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CMS-JME-18-002 ; CERN-EP-2020-037
Identification of heavy, energetic, hadronically decaying particles using machine-learning techniques
JINST 15 (2020) P06005
Abstract: Machine-learning (ML) techniques are explored to identify and classify hadronic decays of highly Lorentz-boosted W/Z/Higgs bosons and top quarks. Techniques without ML have also been evaluated and are included for comparison. The identification performances of a variety of algorithms are characterized in simulated events and directly compared with data. The algorithms are validated using proton-proton collision data at $\sqrt{s} = $ 13 TeV, corresponding to an integrated luminosity of 35.9 fb$^{-1}$. Systematic uncertainties are assessed by comparing the results obtained using simulation and collision data. The new techniques studied in this paper provide significant performance improvements over non-ML techniques, reducing the background rate by up to an order of magnitude at the same signal efficiency.
Figures & Tables Summary References CMS Publications
Figures

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Figure 1:
Matching efficiency as a function of the ${p_{\mathrm {T}}}$ of the generated particle, for hadronically decaying W bosons (left) and t quarks (right). This efficiency is defined as the fraction of the generated particles (t quarks or W bosons) that are within $\Delta R < $ 0.6 with an AK8 or CA15 jet with $ {p_{\mathrm {T}}} > $ 200 GeV and $ {| \eta |} < $ 2.4. Superimposed is the merging efficiency as a function of the generated particle ${p_{\mathrm {T}}}$ when all decay products are within $\smash [b]\Delta R (\text {AK8}, \mathrm{q} _{i}) < $ 0.6 ($\smash [b]\Delta R (\text {CA15}, \mathrm{q} _{i}) < $ 1.2) with an AK8 (CA15) jet.

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Figure 1-a:
Matching efficiency as a function of the ${p_{\mathrm {T}}}$ of the generated particle, for hadronically decaying W bosons (left) and t quarks (right). This efficiency is defined as the fraction of the generated particles (t quarks or W bosons) that are within $\Delta R < $ 0.6 with an AK8 or CA15 jet with $ {p_{\mathrm {T}}} > $ 200 GeV and $ {| \eta |} < $ 2.4. Superimposed is the merging efficiency as a function of the generated particle ${p_{\mathrm {T}}}$ when all decay products are within $\smash [b]\Delta R (\text {AK8}, \mathrm{q} _{i}) < $ 0.6 ($\smash [b]\Delta R (\text {CA15}, \mathrm{q} _{i}) < $ 1.2) with an AK8 (CA15) jet.

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Figure 1-b:
Matching efficiency as a function of the ${p_{\mathrm {T}}}$ of the generated particle, for hadronically decaying W bosons (left) and t quarks (right). This efficiency is defined as the fraction of the generated particles (t quarks or W bosons) that are within $\Delta R < $ 0.6 with an AK8 or CA15 jet with $ {p_{\mathrm {T}}} > $ 200 GeV and $ {| \eta |} < $ 2.4. Superimposed is the merging efficiency as a function of the generated particle ${p_{\mathrm {T}}}$ when all decay products are within $\smash [b]\Delta R (\text {AK8}, \mathrm{q} _{i}) < $ 0.6 ($\smash [b]\Delta R (\text {CA15}, \mathrm{q} _{i}) < $ 1.2) with an AK8 (CA15) jet.

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Figure 2:
Comparison of the ${m_{\text {SD}}}$ shape in signal and background AK8 jets in simulation. The fiducial selection on the jets is displayed on the plots. Signal jets are defined as jets arising from hadronic decays of W/Z/H bosons (left) or t quarks (right), whereas background jets are obtained from the QCD multijet sample.

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Figure 2-a:
Comparison of the ${m_{\text {SD}}}$ shape in signal and background AK8 jets in simulation. The fiducial selection on the jets is displayed on the plots. Signal jets are defined as jets arising from hadronic decays of W/Z/H bosons (left) or t quarks (right), whereas background jets are obtained from the QCD multijet sample.

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Figure 2-b:
Comparison of the ${m_{\text {SD}}}$ shape in signal and background AK8 jets in simulation. The fiducial selection on the jets is displayed on the plots. Signal jets are defined as jets arising from hadronic decays of W/Z/H bosons (left) or t quarks (right), whereas background jets are obtained from the QCD multijet sample.

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Figure 3:
Comparison of the ${\tau _{21}}$ (left) and ${\tau _{32}}$ (right) shape in signal and background AK8 jets. The fiducial selection on the jets is displayed in the plots. As signal jets we consider jets stemming from hadronic decays of W, Z, or H bosons (left), or t quarks (right), whereas background jets are obtained from the QCD multijet sample.

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Figure 3-a:
Comparison of the ${\tau _{21}}$ (left) and ${\tau _{32}}$ (right) shape in signal and background AK8 jets. The fiducial selection on the jets is displayed in the plots. As signal jets we consider jets stemming from hadronic decays of W, Z, or H bosons (left), or t quarks (right), whereas background jets are obtained from the QCD multijet sample.

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Figure 3-b:
Comparison of the ${\tau _{21}}$ (left) and ${\tau _{32}}$ (right) shape in signal and background AK8 jets. The fiducial selection on the jets is displayed in the plots. As signal jets we consider jets stemming from hadronic decays of W, Z, or H bosons (left), or t quarks (right), whereas background jets are obtained from the QCD multijet sample.

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Figure 4:
Shape comparison of the main variables of the HOTVR algorithm for signal and background jets, in two different regions of the jet ${p_{\mathrm {T}}}$ as displayed in the plots.

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Figure 4-a:
Shape comparison of the main variables of the HOTVR algorithm for signal and background jets, in two different regions of the jet ${p_{\mathrm {T}}}$ as displayed in the plots.

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Figure 4-b:
Shape comparison of the main variables of the HOTVR algorithm for signal and background jets, in two different regions of the jet ${p_{\mathrm {T}}}$ as displayed in the plots.

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Figure 4-c:
Shape comparison of the main variables of the HOTVR algorithm for signal and background jets, in two different regions of the jet ${p_{\mathrm {T}}}$ as displayed in the plots.

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Figure 4-d:
Shape comparison of the main variables of the HOTVR algorithm for signal and background jets, in two different regions of the jet ${p_{\mathrm {T}}}$ as displayed in the plots.

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Figure 4-e:
Shape comparison of the main variables of the HOTVR algorithm for signal and background jets, in two different regions of the jet ${p_{\mathrm {T}}}$ as displayed in the plots.

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Figure 4-f:
Shape comparison of the main variables of the HOTVR algorithm for signal and background jets, in two different regions of the jet ${p_{\mathrm {T}}}$ as displayed in the plots.

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Figure 5:
Comparison of the distribution of $N_3^{(2)}$ (left) and the ${N_{3}\text {-}\text {BDT} (\text {CA}15)}$ discriminant (right) in t quarks jets (signal) and jets from QCD multijet processes (background).

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Figure 5-a:
Comparison of the distribution of $N_3^{(2)}$ (left) and the ${N_{3}\text {-}\text {BDT} (\text {CA}15)}$ discriminant (right) in t quarks jets (signal) and jets from QCD multijet processes (background).

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Figure 5-b:
Comparison of the distribution of $N_3^{(2)}$ (left) and the ${N_{3}\text {-}\text {BDT} (\text {CA}15)}$ discriminant (right) in t quarks jets (signal) and jets from QCD multijet processes (background).

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Figure 6:
Distributions of the ${m_\text {SD}+N_{2}}$ (left) and ${m_\text {SD}+N_{2}^{\text {DDT}}}$ (right) in signal and background jets.

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Figure 6-a:
Distributions of the ${m_\text {SD}+N_{2}}$ (left) and ${m_\text {SD}+N_{2}^{\text {DDT}}}$ (right) in signal and background jets.

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Figure 6-b:
Distributions of the ${m_\text {SD}+N_{2}}$ (left) and ${m_\text {SD}+N_{2}^{\text {DDT}}}$ (right) in signal and background jets.

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Figure 7:
The pixelized images used in the ImageTop network with PF candidate colors summed together ("greyscale'') for QCD (left) and t quark (right) jets. The x and y axes are the pixel number, and roughly scale with $\Delta R$. The $z$ axis is the intensity of the greyscale image in the given pixel, related to the PF candidate $ {p_{\mathrm {T}}} $, and has been normalized to unity. This figure shows an ensemble of overlaid images after the image post processing; we can see clear differences between the QCD jet energy and t quark deposition patterns.

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Figure 7-a:
The pixelized images used in the ImageTop network with PF candidate colors summed together ("greyscale'') for QCD (left) and t quark (right) jets. The x and y axes are the pixel number, and roughly scale with $\Delta R$. The $z$ axis is the intensity of the greyscale image in the given pixel, related to the PF candidate $ {p_{\mathrm {T}}} $, and has been normalized to unity. This figure shows an ensemble of overlaid images after the image post processing; we can see clear differences between the QCD jet energy and t quark deposition patterns.

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Figure 7-b:
The pixelized images used in the ImageTop network with PF candidate colors summed together ("greyscale'') for QCD (left) and t quark (right) jets. The x and y axes are the pixel number, and roughly scale with $\Delta R$. The $z$ axis is the intensity of the greyscale image in the given pixel, related to the PF candidate $ {p_{\mathrm {T}}} $, and has been normalized to unity. This figure shows an ensemble of overlaid images after the image post processing; we can see clear differences between the QCD jet energy and t quark deposition patterns.

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Figure 8:
The ImageTop network architecture. The neural network inputs are the 37x37 pixelized PF candidate ${p_{\mathrm {T}}}$ map, which is split into colors based on the PF candidate flavor, and the DeepFlavor subjet b tags applied to both subjets. The pixelized images are sent through a two-dimensional CNN, and the subjet b tags are inputs to a dense layer. After flattening the CNN, the two networks are taken as input to three dense layers and finally to the two-node output, which is used as the top tagging discriminator.

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Figure 9:
The network architecture of DeepAK8.

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Figure 10:
The network architecture of DeepAK8-MD.

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Figure 11:
Comparison of the identification algorithms for hadronically decaying t quark in terms of ROC curves in two regions based on the ${p_{\mathrm {T}}}$ of the generated particle; Left: 300 $ < {p_{\mathrm {T}}} < $ 500 GeV, and Right: 1000 $ < {p_{\mathrm {T}}} < $ 1500 GeV. Additional fiducial selection criteria applied to the jets are listed on the plots.

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Figure 11-a:
Comparison of the identification algorithms for hadronically decaying t quark in terms of ROC curves in two regions based on the ${p_{\mathrm {T}}}$ of the generated particle; Left: 300 $ < {p_{\mathrm {T}}} < $ 500 GeV, and Right: 1000 $ < {p_{\mathrm {T}}} < $ 1500 GeV. Additional fiducial selection criteria applied to the jets are listed on the plots.

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Figure 11-b:
Comparison of the identification algorithms for hadronically decaying t quark in terms of ROC curves in two regions based on the ${p_{\mathrm {T}}}$ of the generated particle; Left: 300 $ < {p_{\mathrm {T}}} < $ 500 GeV, and Right: 1000 $ < {p_{\mathrm {T}}} < $ 1500 GeV. Additional fiducial selection criteria applied to the jets are listed on the plots.

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Figure 12:
Comparison of the identification algorithms for hadronically decaying W boson in terms of ROC curves in two regions based on the ${p_{\mathrm {T}}}$ of the generated particle; Left: 300 $ < {p_{\mathrm {T}}} < $ 500 GeV, and Right: 1000 $ < {p_{\mathrm {T}}} < $ 1500 GeV. Additional fiducial selection criteria applied to the jets are listed on the plots.

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Figure 12-a:
Comparison of the identification algorithms for hadronically decaying W boson in terms of ROC curves in two regions based on the ${p_{\mathrm {T}}}$ of the generated particle; Left: 300 $ < {p_{\mathrm {T}}} < $ 500 GeV, and Right: 1000 $ < {p_{\mathrm {T}}} < $ 1500 GeV. Additional fiducial selection criteria applied to the jets are listed on the plots.

