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Compact Muon Solenoid
LHC, CERN

CMS-B2G-20-011 ; CERN-EP-2022-175
Search for pair production of vector-like quarks in leptonic final states in proton-proton collisions at $ \sqrt{s} = $ 13 TeV
JHEP 07 (2023) 020
Abstract: A search is presented for vector-like $ \mathrm{T} $ and $ \mathrm{B} $ quark-antiquark pairs produced in proton-proton collisions at a center-of-mass energy of 13 TeV. Data were collected by the CMS experiment at the CERN LHC in 2016-2018, with an integrated luminosity of 138 fb$ ^{-1} $. Events are separated into single-lepton, same-sign charge dilepton, and multilepton channels. In the analysis of the single-lepton channel a multilayer neural network and jet identification techniques are employed to select signal events, while the same-sign dilepton and multilepton channels rely on the high-energy signature of the signal to distinguish it from standard model backgrounds. The data are consistent with standard model background predictions, and the production of vector-like quark pairs is excluded at 95% confidence level for $ \mathrm{T} $ quark masses up to 1.54 TeV and $ \mathrm{B} $ quark masses up to 1.56 TeV, depending on the branching fractions assumed, with maximal sensitivity to decay modes that include multiple top quarks. The limits obtained in this search are the strongest limits to date for $ \mathrm{T} \overline{\mathrm{T}} $ production, excluding masses below 1.48 TeV for all decays to third generation quarks, and are the strongest limits to date for $ \mathrm{B} \overline{\mathrm{B}} $ production with $ \mathrm{B} $ quark decays to tW.
Figures & Tables Summary Additional Figures References CMS Publications
Figures

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Figure 1:
Representative Feynman diagrams of the pair production of $ \mathrm{T} \overline{\mathrm{T}} $ (left) and $ \mathrm{B} \overline{\mathrm{B}} $ (right), with decays to third generation quarks and SM bosons.

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Figure 1-a:
Representative Feynman diagram of the pair production of $ \mathrm{T} \overline{\mathrm{T}} $, with decays to third generation quarks and SM bosons.

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Figure 1-b:
Representative Feynman diagram of the pair production of $ \mathrm{B} \overline{\mathrm{B}} $, with decays to third generation quarks and SM bosons.

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Figure 2:
Example single-lepton channel MLP input distributions of $ S_\mathrm{T} $ (left) and the leading jet's DEEPAK8 light quark or gluon score (right) in the training region for the $ \mathrm{T} \overline{\mathrm{T}} $ MLP. The observed data are shown using black markers, predicted $ \mathrm{T} \overline{\mathrm{T}} $ signal with 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 prediction before performing the fit to data are shown by the hatched region. The lower panels show the difference between the data and the background estimate as a multiple of the total uncertainty in both sources. The signal predictions have been scaled for visibility by the factors indicated in the figures.

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Figure 2-a:
Single-lepton channel MLP input distribution of $ S_\mathrm{T} $ in the training region for the $ \mathrm{T} \overline{\mathrm{T}} $ MLP. The observed data are shown using black markers, predicted $ \mathrm{T} \overline{\mathrm{T}} $ signal with 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 prediction before performing the fit to data are shown by the hatched region. The lower panel shows the difference between the data and the background estimate as a multiple of the total uncertainty in both sources. The signal predictions have been scaled for visibility by the factors indicated in the figures.

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Figure 2-b:
Single-lepton channel MLP input distribution of the leading jet's DEEPAK8 light quark or gluon score in the training region for the $ \mathrm{T} \overline{\mathrm{T}} $ MLP. The observed data are shown using black markers, predicted $ \mathrm{T} \overline{\mathrm{T}} $ signal with 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 prediction before performing the fit to data are shown by the hatched region. The lower panel shows the difference between the data and the background estimate as a multiple of the total uncertainty in both sources. The signal predictions have been scaled for visibility by the factors indicated in the figures.

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Figure 3:
Example single-lepton channel $ \mathrm{T} \overline{\mathrm{T}} $ MLP output distributions of the $ \mathrm{T} $ quark score in the inclusive SR (left) and the W +jets score in the CRs (right). The observed data are shown using black markers, predicted $ \mathrm{T} \overline{\mathrm{T}} $ signal with 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 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.

