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Compact Muon Solenoid
LHC, CERN

CMS-B2G-20-014 ; CERN-EP-2024-016
A search for bottom-type vector-like quark pair production in dileptonic and fully hadronic final states in proton-proton collisions at $ \sqrt{s} = $ 13 TeV
Accepted for publication in Phys. Rev. D
Abstract: A search is described for the production of a pair of bottom-type vector-like quarks (B VLQs) with mass greater than 1000 GeV. Each B VLQ decays into a b quark and a Higgs boson, a b quark and a Z boson, or a t quark and a W boson. This analysis considers both fully hadronic final states and those containing a charged lepton pair from a Z boson decay. The products of the $ \mathrm{H} \to \mathrm{b}\mathrm{b} $ boson decay and of the hadronic Z or W boson decays can be resolved as two distinct jets or merged into a single jet, so the final states are classified by the number of reconstructed jets. The analysis uses data corresponding to an integrated luminosity of 138 fb$ ^{-1} $ collected in proton-proton collisions at $ \sqrt{s} = $ 13 TeV with the CMS detector at the LHC from 2016 to 2018. No excess over the expected background is observed. Lower limits are set on the B VLQ mass at 95% confidence level. These depend on the B VLQ branching fractions and are 1570 and 1540 GeV for 100% $ {\mathrm{B}} \to \mathrm{b}\mathrm{H} $ and 100% $ {\mathrm{B}} \to \mathrm{b}\mathrm{Z} $, respectively. In most cases, the mass limits obtained exceed previous limits by at least 100 GeV.
Figures & Tables Summary References CMS Publications
Figures

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Figure 1:
Feynman diagrams for the pair production of bottom-type VLQs that decay into a b or t quark or antiquark and either a Higgs, Z, or W boson with fully hadronic final states. Upper row: $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ and $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $; middle row: $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ and $ \mathrm{b}\mathrm{H}\mathrm{t}\mathrm{W} $; lower row: $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ and $ \mathrm{t}\mathrm{W}\mathrm{t}\mathrm{W} $. The B and $ \overline{\mathrm{B}} $ can be exchanged in the decays.

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Figure 1-a:
Feynman diagrams for the pair production of bottom-type VLQs that decay into a b or t quark or antiquark and either a Higgs, Z, or W boson with fully hadronic final states. Upper row: $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ and $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $; middle row: $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ and $ \mathrm{b}\mathrm{H}\mathrm{t}\mathrm{W} $; lower row: $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ and $ \mathrm{t}\mathrm{W}\mathrm{t}\mathrm{W} $. The B and $ \overline{\mathrm{B}} $ can be exchanged in the decays.

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Figure 1-b:
Feynman diagrams for the pair production of bottom-type VLQs that decay into a b or t quark or antiquark and either a Higgs, Z, or W boson with fully hadronic final states. Upper row: $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ and $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $; middle row: $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ and $ \mathrm{b}\mathrm{H}\mathrm{t}\mathrm{W} $; lower row: $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ and $ \mathrm{t}\mathrm{W}\mathrm{t}\mathrm{W} $. The B and $ \overline{\mathrm{B}} $ can be exchanged in the decays.

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Figure 1-c:
Feynman diagrams for the pair production of bottom-type VLQs that decay into a b or t quark or antiquark and either a Higgs, Z, or W boson with fully hadronic final states. Upper row: $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ and $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $; middle row: $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ and $ \mathrm{b}\mathrm{H}\mathrm{t}\mathrm{W} $; lower row: $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ and $ \mathrm{t}\mathrm{W}\mathrm{t}\mathrm{W} $. The B and $ \overline{\mathrm{B}} $ can be exchanged in the decays.

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Figure 1-d:
Feynman diagrams for the pair production of bottom-type VLQs that decay into a b or t quark or antiquark and either a Higgs, Z, or W boson with fully hadronic final states. Upper row: $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ and $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $; middle row: $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ and $ \mathrm{b}\mathrm{H}\mathrm{t}\mathrm{W} $; lower row: $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ and $ \mathrm{t}\mathrm{W}\mathrm{t}\mathrm{W} $. The B and $ \overline{\mathrm{B}} $ can be exchanged in the decays.

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Figure 1-e:
Feynman diagrams for the pair production of bottom-type VLQs that decay into a b or t quark or antiquark and either a Higgs, Z, or W boson with fully hadronic final states. Upper row: $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ and $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $; middle row: $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ and $ \mathrm{b}\mathrm{H}\mathrm{t}\mathrm{W} $; lower row: $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ and $ \mathrm{t}\mathrm{W}\mathrm{t}\mathrm{W} $. The B and $ \overline{\mathrm{B}} $ can be exchanged in the decays.

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Figure 1-f:
Feynman diagrams for the pair production of bottom-type VLQs that decay into a b or t quark or antiquark and either a Higgs, Z, or W boson with fully hadronic final states. Upper row: $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ and $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $; middle row: $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ and $ \mathrm{b}\mathrm{H}\mathrm{t}\mathrm{W} $; lower row: $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ and $ \mathrm{t}\mathrm{W}\mathrm{t}\mathrm{W} $. The B and $ \overline{\mathrm{B}} $ can be exchanged in the decays.

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Figure 2:
Feynman diagrams of the pair production of bottom-type VLQ quarks that decay into a b quark or antiquark and either a Higgs or Z boson with a dilepton final state: $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ mode (left) and $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ mode (right). The B and $ \overline{\mathrm{B}} $ can be exchanged in the decays.

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Figure 2-a:
Feynman diagrams of the pair production of bottom-type VLQ quarks that decay into a b quark or antiquark and either a Higgs or Z boson with a dilepton final state: $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ mode (left) and $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ mode (right). The B and $ \overline{\mathrm{B}} $ can be exchanged in the decays.

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Figure 2-b:
Feynman diagrams of the pair production of bottom-type VLQ quarks that decay into a b quark or antiquark and either a Higgs or Z boson with a dilepton final state: $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ mode (left) and $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ mode (right). The B and $ \overline{\mathrm{B}} $ can be exchanged in the decays.

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Figure 3:
Reconstructed VLQ mass distributions for simulated events for the channels in the fully hadronic category with $ m_{{\mathrm{B}}} = $ 1400 GeV. Upper row: Channels in the $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (left) and $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (right) decay mode. Middle row: Channels in the $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (left) and $ \mathrm{b}\mathrm{H}\mathrm{t}\mathrm{W} $ (right) decay mode. Lower row: Channels in the $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ decay mode. The different colors indicate the different jet multiplicities. A selection of $ \chi^2_\text{mod}/\text{ndf} < $ 5 has been applied. The values represent the expected number of events over the background in the 2016--2018 data sample.

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Figure 3-a:
Reconstructed VLQ mass distributions for simulated events for the channels in the fully hadronic category with $ m_{{\mathrm{B}}} = $ 1400 GeV. Upper row: Channels in the $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (left) and $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (right) decay mode. Middle row: Channels in the $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (left) and $ \mathrm{b}\mathrm{H}\mathrm{t}\mathrm{W} $ (right) decay mode. Lower row: Channels in the $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ decay mode. The different colors indicate the different jet multiplicities. A selection of $ \chi^2_\text{mod}/\text{ndf} < $ 5 has been applied. The values represent the expected number of events over the background in the 2016--2018 data sample.

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Figure 3-b:
Reconstructed VLQ mass distributions for simulated events for the channels in the fully hadronic category with $ m_{{\mathrm{B}}} = $ 1400 GeV. Upper row: Channels in the $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (left) and $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (right) decay mode. Middle row: Channels in the $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (left) and $ \mathrm{b}\mathrm{H}\mathrm{t}\mathrm{W} $ (right) decay mode. Lower row: Channels in the $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ decay mode. The different colors indicate the different jet multiplicities. A selection of $ \chi^2_\text{mod}/\text{ndf} < $ 5 has been applied. The values represent the expected number of events over the background in the 2016--2018 data sample.

