middle row), and third-generation SM 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.
png pdf	Figure 54-e: Expected HL-LHC exclusion limits for vector-like leptons coupled to first-generation (upper row), second-generation (middle row), and third-generation SM 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.
png pdf	Figure 54-f: Expected HL-LHC exclusion limits for vector-like leptons coupled to first-generation (upper row), second-generation (middle row), and third-generation SM 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.
png pdf	Figure 55: Representative Feynman diagram of a Majorana HNL, labeled as $\mathrm{N}$, produced through the decay of a W or Z boson.
png pdf	Figure 56: Representative Feynman diagram of a Majorana HNL, labeled as $\mathrm{N}$, produced through the $\mathrm{W}\gamma$ fusion process and with two charged leptons and jets in the final state.
png pdf	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 $\pi^{\mp}$.
png pdf	Figure 58: Example Feynman diagrams of VBF processes with heavy Majorana neutrino production (left) and processes mediated by the Weinberg operator (right).
png pdf	Figure 58-a: Example Feynman diagrams of VBF processes with heavy Majorana neutrino production (left) and processes mediated by the Weinberg operator (right).
png pdf	Figure 58-b: Example Feynman diagrams of VBF processes with heavy Majorana neutrino production (left) and processes mediated by the Weinberg operator (right).
png pdf	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.
png pdf	Figure 59-a: 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.
png pdf	Figure 59-b: 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.
png pdf	Figure 60: Representative Feynman diagrams for the production of a heavy Majorana neutrino, labeled as $\mathrm{N} \ell$, via the decay of a $\mathrm{W_R}$ (left) and $\mathrm{Z}^{'}$ boson (right).
png pdf	Figure 60-a: Representative Feynman diagrams for the production of a heavy Majorana neutrino, labeled as $\mathrm{N} \ell$, via the decay of a $\mathrm{W_R}$ (left) and $\mathrm{Z}^{'}$ boson (right).
png pdf	Figure 60-b: Representative Feynman diagrams for the production of a heavy Majorana neutrino, labeled as $\mathrm{N} \ell$, via the decay of a $\mathrm{W_R}$ (left) and $\mathrm{Z}^{'}$ boson (right).
png pdf	Figure 61: The fermion interaction as a sum of gauge (center) and contact (right) interaction contributions.
png pdf	Figure 62: Example diagrams for the decay of a heavy composite Majorana neutrino to $\ell\mathrm{q}{\overline{\mathrm{q}}{\prime}}$.
png pdf	Figure 63: Expected (observed) upper limits at 95% CL shown with a dashed (solid) black line, derived on heavy neutrino mixing parameters $|V_{\mathrm{eN}}|^{2}$, $|V_{\mathrm{\mu N}}|^{2}$, and $| V_{\mathrm{eN}}V_{\mathrm{\mu N}}^\ast|^2/(|V_{\mathrm{eN}}|^2+|V_{\mathrm{\mu N}}|^2)$ as functions of the HNL mass. The dashed brown line in the upper two figures shows constraints from Electroweak Precision Data (EWPD) [254] on the $|V_{\mathrm{eN}}|^{2}$ and $|V_{\mathrm{\mu N}}|^{2}$ parameters. The lower figure, reproduced from Ref. [252], does not show the corresponding EWPD limits. The upper limits from other direct searches at the DELPHI experiment [255], the L3 experiment [256,257], and the ATLAS experiment [258] are superimposed. Also shown are the upper limits from the CMS experiment at $\sqrt{s}=$ 8 TeV using the 2012 data set [253] with a solid red line, and the search in the trilepton final state [259] based on the same 2016 data set as used in this analysis with a dashed red line. Figures adapted from Ref. [252].
png pdf	Figure 63-a: Expected (observed) upper limits at 95% CL shown with a dashed (solid) black line, derived on heavy neutrino mixing parameters $|V_{\mathrm{eN}}|^{2}$, $|V_{\mathrm{\mu N}}|^{2}$, and $| V_{\mathrm{eN}}V_{\mathrm{\mu N}}^\ast|^2/(|V_{\mathrm{eN}}|^2+|V_{\mathrm{\mu N}}|^2)$ as functions of the HNL mass. The dashed brown line in the upper two figures shows constraints from Electroweak Precision Data (EWPD) [254] on the $|V_{\mathrm{eN}}|^{2}$ and $|V_{\mathrm{\mu N}}|^{2}$ parameters. The lower figure, reproduced from Ref. [252], does not show the corresponding EWPD limits. The upper limits from other direct searches at the DELPHI experiment [255], the L3 experiment [256,257], and the ATLAS experiment [258] are superimposed. Also shown are the upper limits from the CMS experiment at $\sqrt{s}=$ 8 TeV using the 2012 data set [253] with a solid red line, and the search in the trilepton final state [259] based on the same 2016 data set as used in this analysis with a dashed red line. Figures adapted from Ref. [252].