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Figure 12-b:
Comparison of the identification algorithms for hadronically decaying W boson in terms of ROC curves in two regions based on the ${p_{\mathrm {T}}}$ of the generated particle; Left: 300 $ < {p_{\mathrm {T}}} < $ 500 GeV, and Right: 1000 $ < {p_{\mathrm {T}}} < $ 1500 GeV. Additional fiducial selection criteria applied to the jets are listed on the plots.

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Figure 13:
Comparison of the identification algorithms for hadronically decaying Z boson in terms of ROC curves in two regions based on the ${p_{\mathrm {T}}}$ of the generated particle; Left: 300 $ < {p_{\mathrm {T}}} < $ 500 GeV, and Right: 1000 $ < {p_{\mathrm {T}}} < $ 1500 GeV. Additional fiducial selection criteria applied to the jets are listed on the plots.

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Figure 13-a:
Comparison of the identification algorithms for hadronically decaying Z boson in terms of ROC curves in two regions based on the ${p_{\mathrm {T}}}$ of the generated particle; Left: 300 $ < {p_{\mathrm {T}}} < $ 500 GeV, and Right: 1000 $ < {p_{\mathrm {T}}} < $ 1500 GeV. Additional fiducial selection criteria applied to the jets are listed on the plots.

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Figure 13-b:
Comparison of the identification algorithms for hadronically decaying Z boson in terms of ROC curves in two regions based on the ${p_{\mathrm {T}}}$ of the generated particle; Left: 300 $ < {p_{\mathrm {T}}} < $ 500 GeV, and Right: 1000 $ < {p_{\mathrm {T}}} < $ 1500 GeV. Additional fiducial selection criteria applied to the jets are listed on the plots.

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Figure 14:
Comparison of the identification algorithms for hadronically decaying H boson in terms of ROC curves in two regions based on the ${p_{\mathrm {T}}}$ of the generated particle; Left: 300 $ < {p_{\mathrm {T}}} < $ 500 GeV, and Right: 1000 $ < {p_{\mathrm {T}}} < $ 1500 GeV. The H boson decays to a pair of b quarks. Additional fiducial selection criteria applied to the jets are listed on the plots.

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Figure 14-a:
Comparison of the identification algorithms for hadronically decaying H boson in terms of ROC curves in two regions based on the ${p_{\mathrm {T}}}$ of the generated particle; Left: 300 $ < {p_{\mathrm {T}}} < $ 500 GeV, and Right: 1000 $ < {p_{\mathrm {T}}} < $ 1500 GeV. The H boson decays to a pair of b quarks. Additional fiducial selection criteria applied to the jets are listed on the plots.

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Figure 14-b:
Comparison of the identification algorithms for hadronically decaying H boson in terms of ROC curves in two regions based on the ${p_{\mathrm {T}}}$ of the generated particle; Left: 300 $ < {p_{\mathrm {T}}} < $ 500 GeV, and Right: 1000 $ < {p_{\mathrm {T}}} < $ 1500 GeV. The H boson decays to a pair of b quarks. Additional fiducial selection criteria applied to the jets are listed on the plots.

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Figure 15:
Alternative versions of DeepAK8 trained using a subset of the input features. The details about each version are discussed in the text. The performances of the three versions of DeepAK8 are compared for t quark (upper) and Z boson (lower) identification. For the latter, the left plot corresponds to Z bosons decaying to a pair of b quarks, and the right plot to a pair of light-flavor quarks.

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Figure 15-a:
Alternative versions of DeepAK8 trained using a subset of the input features. The details about each version are discussed in the text. The performances of the three versions of DeepAK8 are compared for t quark (upper) and Z boson (lower) identification. For the latter, the left plot corresponds to Z bosons decaying to a pair of b quarks, and the right plot to a pair of light-flavor quarks.

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Figure 15-b:
Alternative versions of DeepAK8 trained using a subset of the input features. The details about each version are discussed in the text. The performances of the three versions of DeepAK8 are compared for t quark (upper) and Z boson (lower) identification. For the latter, the left plot corresponds to Z bosons decaying to a pair of b quarks, and the right plot to a pair of light-flavor quarks.

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Figure 15-c:
Alternative versions of DeepAK8 trained using a subset of the input features. The details about each version are discussed in the text. The performances of the three versions of DeepAK8 are compared for t quark (upper) and Z boson (lower) identification. For the latter, the left plot corresponds to Z bosons decaying to a pair of b quarks, and the right plot to a pair of light-flavor quarks.

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Figure 16:
The efficiency ${\epsilon _{\text {S}}}$ as a function of the generated particle ${p_{\mathrm {T}}}$ for a working point corresponding to $ {\epsilon _{\text {S}}}= $ 30 (50)% for t quark (W/Z/H boson) identification. Upper left: t quark, upper right: W boson, lower left: Z boson, lower right: H boson. The error bars represent the statistical uncertainty in each specific bin, due to the limited number of simulated events. Additional fiducial selection criteria applied to the jets are listed in the plots.

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Figure 16-a:
The efficiency ${\epsilon _{\text {S}}}$ as a function of the generated particle ${p_{\mathrm {T}}}$ for a working point corresponding to $ {\epsilon _{\text {S}}}= $ 30 (50)% for t quark (W/Z/H boson) identification. Upper left: t quark, upper right: W boson, lower left: Z boson, lower right: H boson. The error bars represent the statistical uncertainty in each specific bin, due to the limited number of simulated events. Additional fiducial selection criteria applied to the jets are listed in the plots.

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Figure 16-b:
The efficiency ${\epsilon _{\text {S}}}$ as a function of the generated particle ${p_{\mathrm {T}}}$ for a working point corresponding to $ {\epsilon _{\text {S}}}= $ 30 (50)% for t quark (W/Z/H boson) identification. Upper left: t quark, upper right: W boson, lower left: Z boson, lower right: H boson. The error bars represent the statistical uncertainty in each specific bin, due to the limited number of simulated events. Additional fiducial selection criteria applied to the jets are listed in the plots.

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Figure 16-c:
The efficiency ${\epsilon _{\text {S}}}$ as a function of the generated particle ${p_{\mathrm {T}}}$ for a working point corresponding to $ {\epsilon _{\text {S}}}= $ 30 (50)% for t quark (W/Z/H boson) identification. Upper left: t quark, upper right: W boson, lower left: Z boson, lower right: H boson. The error bars represent the statistical uncertainty in each specific bin, due to the limited number of simulated events. Additional fiducial selection criteria applied to the jets are listed in the plots.

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Figure 16-d:
The efficiency ${\epsilon _{\text {S}}}$ as a function of the generated particle ${p_{\mathrm {T}}}$ for a working point corresponding to $ {\epsilon _{\text {S}}}= $ 30 (50)% for t quark (W/Z/H boson) identification. Upper left: t quark, upper right: W boson, lower left: Z boson, lower right: H boson. The error bars represent the statistical uncertainty in each specific bin, due to the limited number of simulated events. Additional fiducial selection criteria applied to the jets are listed in the plots.

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Figure 17:
The distribution of ${\epsilon _{\text {B}}}$ as a function of the generated particle ${p_{\mathrm {T}}}$ for a working point corresponding to $ {\epsilon _{\text {S}}}= $ 30 (50)% for t quark (W/Z/H boson) identification. Upper left: t quark, upper right: W boson, lower left: Z boson, lower right: H boson. The error bars represent the statistical uncertainty in each specific bin, due to the limited number of simulated events. Additional fiducial selection criteria applied to the jets are listed in the plots.

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Figure 17-a:
The distribution of ${\epsilon _{\text {B}}}$ as a function of the generated particle ${p_{\mathrm {T}}}$ for a working point corresponding to $ {\epsilon _{\text {S}}}= $ 30 (50)% for t quark (W/Z/H boson) identification. Upper left: t quark, upper right: W boson, lower left: Z boson, lower right: H boson. The error bars represent the statistical uncertainty in each specific bin, due to the limited number of simulated events. Additional fiducial selection criteria applied to the jets are listed in the plots.

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Figure 17-b:
The distribution of ${\epsilon _{\text {B}}}$ as a function of the generated particle ${p_{\mathrm {T}}}$ for a working point corresponding to $ {\epsilon _{\text {S}}}= $ 30 (50)% for t quark (W/Z/H boson) identification. Upper left: t quark, upper right: W boson, lower left: Z boson, lower right: H boson. The error bars represent the statistical uncertainty in each specific bin, due to the limited number of simulated events. Additional fiducial selection criteria applied to the jets are listed in the plots.

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Figure 17-c:
The distribution of ${\epsilon _{\text {B}}}$ as a function of the generated particle ${p_{\mathrm {T}}}$ for a working point corresponding to $ {\epsilon _{\text {S}}}= $ 30 (50)% for t quark (W/Z/H boson) identification. Upper left: t quark, upper right: W boson, lower left: Z boson, lower right: H boson. The error bars represent the statistical uncertainty in each specific bin, due to the limited number of simulated events. Additional fiducial selection criteria applied to the jets are listed in the plots.

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Figure 17-d:
The distribution of ${\epsilon _{\text {B}}}$ as a function of the generated particle ${p_{\mathrm {T}}}$ for a working point corresponding to $ {\epsilon _{\text {S}}}= $ 30 (50)% for t quark (W/Z/H boson) identification. Upper left: t quark, upper right: W boson, lower left: Z boson, lower right: H boson. The error bars represent the statistical uncertainty in each specific bin, due to the limited number of simulated events. Additional fiducial selection criteria applied to the jets are listed in the plots.

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Figure 18:
The efficiency ${\epsilon _{\text {S}}}$ as a function of the number of primary vertices (${N_{\text {PV}}}$) for generated particles with 500 $ < {p_{\mathrm {T}}} < $ 1000 GeV at a working point corresponding to $ {\epsilon _{\text {S}}}= $ 30 (50)% for t quark (W/Z/H boson) identification. Upper left: t quark, upper right: W boson, lower left: Z boson, lower right: H boson. The error bars represent the statistical uncertainty in each specific bin, due to a limited number of simulated events. Additional fiducial selection criteria applied to the jets are listed in the plots.

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Figure 18-a:
The efficiency ${\epsilon _{\text {S}}}$ as a function of the number of primary vertices (${N_{\text {PV}}}$) for generated particles with 500 $ < {p_{\mathrm {T}}} < $ 1000 GeV at a working point corresponding to $ {\epsilon _{\text {S}}}= $ 30 (50)% for t quark (W/Z/H boson) identification. Upper left: t quark, upper right: W boson, lower left: Z boson, lower right: H boson. The error bars represent the statistical uncertainty in each specific bin, due to a limited number of simulated events. Additional fiducial selection criteria applied to the jets are listed in the plots.

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Figure 18-b:
The efficiency ${\epsilon _{\text {S}}}$ as a function of the number of primary vertices (${N_{\text {PV}}}$) for generated particles with 500 $ < {p_{\mathrm {T}}} < $ 1000 GeV at a working point corresponding to $ {\epsilon _{\text {S}}}= $ 30 (50)% for t quark (W/Z/H boson) identification. Upper left: t quark, upper right: W boson, lower left: Z boson, lower right: H boson. The error bars represent the statistical uncertainty in each specific bin, due to a limited number of simulated events. Additional fiducial selection criteria applied to the jets are listed in the plots.

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Figure 18-c:
The efficiency ${\epsilon _{\text {S}}}$ as a function of the number of primary vertices (${N_{\text {PV}}}$) for generated particles with 500 $ < {p_{\mathrm {T}}} < $ 1000 GeV at a working point corresponding to $ {\epsilon _{\text {S}}}= $ 30 (50)% for t quark (W/Z/H boson) identification. Upper left: t quark, upper right: W boson, lower left: Z boson, lower right: H boson. The error bars represent the statistical uncertainty in each specific bin, due to a limited number of simulated events. Additional fiducial selection criteria applied to the jets are listed in the plots.