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Figure 3-c:
Reconstructed VLQ mass distributions for simulated events for the channels in the fully hadronic category with $ m_{{\mathrm{B}}} = $ 1400 GeV. Upper row: Channels in the $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (left) and $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (right) decay mode. Middle row: Channels in the $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (left) and $ \mathrm{b}\mathrm{H}\mathrm{t}\mathrm{W} $ (right) decay mode. Lower row: Channels in the $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ decay mode. The different colors indicate the different jet multiplicities. A selection of $ \chi^2_\text{mod}/\text{ndf} < $ 5 has been applied. The values represent the expected number of events over the background in the 2016--2018 data sample.

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Figure 3-d:
Reconstructed VLQ mass distributions for simulated events for the channels in the fully hadronic category with $ m_{{\mathrm{B}}} = $ 1400 GeV. Upper row: Channels in the $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (left) and $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (right) decay mode. Middle row: Channels in the $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (left) and $ \mathrm{b}\mathrm{H}\mathrm{t}\mathrm{W} $ (right) decay mode. Lower row: Channels in the $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ decay mode. The different colors indicate the different jet multiplicities. A selection of $ \chi^2_\text{mod}/\text{ndf} < $ 5 has been applied. The values represent the expected number of events over the background in the 2016--2018 data sample.

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Figure 3-e:
Reconstructed VLQ mass distributions for simulated events for the channels in the fully hadronic category with $ m_{{\mathrm{B}}} = $ 1400 GeV. Upper row: Channels in the $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (left) and $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (right) decay mode. Middle row: Channels in the $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (left) and $ \mathrm{b}\mathrm{H}\mathrm{t}\mathrm{W} $ (right) decay mode. Lower row: Channels in the $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ decay mode. The different colors indicate the different jet multiplicities. A selection of $ \chi^2_\text{mod}/\text{ndf} < $ 5 has been applied. The values represent the expected number of events over the background in the 2016--2018 data sample.

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Figure 4:
Reconstructed VLQ mass distributions for simulated events passing the b tag requirement for the channels in the dileptonic category with $ m_{{\mathrm{B}}} = $ 1400 GeV in the $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (left) and $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (right) event modes. A selection of $ \chi^2_\text{mod}/\text{ndf} < $ 5 has been applied. The values represent the expected number of events over the background in the 2016--2018 data sample.

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Figure 4-a:
Reconstructed VLQ mass distributions for simulated events passing the b tag requirement for the channels in the dileptonic category with $ m_{{\mathrm{B}}} = $ 1400 GeV in the $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (left) and $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (right) event modes. A selection of $ \chi^2_\text{mod}/\text{ndf} < $ 5 has been applied. The values represent the expected number of events over the background in the 2016--2018 data sample.

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Figure 4-b:
Reconstructed VLQ mass distributions for simulated events passing the b tag requirement for the channels in the dileptonic category with $ m_{{\mathrm{B}}} = $ 1400 GeV in the $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (left) and $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (right) event modes. A selection of $ \chi^2_\text{mod}/\text{ndf} < $ 5 has been applied. The values represent the expected number of events over the background in the 2016--2018 data sample.

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Figure 5:
Normalized distributions of the value of the least $ \chi^2_\text{mod}/\text{ndf} $ for simulated signal events and data events in the fully hadronic category before any b tagging requirements are applied in the fully hadronic category. Upper row: $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (left), $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (center), and $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (right) decay modes. Lower row: $ \mathrm{b}\mathrm{H}\mathrm{t}\mathrm{W} $ (left), and $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ (right) decay modes. A signal mass of $ m_{{\mathrm{B}}} = $ 1400 GeV is used and compared against all three years of data. All jet multiplicities have been combined together.

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Figure 5-a:
Normalized distributions of the value of the least $ \chi^2_\text{mod}/\text{ndf} $ for simulated signal events and data events in the fully hadronic category before any b tagging requirements are applied in the fully hadronic category. Upper row: $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (left), $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (center), and $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (right) decay modes. Lower row: $ \mathrm{b}\mathrm{H}\mathrm{t}\mathrm{W} $ (left), and $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ (right) decay modes. A signal mass of $ m_{{\mathrm{B}}} = $ 1400 GeV is used and compared against all three years of data. All jet multiplicities have been combined together.

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Figure 5-b:
Normalized distributions of the value of the least $ \chi^2_\text{mod}/\text{ndf} $ for simulated signal events and data events in the fully hadronic category before any b tagging requirements are applied in the fully hadronic category. Upper row: $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (left), $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (center), and $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (right) decay modes. Lower row: $ \mathrm{b}\mathrm{H}\mathrm{t}\mathrm{W} $ (left), and $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ (right) decay modes. A signal mass of $ m_{{\mathrm{B}}} = $ 1400 GeV is used and compared against all three years of data. All jet multiplicities have been combined together.

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Figure 5-c:
Normalized distributions of the value of the least $ \chi^2_\text{mod}/\text{ndf} $ for simulated signal events and data events in the fully hadronic category before any b tagging requirements are applied in the fully hadronic category. Upper row: $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (left), $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (center), and $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (right) decay modes. Lower row: $ \mathrm{b}\mathrm{H}\mathrm{t}\mathrm{W} $ (left), and $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ (right) decay modes. A signal mass of $ m_{{\mathrm{B}}} = $ 1400 GeV is used and compared against all three years of data. All jet multiplicities have been combined together.

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Figure 5-d:
Normalized distributions of the value of the least $ \chi^2_\text{mod}/\text{ndf} $ for simulated signal events and data events in the fully hadronic category before any b tagging requirements are applied in the fully hadronic category. Upper row: $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (left), $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (center), and $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (right) decay modes. Lower row: $ \mathrm{b}\mathrm{H}\mathrm{t}\mathrm{W} $ (left), and $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ (right) decay modes. A signal mass of $ m_{{\mathrm{B}}} = $ 1400 GeV is used and compared against all three years of data. All jet multiplicities have been combined together.

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Figure 5-e:
Normalized distributions of the value of the least $ \chi^2_\text{mod}/\text{ndf} $ for simulated signal events and data events in the fully hadronic category before any b tagging requirements are applied in the fully hadronic category. Upper row: $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (left), $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (center), and $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (right) decay modes. Lower row: $ \mathrm{b}\mathrm{H}\mathrm{t}\mathrm{W} $ (left), and $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ (right) decay modes. A signal mass of $ m_{{\mathrm{B}}} = $ 1400 GeV is used and compared against all three years of data. All jet multiplicities have been combined together.

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Figure 6:
Normalized distributions of the value of the least $ \chi^2_\text{mod}/\text{ndf} $ for simulated signal events and data events in the leptonic category before any b tagging requirements are applied. Upper row: $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ decay mode, 3-jet (left) and 4-jet (right) events. Lower row: $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ decay mode, 3-jet (left) and 4-jet (right) events. A signal mass of $ m_{{\mathrm{B}}} = $ 1400 GeV is used and compared against all three years of data.

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Figure 6-a:
Normalized distributions of the value of the least $ \chi^2_\text{mod}/\text{ndf} $ for simulated signal events and data events in the leptonic category before any b tagging requirements are applied. Upper row: $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ decay mode, 3-jet (left) and 4-jet (right) events. Lower row: $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ decay mode, 3-jet (left) and 4-jet (right) events. A signal mass of $ m_{{\mathrm{B}}} = $ 1400 GeV is used and compared against all three years of data.

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Figure 6-b:
Normalized distributions of the value of the least $ \chi^2_\text{mod}/\text{ndf} $ for simulated signal events and data events in the leptonic category before any b tagging requirements are applied. Upper row: $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ decay mode, 3-jet (left) and 4-jet (right) events. Lower row: $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ decay mode, 3-jet (left) and 4-jet (right) events. A signal mass of $ m_{{\mathrm{B}}} = $ 1400 GeV is used and compared against all three years of data.

