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| CMS-PAS-JME-25-001 | ||
| Particle transformers for identifying Lorentz-boosted Higgs bosons decaying to a pair of W bosons | ||
| CMS Collaboration | ||
| 2025-08-03 | ||
| Abstract: A novel deep neural network classifier, the "particle transformer" (ParT), is introduced for the identification of highly Lorentz-boosted, multi-pronged jets in measurements and searches performed with the CMS detector at the LHC. Based on a self-attention mechanism that allows the model to weigh the importance of different particles, ParT is trained on a wide variety of topologies, notably demonstrating strong performance for the first time on jets originating from boosted Higgs boson decays to W bosons. The ParT algorithm achieves a tagging efficiency of $ {>}$50% for such jets at a QCD multijet background efficiency of 1%, while maintaining decorrelation from the jet mass. This performance is calibrated in data collected by CMS from proton-proton collisions at 13 TeV center-of-mass energy, with a dataset corresponding to a total luminosity of 138 fb$ ^{-1} $, using the primary Lund jet planes of individual subjets. Data-to-simulation selection efficiency scale factors are measured to be in the 0.9-1 range, with relative uncertainties ranging between 7 and 23%. | ||
| Links: CDS record (PDF) ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Diagram of the ParT model architecture. The model processes three different sets of input features per jet, from charged PF candidates, neutral PF candidates, and SVs. These features are embedded using separate MLPs into 128-dimensional representations before being concatenated and passed through eight PABs. Pairwise features are also calculated between each input element, which are embedded using one-dimensional convolutional layers and used as attention biases for each PAB. Two CABs then use the learned features to update a randomly initialized class token, which aggregates these features into a global representation of the jet. Their output is then finally passed through an MLP that outputs the class probabilities, which are normalized by a softmax function, as well as the jet mass. |
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Figure 2:
Full suite of AK8 jet topologies used for the ParT model training. Jet types are first categorized by the number of quarks and leptons in the final state, and then further separated by flavor, as shown in the table on the left. The total number of subclasses for each process, therefore, is given by the tensor product ($ \otimes $) between the different final states and flavors. Diagrams illustrating the corresponding jet topologies are shown on the right. |
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Figure 3:
Evolution of the loss function values for the ParT model on the training and validation datasets over training epochs, shown separately for the classification (cross-entropy) and regression (log-cosh) terms. |
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Figure 4:
Comparison of jet mass reconstruction ($ {m_\mathrm{reco}} $) using the SD, ParticleNet, and ParT algorithms, for $ \mathrm{H}\to\mathrm{b}\overline{\mathrm{b}} $ (upper left), $ \mathrm{H}\to\mathrm{W}\mathrm{W} $ (upper right), $ \mathrm{t}\to\mathrm{b}\mathrm{q}\overline{\mathrm{q}} $(lower left), and QCD (lower right) jets with SM $ {m_\mathrm{H}} $ and $ {m_\mathrm{t}} $. An offline selection is applied to the AK8 jets of $ p_{\mathrm{T}} > $ 400 GeV and $ |\eta| < $ 2.4. Statistical uncertainties in the bin yields originating from the limited number of simulated events are represented by vertical error bars. The mass at the peak ($ {m_\text{peak}} $) for each algorithm, calculated using Gaussian kernel density estimation, and the mass resolution, quantified by the FWHM of the resonance peak, are shown as well for H and t jets. |
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Figure 4-a:
Comparison of jet mass reconstruction ($ {m_\mathrm{reco}} $) using the SD, ParticleNet, and ParT algorithms, for $ \mathrm{H}\to\mathrm{b}\overline{\mathrm{b}} $ (upper left), $ \mathrm{H}\to\mathrm{W}\mathrm{W} $ (upper right), $ \mathrm{t}\to\mathrm{b}\mathrm{q}\overline{\mathrm{q}} $(lower left), and QCD (lower right) jets with SM $ {m_\mathrm{H}} $ and $ {m_\mathrm{t}} $. An offline selection is applied to the AK8 jets of $ p_{\mathrm{T}} > $ 400 GeV and $ |\eta| < $ 2.4. Statistical uncertainties in the bin yields originating from the limited number of simulated events are represented by vertical error bars. The mass at the peak ($ {m_\text{peak}} $) for each algorithm, calculated using Gaussian kernel density estimation, and the mass resolution, quantified by the FWHM of the resonance peak, are shown as well for H and t jets. |
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Figure 4-b:
Comparison of jet mass reconstruction ($ {m_\mathrm{reco}} $) using the SD, ParticleNet, and ParT algorithms, for $ \mathrm{H}\to\mathrm{b}\overline{\mathrm{b}} $ (upper left), $ \mathrm{H}\to\mathrm{W}\mathrm{W} $ (upper right), $ \mathrm{t}\to\mathrm{b}\mathrm{q}\overline{\mathrm{q}} $(lower left), and QCD (lower right) jets with SM $ {m_\mathrm{H}} $ and $ {m_\mathrm{t}} $. An offline selection is applied to the AK8 jets of $ p_{\mathrm{T}} > $ 400 GeV and $ |\eta| < $ 2.4. Statistical uncertainties in the bin yields originating from the limited number of simulated events are represented by vertical error bars. The mass at the peak ($ {m_\text{peak}} $) for each algorithm, calculated using Gaussian kernel density estimation, and the mass resolution, quantified by the FWHM of the resonance peak, are shown as well for H and t jets. |
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Figure 4-c:
Comparison of jet mass reconstruction ($ {m_\mathrm{reco}} $) using the SD, ParticleNet, and ParT algorithms, for $ \mathrm{H}\to\mathrm{b}\overline{\mathrm{b}} $ (upper left), $ \mathrm{H}\to\mathrm{W}\mathrm{W} $ (upper right), $ \mathrm{t}\to\mathrm{b}\mathrm{q}\overline{\mathrm{q}} $(lower left), and QCD (lower right) jets with SM $ {m_\mathrm{H}} $ and $ {m_\mathrm{t}} $. An offline selection is applied to the AK8 jets of $ p_{\mathrm{T}} > $ 400 GeV and $ |\eta| < $ 2.4. Statistical uncertainties in the bin yields originating from the limited number of simulated events are represented by vertical error bars. The mass at the peak ($ {m_\text{peak}} $) for each algorithm, calculated using Gaussian kernel density estimation, and the mass resolution, quantified by the FWHM of the resonance peak, are shown as well for H and t jets. |
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Figure 4-d:
Comparison of jet mass reconstruction ($ {m_\mathrm{reco}} $) using the SD, ParticleNet, and ParT algorithms, for $ \mathrm{H}\to\mathrm{b}\overline{\mathrm{b}} $ (upper left), $ \mathrm{H}\to\mathrm{W}\mathrm{W} $ (upper right), $ \mathrm{t}\to\mathrm{b}\mathrm{q}\overline{\mathrm{q}} $(lower left), and QCD (lower right) jets with SM $ {m_\mathrm{H}} $ and $ {m_\mathrm{t}} $. An offline selection is applied to the AK8 jets of $ p_{\mathrm{T}} > $ 400 GeV and $ |\eta| < $ 2.4. Statistical uncertainties in the bin yields originating from the limited number of simulated events are represented by vertical error bars. The mass at the peak ($ {m_\text{peak}} $) for each algorithm, calculated using Gaussian kernel density estimation, and the mass resolution, quantified by the FWHM of the resonance peak, are shown as well for H and t jets. |
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Figure 5:
Receiver operating characteristic curves for $ \mathrm{H}\to\mathrm{W}\mathrm{W} $ signal jets, with SM $ {m_\mathrm{H}} $, versus background jets from simulated QCD multijet (left) and $ \mathrm{t} \overline{\mathrm{t}} $ events (right), for the ParT $T_{\text{HWW}}$ and the DeepAK8-MD scores in the $ p_{\mathrm{T}} $ ranges 200-400, 400-600, and 600-1000 GeV. An offline selection is applied to the AK8 jets of $ p_{\mathrm{T}} > $ 200 GeV and $ |\eta| < $ 2.4. Signal jets are required to contain all four generator-level quarks from the W boson decays within $ \Delta R $ (jet},\,\mathrm{q) $ < $ 0.8. |