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Figure 18-d:
The efficiency ${\epsilon _{\text {S}}}$ as a function of the number of primary vertices (${N_{\text {PV}}}$) for generated particles with 500 $ < {p_{\mathrm {T}}} < $ 1000 GeV at a working point corresponding to $ {\epsilon _{\text {S}}}= $ 30 (50)% for t quark (W/Z/H boson) identification. Upper left: t quark, upper right: W boson, lower left: Z boson, lower right: H boson. The error bars represent the statistical uncertainty in each specific bin, due to a limited number of simulated events. Additional fiducial selection criteria applied to the jets are listed in the plots.

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Figure 19:
The efficiency ${\epsilon _{\text {B}}}$ as a function of the number of primary vertices (${N_{\text {PV}}}$) for generated particles with 500 $ < {p_{\mathrm {T}}} < $ 1000 GeV at a working point corresponding to $ {\epsilon _{\text {S}}}= $ 30 (50)% for t quark (W/Z/H boson) identification. Upper left: t quark, upper right: W boson, lower left: Z boson, lower right: H boson. The error bars represent the statistical uncertainty in each specific bin, due to the limited number of simulated events. Additional fiducial selection criteria applied to the jets are listed in the plots.

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Figure 19-a:
The efficiency ${\epsilon _{\text {B}}}$ as a function of the number of primary vertices (${N_{\text {PV}}}$) for generated particles with 500 $ < {p_{\mathrm {T}}} < $ 1000 GeV at a working point corresponding to $ {\epsilon _{\text {S}}}= $ 30 (50)% for t quark (W/Z/H boson) identification. Upper left: t quark, upper right: W boson, lower left: Z boson, lower right: H boson. The error bars represent the statistical uncertainty in each specific bin, due to the limited number of simulated events. Additional fiducial selection criteria applied to the jets are listed in the plots.

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Figure 19-b:
The efficiency ${\epsilon _{\text {B}}}$ as a function of the number of primary vertices (${N_{\text {PV}}}$) for generated particles with 500 $ < {p_{\mathrm {T}}} < $ 1000 GeV at a working point corresponding to $ {\epsilon _{\text {S}}}= $ 30 (50)% for t quark (W/Z/H boson) identification. Upper left: t quark, upper right: W boson, lower left: Z boson, lower right: H boson. The error bars represent the statistical uncertainty in each specific bin, due to the limited number of simulated events. Additional fiducial selection criteria applied to the jets are listed in the plots.

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Figure 19-c:
The efficiency ${\epsilon _{\text {B}}}$ as a function of the number of primary vertices (${N_{\text {PV}}}$) for generated particles with 500 $ < {p_{\mathrm {T}}} < $ 1000 GeV at a working point corresponding to $ {\epsilon _{\text {S}}}= $ 30 (50)% for t quark (W/Z/H boson) identification. Upper left: t quark, upper right: W boson, lower left: Z boson, lower right: H boson. The error bars represent the statistical uncertainty in each specific bin, due to the limited number of simulated events. Additional fiducial selection criteria applied to the jets are listed in the plots.

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Figure 19-d:
The efficiency ${\epsilon _{\text {B}}}$ as a function of the number of primary vertices (${N_{\text {PV}}}$) for generated particles with 500 $ < {p_{\mathrm {T}}} < $ 1000 GeV at a working point corresponding to $ {\epsilon _{\text {S}}}= $ 30 (50)% for t quark (W/Z/H boson) identification. Upper left: t quark, upper right: W boson, lower left: Z boson, lower right: H boson. The error bars represent the statistical uncertainty in each specific bin, due to the limited number of simulated events. Additional fiducial selection criteria applied to the jets are listed in the plots.

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Figure 20:
The normalized ${m_{\text {SD}}}$ distribution for background QCD jets with 600 $ < {p_{\mathrm {T}}} < $ 1000 GeV, inclusively and after selection by each algorithm. The working point chosen corresponds to $ {\epsilon _{\text {S}}}=$ 30 ($ {\epsilon _{\text {S}}}=$ 50)% for t quark (W/Z/H boson) identification. Upper left: t quark, upper right: W boson, lower left: Z boson, lower right: H boson. The error bars represent the statistical uncertainty in each specific bin, which is related to the limited number of simulated events. Additional fiducial selection criteria applied to the jets are listed on the plots.

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Figure 20-a:
The normalized ${m_{\text {SD}}}$ distribution for background QCD jets with 600 $ < {p_{\mathrm {T}}} < $ 1000 GeV, inclusively and after selection by each algorithm. The working point chosen corresponds to $ {\epsilon _{\text {S}}}=$ 30 ($ {\epsilon _{\text {S}}}=$ 50)% for t quark (W/Z/H boson) identification. Upper left: t quark, upper right: W boson, lower left: Z boson, lower right: H boson. The error bars represent the statistical uncertainty in each specific bin, which is related to the limited number of simulated events. Additional fiducial selection criteria applied to the jets are listed on the plots.

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Figure 20-b:
The normalized ${m_{\text {SD}}}$ distribution for background QCD jets with 600 $ < {p_{\mathrm {T}}} < $ 1000 GeV, inclusively and after selection by each algorithm. The working point chosen corresponds to $ {\epsilon _{\text {S}}}=$ 30 ($ {\epsilon _{\text {S}}}=$ 50)% for t quark (W/Z/H boson) identification. Upper left: t quark, upper right: W boson, lower left: Z boson, lower right: H boson. The error bars represent the statistical uncertainty in each specific bin, which is related to the limited number of simulated events. Additional fiducial selection criteria applied to the jets are listed on the plots.

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Figure 20-c:
The normalized ${m_{\text {SD}}}$ distribution for background QCD jets with 600 $ < {p_{\mathrm {T}}} < $ 1000 GeV, inclusively and after selection by each algorithm. The working point chosen corresponds to $ {\epsilon _{\text {S}}}=$ 30 ($ {\epsilon _{\text {S}}}=$ 50)% for t quark (W/Z/H boson) identification. Upper left: t quark, upper right: W boson, lower left: Z boson, lower right: H boson. The error bars represent the statistical uncertainty in each specific bin, which is related to the limited number of simulated events. Additional fiducial selection criteria applied to the jets are listed on the plots.

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Figure 20-d:
The normalized ${m_{\text {SD}}}$ distribution for background QCD jets with 600 $ < {p_{\mathrm {T}}} < $ 1000 GeV, inclusively and after selection by each algorithm. The working point chosen corresponds to $ {\epsilon _{\text {S}}}=$ 30 ($ {\epsilon _{\text {S}}}=$ 50)% for t quark (W/Z/H boson) identification. Upper left: t quark, upper right: W boson, lower left: Z boson, lower right: H boson. The error bars represent the statistical uncertainty in each specific bin, which is related to the limited number of simulated events. Additional fiducial selection criteria applied to the jets are listed on the plots.

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Figure 21:
Normalized ratio of the QCD background jet mass distribution for the passing and failing jets with 600 $ < {p_{\mathrm {T}}} < $ 1000 GeV, by each algorithm. The working point chosen corresponds to $ {\epsilon _{\text {S}}}=$ 30 ($ {\epsilon _{\text {S}}}=$ 50)% for t quark (W/Z/H boson) identification. Upper left: t quark, upper right: W boson, lower left: Z boson, lower right: H boson. The error bars represent the statistical uncertainty in each specific bin, which is related to the limited number of simulated events. Additional fiducial selection criteria applied to the jets are listed on the plots.

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Figure 21-a:
Normalized ratio of the QCD background jet mass distribution for the passing and failing jets with 600 $ < {p_{\mathrm {T}}} < $ 1000 GeV, by each algorithm. The working point chosen corresponds to $ {\epsilon _{\text {S}}}=$ 30 ($ {\epsilon _{\text {S}}}=$ 50)% for t quark (W/Z/H boson) identification. Upper left: t quark, upper right: W boson, lower left: Z boson, lower right: H boson. The error bars represent the statistical uncertainty in each specific bin, which is related to the limited number of simulated events. Additional fiducial selection criteria applied to the jets are listed on the plots.

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Figure 21-b:
Normalized ratio of the QCD background jet mass distribution for the passing and failing jets with 600 $ < {p_{\mathrm {T}}} < $ 1000 GeV, by each algorithm. The working point chosen corresponds to $ {\epsilon _{\text {S}}}=$ 30 ($ {\epsilon _{\text {S}}}=$ 50)% for t quark (W/Z/H boson) identification. Upper left: t quark, upper right: W boson, lower left: Z boson, lower right: H boson. The error bars represent the statistical uncertainty in each specific bin, which is related to the limited number of simulated events. Additional fiducial selection criteria applied to the jets are listed on the plots.

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Figure 21-c:
Normalized ratio of the QCD background jet mass distribution for the passing and failing jets with 600 $ < {p_{\mathrm {T}}} < $ 1000 GeV, by each algorithm. The working point chosen corresponds to $ {\epsilon _{\text {S}}}=$ 30 ($ {\epsilon _{\text {S}}}=$ 50)% for t quark (W/Z/H boson) identification. Upper left: t quark, upper right: W boson, lower left: Z boson, lower right: H boson. The error bars represent the statistical uncertainty in each specific bin, which is related to the limited number of simulated events. Additional fiducial selection criteria applied to the jets are listed on the plots.

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Figure 21-d:
Normalized ratio of the QCD background jet mass distribution for the passing and failing jets with 600 $ < {p_{\mathrm {T}}} < $ 1000 GeV, by each algorithm. The working point chosen corresponds to $ {\epsilon _{\text {S}}}=$ 30 ($ {\epsilon _{\text {S}}}=$ 50)% for t quark (W/Z/H boson) identification. Upper left: t quark, upper right: W boson, lower left: Z boson, lower right: H boson. The error bars represent the statistical uncertainty in each specific bin, which is related to the limited number of simulated events. Additional fiducial selection criteria applied to the jets are listed on the plots.

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Figure 22:
The JSD as a function of successively tighter selections (expressed in terms of ${\epsilon _{\text {B}}}$) for the various t (left) and W (right) tagging algorithms. Lower values of JSD indicate larger similarity of the $m {{}_{\text {SD}}}$ in QCD multijet events passing and failing the selection on the tagging algorithm. Additional fiducial selection criteria applied to the jets are listed in the plots.

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Figure 22-a:
The JSD as a function of successively tighter selections (expressed in terms of ${\epsilon _{\text {B}}}$) for the various t (left) and W (right) tagging algorithms. Lower values of JSD indicate larger similarity of the $m {{}_{\text {SD}}}$ in QCD multijet events passing and failing the selection on the tagging algorithm. Additional fiducial selection criteria applied to the jets are listed in the plots.

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Figure 22-b:
The JSD as a function of successively tighter selections (expressed in terms of ${\epsilon _{\text {B}}}$) for the various t (left) and W (right) tagging algorithms. Lower values of JSD indicate larger similarity of the $m {{}_{\text {SD}}}$ in QCD multijet events passing and failing the selection on the tagging algorithm. Additional fiducial selection criteria applied to the jets are listed in the plots.

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Figure 23:
The JSD, as a function of the jet ${p_{\mathrm {T}}}$ for the various t (left) and W (right) tagging algorithms. Lower values of JSD indicate larger similarity of the $m {{}_{\text {SD}}}$ in QCD multijet events passing and failing the selection on the tagging algorithm. Additional fiducial selection criteria applied to the jets are listed in the plots.

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Figure 23-a:
The JSD, as a function of the jet ${p_{\mathrm {T}}}$ for the various t (left) and W (right) tagging algorithms. Lower values of JSD indicate larger similarity of the $m {{}_{\text {SD}}}$ in QCD multijet events passing and failing the selection on the tagging algorithm. Additional fiducial selection criteria applied to the jets are listed in the plots.

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Figure 23-b:
The JSD, as a function of the jet ${p_{\mathrm {T}}}$ for the various t (left) and W (right) tagging algorithms. Lower values of JSD indicate larger similarity of the $m {{}_{\text {SD}}}$ in QCD multijet events passing and failing the selection on the tagging algorithm. Additional fiducial selection criteria applied to the jets are listed in the plots.