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Figure 6-c:
Normalized distributions of the value of the least $ \chi^2_\text{mod}/\text{ndf} $ for simulated signal events and data events in the leptonic category before any b tagging requirements are applied. Upper row: $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ decay mode, 3-jet (left) and 4-jet (right) events. Lower row: $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ decay mode, 3-jet (left) and 4-jet (right) events. A signal mass of $ m_{{\mathrm{B}}} = $ 1400 GeV is used and compared against all three years of data.

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Figure 6-d:
Normalized distributions of the value of the least $ \chi^2_\text{mod}/\text{ndf} $ for simulated signal events and data events in the leptonic category before any b tagging requirements are applied. Upper row: $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ decay mode, 3-jet (left) and 4-jet (right) events. Lower row: $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ decay mode, 3-jet (left) and 4-jet (right) events. A signal mass of $ m_{{\mathrm{B}}} = $ 1400 GeV is used and compared against all three years of data.

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Figure 7:
Distributions of $ m_{\text{VLQ}} $ for the preselected data sample in the fully hadronic category for some selected channels. Upper row: 4-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (left) and 4-jet $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (right) modes. Middle row: 5-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (left) and 5-jet $ \mathrm{b}\mathrm{H}\mathrm{t}\mathrm{W} $ (right) modes. Lower row: 6-jet $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (left) and 6-jet $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ (right) modes. The fit to the data (shown by the black points) is given by the red line, and the bottom panel displays the fractional difference between the data and fit, (data-fit)/fit.

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Figure 7-a:
Distributions of $ m_{\text{VLQ}} $ for the preselected data sample in the fully hadronic category for some selected channels. Upper row: 4-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (left) and 4-jet $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (right) modes. Middle row: 5-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (left) and 5-jet $ \mathrm{b}\mathrm{H}\mathrm{t}\mathrm{W} $ (right) modes. Lower row: 6-jet $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (left) and 6-jet $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ (right) modes. The fit to the data (shown by the black points) is given by the red line, and the bottom panel displays the fractional difference between the data and fit, (data-fit)/fit.

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Figure 7-b:
Distributions of $ m_{\text{VLQ}} $ for the preselected data sample in the fully hadronic category for some selected channels. Upper row: 4-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (left) and 4-jet $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (right) modes. Middle row: 5-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (left) and 5-jet $ \mathrm{b}\mathrm{H}\mathrm{t}\mathrm{W} $ (right) modes. Lower row: 6-jet $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (left) and 6-jet $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ (right) modes. The fit to the data (shown by the black points) is given by the red line, and the bottom panel displays the fractional difference between the data and fit, (data-fit)/fit.

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Figure 7-c:
Distributions of $ m_{\text{VLQ}} $ for the preselected data sample in the fully hadronic category for some selected channels. Upper row: 4-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (left) and 4-jet $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (right) modes. Middle row: 5-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (left) and 5-jet $ \mathrm{b}\mathrm{H}\mathrm{t}\mathrm{W} $ (right) modes. Lower row: 6-jet $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (left) and 6-jet $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ (right) modes. The fit to the data (shown by the black points) is given by the red line, and the bottom panel displays the fractional difference between the data and fit, (data-fit)/fit.

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Figure 7-d:
Distributions of $ m_{\text{VLQ}} $ for the preselected data sample in the fully hadronic category for some selected channels. Upper row: 4-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (left) and 4-jet $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (right) modes. Middle row: 5-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (left) and 5-jet $ \mathrm{b}\mathrm{H}\mathrm{t}\mathrm{W} $ (right) modes. Lower row: 6-jet $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (left) and 6-jet $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ (right) modes. The fit to the data (shown by the black points) is given by the red line, and the bottom panel displays the fractional difference between the data and fit, (data-fit)/fit.

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Figure 7-e:
Distributions of $ m_{\text{VLQ}} $ for the preselected data sample in the fully hadronic category for some selected channels. Upper row: 4-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (left) and 4-jet $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (right) modes. Middle row: 5-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (left) and 5-jet $ \mathrm{b}\mathrm{H}\mathrm{t}\mathrm{W} $ (right) modes. Lower row: 6-jet $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (left) and 6-jet $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ (right) modes. The fit to the data (shown by the black points) is given by the red line, and the bottom panel displays the fractional difference between the data and fit, (data-fit)/fit.

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Figure 7-f:
Distributions of $ m_{\text{VLQ}} $ for the preselected data sample in the fully hadronic category for some selected channels. Upper row: 4-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (left) and 4-jet $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (right) modes. Middle row: 5-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (left) and 5-jet $ \mathrm{b}\mathrm{H}\mathrm{t}\mathrm{W} $ (right) modes. Lower row: 6-jet $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (left) and 6-jet $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ (right) modes. The fit to the data (shown by the black points) is given by the red line, and the bottom panel displays the fractional difference between the data and fit, (data-fit)/fit.

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Figure 8:
Value of BJTF as a function of $ m_{\text{VLQ}} $ in the control region with 12 $ < \chi^2_\text{mod}/\text{ndf} < $ 48 for some selected fully hadronic channels. Upper row: 4-jet events in the $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (left), $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (center), and $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (right) modes. Middle row: 5-jet events in the $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (left), $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (center), and $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ (right) modes. Lower row: 6-jet events in the $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (left), $ \mathrm{b}\mathrm{H}\mathrm{t}\mathrm{W} $ (center), and $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ (right) modes. The linear fit is shown by the red line, and the associated uncertainty in the fit is shown by the shaded band.

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Figure 8-a:
Value of BJTF as a function of $ m_{\text{VLQ}} $ in the control region with 12 $ < \chi^2_\text{mod}/\text{ndf} < $ 48 for some selected fully hadronic channels. Upper row: 4-jet events in the $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (left), $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (center), and $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (right) modes. Middle row: 5-jet events in the $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (left), $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (center), and $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ (right) modes. Lower row: 6-jet events in the $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (left), $ \mathrm{b}\mathrm{H}\mathrm{t}\mathrm{W} $ (center), and $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ (right) modes. The linear fit is shown by the red line, and the associated uncertainty in the fit is shown by the shaded band.

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Figure 8-b:
Value of BJTF as a function of $ m_{\text{VLQ}} $ in the control region with 12 $ < \chi^2_\text{mod}/\text{ndf} < $ 48 for some selected fully hadronic channels. Upper row: 4-jet events in the $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (left), $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (center), and $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (right) modes. Middle row: 5-jet events in the $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (left), $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (center), and $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ (right) modes. Lower row: 6-jet events in the $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (left), $ \mathrm{b}\mathrm{H}\mathrm{t}\mathrm{W} $ (center), and $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ (right) modes. The linear fit is shown by the red line, and the associated uncertainty in the fit is shown by the shaded band.

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Figure 8-c:
Value of BJTF as a function of $ m_{\text{VLQ}} $ in the control region with 12 $ < \chi^2_\text{mod}/\text{ndf} < $ 48 for some selected fully hadronic channels. Upper row: 4-jet events in the $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (left), $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (center), and $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (right) modes. Middle row: 5-jet events in the $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (left), $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (center), and $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ (right) modes. Lower row: 6-jet events in the $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (left), $ \mathrm{b}\mathrm{H}\mathrm{t}\mathrm{W} $ (center), and $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ (right) modes. The linear fit is shown by the red line, and the associated uncertainty in the fit is shown by the shaded band.

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Figure 8-d:
Value of BJTF as a function of $ m_{\text{VLQ}} $ in the control region with 12 $ < \chi^2_\text{mod}/\text{ndf} < $ 48 for some selected fully hadronic channels. Upper row: 4-jet events in the $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (left), $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (center), and $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (right) modes. Middle row: 5-jet events in the $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (left), $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (center), and $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ (right) modes. Lower row: 6-jet events in the $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (left), $ \mathrm{b}\mathrm{H}\mathrm{t}\mathrm{W} $ (center), and $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ (right) modes. The linear fit is shown by the red line, and the associated uncertainty in the fit is shown by the shaded band.

