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| CMS-MLG-23-002 ; CERN-EP-2025-269 | ||
| Machine-learning techniques for model-independent searches in dijet final states | ||
| CMS Collaboration | ||
| 23 December 2025 | ||
| Submitted to Machine Learning: Science and Technology | ||
| Abstract: Anomaly detection methods used in a recent search for new phenomena by CMS at the CERN LHC are presented. The methods use machine learning to detect anomalous jets produced in the decay of new massive particles. The effectiveness of these approaches in enhancing sensitivity to various signals is studied and compared using data collected in proton-proton collisions at a center-of-mass energy of 13 TeV. In an example analysis, the capabilities of anomaly detection methods are further demonstrated by identifying large-radius jets consistent with Lorentz-boosted hadronically decaying top quarks in a model-agnostic framework. | ||
| Links: e-print arXiv:2512.20395 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Diagram of the $ \text{A}\to\text{BC}\to\text{2 jets} $ signal topology targeted in this work. The particle A is produced in a collision between two protons. Reproduced from Ref. [6]. |
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Figure 2:
The VAE architecture used for jet anomaly detection. |
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Figure 3:
Jet $ p_{\mathrm{T}} $ (left) and $ \eta $ (right) distributions before and after resampling jets from the 2 $ < |\Delta\eta_\text{jj}| < $ 2.5 sideband (green) to match the distribution in the signal region (blue). The distributions of resampled jets are shown in orange. Histograms are normalized to unity. The details are given in the text. |
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Figure 3-a:
Jet $ p_{\mathrm{T}} $ (left) and $ \eta $ (right) distributions before and after resampling jets from the 2 $ < |\Delta\eta_\text{jj}| < $ 2.5 sideband (green) to match the distribution in the signal region (blue). The distributions of resampled jets are shown in orange. Histograms are normalized to unity. The details are given in the text. |
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Figure 3-b:
Jet $ p_{\mathrm{T}} $ (left) and $ \eta $ (right) distributions before and after resampling jets from the 2 $ < |\Delta\eta_\text{jj}| < $ 2.5 sideband (green) to match the distribution in the signal region (blue). The distributions of resampled jets are shown in orange. Histograms are normalized to unity. The details are given in the text. |
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Figure 4:
Quality of jet constituent $ p_{\mathrm{T}} $ reconstruction for SM background jets (upper row), jets from a $ \mathrm{W^{'}} \to \mathrm{B}' \mathrm{t} \to \mathrm{b} \mathrm{Z} \mathrm{t} $ decay (middle row), and jets from an $ \mathrm{X}\to \mathrm{Y} \mathrm{Y}' \to 4 \mathrm{q} $ decay (lower row). The first (left column), fourth (middle column), and seventh (right column) constituents are shown. The Pearson correlation coefficient $ R $ between the input and output is also shown. |
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Figure 4-a:
Quality of jet constituent $ p_{\mathrm{T}} $ reconstruction for SM background jets (upper row), jets from a $ \mathrm{W^{'}} \to \mathrm{B}' \mathrm{t} \to \mathrm{b} \mathrm{Z} \mathrm{t} $ decay (middle row), and jets from an $ \mathrm{X}\to \mathrm{Y} \mathrm{Y}' \to 4 \mathrm{q} $ decay (lower row). The first (left column), fourth (middle column), and seventh (right column) constituents are shown. The Pearson correlation coefficient $ R $ between the input and output is also shown. |
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Figure 4-b:
Quality of jet constituent $ p_{\mathrm{T}} $ reconstruction for SM background jets (upper row), jets from a $ \mathrm{W^{'}} \to \mathrm{B}' \mathrm{t} \to \mathrm{b} \mathrm{Z} \mathrm{t} $ decay (middle row), and jets from an $ \mathrm{X}\to \mathrm{Y} \mathrm{Y}' \to 4 \mathrm{q} $ decay (lower row). The first (left column), fourth (middle column), and seventh (right column) constituents are shown. The Pearson correlation coefficient $ R $ between the input and output is also shown. |
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Figure 4-c:
Quality of jet constituent $ p_{\mathrm{T}} $ reconstruction for SM background jets (upper row), jets from a $ \mathrm{W^{'}} \to \mathrm{B}' \mathrm{t} \to \mathrm{b} \mathrm{Z} \mathrm{t} $ decay (middle row), and jets from an $ \mathrm{X}\to \mathrm{Y} \mathrm{Y}' \to 4 \mathrm{q} $ decay (lower row). The first (left column), fourth (middle column), and seventh (right column) constituents are shown. The Pearson correlation coefficient $ R $ between the input and output is also shown. |
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Figure 4-d:
Quality of jet constituent $ p_{\mathrm{T}} $ reconstruction for SM background jets (upper row), jets from a $ \mathrm{W^{'}} \to \mathrm{B}' \mathrm{t} \to \mathrm{b} \mathrm{Z} \mathrm{t} $ decay (middle row), and jets from an $ \mathrm{X}\to \mathrm{Y} \mathrm{Y}' \to 4 \mathrm{q} $ decay (lower row). The first (left column), fourth (middle column), and seventh (right column) constituents are shown. The Pearson correlation coefficient $ R $ between the input and output is also shown. |
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Figure 4-e:
Quality of jet constituent $ p_{\mathrm{T}} $ reconstruction for SM background jets (upper row), jets from a $ \mathrm{W^{'}} \to \mathrm{B}' \mathrm{t} \to \mathrm{b} \mathrm{Z} \mathrm{t} $ decay (middle row), and jets from an $ \mathrm{X}\to \mathrm{Y} \mathrm{Y}' \to 4 \mathrm{q} $ decay (lower row). The first (left column), fourth (middle column), and seventh (right column) constituents are shown. The Pearson correlation coefficient $ R $ between the input and output is also shown. |
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Figure 4-f:
Quality of jet constituent $ p_{\mathrm{T}} $ reconstruction for SM background jets (upper row), jets from a $ \mathrm{W^{'}} \to \mathrm{B}' \mathrm{t} \to \mathrm{b} \mathrm{Z} \mathrm{t} $ decay (middle row), and jets from an $ \mathrm{X}\to \mathrm{Y} \mathrm{Y}' \to 4 \mathrm{q} $ decay (lower row). The first (left column), fourth (middle column), and seventh (right column) constituents are shown. The Pearson correlation coefficient $ R $ between the input and output is also shown. |
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Figure 4-g:
Quality of jet constituent $ p_{\mathrm{T}} $ reconstruction for SM background jets (upper row), jets from a $ \mathrm{W^{'}} \to \mathrm{B}' \mathrm{t} \to \mathrm{b} \mathrm{Z} \mathrm{t} $ decay (middle row), and jets from an $ \mathrm{X}\to \mathrm{Y} \mathrm{Y}' \to 4 \mathrm{q} $ decay (lower row). The first (left column), fourth (middle column), and seventh (right column) constituents are shown. The Pearson correlation coefficient $ R $ between the input and output is also shown. |
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Figure 4-h:
Quality of jet constituent $ p_{\mathrm{T}} $ reconstruction for SM background jets (upper row), jets from a $ \mathrm{W^{'}} \to \mathrm{B}' \mathrm{t} \to \mathrm{b} \mathrm{Z} \mathrm{t} $ decay (middle row), and jets from an $ \mathrm{X}\to \mathrm{Y} \mathrm{Y}' \to 4 \mathrm{q} $ decay (lower row). The first (left column), fourth (middle column), and seventh (right column) constituents are shown. The Pearson correlation coefficient $ R $ between the input and output is also shown. |
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Figure 4-i:
Quality of jet constituent $ p_{\mathrm{T}} $ reconstruction for SM background jets (upper row), jets from a $ \mathrm{W^{'}} \to \mathrm{B}' \mathrm{t} \to \mathrm{b} \mathrm{Z} \mathrm{t} $ decay (middle row), and jets from an $ \mathrm{X}\to \mathrm{Y} \mathrm{Y}' \to 4 \mathrm{q} $ decay (lower row). The first (left column), fourth (middle column), and seventh (right column) constituents are shown. The Pearson correlation coefficient $ R $ between the input and output is also shown. |
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Figure 5:
Simulated dijet invariant mass spectrum after selecting events based on the score of the VAE-QR} method. The distributions are shown in the upper panel for the SM background (blue) and the $ \mathrm{X}\to \mathrm{Y} \mathrm{Y}' \to 4 \mathrm{q} $ signal model with $ m_{\mathrm{X}}= $ 3 TeV and $ m_{\mathrm{Y} }=m_{\mathrm{Y}' }= $ 170 GeV (red). The inclusive selection is compared to the three quantile ranges used in the statistical analysis. No significant difference is observed between the shapes, showing that the quantile regression performs as expected. The lower panel shows the ratio of the quantile ranges to the inclusive distribution for the SM background, scaled by the respective quantile probabilities. |
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Figure 6:
A schematic showing the training algorithm for TNT. The two jets in the event are randomly assigned the labels 1 and 2. The dijet invariant masses and the autoencoder scores are used to construct signal- and background-like subsets of J1 and J2. These subsets are then merged, and a single classifier is trained to distinguish between signal- and background-like jets. |
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Figure 7:
The three main steps of CATHODE. a) Given a signal mass hypothesis, $ m_\mathrm{jj} $ is used to define the signal region in which the signal would be localized. b) A background estimate for the input features $ x $ is obtained from events outside the signal region by training a generative model and interpolating it. c) A weakly supervised classifier is trained to distinguish between the interpolated background and the observed signal region data, singling out any difference between them caused by signal events. |
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Figure 8:
Signal selection efficiency of the weakly supervised classifier in the CATHODE method, evaluated for the $ \mathrm{X}\to \mathrm{Y} \mathrm{Y}' \to 4 \mathrm{q} $ signal at 3 TeV in SR B3. The shaded region represents the total statistical and systematic uncertainty evaluated as described in the text. The uncertainty is largely correlated between the different signal injection points, such that the rise in the signal efficiency is statistically meaningful despite the change over the considered range being smaller than the uncertainty band. |
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Figure 9:
The $ p $-values as a function of the injected signal cross sections for the different analysis procedures for two different signals. The upper panel shows results for the 2-prong $ \mathrm{X}\to \mathrm{Y} \mathrm{Y}' \to 4 \mathrm{q} $ signal with $ m_{\mathrm{X}}= $ 3 TeV and $ m_{\mathrm{Y} }=m_{\mathrm{Y}' }= $ 170 GeV, while the lower panel shows results for the 3-prong $ \mathrm{W^{'}} \to \mathrm{B}' \mathrm{t} \to \mathrm{b} \mathrm{Z} \mathrm{t} $ signal with $ m_\mathrm{W^{'}}= $ 3 TeV and $ m_{\mathrm{B}' }= $ 400 GeV. Significance values larger than 7 standard deviations ($ \sigma $) are denoted with downwards facing triangles. Reproduced from Ref. [6]. |