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Figure 24:
Distribution of the the jet ${p_{\mathrm {T}}}$ (upper left), jet mass, ${m_{\text {SD}}}$ (upper right), the $N$-subjettiness ratios $ {\tau _{32}}$ (middle left) and $ {\tau _{21}}$ (middle right), and the $N_2$ (lower left) and $N_2^{\text {DDT}}$ (lower right) in data and simulation in the single-$\mu $ signal sample. The pink line corresponds to the simulation distribution obtained using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The distributions are weighted according to the top quark ${p_{\mathrm {T}}}$ weighting procedure described in the text.

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Figure 24-a:
Distribution of the the jet ${p_{\mathrm {T}}}$ (upper left), jet mass, ${m_{\text {SD}}}$ (upper right), the $N$-subjettiness ratios $ {\tau _{32}}$ (middle left) and $ {\tau _{21}}$ (middle right), and the $N_2$ (lower left) and $N_2^{\text {DDT}}$ (lower right) in data and simulation in the single-$\mu $ signal sample. The pink line corresponds to the simulation distribution obtained using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The distributions are weighted according to the top quark ${p_{\mathrm {T}}}$ weighting procedure described in the text.

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Figure 24-b:
Distribution of the the jet ${p_{\mathrm {T}}}$ (upper left), jet mass, ${m_{\text {SD}}}$ (upper right), the $N$-subjettiness ratios $ {\tau _{32}}$ (middle left) and $ {\tau _{21}}$ (middle right), and the $N_2$ (lower left) and $N_2^{\text {DDT}}$ (lower right) in data and simulation in the single-$\mu $ signal sample. The pink line corresponds to the simulation distribution obtained using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The distributions are weighted according to the top quark ${p_{\mathrm {T}}}$ weighting procedure described in the text.

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Figure 24-c:
Distribution of the the jet ${p_{\mathrm {T}}}$ (upper left), jet mass, ${m_{\text {SD}}}$ (upper right), the $N$-subjettiness ratios $ {\tau _{32}}$ (middle left) and $ {\tau _{21}}$ (middle right), and the $N_2$ (lower left) and $N_2^{\text {DDT}}$ (lower right) in data and simulation in the single-$\mu $ signal sample. The pink line corresponds to the simulation distribution obtained using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The distributions are weighted according to the top quark ${p_{\mathrm {T}}}$ weighting procedure described in the text.

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Figure 24-d:
Distribution of the the jet ${p_{\mathrm {T}}}$ (upper left), jet mass, ${m_{\text {SD}}}$ (upper right), the $N$-subjettiness ratios $ {\tau _{32}}$ (middle left) and $ {\tau _{21}}$ (middle right), and the $N_2$ (lower left) and $N_2^{\text {DDT}}$ (lower right) in data and simulation in the single-$\mu $ signal sample. The pink line corresponds to the simulation distribution obtained using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The distributions are weighted according to the top quark ${p_{\mathrm {T}}}$ weighting procedure described in the text.

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Figure 24-e:
Distribution of the the jet ${p_{\mathrm {T}}}$ (upper left), jet mass, ${m_{\text {SD}}}$ (upper right), the $N$-subjettiness ratios $ {\tau _{32}}$ (middle left) and $ {\tau _{21}}$ (middle right), and the $N_2$ (lower left) and $N_2^{\text {DDT}}$ (lower right) in data and simulation in the single-$\mu $ signal sample. The pink line corresponds to the simulation distribution obtained using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The distributions are weighted according to the top quark ${p_{\mathrm {T}}}$ weighting procedure described in the text.

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Figure 24-f:
Distribution of the the jet ${p_{\mathrm {T}}}$ (upper left), jet mass, ${m_{\text {SD}}}$ (upper right), the $N$-subjettiness ratios $ {\tau _{32}}$ (middle left) and $ {\tau _{21}}$ (middle right), and the $N_2$ (lower left) and $N_2^{\text {DDT}}$ (lower right) in data and simulation in the single-$\mu $ signal sample. The pink line corresponds to the simulation distribution obtained using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The distributions are weighted according to the top quark ${p_{\mathrm {T}}}$ weighting procedure described in the text.

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Figure 25:
Distribution of the main observables of the HOTVR algorithm, HOTVR jet ${p_{\mathrm {T}}}$ (upper left), $m_{\text {HOTVR}}$ (upper right), $m_{\text {min,HOTVR}}$ (lower left), and $N_{\text {sub,HOTVR}}$ (lower right) in data and simulation in the single-$\mu $ signal sample. The pink line corresponds to the simulation distribution obtained using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The distributions are weighted according to the top quark ${p_{\mathrm {T}}}$ weighting procedure described in the text.

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Figure 25-a:
Distribution of the main observables of the HOTVR algorithm, HOTVR jet ${p_{\mathrm {T}}}$ (upper left), $m_{\text {HOTVR}}$ (upper right), $m_{\text {min,HOTVR}}$ (lower left), and $N_{\text {sub,HOTVR}}$ (lower right) in data and simulation in the single-$\mu $ signal sample. The pink line corresponds to the simulation distribution obtained using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The distributions are weighted according to the top quark ${p_{\mathrm {T}}}$ weighting procedure described in the text.

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Figure 25-b:
Distribution of the main observables of the HOTVR algorithm, HOTVR jet ${p_{\mathrm {T}}}$ (upper left), $m_{\text {HOTVR}}$ (upper right), $m_{\text {min,HOTVR}}$ (lower left), and $N_{\text {sub,HOTVR}}$ (lower right) in data and simulation in the single-$\mu $ signal sample. The pink line corresponds to the simulation distribution obtained using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The distributions are weighted according to the top quark ${p_{\mathrm {T}}}$ weighting procedure described in the text.

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Figure 25-c:
Distribution of the main observables of the HOTVR algorithm, HOTVR jet ${p_{\mathrm {T}}}$ (upper left), $m_{\text {HOTVR}}$ (upper right), $m_{\text {min,HOTVR}}$ (lower left), and $N_{\text {sub,HOTVR}}$ (lower right) in data and simulation in the single-$\mu $ signal sample. The pink line corresponds to the simulation distribution obtained using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The distributions are weighted according to the top quark ${p_{\mathrm {T}}}$ weighting procedure described in the text.

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Figure 25-d:
Distribution of the main observables of the HOTVR algorithm, HOTVR jet ${p_{\mathrm {T}}}$ (upper left), $m_{\text {HOTVR}}$ (upper right), $m_{\text {min,HOTVR}}$ (lower left), and $N_{\text {sub,HOTVR}}$ (lower right) in data and simulation in the single-$\mu $ signal sample. The pink line corresponds to the simulation distribution obtained using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The distributions are weighted according to the top quark ${p_{\mathrm {T}}}$ weighting procedure described in the text.

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Figure 26:
Distribution of the t quark (upper left) and W boson (upper right) identification probabilities for the BEST algorithm, and the ${N_{3}\text {-}\text {BDT} (\text {CA}15)}$ discriminant in data and simulation in the single-$\mu $ signal sample. The pink line corresponds to the simulation distribution obtained using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The distributions are weighted according to the top quark ${p_{\mathrm {T}}}$ weighting procedure described in the text.

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Figure 26-a:
Distribution of the t quark (upper left) and W boson (upper right) identification probabilities for the BEST algorithm, and the ${N_{3}\text {-}\text {BDT} (\text {CA}15)}$ discriminant in data and simulation in the single-$\mu $ signal sample. The pink line corresponds to the simulation distribution obtained using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The distributions are weighted according to the top quark ${p_{\mathrm {T}}}$ weighting procedure described in the text.

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Figure 26-b:
Distribution of the t quark (upper left) and W boson (upper right) identification probabilities for the BEST algorithm, and the ${N_{3}\text {-}\text {BDT} (\text {CA}15)}$ discriminant in data and simulation in the single-$\mu $ signal sample. The pink line corresponds to the simulation distribution obtained using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The distributions are weighted according to the top quark ${p_{\mathrm {T}}}$ weighting procedure described in the text.

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Figure 26-c:
Distribution of the t quark (upper left) and W boson (upper right) identification probabilities for the BEST algorithm, and the ${N_{3}\text {-}\text {BDT} (\text {CA}15)}$ discriminant in data and simulation in the single-$\mu $ signal sample. The pink line corresponds to the simulation distribution obtained using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The distributions are weighted according to the top quark ${p_{\mathrm {T}}}$ weighting procedure described in the text.

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Figure 27:
Distribution of the ImageTop (upper left) and ImageTop-MD (upper right) discriminant in data and simulation in the single-$\mu $ sample. The plots in the middle row show the t quark (left) and W boson (right) identification probabilities in data and simulation for the DeepAK8 algorithm. The corresponding plots for DeepAK8-MD are displayed in the lower row. The pink line corresponds to the simulation distribution obtained using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The distributions are weighted according to the top quark ${p_{\mathrm {T}}}$ weighting procedure described in the text.

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Figure 27-a:
Distribution of the ImageTop (upper left) and ImageTop-MD (upper right) discriminant in data and simulation in the single-$\mu $ sample. The plots in the middle row show the t quark (left) and W boson (right) identification probabilities in data and simulation for the DeepAK8 algorithm. The corresponding plots for DeepAK8-MD are displayed in the lower row. The pink line corresponds to the simulation distribution obtained using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The distributions are weighted according to the top quark ${p_{\mathrm {T}}}$ weighting procedure described in the text.

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Figure 27-b:
Distribution of the ImageTop (upper left) and ImageTop-MD (upper right) discriminant in data and simulation in the single-$\mu $ sample. The plots in the middle row show the t quark (left) and W boson (right) identification probabilities in data and simulation for the DeepAK8 algorithm. The corresponding plots for DeepAK8-MD are displayed in the lower row. The pink line corresponds to the simulation distribution obtained using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The distributions are weighted according to the top quark ${p_{\mathrm {T}}}$ weighting procedure described in the text.

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Figure 27-c:
Distribution of the ImageTop (upper left) and ImageTop-MD (upper right) discriminant in data and simulation in the single-$\mu $ sample. The plots in the middle row show the t quark (left) and W boson (right) identification probabilities in data and simulation for the DeepAK8 algorithm. The corresponding plots for DeepAK8-MD are displayed in the lower row. The pink line corresponds to the simulation distribution obtained using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The distributions are weighted according to the top quark ${p_{\mathrm {T}}}$ weighting procedure described in the text.

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Figure 27-d:
Distribution of the ImageTop (upper left) and ImageTop-MD (upper right) discriminant in data and simulation in the single-$\mu $ sample. The plots in the middle row show the t quark (left) and W boson (right) identification probabilities in data and simulation for the DeepAK8 algorithm. The corresponding plots for DeepAK8-MD are displayed in the lower row. The pink line corresponds to the simulation distribution obtained using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The distributions are weighted according to the top quark ${p_{\mathrm {T}}}$ weighting procedure described in the text.

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Figure 27-e:
Distribution of the ImageTop (upper left) and ImageTop-MD (upper right) discriminant in data and simulation in the single-$\mu $ sample. The plots in the middle row show the t quark (left) and W boson (right) identification probabilities in data and simulation for the DeepAK8 algorithm. The corresponding plots for DeepAK8-MD are displayed in the lower row. The pink line corresponds to the simulation distribution obtained using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The distributions are weighted according to the top quark ${p_{\mathrm {T}}}$ weighting procedure described in the text.

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Figure 27-f:
Distribution of the ImageTop (upper left) and ImageTop-MD (upper right) discriminant in data and simulation in the single-$\mu $ sample. The plots in the middle row show the t quark (left) and W boson (right) identification probabilities in data and simulation for the DeepAK8 algorithm. The corresponding plots for DeepAK8-MD are displayed in the lower row. The pink line corresponds to the simulation distribution obtained using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The distributions are weighted according to the top quark ${p_{\mathrm {T}}}$ weighting procedure described in the text.