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Figure 8-e:
Value of BJTF as a function of $ m_{\text{VLQ}} $ in the control region with 12 $ < \chi^2_\text{mod}/\text{ndf} < $ 48 for some selected fully hadronic channels. Upper row: 4-jet events in the $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (left), $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (center), and $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (right) modes. Middle row: 5-jet events in the $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (left), $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (center), and $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ (right) modes. Lower row: 6-jet events in the $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (left), $ \mathrm{b}\mathrm{H}\mathrm{t}\mathrm{W} $ (center), and $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ (right) modes. The linear fit is shown by the red line, and the associated uncertainty in the fit is shown by the shaded band.

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Figure 8-f:
Value of BJTF as a function of $ m_{\text{VLQ}} $ in the control region with 12 $ < \chi^2_\text{mod}/\text{ndf} < $ 48 for some selected fully hadronic channels. Upper row: 4-jet events in the $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (left), $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (center), and $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (right) modes. Middle row: 5-jet events in the $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (left), $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (center), and $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ (right) modes. Lower row: 6-jet events in the $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (left), $ \mathrm{b}\mathrm{H}\mathrm{t}\mathrm{W} $ (center), and $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ (right) modes. The linear fit is shown by the red line, and the associated uncertainty in the fit is shown by the shaded band.

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Figure 8-g:
Value of BJTF as a function of $ m_{\text{VLQ}} $ in the control region with 12 $ < \chi^2_\text{mod}/\text{ndf} < $ 48 for some selected fully hadronic channels. Upper row: 4-jet events in the $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (left), $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (center), and $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (right) modes. Middle row: 5-jet events in the $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (left), $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (center), and $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ (right) modes. Lower row: 6-jet events in the $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (left), $ \mathrm{b}\mathrm{H}\mathrm{t}\mathrm{W} $ (center), and $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ (right) modes. The linear fit is shown by the red line, and the associated uncertainty in the fit is shown by the shaded band.

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Figure 8-h:
Value of BJTF as a function of $ m_{\text{VLQ}} $ in the control region with 12 $ < \chi^2_\text{mod}/\text{ndf} < $ 48 for some selected fully hadronic channels. Upper row: 4-jet events in the $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (left), $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (center), and $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (right) modes. Middle row: 5-jet events in the $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (left), $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (center), and $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ (right) modes. Lower row: 6-jet events in the $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (left), $ \mathrm{b}\mathrm{H}\mathrm{t}\mathrm{W} $ (center), and $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ (right) modes. The linear fit is shown by the red line, and the associated uncertainty in the fit is shown by the shaded band.

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Figure 8-i:
Value of BJTF as a function of $ m_{\text{VLQ}} $ in the control region with 12 $ < \chi^2_\text{mod}/\text{ndf} < $ 48 for some selected fully hadronic channels. Upper row: 4-jet events in the $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (left), $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (center), and $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (right) modes. Middle row: 5-jet events in the $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (left), $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (center), and $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ (right) modes. Lower row: 6-jet events in the $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (left), $ \mathrm{b}\mathrm{H}\mathrm{t}\mathrm{W} $ (center), and $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ (right) modes. The linear fit is shown by the red line, and the associated uncertainty in the fit is shown by the shaded band.

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Figure 9:
Distributions of $ m_{\text{VLQ}} $ for events in the control region for the channels in the leptonic category. Upper row: 3-jet events in the $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (left) and $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (right) modes. Lower row: 4-jet events in the $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (left) and $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (right) modes. The exponential fit and its uncertainty are shown by the red line and the light red shaded band, respectively. The bottom panel shows the fractional difference between the data and fit, (data-fit)/fit.

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Figure 9-a:
Distributions of $ m_{\text{VLQ}} $ for events in the control region for the channels in the leptonic category. Upper row: 3-jet events in the $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (left) and $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (right) modes. Lower row: 4-jet events in the $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (left) and $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (right) modes. The exponential fit and its uncertainty are shown by the red line and the light red shaded band, respectively. The bottom panel shows the fractional difference between the data and fit, (data-fit)/fit.

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Figure 9-b:
Distributions of $ m_{\text{VLQ}} $ for events in the control region for the channels in the leptonic category. Upper row: 3-jet events in the $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (left) and $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (right) modes. Lower row: 4-jet events in the $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (left) and $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (right) modes. The exponential fit and its uncertainty are shown by the red line and the light red shaded band, respectively. The bottom panel shows the fractional difference between the data and fit, (data-fit)/fit.

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Figure 9-c:
Distributions of $ m_{\text{VLQ}} $ for events in the control region for the channels in the leptonic category. Upper row: 3-jet events in the $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (left) and $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (right) modes. Lower row: 4-jet events in the $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (left) and $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (right) modes. The exponential fit and its uncertainty are shown by the red line and the light red shaded band, respectively. The bottom panel shows the fractional difference between the data and fit, (data-fit)/fit.

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Figure 9-d:
Distributions of $ m_{\text{VLQ}} $ for events in the control region for the channels in the leptonic category. Upper row: 3-jet events in the $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (left) and $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (right) modes. Lower row: 4-jet events in the $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (left) and $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (right) modes. The exponential fit and its uncertainty are shown by the red line and the light red shaded band, respectively. The bottom panel shows the fractional difference between the data and fit, (data-fit)/fit.

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Figure 10:
Normalization factor as a function of $ m_{\text{VLQ}} $ for leptonic events in the 5 $ < \chi^2_\text{mod}/\text{ndf} < $ 20 region. Upper row: $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ events in the 3-jet (left) and 4-jet (right) channels. Lower row: $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ events in the 3-jet (left) and 4-jet (right) channels. The fit to a constant value and its uncertainty are shown by the red line and the light red shaded band, respectively.

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Figure 10-a:
Normalization factor as a function of $ m_{\text{VLQ}} $ for leptonic events in the 5 $ < \chi^2_\text{mod}/\text{ndf} < $ 20 region. Upper row: $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ events in the 3-jet (left) and 4-jet (right) channels. Lower row: $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ events in the 3-jet (left) and 4-jet (right) channels. The fit to a constant value and its uncertainty are shown by the red line and the light red shaded band, respectively.

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Figure 10-b:
Normalization factor as a function of $ m_{\text{VLQ}} $ for leptonic events in the 5 $ < \chi^2_\text{mod}/\text{ndf} < $ 20 region. Upper row: $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ events in the 3-jet (left) and 4-jet (right) channels. Lower row: $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ events in the 3-jet (left) and 4-jet (right) channels. The fit to a constant value and its uncertainty are shown by the red line and the light red shaded band, respectively.

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Figure 10-c:
Normalization factor as a function of $ m_{\text{VLQ}} $ for leptonic events in the 5 $ < \chi^2_\text{mod}/\text{ndf} < $ 20 region. Upper row: $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ events in the 3-jet (left) and 4-jet (right) channels. Lower row: $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ events in the 3-jet (left) and 4-jet (right) channels. The fit to a constant value and its uncertainty are shown by the red line and the light red shaded band, respectively.

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Figure 10-d:
Normalization factor as a function of $ m_{\text{VLQ}} $ for leptonic events in the 5 $ < \chi^2_\text{mod}/\text{ndf} < $ 20 region. Upper row: $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ events in the 3-jet (left) and 4-jet (right) channels. Lower row: $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ events in the 3-jet (left) and 4-jet (right) channels. The fit to a constant value and its uncertainty are shown by the red line and the light red shaded band, respectively.

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Figure 11:
Normalization factor in the leptonic category as a function of $ m_{\text{VLQ}} $ for simulated Drell--Yan events with $ \chi^2_\text{mod}/\text{ndf} < $ 5. Upper row: $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ events in the 3-jet (left) and 4-jet (right) channels. Lower row: $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ events in the 3-jet (left) and 4-jet (right) channels. The fit to a constant value and its uncertainty are shown by the red line and the light red shaded band, respectively.

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Figure 11-a:
Normalization factor in the leptonic category as a function of $ m_{\text{VLQ}} $ for simulated Drell--Yan events with $ \chi^2_\text{mod}/\text{ndf} < $ 5. Upper row: $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ events in the 3-jet (left) and 4-jet (right) channels. Lower row: $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ events in the 3-jet (left) and 4-jet (right) channels. The fit to a constant value and its uncertainty are shown by the red line and the light red shaded band, respectively.

