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CMS-B2G-18-005 ; CERN-EP-2019-129
Search for pair production of vector-like quarks in the fully hadronic final state
Phys. Rev. D 100 (2019) 072001
Abstract: The results of two searches for pair production of vector-like T or B quarks in fully hadronic final states are presented, using data from the CMS experiment at a center-of-mass energy of 13 TeV. The data were collected at the LHC during 2016 and correspond to an integrated luminosity of 35.9 fb$^{-1}$. A cut-based analysis specifically targets the qW decay mode of the T quark and allows for the reconstruction of the T quark candidates. In a second analysis, a multiclassification algorithm, the "boosted event shape tagger,'' is deployed to label candidate jets as originating from top quarks, and W, Z, and H. Candidate events are categorized according to the multiplicities of identified jets, and the scalar sum of all observed jet momenta is used to discriminate signal events from the quantum chromodynamics multijet background. Both analyses probe all possible branching fraction combinations of the T and B quarks and set limits at 95% confidence level on their masses, ranging from 740 to 1370 GeV. These results represent a significant improvement relative to existing searches in the fully hadronic final state.
Figures & Tables Summary Additional Figures References CMS Publications
Figures

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Figure 1:
classification fractions for the six categories of the BEST algorithm, measured in data events as a function of jet ${p_{\mathrm {T}}}$. Error bars shown indicate statistical uncertainties in the fractions to be propagated to the estimate of the QCD multijet background contribution. The rightmost bin includes jets with ${p_{\mathrm {T}}}$ values above 3 TeV.

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Figure 2:
The distributions of ${{H_{\mathrm {T}}} ^{\mathrm {AK4}}}$ for each of the four signal region categories in the cut-based analysis. The upper row shows channels with 2W tags, and 2 or 1b tags, respectively. The lower row is for 1W tag. The shaded error band represents the statistical uncertainty in the background. These distributions reflect the nuisance parameters evaluated after a likelihood fit to a background plus signal hypothesis, where the hypothesized signal is a T quark with a mass of 1200 GeV and 100% branching fraction to bW. The signal distributions show the expected yield of events assuming the cross section values in Table 1. The vertical axis labels denote that bin contents in these distributions have been scaled by their corresponding bin widths. The lower panel of each plot shows the ratio of the observed number of events in a bin to the expected number.

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Figure 2-a:
The distribution of ${{H_{\mathrm {T}}} ^{\mathrm {AK4}}}$ for the 2W2b signal region category in the cut-based analysis. The shaded error band represents the statistical uncertainty in the background. These distributions reflect the nuisance parameters evaluated after a likelihood fit to a background plus signal hypothesis, where the hypothesized signal is a T quark with a mass of 1200 GeV and 100% branching fraction to bW. The signal distributions show the expected yield of events assuming the cross section values in Table 1. The vertical axis labels denote that bin contents in these distributions have been scaled by their corresponding bin widths. The lower panel shows the ratio of the observed number of events in a bin to the expected number.

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Figure 2-b:
The distribution of ${{H_{\mathrm {T}}} ^{\mathrm {AK4}}}$ for the 2W1b signal region category in the cut-based analysis. The shaded error band represents the statistical uncertainty in the background. These distributions reflect the nuisance parameters evaluated after a likelihood fit to a background plus signal hypothesis, where the hypothesized signal is a T quark with a mass of 1200 GeV and 100% branching fraction to bW. The signal distributions show the expected yield of events assuming the cross section values in Table 1. The vertical axis labels denote that bin contents in these distributions have been scaled by their corresponding bin widths. The lower panel shows the ratio of the observed number of events in a bin to the expected number.

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Figure 2-c:
The distribution of ${{H_{\mathrm {T}}} ^{\mathrm {AK4}}}$ for the 1W2b signal region category in the cut-based analysis. The shaded error band represents the statistical uncertainty in the background. These distributions reflect the nuisance parameters evaluated after a likelihood fit to a background plus signal hypothesis, where the hypothesized signal is a T quark with a mass of 1200 GeV and 100% branching fraction to bW. The signal distributions show the expected yield of events assuming the cross section values in Table 1. The vertical axis labels denote that bin contents in these distributions have been scaled by their corresponding bin widths. The lower panel shows the ratio of the observed number of events in a bin to the expected number.