png pdf	Figure 63-b: Expected (observed) upper limits at 95% CL shown with a dashed (solid) black line, derived on heavy neutrino mixing parameters $|V_{\mathrm{eN}}|^{2}$, $|V_{\mathrm{\mu N}}|^{2}$, and $| V_{\mathrm{eN}}V_{\mathrm{\mu N}}^\ast|^2/(|V_{\mathrm{eN}}|^2+|V_{\mathrm{\mu N}}|^2)$ as functions of the HNL mass. The dashed brown line in the upper two figures shows constraints from Electroweak Precision Data (EWPD) [254] on the $|V_{\mathrm{eN}}|^{2}$ and $|V_{\mathrm{\mu N}}|^{2}$ parameters. The lower figure, reproduced from Ref. [252], does not show the corresponding EWPD limits. The upper limits from other direct searches at the DELPHI experiment [255], the L3 experiment [256,257], and the ATLAS experiment [258] are superimposed. Also shown are the upper limits from the CMS experiment at $\sqrt{s}=$ 8 TeV using the 2012 data set [253] with a solid red line, and the search in the trilepton final state [259] based on the same 2016 data set as used in this analysis with a dashed red line. Figures adapted from Ref. [252].
png pdf	Figure 63-c: Expected (observed) upper limits at 95% CL shown with a dashed (solid) black line, derived on heavy neutrino mixing parameters $|V_{\mathrm{eN}}|^{2}$, $|V_{\mathrm{\mu N}}|^{2}$, and $| V_{\mathrm{eN}}V_{\mathrm{\mu N}}^\ast|^2/(|V_{\mathrm{eN}}|^2+|V_{\mathrm{\mu N}}|^2)$ as functions of the HNL mass. The dashed brown line in the upper two figures shows constraints from Electroweak Precision Data (EWPD) [254] on the $|V_{\mathrm{eN}}|^{2}$ and $|V_{\mathrm{\mu N}}|^{2}$ parameters. The lower figure, reproduced from Ref. [252], does not show the corresponding EWPD limits. The upper limits from other direct searches at the DELPHI experiment [255], the L3 experiment [256,257], and the ATLAS experiment [258] are superimposed. Also shown are the upper limits from the CMS experiment at $\sqrt{s}=$ 8 TeV using the 2012 data set [253] with a solid red line, and the search in the trilepton final state [259] based on the same 2016 data set as used in this analysis with a dashed red line. Figures adapted from Ref. [252].
png pdf	Figure 64: Expected (observed) upper limits at 95% CL derived on heavy neutrino mixing parameters $|V_{\mathrm{eN}}|^{2}$, $|V_{\mathrm{\mu N}}|^{2}$, 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 high-mass 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 [255] and the CMS experiment [259,261,262,263] are superimposed. Figures taken from Ref. [260].
png pdf	Figure 64-a: Expected (observed) upper limits at 95% CL derived on heavy neutrino mixing parameters $|V_{\mathrm{eN}}|^{2}$, $|V_{\mathrm{\mu N}}|^{2}$, 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 high-mass 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 [255] and the CMS experiment [259,261,262,263] are superimposed. Figures taken from Ref. [260].
png pdf	Figure 64-b: Expected (observed) upper limits at 95% CL derived on heavy neutrino mixing parameters $|V_{\mathrm{eN}}|^{2}$, $|V_{\mathrm{\mu N}}|^{2}$, 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 high-mass 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 [255] and the CMS experiment [259,261,262,263] are superimposed. Figures taken from Ref. [260].
png pdf	Figure 64-c: Expected (observed) upper limits at 95% CL derived on heavy neutrino mixing parameters $|V_{\mathrm{eN}}|^{2}$, $|V_{\mathrm{\mu N}}|^{2}$, 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 high-mass 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 [255] and the CMS experiment [259,261,262,263] are superimposed. Figures taken from Ref. [260].
png pdf	Figure 65: Upper limits on $|V_{\mathrm{\mu N}}|^{2}$ 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 background-only hypothesis. The solid black curve is the observed upper limit [262]. The red dashed curve displays the observed upper limits from Ref. [259], while the blue dashed curve shows the observed upper limits from Ref. [252]. Figure adapted from Ref. [262].