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Figure 11-b:
Normalization factor in the leptonic category as a function of $ m_{\text{VLQ}} $ for simulated Drell--Yan events with $ \chi^2_\text{mod}/\text{ndf} < $ 5. Upper row: $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ events in the 3-jet (left) and 4-jet (right) channels. Lower row: $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ events in the 3-jet (left) and 4-jet (right) channels. The fit to a constant value and its uncertainty are shown by the red line and the light red shaded band, respectively.

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Figure 11-c:
Normalization factor in the leptonic category as a function of $ m_{\text{VLQ}} $ for simulated Drell--Yan events with $ \chi^2_\text{mod}/\text{ndf} < $ 5. Upper row: $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ events in the 3-jet (left) and 4-jet (right) channels. Lower row: $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ events in the 3-jet (left) and 4-jet (right) channels. The fit to a constant value and its uncertainty are shown by the red line and the light red shaded band, respectively.

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Figure 11-d:
Normalization factor in the leptonic category as a function of $ m_{\text{VLQ}} $ for simulated Drell--Yan events with $ \chi^2_\text{mod}/\text{ndf} < $ 5. Upper row: $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ events in the 3-jet (left) and 4-jet (right) channels. Lower row: $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ events in the 3-jet (left) and 4-jet (right) channels. The fit to a constant value and its uncertainty are shown by the red line and the light red shaded band, respectively.

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Figure 12:
Normalization factor in the leptonic category as a function of $ \chi^2_\text{mod}/\text{ndf} $. Upper row: 3-jet events in the $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (left) and $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (right) decay modes. Lower row: 4-jet events in the $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (left) and $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (right) decay modes. The fit to a constant value and its uncertainty are shown by the red line and the light red shaded band, respectively.

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Figure 12-a:
Normalization factor in the leptonic category as a function of $ \chi^2_\text{mod}/\text{ndf} $. Upper row: 3-jet events in the $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (left) and $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (right) decay modes. Lower row: 4-jet events in the $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (left) and $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (right) decay modes. The fit to a constant value and its uncertainty are shown by the red line and the light red shaded band, respectively.

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Figure 12-b:
Normalization factor in the leptonic category as a function of $ \chi^2_\text{mod}/\text{ndf} $. Upper row: 3-jet events in the $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (left) and $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (right) decay modes. Lower row: 4-jet events in the $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (left) and $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (right) decay modes. The fit to a constant value and its uncertainty are shown by the red line and the light red shaded band, respectively.

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Figure 12-c:
Normalization factor in the leptonic category as a function of $ \chi^2_\text{mod}/\text{ndf} $. Upper row: 3-jet events in the $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (left) and $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (right) decay modes. Lower row: 4-jet events in the $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (left) and $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (right) decay modes. The fit to a constant value and its uncertainty are shown by the red line and the light red shaded band, respectively.

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Figure 12-d:
Normalization factor in the leptonic category as a function of $ \chi^2_\text{mod}/\text{ndf} $. Upper row: 3-jet events in the $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (left) and $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (right) decay modes. Lower row: 4-jet events in the $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (left) and $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (right) decay modes. The fit to a constant value and its uncertainty are shown by the red line and the light red shaded band, respectively.

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Figure 13:
Normalization factor in the low-mass region (450 to 900 GeV) and the high-mass region (800 to 2000 GeV) for events with 5 $ < \chi^2_\text{mod}/\text{ndf} < $ 20 in data (left) and simulated Drell--Yan events with $ \chi^2_\text{mod}/\text{ndf} < $ 5 (right).

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Figure 13-a:
Normalization factor in the low-mass region (450 to 900 GeV) and the high-mass region (800 to 2000 GeV) for events with 5 $ < \chi^2_\text{mod}/\text{ndf} < $ 20 in data (left) and simulated Drell--Yan events with $ \chi^2_\text{mod}/\text{ndf} < $ 5 (right).

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Figure 13-b:
Normalization factor in the low-mass region (450 to 900 GeV) and the high-mass region (800 to 2000 GeV) for events with 5 $ < \chi^2_\text{mod}/\text{ndf} < $ 20 in data (left) and simulated Drell--Yan events with $ \chi^2_\text{mod}/\text{ndf} < $ 5 (right).

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Figure 14:
Distributions of reconstructed VLQ mass for expected postfit background (blue histogram), signal plus background (colored lines), and observed data (black points) for events in the hadronic category. The channels shown are 4-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (upper left), 4-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (upper right), 4-jet $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (lower center). Five signal masses are shown: 1000 (magenta), 1200 (red), 1400 (maroon), 1600 (orange), and 1800 GeV (purple). The signal distributions are normalized to the number of events estimated from the expected VLQ production cross section. The assumed branching fractions are $ \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{H}) = \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{Z}) = $ 50%, $ \mathcal{B}({\mathrm{B}} \to \mathrm{t}\mathrm{W}) = $ 0%. The background distribution is independent of the signal branching fractions. The hatched regions indicate the total systematic uncertainties in the background estimate.

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Figure 14-a:
Distributions of reconstructed VLQ mass for expected postfit background (blue histogram), signal plus background (colored lines), and observed data (black points) for events in the hadronic category. The channels shown are 4-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (upper left), 4-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (upper right), 4-jet $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (lower center). Five signal masses are shown: 1000 (magenta), 1200 (red), 1400 (maroon), 1600 (orange), and 1800 GeV (purple). The signal distributions are normalized to the number of events estimated from the expected VLQ production cross section. The assumed branching fractions are $ \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{H}) = \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{Z}) = $ 50%, $ \mathcal{B}({\mathrm{B}} \to \mathrm{t}\mathrm{W}) = $ 0%. The background distribution is independent of the signal branching fractions. The hatched regions indicate the total systematic uncertainties in the background estimate.

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Figure 14-b:
Distributions of reconstructed VLQ mass for expected postfit background (blue histogram), signal plus background (colored lines), and observed data (black points) for events in the hadronic category. The channels shown are 4-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (upper left), 4-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (upper right), 4-jet $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (lower center). Five signal masses are shown: 1000 (magenta), 1200 (red), 1400 (maroon), 1600 (orange), and 1800 GeV (purple). The signal distributions are normalized to the number of events estimated from the expected VLQ production cross section. The assumed branching fractions are $ \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{H}) = \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{Z}) = $ 50%, $ \mathcal{B}({\mathrm{B}} \to \mathrm{t}\mathrm{W}) = $ 0%. The background distribution is independent of the signal branching fractions. The hatched regions indicate the total systematic uncertainties in the background estimate.

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Figure 14-c:
Distributions of reconstructed VLQ mass for expected postfit background (blue histogram), signal plus background (colored lines), and observed data (black points) for events in the hadronic category. The channels shown are 4-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (upper left), 4-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (upper right), 4-jet $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (lower center). Five signal masses are shown: 1000 (magenta), 1200 (red), 1400 (maroon), 1600 (orange), and 1800 GeV (purple). The signal distributions are normalized to the number of events estimated from the expected VLQ production cross section. The assumed branching fractions are $ \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{H}) = \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{Z}) = $ 50%, $ \mathcal{B}({\mathrm{B}} \to \mathrm{t}\mathrm{W}) = $ 0%. The background distribution is independent of the signal branching fractions. The hatched regions indicate the total systematic uncertainties in the background estimate.

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Figure 15:
Distributions of reconstructed VLQ mass for expected postfit background (blue histogram), signal plus background (colored lines), and observed data (black points) for events in the hadronic category. The channels shown are 5-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (upper left), 5-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (upper right), 5-jet $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (middle left), 5-jet $ \mathrm{b}\mathrm{H}\mathrm{t}\mathrm{W} $ (middle right), and 5-jet $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ (lower center). Five signal masses are shown: 1000 (magenta), 1200 (red), 1400 (maroon), 1600 (orange), and 1800 GeV (purple). The signal distributions are normalized to the number of events estimated from the expected VLQ production cross section. The assumed branching fractions are $ \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{H}) = \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{Z}) = $ 50%, $ \mathcal{B}({\mathrm{B}} \to \mathrm{t}\mathrm{W}) = $ 0%. The background distribution is independent of the signal branching fractions. The hatched regions indicate the total systematic uncertainties in the background estimate.