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Figure 3-a:
Single-lepton channel $ \mathrm{T} \overline{\mathrm{T}} $ MLP output distribution of the $ \mathrm{T} $ quark score in the inclusive SR. The observed data are shown using black markers, predicted $ \mathrm{T} \overline{\mathrm{T}} $ signal with 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 panel shows the difference between the 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.

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Figure 3-b:
Single-lepton channel $ \mathrm{T} \overline{\mathrm{T}} $ MLP output distribution of the W +jets score in the CRs. The observed data are shown using black markers, predicted $ \mathrm{T} \overline{\mathrm{T}} $ signal with 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 panel shows the difference between the 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.

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Figure 4:
Single-lepton channel template histograms of the DEEPAK8 jet tags in the DEEPAK8 CR (upper left), and $ H_{\mathrm{T}} $ in the W +jets (upper right) and $ \mathrm{t}\overline{\mathrm{t}} $ (lower) CRs for the $ \mathrm{T} \overline{\mathrm{T}} $ search. The observed data are shown using black markers and the post-fit background estimates, using filled histograms. Statistical and systematic uncertainties in the background estimate after performing the fit to data are shown by the hatched region. The lower panels show the difference between the data and the background estimate as a multiple of the total uncertainty in both sources. Electron and muon categories have been combined for illustration with their uncertainties added in quadrature.

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Figure 4-a:
Single-lepton channel template histogram of the DEEPAK8 jet tags in the DEEPAK8 CR for the $ \mathrm{T} \overline{\mathrm{T}} $ search. The observed data are shown using black markers and the post-fit background estimates, using filled histograms. Statistical and systematic uncertainties in the background estimate after performing the fit to data are shown by the hatched region. The lower panel shows the difference between the data and the background estimate as a multiple of the total uncertainty in both sources. Electron and muon categories have been combined for illustration with their uncertainties added in quadrature.

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Figure 4-b:
Single-lepton channel template histogram of $ H_{\mathrm{T}} $ in the W +jets CR for the $ \mathrm{T} \overline{\mathrm{T}} $ search. The observed data are shown using black markers and the post-fit background estimates, using filled histograms. Statistical and systematic uncertainties in the background estimate after performing the fit to data are shown by the hatched region. The lower panel shows the difference between the data and the background estimate as a multiple of the total uncertainty in both sources. Electron and muon categories have been combined for illustration with their uncertainties added in quadrature.

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Figure 4-c:
Single-lepton channel template histogram of $ H_{\mathrm{T}} $ in the $ \mathrm{t}\overline{\mathrm{t}} $ CR for the $ \mathrm{T} \overline{\mathrm{T}} $ search. The observed data are shown using black markers and the post-fit background estimates, using filled histograms. Statistical and systematic uncertainties in the background estimate after performing the fit to data are shown by the hatched region. The lower panel shows the difference between the data and the background estimate as a multiple of the total uncertainty in both sources. Electron and muon categories have been combined for illustration with their uncertainties added in quadrature.

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Figure 5:
Distribution of lepton $ p_{\mathrm{T}} $ in 2017 (left) and 2018 (right) in the multilepton channel nonprompt lepton CR for all flavor categories, evaluated with the best fit nonprompt rates. The $ p_{\mathrm{T}} $ values of the three leptons in each event are included in the histogram. The uncertainty shown is the quadratic sum of the statistical and systematic components. The lower panel shows the difference between the data and the background estimate as a multiple of the total uncertainty in both sources. The signal predictions have been scaled for visibility by the factors indicated in the figures.

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Figure 5-a:
Distribution of lepton $ p_{\mathrm{T}} $ in 2017 in the multilepton channel nonprompt lepton CR for all flavor categories, evaluated with the best fit nonprompt rates. The $ p_{\mathrm{T}} $ values of the three leptons in each event are included in the histogram. The uncertainty shown is the quadratic sum of the statistical and systematic components. The lower panel shows the difference between the data and the background estimate as a multiple of the total uncertainty in both sources. The signal predictions have been scaled for visibility by the factors indicated in the figures.

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Figure 5-b:
Distribution of lepton $ p_{\mathrm{T}} $ in 2018 in the multilepton channel nonprompt lepton CR for all flavor categories, evaluated with the best fit nonprompt rates. The $ p_{\mathrm{T}} $ values of the three leptons in each event are included in the histogram. The uncertainty shown is the quadratic sum of the statistical and systematic components. The lower panel shows the difference between the data and the background estimate as a multiple of the total uncertainty in both sources. The signal predictions have been scaled for visibility by the factors indicated in the figures.