png pdf	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$\,\text{mm}$, respectively. The $d_{xy}^{\text{sig}}$ quantity is the significance of the impact parameter of the second lepton track. Figures taken from Ref. [263].
png pdf	Figure 66-a: 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$\,\text{mm}$, respectively. The $d_{xy}^{\text{sig}}$ quantity is the significance of the impact parameter of the second lepton track. Figures taken from Ref. [263].
png pdf	Figure 66-b: 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$\,\text{mm}$, respectively. The $d_{xy}^{\text{sig}}$ quantity is the significance of the impact parameter of the second lepton track. Figures taken from Ref. [263].
png pdf	Figure 67: Observed 95% CL lower limits on the mass (left) and the proper lifetime (right) for Majorana HNL production with $c\tau_{\mathrm{N}}=1\,\text{mm}$ 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. [263].
png pdf	Figure 67-a: Observed 95% CL lower limits on the mass (left) and the proper lifetime (right) for Majorana HNL production with $c\tau_{\mathrm{N}}=1\,\text{mm}$ 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. [263].
png pdf	Figure 67-b: Observed 95% CL lower limits on the mass (left) and the proper lifetime (right) for Majorana HNL production with $c\tau_{\mathrm{N}}=1\,\text{mm}$ 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. [263].
png pdf	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_{\mathrm{\ell N}}|^{2} =$0.8$\times$10$^{-4} $(HNL2),$ m_{\mathrm{N}}= $6 GeV and$ $|V_{\mathrm{\ell N}}|^{2} =$ 1.3$\times$10$^{-6}$ (HNL6), $m_{\mathrm{N}}=$ 12 GeV and |V_{\mathrm{\ell 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. [261].
png pdf	Figure 68-a: 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_{\mathrm{\ell N}}|^{2} =$0.8$\times$10$^{-4} $(HNL2),$ m_{\mathrm{N}}= $6 GeV and$ $|V_{\mathrm{\ell N}}|^{2} =$ 1.3$\times$10$^{-6}$ (HNL6), $m_{\mathrm{N}}=$ 12 GeV and |V_{\mathrm{\ell 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. [261].
png pdf	Figure 68-b: 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_{\mathrm{\ell N}}|^{2} =$0.8$\times$10$^{-4} $(HNL2),$ m_{\mathrm{N}}= $6 GeV and$ $|V_{\mathrm{\ell N}}|^{2} =$ 1.3$\times$10$^{-6}$ (HNL6), $m_{\mathrm{N}}=$ 12 GeV and |V_{\mathrm{\ell 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. [261].
png pdf	Figure 69: The limits at 95% CL on $|V_{\mathrm{eN}}|^{2}$ (left) and $|V_{\mathrm{\mu N}}|^{2}$ (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 [255] and the CMS [259,252] Collaborations are shown as upper limits, i.e.,, the area above the curves indicates the respective observed exclusion region. Figures adapted from Ref. [261].
png pdf	Figure 69-a: The limits at 95% CL on $|V_{\mathrm{eN}}|^{2}$ (left) and $|V_{\mathrm{\mu N}}|^{2}$ (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 [255] and the CMS [259,252] Collaborations are shown as upper limits, i.e.,, the area above the curves indicates the respective observed exclusion region. Figures adapted from Ref. [261].
png pdf	Figure 69-b: The limits at 95% CL on $|V_{\mathrm{eN}}|^{2}$ (left) and $|V_{\mathrm{\mu N}}|^{2}$ (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 [255] and the CMS [259,252] Collaborations are shown as upper limits, i.e.,, the area above the curves indicates the respective observed exclusion region. Figures adapted from Ref. [261].
png pdf	Figure 69-c: The limits at 95% CL on $|V_{\mathrm{eN}}|^{2}$ (left) and $|V_{\mathrm{\mu N}}|^{2}$ (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 [255] and the CMS [259,252] Collaborations are shown as upper limits, i.e.,, the area above the curves indicates the respective observed exclusion region. Figures adapted from Ref. [261].
png pdf	Figure 69-d: The limits at 95% CL on $|V_{\mathrm{eN}}|^{2}$ (left) and $|V_{\mathrm{\mu N}}|^{2}$ (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 [255] and the CMS [259,252] Collaborations are shown as upper limits, i.e.,, the area above the curves indicates the respective observed exclusion region. Figures adapted from Ref. [261].
png pdf	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. [270].
png pdf	Figure 71: Expected and observed upper limits at 95% CL on Majorana HNL production as functions of the HNL mass ($m_{\mathrm{N}}$), and assuming mixing of the HNL with only one generation. The limits are shown 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. [270].