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Figure 15-a:
Distributions of reconstructed VLQ mass for expected postfit background (blue histogram), signal plus background (colored lines), and observed data (black points) for events in the hadronic category. The channels shown are 5-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (upper left), 5-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (upper right), 5-jet $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (middle left), 5-jet $ \mathrm{b}\mathrm{H}\mathrm{t}\mathrm{W} $ (middle right), and 5-jet $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ (lower center). Five signal masses are shown: 1000 (magenta), 1200 (red), 1400 (maroon), 1600 (orange), and 1800 GeV (purple). The signal distributions are normalized to the number of events estimated from the expected VLQ production cross section. The assumed branching fractions are $ \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{H}) = \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{Z}) = $ 50%, $ \mathcal{B}({\mathrm{B}} \to \mathrm{t}\mathrm{W}) = $ 0%. The background distribution is independent of the signal branching fractions. The hatched regions indicate the total systematic uncertainties in the background estimate.

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Figure 15-b:
Distributions of reconstructed VLQ mass for expected postfit background (blue histogram), signal plus background (colored lines), and observed data (black points) for events in the hadronic category. The channels shown are 5-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (upper left), 5-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (upper right), 5-jet $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (middle left), 5-jet $ \mathrm{b}\mathrm{H}\mathrm{t}\mathrm{W} $ (middle right), and 5-jet $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ (lower center). Five signal masses are shown: 1000 (magenta), 1200 (red), 1400 (maroon), 1600 (orange), and 1800 GeV (purple). The signal distributions are normalized to the number of events estimated from the expected VLQ production cross section. The assumed branching fractions are $ \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{H}) = \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{Z}) = $ 50%, $ \mathcal{B}({\mathrm{B}} \to \mathrm{t}\mathrm{W}) = $ 0%. The background distribution is independent of the signal branching fractions. The hatched regions indicate the total systematic uncertainties in the background estimate.

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Figure 15-c:
Distributions of reconstructed VLQ mass for expected postfit background (blue histogram), signal plus background (colored lines), and observed data (black points) for events in the hadronic category. The channels shown are 5-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (upper left), 5-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (upper right), 5-jet $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (middle left), 5-jet $ \mathrm{b}\mathrm{H}\mathrm{t}\mathrm{W} $ (middle right), and 5-jet $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ (lower center). Five signal masses are shown: 1000 (magenta), 1200 (red), 1400 (maroon), 1600 (orange), and 1800 GeV (purple). The signal distributions are normalized to the number of events estimated from the expected VLQ production cross section. The assumed branching fractions are $ \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{H}) = \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{Z}) = $ 50%, $ \mathcal{B}({\mathrm{B}} \to \mathrm{t}\mathrm{W}) = $ 0%. The background distribution is independent of the signal branching fractions. The hatched regions indicate the total systematic uncertainties in the background estimate.

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Figure 15-d:
Distributions of reconstructed VLQ mass for expected postfit background (blue histogram), signal plus background (colored lines), and observed data (black points) for events in the hadronic category. The channels shown are 5-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (upper left), 5-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (upper right), 5-jet $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (middle left), 5-jet $ \mathrm{b}\mathrm{H}\mathrm{t}\mathrm{W} $ (middle right), and 5-jet $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ (lower center). Five signal masses are shown: 1000 (magenta), 1200 (red), 1400 (maroon), 1600 (orange), and 1800 GeV (purple). The signal distributions are normalized to the number of events estimated from the expected VLQ production cross section. The assumed branching fractions are $ \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{H}) = \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{Z}) = $ 50%, $ \mathcal{B}({\mathrm{B}} \to \mathrm{t}\mathrm{W}) = $ 0%. The background distribution is independent of the signal branching fractions. The hatched regions indicate the total systematic uncertainties in the background estimate.

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Figure 15-e:
Distributions of reconstructed VLQ mass for expected postfit background (blue histogram), signal plus background (colored lines), and observed data (black points) for events in the hadronic category. The channels shown are 5-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (upper left), 5-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (upper right), 5-jet $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (middle left), 5-jet $ \mathrm{b}\mathrm{H}\mathrm{t}\mathrm{W} $ (middle right), and 5-jet $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ (lower center). Five signal masses are shown: 1000 (magenta), 1200 (red), 1400 (maroon), 1600 (orange), and 1800 GeV (purple). The signal distributions are normalized to the number of events estimated from the expected VLQ production cross section. The assumed branching fractions are $ \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{H}) = \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{Z}) = $ 50%, $ \mathcal{B}({\mathrm{B}} \to \mathrm{t}\mathrm{W}) = $ 0%. The background distribution is independent of the signal branching fractions. The hatched regions indicate the total systematic uncertainties in the background estimate.

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Figure 16:
Distributions of reconstructed VLQ mass for expected postfit background (blue histogram), signal plus background (colored lines), and observed data (black points) for events in the hadronic category. The channels shown are 6-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (upper left), 6-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (upper right), 6-jet $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (middle left), 6-jet $ \mathrm{b}\mathrm{H}\mathrm{t}\mathrm{W} $ (middle right), and 6-jet $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ (lower center). Five signal masses are shown: 1000 (magenta), 1200 (red), 1400 (maroon), 1600 (orange), and 1800 GeV (purple). The signal distributions are normalized to the number of events estimated from the expected VLQ production cross section. The assumed branching fractions are $ \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{H}) = \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{Z}) = $ 50%, $ \mathcal{B}({\mathrm{B}} \to \mathrm{t}\mathrm{W}) = $ 0%. The background distribution is independent of the signal branching fractions. The hatched regions indicate the total systematic uncertainties in the background estimate.

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Figure 16-a:
Distributions of reconstructed VLQ mass for expected postfit background (blue histogram), signal plus background (colored lines), and observed data (black points) for events in the hadronic category. The channels shown are 6-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (upper left), 6-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (upper right), 6-jet $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (middle left), 6-jet $ \mathrm{b}\mathrm{H}\mathrm{t}\mathrm{W} $ (middle right), and 6-jet $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ (lower center). Five signal masses are shown: 1000 (magenta), 1200 (red), 1400 (maroon), 1600 (orange), and 1800 GeV (purple). The signal distributions are normalized to the number of events estimated from the expected VLQ production cross section. The assumed branching fractions are $ \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{H}) = \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{Z}) = $ 50%, $ \mathcal{B}({\mathrm{B}} \to \mathrm{t}\mathrm{W}) = $ 0%. The background distribution is independent of the signal branching fractions. The hatched regions indicate the total systematic uncertainties in the background estimate.

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Figure 16-b:
Distributions of reconstructed VLQ mass for expected postfit background (blue histogram), signal plus background (colored lines), and observed data (black points) for events in the hadronic category. The channels shown are 6-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (upper left), 6-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (upper right), 6-jet $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (middle left), 6-jet $ \mathrm{b}\mathrm{H}\mathrm{t}\mathrm{W} $ (middle right), and 6-jet $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ (lower center). Five signal masses are shown: 1000 (magenta), 1200 (red), 1400 (maroon), 1600 (orange), and 1800 GeV (purple). The signal distributions are normalized to the number of events estimated from the expected VLQ production cross section. The assumed branching fractions are $ \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{H}) = \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{Z}) = $ 50%, $ \mathcal{B}({\mathrm{B}} \to \mathrm{t}\mathrm{W}) = $ 0%. The background distribution is independent of the signal branching fractions. The hatched regions indicate the total systematic uncertainties in the background estimate.