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Figure 5-a:
Receiver operating characteristic curves for $ \mathrm{H}\to\mathrm{W}\mathrm{W} $ signal jets, with SM $ {m_\mathrm{H}} $, versus background jets from simulated QCD multijet (left) and $ \mathrm{t} \overline{\mathrm{t}} $ events (right), for the ParT $T_{\text{HWW}}$ and the DeepAK8-MD scores in the $ p_{\mathrm{T}} $ ranges 200-400, 400-600, and 600-1000 GeV. An offline selection is applied to the AK8 jets of $ p_{\mathrm{T}} > $ 200 GeV and $ |\eta| < $ 2.4. Signal jets are required to contain all four generator-level quarks from the W boson decays within $ \Delta R $ (jet},\,\mathrm{q) $ < $ 0.8. |
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Figure 5-b:
Receiver operating characteristic curves for $ \mathrm{H}\to\mathrm{W}\mathrm{W} $ signal jets, with SM $ {m_\mathrm{H}} $, versus background jets from simulated QCD multijet (left) and $ \mathrm{t} \overline{\mathrm{t}} $ events (right), for the ParT $T_{\text{HWW}}$ and the DeepAK8-MD scores in the $ p_{\mathrm{T}} $ ranges 200-400, 400-600, and 600-1000 GeV. An offline selection is applied to the AK8 jets of $ p_{\mathrm{T}} > $ 200 GeV and $ |\eta| < $ 2.4. Signal jets are required to contain all four generator-level quarks from the W boson decays within $ \Delta R $ (jet},\,\mathrm{q) $ < $ 0.8. |
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Figure 6:
Receiver operating characteristic curves for $ \mathrm{Y}\to\mathrm{W}\mathrm{W} $ signal jets, with varying $ {m_\mathrm{Y}} $ and SM $ {m_\mathrm{W}} $, versus background jets from simulated QCD multijet (left) and $ \mathrm{t} \overline{\mathrm{t}} $ events (right), for the ParT $T_{\text{HWW}}$ score. An offline selection is applied to the AK8 jets of 600 $ < p_{\mathrm{T}} < $ 1000 GeV, $ |\eta| < $ 2.4, and $ {m_\mathrm{SD}} > $ 30 GeV. |
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Figure 6-a:
Receiver operating characteristic curves for $ \mathrm{Y}\to\mathrm{W}\mathrm{W} $ signal jets, with varying $ {m_\mathrm{Y}} $ and SM $ {m_\mathrm{W}} $, versus background jets from simulated QCD multijet (left) and $ \mathrm{t} \overline{\mathrm{t}} $ events (right), for the ParT $T_{\text{HWW}}$ score. An offline selection is applied to the AK8 jets of 600 $ < p_{\mathrm{T}} < $ 1000 GeV, $ |\eta| < $ 2.4, and $ {m_\mathrm{SD}} > $ 30 GeV. |
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Figure 6-b:
Receiver operating characteristic curves for $ \mathrm{Y}\to\mathrm{W}\mathrm{W} $ signal jets, with varying $ {m_\mathrm{Y}} $ and SM $ {m_\mathrm{W}} $, versus background jets from simulated QCD multijet (left) and $ \mathrm{t} \overline{\mathrm{t}} $ events (right), for the ParT $T_{\text{HWW}}$ score. An offline selection is applied to the AK8 jets of 600 $ < p_{\mathrm{T}} < $ 1000 GeV, $ |\eta| < $ 2.4, and $ {m_\mathrm{SD}} > $ 30 GeV. |
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Figure 7:
Error matrix with each row indicating the fraction of jets per category classified as the column category by PART. An offline selection is applied to the AK8 jets of $ p_{\mathrm{T}} > $ 200 GeV and $ |\eta| < $ 2.4. |
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Figure 8:
Distributions of $ {m_\mathrm{SD}} $ for jets from QCD multijet events, in the $ p_{\mathrm{T}} $ ranges 200-400 GeV (top), 400-600 GeV (middle) and 600-1000 GeV (bottom), after no selections (``inclusive'') on the ParT $T_{\text{HWW}}$ score (left) and the DeepAK8-MD score (right) as well as selections corresponding to QCD jet selection efficiencies ($ \epsilon_B $) of 5.0%, 1.0%, and 0.5%. The lower panels display the ratio of the normalized $ {m_\mathrm{SD}} $ distributions for the different selection efficiencies (N(mistag)) to the normalized inclusive $ {m_\mathrm{SD}} $ distribution (N(inclusive)). An offline selection is applied to the AK8 jets of $ p_{\mathrm{T}} > $ 400 GeV, $ |\eta| < $ 2.4, and $ {m_\mathrm{SD}} > $ 30 GeV. |