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Figure 9-a:
The $ p $-values as a function of the injected signal cross sections for the different analysis procedures for two different signals. The upper panel shows results for the 2-prong $ \mathrm{X}\to \mathrm{Y} \mathrm{Y}' \to 4 \mathrm{q} $ signal with $ m_{\mathrm{X}}= $ 3 TeV and $ m_{\mathrm{Y} }=m_{\mathrm{Y}' }= $ 170 GeV, while the lower panel shows results for the 3-prong $ \mathrm{W^{'}} \to \mathrm{B}' \mathrm{t} \to \mathrm{b} \mathrm{Z} \mathrm{t} $ signal with $ m_\mathrm{W^{'}}= $ 3 TeV and $ m_{\mathrm{B}' }= $ 400 GeV. Significance values larger than 7 standard deviations ($ \sigma $) are denoted with downwards facing triangles. Reproduced from Ref. [6]. |
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Figure 9-b:
The $ p $-values as a function of the injected signal cross sections for the different analysis procedures for two different signals. The upper panel shows results for the 2-prong $ \mathrm{X}\to \mathrm{Y} \mathrm{Y}' \to 4 \mathrm{q} $ signal with $ m_{\mathrm{X}}= $ 3 TeV and $ m_{\mathrm{Y} }=m_{\mathrm{Y}' }= $ 170 GeV, while the lower panel shows results for the 3-prong $ \mathrm{W^{'}} \to \mathrm{B}' \mathrm{t} \to \mathrm{b} \mathrm{Z} \mathrm{t} $ signal with $ m_\mathrm{W^{'}}= $ 3 TeV and $ m_{\mathrm{B}' }= $ 400 GeV. Significance values larger than 7 standard deviations ($ \sigma $) are denoted with downwards facing triangles. Reproduced from Ref. [6]. |
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Figure 10:
The $ p $-values as a function of the injected signal cross sections for the different analysis procedures modified to use a common set of input features, for two different signals: (upper) the 2-prong $ \mathrm{X}\to \mathrm{Y} \mathrm{Y}' \to 4 \mathrm{q} $ signal with $ m_{\mathrm{X}}= $ 3 TeV and $ m_{\mathrm{Y} }=m_{\mathrm{Y}' }= $ 170 GeV, and (lower) 3-prong $ \mathrm{W^{'}} \to \mathrm{B}' \mathrm{t} \to \mathrm{b} \mathrm{Z} \mathrm{t} $ signal with $ m_\mathrm{W^{'}}= $ 3 TeV and $ m_{\mathrm{B}' }= $ 400 GeV. Significance values larger than 7 standard deviations ($ \sigma $) are denoted with downwards facing triangles. |
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Figure 10-a:
The $ p $-values as a function of the injected signal cross sections for the different analysis procedures modified to use a common set of input features, for two different signals: (upper) the 2-prong $ \mathrm{X}\to \mathrm{Y} \mathrm{Y}' \to 4 \mathrm{q} $ signal with $ m_{\mathrm{X}}= $ 3 TeV and $ m_{\mathrm{Y} }=m_{\mathrm{Y}' }= $ 170 GeV, and (lower) 3-prong $ \mathrm{W^{'}} \to \mathrm{B}' \mathrm{t} \to \mathrm{b} \mathrm{Z} \mathrm{t} $ signal with $ m_\mathrm{W^{'}}= $ 3 TeV and $ m_{\mathrm{B}' }= $ 400 GeV. Significance values larger than 7 standard deviations ($ \sigma $) are denoted with downwards facing triangles. |
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Figure 10-b:
The $ p $-values as a function of the injected signal cross sections for the different analysis procedures modified to use a common set of input features, for two different signals: (upper) the 2-prong $ \mathrm{X}\to \mathrm{Y} \mathrm{Y}' \to 4 \mathrm{q} $ signal with $ m_{\mathrm{X}}= $ 3 TeV and $ m_{\mathrm{Y} }=m_{\mathrm{Y}' }= $ 170 GeV, and (lower) 3-prong $ \mathrm{W^{'}} \to \mathrm{B}' \mathrm{t} \to \mathrm{b} \mathrm{Z} \mathrm{t} $ signal with $ m_\mathrm{W^{'}}= $ 3 TeV and $ m_{\mathrm{B}' }= $ 400 GeV. Significance values larger than 7 standard deviations ($ \sigma $) are denoted with downwards facing triangles. |
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Figure 11:
Anomaly score correlations of different methods on the background sample. Scores are transformed to follow a normal distribution. The Pearson linear correlation coefficient and distance correlation (DisCo) are listed for each pairing. Details are given in the text. |
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Figure 11-a:
Anomaly score correlations of different methods on the background sample. Scores are transformed to follow a normal distribution. The Pearson linear correlation coefficient and distance correlation (DisCo) are listed for each pairing. Details are given in the text. |
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Figure 11-b:
Anomaly score correlations of different methods on the background sample. Scores are transformed to follow a normal distribution. The Pearson linear correlation coefficient and distance correlation (DisCo) are listed for each pairing. Details are given in the text. |
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Figure 11-c:
Anomaly score correlations of different methods on the background sample. Scores are transformed to follow a normal distribution. The Pearson linear correlation coefficient and distance correlation (DisCo) are listed for each pairing. Details are given in the text. |
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Figure 11-d:
Anomaly score correlations of different methods on the background sample. Scores are transformed to follow a normal distribution. The Pearson linear correlation coefficient and distance correlation (DisCo) are listed for each pairing. Details are given in the text. |