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Figure 28:
Distribution of the jet ${p_{\mathrm {T}}}$ (upper left), the jet mass, ${m_{\text {SD}}}$ (upper right), the $N$-subjettiness ratios $ {\tau _{32}}$ (middle left) and $ {\tau _{21}}$ (middle right), and the $N_2$ (lower left) and $N_2^{\text {DDT}}$ (lower right) in data and simulation in the single-$\mu $ signal sample after applying a jet momentum cut $ {p_{\mathrm {T}}} > $ 500 GeV. The pink line corresponds to the simulation distribution obtained using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The distributions are weighted according to the top quark ${p_{\mathrm {T}}}$ weighting procedure described in the text.

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Figure 28-a:
Distribution of the jet ${p_{\mathrm {T}}}$ (upper left), the jet mass, ${m_{\text {SD}}}$ (upper right), the $N$-subjettiness ratios $ {\tau _{32}}$ (middle left) and $ {\tau _{21}}$ (middle right), and the $N_2$ (lower left) and $N_2^{\text {DDT}}$ (lower right) in data and simulation in the single-$\mu $ signal sample after applying a jet momentum cut $ {p_{\mathrm {T}}} > $ 500 GeV. The pink line corresponds to the simulation distribution obtained using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The distributions are weighted according to the top quark ${p_{\mathrm {T}}}$ weighting procedure described in the text.

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Figure 28-b:
Distribution of the jet ${p_{\mathrm {T}}}$ (upper left), the jet mass, ${m_{\text {SD}}}$ (upper right), the $N$-subjettiness ratios $ {\tau _{32}}$ (middle left) and $ {\tau _{21}}$ (middle right), and the $N_2$ (lower left) and $N_2^{\text {DDT}}$ (lower right) in data and simulation in the single-$\mu $ signal sample after applying a jet momentum cut $ {p_{\mathrm {T}}} > $ 500 GeV. The pink line corresponds to the simulation distribution obtained using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The distributions are weighted according to the top quark ${p_{\mathrm {T}}}$ weighting procedure described in the text.

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Figure 28-c:
Distribution of the jet ${p_{\mathrm {T}}}$ (upper left), the jet mass, ${m_{\text {SD}}}$ (upper right), the $N$-subjettiness ratios $ {\tau _{32}}$ (middle left) and $ {\tau _{21}}$ (middle right), and the $N_2$ (lower left) and $N_2^{\text {DDT}}$ (lower right) in data and simulation in the single-$\mu $ signal sample after applying a jet momentum cut $ {p_{\mathrm {T}}} > $ 500 GeV. The pink line corresponds to the simulation distribution obtained using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The distributions are weighted according to the top quark ${p_{\mathrm {T}}}$ weighting procedure described in the text.

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Figure 28-d:
Distribution of the jet ${p_{\mathrm {T}}}$ (upper left), the jet mass, ${m_{\text {SD}}}$ (upper right), the $N$-subjettiness ratios $ {\tau _{32}}$ (middle left) and $ {\tau _{21}}$ (middle right), and the $N_2$ (lower left) and $N_2^{\text {DDT}}$ (lower right) in data and simulation in the single-$\mu $ signal sample after applying a jet momentum cut $ {p_{\mathrm {T}}} > $ 500 GeV. The pink line corresponds to the simulation distribution obtained using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The distributions are weighted according to the top quark ${p_{\mathrm {T}}}$ weighting procedure described in the text.

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Figure 28-e:
Distribution of the jet ${p_{\mathrm {T}}}$ (upper left), the jet mass, ${m_{\text {SD}}}$ (upper right), the $N$-subjettiness ratios $ {\tau _{32}}$ (middle left) and $ {\tau _{21}}$ (middle right), and the $N_2$ (lower left) and $N_2^{\text {DDT}}$ (lower right) in data and simulation in the single-$\mu $ signal sample after applying a jet momentum cut $ {p_{\mathrm {T}}} > $ 500 GeV. The pink line corresponds to the simulation distribution obtained using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The distributions are weighted according to the top quark ${p_{\mathrm {T}}}$ weighting procedure described in the text.

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Figure 28-f:
Distribution of the jet ${p_{\mathrm {T}}}$ (upper left), the jet mass, ${m_{\text {SD}}}$ (upper right), the $N$-subjettiness ratios $ {\tau _{32}}$ (middle left) and $ {\tau _{21}}$ (middle right), and the $N_2$ (lower left) and $N_2^{\text {DDT}}$ (lower right) in data and simulation in the single-$\mu $ signal sample after applying a jet momentum cut $ {p_{\mathrm {T}}} > $ 500 GeV. The pink line corresponds to the simulation distribution obtained using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The distributions are weighted according to the top quark ${p_{\mathrm {T}}}$ weighting procedure described in the text.

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Figure 29:
Distribution of the main observables of the HOTVR algorithm, HOTVR jet ${p_{\mathrm {T}}}$ (upper left), $m_{\text {HOTVR}}$ (upper right), $m_{\text {min,HOTVR}}$ (lower left) and $N_{\text {sub,HOTVR}}$ (lower right) in data and simulation in the single-$\mu $ signal sample, after applying a jet momentum cut $ {p_{\mathrm {T}}} > $ 500 GeV. The pink line corresponds to the simulation distribution obtained using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The distributions are weighted according to the top quark ${p_{\mathrm {T}}}$ weighting procedure described in the text.

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Figure 29-a:
Distribution of the main observables of the HOTVR algorithm, HOTVR jet ${p_{\mathrm {T}}}$ (upper left), $m_{\text {HOTVR}}$ (upper right), $m_{\text {min,HOTVR}}$ (lower left) and $N_{\text {sub,HOTVR}}$ (lower right) in data and simulation in the single-$\mu $ signal sample, after applying a jet momentum cut $ {p_{\mathrm {T}}} > $ 500 GeV. The pink line corresponds to the simulation distribution obtained using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The distributions are weighted according to the top quark ${p_{\mathrm {T}}}$ weighting procedure described in the text.

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Figure 29-b:
Distribution of the main observables of the HOTVR algorithm, HOTVR jet ${p_{\mathrm {T}}}$ (upper left), $m_{\text {HOTVR}}$ (upper right), $m_{\text {min,HOTVR}}$ (lower left) and $N_{\text {sub,HOTVR}}$ (lower right) in data and simulation in the single-$\mu $ signal sample, after applying a jet momentum cut $ {p_{\mathrm {T}}} > $ 500 GeV. The pink line corresponds to the simulation distribution obtained using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The distributions are weighted according to the top quark ${p_{\mathrm {T}}}$ weighting procedure described in the text.

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Figure 29-c:
Distribution of the main observables of the HOTVR algorithm, HOTVR jet ${p_{\mathrm {T}}}$ (upper left), $m_{\text {HOTVR}}$ (upper right), $m_{\text {min,HOTVR}}$ (lower left) and $N_{\text {sub,HOTVR}}$ (lower right) in data and simulation in the single-$\mu $ signal sample, after applying a jet momentum cut $ {p_{\mathrm {T}}} > $ 500 GeV. The pink line corresponds to the simulation distribution obtained using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The distributions are weighted according to the top quark ${p_{\mathrm {T}}}$ weighting procedure described in the text.

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Figure 29-d:
Distribution of the main observables of the HOTVR algorithm, HOTVR jet ${p_{\mathrm {T}}}$ (upper left), $m_{\text {HOTVR}}$ (upper right), $m_{\text {min,HOTVR}}$ (lower left) and $N_{\text {sub,HOTVR}}$ (lower right) in data and simulation in the single-$\mu $ signal sample, after applying a jet momentum cut $ {p_{\mathrm {T}}} > $ 500 GeV. The pink line corresponds to the simulation distribution obtained using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The distributions are weighted according to the top quark ${p_{\mathrm {T}}}$ weighting procedure described in the text.

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Figure 30:
Distribution of the t quark (upper left) and W boson (upper right) identification probabilities for the BEST algorithm, and the ${N_{3}\text {-}\text {BDT} (\text {CA}15)}$ discriminant in data and simulation in the single-$\mu $ signal sample, after applying a jet momentum cut $ {p_{\mathrm {T}}} > $ 500 GeV. The pink line corresponds to the simulation distribution obtained using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The distributions are weighted according to the top quark ${p_{\mathrm {T}}}$ weighting procedure described in the text.

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Figure 30-a:
Distribution of the t quark (upper left) and W boson (upper right) identification probabilities for the BEST algorithm, and the ${N_{3}\text {-}\text {BDT} (\text {CA}15)}$ discriminant in data and simulation in the single-$\mu $ signal sample, after applying a jet momentum cut $ {p_{\mathrm {T}}} > $ 500 GeV. The pink line corresponds to the simulation distribution obtained using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The distributions are weighted according to the top quark ${p_{\mathrm {T}}}$ weighting procedure described in the text.

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Figure 30-b:
Distribution of the t quark (upper left) and W boson (upper right) identification probabilities for the BEST algorithm, and the ${N_{3}\text {-}\text {BDT} (\text {CA}15)}$ discriminant in data and simulation in the single-$\mu $ signal sample, after applying a jet momentum cut $ {p_{\mathrm {T}}} > $ 500 GeV. The pink line corresponds to the simulation distribution obtained using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The distributions are weighted according to the top quark ${p_{\mathrm {T}}}$ weighting procedure described in the text.

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Figure 30-c:
Distribution of the t quark (upper left) and W boson (upper right) identification probabilities for the BEST algorithm, and the ${N_{3}\text {-}\text {BDT} (\text {CA}15)}$ discriminant in data and simulation in the single-$\mu $ signal sample, after applying a jet momentum cut $ {p_{\mathrm {T}}} > $ 500 GeV. The pink line corresponds to the simulation distribution obtained using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The distributions are weighted according to the top quark ${p_{\mathrm {T}}}$ weighting procedure described in the text.

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Figure 31:
Distribution of the ImageTop (upper left) and ImageTop-MD (upper right) discriminant in data and simulation in the single-$\mu $ sample. The plots in the middle row show the t quark (left) and W boson (right) identification probabilities in data and simulation for the DeepAK8 algorithm after applying a jet momentum cut $ {p_{\mathrm {T}}} > $ 500 GeV. The corresponding plots for DeepAK8-MD are displayed in the lower row. The pink line corresponds to the simulation distribution obtained using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The distributions are weighted according to the top quark ${p_{\mathrm {T}}}$ weighting procedure described in the text.

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Figure 31-a:
Distribution of the ImageTop (upper left) and ImageTop-MD (upper right) discriminant in data and simulation in the single-$\mu $ sample. The plots in the middle row show the t quark (left) and W boson (right) identification probabilities in data and simulation for the DeepAK8 algorithm after applying a jet momentum cut $ {p_{\mathrm {T}}} > $ 500 GeV. The corresponding plots for DeepAK8-MD are displayed in the lower row. The pink line corresponds to the simulation distribution obtained using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The distributions are weighted according to the top quark ${p_{\mathrm {T}}}$ weighting procedure described in the text.

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Figure 31-b:
Distribution of the ImageTop (upper left) and ImageTop-MD (upper right) discriminant in data and simulation in the single-$\mu $ sample. The plots in the middle row show the t quark (left) and W boson (right) identification probabilities in data and simulation for the DeepAK8 algorithm after applying a jet momentum cut $ {p_{\mathrm {T}}} > $ 500 GeV. The corresponding plots for DeepAK8-MD are displayed in the lower row. The pink line corresponds to the simulation distribution obtained using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The distributions are weighted according to the top quark ${p_{\mathrm {T}}}$ weighting procedure described in the text.

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Figure 31-c:
Distribution of the ImageTop (upper left) and ImageTop-MD (upper right) discriminant in data and simulation in the single-$\mu $ sample. The plots in the middle row show the t quark (left) and W boson (right) identification probabilities in data and simulation for the DeepAK8 algorithm after applying a jet momentum cut $ {p_{\mathrm {T}}} > $ 500 GeV. The corresponding plots for DeepAK8-MD are displayed in the lower row. The pink line corresponds to the simulation distribution obtained using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The distributions are weighted according to the top quark ${p_{\mathrm {T}}}$ weighting procedure described in the text.

