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| CMS-BTV-22-001 ; CERN-EP-2025-161 | ||
| Performance of heavy-flavour jet identification in Lorentz-boosted topologies in proton-proton collisions at $ \sqrt{s} = $ 13 TeV | ||
| CMS Collaboration | ||
| 11 October 2025 | ||
| JINST 20 (2025) P11006 | ||
| Abstract: Measurements in the highly Lorentz-boosted regime provoke increased interest in probing the Higgs boson properties and in searching for particles beyond the standard model at the LHC. In the CMS Collaboration, various boosted-object tagging algorithms, designed to identify hadronic jets originating from a massive particle decaying to $ \mathrm{b}\overline{\mathrm{b}} $ or $ \mathrm{c}\overline{\mathrm{c}} $, have been developed and deployed across a range of physics analyses. This paper highlights their performance on simulated events, and summarizes novel calibration techniques using proton-proton collision data collected at $ \sqrt{s} = $ 13 TeV during the 2016-2018 LHC data-taking period. Three dedicated methods are used for the calibration in multijet events, leveraging either machine learning techniques, the presence of muons within energetic boosted jets, or the reconstruction of hadronically decaying high-energy Z bosons. The calibration results, obtained through a combination of these approaches, are presented and discussed. | ||
| Links: e-print arXiv:2510.10228 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Shape comparison of the ParticleNet-MD bbvsQCD (left) and ParticleNet-MD ccvsQCD (right) discriminants for the simulated standard model $ \mathrm{H} \to \mathrm{b} \overline{\mathrm{b}} $ and $ \mathrm{H} \to \mathrm{c} \overline{\mathrm{c}} $ jets, the bb and cc components of QCD multijet background jets, and inclusive QCD jets (without flavour-specific selection), using simulated events corresponding to the 2018 data-taking conditions for jets with $ p_{\mathrm{T}} > $ 450 GeV and $ |\eta| < $ 2.4. The error bars represent the statistical uncertainties due to the limited number of simulated events. |
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Figure 1-a:
Shape comparison of the ParticleNet-MD bbvsQCD (left) and ParticleNet-MD ccvsQCD (right) discriminants for the simulated standard model $ \mathrm{H} \to \mathrm{b} \overline{\mathrm{b}} $ and $ \mathrm{H} \to \mathrm{c} \overline{\mathrm{c}} $ jets, the bb and cc components of QCD multijet background jets, and inclusive QCD jets (without flavour-specific selection), using simulated events corresponding to the 2018 data-taking conditions for jets with $ p_{\mathrm{T}} > $ 450 GeV and $ |\eta| < $ 2.4. The error bars represent the statistical uncertainties due to the limited number of simulated events. |
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Figure 1-b:
Shape comparison of the ParticleNet-MD bbvsQCD (left) and ParticleNet-MD ccvsQCD (right) discriminants for the simulated standard model $ \mathrm{H} \to \mathrm{b} \overline{\mathrm{b}} $ and $ \mathrm{H} \to \mathrm{c} \overline{\mathrm{c}} $ jets, the bb and cc components of QCD multijet background jets, and inclusive QCD jets (without flavour-specific selection), using simulated events corresponding to the 2018 data-taking conditions for jets with $ p_{\mathrm{T}} > $ 450 GeV and $ |\eta| < $ 2.4. The error bars represent the statistical uncertainties due to the limited number of simulated events. |
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Figure 2:
Shape comparison of the DeepDoubleBvL (left) and DeepDoubleCvL (right) discriminants for the simulated standard model $ \mathrm{H} \to \mathrm{b} \overline{\mathrm{b}} $ and $ \mathrm{H} \to \mathrm{c} \overline{\mathrm{c}} $ jets, the bb and cc components of QCD multijet background jets, and inclusive QCD jets, using simulated events corresponding to the 2018 data-taking conditions for jets with $ p_{\mathrm{T}} > $ 450 GeV and $ |\eta| < $ 2.4. The error bars represent the statistical uncertainties due to the limited number of simulated events. |
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Figure 2-a:
Shape comparison of the DeepDoubleBvL (left) and DeepDoubleCvL (right) discriminants for the simulated standard model $ \mathrm{H} \to \mathrm{b} \overline{\mathrm{b}} $ and $ \mathrm{H} \to \mathrm{c} \overline{\mathrm{c}} $ jets, the bb and cc components of QCD multijet background jets, and inclusive QCD jets, using simulated events corresponding to the 2018 data-taking conditions for jets with $ p_{\mathrm{T}} > $ 450 GeV and $ |\eta| < $ 2.4. The error bars represent the statistical uncertainties due to the limited number of simulated events. |
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Figure 2-b:
Shape comparison of the DeepDoubleBvL (left) and DeepDoubleCvL (right) discriminants for the simulated standard model $ \mathrm{H} \to \mathrm{b} \overline{\mathrm{b}} $ and $ \mathrm{H} \to \mathrm{c} \overline{\mathrm{c}} $ jets, the bb and cc components of QCD multijet background jets, and inclusive QCD jets, using simulated events corresponding to the 2018 data-taking conditions for jets with $ p_{\mathrm{T}} > $ 450 GeV and $ |\eta| < $ 2.4. The error bars represent the statistical uncertainties due to the limited number of simulated events. |
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Figure 3:
Shape comparison of the DeepAK8-MD bbvsQCD (left) and DeepAK8-MD ccvsQCD (right) discriminants for the simulated standard model $ \mathrm{H} \to \mathrm{b} \overline{\mathrm{b}} $ and $ \mathrm{H} \to \mathrm{c} \overline{\mathrm{c}} $ jets, the bb and cc components of QCD multijet background jets, and inclusive QCD jets, using simulated events corresponding to the 2018 data-taking conditions for jets with $ p_{\mathrm{T}} > $ 450 GeV and $ |\eta| < $ 2.4. The error bars represent the statistical uncertainties due to the limited number of simulated events. |
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Figure 3-a:
Shape comparison of the DeepAK8-MD bbvsQCD (left) and DeepAK8-MD ccvsQCD (right) discriminants for the simulated standard model $ \mathrm{H} \to \mathrm{b} \overline{\mathrm{b}} $ and $ \mathrm{H} \to \mathrm{c} \overline{\mathrm{c}} $ jets, the bb and cc components of QCD multijet background jets, and inclusive QCD jets, using simulated events corresponding to the 2018 data-taking conditions for jets with $ p_{\mathrm{T}} > $ 450 GeV and $ |\eta| < $ 2.4. The error bars represent the statistical uncertainties due to the limited number of simulated events. |
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Figure 3-b:
Shape comparison of the DeepAK8-MD bbvsQCD (left) and DeepAK8-MD ccvsQCD (right) discriminants for the simulated standard model $ \mathrm{H} \to \mathrm{b} \overline{\mathrm{b}} $ and $ \mathrm{H} \to \mathrm{c} \overline{\mathrm{c}} $ jets, the bb and cc components of QCD multijet background jets, and inclusive QCD jets, using simulated events corresponding to the 2018 data-taking conditions for jets with $ p_{\mathrm{T}} > $ 450 GeV and $ |\eta| < $ 2.4. The error bars represent the statistical uncertainties due to the limited number of simulated events. |
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Figure 4:
Shape comparison of the double-b discriminant for the simulated standard model $ \mathrm{H} \to \mathrm{b} \overline{\mathrm{b}} $ and $ \mathrm{H} \to \mathrm{c} \overline{\mathrm{c}} $ jets, the bb and cc components of QCD multijet background jets, and inclusive QCD jets, using simulated events corresponding to the 2018 data-taking conditions for jets with $ p_{\mathrm{T}} > $ 450 GeV and $ |\eta| < $ 2.4. The error bars represent the statistical uncertainties due to the limited number of simulated events. |
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Figure 5:
Comparison of the performance of the $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ identification algorithms in terms of receiver operating characteristic (ROC) curves for $ \mathrm{H} \to \mathrm{b} \overline{\mathrm{b}} $ signal jets versus the inclusive QCD jets as background, using simulated events with the 2018 data-taking conditions. Performance is shown in the 450 $ < p_{\mathrm{T}} < $ 600 GeV (left) and $ p_{\mathrm{T}} > $ 600 GeV (right) regions. Additional selection criteria applied to the jets are displayed on the plots. |
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Figure 5-a:
Comparison of the performance of the $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ identification algorithms in terms of receiver operating characteristic (ROC) curves for $ \mathrm{H} \to \mathrm{b} \overline{\mathrm{b}} $ signal jets versus the inclusive QCD jets as background, using simulated events with the 2018 data-taking conditions. Performance is shown in the 450 $ < p_{\mathrm{T}} < $ 600 GeV (left) and $ p_{\mathrm{T}} > $ 600 GeV (right) regions. Additional selection criteria applied to the jets are displayed on the plots. |