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Figure 8-a:
Distributions of $ {m_\mathrm{SD}} $ for jets from QCD multijet events, in the $ p_{\mathrm{T}} $ ranges 200-400 GeV (top), 400-600 GeV (middle) and 600-1000 GeV (bottom), after no selections (``inclusive'') on the ParT $T_{\text{HWW}}$ score (left) and the DeepAK8-MD score (right) as well as selections corresponding to QCD jet selection efficiencies ($ \epsilon_B $) of 5.0%, 1.0%, and 0.5%. The lower panels display the ratio of the normalized $ {m_\mathrm{SD}} $ distributions for the different selection efficiencies (N(mistag)) to the normalized inclusive $ {m_\mathrm{SD}} $ distribution (N(inclusive)). An offline selection is applied to the AK8 jets of $ p_{\mathrm{T}} > $ 400 GeV, $ |\eta| < $ 2.4, and $ {m_\mathrm{SD}} > $ 30 GeV. |
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Figure 8-b:
Distributions of $ {m_\mathrm{SD}} $ for jets from QCD multijet events, in the $ p_{\mathrm{T}} $ ranges 200-400 GeV (top), 400-600 GeV (middle) and 600-1000 GeV (bottom), after no selections (``inclusive'') on the ParT $T_{\text{HWW}}$ score (left) and the DeepAK8-MD score (right) as well as selections corresponding to QCD jet selection efficiencies ($ \epsilon_B $) of 5.0%, 1.0%, and 0.5%. The lower panels display the ratio of the normalized $ {m_\mathrm{SD}} $ distributions for the different selection efficiencies (N(mistag)) to the normalized inclusive $ {m_\mathrm{SD}} $ distribution (N(inclusive)). An offline selection is applied to the AK8 jets of $ p_{\mathrm{T}} > $ 400 GeV, $ |\eta| < $ 2.4, and $ {m_\mathrm{SD}} > $ 30 GeV. |
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Figure 8-c:
Distributions of $ {m_\mathrm{SD}} $ for jets from QCD multijet events, in the $ p_{\mathrm{T}} $ ranges 200-400 GeV (top), 400-600 GeV (middle) and 600-1000 GeV (bottom), after no selections (``inclusive'') on the ParT $T_{\text{HWW}}$ score (left) and the DeepAK8-MD score (right) as well as selections corresponding to QCD jet selection efficiencies ($ \epsilon_B $) of 5.0%, 1.0%, and 0.5%. The lower panels display the ratio of the normalized $ {m_\mathrm{SD}} $ distributions for the different selection efficiencies (N(mistag)) to the normalized inclusive $ {m_\mathrm{SD}} $ distribution (N(inclusive)). An offline selection is applied to the AK8 jets of $ p_{\mathrm{T}} > $ 400 GeV, $ |\eta| < $ 2.4, and $ {m_\mathrm{SD}} > $ 30 GeV. |
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Figure 8-d:
Distributions of $ {m_\mathrm{SD}} $ for jets from QCD multijet events, in the $ p_{\mathrm{T}} $ ranges 200-400 GeV (top), 400-600 GeV (middle) and 600-1000 GeV (bottom), after no selections (``inclusive'') on the ParT $T_{\text{HWW}}$ score (left) and the DeepAK8-MD score (right) as well as selections corresponding to QCD jet selection efficiencies ($ \epsilon_B $) of 5.0%, 1.0%, and 0.5%. The lower panels display the ratio of the normalized $ {m_\mathrm{SD}} $ distributions for the different selection efficiencies (N(mistag)) to the normalized inclusive $ {m_\mathrm{SD}} $ distribution (N(inclusive)). An offline selection is applied to the AK8 jets of $ p_{\mathrm{T}} > $ 400 GeV, $ |\eta| < $ 2.4, and $ {m_\mathrm{SD}} > $ 30 GeV. |
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Figure 8-e:
Distributions of $ {m_\mathrm{SD}} $ for jets from QCD multijet events, in the $ p_{\mathrm{T}} $ ranges 200-400 GeV (top), 400-600 GeV (middle) and 600-1000 GeV (bottom), after no selections (``inclusive'') on the ParT $T_{\text{HWW}}$ score (left) and the DeepAK8-MD score (right) as well as selections corresponding to QCD jet selection efficiencies ($ \epsilon_B $) of 5.0%, 1.0%, and 0.5%. The lower panels display the ratio of the normalized $ {m_\mathrm{SD}} $ distributions for the different selection efficiencies (N(mistag)) to the normalized inclusive $ {m_\mathrm{SD}} $ distribution (N(inclusive)). An offline selection is applied to the AK8 jets of $ p_{\mathrm{T}} > $ 400 GeV, $ |\eta| < $ 2.4, and $ {m_\mathrm{SD}} > $ 30 GeV. |