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Figure 31-d:
Distribution of the ImageTop (upper left) and ImageTop-MD (upper right) discriminant in data and simulation in the single-$\mu $ sample. The plots in the middle row show the t quark (left) and W boson (right) identification probabilities in data and simulation for the DeepAK8 algorithm after applying a jet momentum cut $ {p_{\mathrm {T}}} > $ 500 GeV. The corresponding plots for DeepAK8-MD are displayed in the lower row. The pink line corresponds to the simulation distribution obtained using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The distributions are weighted according to the top quark ${p_{\mathrm {T}}}$ weighting procedure described in the text.

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Figure 31-e:
Distribution of the ImageTop (upper left) and ImageTop-MD (upper right) discriminant in data and simulation in the single-$\mu $ sample. The plots in the middle row show the t quark (left) and W boson (right) identification probabilities in data and simulation for the DeepAK8 algorithm after applying a jet momentum cut $ {p_{\mathrm {T}}} > $ 500 GeV. The corresponding plots for DeepAK8-MD are displayed in the lower row. The pink line corresponds to the simulation distribution obtained using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The distributions are weighted according to the top quark ${p_{\mathrm {T}}}$ weighting procedure described in the text.

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Figure 31-f:
Distribution of the ImageTop (upper left) and ImageTop-MD (upper right) discriminant in data and simulation in the single-$\mu $ sample. The plots in the middle row show the t quark (left) and W boson (right) identification probabilities in data and simulation for the DeepAK8 algorithm after applying a jet momentum cut $ {p_{\mathrm {T}}} > $ 500 GeV. The corresponding plots for DeepAK8-MD are displayed in the lower row. The pink line corresponds to the simulation distribution obtained using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. The distributions are weighted according to the top quark ${p_{\mathrm {T}}}$ weighting procedure described in the text.

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Figure 32:
Distribution of the jet ${p_{\mathrm {T}}}$ (upper left), the jet mass, ${m_{\text {SD}}}$ (upper right), the $N$-subjettiness ratios $ {\tau _{32}}$ (middle left) and $ {\tau _{21}}$ (middle right), and the $N_2$ (lower left) and $N_{2}^{\text {DDT}}$ (lower right) in data and simulation in the dijet sample. The pink line corresponds to the simulation distribution obtained using the alternative QCD multijet sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative QCD multijet sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative QCD multijet sample. The distributions are weighted so that the jet ${p_{\mathrm {T}}}$ distribution of the simulation matches the data.

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Figure 32-a:
Distribution of the jet ${p_{\mathrm {T}}}$ (upper left), the jet mass, ${m_{\text {SD}}}$ (upper right), the $N$-subjettiness ratios $ {\tau _{32}}$ (middle left) and $ {\tau _{21}}$ (middle right), and the $N_2$ (lower left) and $N_{2}^{\text {DDT}}$ (lower right) in data and simulation in the dijet sample. The pink line corresponds to the simulation distribution obtained using the alternative QCD multijet sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative QCD multijet sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative QCD multijet sample. The distributions are weighted so that the jet ${p_{\mathrm {T}}}$ distribution of the simulation matches the data.

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Figure 32-b:
Distribution of the jet ${p_{\mathrm {T}}}$ (upper left), the jet mass, ${m_{\text {SD}}}$ (upper right), the $N$-subjettiness ratios $ {\tau _{32}}$ (middle left) and $ {\tau _{21}}$ (middle right), and the $N_2$ (lower left) and $N_{2}^{\text {DDT}}$ (lower right) in data and simulation in the dijet sample. The pink line corresponds to the simulation distribution obtained using the alternative QCD multijet sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative QCD multijet sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative QCD multijet sample. The distributions are weighted so that the jet ${p_{\mathrm {T}}}$ distribution of the simulation matches the data.

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Figure 32-c:
Distribution of the jet ${p_{\mathrm {T}}}$ (upper left), the jet mass, ${m_{\text {SD}}}$ (upper right), the $N$-subjettiness ratios $ {\tau _{32}}$ (middle left) and $ {\tau _{21}}$ (middle right), and the $N_2$ (lower left) and $N_{2}^{\text {DDT}}$ (lower right) in data and simulation in the dijet sample. The pink line corresponds to the simulation distribution obtained using the alternative QCD multijet sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative QCD multijet sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative QCD multijet sample. The distributions are weighted so that the jet ${p_{\mathrm {T}}}$ distribution of the simulation matches the data.

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Figure 32-d:
Distribution of the jet ${p_{\mathrm {T}}}$ (upper left), the jet mass, ${m_{\text {SD}}}$ (upper right), the $N$-subjettiness ratios $ {\tau _{32}}$ (middle left) and $ {\tau _{21}}$ (middle right), and the $N_2$ (lower left) and $N_{2}^{\text {DDT}}$ (lower right) in data and simulation in the dijet sample. The pink line corresponds to the simulation distribution obtained using the alternative QCD multijet sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative QCD multijet sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative QCD multijet sample. The distributions are weighted so that the jet ${p_{\mathrm {T}}}$ distribution of the simulation matches the data.

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Figure 32-e:
Distribution of the jet ${p_{\mathrm {T}}}$ (upper left), the jet mass, ${m_{\text {SD}}}$ (upper right), the $N$-subjettiness ratios $ {\tau _{32}}$ (middle left) and $ {\tau _{21}}$ (middle right), and the $N_2$ (lower left) and $N_{2}^{\text {DDT}}$ (lower right) in data and simulation in the dijet sample. The pink line corresponds to the simulation distribution obtained using the alternative QCD multijet sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative QCD multijet sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative QCD multijet sample. The distributions are weighted so that the jet ${p_{\mathrm {T}}}$ distribution of the simulation matches the data.

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Figure 32-f:
Distribution of the jet ${p_{\mathrm {T}}}$ (upper left), the jet mass, ${m_{\text {SD}}}$ (upper right), the $N$-subjettiness ratios $ {\tau _{32}}$ (middle left) and $ {\tau _{21}}$ (middle right), and the $N_2$ (lower left) and $N_{2}^{\text {DDT}}$ (lower right) in data and simulation in the dijet sample. The pink line corresponds to the simulation distribution obtained using the alternative QCD multijet sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative QCD multijet sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative QCD multijet sample. The distributions are weighted so that the jet ${p_{\mathrm {T}}}$ distribution of the simulation matches the data.

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Figure 33:
Distribution of the jet ${p_{\mathrm {T}}}$ (upper left), the jet mass, ${m_{\text {SD}}}$ (upper right), the $N$-subjettiness ratios $ {\tau _{32}}$ (middle left) and $ {\tau _{21}}$ (middle right), and the $N_2$ (lower left) and $N_{2}^{\text {DDT}}$ (lower right) in data and simulation in the single-$\gamma $ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), and the vertical lines correspond to the statistical uncertainty of the data. The distributions are weighted so that the jet ${p_{\mathrm {T}}}$ distribution of the simulation matches the data.

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Figure 33-a:
Distribution of the jet ${p_{\mathrm {T}}}$ (upper left), the jet mass, ${m_{\text {SD}}}$ (upper right), the $N$-subjettiness ratios $ {\tau _{32}}$ (middle left) and $ {\tau _{21}}$ (middle right), and the $N_2$ (lower left) and $N_{2}^{\text {DDT}}$ (lower right) in data and simulation in the single-$\gamma $ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), and the vertical lines correspond to the statistical uncertainty of the data. The distributions are weighted so that the jet ${p_{\mathrm {T}}}$ distribution of the simulation matches the data.

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Figure 33-b:
Distribution of the jet ${p_{\mathrm {T}}}$ (upper left), the jet mass, ${m_{\text {SD}}}$ (upper right), the $N$-subjettiness ratios $ {\tau _{32}}$ (middle left) and $ {\tau _{21}}$ (middle right), and the $N_2$ (lower left) and $N_{2}^{\text {DDT}}$ (lower right) in data and simulation in the single-$\gamma $ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), and the vertical lines correspond to the statistical uncertainty of the data. The distributions are weighted so that the jet ${p_{\mathrm {T}}}$ distribution of the simulation matches the data.

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Figure 33-c:
Distribution of the jet ${p_{\mathrm {T}}}$ (upper left), the jet mass, ${m_{\text {SD}}}$ (upper right), the $N$-subjettiness ratios $ {\tau _{32}}$ (middle left) and $ {\tau _{21}}$ (middle right), and the $N_2$ (lower left) and $N_{2}^{\text {DDT}}$ (lower right) in data and simulation in the single-$\gamma $ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), and the vertical lines correspond to the statistical uncertainty of the data. The distributions are weighted so that the jet ${p_{\mathrm {T}}}$ distribution of the simulation matches the data.

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Figure 33-d:
Distribution of the jet ${p_{\mathrm {T}}}$ (upper left), the jet mass, ${m_{\text {SD}}}$ (upper right), the $N$-subjettiness ratios $ {\tau _{32}}$ (middle left) and $ {\tau _{21}}$ (middle right), and the $N_2$ (lower left) and $N_{2}^{\text {DDT}}$ (lower right) in data and simulation in the single-$\gamma $ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), and the vertical lines correspond to the statistical uncertainty of the data. The distributions are weighted so that the jet ${p_{\mathrm {T}}}$ distribution of the simulation matches the data.

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Figure 33-e:
Distribution of the jet ${p_{\mathrm {T}}}$ (upper left), the jet mass, ${m_{\text {SD}}}$ (upper right), the $N$-subjettiness ratios $ {\tau _{32}}$ (middle left) and $ {\tau _{21}}$ (middle right), and the $N_2$ (lower left) and $N_{2}^{\text {DDT}}$ (lower right) in data and simulation in the single-$\gamma $ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), and the vertical lines correspond to the statistical uncertainty of the data. The distributions are weighted so that the jet ${p_{\mathrm {T}}}$ distribution of the simulation matches the data.

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Figure 33-f:
Distribution of the jet ${p_{\mathrm {T}}}$ (upper left), the jet mass, ${m_{\text {SD}}}$ (upper right), the $N$-subjettiness ratios $ {\tau _{32}}$ (middle left) and $ {\tau _{21}}$ (middle right), and the $N_2$ (lower left) and $N_{2}^{\text {DDT}}$ (lower right) in data and simulation in the single-$\gamma $ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), and the vertical lines correspond to the statistical uncertainty of the data. The distributions are weighted so that the jet ${p_{\mathrm {T}}}$ distribution of the simulation matches the data.

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Figure 34:
Distribution of the main observables of the HOTVR algorithm, HOTVR jet ${p_{\mathrm {T}}}$ (upper left), $m_{\text {HOTVR}}$ (upper right), $m_{\text {min,HOTVR}}$ (lower left) and $N_{\text {sub,HOTVR}}$ (lower right) in data and simulation in the dijet sample. The pink line corresponds to the simulation distribution obtained using the alternative QCD multijet sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative QCD multijet sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative QCD multijet sample. The distributions are weighted so that the jet ${p_{\mathrm {T}}}$ distribution of the simulation matches the data.

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Figure 34-a:
Distribution of the main observables of the HOTVR algorithm, HOTVR jet ${p_{\mathrm {T}}}$ (upper left), $m_{\text {HOTVR}}$ (upper right), $m_{\text {min,HOTVR}}$ (lower left) and $N_{\text {sub,HOTVR}}$ (lower right) in data and simulation in the dijet sample. The pink line corresponds to the simulation distribution obtained using the alternative QCD multijet sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative QCD multijet sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative QCD multijet sample. The distributions are weighted so that the jet ${p_{\mathrm {T}}}$ distribution of the simulation matches the data.

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Figure 34-b:
Distribution of the main observables of the HOTVR algorithm, HOTVR jet ${p_{\mathrm {T}}}$ (upper left), $m_{\text {HOTVR}}$ (upper right), $m_{\text {min,HOTVR}}$ (lower left) and $N_{\text {sub,HOTVR}}$ (lower right) in data and simulation in the dijet sample. The pink line corresponds to the simulation distribution obtained using the alternative QCD multijet sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative QCD multijet sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative QCD multijet sample. The distributions are weighted so that the jet ${p_{\mathrm {T}}}$ distribution of the simulation matches the data.