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Figure 12:
Anomaly score correlations of different methods on the $ \mathrm{X}\to \mathrm{Y} \mathrm{Y}' \to 4 \mathrm{q} $ signal model. Scores are transformed to follow a normal distribution. The Pearson linear correlation coefficient and distance correlation (DisCo) are listed for each pairing. Details are given in the text. |
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Figure 12-a:
Anomaly score correlations of different methods on the $ \mathrm{X}\to \mathrm{Y} \mathrm{Y}' \to 4 \mathrm{q} $ signal model. Scores are transformed to follow a normal distribution. The Pearson linear correlation coefficient and distance correlation (DisCo) are listed for each pairing. Details are given in the text. |
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Figure 12-b:
Anomaly score correlations of different methods on the $ \mathrm{X}\to \mathrm{Y} \mathrm{Y}' \to 4 \mathrm{q} $ signal model. Scores are transformed to follow a normal distribution. The Pearson linear correlation coefficient and distance correlation (DisCo) are listed for each pairing. Details are given in the text. |
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Figure 12-c:
Anomaly score correlations of different methods on the $ \mathrm{X}\to \mathrm{Y} \mathrm{Y}' \to 4 \mathrm{q} $ signal model. Scores are transformed to follow a normal distribution. The Pearson linear correlation coefficient and distance correlation (DisCo) are listed for each pairing. Details are given in the text. |
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Figure 12-d:
Anomaly score correlations of different methods on the $ \mathrm{X}\to \mathrm{Y} \mathrm{Y}' \to 4 \mathrm{q} $ signal model. Scores are transformed to follow a normal distribution. The Pearson linear correlation coefficient and distance correlation (DisCo) are listed for each pairing. Details are given in the text. |
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Figure 13:
Anomaly score correlations of different methods on the $ \mathrm{W^{'}} \to \mathrm{B}' \mathrm{t} \to \mathrm{b} \mathrm{Z} \mathrm{t} $ signal model. Scores are transformed to follow a normal distribution. The Pearson linear correlation coefficient and distance correlation (DisCo) are listed for each pairing. Details are given in the text. |
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Figure 13-a:
Anomaly score correlations of different methods on the $ \mathrm{W^{'}} \to \mathrm{B}' \mathrm{t} \to \mathrm{b} \mathrm{Z} \mathrm{t} $ signal model. Scores are transformed to follow a normal distribution. The Pearson linear correlation coefficient and distance correlation (DisCo) are listed for each pairing. Details are given in the text. |
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Figure 13-b:
Anomaly score correlations of different methods on the $ \mathrm{W^{'}} \to \mathrm{B}' \mathrm{t} \to \mathrm{b} \mathrm{Z} \mathrm{t} $ signal model. Scores are transformed to follow a normal distribution. The Pearson linear correlation coefficient and distance correlation (DisCo) are listed for each pairing. Details are given in the text. |
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Figure 13-c:
Anomaly score correlations of different methods on the $ \mathrm{W^{'}} \to \mathrm{B}' \mathrm{t} \to \mathrm{b} \mathrm{Z} \mathrm{t} $ signal model. Scores are transformed to follow a normal distribution. The Pearson linear correlation coefficient and distance correlation (DisCo) are listed for each pairing. Details are given in the text. |
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Figure 13-d:
Anomaly score correlations of different methods on the $ \mathrm{W^{'}} \to \mathrm{B}' \mathrm{t} \to \mathrm{b} \mathrm{Z} \mathrm{t} $ signal model. Scores are transformed to follow a normal distribution. The Pearson linear correlation coefficient and distance correlation (DisCo) are listed for each pairing. Details are given in the text. |
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Figure 14:
Summary plots showing the Pearson correlation coefficient for each pair of anomaly detection algorithms as evaluated on events from the SM backgrounds (upper), $ \mathrm{X}\to \mathrm{Y} \mathrm{Y}' \to 4 \mathrm{q} $ signal (lower left), and $ \mathrm{W^{'}} \to \mathrm{B}' \mathrm{t} \to \mathrm{b} \mathrm{Z} \mathrm{t} $ signal (lower right). In many cases, the correlations are weak, indicating complementarity between the different approaches. |
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Figure 14-a:
Summary plots showing the Pearson correlation coefficient for each pair of anomaly detection algorithms as evaluated on events from the SM backgrounds (upper), $ \mathrm{X}\to \mathrm{Y} \mathrm{Y}' \to 4 \mathrm{q} $ signal (lower left), and $ \mathrm{W^{'}} \to \mathrm{B}' \mathrm{t} \to \mathrm{b} \mathrm{Z} \mathrm{t} $ signal (lower right). In many cases, the correlations are weak, indicating complementarity between the different approaches. |
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Figure 14-b:
Summary plots showing the Pearson correlation coefficient for each pair of anomaly detection algorithms as evaluated on events from the SM backgrounds (upper), $ \mathrm{X}\to \mathrm{Y} \mathrm{Y}' \to 4 \mathrm{q} $ signal (lower left), and $ \mathrm{W^{'}} \to \mathrm{B}' \mathrm{t} \to \mathrm{b} \mathrm{Z} \mathrm{t} $ signal (lower right). In many cases, the correlations are weak, indicating complementarity between the different approaches. |