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Figure 5-b:
Comparison of the performance of the $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ identification algorithms in terms of receiver operating characteristic (ROC) curves for $ \mathrm{H} \to \mathrm{b} \overline{\mathrm{b}} $ signal jets versus the inclusive QCD jets as background, using simulated events with the 2018 data-taking conditions. Performance is shown in the 450 $ < p_{\mathrm{T}} < $ 600 GeV (left) and $ p_{\mathrm{T}} > $ 600 GeV (right) regions. Additional selection criteria applied to the jets are displayed on the plots. |
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Figure 6:
Comparison of the performance of the $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ identification algorithms in terms of receiver operating characteristic (ROC) curves for $ \mathrm{H} \to \mathrm{c} \overline{\mathrm{c}} $ signal jets versus the inclusive QCD jets as background, using simulated events with the 2018 data-taking conditions. Performance is shown in the 450 $ < p_{\mathrm{T}} < $ 600 GeV (left) and $ p_{\mathrm{T}} > $ 600 GeV (right) regions. Additional selection criteria applied to the jets are displayed on the plots. |
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Figure 6-a:
Comparison of the performance of the $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ identification algorithms in terms of receiver operating characteristic (ROC) curves for $ \mathrm{H} \to \mathrm{c} \overline{\mathrm{c}} $ signal jets versus the inclusive QCD jets as background, using simulated events with the 2018 data-taking conditions. Performance is shown in the 450 $ < p_{\mathrm{T}} < $ 600 GeV (left) and $ p_{\mathrm{T}} > $ 600 GeV (right) regions. Additional selection criteria applied to the jets are displayed on the plots. |
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Figure 6-b:
Comparison of the performance of the $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ identification algorithms in terms of receiver operating characteristic (ROC) curves for $ \mathrm{H} \to \mathrm{c} \overline{\mathrm{c}} $ signal jets versus the inclusive QCD jets as background, using simulated events with the 2018 data-taking conditions. Performance is shown in the 450 $ < p_{\mathrm{T}} < $ 600 GeV (left) and $ p_{\mathrm{T}} > $ 600 GeV (right) regions. Additional selection criteria applied to the jets are displayed on the plots. |
png pdf |
Figure 7:
Comparison of the performance of the $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ identification algorithms in terms of receiver operating characteristic (ROC) curves for $ \mathrm{H} \to \mathrm{b} \overline{\mathrm{b}} $ signal jets versus the bb component of the QCD jets as background, using simulated events with the 2018 data-taking conditions. Performance is shown in the 450 $ < p_{\mathrm{T}} < $ 600 GeV (left) and $ p_{\mathrm{T}} > $ 600 GeV (right) regions. Additional selection criteria applied to the jets are displayed on the plots. |
png pdf |
Figure 7-a:
Comparison of the performance of the $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ identification algorithms in terms of receiver operating characteristic (ROC) curves for $ \mathrm{H} \to \mathrm{b} \overline{\mathrm{b}} $ signal jets versus the bb component of the QCD jets as background, using simulated events with the 2018 data-taking conditions. Performance is shown in the 450 $ < p_{\mathrm{T}} < $ 600 GeV (left) and $ p_{\mathrm{T}} > $ 600 GeV (right) regions. Additional selection criteria applied to the jets are displayed on the plots. |
png pdf |
Figure 7-b:
Comparison of the performance of the $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ identification algorithms in terms of receiver operating characteristic (ROC) curves for $ \mathrm{H} \to \mathrm{b} \overline{\mathrm{b}} $ signal jets versus the bb component of the QCD jets as background, using simulated events with the 2018 data-taking conditions. Performance is shown in the 450 $ < p_{\mathrm{T}} < $ 600 GeV (left) and $ p_{\mathrm{T}} > $ 600 GeV (right) regions. Additional selection criteria applied to the jets are displayed on the plots. |
png pdf |
Figure 8:
Comparison of the performance of the $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ identification algorithms in terms of receiver operating characteristic (ROC) curves for $ \mathrm{H} \to \mathrm{c} \overline{\mathrm{c}} $ signal jets versus the cc component of the QCD jets as background, using simulated events with the 2018 data-taking conditions. Performance is shown in the 450 $ < p_{\mathrm{T}} < $ 600 GeV (left) and $ p_{\mathrm{T}} > $ 600 GeV (right) regions. Additional selection criteria applied to the jets are displayed on the plots. |
png pdf |
Figure 8-a:
Comparison of the performance of the $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ identification algorithms in terms of receiver operating characteristic (ROC) curves for $ \mathrm{H} \to \mathrm{c} \overline{\mathrm{c}} $ signal jets versus the cc component of the QCD jets as background, using simulated events with the 2018 data-taking conditions. Performance is shown in the 450 $ < p_{\mathrm{T}} < $ 600 GeV (left) and $ p_{\mathrm{T}} > $ 600 GeV (right) regions. Additional selection criteria applied to the jets are displayed on the plots. |
png pdf |
Figure 8-b:
Comparison of the performance of the $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ identification algorithms in terms of receiver operating characteristic (ROC) curves for $ \mathrm{H} \to \mathrm{c} \overline{\mathrm{c}} $ signal jets versus the cc component of the QCD jets as background, using simulated events with the 2018 data-taking conditions. Performance is shown in the 450 $ < p_{\mathrm{T}} < $ 600 GeV (left) and $ p_{\mathrm{T}} > $ 600 GeV (right) regions. Additional selection criteria applied to the jets are displayed on the plots. |
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Figure 9:
Signal efficiency $ \epsilon_\mathrm{S} $ as a function of jet $ p_{\mathrm{T}} $ for a working point corresponding to overall selection efficiencies of 40% in $ \mathrm{H} \to \mathrm{b} \overline{\mathrm{b}} $ and 15% in $ \mathrm{H} \to \mathrm{c} \overline{\mathrm{c}} $ jets. The left and right plots compare the performance of various $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ and $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ tagging algorithms, respectively. The error bars represent the statistical uncertainties due to the limited number of simulated events. Additional selection criteria applied to the jets are displayed on the plots. |
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Figure 9-a:
Signal efficiency $ \epsilon_\mathrm{S} $ as a function of jet $ p_{\mathrm{T}} $ for a working point corresponding to overall selection efficiencies of 40% in $ \mathrm{H} \to \mathrm{b} \overline{\mathrm{b}} $ and 15% in $ \mathrm{H} \to \mathrm{c} \overline{\mathrm{c}} $ jets. The left and right plots compare the performance of various $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ and $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ tagging algorithms, respectively. The error bars represent the statistical uncertainties due to the limited number of simulated events. Additional selection criteria applied to the jets are displayed on the plots. |
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Figure 9-b:
Signal efficiency $ \epsilon_\mathrm{S} $ as a function of jet $ p_{\mathrm{T}} $ for a working point corresponding to overall selection efficiencies of 40% in $ \mathrm{H} \to \mathrm{b} \overline{\mathrm{b}} $ and 15% in $ \mathrm{H} \to \mathrm{c} \overline{\mathrm{c}} $ jets. The left and right plots compare the performance of various $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ and $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ tagging algorithms, respectively. The error bars represent the statistical uncertainties due to the limited number of simulated events. Additional selection criteria applied to the jets are displayed on the plots. |
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Figure 10:
Distributions of the sfBDT discriminant for data and simulation, illustrated using the 2018 data-taking conditions, for jets with $ p_{\mathrm{T}} > $ 450 GeV. The error bars indicate statistical uncertainties in observed data, which may be too small to be visible. |