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Figure 34-c:
Distribution of the main observables of the HOTVR algorithm, HOTVR jet ${p_{\mathrm {T}}}$ (upper left), $m_{\text {HOTVR}}$ (upper right), $m_{\text {min,HOTVR}}$ (lower left) and $N_{\text {sub,HOTVR}}$ (lower right) in data and simulation in the dijet sample. The pink line corresponds to the simulation distribution obtained using the alternative QCD multijet sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative QCD multijet sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative QCD multijet sample. The distributions are weighted so that the jet ${p_{\mathrm {T}}}$ distribution of the simulation matches the data.

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Figure 34-d:
Distribution of the main observables of the HOTVR algorithm, HOTVR jet ${p_{\mathrm {T}}}$ (upper left), $m_{\text {HOTVR}}$ (upper right), $m_{\text {min,HOTVR}}$ (lower left) and $N_{\text {sub,HOTVR}}$ (lower right) in data and simulation in the dijet sample. The pink line corresponds to the simulation distribution obtained using the alternative QCD multijet sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative QCD multijet sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative QCD multijet sample. The distributions are weighted so that the jet ${p_{\mathrm {T}}}$ distribution of the simulation matches the data.

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Figure 35:
Distribution of the main observables of the HOTVR algorithm, HOTVR jet ${p_{\mathrm {T}}}$ (upper left), $m_{\text {HOTVR}}$ (upper right), $m_{\text {min,HOTVR}}$ (lower left) and $N_{\text {sub,HOTVR}}$ (lower right) in data and simulation in the single-$\gamma $ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), and the vertical lines correspond to the statistical uncertainty of the data. The distributions are weighted so that the jet ${p_{\mathrm {T}}}$ distribution of the simulation matches the data.

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Figure 35-a:
Distribution of the main observables of the HOTVR algorithm, HOTVR jet ${p_{\mathrm {T}}}$ (upper left), $m_{\text {HOTVR}}$ (upper right), $m_{\text {min,HOTVR}}$ (lower left) and $N_{\text {sub,HOTVR}}$ (lower right) in data and simulation in the single-$\gamma $ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), and the vertical lines correspond to the statistical uncertainty of the data. The distributions are weighted so that the jet ${p_{\mathrm {T}}}$ distribution of the simulation matches the data.

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Figure 35-b:
Distribution of the main observables of the HOTVR algorithm, HOTVR jet ${p_{\mathrm {T}}}$ (upper left), $m_{\text {HOTVR}}$ (upper right), $m_{\text {min,HOTVR}}$ (lower left) and $N_{\text {sub,HOTVR}}$ (lower right) in data and simulation in the single-$\gamma $ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), and the vertical lines correspond to the statistical uncertainty of the data. The distributions are weighted so that the jet ${p_{\mathrm {T}}}$ distribution of the simulation matches the data.

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Figure 35-c:
Distribution of the main observables of the HOTVR algorithm, HOTVR jet ${p_{\mathrm {T}}}$ (upper left), $m_{\text {HOTVR}}$ (upper right), $m_{\text {min,HOTVR}}$ (lower left) and $N_{\text {sub,HOTVR}}$ (lower right) in data and simulation in the single-$\gamma $ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), and the vertical lines correspond to the statistical uncertainty of the data. The distributions are weighted so that the jet ${p_{\mathrm {T}}}$ distribution of the simulation matches the data.

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Figure 35-d:
Distribution of the main observables of the HOTVR algorithm, HOTVR jet ${p_{\mathrm {T}}}$ (upper left), $m_{\text {HOTVR}}$ (upper right), $m_{\text {min,HOTVR}}$ (lower left) and $N_{\text {sub,HOTVR}}$ (lower right) in data and simulation in the single-$\gamma $ sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), and the vertical lines correspond to the statistical uncertainty of the data. The distributions are weighted so that the jet ${p_{\mathrm {T}}}$ distribution of the simulation matches the data.

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Figure 36:
Distribution of the t quark (upper left) and W boson (upper right) identification probabilities for the BEST algorithm, and the ${N_{3}\text {-}\text {BDT} (\text {CA}15)}$ discriminant in data and simulation in the dijet sample. The background event yield is normalized to the total observed data yield. The pink line corresponds to the simulation distribution obtained using the alternative QCD multijet sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative QCD multijet sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative QCD multijet sample. The distributions are weighted so that the jet ${p_{\mathrm {T}}}$ distribution of the simulation matches the data.

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Figure 36-a:
Distribution of the t quark (upper left) and W boson (upper right) identification probabilities for the BEST algorithm, and the ${N_{3}\text {-}\text {BDT} (\text {CA}15)}$ discriminant in data and simulation in the dijet sample. The background event yield is normalized to the total observed data yield. The pink line corresponds to the simulation distribution obtained using the alternative QCD multijet sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative QCD multijet sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative QCD multijet sample. The distributions are weighted so that the jet ${p_{\mathrm {T}}}$ distribution of the simulation matches the data.

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Figure 36-b:
Distribution of the t quark (upper left) and W boson (upper right) identification probabilities for the BEST algorithm, and the ${N_{3}\text {-}\text {BDT} (\text {CA}15)}$ discriminant in data and simulation in the dijet sample. The background event yield is normalized to the total observed data yield. The pink line corresponds to the simulation distribution obtained using the alternative QCD multijet sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative QCD multijet sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative QCD multijet sample. The distributions are weighted so that the jet ${p_{\mathrm {T}}}$ distribution of the simulation matches the data.

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Figure 36-c:
Distribution of the t quark (upper left) and W boson (upper right) identification probabilities for the BEST algorithm, and the ${N_{3}\text {-}\text {BDT} (\text {CA}15)}$ discriminant in data and simulation in the dijet sample. The background event yield is normalized to the total observed data yield. The pink line corresponds to the simulation distribution obtained using the alternative QCD multijet sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative QCD multijet sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative QCD multijet sample. The distributions are weighted so that the jet ${p_{\mathrm {T}}}$ distribution of the simulation matches the data.

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Figure 37:
Distribution of the t quark (upper left) and W boson (upper right) identification probabilities for the BEST algorithm, and the ${N_{3}\text {-}\text {BDT} (\text {CA}15)}$ discriminant in data and simulation in the single-$\gamma $ sample. The background event yield is normalized to the total observed data yield. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), and the vertical lines correspond to the statistical uncertainty of the data. The distributions are weighted so that the jet ${p_{\mathrm {T}}}$ distribution of the simulation matches the data.

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Figure 37-a:
Distribution of the t quark (upper left) and W boson (upper right) identification probabilities for the BEST algorithm, and the ${N_{3}\text {-}\text {BDT} (\text {CA}15)}$ discriminant in data and simulation in the single-$\gamma $ sample. The background event yield is normalized to the total observed data yield. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), and the vertical lines correspond to the statistical uncertainty of the data. The distributions are weighted so that the jet ${p_{\mathrm {T}}}$ distribution of the simulation matches the data.

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Figure 37-b:
Distribution of the t quark (upper left) and W boson (upper right) identification probabilities for the BEST algorithm, and the ${N_{3}\text {-}\text {BDT} (\text {CA}15)}$ discriminant in data and simulation in the single-$\gamma $ sample. The background event yield is normalized to the total observed data yield. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), and the vertical lines correspond to the statistical uncertainty of the data. The distributions are weighted so that the jet ${p_{\mathrm {T}}}$ distribution of the simulation matches the data.

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Figure 37-c:
Distribution of the t quark (upper left) and W boson (upper right) identification probabilities for the BEST algorithm, and the ${N_{3}\text {-}\text {BDT} (\text {CA}15)}$ discriminant in data and simulation in the single-$\gamma $ sample. The background event yield is normalized to the total observed data yield. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), and the vertical lines correspond to the statistical uncertainty of the data. The distributions are weighted so that the jet ${p_{\mathrm {T}}}$ distribution of the simulation matches the data.

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Figure 38:
Distribution of the ImageTop (upper left) and ImageTop-MD (upper right) discriminant in data and simulation in the dijet sample. The plots in the middle row show the t quark (left) and W boson (right) identification probabilities in data and simulation for the DeepAK8 algorithm. The corresponding plots for DeepAK8-MD are displayed in the lower row. The pink line corresponds to the simulation distribution obtained using the alternative QCD multijet sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative QCD multijet sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative QCD multijet sample. The distributions are weighted so that the jet ${p_{\mathrm {T}}}$ distribution of the simulation matches the data.

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Figure 38-a:
Distribution of the ImageTop (upper left) and ImageTop-MD (upper right) discriminant in data and simulation in the dijet sample. The plots in the middle row show the t quark (left) and W boson (right) identification probabilities in data and simulation for the DeepAK8 algorithm. The corresponding plots for DeepAK8-MD are displayed in the lower row. The pink line corresponds to the simulation distribution obtained using the alternative QCD multijet sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative QCD multijet sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative QCD multijet sample. The distributions are weighted so that the jet ${p_{\mathrm {T}}}$ distribution of the simulation matches the data.

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Figure 38-b:
Distribution of the ImageTop (upper left) and ImageTop-MD (upper right) discriminant in data and simulation in the dijet sample. The plots in the middle row show the t quark (left) and W boson (right) identification probabilities in data and simulation for the DeepAK8 algorithm. The corresponding plots for DeepAK8-MD are displayed in the lower row. The pink line corresponds to the simulation distribution obtained using the alternative QCD multijet sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative QCD multijet sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative QCD multijet sample. The distributions are weighted so that the jet ${p_{\mathrm {T}}}$ distribution of the simulation matches the data.

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Figure 38-c:
Distribution of the ImageTop (upper left) and ImageTop-MD (upper right) discriminant in data and simulation in the dijet sample. The plots in the middle row show the t quark (left) and W boson (right) identification probabilities in data and simulation for the DeepAK8 algorithm. The corresponding plots for DeepAK8-MD are displayed in the lower row. The pink line corresponds to the simulation distribution obtained using the alternative QCD multijet sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative QCD multijet sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative QCD multijet sample. The distributions are weighted so that the jet ${p_{\mathrm {T}}}$ distribution of the simulation matches the data.

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Figure 38-d:
Distribution of the ImageTop (upper left) and ImageTop-MD (upper right) discriminant in data and simulation in the dijet sample. The plots in the middle row show the t quark (left) and W boson (right) identification probabilities in data and simulation for the DeepAK8 algorithm. The corresponding plots for DeepAK8-MD are displayed in the lower row. The pink line corresponds to the simulation distribution obtained using the alternative QCD multijet sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative QCD multijet sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative QCD multijet sample. The distributions are weighted so that the jet ${p_{\mathrm {T}}}$ distribution of the simulation matches the data.

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Figure 38-e:
Distribution of the ImageTop (upper left) and ImageTop-MD (upper right) discriminant in data and simulation in the dijet sample. The plots in the middle row show the t quark (left) and W boson (right) identification probabilities in data and simulation for the DeepAK8 algorithm. The corresponding plots for DeepAK8-MD are displayed in the lower row. The pink line corresponds to the simulation distribution obtained using the alternative QCD multijet sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative QCD multijet sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative QCD multijet sample. The distributions are weighted so that the jet ${p_{\mathrm {T}}}$ distribution of the simulation matches the data.

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Figure 38-f:
Distribution of the ImageTop (upper left) and ImageTop-MD (upper right) discriminant in data and simulation in the dijet sample. The plots in the middle row show the t quark (left) and W boson (right) identification probabilities in data and simulation for the DeepAK8 algorithm. The corresponding plots for DeepAK8-MD are displayed in the lower row. The pink line corresponds to the simulation distribution obtained using the alternative QCD multijet sample. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), the pink line to the data to simulation ratio using the alternative QCD multijet sample, and the vertical black lines correspond to the statistical uncertainty of the data. The vertical pink lines correspond to the statistical uncertainty of the alternative QCD multijet sample. The distributions are weighted so that the jet ${p_{\mathrm {T}}}$ distribution of the simulation matches the data.