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Figure 2-d:
The distribution of ${{H_{\mathrm {T}}} ^{\mathrm {AK4}}}$ for the 1W1b signal region category in the cut-based analysis. The shaded error band represents the statistical uncertainty in the background. These distributions reflect the nuisance parameters evaluated after a likelihood fit to a background plus signal hypothesis, where the hypothesized signal is a T quark with a mass of 1200 GeV and 100% branching fraction to bW. The signal distributions show the expected yield of events assuming the cross section values in Table 1. The vertical axis labels denote that bin contents in these distributions have been scaled by their corresponding bin widths. The lower panel shows the ratio of the observed number of events in a bin to the expected number.

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Figure 3:
A summary of the 126 signal region categories used in the NN analysis. This figure shows the expected yields in each category, while the signal discrimination is performed with the ${{H_{\mathrm {T}}} ^{\mathrm {AK8}}}$ distributions from each of the categories. The bottom panel shows the ratio of observed data to total background in each category, with Poisson error bars where applicable, along with the total background uncertainty shown for each category by the gray band.

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Figure 4:
Distributions of ${{H_{\mathrm {T}}} ^{\mathrm {AK8}}}$ for all events entering the 126 signal regions of the NN analysis (upper left), as well as for only categories containing at least one candidate of each of the particle types identified by the BEST algorithm: $\geq $1W jet (upper right), $\geq $1Z jet (middle left), $\geq $1H jet (middle right), $\geq $1t jet (lower left), and $\geq $1b jet (lower right). The plots shown here are not mutually exclusive, as a particular signal region may satisfy several of the criteria for the individual summary categories. The vertical axis labels denote that bin contents in these distributions have been scaled by their corresponding bin widths. The lower panel of each plot shows the ratio of the observed number of events in a bin to the expected number.

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Figure 4-a:
Distribution of ${{H_{\mathrm {T}}} ^{\mathrm {AK8}}}$ for all events entering the 126 signal regions of the NN analysis. The vertical axis labels denote that bin contents in these distributions have been scaled by their corresponding bin widths. The lower panel shows the ratio of the observed number of events in a bin to the expected number.

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Figure 4-b:
Distribution of ${{H_{\mathrm {T}}} ^{\mathrm {AK8}}}$ for the $\geq $1W jet category, which contains at least one candidate of each of the particle types identified by the BEST algorithm. The vertical axis labels denote that bin contents in these distributions have been scaled by their corresponding bin widths. The lower panel shows the ratio of the observed number of events in a bin to the expected number.

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Figure 4-c:
Distribution of ${{H_{\mathrm {T}}} ^{\mathrm {AK8}}}$ for the $\geq $1Z jet category, which contains at least one candidate of each of the particle types identified by the BEST algorithm. The vertical axis labels denote that bin contents in these distributions have been scaled by their corresponding bin widths. The lower panel shows the ratio of the observed number of events in a bin to the expected number.

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Figure 4-d:
Distribution of ${{H_{\mathrm {T}}} ^{\mathrm {AK8}}}$ for the $\geq $1H jet category, which contains at least one candidate of each of the particle types identified by the BEST algorithm. The vertical axis labels denote that bin contents in these distributions have been scaled by their corresponding bin widths. The lower panel shows the ratio of the observed number of events in a bin to the expected number.

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Figure 4-e:
Distribution of ${{H_{\mathrm {T}}} ^{\mathrm {AK8}}}$ for the $\geq $1t jet category, which contains at least one candidate of each of the particle types identified by the BEST algorithm. The vertical axis labels denote that bin contents in these distributions have been scaled by their corresponding bin widths. The lower panel shows the ratio of the observed number of events in a bin to the expected number.

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Figure 4-f:
Distribution of ${{H_{\mathrm {T}}} ^{\mathrm {AK8}}}$ for the $\geq $1b jet category, which contains at least one candidate of each of the particle types identified by the BEST algorithm. The vertical axis labels denote that bin contents in these distributions have been scaled by their corresponding bin widths. The lower panel shows the ratio of the observed number of events in a bin to the expected number.