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Figure 6:
Template histograms of the VLQ score in single-lepton SRs 1 and 2 combined, and SRs 3-12 (left-to-right, upper-to-lower). The observed data 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 post-fit background estimates, using filled histograms. Statistical and systematic uncertainties in the background estimate after performing the fit to data are shown by the hatched region. The lower panels show the difference between the data and the background estimate as a multiple of the total uncertainty in both sources. Electron and muon categories have been combined for illustration with their uncertainties added in quadrature.

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Figure 6-a:
Template histograms of the VLQ score in single-lepton SRs 1 and 2 combined. The observed data 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 post-fit background estimates, using filled histograms. Statistical and systematic uncertainties in the background estimate after performing the fit to data are shown by the hatched region. The lower panels show the difference between the data and the background estimate as a multiple of the total uncertainty in both sources. Electron and muon categories have been combined for illustration with their uncertainties added in quadrature.

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Figure 6-b:
Template histograms of the VLQ score in single-lepton SR 3. The observed data 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 post-fit background estimates, using filled histograms. Statistical and systematic uncertainties in the background estimate after performing the fit to data are shown by the hatched region. The lower panels show the difference between the data and the background estimate as a multiple of the total uncertainty in both sources. Electron and muon categories have been combined for illustration with their uncertainties added in quadrature.

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Figure 6-c:
Template histograms of the VLQ score in single-lepton SR 4. The observed data 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 post-fit background estimates, using filled histograms. Statistical and systematic uncertainties in the background estimate after performing the fit to data are shown by the hatched region. The lower panels show the difference between the data and the background estimate as a multiple of the total uncertainty in both sources. Electron and muon categories have been combined for illustration with their uncertainties added in quadrature.

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Figure 6-d:
Template histograms of the VLQ score in single-lepton SR 5. The observed data 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 post-fit background estimates, using filled histograms. Statistical and systematic uncertainties in the background estimate after performing the fit to data are shown by the hatched region. The lower panels show the difference between the data and the background estimate as a multiple of the total uncertainty in both sources. Electron and muon categories have been combined for illustration with their uncertainties added in quadrature.

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Figure 6-e:
Template histograms of the VLQ score in single-lepton SR 6. The observed data 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 post-fit background estimates, using filled histograms. Statistical and systematic uncertainties in the background estimate after performing the fit to data are shown by the hatched region. The lower panels show the difference between the data and the background estimate as a multiple of the total uncertainty in both sources. Electron and muon categories have been combined for illustration with their uncertainties added in quadrature.

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Figure 6-f:
Template histograms of the VLQ score in single-lepton SR 7. The observed data 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 post-fit background estimates, using filled histograms. Statistical and systematic uncertainties in the background estimate after performing the fit to data are shown by the hatched region. The lower panels show the difference between the data and the background estimate as a multiple of the total uncertainty in both sources. Electron and muon categories have been combined for illustration with their uncertainties added in quadrature.

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Figure 6-g:
Template histograms of the VLQ score in single-lepton SR 8. The observed data 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 post-fit background estimates, using filled histograms. Statistical and systematic uncertainties in the background estimate after performing the fit to data are shown by the hatched region. The lower panels show the difference between the data and the background estimate as a multiple of the total uncertainty in both sources. Electron and muon categories have been combined for illustration with their uncertainties added in quadrature.

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Figure 6-h:
Template histograms of the VLQ score in single-lepton SR 9. The observed data 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 post-fit background estimates, using filled histograms. Statistical and systematic uncertainties in the background estimate after performing the fit to data are shown by the hatched region. The lower panels show the difference between the data and the background estimate as a multiple of the total uncertainty in both sources. Electron and muon categories have been combined for illustration with their uncertainties added in quadrature.

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Figure 6-i:
Template histograms of the VLQ score in single-lepton SR 10. The observed data 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 post-fit background estimates, using filled histograms. Statistical and systematic uncertainties in the background estimate after performing the fit to data are shown by the hatched region. The lower panels show the difference between the data and the background estimate as a multiple of the total uncertainty in both sources. Electron and muon categories have been combined for illustration with their uncertainties added in quadrature.