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Figure 16-c:
Distributions of reconstructed VLQ mass for expected postfit background (blue histogram), signal plus background (colored lines), and observed data (black points) for events in the hadronic category. The channels shown are 6-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (upper left), 6-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (upper right), 6-jet $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (middle left), 6-jet $ \mathrm{b}\mathrm{H}\mathrm{t}\mathrm{W} $ (middle right), and 6-jet $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ (lower center). Five signal masses are shown: 1000 (magenta), 1200 (red), 1400 (maroon), 1600 (orange), and 1800 GeV (purple). The signal distributions are normalized to the number of events estimated from the expected VLQ production cross section. The assumed branching fractions are $ \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{H}) = \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{Z}) = $ 50%, $ \mathcal{B}({\mathrm{B}} \to \mathrm{t}\mathrm{W}) = $ 0%. The background distribution is independent of the signal branching fractions. The hatched regions indicate the total systematic uncertainties in the background estimate.

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Figure 16-d:
Distributions of reconstructed VLQ mass for expected postfit background (blue histogram), signal plus background (colored lines), and observed data (black points) for events in the hadronic category. The channels shown are 6-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (upper left), 6-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (upper right), 6-jet $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (middle left), 6-jet $ \mathrm{b}\mathrm{H}\mathrm{t}\mathrm{W} $ (middle right), and 6-jet $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ (lower center). Five signal masses are shown: 1000 (magenta), 1200 (red), 1400 (maroon), 1600 (orange), and 1800 GeV (purple). The signal distributions are normalized to the number of events estimated from the expected VLQ production cross section. The assumed branching fractions are $ \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{H}) = \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{Z}) = $ 50%, $ \mathcal{B}({\mathrm{B}} \to \mathrm{t}\mathrm{W}) = $ 0%. The background distribution is independent of the signal branching fractions. The hatched regions indicate the total systematic uncertainties in the background estimate.

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Figure 16-e:
Distributions of reconstructed VLQ mass for expected postfit background (blue histogram), signal plus background (colored lines), and observed data (black points) for events in the hadronic category. The channels shown are 6-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{H} $ (upper left), 6-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (upper right), 6-jet $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (middle left), 6-jet $ \mathrm{b}\mathrm{H}\mathrm{t}\mathrm{W} $ (middle right), and 6-jet $ \mathrm{b}\mathrm{Z}\mathrm{t}\mathrm{W} $ (lower center). Five signal masses are shown: 1000 (magenta), 1200 (red), 1400 (maroon), 1600 (orange), and 1800 GeV (purple). The signal distributions are normalized to the number of events estimated from the expected VLQ production cross section. The assumed branching fractions are $ \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{H}) = \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{Z}) = $ 50%, $ \mathcal{B}({\mathrm{B}} \to \mathrm{t}\mathrm{W}) = $ 0%. The background distribution is independent of the signal branching fractions. The hatched regions indicate the total systematic uncertainties in the background estimate.

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Figure 17:
Distributions of reconstructed VLQ mass for expected postfit background (blue histogram), signal plus background (colored lines), and observed data (black points) for events in the leptonic category. The channels shown are 3-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (upper left), 4-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (upper right), 3-jet $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (lower left), and 4-jet $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (lower right). Five signal masses are shown: 1000 (magenta), 1200 (red), 1400 (maroon), 1600 (orange), and 1800 GeV (purple). The signal distributions are normalized to the number of events estimated from the expected VLQ production cross section. The assumed branching fractions are $ \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{H}) = \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{Z}) = $ 50%, $ \mathcal{B}({\mathrm{B}} \to \mathrm{t}\mathrm{W}) = $ 0%. The background distribution is independent of the signal branching fractions. The hatched regions indicate the total systematic uncertainties in the background estimate.

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Figure 17-a:
Distributions of reconstructed VLQ mass for expected postfit background (blue histogram), signal plus background (colored lines), and observed data (black points) for events in the leptonic category. The channels shown are 3-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (upper left), 4-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (upper right), 3-jet $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (lower left), and 4-jet $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (lower right). Five signal masses are shown: 1000 (magenta), 1200 (red), 1400 (maroon), 1600 (orange), and 1800 GeV (purple). The signal distributions are normalized to the number of events estimated from the expected VLQ production cross section. The assumed branching fractions are $ \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{H}) = \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{Z}) = $ 50%, $ \mathcal{B}({\mathrm{B}} \to \mathrm{t}\mathrm{W}) = $ 0%. The background distribution is independent of the signal branching fractions. The hatched regions indicate the total systematic uncertainties in the background estimate.

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Figure 17-b:
Distributions of reconstructed VLQ mass for expected postfit background (blue histogram), signal plus background (colored lines), and observed data (black points) for events in the leptonic category. The channels shown are 3-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (upper left), 4-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (upper right), 3-jet $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (lower left), and 4-jet $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (lower right). Five signal masses are shown: 1000 (magenta), 1200 (red), 1400 (maroon), 1600 (orange), and 1800 GeV (purple). The signal distributions are normalized to the number of events estimated from the expected VLQ production cross section. The assumed branching fractions are $ \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{H}) = \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{Z}) = $ 50%, $ \mathcal{B}({\mathrm{B}} \to \mathrm{t}\mathrm{W}) = $ 0%. The background distribution is independent of the signal branching fractions. The hatched regions indicate the total systematic uncertainties in the background estimate.

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Figure 17-c:
Distributions of reconstructed VLQ mass for expected postfit background (blue histogram), signal plus background (colored lines), and observed data (black points) for events in the leptonic category. The channels shown are 3-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (upper left), 4-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (upper right), 3-jet $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (lower left), and 4-jet $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (lower right). Five signal masses are shown: 1000 (magenta), 1200 (red), 1400 (maroon), 1600 (orange), and 1800 GeV (purple). The signal distributions are normalized to the number of events estimated from the expected VLQ production cross section. The assumed branching fractions are $ \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{H}) = \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{Z}) = $ 50%, $ \mathcal{B}({\mathrm{B}} \to \mathrm{t}\mathrm{W}) = $ 0%. The background distribution is independent of the signal branching fractions. The hatched regions indicate the total systematic uncertainties in the background estimate.

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Figure 17-d:
Distributions of reconstructed VLQ mass for expected postfit background (blue histogram), signal plus background (colored lines), and observed data (black points) for events in the leptonic category. The channels shown are 3-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (upper left), 4-jet $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ (upper right), 3-jet $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (lower left), and 4-jet $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ (lower right). Five signal masses are shown: 1000 (magenta), 1200 (red), 1400 (maroon), 1600 (orange), and 1800 GeV (purple). The signal distributions are normalized to the number of events estimated from the expected VLQ production cross section. The assumed branching fractions are $ \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{H}) = \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{Z}) = $ 50%, $ \mathcal{B}({\mathrm{B}} \to \mathrm{t}\mathrm{W}) = $ 0%. The background distribution is independent of the signal branching fractions. The hatched regions indicate the total systematic uncertainties in the background estimate.

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Figure 18:
The limit at 95% CL on the cross section for VLQ pair production for four different branching fraction hypothesis: $ \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{H}) = $ 100% (upper left), $ \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{Z}) = $ 100% (upper right), $ \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{H}) = \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{Z}) = $ 50%, corresponding to the $ \VLQT{\mathrm{B}} $ doublet model with no $ \VLQT\mathrm{t} $ mixing and also to the large VLQ mass $ \mathrm{X}\VLQT{\mathrm{B}} $ triplet model (lower left), and $ \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{H}) = \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{Z}) = 25% $, $ \mathcal{B}({\mathrm{B}} \to \mathrm{t}\mathrm{W}) = $ 50%, corresponding to the large VLQ mass $ \VLQT{\mathrm{B}}\VLQY $ triplet model (lower right). The expected limit is shown as the dashed line, with the 68 and 95% uncertainties shown by the green (inner) and yellow (outer) bands, respectively. The theoretical cross section and its uncertainty are shown by the red line and light-red band.