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Figure 5:
Limits at 95% confidence level on the ratio of the cross section to the theoretical cross section for pair production T quarks (left) and B quarks (right) in the cut-based analysis, with decays solely to $\mathrm{t} {}\mathrm{Z} {}/\mathrm{b} {}\mathrm{Z}$ (upper), $\mathrm{t} {}\mathrm{H} {}/\mathrm{b} {}\mathrm{H} $ (middle), and $ \mathrm{b} {}\mathrm{W} {}/\mathrm{t} {}\mathrm{W} $ (lower). The solid black line shows the observed limit, while the dashed black line shows the median of the distribution of limits expected under the background-only hypothesis. The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis.

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Figure 5-a:
Limits at 95% confidence level on the ratio of the cross section to the theoretical cross section for pair production T quarks in the cut-based analysis, with decays solely to $\mathrm{t} {}\mathrm{Z} {}/\mathrm{b} {}\mathrm{Z}$. The solid black line shows the observed limit, while the dashed black line shows the median of the distribution of limits expected under the background-only hypothesis. The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis.

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Figure 5-b:
Limits at 95% confidence level on the ratio of the cross section to the theoretical cross section for pair production B quarks in the cut-based analysis, with decays solely to $\mathrm{t} {}\mathrm{Z} {}/\mathrm{b} {}\mathrm{Z}$. The solid black line shows the observed limit, while the dashed black line shows the median of the distribution of limits expected under the background-only hypothesis. The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis.

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Figure 5-c:
Limits at 95% confidence level on the ratio of the cross section to the theoretical cross section for pair production T quarks in the cut-based analysis, with decays solely to $\mathrm{t} {}\mathrm{H} {}/\mathrm{b} {}\mathrm{H} $. The solid black line shows the observed limit, while the dashed black line shows the median of the distribution of limits expected under the background-only hypothesis. The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis.

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Figure 5-d:
Limits at 95% confidence level on the ratio of the cross section to the theoretical cross section for pair production B quarks in the cut-based analysis, with decays solely to $\mathrm{t} {}\mathrm{H} {}/\mathrm{b} {}\mathrm{H} $. The solid black line shows the observed limit, while the dashed black line shows the median of the distribution of limits expected under the background-only hypothesis. The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis.

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Figure 5-e:
Limits at 95% confidence level on the ratio of the cross section to the theoretical cross section for pair production T quarks in the cut-based analysis, with decays solely to $ \mathrm{b} {}\mathrm{W} {}/\mathrm{t} {}\mathrm{W} $. The solid black line shows the observed limit, while the dashed black line shows the median of the distribution of limits expected under the background-only hypothesis. The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis.

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Figure 5-f:
Limits at 95% confidence level on the ratio of the cross section to the theoretical cross section for pair production B quarks in the cut-based analysis, with decays solely to $ \mathrm{b} {}\mathrm{W} {}/\mathrm{t} {}\mathrm{W} $. The solid black line shows the observed limit, while the dashed black line shows the median of the distribution of limits expected under the background-only hypothesis. The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis.

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Figure 6:
Limits at 95% confidence level on the ratio of the cross section to the theoretical cross section for pair production T quarks (left) and B quarks (right) in the NN analysis, with decays solely to $\mathrm{t} {}\mathrm{Z} {}/\mathrm{b} {}\mathrm{Z}$ (upper), $\mathrm{t} {}\mathrm{H} {}/\mathrm{b} {}\mathrm{H} $ (middle), and $ \mathrm{b} {}\mathrm{W} {}/\mathrm{t} {}\mathrm{W} $ (lower). The solid black line shows the observed limit, while the dashed black line shows the median of the distribution of limits expected under the background-only hypothesis. The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis.

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Figure 6-a:
Limits at 95% confidence level on the ratio of the cross section to the theoretical cross section for pair production T quarks in the NN analysis, with decays solely to $\mathrm{t} {}\mathrm{Z} {}/\mathrm{b} {}\mathrm{Z}$. The solid black line shows the observed limit, while the dashed black line shows the median of the distribution of limits expected under the background-only hypothesis. The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis.