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Figure 8-f:
Distributions of $ {m_\mathrm{SD}} $ for jets from QCD multijet events, in the $ p_{\mathrm{T}} $ ranges 200-400 GeV (top), 400-600 GeV (middle) and 600-1000 GeV (bottom), after no selections (``inclusive'') on the ParT $T_{\text{HWW}}$ score (left) and the DeepAK8-MD score (right) as well as selections corresponding to QCD jet selection efficiencies ($ \epsilon_B $) of 5.0%, 1.0%, and 0.5%. The lower panels display the ratio of the normalized $ {m_\mathrm{SD}} $ distributions for the different selection efficiencies (N(mistag)) to the normalized inclusive $ {m_\mathrm{SD}} $ distribution (N(inclusive)). An offline selection is applied to the AK8 jets of $ p_{\mathrm{T}} > $ 400 GeV, $ |\eta| < $ 2.4, and $ {m_\mathrm{SD}} > $ 30 GeV. |
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Figure 9:
The Jensen-Shannon divergence (JSD) between the $ {m_\mathrm{SD}} $ distribution of jets from QCD multijet events with and without a selection on the ParT and DeepAK8-MD tagger scores. On the left, the JSD is plotted for tagger selections corresponding to different QCD jet selection efficiencies ($ {\epsilon_\mathrm{B}} $), with an offline selection of 600 $ < p_{\mathrm{T}} < $ 1000 GeV, $ |\eta| < $ 2.4, and 30 $ < {m_\mathrm{SD}} < $ 250 GeV applied to the jets. On the right, the JSD is plotted for different jet $ p_{\mathrm{T}} $ bins, at a fixed $ {\epsilon_\mathrm{B}} $ of 1%. |
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Figure 9-a:
The Jensen-Shannon divergence (JSD) between the $ {m_\mathrm{SD}} $ distribution of jets from QCD multijet events with and without a selection on the ParT and DeepAK8-MD tagger scores. On the left, the JSD is plotted for tagger selections corresponding to different QCD jet selection efficiencies ($ {\epsilon_\mathrm{B}} $), with an offline selection of 600 $ < p_{\mathrm{T}} < $ 1000 GeV, $ |\eta| < $ 2.4, and 30 $ < {m_\mathrm{SD}} < $ 250 GeV applied to the jets. On the right, the JSD is plotted for different jet $ p_{\mathrm{T}} $ bins, at a fixed $ {\epsilon_\mathrm{B}} $ of 1%. |
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Figure 9-b:
The Jensen-Shannon divergence (JSD) between the $ {m_\mathrm{SD}} $ distribution of jets from QCD multijet events with and without a selection on the ParT and DeepAK8-MD tagger scores. On the left, the JSD is plotted for tagger selections corresponding to different QCD jet selection efficiencies ($ {\epsilon_\mathrm{B}} $), with an offline selection of 600 $ < p_{\mathrm{T}} < $ 1000 GeV, $ |\eta| < $ 2.4, and 30 $ < {m_\mathrm{SD}} < $ 250 GeV applied to the jets. On the right, the JSD is plotted for different jet $ p_{\mathrm{T}} $ bins, at a fixed $ {\epsilon_\mathrm{B}} $ of 1%. |
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Figure 10:
Schematic of the LJP calibration method for $ \mathrm{H}\to\mathrm{W}\mathrm{W} $ tagging. Ratios of primary LJP densities in data and simulation are first measured per subjet in merged two-pronged W jets, with an example of such a ratio reproduced from Ref. [26]. These are then used to derive correction factors $ \mathrm{H}\to\mathrm{W}\mathrm{W} $ signal jets per prong. |
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Figure 11:
Distributions of the ParT $T_{\text{HWW}}^{\text{no top}}$ (left) and DeepAK8-MD (No top) (right) discriminants with and without the LJP corrections for top-matched jets for data and individual simulated processes in the top panels, and data versus simulation ratios in the bottom panels. The combined uncertainties from LJP-based SFs per bin are shown in shaded gray, and the statistical uncertainty in the number of data events per bin is represented by vertical error bars in the top and bottom panels. The $ \chi^2 $ test statistic values between data and simulation, normalized to the number of degrees of freedom (ndof), are also shown for both discriminants with and without LJP corrections. |