png pdf	Figure 71-a: Expected and observed upper limits at 95% CL on Majorana HNL production as functions of the HNL mass ($m_{\mathrm{N}}$), and assuming mixing of the HNL with only one generation. The limits are shown 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. [270].
png pdf	Figure 71-b: Expected and observed upper limits at 95% CL on Majorana HNL production as functions of the HNL mass ($m_{\mathrm{N}}$), and assuming mixing of the HNL with only one generation. The limits are shown 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. [270].
png pdf	Figure 71-c: Expected and observed upper limits at 95% CL on Majorana HNL production as functions of the HNL mass ($m_{\mathrm{N}}$), and assuming mixing of the HNL with only one generation. The limits are shown 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. [270].
png pdf	Figure 72: Expected and observed limits at 95% CL on $|V_{\mathrm{N}}|^{2}$ 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 [261,270,263], ATLAS [265], LHCb [276], and Belle [277] 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. [220].
png pdf	Figure 72-a: Expected and observed limits at 95% CL on $|V_{\mathrm{N}}|^{2}$ 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 [261,270,263], ATLAS [265], LHCb [276], and Belle [277] 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. [220].
png pdf	Figure 72-b: Expected and observed limits at 95% CL on $|V_{\mathrm{N}}|^{2}$ 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 [261,270,263], ATLAS [265], LHCb [276], and Belle [277] 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. [220].
png pdf	Figure 72-c: Expected and observed limits at 95% CL on $|V_{\mathrm{N}}|^{2}$ 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 [261,270,263], ATLAS [265], LHCb [276], and Belle [277] 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. [220].
png pdf	Figure 72-d: Expected and observed limits at 95% CL on $|V_{\mathrm{N}}|^{2}$ 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 [261,270,263], ATLAS [265], LHCb [276], and Belle [277] 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. [220].
png pdf	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. [220].
png pdf	Figure 73-a: 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. [220].
png pdf	Figure 73-b: 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. [220].
png pdf	Figure 74: Summary of searches at the CMS experiment for long-lived HNLs in the $Type I$ seesaw model. The observed limits at 95% CL on the mixing parameter \mixparsq\ell$\mathrm{N}$ 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).
png pdf	Figure 74-a: Summary of searches at the CMS experiment for long-lived HNLs in the $Type I$ seesaw model. The observed limits at 95% CL on the mixing parameter \mixparsq\ell$\mathrm{N}$ 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).
png pdf	Figure 74-b: Summary of searches at the CMS experiment for long-lived HNLs in the $Type I$ seesaw model. The observed limits at 95% CL on the mixing parameter \mixparsq\ell$\mathrm{N}$ 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).
png pdf	Figure 74-c: Summary of searches at the CMS experiment for long-lived HNLs in the $Type I$ seesaw model. The observed limits at 95% CL on the mixing parameter \mixparsq\ell$\mathrm{N}$ 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).
png pdf	Figure 74-d: Summary of searches at the CMS experiment for long-lived HNLs in the $Type I$ seesaw model. The observed limits at 95% CL on the mixing parameter \mixparsq\ell$\mathrm{N}$ 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).
png pdf	Figure 75: Observed and expected upper limits at 95% CL on the production cross section for $Type III$ seesaw HNLs in the flavor-democratic scenario using the model-independent schemes and the BDT regions. To the left of the vertical dashed gray line, the limits are shown from the model-independent SR, and to the right the limits are shown obtained using the BDT regions. Figure adapted from Ref. [204]. Production cross sections for the signal model are calculated at NLO plus next-to-leading logarithmic precision, assuming that the heavy leptons are SU(2) triplet fermions [60,61].
png pdf	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. [204].
png pdf	Figure 76-a: 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. [204].
png pdf	Figure 76-b: 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. [204].
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 right-handed $\mathrm{W_R}$ 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 dash-dotted 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 [284] 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. [281].
png pdf	Figure 77-a: The observed upper limits at 95% CL on the product of the production cross section and the branching fraction of a right-handed $\mathrm{W_R}$ 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 dash-dotted 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 [284] 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. [281].
png pdf	Figure 77-b: The observed upper limits at 95% CL on the product of the production cross section and the branching fraction of a right-handed $\mathrm{W_R}$ 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 dash-dotted 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 [284] 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. [281].
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 background-only 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. Figures taken from Ref. [285].
png	Figure 78-a: 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 background-only 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. Figures taken from Ref. [285].
png	Figure 78-b: 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 background-only 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. Figures taken from Ref. [285].