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Figure 6-b:
Limits at 95% confidence level on the ratio of the cross section to the theoretical cross section for pair production B quarks in the NN analysis, with decays solely to $\mathrm{t} {}\mathrm{Z} {}/\mathrm{b} {}\mathrm{Z}$. The solid black line shows the observed limit, while the dashed black line shows the median of the distribution of limits expected under the background-only hypothesis. The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis.

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Figure 6-c:
Limits at 95% confidence level on the ratio of the cross section to the theoretical cross section for pair production T quarks in the NN analysis, with decays solely to $\mathrm{t} {}\mathrm{H} {}/\mathrm{b} {}\mathrm{H} $. The solid black line shows the observed limit, while the dashed black line shows the median of the distribution of limits expected under the background-only hypothesis. The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis.

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Figure 6-d:
Limits at 95% confidence level on the ratio of the cross section to the theoretical cross section for pair production B quarks in the NN analysis, with decays solely to $\mathrm{t} {}\mathrm{H} {}/\mathrm{b} {}\mathrm{H} $. The solid black line shows the observed limit, while the dashed black line shows the median of the distribution of limits expected under the background-only hypothesis. The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis.

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Figure 6-e:
Limits at 95% confidence level on the ratio of the cross section to the theoretical cross section for pair production T quarks in the NN analysis, with decays solely to $ \mathrm{b} {}\mathrm{W} {}/\mathrm{t} {}\mathrm{W} $. The solid black line shows the observed limit, while the dashed black line shows the median of the distribution of limits expected under the background-only hypothesis. The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis.

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Figure 6-f:
Limits at 95% confidence level on the ratio of the cross section to the theoretical cross section for pair production B quarks in the NN analysis, with decays solely to $ \mathrm{b} {}\mathrm{W} {}/\mathrm{t} {}\mathrm{W} $. The solid black line shows the observed limit, while the dashed black line shows the median of the distribution of limits expected under the background-only hypothesis. The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis.

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Figure 7:
Observed (left) and expected (right) mass exclusion limits at 95% confidence level for each combination of T quark branching fractions, in the cut-based analysis (upper) and NN analysis (lower).

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Figure 7-a:
Observed mass exclusion limits at 95% confidence level for each combination of T quark branching fractions, in the cut-based analysis.

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Figure 7-b:
Expected mass exclusion limits at 95% confidence level for each combination of T quark branching fractions, in the NN analysis.

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Figure 7-c:
Observed mass exclusion limits at 95% confidence level for each combination of T quark branching fractions, in the cut-based analysis.

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Figure 7-d:
Expected mass exclusion limits at 95% confidence level for each combination of T quark branching fractions, in the NN analysis.

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Figure 8:
Observed (left) and expected (right) mass exclusion limits at 95% confidence level for each combination of B quark branching fractions, in the cut-based analysis (upper) and NN analysis (lower).

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Figure 8-a:
Observed mass exclusion limits at 95% confidence level for each combination of B quark branching fractions, in the cut-based analysis.

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Figure 8-b:
Expected mass exclusion limits at 95% confidence level for each combination of B quark branching fractions, in the NN analysis.

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Figure 8-c:
Observed mass exclusion limits at 95% confidence level for each combination of B quark branching fractions, in the cut-based analysis.

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Figure 8-d:
Expected mass exclusion limits at 95% confidence level for each combination of B quark branching fractions, in the NN analysis.
Tables

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Table 1:
Theoretical cross sections for TT and BB production, calculated at NNLO with Top++2.0.

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Table 2:
Sources of systematic uncertainties that affect the ${{H_{\mathrm {T}}} ^{\mathrm {AK4}}}$ or ${{H_{\mathrm {T}}} ^{\mathrm {AK8}}}$ distribution in each analysis. Systematic sources with an uncertainty of "$ \pm $1$ \sigma $'' affect the shape and rate, all others affect the rate only. Sources of systematic error that affect "all simulation'' impact both the signal simulation and simulated backgrounds.

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Table 3:
Exclusion limits at 95% confidence level presented in terms of the T quark mass, for the different branching fraction scenarios considered, in each of the two analyses.