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Figure 11:
Illustration of nine predefined ``reference selection thresholds'' visualized on the two-dimensional plane spanned by the sfBDT score and the transformed tagger discriminant scores. Selections based on these thresholds can be interpreted as sfBDT selections with thresholds as a function of the tagger discriminant score. Each selection aims to match the tagger discriminant distribution of the proxy jet to that of the signal. The examples shown correspond to the calibration of the ParticleNet-MD $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ (left) and ParticleNet-MD $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ (right) discriminants, using simulated events under 2018 data-taking conditions in the jet $ p_{\mathrm{T}} $ range of (450, 500) GeV. |
png pdf |
Figure 11-a:
Illustration of nine predefined ``reference selection thresholds'' visualized on the two-dimensional plane spanned by the sfBDT score and the transformed tagger discriminant scores. Selections based on these thresholds can be interpreted as sfBDT selections with thresholds as a function of the tagger discriminant score. Each selection aims to match the tagger discriminant distribution of the proxy jet to that of the signal. The examples shown correspond to the calibration of the ParticleNet-MD $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ (left) and ParticleNet-MD $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ (right) discriminants, using simulated events under 2018 data-taking conditions in the jet $ p_{\mathrm{T}} $ range of (450, 500) GeV. |
png pdf |
Figure 11-b:
Illustration of nine predefined ``reference selection thresholds'' visualized on the two-dimensional plane spanned by the sfBDT score and the transformed tagger discriminant scores. Selections based on these thresholds can be interpreted as sfBDT selections with thresholds as a function of the tagger discriminant score. Each selection aims to match the tagger discriminant distribution of the proxy jet to that of the signal. The examples shown correspond to the calibration of the ParticleNet-MD $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ (left) and ParticleNet-MD $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ (right) discriminants, using simulated events under 2018 data-taking conditions in the jet $ p_{\mathrm{T}} $ range of (450, 500) GeV. |
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Figure 12:
Shapes of the transformed ParticleNet-MD $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ (left) and $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ (right) discriminants for SM $ \mathrm{H} \to \mathrm{b} \overline{\mathrm{b}} $ ($ \mathrm{c} \overline{\mathrm{c}} $) signal jets and proxy jets selected with different sfBDT selection thresholds. The examples correspond to the calibration of the ParticleNet-MD $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ and $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ discriminants with the sfBDT method, using simulated events under 2018 data-taking conditions for jets with $ p_{\mathrm{T}} > $ 450 GeV. The error bars represent the statistical uncertainties due to the limited number of simulated events. |
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Figure 12-a:
Shapes of the transformed ParticleNet-MD $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ (left) and $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ (right) discriminants for SM $ \mathrm{H} \to \mathrm{b} \overline{\mathrm{b}} $ ($ \mathrm{c} \overline{\mathrm{c}} $) signal jets and proxy jets selected with different sfBDT selection thresholds. The examples correspond to the calibration of the ParticleNet-MD $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ and $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ discriminants with the sfBDT method, using simulated events under 2018 data-taking conditions for jets with $ p_{\mathrm{T}} > $ 450 GeV. The error bars represent the statistical uncertainties due to the limited number of simulated events. |
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Figure 12-b:
Shapes of the transformed ParticleNet-MD $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ (left) and $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ (right) discriminants for SM $ \mathrm{H} \to \mathrm{b} \overline{\mathrm{b}} $ ($ \mathrm{c} \overline{\mathrm{c}} $) signal jets and proxy jets selected with different sfBDT selection thresholds. The examples correspond to the calibration of the ParticleNet-MD $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ and $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ discriminants with the sfBDT method, using simulated events under 2018 data-taking conditions for jets with $ p_{\mathrm{T}} > $ 450 GeV. The error bars represent the statistical uncertainties due to the limited number of simulated events. |
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Figure 13:
An example of the transformed ParticleNet-MD $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ (left) and $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ (right) distribution in data and simulated events, after applying the preselection and the middle sfBDT selection threshold in the sfBDT method. The high-purity (HP), medium-purity (MP), and low-purity (LP) working points for the left (right) plot correspond to selections of $ X > 0.6, 0.4, 0.2 (0.85, 0.7, 0.5) $ on the transformed tagger discriminant. The error bars represent the statistical uncertainties in observed data. The lower panels display the ratio of data to simulation, with the hatched bands representing the normalized statistical uncertainty of simulated events for each bin. The distributions are based on data and simulated events with the 2018 data-taking conditions, in the jet $ p_{\mathrm{T}} $ range of (450, 500) GeV. |
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Figure 13-a:
An example of the transformed ParticleNet-MD $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ (left) and $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ (right) distribution in data and simulated events, after applying the preselection and the middle sfBDT selection threshold in the sfBDT method. The high-purity (HP), medium-purity (MP), and low-purity (LP) working points for the left (right) plot correspond to selections of $ X > 0.6, 0.4, 0.2 (0.85, 0.7, 0.5) $ on the transformed tagger discriminant. The error bars represent the statistical uncertainties in observed data. The lower panels display the ratio of data to simulation, with the hatched bands representing the normalized statistical uncertainty of simulated events for each bin. The distributions are based on data and simulated events with the 2018 data-taking conditions, in the jet $ p_{\mathrm{T}} $ range of (450, 500) GeV. |
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Figure 13-b:
An example of the transformed ParticleNet-MD $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ (left) and $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ (right) distribution in data and simulated events, after applying the preselection and the middle sfBDT selection threshold in the sfBDT method. The high-purity (HP), medium-purity (MP), and low-purity (LP) working points for the left (right) plot correspond to selections of $ X > 0.6, 0.4, 0.2 (0.85, 0.7, 0.5) $ on the transformed tagger discriminant. The error bars represent the statistical uncertainties in observed data. The lower panels display the ratio of data to simulation, with the hatched bands representing the normalized statistical uncertainty of simulated events for each bin. The distributions are based on data and simulated events with the 2018 data-taking conditions, in the jet $ p_{\mathrm{T}} $ range of (450, 500) GeV. |
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Figure 14:
An example of the transformed DeepDoubleX $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ (left) and $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ (right) distribution in data and simulated events, after applying the preselection and the middle sfBDT selection threshold in the sfBDT method. The high-purity (HP), medium-purity (MP), and low-purity (LP) working points for the left (right) plot correspond to selections of $ X > 0.6, 0.4, 0.2 (0.85, 0.7, 0.5) $ on the transformed tagger discriminant. The error bars represent the statistical uncertainties in observed data. The lower panels display the ratio of data to simulation, with the hatched bands representing the normalized statistical uncertainty of simulated events for each bin. The distributions are based on data and simulated events with the 2018 data-taking conditions, in the jet $ p_{\mathrm{T}} $ range of (450, 500) GeV. |