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 background-only 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. [286].
png	Figure 79-a: 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 background-only 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. [286].
png	Figure 79-b: 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 background-only 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. [286].
png pdf	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. [289].
png pdf	Figure 80-a: 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. [289].
png pdf	Figure 80-b: 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. [289].
png pdf	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 two-dimensional $m_{\mathrm{N}}$--$m_{\mathrm{V}}$ plane are shown in the electron and muon channel (left and right, respectively).
png pdf	Figure 81-a: 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 two-dimensional $m_{\mathrm{N}}$--$m_{\mathrm{V}}$ plane are shown in the electron and muon channel (left and right, respectively).
png pdf	Figure 81-b: 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 two-dimensional $m_{\mathrm{N}}$--$m_{\mathrm{V}}$ plane are shown in the electron and muon channel (left and right, respectively).
png pdf	Figure 82: Expected (dashed black) and observed (blue solid) exclusion limits for the $\mathrm{e}\mathrm{e}\mathrm{q}{\overline{\mathrm{q}}{\prime}}$ (left) and $\mu\mu\mathrm{q}{\overline{\mathrm{q}}{\prime}}$ (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 background-only hypothesis. Figures taken from Ref. [290].
png pdf	Figure 82-a: Expected (dashed black) and observed (blue solid) exclusion limits for the $\mathrm{e}\mathrm{e}\mathrm{q}{\overline{\mathrm{q}}{\prime}}$ (left) and $\mu\mu\mathrm{q}{\overline{\mathrm{q}}{\prime}}$ (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 background-only hypothesis. Figures taken from Ref. [290].
png pdf	Figure 82-b: Expected (dashed black) and observed (blue solid) exclusion limits for the $\mathrm{e}\mathrm{e}\mathrm{q}{\overline{\mathrm{q}}{\prime}}$ (left) and $\mu\mu\mathrm{q}{\overline{\mathrm{q}}{\prime}}$ (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 background-only hypothesis. Figures taken from Ref. [290].
png pdf	Figure 83: Expected (dashed black) and observed (blue solid) exclusion limits for the $\mathrm{e}\mathrm{e}\mathrm{q}{\overline{\mathrm{q}}{\prime}}$ (left) and $\mu\mu\mathrm{q}{\overline{\mathrm{q}}{\prime}}$ (right) channel in the two-dimensional 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 [292] 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 background-only hypothesis. Figures taken from Ref. [290].
png pdf	Figure 83-a: Expected (dashed black) and observed (blue solid) exclusion limits for the $\mathrm{e}\mathrm{e}\mathrm{q}{\overline{\mathrm{q}}{\prime}}$ (left) and $\mu\mu\mathrm{q}{\overline{\mathrm{q}}{\prime}}$ (right) channel in the two-dimensional 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 [292] 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 background-only hypothesis. Figures taken from Ref. [290].
png pdf	Figure 83-b: Expected (dashed black) and observed (blue solid) exclusion limits for the $\mathrm{e}\mathrm{e}\mathrm{q}{\overline{\mathrm{q}}{\prime}}$ (left) and $\mu\mu\mathrm{q}{\overline{\mathrm{q}}{\prime}}$ (right) channel in the two-dimensional 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 [292] 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 background-only hypothesis. Figures taken from Ref. [290].
png pdf	Figure 84: Coverage in the ($p_{\mathrm{T}}$, $d_0$) plane for displaced leptons with the 2016 and 2018 triggers, and the new Run-3 triggers, indicated in light blue, dark blue, and red, respectively [293]. Here, $d_0$ is the impact parameter of the charged lepton track with respect to the PV in the transverse plane.

Tables
png pdf	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 all-hadronic final state. For the 2\ell channels, it is indicated whether the leptons have opposite-sign (OS) or same-sign (SS) charges. For single VLQ searches, the channels are indicated through the decay products of the W, Z, and Higgs bosons, and t quarks.
png pdf	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 single-lepton multilayer perceptron network. Table taken from Ref. [none-none-none].
png pdf	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. [142].

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 vector-like quarks (VLQs), vector-like 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 third-generation 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 charged-lepton partners. The HNLs provide yet another perspective on the interplay between chirality and neutrino mass-generating 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 Run 2 proton-proton 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 third-generation decay of the B quark. Single production of T quarks in the narrow-width 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 background-only prediction that requires further investigation using more data. No VLQ and HNL searches report excesses. Using projections in the context of the future High-Luminosity LHC (HL-LHC) 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 HL-LHC 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 high-pseudorapidity 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 HL-LHC 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 Lorentz-boosted 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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