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Table 4:
Exclusion limits at 95% confidence level presented in terms of the B quark mass, for the different branching fraction scenarios considered, in each of the two analyses.
Summary
Two independent searches for vector-like T and B quarks using the fully hadronic final states have been presented. Both searches use data collected by the CMS experiment in 2016 at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 35.9 fb$^{-1}$. A cut-based analysis, using jet substructure observables to identify hadronic decays of boosted W bosons, targets the qW decay mode of the T quark, and improves sensitivity relative to results of such searches conducted previously. The analysis uses a quantum chromodynamics multijet background estimation method based on shape and rate extrapolations from various control regions to the signal region. Improvements in W tagging techniques, as well as the addition of signal regions requiring just a single W-tagged jet, enhance the performance of this analysis relative to previous searches based on different strategies. This search extends the T quark mass exclusion to 1040 GeV, relative to the previous exclusion of 705 GeV obtained by a similar analysis targeting the qW decay mode using data collected at 8 TeV [56].

A new strategy is presented and compared with the traditional cut-based approach. The neural network analysis uses a multiclassification technique, the boosted event shape tagger algorithm, to identify jets originating from heavy objects such as t or b quarks, and W, Z, or H. This allows the analysis to be sensitive to all decay modes of the T and B quarks. Using classification fractions, the dominant multijet background is estimated using data. The neural network analysis provides sensitivity for the tH and tZ decay modes competitive with that obtained by other searches utilizing lepton+jets or multilepton topologies.

For each analysis, results are presented in terms of cross section limits for the pair production of T and B quarks, along with exclusion limits in terms of the T and B quark masses, for the different combinations of branching fractions considered. The mass exclusion limits at 95% confidence level for the neural network analysis range from 740 to 1370 GeV, providing comparable sensitivity to the searches utilizing leptons, which exclude vector-like quark masses in the range 910-1300 GeV [13]. These results represent the most stringent limits on pair produced vector-like quarks in the fully hadronic channel to date.
Additional Figures

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Additional Figure 1:
The confusion matrix from the training of the BEST algorithm. The y-axis shows the truth-level information about the particle species from which the jet originates, while the x-axis shows the predicted categories after evaluating the BEST algorithm. Good performance is seen on the diagonal, which represents correct classifications. The label 'j' represents light-flavor jets (u/d/s/c quark and gluon).

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Additional Figure 2:
Distribution of the predicted categories of the BEST algorithm for the leading jet in the inclusive 4-jet sample. The category 'j' represents light flavor jets (u/d/s/c/g). The yellow histogram shows the expectation from QCD multijet processes, and here is shown taken from simulation. This component is scaled by a k-factor to equalize the total normalization between data and the summed background components. The shaded band represents the statistical uncertainty on the backgrounds only. The mistag rates used in the analysis are derived from data in this sample. Jets entering this distribution are not matched to any generator-level particles, meaning the leading jet in a given process may not be the heavy object of interest and may be categorized differently than expected.

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Additional Figure 3:
The jet soft drop mass distribution shown for the training samples (t, W, Z, H, b, light flavor jets) of the BEST algorithm. The histograms are each normalized to unit area. This quantity is one of the inputs to the BEST algorithm.

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Additional Figure 4:
The output probability for H classification, after evaluating the samples (t, W, Z, H, b, light flavor jets) used with the BEST algorithm training/testing procedure. The histograms are each normalized to unit area.

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Additional Figure 5:
The output probability for W classification, after evaluating the samples (t, W, Z, H, b, light flavor jets) used with the BEST algorithm training/testing procedure. The histograms are each normalized to unit area.

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Additional Figure 6:
The output probability for Z classification, after evaluating the samples (t, W, Z, H, b, light flavor jets) used with the BEST algorithm training/testing procedure. The histograms are each normalized to unit area.

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Additional Figure 7:
The output probability for b classification, after evaluating the samples (t, W, Z, H, b, light flavor jets) used with the BEST algorithm training/testing procedure. The histograms are each normalized to unit area.

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Additional Figure 8:
The output probability for light flavor classification, after evaluating the samples (t, W, Z, H, b, light flavor jets) used with the BEST algorithm training/testing procedure. The histograms are each normalized to unit area.

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Additional Figure 9:
The output probability for t classification, after evaluating the samples (t, W, Z, H, b, light flavor jets) used with the BEST algorithm training/testing procedure. The histograms are each normalized to unit area.