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Figure 6-j:
Template histograms of the VLQ score in single-lepton SR 11. The observed data 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 post-fit background estimates, using filled histograms. Statistical and systematic uncertainties in the background estimate after performing the fit to data are shown by the hatched region. The lower panels show the difference between the data and the background estimate as a multiple of the total uncertainty in both sources. Electron and muon categories have been combined for illustration with their uncertainties added in quadrature.

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Figure 6-k:
Template histograms of the VLQ score in single-lepton SR 12. The observed data 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 post-fit background estimates, using filled histograms. Statistical and systematic uncertainties in the background estimate after performing the fit to data are shown by the hatched region. The lower panels show the difference between the data and the background estimate as a multiple of the total uncertainty in both sources. Electron and muon categories have been combined for illustration with their uncertainties added in quadrature.

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Figure 7:
Template histograms of $ H_{\mathrm{T}} ^{\mathrm{lep}} $ in the same-sign dilepton signal region for $ \mathrm{e} \mathrm{e} $ (upper left), $ \mathrm{e} \mu $ (upper right), and $ \mu \mu $ categories (lower). 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 post-fit background estimates, using filled histograms. Statistical and systematic uncertainties in the background estimate after performing the fit to data are shown by the hatched region. The lower panels show the difference between the data and the background estimate as a multiple of the total uncertainty in both sources.

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Figure 7-a:
Template histogram of $ H_{\mathrm{T}} ^{\mathrm{lep}} $ in the same-sign dilepton signal region for $ \mathrm{e} \mathrm{e} $ category. 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 post-fit background estimates, using filled histograms. Statistical and systematic uncertainties in the background estimate after performing the fit to data are shown by the hatched region. The lower panel shows the difference between the data and the background estimate as a multiple of the total uncertainty in both sources.

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Figure 7-b:
Template histogram of $ H_{\mathrm{T}} ^{\mathrm{lep}} $ in the same-sign dilepton signal region for $ \mathrm{e} \mu $ category. 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 post-fit background estimates, using filled histograms. Statistical and systematic uncertainties in the background estimate after performing the fit to data are shown by the hatched region. The lower panel shows the difference between the data and the background estimate as a multiple of the total uncertainty in both sources.

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Figure 7-c:
Template histogram of $ H_{\mathrm{T}} ^{\mathrm{lep}} $ in the same-sign dilepton signal region for $ \mu \mu $ category. 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 post-fit background estimates, using filled histograms. Statistical and systematic uncertainties in the background estimate after performing the fit to data are shown by the hatched region. The lower panel shows the difference between the data and the background estimate as a multiple of the total uncertainty in both sources.

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Figure 8:
Template histograms of $ S_\mathrm{T} $ in the multilepton signal region for $ \mathrm{e} \mathrm{e} \mathrm{e} $, $ \mathrm{e} \mathrm{e} \mu $, $ \mathrm{e} \mu \mu $, and $ \mu \mu \mu $ categories (left-to-right, upper-to-lower). 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 post-fit background estimates, using filled histograms. Statistical and systematic uncertainties in the background estimate after performing the fit to data are shown by the hatched region. The lower panels show the difference between the data and the background estimate as a multiple of the total uncertainty in both sources.

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Figure 8-a:
Template histograms of $ S_\mathrm{T} $ in the multilepton signal region for $ \mathrm{e} \mathrm{e} \mathrm{e} $ category. 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 post-fit background estimates, using filled histograms. Statistical and systematic uncertainties in the background estimate after performing the fit to data are shown by the hatched region. The lower panel shows the difference between the data and the background estimate as a multiple of the total uncertainty in both sources.

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Figure 8-b:
Template histograms of $ S_\mathrm{T} $ in the multilepton signal region for $ \mathrm{e} \mathrm{e} \mu $ category. 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 post-fit background estimates, using filled histograms. Statistical and systematic uncertainties in the background estimate after performing the fit to data are shown by the hatched region. The lower panel shows the difference between the data and the background estimate as a multiple of the total uncertainty in both sources.

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Figure 8-c:
Template histograms of $ S_\mathrm{T} $ in the multilepton signal region for $ \mathrm{e} \mu \mu $ category. 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 post-fit background estimates, using filled histograms. Statistical and systematic uncertainties in the background estimate after performing the fit to data are shown by the hatched region. The lower panel shows the difference between the data and the background estimate as a multiple of the total uncertainty in both sources.