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Figure 11-a:
Distributions of the ParT $T_{\text{HWW}}^{\text{no top}}$ (left) and DeepAK8-MD (No top) (right) discriminants with and without the LJP corrections for top-matched jets for data and individual simulated processes in the top panels, and data versus simulation ratios in the bottom panels. The combined uncertainties from LJP-based SFs per bin are shown in shaded gray, and the statistical uncertainty in the number of data events per bin is represented by vertical error bars in the top and bottom panels. The $ \chi^2 $ test statistic values between data and simulation, normalized to the number of degrees of freedom (ndof), are also shown for both discriminants with and without LJP corrections. |
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Figure 11-b:
Distributions of the ParT $T_{\text{HWW}}^{\text{no top}}$ (left) and DeepAK8-MD (No top) (right) discriminants with and without the LJP corrections for top-matched jets for data and individual simulated processes in the top panels, and data versus simulation ratios in the bottom panels. The combined uncertainties from LJP-based SFs per bin are shown in shaded gray, and the statistical uncertainty in the number of data events per bin is represented by vertical error bars in the top and bottom panels. The $ \chi^2 $ test statistic values between data and simulation, normalized to the number of degrees of freedom (ndof), are also shown for both discriminants with and without LJP corrections. |
| Tables | |
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Table 1:
Summary of particle masses in the ParT training samples. |
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Table 2:
The complete set of input features per AK8 jet used for the ParT model training. Three types of inputs are considered: charged PF candidates, neutral PF candidates, and secondary vertices (SVs). |
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Table 3:
Relative weights of each of the classes used for training the ParT model. Each of the four major processes: $ \mathrm{H}\to\mathrm{W}\mathrm{W} $, $ \mathrm{H}\to $ 2-pronged, $ \mathrm{t}\to\mathrm{b}\mathrm{W} $, and QCD jets, are weighted equally and have one row dedicated to them each. |
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Table 4:
Signal efficiency SFs and uncertainties for BDT selections on the ParT ${\mathrm{H}\to\mathrm{W}\mathrm{W}}$ tagging outputs for the $ {\mathrm{H}\mathrm{H}\to\mathrm{b}\overline{\mathrm{b}}\mathrm{W}\mathrm{W}} $ search, measured using the LJP calibration method for different $ {\mathrm{H}\mathrm{H}} $ signals and analysis regions. Both the total combined uncertainty and the components defined in the text are shown. |
| Summary |
| The particle transformer (ParT) deep neural network for classifying a wide variety of Lorentz-boosted jet topologies has been presented. In particular, ParT enables effective identification of all-hadronic Higgs boson to vector boson ($ \mathrm{H}\to\mathrm{W}\mathrm{W} $) decays by the CMS experiment for the first time. A novel training strategy is used to address challenges pertaining to $ \mathrm{H}\to\mathrm{W}\mathrm{W} $ classification, through which ParT achieves $ > $50% $ \mathrm{H}\to\mathrm{W}\mathrm{W} $ selection efficiency for a QCD multijet background efficiency of 1%, while maintaining decorrelation with the jet mass. The performance is calibrated on data using the primary Lund jet planes of individual subjets, with data-to-simulation scale factors measured in the 0.9-1 range, and relative uncertainties between 7 and 23%. The ParT algorithm represents a significant advancement in CMS' boosted jet identification capabilities, illustrated in the first search for boosted H pair production in the all-hadronic $ \mathrm{b}\overline{\mathrm{b}}\mathrm{W}\mathrm{W} $ channel. |
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