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Additional Figure 10:
The longitudinal jet asymmetry ($A_L$, defined as the ratio of the sum of the subjet momenta longitudinal components to the sum of subjet momenta magnitudes) distribution shown for the training samples (t, W, Z, H, b, light flavor jets) of the BEST algorithm after boosting the jet constituents assuming the H rest frame. The histograms are each normalized to unit area. This quantity is one of the inputs to the BEST algorithm.

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Additional Figure 11:
The longitudinal jet asymmetry ($A_L$, defined as the ratio of the sum of the subjet momenta longitudinal components to the sum of subjet momenta magnitudes) distribution shown for the training samples (t, W, Z, H, b, light flavor jets) of the BEST algorithm after boosting the jet constituents assuming the W rest frame. The histograms are each normalized to unit area. This quantity is one of the inputs to the BEST algorithm.

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Additional Figure 12:
The longitudinal jet asymmetry ($A_L$, defined as the ratio of the sum of the subjet momenta longitudinal components to the sum of subjet momenta magnitudes) distribution shown for the training samples (t, W, Z, H, b, light flavor jets) of the BEST algorithm after boosting the jet constituents assuming the Z rest frame. The histograms are each normalized to unit area. This quantity is one of the inputs to the BEST algorithm.

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Additional Figure 13:
The longitudinal jet asymmetry ($A_L$, defined as the ratio of the sum of the subjet momenta longitudinal components to the sum of subjet momenta magnitudes) distribution shown for the training samples (t, W, Z, H, b, light flavor jets) of the BEST algorithm after boosting the jet constituents assuming the top quark rest frame. The histograms are each normalized to unit area. This quantity is one of the inputs to the BEST algorithm.

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Additional Figure 14:
The distribution of the ratio of two Fox-Wolfram moments (indices 2 and 0), shown for the training samples (t, W, Z, H, b, light flavor jets) of the BEST algorithm after boosting the jet constituents assuming the H rest frame. The histograms are each normalized to unit area. This quantity is one of the inputs to the BEST algorithm.

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Additional Figure 15:
The distribution of the ratio of two Fox-Wolfram moments (indices 2 and 0), shown for the training samples (t, W, Z, H, b, light flavor jets) of the BEST algorithm after boosting the jet constituents assuming the W rest frame. The histograms are each normalized to unit area. This quantity is one of the inputs to the BEST algorithm.

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Additional Figure 16:
The distribution of the ratio of two Fox-Wolfram moments (indices 2 and 0), shown for the training samples (t, W, Z, H, b, light flavor jets) of the BEST algorithm after boosting the jet constituents assuming the Z rest frame. The histograms are each normalized to unit area. This quantity is one of the inputs to the BEST algorithm.

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Additional Figure 17:
The distribution of the ratio of two Fox-Wolfram moments (indices 2 and 0), shown for the training samples (t, W, Z, H, b, light flavor jets) of the BEST algorithm after boosting the jet constituents assuming the top quark rest frame. The histograms are each normalized to unit area. This quantity is one of the inputs to the BEST algorithm.

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Additional Figure 18:
The distribution of the sphericity, shown for the training samples (t, W, Z, H, b, light flavor jets) of the BEST algorithm after boosting the jet constituents assuming the H rest frame. The histograms are each normalized to unit area. This quantity is one of the inputs to the BEST algorithm.

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Additional Figure 19:
The distribution of the sphericity, shown for the training samples (t, W, Z, H, b, light flavor jets) of the BEST algorithm after boosting the jet constituents assuming the W rest frame. The histograms are each normalized to unit area. This quantity is one of the inputs to the BEST algorithm.

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Additional Figure 20:
The distribution of the sphericity, shown for the training samples (t, W, Z, H, b, light flavor jets) of the BEST algorithm after boosting the jet constituents assuming the Z rest frame. The histograms are each normalized to unit area. This quantity is one of the inputs to the BEST algorithm.

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Additional Figure 21:
The distribution of the sphericity, shown for the training samples (t, W, Z, H, b, light flavor jets) of the BEST algorithm after boosting the jet constituents assuming the top quark rest frame. The histograms are each normalized to unit area. This quantity is one of the inputs to the BEST algorithm.
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