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Figure 18-a:
The limit at 95% CL on the cross section for VLQ pair production for four different branching fraction hypothesis: $ \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{H}) = $ 100% (upper left), $ \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{Z}) = $ 100% (upper right), $ \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{H}) = \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{Z}) = $ 50%, corresponding to the $ \VLQT{\mathrm{B}} $ doublet model with no $ \VLQT\mathrm{t} $ mixing and also to the large VLQ mass $ \mathrm{X}\VLQT{\mathrm{B}} $ triplet model (lower left), and $ \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{H}) = \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{Z}) = 25% $, $ \mathcal{B}({\mathrm{B}} \to \mathrm{t}\mathrm{W}) = $ 50%, corresponding to the large VLQ mass $ \VLQT{\mathrm{B}}\VLQY $ triplet model (lower right). The expected limit is shown as the dashed line, with the 68 and 95% uncertainties shown by the green (inner) and yellow (outer) bands, respectively. The theoretical cross section and its uncertainty are shown by the red line and light-red band.

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Figure 18-b:
The limit at 95% CL on the cross section for VLQ pair production for four different branching fraction hypothesis: $ \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{H}) = $ 100% (upper left), $ \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{Z}) = $ 100% (upper right), $ \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{H}) = \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{Z}) = $ 50%, corresponding to the $ \VLQT{\mathrm{B}} $ doublet model with no $ \VLQT\mathrm{t} $ mixing and also to the large VLQ mass $ \mathrm{X}\VLQT{\mathrm{B}} $ triplet model (lower left), and $ \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{H}) = \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{Z}) = 25% $, $ \mathcal{B}({\mathrm{B}} \to \mathrm{t}\mathrm{W}) = $ 50%, corresponding to the large VLQ mass $ \VLQT{\mathrm{B}}\VLQY $ triplet model (lower right). The expected limit is shown as the dashed line, with the 68 and 95% uncertainties shown by the green (inner) and yellow (outer) bands, respectively. The theoretical cross section and its uncertainty are shown by the red line and light-red band.

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Figure 18-c:
The limit at 95% CL on the cross section for VLQ pair production for four different branching fraction hypothesis: $ \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{H}) = $ 100% (upper left), $ \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{Z}) = $ 100% (upper right), $ \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{H}) = \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{Z}) = $ 50%, corresponding to the $ \VLQT{\mathrm{B}} $ doublet model with no $ \VLQT\mathrm{t} $ mixing and also to the large VLQ mass $ \mathrm{X}\VLQT{\mathrm{B}} $ triplet model (lower left), and $ \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{H}) = \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{Z}) = 25% $, $ \mathcal{B}({\mathrm{B}} \to \mathrm{t}\mathrm{W}) = $ 50%, corresponding to the large VLQ mass $ \VLQT{\mathrm{B}}\VLQY $ triplet model (lower right). The expected limit is shown as the dashed line, with the 68 and 95% uncertainties shown by the green (inner) and yellow (outer) bands, respectively. The theoretical cross section and its uncertainty are shown by the red line and light-red band.

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Figure 18-d:
The limit at 95% CL on the cross section for VLQ pair production for four different branching fraction hypothesis: $ \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{H}) = $ 100% (upper left), $ \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{Z}) = $ 100% (upper right), $ \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{H}) = \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{Z}) = $ 50%, corresponding to the $ \VLQT{\mathrm{B}} $ doublet model with no $ \VLQT\mathrm{t} $ mixing and also to the large VLQ mass $ \mathrm{X}\VLQT{\mathrm{B}} $ triplet model (lower left), and $ \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{H}) = \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{Z}) = 25% $, $ \mathcal{B}({\mathrm{B}} \to \mathrm{t}\mathrm{W}) = $ 50%, corresponding to the large VLQ mass $ \VLQT{\mathrm{B}}\VLQY $ triplet model (lower right). The expected limit is shown as the dashed line, with the 68 and 95% uncertainties shown by the green (inner) and yellow (outer) bands, respectively. The theoretical cross section and its uncertainty are shown by the red line and light-red band.

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Figure 19:
Median expected exclusion limits on the VLQ mass at 95% CL as a function of the branching fractions $ \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{H}) $ and $ \mathcal{B}({\mathrm{B}} \to \mathrm{t}\mathrm{W}) $, with $ \mathcal{B}({\mathrm{B}} \to \mathrm{t}\mathrm{W}) = 1 - \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{H}) - \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{Z}) $. The gray area corresponds to the region where the exclusion limit is less than 1000 GeV.

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Figure 20:
Observed exclusion limits on the VLQ mass at 95% CL as a function of the branching fractions $ \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{H}) $ and $ \mathcal{B}({\mathrm{B}} \to \mathrm{t}\mathrm{W}) $, with $ \mathcal{B}({\mathrm{B}} \to \mathrm{t}\mathrm{W}) = 1 - \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{H}) - \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{Z}) $. The gray area corresponds to the region where the exclusion limit is less than 1000 GeV.
Tables

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Table 1:
Summary of channels considered for each category and jet multiplicity. Although events with a jet from ISR or FSR are included in the leptonic category, for these events the extra jet is not included in the categorization of the jet multiplicity of the event.

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Table 2:
Required minimum number of single ($ N_{\mathrm{b}} $) and double ($ N_{\mathrm{b}\overline{\mathrm{b}}} $) b tags, and working points (WPs) used for each category, decay mode, and jet multiplicity. The working points are described in the text. For a given event mode, there can be several jet multiplicities depending on the number of merged jets.

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Table 3:
Optimized upper limit values of the $ \chi^2_\text{mod}/\text{ndf} $ selection as a function of jet multiplicity and decay mode.

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Table 4:
Values of the BJTF for data events in the control region with 500 $ < m_{\text{VLQ}} < $ 800 GeV for each of the fully hadronic channels considered. The uncertainties shown are statistical.

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Table 5:
Values of the b-tag to b-veto ratio for events in the mass range 450 $ < m_{\text{VLQ}} < $ 900 GeV with $ \chi^2_\text{mod}/\text{ndf} < $ 5, for each of the dileptonic channels. The uncertainties shown are statistical only.

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Table 6:
Systematic uncertainties for the fully hadronic channels for a simulated signal mass of 1400 GeV and branching fractions of $ \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{H}) = 40% $, $ \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{Z}) = 40% $, and $ \mathcal{B}({\mathrm{B}} \to \mathrm{t}\mathrm{W}) = 20% $. The only parameters in the fits that have significant uncertainties ($ > $0.01%) are the scaling parameters (denoted by $ p_0 $).

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Table 7:
Systematic uncertainties for the dileptonic $ \mathrm{b}\mathrm{H}\mathrm{b}\mathrm{Z} $ and $ \mathrm{b}\mathrm{Z}\mathrm{b}\mathrm{Z} $ channels for a simulated signal mass of 1400 GeV and branching fractions of $ \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{H}) = 40% $, $ \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{Z}) = 40% $, and $ \mathcal{B}({\mathrm{B}} \to \mathrm{t}\mathrm{W}) = 20% $.
Summary
A search for bottom-type vector-like quarks (B VLQs) has been presented, using data from proton-proton collisions collected by the CMS detector in 2016--2018 at $ \sqrt{s} = $ 13 TeV. Results are combined from the fully hadronic category, where each B VLQ decays into either a b quark and a Higgs boson (H), a b quark and a Z boson, or a t quark and a W boson, and the leptonic category, where each B VLQ decays into a b quark and either an H or a Z boson, and at least one decay includes a Z boson that decays into a pair of charged leptons. To account for the fact that the two jets from an H, Z, or W boson decay may be reconstructed separately, or may be merged into a single reconstructed jet due to a high Lorentz boost, events are separated into different jet multiplicity categories and reconstructed appropriately. Backgrounds are estimated from data and limits are set on the VLQ mass at 95% confidence level as a function of the branching fractions $ \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{H}) $, $ \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{Z}) $, and $ \mathcal{B}({\mathrm{B}} \to \mathrm{t}\mathrm{W}) $. The most significant improvement over previous results is an increased sensitivity for scenarios with large $ \mathcal{B}({\mathrm{B}} \to \mathrm{b}\mathrm{Z}) $ due to the inclusion of events with leptonic Z boson decays. The current results represent the most stringent limits on B VLQs to date.
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