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Figure 8-d:
Template histograms of $ S_\mathrm{T} $ in the multilepton signal region for $ \mu \mu \mu $ category. 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 post-fit background estimates, using filled histograms. Statistical and systematic uncertainties in the background estimate after performing the fit to data are shown by the hatched region. The lower panel shows the difference between the data and the background estimate as a multiple of the total uncertainty in both sources.

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Figure 9:
Observed (solid lines) and expected (dashed lines) 95% CL upper limits on $ \mathrm{T} \overline{\mathrm{T}} $ (upper) and $ \mathrm{B} \overline{\mathrm{B}} $ (lower) production cross sections for the singlet (left) and doublet (right) hypotheses, from the combined fit to all channels. Predicted cross sections are shown by the red line surrounded by a band representing energy scale and PDF uncertainties in the calculation.

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Figure 9-a:
Observed (solid lines) and expected (dashed lines) 95% CL upper limits on $ \mathrm{T} \overline{\mathrm{T}} $ production cross sections for the singlet hypothesis, from the combined fit to all channels. Predicted cross sections are shown by the red line surrounded by a band representing energy scale and PDF uncertainties in the calculation.

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Figure 9-b:
Observed (solid lines) and expected (dashed lines) 95% CL upper limits on $ \mathrm{T} \overline{\mathrm{T}} $ production cross sections for the doublet hypothesis, from the combined fit to all channels. Predicted cross sections are shown by the red line surrounded by a band representing energy scale and PDF uncertainties in the calculation.

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Figure 9-c:
Observed (solid lines) and expected (dashed lines) 95% CL upper limits on $ \mathrm{B} \overline{\mathrm{B}} $ production cross sections for the singlet hypothesis, from the combined fit to all channels. Predicted cross sections are shown by the red line surrounded by a band representing energy scale and PDF uncertainties in the calculation.

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Figure 9-d:
Observed (solid lines) and expected (dashed lines) 95% CL upper limits on $ \mathrm{B} \overline{\mathrm{B}} $ production cross sections for the doublet hypothesis, from the combined fit to all channels. Predicted cross sections are shown by the red line surrounded by a band representing energy scale and PDF uncertainties in the calculation.

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Figure 10:
The 95% CL expected (left) and observed (right) lower mass limits on pair-produced $ \mathrm{T} $ (upper) and $ \mathrm{B} $ (lower) quark masses, from the combined fit to all channels, as functions of their branching ratios to H and W bosons. Mass contours are shown with lines of various styles.

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Figure 10-a:
The 95% CL expected lower mass limits on pair-produced $ \mathrm{T} $ quark masses, from the combined fit to all channels, as functions of their branching ratios to H and W bosons. Mass contours are shown with lines of various styles.

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Figure 10-b:
The 95% CL observed lower mass limits on pair-produced $ \mathrm{T} $ quark masses, from the combined fit to all channels, as functions of their branching ratios to H and W bosons. Mass contours are shown with lines of various styles.

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Figure 10-c:
The 95% CL expected lower mass limits on pair-produced $ \mathrm{B} $ quark masses, from the combined fit to all channels, as functions of their branching ratios to H and W bosons. Mass contours are shown with lines of various styles.

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Figure 10-d:
The 95% CL observed lower mass limits on pair-produced $ \mathrm{B} $ quark masses, from the combined fit to all channels, as functions of their branching ratios to H and W bosons. Mass contours are shown with lines of various styles.
Tables

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Table 1:
Summary of event selection criteria for the primary CRs and SRs in the three search channels. The label ``OSSF'' refers to opposite-sign charge, same-flavor lepton pairs, and the phrase ``max MLP'' refers to the largest score from the single-lepton MLP network.

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Table 2:
Numbers of predicted and observed CR events in 2016-2018 data (138 fb$ ^{-1} $) for the $ \mathrm{T} \overline{\mathrm{T}} $ (upper section) and $ \mathrm{B} \overline{\mathrm{B}} $ (lower section) signal hypotheses in the single-lepton channel, after a background-only fit to data described in Section 10. Predicted numbers of signal events before the fit to data are included for comparison, using the singlet branching fraction scenario. Uncertainties include statistical and systematic components, and lepton flavor categories are combined for illustration with their uncertainties added in quadrature. Values in the DEEPAK8 CR represent the number of large-radius jets rather than the number of events.