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Figure 14-c:
Summary plots showing the Pearson correlation coefficient for each pair of anomaly detection algorithms as evaluated on events from the SM backgrounds (upper), $ \mathrm{X}\to \mathrm{Y} \mathrm{Y}' \to 4 \mathrm{q} $ signal (lower left), and $ \mathrm{W^{'}} \to \mathrm{B}' \mathrm{t} \to \mathrm{b} \mathrm{Z} \mathrm{t} $ signal (lower right). In many cases, the correlations are weak, indicating complementarity between the different approaches. |
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Figure 15:
Overlap between the events selected using the anomaly detection methods, for the $ \mathrm{X}\to \mathrm{Y} \mathrm{Y}' \to 4 \mathrm{q} $ (left) and $ \mathrm{W^{'}} \to \mathrm{B}' \mathrm{t} \to \mathrm{b} \mathrm{Z} \mathrm{t} $ (right) signals with a false positive rate of 1%. Each cell corresponds to the fraction of the events selected by the method shown on the horizontal axis that are also selected by the method on the vertical axis. The last column denotes the overall efficiency of selecting signal events for each method. For instance, the CATHODE method selects 50% of all $ \mathrm{X}\to \mathrm{Y} \mathrm{Y}' \to 4 \mathrm{q} $ events. Of those events selected by CATHODE, 46% are also selected by TNT, but only 4% are found by CWoLa Hunting. |
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Figure 15-a:
Overlap between the events selected using the anomaly detection methods, for the $ \mathrm{X}\to \mathrm{Y} \mathrm{Y}' \to 4 \mathrm{q} $ (left) and $ \mathrm{W^{'}} \to \mathrm{B}' \mathrm{t} \to \mathrm{b} \mathrm{Z} \mathrm{t} $ (right) signals with a false positive rate of 1%. Each cell corresponds to the fraction of the events selected by the method shown on the horizontal axis that are also selected by the method on the vertical axis. The last column denotes the overall efficiency of selecting signal events for each method. For instance, the CATHODE method selects 50% of all $ \mathrm{X}\to \mathrm{Y} \mathrm{Y}' \to 4 \mathrm{q} $ events. Of those events selected by CATHODE, 46% are also selected by TNT, but only 4% are found by CWoLa Hunting. |
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Figure 15-b:
Overlap between the events selected using the anomaly detection methods, for the $ \mathrm{X}\to \mathrm{Y} \mathrm{Y}' \to 4 \mathrm{q} $ (left) and $ \mathrm{W^{'}} \to \mathrm{B}' \mathrm{t} \to \mathrm{b} \mathrm{Z} \mathrm{t} $ (right) signals with a false positive rate of 1%. Each cell corresponds to the fraction of the events selected by the method shown on the horizontal axis that are also selected by the method on the vertical axis. The last column denotes the overall efficiency of selecting signal events for each method. For instance, the CATHODE method selects 50% of all $ \mathrm{X}\to \mathrm{Y} \mathrm{Y}' \to 4 \mathrm{q} $ events. Of those events selected by CATHODE, 46% are also selected by TNT, but only 4% are found by CWoLa Hunting. |
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Figure 16:
Significance improvement obtained from supervised classifiers trained using the same inputs as the anomaly detection methods. The left (right) panel shows the 3 (5 TeV) mass point for all signal models. The masses of intermediate decay particles are listed in GeVns. The QUAK method was not tested on all models. |
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Figure 16-a:
Significance improvement obtained from supervised classifiers trained using the same inputs as the anomaly detection methods. The left (right) panel shows the 3 (5 TeV) mass point for all signal models. The masses of intermediate decay particles are listed in GeVns. The QUAK method was not tested on all models. |
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Figure 16-b:
Significance improvement obtained from supervised classifiers trained using the same inputs as the anomaly detection methods. The left (right) panel shows the 3 (5 TeV) mass point for all signal models. The masses of intermediate decay particles are listed in GeVns. The QUAK method was not tested on all models. |
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Figure 17:
Comparison of anomaly detection and supervised classification performance. The factors by which the anomaly detection methods improve the upper limits on the signal cross sections are compared to the SIC of classifiers trained with the same inputs. The 3 TeV mass point is shown for all models. |
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Figure 18:
Distribution of the J1 soft-drop mass after the basic (left) and b-tagged (right) preselections. The black dots represent the data and the colored histograms correspond to simulated events. The b tagging preselection increases the relative contribution of $ \mathrm{t} \overline{\mathrm{t}} $ (red) in the sample, but in both cases the sample is dominated by the QCD multijet background (blue). Other background processes are shown in yellow. |
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Figure 18-a:
Distribution of the J1 soft-drop mass after the basic (left) and b-tagged (right) preselections. The black dots represent the data and the colored histograms correspond to simulated events. The b tagging preselection increases the relative contribution of $ \mathrm{t} \overline{\mathrm{t}} $ (red) in the sample, but in both cases the sample is dominated by the QCD multijet background (blue). Other background processes are shown in yellow. |
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Figure 18-b:
Distribution of the J1 soft-drop mass after the basic (left) and b-tagged (right) preselections. The black dots represent the data and the colored histograms correspond to simulated events. The b tagging preselection increases the relative contribution of $ \mathrm{t} \overline{\mathrm{t}} $ (red) in the sample, but in both cases the sample is dominated by the QCD multijet background (blue). Other background processes are shown in yellow. |
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Figure 19:
Post-fit plots of the fail (left) and pass (right) regions for the $ \mathrm{t} \overline{\mathrm{t}} $ extraction procedure performed for the 65-150 (upper), 105-220 (middle), and 145-250 GeV (lower) signal windows. Data (black points with error bars) is compared to the fitted estimates of the QCD multijet (blue), Z+jets (orange), W+jets (purple), and $ \mathrm{t} \overline{\mathrm{t}} $ (red) processes. The lower panel shows the ratio between the observed data points and the fitted estimates. The gray shading denotes the systematic uncertainty. The contribution from $ \mathrm{t} \overline{\mathrm{t}} $ is clearly visible in the pass region of the 105-220 and 145-250 GeV signal windows. |
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Figure 19-a:
Post-fit plots of the fail (left) and pass (right) regions for the $ \mathrm{t} \overline{\mathrm{t}} $ extraction procedure performed for the 65-150 (upper), 105-220 (middle), and 145-250 GeV (lower) signal windows. Data (black points with error bars) is compared to the fitted estimates of the QCD multijet (blue), Z+jets (orange), W+jets (purple), and $ \mathrm{t} \overline{\mathrm{t}} $ (red) processes. The lower panel shows the ratio between the observed data points and the fitted estimates. The gray shading denotes the systematic uncertainty. The contribution from $ \mathrm{t} \overline{\mathrm{t}} $ is clearly visible in the pass region of the 105-220 and 145-250 GeV signal windows. |
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Figure 19-b:
Post-fit plots of the fail (left) and pass (right) regions for the $ \mathrm{t} \overline{\mathrm{t}} $ extraction procedure performed for the 65-150 (upper), 105-220 (middle), and 145-250 GeV (lower) signal windows. Data (black points with error bars) is compared to the fitted estimates of the QCD multijet (blue), Z+jets (orange), W+jets (purple), and $ \mathrm{t} \overline{\mathrm{t}} $ (red) processes. The lower panel shows the ratio between the observed data points and the fitted estimates. The gray shading denotes the systematic uncertainty. The contribution from $ \mathrm{t} \overline{\mathrm{t}} $ is clearly visible in the pass region of the 105-220 and 145-250 GeV signal windows. |
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Figure 19-c:
Post-fit plots of the fail (left) and pass (right) regions for the $ \mathrm{t} \overline{\mathrm{t}} $ extraction procedure performed for the 65-150 (upper), 105-220 (middle), and 145-250 GeV (lower) signal windows. Data (black points with error bars) is compared to the fitted estimates of the QCD multijet (blue), Z+jets (orange), W+jets (purple), and $ \mathrm{t} \overline{\mathrm{t}} $ (red) processes. The lower panel shows the ratio between the observed data points and the fitted estimates. The gray shading denotes the systematic uncertainty. The contribution from $ \mathrm{t} \overline{\mathrm{t}} $ is clearly visible in the pass region of the 105-220 and 145-250 GeV signal windows. |
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Figure 19-d:
Post-fit plots of the fail (left) and pass (right) regions for the $ \mathrm{t} \overline{\mathrm{t}} $ extraction procedure performed for the 65-150 (upper), 105-220 (middle), and 145-250 GeV (lower) signal windows. Data (black points with error bars) is compared to the fitted estimates of the QCD multijet (blue), Z+jets (orange), W+jets (purple), and $ \mathrm{t} \overline{\mathrm{t}} $ (red) processes. The lower panel shows the ratio between the observed data points and the fitted estimates. The gray shading denotes the systematic uncertainty. The contribution from $ \mathrm{t} \overline{\mathrm{t}} $ is clearly visible in the pass region of the 105-220 and 145-250 GeV signal windows. |
png pdf |
Figure 19-e:
Post-fit plots of the fail (left) and pass (right) regions for the $ \mathrm{t} \overline{\mathrm{t}} $ extraction procedure performed for the 65-150 (upper), 105-220 (middle), and 145-250 GeV (lower) signal windows. Data (black points with error bars) is compared to the fitted estimates of the QCD multijet (blue), Z+jets (orange), W+jets (purple), and $ \mathrm{t} \overline{\mathrm{t}} $ (red) processes. The lower panel shows the ratio between the observed data points and the fitted estimates. The gray shading denotes the systematic uncertainty. The contribution from $ \mathrm{t} \overline{\mathrm{t}} $ is clearly visible in the pass region of the 105-220 and 145-250 GeV signal windows. |
png pdf |
Figure 19-f:
Post-fit plots of the fail (left) and pass (right) regions for the $ \mathrm{t} \overline{\mathrm{t}} $ extraction procedure performed for the 65-150 (upper), 105-220 (middle), and 145-250 GeV (lower) signal windows. Data (black points with error bars) is compared to the fitted estimates of the QCD multijet (blue), Z+jets (orange), W+jets (purple), and $ \mathrm{t} \overline{\mathrm{t}} $ (red) processes. The lower panel shows the ratio between the observed data points and the fitted estimates. The gray shading denotes the systematic uncertainty. The contribution from $ \mathrm{t} \overline{\mathrm{t}} $ is clearly visible in the pass region of the 105-220 and 145-250 GeV signal windows. |
png pdf |
Figure 20:
A comparison of the top quark identification performance of classifiers trained in different ways, evaluated in simulation. The two models trained in the 145-250 GeV mass window (red and yellow), as well as the one trained using the b tagging preselection in the in the 105-220 GeV mass window (blue), nearly match the performance of a supervised classifier (gray). The classifier trained with the baseline preselection in the 105-220 GeV mass window (purple) exhibits an improvement that is smaller than the others, yet larger than one. |
png pdf |
Figure 21:
Excess characterization for the weakly supervised anomaly detection strategy applied to the $ \mathrm{t} \overline{\mathrm{t}} $ region with the b tagging preselection. The sensitivity of the anomaly score to the different input observables is assessed to aid in the determination of the properties of the excess. The jet mass, b tagging score, and $ \tau_{32} $ are seen to be the most important observables, consistent with the properties of large-radius top quark jets. |
png pdf |
Figure 22:
Excess characterization for the weakly supervised anomaly detection strategy applied to the $ \mathrm{t} \overline{\mathrm{t}} $ region with the b tagging preselection. The plots compare the properties of the jets with the highest anomaly score (red) to those for all jets in the region of the excess (blue). The variables shown are the soft-drop mass $ m_\mathrm{SD} $ (upper left), the number of jet constituents $ n_\mathrm{PF} $ (upper right), the DEEPCSV score (middle left), and the three subjettiness ratios $ \tau_{21} $ (middle right), $ \tau_{32} $ (lower left), and $ \tau_{43} $ (lower right). The three-pronged nature of the signal is clear from the low $ \tau_{32} $ scores, the presence of b tags from the high DEEPCSV score, and the jet mass ($ m_\mathrm{SD} $) distribution peaking at 175 GeV indicates the top quark mass. |
png pdf |
Figure 22-a:
Excess characterization for the weakly supervised anomaly detection strategy applied to the $ \mathrm{t} \overline{\mathrm{t}} $ region with the b tagging preselection. The plots compare the properties of the jets with the highest anomaly score (red) to those for all jets in the region of the excess (blue). The variables shown are the soft-drop mass $ m_\mathrm{SD} $ (upper left), the number of jet constituents $ n_\mathrm{PF} $ (upper right), the DEEPCSV score (middle left), and the three subjettiness ratios $ \tau_{21} $ (middle right), $ \tau_{32} $ (lower left), and $ \tau_{43} $ (lower right). The three-pronged nature of the signal is clear from the low $ \tau_{32} $ scores, the presence of b tags from the high DEEPCSV score, and the jet mass ($ m_\mathrm{SD} $) distribution peaking at 175 GeV indicates the top quark mass. |
png pdf |
Figure 22-b:
Excess characterization for the weakly supervised anomaly detection strategy applied to the $ \mathrm{t} \overline{\mathrm{t}} $ region with the b tagging preselection. The plots compare the properties of the jets with the highest anomaly score (red) to those for all jets in the region of the excess (blue). The variables shown are the soft-drop mass $ m_\mathrm{SD} $ (upper left), the number of jet constituents $ n_\mathrm{PF} $ (upper right), the DEEPCSV score (middle left), and the three subjettiness ratios $ \tau_{21} $ (middle right), $ \tau_{32} $ (lower left), and $ \tau_{43} $ (lower right). The three-pronged nature of the signal is clear from the low $ \tau_{32} $ scores, the presence of b tags from the high DEEPCSV score, and the jet mass ($ m_\mathrm{SD} $) distribution peaking at 175 GeV indicates the top quark mass. |
png pdf |
Figure 22-c:
Excess characterization for the weakly supervised anomaly detection strategy applied to the $ \mathrm{t} \overline{\mathrm{t}} $ region with the b tagging preselection. The plots compare the properties of the jets with the highest anomaly score (red) to those for all jets in the region of the excess (blue). The variables shown are the soft-drop mass $ m_\mathrm{SD} $ (upper left), the number of jet constituents $ n_\mathrm{PF} $ (upper right), the DEEPCSV score (middle left), and the three subjettiness ratios $ \tau_{21} $ (middle right), $ \tau_{32} $ (lower left), and $ \tau_{43} $ (lower right). The three-pronged nature of the signal is clear from the low $ \tau_{32} $ scores, the presence of b tags from the high DEEPCSV score, and the jet mass ($ m_\mathrm{SD} $) distribution peaking at 175 GeV indicates the top quark mass. |
png pdf |
Figure 22-d:
Excess characterization for the weakly supervised anomaly detection strategy applied to the $ \mathrm{t} \overline{\mathrm{t}} $ region with the b tagging preselection. The plots compare the properties of the jets with the highest anomaly score (red) to those for all jets in the region of the excess (blue). The variables shown are the soft-drop mass $ m_\mathrm{SD} $ (upper left), the number of jet constituents $ n_\mathrm{PF} $ (upper right), the DEEPCSV score (middle left), and the three subjettiness ratios $ \tau_{21} $ (middle right), $ \tau_{32} $ (lower left), and $ \tau_{43} $ (lower right). The three-pronged nature of the signal is clear from the low $ \tau_{32} $ scores, the presence of b tags from the high DEEPCSV score, and the jet mass ($ m_\mathrm{SD} $) distribution peaking at 175 GeV indicates the top quark mass. |
png pdf |
Figure 22-e:
Excess characterization for the weakly supervised anomaly detection strategy applied to the $ \mathrm{t} \overline{\mathrm{t}} $ region with the b tagging preselection. The plots compare the properties of the jets with the highest anomaly score (red) to those for all jets in the region of the excess (blue). The variables shown are the soft-drop mass $ m_\mathrm{SD} $ (upper left), the number of jet constituents $ n_\mathrm{PF} $ (upper right), the DEEPCSV score (middle left), and the three subjettiness ratios $ \tau_{21} $ (middle right), $ \tau_{32} $ (lower left), and $ \tau_{43} $ (lower right). The three-pronged nature of the signal is clear from the low $ \tau_{32} $ scores, the presence of b tags from the high DEEPCSV score, and the jet mass ($ m_\mathrm{SD} $) distribution peaking at 175 GeV indicates the top quark mass. |
png pdf |
Figure 22-f:
Excess characterization for the weakly supervised anomaly detection strategy applied to the $ \mathrm{t} \overline{\mathrm{t}} $ region with the b tagging preselection. The plots compare the properties of the jets with the highest anomaly score (red) to those for all jets in the region of the excess (blue). The variables shown are the soft-drop mass $ m_\mathrm{SD} $ (upper left), the number of jet constituents $ n_\mathrm{PF} $ (upper right), the DEEPCSV score (middle left), and the three subjettiness ratios $ \tau_{21} $ (middle right), $ \tau_{32} $ (lower left), and $ \tau_{43} $ (lower right). The three-pronged nature of the signal is clear from the low $ \tau_{32} $ scores, the presence of b tags from the high DEEPCSV score, and the jet mass ($ m_\mathrm{SD} $) distribution peaking at 175 GeV indicates the top quark mass. |
| Tables | |
png pdf |
Table 1:
Signal processes considered in the analysis, categorized according to the number of partons produced in the decay of each jet. |
png pdf |
Table 2:
Summary of the methods used in this paper. The type column distinguishes between unsupervised (Uns.), weakly supervised (Weak.), and semi-supervised (Semi.) methods. Depending on the method, the ML models use single jets or complete dijet events as inputs. We also list the input features and types of ML models used, with the following abbreviations: ``AE'' for autoencoders, ``VAE'' for variational autoencoders, ``DNN'' for fully connected deep neural networks, and ``NF'' for normalizing flows. The two variants of CATHODE are shown separately. Details are given in the text. |
png pdf |
Table 3:
Mass regions used by the weakly supervised methods and corresponding observed number of events. Signal regions are required to have sideband mass regions on either side for reliable background estimation. This means only the A1-A6 and B1-B6 regions are used to seek signals, with the A0, B0, A7, and B7 regions used solely as sideband control regions. |
png pdf |
Table 4:
Signal models used to train the six signal normalizing flows used in the QUAK method. Each flow uses signals with specific masses for the daughter particles B and C. For signals decaying to an SM and a BSM particle, the BSM particle is always the heavier of the two. |
| Summary |
| We have presented a detailed description of the five anomaly detection methods used to search for new particles decaying to two anomalous jets in Ref. [6], using data collected by CMS between 2016 and 2018. Approaches based on weakly supervised, unsupervised, and semi-supervised training paradigms have been explored. All methods were successfully able to identify some classes of anomalous jets as distinct from standard model backgrounds, and were therefore able to enhance the sensitivity to the signatures of new particles in CMS data in a model-agnostic fashion. The sensitivity of the methods to the presence of an anomalous signal in the data has been shown to be higher than an inclusive search or simple selections based on jet substructure. The performance of the five methods has been found to depend on the considered signal model, with no single method outperforming all others. Further investigation has shown that correlations between the anomaly scores are low, indicating that methods identify anomalous signal events in different ways. Furthermore, the impact of differences in the input features has been explored and shown to explain performance differences between signal models, but not between methods. Finally, a weakly supervised anomaly detection method has been used to separate top quark jets from jets produced in other standard model processes. The achieved separation power comes very close to that of a fully supervised classifier trained with the same input variables. This constitutes a validation of resonant anomaly detection in collider data. In addition, interpretation techniques have been used to successfully retrieve some of the main properties of the top quark. This would enable further investigation and confirmation of the signal in the event of a positive result from an anomaly search. |
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