png pdf |
Figure 14-a:
An example of the transformed DeepDoubleX $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ (left) and $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ (right) distribution in data and simulated events, after applying the preselection and the middle sfBDT selection threshold in the sfBDT method. The high-purity (HP), medium-purity (MP), and low-purity (LP) working points for the left (right) plot correspond to selections of $ X > 0.6, 0.4, 0.2 (0.85, 0.7, 0.5) $ on the transformed tagger discriminant. The error bars represent the statistical uncertainties in observed data. The lower panels display the ratio of data to simulation, with the hatched bands representing the normalized statistical uncertainty of simulated events for each bin. The distributions are based on data and simulated events with the 2018 data-taking conditions, in the jet $ p_{\mathrm{T}} $ range of (450, 500) GeV. |
png pdf |
Figure 14-b:
An example of the transformed DeepDoubleX $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ (left) and $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ (right) distribution in data and simulated events, after applying the preselection and the middle sfBDT selection threshold in the sfBDT method. The high-purity (HP), medium-purity (MP), and low-purity (LP) working points for the left (right) plot correspond to selections of $ X > 0.6, 0.4, 0.2 (0.85, 0.7, 0.5) $ on the transformed tagger discriminant. The error bars represent the statistical uncertainties in observed data. The lower panels display the ratio of data to simulation, with the hatched bands representing the normalized statistical uncertainty of simulated events for each bin. The distributions are based on data and simulated events with the 2018 data-taking conditions, in the jet $ p_{\mathrm{T}} $ range of (450, 500) GeV. |
png pdf |
Figure 15:
An example of the transformed DeepAK8-MD $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ (left) and $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ (right) distribution in data and simulated events, after applying the preselection and the middle sfBDT selection threshold in the sfBDT method. The high-purity (HP), medium-purity (MP), and low-purity (LP) working points for the left (right) plot correspond to selections of $ X > 0.6, 0.4, 0.2 (0.85, 0.7, 0.5) $ on the transformed tagger discriminant. The error bars represent the statistical uncertainties in observed data, which may be too small to be visible. The lower panels display the ratio of data to simulation, with the hatched bands representing the normalized statistical uncertainty of simulated events for each bin. The distributions are based on data and simulated events with the 2018 data-taking conditions, in the jet $ p_{\mathrm{T}} $ range of (450, 500) GeV. |
png pdf |
Figure 15-a:
An example of the transformed DeepAK8-MD $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ (left) and $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ (right) distribution in data and simulated events, after applying the preselection and the middle sfBDT selection threshold in the sfBDT method. The high-purity (HP), medium-purity (MP), and low-purity (LP) working points for the left (right) plot correspond to selections of $ X > 0.6, 0.4, 0.2 (0.85, 0.7, 0.5) $ on the transformed tagger discriminant. The error bars represent the statistical uncertainties in observed data, which may be too small to be visible. The lower panels display the ratio of data to simulation, with the hatched bands representing the normalized statistical uncertainty of simulated events for each bin. The distributions are based on data and simulated events with the 2018 data-taking conditions, in the jet $ p_{\mathrm{T}} $ range of (450, 500) GeV. |
png pdf |
Figure 15-b:
An example of the transformed DeepAK8-MD $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ (left) and $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ (right) distribution in data and simulated events, after applying the preselection and the middle sfBDT selection threshold in the sfBDT method. The high-purity (HP), medium-purity (MP), and low-purity (LP) working points for the left (right) plot correspond to selections of $ X > 0.6, 0.4, 0.2 (0.85, 0.7, 0.5) $ on the transformed tagger discriminant. The error bars represent the statistical uncertainties in observed data, which may be too small to be visible. The lower panels display the ratio of data to simulation, with the hatched bands representing the normalized statistical uncertainty of simulated events for each bin. The distributions are based on data and simulated events with the 2018 data-taking conditions, in the jet $ p_{\mathrm{T}} $ range of (450, 500) GeV. |
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Figure 16:
An example of the transformed double-b distribution in data and simulated events, after applying the preselection and the middle sfBDT selection threshold in the sfBDT method. The high-purity (HP), medium-purity (MP), and low-purity (LP) working points correspond to selections of $ X > 0.6, 0.4, $ 0.2 on the transformed tagger discriminant. The error bars represent the statistical uncertainties in observed data, which may be too small to be visible. The lower panel displays the ratio of data to simulation, with the hatched bands representing the normalized statistical uncertainty of simulated events for each bin. The distribution is based on data and simulated events with the 2018 data-taking conditions, in the jet $ p_{\mathrm{T}} $ range of (450, 500) GeV. |
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Figure 17:
Post-fit distributions from the sfBDT method for events passing (left) and failing (right) the tagger selection, used in the derivation of the scale factor for the ParticleNet-MD $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ discriminant at the high-purity working point. Error bars represent statistical uncertainties in data, whereas hatched bands denote the total uncertainties in the simulation. The example corresponds to data and simulated events from the 2018 data-taking conditions, in the jet $ p_{\mathrm{T}} $ range of (450, 500) GeV. |
png pdf |
Figure 17-a:
Post-fit distributions from the sfBDT method for events passing (left) and failing (right) the tagger selection, used in the derivation of the scale factor for the ParticleNet-MD $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ discriminant at the high-purity working point. Error bars represent statistical uncertainties in data, whereas hatched bands denote the total uncertainties in the simulation. The example corresponds to data and simulated events from the 2018 data-taking conditions, in the jet $ p_{\mathrm{T}} $ range of (450, 500) GeV. |
png pdf |
Figure 17-b:
Post-fit distributions from the sfBDT method for events passing (left) and failing (right) the tagger selection, used in the derivation of the scale factor for the ParticleNet-MD $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ discriminant at the high-purity working point. Error bars represent statistical uncertainties in data, whereas hatched bands denote the total uncertainties in the simulation. The example corresponds to data and simulated events from the 2018 data-taking conditions, in the jet $ p_{\mathrm{T}} $ range of (450, 500) GeV. |
png pdf |
Figure 18:
Post-fit distributions from the sfBDT method for events passing (left) and failing (right) the tagger selection, used in the derivation of the scale factor for the ParticleNet-MD $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ discriminant at the high-purity working point. Error bars represent statistical uncertainties in data, whereas hatched bands denote the total uncertainties in the simulation. The example corresponds to data and simulated events from the 2018 data-taking conditions, in the jet $ p_{\mathrm{T}} $ range of (450, 500) GeV. |
png pdf |
Figure 18-a:
Post-fit distributions from the sfBDT method for events passing (left) and failing (right) the tagger selection, used in the derivation of the scale factor for the ParticleNet-MD $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ discriminant at the high-purity working point. Error bars represent statistical uncertainties in data, whereas hatched bands denote the total uncertainties in the simulation. The example corresponds to data and simulated events from the 2018 data-taking conditions, in the jet $ p_{\mathrm{T}} $ range of (450, 500) GeV. |
png pdf |
Figure 18-b:
Post-fit distributions from the sfBDT method for events passing (left) and failing (right) the tagger selection, used in the derivation of the scale factor for the ParticleNet-MD $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ discriminant at the high-purity working point. Error bars represent statistical uncertainties in data, whereas hatched bands denote the total uncertainties in the simulation. The example corresponds to data and simulated events from the 2018 data-taking conditions, in the jet $ p_{\mathrm{T}} $ range of (450, 500) GeV. |
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Figure 19:
Shapes of the transformed ParticleNet-MD $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ (left) and $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ (right) discriminants for SM $ \mathrm{H} \to \mathrm{b} \overline{\mathrm{b}} $ ($ \mathrm{c} \overline{\mathrm{c}} $) signal jets and proxy jets selected with different $ \tau_{21} $ selection thresholds. The examples correspond to the calibration of the ParticleNet-MD $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ and $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ discriminants with the $ \mu $-tagged method, using simulated events under 2018 data-taking conditions for jets with $ p_{\mathrm{T}} > $ 450 GeV. The error bars represent the statistical uncertainties due to the limited number of simulated events. |
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Figure 19-a:
Shapes of the transformed ParticleNet-MD $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ (left) and $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ (right) discriminants for SM $ \mathrm{H} \to \mathrm{b} \overline{\mathrm{b}} $ ($ \mathrm{c} \overline{\mathrm{c}} $) signal jets and proxy jets selected with different $ \tau_{21} $ selection thresholds. The examples correspond to the calibration of the ParticleNet-MD $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ and $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ discriminants with the $ \mu $-tagged method, using simulated events under 2018 data-taking conditions for jets with $ p_{\mathrm{T}} > $ 450 GeV. The error bars represent the statistical uncertainties due to the limited number of simulated events. |
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Figure 19-b:
Shapes of the transformed ParticleNet-MD $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ (left) and $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ (right) discriminants for SM $ \mathrm{H} \to \mathrm{b} \overline{\mathrm{b}} $ ($ \mathrm{c} \overline{\mathrm{c}} $) signal jets and proxy jets selected with different $ \tau_{21} $ selection thresholds. The examples correspond to the calibration of the ParticleNet-MD $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ and $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ discriminants with the $ \mu $-tagged method, using simulated events under 2018 data-taking conditions for jets with $ p_{\mathrm{T}} > $ 450 GeV. The error bars represent the statistical uncertainties due to the limited number of simulated events. |
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Figure 20:
An example of the transformed ParticleNet-MD $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ (left) and $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ (right) distribution in data and simulated events, passing the preselection of the $ \mu $-tagged method. The high-purity (HP), medium-purity (MP), and low-purity (LP) working points for the left (right) plot correspond to selections of $ X > 0.6, 0.4, 0.2 (0.85, 0.7, 0.5) $ on the transformed tagger discriminant. The error bars represent the statistical uncertainties in observed data. The lower panels display the ratio of data to simulation, with the hatched bands representing the normalized statistical uncertainty of simulated events for each bin. The distributions are based on data and simulated events with the 2018 data-taking conditions, in the jet $ p_{\mathrm{T}} $ range of (450, 500) GeV. |
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Figure 20-a:
An example of the transformed ParticleNet-MD $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ (left) and $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ (right) distribution in data and simulated events, passing the preselection of the $ \mu $-tagged method. The high-purity (HP), medium-purity (MP), and low-purity (LP) working points for the left (right) plot correspond to selections of $ X > 0.6, 0.4, 0.2 (0.85, 0.7, 0.5) $ on the transformed tagger discriminant. The error bars represent the statistical uncertainties in observed data. The lower panels display the ratio of data to simulation, with the hatched bands representing the normalized statistical uncertainty of simulated events for each bin. The distributions are based on data and simulated events with the 2018 data-taking conditions, in the jet $ p_{\mathrm{T}} $ range of (450, 500) GeV. |
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Figure 20-b:
An example of the transformed ParticleNet-MD $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ (left) and $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ (right) distribution in data and simulated events, passing the preselection of the $ \mu $-tagged method. The high-purity (HP), medium-purity (MP), and low-purity (LP) working points for the left (right) plot correspond to selections of $ X > 0.6, 0.4, 0.2 (0.85, 0.7, 0.5) $ on the transformed tagger discriminant. The error bars represent the statistical uncertainties in observed data. The lower panels display the ratio of data to simulation, with the hatched bands representing the normalized statistical uncertainty of simulated events for each bin. The distributions are based on data and simulated events with the 2018 data-taking conditions, in the jet $ p_{\mathrm{T}} $ range of (450, 500) GeV. |
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Figure 21:
An example of the transformed DeepDoubleX $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ (left) and $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ (right) distribution in data and simulated events, passing the preselection of the $ \mu $-tagged method. The high-purity (HP), medium-purity (MP), and low-purity (LP) working points for the left (right) plot correspond to selections of $ X > 0.6, 0.4, 0.2 (0.85, 0.7, 0.5) $ on the transformed tagger discriminant. The error bars represent the statistical uncertainties in observed data. The lower panels display the ratio of data to simulation, with the hatched bands representing the normalized statistical uncertainty of simulated events for each bin. The distributions are based on data and simulated events with the 2018 data-taking conditions, in the jet $ p_{\mathrm{T}} $ range of (450, 500) GeV. |
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Figure 21-a:
An example of the transformed DeepDoubleX $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ (left) and $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ (right) distribution in data and simulated events, passing the preselection of the $ \mu $-tagged method. The high-purity (HP), medium-purity (MP), and low-purity (LP) working points for the left (right) plot correspond to selections of $ X > 0.6, 0.4, 0.2 (0.85, 0.7, 0.5) $ on the transformed tagger discriminant. The error bars represent the statistical uncertainties in observed data. The lower panels display the ratio of data to simulation, with the hatched bands representing the normalized statistical uncertainty of simulated events for each bin. The distributions are based on data and simulated events with the 2018 data-taking conditions, in the jet $ p_{\mathrm{T}} $ range of (450, 500) GeV. |
png pdf |
Figure 21-b:
An example of the transformed DeepDoubleX $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ (left) and $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ (right) distribution in data and simulated events, passing the preselection of the $ \mu $-tagged method. The high-purity (HP), medium-purity (MP), and low-purity (LP) working points for the left (right) plot correspond to selections of $ X > 0.6, 0.4, 0.2 (0.85, 0.7, 0.5) $ on the transformed tagger discriminant. The error bars represent the statistical uncertainties in observed data. The lower panels display the ratio of data to simulation, with the hatched bands representing the normalized statistical uncertainty of simulated events for each bin. The distributions are based on data and simulated events with the 2018 data-taking conditions, in the jet $ p_{\mathrm{T}} $ range of (450, 500) GeV. |
png pdf |
Figure 22:
An example of the transformed DeepAK8-MD $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ (left) and $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ (right) distribution in data and simulated events, passing the preselection of the $ \mu $-tagged method. The high-purity (HP), medium-purity (MP), and low-purity (LP) working points for the left (right) plot correspond to selections of $ X > 0.6, 0.4, 0.2 (0.85, 0.7, 0.5) $ on the transformed tagger discriminant. The error bars represent the statistical uncertainties in observed data. The lower panels display the ratio of data to simulation, with the hatched bands representing the normalized statistical uncertainty of simulated events for each bin. The distributions are based on data and simulated events with the 2018 data-taking conditions, in the jet $ p_{\mathrm{T}} $ range of (450, 500) GeV. |
png pdf |
Figure 22-a:
An example of the transformed DeepAK8-MD $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ (left) and $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ (right) distribution in data and simulated events, passing the preselection of the $ \mu $-tagged method. The high-purity (HP), medium-purity (MP), and low-purity (LP) working points for the left (right) plot correspond to selections of $ X > 0.6, 0.4, 0.2 (0.85, 0.7, 0.5) $ on the transformed tagger discriminant. The error bars represent the statistical uncertainties in observed data. The lower panels display the ratio of data to simulation, with the hatched bands representing the normalized statistical uncertainty of simulated events for each bin. The distributions are based on data and simulated events with the 2018 data-taking conditions, in the jet $ p_{\mathrm{T}} $ range of (450, 500) GeV. |
png pdf |
Figure 22-b:
An example of the transformed DeepAK8-MD $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ (left) and $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ (right) distribution in data and simulated events, passing the preselection of the $ \mu $-tagged method. The high-purity (HP), medium-purity (MP), and low-purity (LP) working points for the left (right) plot correspond to selections of $ X > 0.6, 0.4, 0.2 (0.85, 0.7, 0.5) $ on the transformed tagger discriminant. The error bars represent the statistical uncertainties in observed data. The lower panels display the ratio of data to simulation, with the hatched bands representing the normalized statistical uncertainty of simulated events for each bin. The distributions are based on data and simulated events with the 2018 data-taking conditions, in the jet $ p_{\mathrm{T}} $ range of (450, 500) GeV. |
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Figure 23:
An example of the transformed double-b distribution in data and simulated events, passing the preselection of the $ \mu $-tagged method. The high-purity (HP), medium-purity (MP), and low-purity (LP) working points correspond to selections of $ X > 0.6, 0.4, $ 0.2 on the transformed tagger discriminant. The error bars represent the statistical uncertainties in observed data. The lower panel displays the ratio of data to simulation, with the hatched bands representing the normalized statistical uncertainty of simulated events for each bin. The distribution is based on data and simulated events with the 2018 data-taking conditions, in the jet $ p_{\mathrm{T}} $ range of (450, 500) GeV. |
png pdf |
Figure 24:
Post-fit distributions from the $ \mu $-tagged method for events passing (left) and failing (right) the tagger selection, used in the derivation of the scale factor for the ParticleNet-MD $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ discriminant at the high-purity working point. Error bars represent statistical uncertainties in data, where hatched bands denote the total uncertainties in the simulation. The example corresponds to data and simulated events from the 2018 data-taking conditions, in the jet $ p_{\mathrm{T}} $ range of (450, 500) GeV. |
png pdf |
Figure 24-a:
Post-fit distributions from the $ \mu $-tagged method for events passing (left) and failing (right) the tagger selection, used in the derivation of the scale factor for the ParticleNet-MD $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ discriminant at the high-purity working point. Error bars represent statistical uncertainties in data, where hatched bands denote the total uncertainties in the simulation. The example corresponds to data and simulated events from the 2018 data-taking conditions, in the jet $ p_{\mathrm{T}} $ range of (450, 500) GeV. |
png pdf |
Figure 24-b:
Post-fit distributions from the $ \mu $-tagged method for events passing (left) and failing (right) the tagger selection, used in the derivation of the scale factor for the ParticleNet-MD $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ discriminant at the high-purity working point. Error bars represent statistical uncertainties in data, where hatched bands denote the total uncertainties in the simulation. The example corresponds to data and simulated events from the 2018 data-taking conditions, in the jet $ p_{\mathrm{T}} $ range of (450, 500) GeV. |
png pdf |
Figure 25:
Post-fit distributions from the $ \mu $-tagged method for events passing (left) and failing (right) the tagger selection, used in the derivation of the scale factor for the ParticleNet-MD $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ discriminant at the high-purity working point. Error bars represent statistical uncertainties in data, whereas hatched bands denote the total uncertainties in the simulation. The example corresponds to data and simulated events from the 2018 data-taking conditions, in the jet $ p_{\mathrm{T}} $ range of (450, 500) GeV. |
png pdf |
Figure 25-a:
Post-fit distributions from the $ \mu $-tagged method for events passing (left) and failing (right) the tagger selection, used in the derivation of the scale factor for the ParticleNet-MD $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ discriminant at the high-purity working point. Error bars represent statistical uncertainties in data, whereas hatched bands denote the total uncertainties in the simulation. The example corresponds to data and simulated events from the 2018 data-taking conditions, in the jet $ p_{\mathrm{T}} $ range of (450, 500) GeV. |
png pdf |
Figure 25-b:
Post-fit distributions from the $ \mu $-tagged method for events passing (left) and failing (right) the tagger selection, used in the derivation of the scale factor for the ParticleNet-MD $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ discriminant at the high-purity working point. Error bars represent statistical uncertainties in data, whereas hatched bands denote the total uncertainties in the simulation. The example corresponds to data and simulated events from the 2018 data-taking conditions, in the jet $ p_{\mathrm{T}} $ range of (450, 500) GeV. |
png pdf |
Figure 26:
Post-fit distributions from the boosted Z boson method for events passing (left) and failing (right) the tagger selection, used in the derivation of the scale factor for the ParticleNet-MD $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ discriminant at the high-purity working point. The error bars represent the statistical uncertainties in observed data. The lower panels show the pulls defined as (observed events} - \text{expected events) $ /\sqrt{\smash[b]{\sigma_{\text{obs}}^{2} + \sigma_{\text{exp}}^{2}}} $, where $ \sigma_{\text{obs}} $ and $ \sigma_{\text{exp}} $ are the total uncertainties in the observation and the background estimation, respectively. The example corresponds to data and simulated events from the 2018 data-taking conditions, in the jet $ p_{\mathrm{T}} $ range of (450, 500) GeV. |
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Figure 26-a:
Post-fit distributions from the boosted Z boson method for events passing (left) and failing (right) the tagger selection, used in the derivation of the scale factor for the ParticleNet-MD $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ discriminant at the high-purity working point. The error bars represent the statistical uncertainties in observed data. The lower panels show the pulls defined as (observed events} - \text{expected events) $ /\sqrt{\smash[b]{\sigma_{\text{obs}}^{2} + \sigma_{\text{exp}}^{2}}} $, where $ \sigma_{\text{obs}} $ and $ \sigma_{\text{exp}} $ are the total uncertainties in the observation and the background estimation, respectively. The example corresponds to data and simulated events from the 2018 data-taking conditions, in the jet $ p_{\mathrm{T}} $ range of (450, 500) GeV. |
png pdf |
Figure 26-b:
Post-fit distributions from the boosted Z boson method for events passing (left) and failing (right) the tagger selection, used in the derivation of the scale factor for the ParticleNet-MD $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ discriminant at the high-purity working point. The error bars represent the statistical uncertainties in observed data. The lower panels show the pulls defined as (observed events} - \text{expected events) $ /\sqrt{\smash[b]{\sigma_{\text{obs}}^{2} + \sigma_{\text{exp}}^{2}}} $, where $ \sigma_{\text{obs}} $ and $ \sigma_{\text{exp}} $ are the total uncertainties in the observation and the background estimation, respectively. The example corresponds to data and simulated events from the 2018 data-taking conditions, in the jet $ p_{\mathrm{T}} $ range of (450, 500) GeV. |
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Figure 27:
Receiver operating characteristic (ROC) curve of the ParticleNet-MD $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ discriminant obtained from simulation (blue), under 2018 data-taking conditions with $ p_{\mathrm{T}} > $ 450 GeV. The high-purity (HP), medium-purity (MP), and low-purity (LP) working points are indicated by filled circles for simulation and hollow circles for data. The error bars represent the statistical uncertainties in observed data. |
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Figure 28:
The measured scale factors of the ParticleNet-MD $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ discriminant in the high-purity (left), medium-purity (middle), and low-purity (right) working points. Three methods are presented in the measurements: the sfBDT method, the $ \mu $-tagged method, and the boosted Z boson method. The combined measurements from available methods are also shown. |
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Figure 28-a:
The measured scale factors of the ParticleNet-MD $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ discriminant in the high-purity (left), medium-purity (middle), and low-purity (right) working points. Three methods are presented in the measurements: the sfBDT method, the $ \mu $-tagged method, and the boosted Z boson method. The combined measurements from available methods are also shown. |
png pdf |
Figure 28-b:
The measured scale factors of the ParticleNet-MD $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ discriminant in the high-purity (left), medium-purity (middle), and low-purity (right) working points. Three methods are presented in the measurements: the sfBDT method, the $ \mu $-tagged method, and the boosted Z boson method. The combined measurements from available methods are also shown. |
png pdf |
Figure 28-c:
The measured scale factors of the ParticleNet-MD $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ discriminant in the high-purity (left), medium-purity (middle), and low-purity (right) working points. Three methods are presented in the measurements: the sfBDT method, the $ \mu $-tagged method, and the boosted Z boson method. The combined measurements from available methods are also shown. |
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Figure 29:
The measured scale factors of the DeepDoubleX $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ discriminant in the high-purity (left), medium-purity (middle), and low-purity (right) working points. Three methods are presented in the measurements: the sfBDT method, the $ \mu $-tagged method, and the boosted Z boson method. The combined measurements from available methods are also shown. |
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Figure 29-a:
The measured scale factors of the DeepDoubleX $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ discriminant in the high-purity (left), medium-purity (middle), and low-purity (right) working points. Three methods are presented in the measurements: the sfBDT method, the $ \mu $-tagged method, and the boosted Z boson method. The combined measurements from available methods are also shown. |
png pdf |
Figure 29-b:
The measured scale factors of the DeepDoubleX $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ discriminant in the high-purity (left), medium-purity (middle), and low-purity (right) working points. Three methods are presented in the measurements: the sfBDT method, the $ \mu $-tagged method, and the boosted Z boson method. The combined measurements from available methods are also shown. |
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Figure 29-c:
The measured scale factors of the DeepDoubleX $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ discriminant in the high-purity (left), medium-purity (middle), and low-purity (right) working points. Three methods are presented in the measurements: the sfBDT method, the $ \mu $-tagged method, and the boosted Z boson method. The combined measurements from available methods are also shown. |
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Figure 30:
The measured scale factors of the DeepAK8-MD $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ discriminant in the high-purity (left), medium-purity (middle), and low-purity (right) working points. Two methods are presented in the measurements: the sfBDT method and the $ \mu $-tagged method. The combined measurements from available methods are also shown. |
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Figure 30-a:
The measured scale factors of the DeepAK8-MD $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ discriminant in the high-purity (left), medium-purity (middle), and low-purity (right) working points. Two methods are presented in the measurements: the sfBDT method and the $ \mu $-tagged method. The combined measurements from available methods are also shown. |
png pdf |
Figure 30-b:
The measured scale factors of the DeepAK8-MD $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ discriminant in the high-purity (left), medium-purity (middle), and low-purity (right) working points. Two methods are presented in the measurements: the sfBDT method and the $ \mu $-tagged method. The combined measurements from available methods are also shown. |
png pdf |
Figure 30-c:
The measured scale factors of the DeepAK8-MD $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ discriminant in the high-purity (left), medium-purity (middle), and low-purity (right) working points. Two methods are presented in the measurements: the sfBDT method and the $ \mu $-tagged method. The combined measurements from available methods are also shown. |
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Figure 31:
The measured scale factors of the double-b $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ discriminant in the high-purity (left), medium-purity (middle), and low-purity (right) working points. Three methods are presented in the measurements: the sfBDT method, the $ \mu $-tagged method, and the boosted Z boson method. The combined measurements from available methods are also shown. |
png pdf |
Figure 31-a:
The measured scale factors of the double-b $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ discriminant in the high-purity (left), medium-purity (middle), and low-purity (right) working points. Three methods are presented in the measurements: the sfBDT method, the $ \mu $-tagged method, and the boosted Z boson method. The combined measurements from available methods are also shown. |
png pdf |
Figure 31-b:
The measured scale factors of the double-b $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ discriminant in the high-purity (left), medium-purity (middle), and low-purity (right) working points. Three methods are presented in the measurements: the sfBDT method, the $ \mu $-tagged method, and the boosted Z boson method. The combined measurements from available methods are also shown. |
png pdf |
Figure 31-c:
The measured scale factors of the double-b $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ discriminant in the high-purity (left), medium-purity (middle), and low-purity (right) working points. Three methods are presented in the measurements: the sfBDT method, the $ \mu $-tagged method, and the boosted Z boson method. The combined measurements from available methods are also shown. |
png pdf |
Figure 32:
The measured scale factors of the ParticleNet-MD $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ discriminant in the high-purity (left), medium-purity (middle), and low-purity (right) working points. Two methods are presented in the measurements: the sfBDT method and the $ \mu $-tagged method. The combined measurements from available methods are also shown. |
png pdf |
Figure 32-a:
The measured scale factors of the ParticleNet-MD $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ discriminant in the high-purity (left), medium-purity (middle), and low-purity (right) working points. Two methods are presented in the measurements: the sfBDT method and the $ \mu $-tagged method. The combined measurements from available methods are also shown. |
png pdf |
Figure 32-b:
The measured scale factors of the ParticleNet-MD $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ discriminant in the high-purity (left), medium-purity (middle), and low-purity (right) working points. Two methods are presented in the measurements: the sfBDT method and the $ \mu $-tagged method. The combined measurements from available methods are also shown. |
png pdf |
Figure 32-c:
The measured scale factors of the ParticleNet-MD $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ discriminant in the high-purity (left), medium-purity (middle), and low-purity (right) working points. Two methods are presented in the measurements: the sfBDT method and the $ \mu $-tagged method. The combined measurements from available methods are also shown. |
png pdf |
Figure 33:
The measured scale factors of the DeepDoubleX $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ discriminant in the high-purity (left), medium-purity (middle), and low-purity (right) working points. Two methods are presented in the measurements: the sfBDT method and the $ \mu $-tagged method. The combined measurements from available methods are also shown. |
png pdf |
Figure 33-a:
The measured scale factors of the DeepDoubleX $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ discriminant in the high-purity (left), medium-purity (middle), and low-purity (right) working points. Two methods are presented in the measurements: the sfBDT method and the $ \mu $-tagged method. The combined measurements from available methods are also shown. |
png pdf |
Figure 33-b:
The measured scale factors of the DeepDoubleX $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ discriminant in the high-purity (left), medium-purity (middle), and low-purity (right) working points. Two methods are presented in the measurements: the sfBDT method and the $ \mu $-tagged method. The combined measurements from available methods are also shown. |
png pdf |
Figure 33-c:
The measured scale factors of the DeepDoubleX $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ discriminant in the high-purity (left), medium-purity (middle), and low-purity (right) working points. Two methods are presented in the measurements: the sfBDT method and the $ \mu $-tagged method. The combined measurements from available methods are also shown. |
png pdf |
Figure 34:
The measured scale factors of the DeepAK8-MD $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ discriminant in the high-purity (left), medium-purity (middle), and low-purity (right) working points. Two methods are presented in the measurements: the sfBDT method and the $ \mu $-tagged method. The combined measurements from available methods are also shown. |
png pdf |
Figure 34-a:
The measured scale factors of the DeepAK8-MD $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ discriminant in the high-purity (left), medium-purity (middle), and low-purity (right) working points. Two methods are presented in the measurements: the sfBDT method and the $ \mu $-tagged method. The combined measurements from available methods are also shown. |
png pdf |
Figure 34-b:
The measured scale factors of the DeepAK8-MD $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ discriminant in the high-purity (left), medium-purity (middle), and low-purity (right) working points. Two methods are presented in the measurements: the sfBDT method and the $ \mu $-tagged method. The combined measurements from available methods are also shown. |
png pdf |
Figure 34-c:
The measured scale factors of the DeepAK8-MD $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ discriminant in the high-purity (left), medium-purity (middle), and low-purity (right) working points. Two methods are presented in the measurements: the sfBDT method and the $ \mu $-tagged method. The combined measurements from available methods are also shown. |
| Tables | |
png pdf |
Table 1:
Breakdown of the contributions to the total uncertainty in the fitted scale factor (SF) of the ParticleNet-MD $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ discriminant at the high-purity working point, using the sfBDT method. The numbers are averaged over multiple SF derivation points, including all relevant $ p_{\mathrm{T}} $ bins and data-taking eras. |
png pdf |
Table 2:
Breakdown of the contributions to the total uncertainty in the fitted scale factor (SF) of the ParticleNet-MD $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ discriminant at the high-purity working point, using the $ \mu $-tagged method. The numbers are averaged over multiple SF derivation points, including all relevant $ p_{\mathrm{T}} $ bins and data-taking eras. |
png pdf |
Table 3:
Breakdown of the contributions to the total uncertainty in the fitted scale factor (SF) of the ParticleNet-MD $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ discriminant at the high-purity working point, using the boosted Z boson method. The numbers are averaged over multiple SF derivation points, including all relevant $ p_{\mathrm{T}} $ bins and data-taking eras. |
| Summary |
| This paper presents the performance of heavy-flavour $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ and $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ jet tagging algorithms in the boosted topology, with a focus on the performance of various taggers in simulation and the calibration of tagging efficiencies using data collected by the CMS detector during the 2016-2018 data-taking period (LHC Run 2). With the boosted topology gaining increasing relevance in physics searches during Run 2, the development of dedicated jet-tagging techniques and robust calibration methods for taggers on data has become increasingly important. In this paper, we first provide a complete review and a comparison of $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ and $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ tagging algorithms, which were developed by the CMS Collaboration for analyzing Run 2 data and have been used for various physics measurements. These algorithms include the ParticleNet-MD, DeepDoubleX, DeepAK8-MD, and the double-b tagging algorithms. Three methods for evaluating the performance of the algorithms on data, in terms of deriving the scale factors to correct the selection efficiency of simulated $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ and $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ jets, are presented in detail. The three methods define the proxy jets based on (1) a novel phase space selected from gluon-splitting $ \mathrm{b} \overline{\mathrm{b}} $ and $ \mathrm{c} \overline{\mathrm{c}} $ jets via a dedicated boosted decision tree discriminant; (2) gluon-splitting $ \mathrm{b} \overline{\mathrm{b}} $ and $ \mathrm{c} \overline{\mathrm{c}} $ jets containing a soft muon, with an auxiliary selection on the $ N $-subjettiness variable; and (3) boosted $ \mathrm{Z} \to \mathrm{b} \overline{\mathrm{b}} $ jets for representing the $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ signal jet. The phase space of the selected proxy jets is largely orthogonal across the methods, which enables a meaningful comparison of their calibration results. Scale factors and their uncertainties are derived for all working points of the seven tagging discriminants developed for $ \mathrm{X} \to \mathrm{b} \overline{\mathrm{b}} $ and $ \mathrm{X} \to \mathrm{c} \overline{\mathrm{c}} $ tagging. These scale factors are presented both individually and in a combined form, obtained using the best linear unbiased estimator method. A reasonable agreement is found when comparing the results with previous CMS studies, which calibrated some of the discriminants studied in this work, either partially or under full Run 2 conditions. Additionally, the scale factors presented by the three methods remain consistent within the uncertainty range. Their combination provides the highest measurement precision for the scale factor while also reducing the systematic biases inherent to each individual method. The tagging algorithms and calibration approaches documented in this paper serve as a comprehensive summary and are considered as benchmarks for the techniques adopted by the CMS Collaboration during Run 2. These outcomes will facilitate further in-depth studies and wider experimental explorations of the boosted phase space with heavy-flavour tagging in the future. |
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