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Table 3:
Numbers of predicted and observed CR events in 2017-2018 data (101 fb$ ^{-1} $) in the SS dilepton channel, after a background-only fit to data. Predicted numbers of signal events before the fit to data are included for comparison, using the singlet branching fraction scenario. Uncertainties include statistical and systematic components. Predictions for 2017 and 2018 are combined with their uncertainties added in quadrature.

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Table 4:
Numbers of predicted and observed CR events in 2017-2018 data (101 fb$ ^{-1} $) in the multilepton channel, after a background-only fit to data. Predicted numbers of signal events before the fit to data are included for comparison, using the singlet branching fraction scenario. Uncertainties include statistical and systematic components. Predictions for 2017 and 2018 are combined with their uncertainties added in quadrature.

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Table 5:
Summary of systematic uncertainties for the various analysis channels, grouped according to the channel. The second column shows uncertainties for the single-lepton channel, evaluated with 2016-2018 data combined. The third and fourth columns show uncertainties for the other channels, evaluated using 2017 or 2018 data. Uncertainties that are common across multiple channels appear in the first relevant column, followed by the label ``same'' in other columns. Ranges indicate values across different lepton flavor categories, and functional forms describe the quantities on which the uncertainty's numerical value depends. The final column shows which predictions are affected by each uncertainty: ``MC'' denotes all simulation (including signal), ``OS'' denotes charge misidentification background, and ``NP'' denotes nonprompt lepton background.

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Table 6:
Category labels and definitions for the SRs of the single-lepton channel $ \mathrm{T} \overline{\mathrm{T}} $ analysis. Electron and muon events are analyzed separately in all categories. The VLQ candidate tag describes the pairings formed from the leptonic particle candidate and three large-radius jets. The hadronic VLQ candidate is reconstructed from two large-radius jets, and a VLQ candidate tag of ``other'' indicates that the hadronic VLQ candidate did not consist of $ \mathrm{b} \mathrm{W} $-, $ \mathrm{t} \mathrm{Z} $-, or $ \mathrm{t} \mathrm{H} $-tagged jets. In the $ \mathrm{B} \overline{\mathrm{B}} $ analysis, the VLQ candidate tags considered are tW, $ \mathrm{b} \mathrm{Z} $, and $ \mathrm{b} \mathrm{H} $. Categories 4, 6, and 7 are not included in the $ \mathrm{B} \overline{\mathrm{B}} $ analysis.

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Table 7:
Numbers of predicted and observed events in 2016-2018 data (138 fb$ ^{-1} $) in the $ \mathrm{T} \overline{\mathrm{T}} $ SR categories considered in the single-lepton channel, after a background-only fit to data. Electron and muon categories have been combined for illustration. Predicted numbers of signal events before the fit to data are included for comparison, using the singlet branching fraction scenario. Uncertainties include statistical and systematic components, with the uncertainties in the electron and muon categories added in quadrature.

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Table 8:
Numbers of predicted and observed events in 2016-2018 data (138 fb$ ^{-1} $) in the $ \mathrm{B} \overline{\mathrm{B}} $ SR categories considered in the single-lepton channel, after a background-only fit to data. Electron and muon categories have been combined for illustration. Predicted numbers of signal events before the fit to data are included for comparison, using the singlet branching fraction scenario. Uncertainties include statistical and systematic components, with the uncertainties in the electron and muon categories added in quadrature.

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Table 9:
Numbers of predicted and observed SR events in 2017-2018 data (101 fb$ ^{-1} $) in the SS dilepton channel, after a background-only fit to data. Predicted numbers of signal events before the fit to data are included for comparison, using the singlet branching fraction scenario. Uncertainties include statistical and systematic components. Predictions for 2017 and 2018 are combined for illustration with their uncertainties added in quadrature.

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Table 10:
Numbers of predicted and observed SR events in 2017-2018 data (101 fb$ ^{-1} $) in the multilepton channel, after a background-only fit to data. Predicted numbers of signal events before the fit to data are included for comparison, using the singlet branching fraction scenario. Uncertainties include statistical and systematic components. Predictions for 2017 and 2018 are combined for illustration with their uncertainties added in quadrature.