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Figure 39:
Distribution of the ImageTop (upper left) and ImageTop-MD (upper right) discriminant in data and simulation in the single-$\gamma $ sample. The plots in the middle row show the t quark (left) and W boson (right) identification probabilities in data and simulation for the DeepAK8 algorithm. The corresponding plots for DeepAK8-MD are displayed in the lower row. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), and the vertical lines correspond to the statistical uncertainty of the data. The distributions are weighted so that the jet ${p_{\mathrm {T}}}$ distribution of the simulation matches the data.

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Figure 39-a:
Distribution of the ImageTop (upper left) and ImageTop-MD (upper right) discriminant in data and simulation in the single-$\gamma $ sample. The plots in the middle row show the t quark (left) and W boson (right) identification probabilities in data and simulation for the DeepAK8 algorithm. The corresponding plots for DeepAK8-MD are displayed in the lower row. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), and the vertical lines correspond to the statistical uncertainty of the data. The distributions are weighted so that the jet ${p_{\mathrm {T}}}$ distribution of the simulation matches the data.

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Figure 39-b:
Distribution of the ImageTop (upper left) and ImageTop-MD (upper right) discriminant in data and simulation in the single-$\gamma $ sample. The plots in the middle row show the t quark (left) and W boson (right) identification probabilities in data and simulation for the DeepAK8 algorithm. The corresponding plots for DeepAK8-MD are displayed in the lower row. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), and the vertical lines correspond to the statistical uncertainty of the data. The distributions are weighted so that the jet ${p_{\mathrm {T}}}$ distribution of the simulation matches the data.

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Figure 39-c:
Distribution of the ImageTop (upper left) and ImageTop-MD (upper right) discriminant in data and simulation in the single-$\gamma $ sample. The plots in the middle row show the t quark (left) and W boson (right) identification probabilities in data and simulation for the DeepAK8 algorithm. The corresponding plots for DeepAK8-MD are displayed in the lower row. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), and the vertical lines correspond to the statistical uncertainty of the data. The distributions are weighted so that the jet ${p_{\mathrm {T}}}$ distribution of the simulation matches the data.

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Figure 39-d:
Distribution of the ImageTop (upper left) and ImageTop-MD (upper right) discriminant in data and simulation in the single-$\gamma $ sample. The plots in the middle row show the t quark (left) and W boson (right) identification probabilities in data and simulation for the DeepAK8 algorithm. The corresponding plots for DeepAK8-MD are displayed in the lower row. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), and the vertical lines correspond to the statistical uncertainty of the data. The distributions are weighted so that the jet ${p_{\mathrm {T}}}$ distribution of the simulation matches the data.

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Figure 39-e:
Distribution of the ImageTop (upper left) and ImageTop-MD (upper right) discriminant in data and simulation in the single-$\gamma $ sample. The plots in the middle row show the t quark (left) and W boson (right) identification probabilities in data and simulation for the DeepAK8 algorithm. The corresponding plots for DeepAK8-MD are displayed in the lower row. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), and the vertical lines correspond to the statistical uncertainty of the data. The distributions are weighted so that the jet ${p_{\mathrm {T}}}$ distribution of the simulation matches the data.

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Figure 39-f:
Distribution of the ImageTop (upper left) and ImageTop-MD (upper right) discriminant in data and simulation in the single-$\gamma $ sample. The plots in the middle row show the t quark (left) and W boson (right) identification probabilities in data and simulation for the DeepAK8 algorithm. The corresponding plots for DeepAK8-MD are displayed in the lower row. The background event yield is normalized to the total observed data yield. The lower panel shows the data to simulation ratio. The solid dark-gray (shaded light-gray) band corresponds to the total uncertainty (statistical uncertainty of the simulated samples), and the vertical lines correspond to the statistical uncertainty of the data. The distributions are weighted so that the jet ${p_{\mathrm {T}}}$ distribution of the simulation matches the data.

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Figure 40:
The ${m_{\text {SD}}}$ distribution in data and simulation in the passing (left) and failing (right) categories for DeepAK8-MD for the jet ${p_{\mathrm {T}}}$ in the 400-800 GeV range. The solid lines correspond to the contribution of each category after performing the maximum likelihood fit as described in the text. The dashed lines are the expectation from simulation before the fit. The lower panel shows the data to simulation ratio. The vertical black lines correspond to the total uncertainty, including the statistical uncertainty of the data, after the fit.

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Figure 40-a:
The ${m_{\text {SD}}}$ distribution in data and simulation in the passing (left) and failing (right) categories for DeepAK8-MD for the jet ${p_{\mathrm {T}}}$ in the 400-800 GeV range. The solid lines correspond to the contribution of each category after performing the maximum likelihood fit as described in the text. The dashed lines are the expectation from simulation before the fit. The lower panel shows the data to simulation ratio. The vertical black lines correspond to the total uncertainty, including the statistical uncertainty of the data, after the fit.

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Figure 40-b:
The ${m_{\text {SD}}}$ distribution in data and simulation in the passing (left) and failing (right) categories for DeepAK8-MD for the jet ${p_{\mathrm {T}}}$ in the 400-800 GeV range. The solid lines correspond to the contribution of each category after performing the maximum likelihood fit as described in the text. The dashed lines are the expectation from simulation before the fit. The lower panel shows the data to simulation ratio. The vertical black lines correspond to the total uncertainty, including the statistical uncertainty of the data, after the fit.

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Figure 41:
Summary of the scale factors (SF) measured for each of the t quark (upper) and W boson (lower) identification algorithms. The markers correspond to the SF value, the error bars to the statistical uncertainty on the SF measurement, and the band is the total uncertainty, including the systematic component.

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Figure 41-a:
Summary of the scale factors (SF) measured for each of the t quark (upper) and W boson (lower) identification algorithms. The markers correspond to the SF value, the error bars to the statistical uncertainty on the SF measurement, and the band is the total uncertainty, including the systematic component.

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Figure 41-b:
Summary of the scale factors (SF) measured for each of the t quark (upper) and W boson (lower) identification algorithms. The markers correspond to the SF value, the error bars to the statistical uncertainty on the SF measurement, and the band is the total uncertainty, including the systematic component.

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Figure 42:
The ratio of the misidentification rate of t quarks in data and simulation in the dijet (upper and middle rows) and the single-$\gamma $ (lower row) samples. The QCD multijet process is simulated using MadGraph for the hard process and {pythia} for parton showering (upper) and {herwig++} for both (middle). The vertical lines correspond to the statistical uncertainty of the data and the simulated samples.

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Figure 42-a:
The ratio of the misidentification rate of t quarks in data and simulation in the dijet (upper and middle rows) and the single-$\gamma $ (lower row) samples. The QCD multijet process is simulated using MadGraph for the hard process and {pythia} for parton showering (upper) and {herwig++} for both (middle). The vertical lines correspond to the statistical uncertainty of the data and the simulated samples.

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Figure 42-b:
The ratio of the misidentification rate of t quarks in data and simulation in the dijet (upper and middle rows) and the single-$\gamma $ (lower row) samples. The QCD multijet process is simulated using MadGraph for the hard process and {pythia} for parton showering (upper) and {herwig++} for both (middle). The vertical lines correspond to the statistical uncertainty of the data and the simulated samples.

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Figure 42-c:
The ratio of the misidentification rate of t quarks in data and simulation in the dijet (upper and middle rows) and the single-$\gamma $ (lower row) samples. The QCD multijet process is simulated using MadGraph for the hard process and {pythia} for parton showering (upper) and {herwig++} for both (middle). The vertical lines correspond to the statistical uncertainty of the data and the simulated samples.

png pdf
Figure 43:
The ratio of the misidentification rate of W bosons in data and simulation in the dijet (upper and middle rows) and the single-$\gamma $ (lower row) samples. The QCD multijet process is simulated using MadGraph for the hard process and {pythia} for parton showering (upper) and {herwig++} for both (middle). The vertical lines correspond to the statistical uncertainty of the data and the simulated samples.

png pdf
Figure 43-a:
The ratio of the misidentification rate of W bosons in data and simulation in the dijet (upper and middle rows) and the single-$\gamma $ (lower row) samples. The QCD multijet process is simulated using MadGraph for the hard process and {pythia} for parton showering (upper) and {herwig++} for both (middle). The vertical lines correspond to the statistical uncertainty of the data and the simulated samples.

png pdf
Figure 43-b:
The ratio of the misidentification rate of W bosons in data and simulation in the dijet (upper and middle rows) and the single-$\gamma $ (lower row) samples. The QCD multijet process is simulated using MadGraph for the hard process and {pythia} for parton showering (upper) and {herwig++} for both (middle). The vertical lines correspond to the statistical uncertainty of the data and the simulated samples.

png pdf
Figure 43-c:
The ratio of the misidentification rate of W bosons in data and simulation in the dijet (upper and middle rows) and the single-$\gamma $ (lower row) samples. The QCD multijet process is simulated using MadGraph for the hard process and {pythia} for parton showering (upper) and {herwig++} for both (middle). The vertical lines correspond to the statistical uncertainty of the data and the simulated samples.
Tables

png pdf
Table 1:
Summary of the CMS algorithms for the identification of hadronically decaying t quarks and W, Z and H bosons. See text for explanation of the algorithm names. The column "Subsection'' indicates the subsection where the algorithm is described, and the column "jet ${p_{\mathrm {T}}}$ [GeV]'' indicates the jet ${p_{\mathrm {T}}}$ threshold to be used in each algorithm. The $^{*}$ in DeepAK8 and DeepAK8-MD algorithms indicates the ability of these algorithm to also identify the decay modes of each particle.

png pdf
Table 2:
Summary of the HOTVR parameters used in CMS. The $ {p_{\mathrm {T}}} {}_{\text {sub}}$ is the minimum ${p_{\mathrm {T}}}$ threshold of each subjet.

png pdf
Table 3:
List of input quantities used for the training and evaluation of the BEST algorithm on AK8 jets.
Summary
A review of the heavy-object tagging methods recently developed in CMS has been presented. The variety of tagging strategies is diverse, including algorithms based on more traditional theory-inspired high-level per-jet observables with and without multivariate techniques, as well as methods based on lower-level information from individual particles. New tagging approaches, such as the Energy Correlation Functions (ECF) tagger and the Boosted Event Shape Tagger (BEST), utilize multivariate methods (i.e., boosted decision trees and deep neural networks) on physically motivated high-level observables and attain enhanced performance. Two novel tagging algorithms, ImageTop and DeepAK8, are developed based on candidate-level information, allowing the exploitation of more information, where lower-level information is processed using advanced machine-learning methods. Moreover, the BEST and DeepAK8 algorithms are developed to provide multi-class tagging capabilities. Finally, dedicated versions of the algorithms that are only weakly correlated with the jet mass are developed. Such tools are particularly important for analyses that rely on the jet mass sidebands to estimate the background contribution under the heavy resonance mass. The mass-decorrelated algorithms (${m_\text{SD}+N_{2}^{\text{DDT}}}$, ImageTop-MD, and DeepAK8-MD) typically show weaker discriminating power than their counterparts. However, they can yield better sensitivity in some physics analyses because of smaller uncertainties in background estimations.

The performances of the various tagging algorithms are directly compared using simulation in a jet ${p_{\mathrm{T}}}$ range from 200 to 2000 GeV. Overall, the application of machine-learning techniques for jet tagging shows strong improvement compared to cutoff-based methods. The approaches based on low-level information yield the best performance, with as much as an order of magnitude gain in background rejection for the same signal efficiency. Another important aspect essential for the application of the new techniques in physics analysis is the systematic uncertainties associated to each algorithm. Those based on low-level features and advanced machine-learning techniques are typically prone to larger systematic uncertainties. However, these uncertainties are usually small enough to preserve the significant improvements observed. The techniques have also been validated in collision data, with scale factors extracted, including systematic uncertainties. The performances of these tagging algorithms are in good agreement between data and simulation.
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Compact Muon Solenoid
LHC, CERN