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Table 11:
Expected and observed 95% CL lower limits on the $ \mathrm{T} $ (upper section) and $ \mathrm{B} $ (lower section) quark masses.
Summary
A search has been presented for vector-like $ \mathrm{T} $ and $ \mathrm{B} $ quark-antiquark pairs produced in proton-proton collisions at a center-of-mass energy of 13 TeV. Data collected by the CMS experiment at the LHC in 2016-2018 are analyzed in the single-lepton final state, and data from 2017-2018 are analyzed in the same-sign charge dilepton and multilepton final states. In the single-lepton channel, parent particles of large-radius jets are identified using the DEEPAK8 algorithm, and vector-like quark candidates are reconstructed. A multilayer perceptron network is trained to separate signal events from standard model backgrounds. In the same-sign charge dilepton and multilepton channels, low background rates and the large energy signature of the signal are exploited by studying jet and lepton momentum scalar sum distributions. Pair production is excluded at 95% confidence level for $ \mathrm{T} $ quarks with masses up to 1.54 TeV and for $ \mathrm{B} $ quarks with masses up to 1.56 TeV, depending on the branching fraction scenario, and $ \mathrm{T} $ quarks with masses below 1.48 TeV are excluded in any scenario. The limits obtained in this search are the strongest limits to date for $ \mathrm{T} \overline{\mathrm{T}} $ production with all $ \mathrm{T} $ quark decay modes, and are the strongest limits to date for $ \mathrm{B} \overline{\mathrm{B}} $ production with $ \mathrm{B} $ quark decays to tW.
Additional Figures

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Additional Figure 1:
Observed (solid lines) and expected (dashed lines) 95% CL upper limits on the $ {\mathrm{T}} \overline{\mathrm{T}} $ production cross section for the hypotheses of 100% branching fraction to $ \mathrm{b}\mathrm{W} $ (upper left), $ \mathrm{t}\mathrm{Z} $ (upper right), or $ \mathrm{t}\mathrm{H} $ (lower), from the combined fit to all channels. Predicted cross sections are shown by the red line surrounded by a band representing energy scale and PDF uncertainties in the calculation.

png pdf
Additional Figure 1-a:
Observed (solid lines) and expected (dashed lines) 95% CL upper limits on the $ {\mathrm{T}} \overline{\mathrm{T}} $ production cross section for the hypotheses of 100% branching fraction to $ \mathrm{b}\mathrm{W} $ (upper left), $ \mathrm{t}\mathrm{Z} $ (upper right), or $ \mathrm{t}\mathrm{H} $ (lower), from the combined fit to all channels. Predicted cross sections are shown by the red line surrounded by a band representing energy scale and PDF uncertainties in the calculation.

png pdf
Additional Figure 1-b:
Observed (solid lines) and expected (dashed lines) 95% CL upper limits on the $ {\mathrm{T}} \overline{\mathrm{T}} $ production cross section for the hypotheses of 100% branching fraction to $ \mathrm{b}\mathrm{W} $ (upper left), $ \mathrm{t}\mathrm{Z} $ (upper right), or $ \mathrm{t}\mathrm{H} $ (lower), from the combined fit to all channels. Predicted cross sections are shown by the red line surrounded by a band representing energy scale and PDF uncertainties in the calculation.

png pdf
Additional Figure 1-c:
Observed (solid lines) and expected (dashed lines) 95% CL upper limits on the $ {\mathrm{T}} \overline{\mathrm{T}} $ production cross section for the hypotheses of 100% branching fraction to $ \mathrm{b}\mathrm{W} $ (upper left), $ \mathrm{t}\mathrm{Z} $ (upper right), or $ \mathrm{t}\mathrm{H} $ (lower), from the combined fit to all channels. Predicted cross sections are shown by the red line surrounded by a band representing energy scale and PDF uncertainties in the calculation.

png pdf
Additional Figure 2:
Observed (solid lines) and expected (dashed lines) 95% CL upper limits on the $ {\mathrm{B}} \overline{\mathrm{B}} $ production cross section for the hypothesis of 100% branching fraction to $ \mathrm{t}\mathrm{W} $, from the combined fit to all channels. Predicted cross sections are shown by the red line surrounded by a band representing energy scale and PDF uncertainties in the calculation.
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