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| CMS-EGM-24-002 ; CERN-EP-2026-092 | ||
| Highly boosted dielectron identification in proton-proton collisions at $ \sqrt{s} = $ 13 TeV | ||
| CMS Collaboration | ||
| 14 April 2026 | ||
| Submitted to Physical Review D | ||
| Abstract: A new technique is developed to identify dielectrons ($ \mathrm{e}^+\mathrm{e}^- $) with Lorentz boost $ \gamma_{\mathrm{L}} > $ 20 that produce one single merged cluster in the electromagnetic calorimeter of the CMS detector. The identification uses two multivariate models: one for the case where both electron tracks are reconstructed, and another where only one of the tracks is reconstructed. The efficiency is determined using proton-proton collision data collected at a center-of-mass energy of 13 TeV. Boosted $ \mathrm{J}/\psi $ mesons decaying into $ \mathrm{e}^+\mathrm{e}^- $ pairs are used to estimate the efficiency of the model with two tracks, yielding an overall efficiency of 80%. The $ \mathrm{Z}\to\mu^{+}\mu^{-}\gamma $ events, where the photon converts into a collimated dielectron, are used for the model with a single track, yielding an efficiency of about 60%. A dedicated energy correction for dielectron candidates is also developed using $ {\mathrm{B}^{\pm}}\to\mathrm{J}/\psi\mathrm{K^{\pm}}\to\mathrm{e}^+\mathrm{e}^-\mathrm{K^{\pm}} $ data. | ||
| Links: e-print arXiv:2604.13320 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Visual representations of the variables $ \alpha_{\text{track}} $, $ \Delta u $ and $ \Delta v $. Cyan-colored lines depict the incoming tracks of the dielectron. The black dashed line is used to define the $ u $ and $ v $ directions. The red dashed line represents the $ \mathrm{U}_{5\times5} $ cluster around the closest crystal from the tracks. The cyan-colored star is the log-weighted CoG of the $ \mathrm{U}_{5\times5} $ cluster. |
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Figure 2:
The distribution of the two most contributing variables for the (upper) two-track and (lower) single-track models: (upper left) $ \Delta v/\Delta R $, (upper right) $ \alpha_{\text{track}} $, (lower left) $ E/p $, and (lower right) \dXIn\phi. The signal samples are displayed according to the resonance masses that match the model. The vertical bar and shaded band represent the statistical uncertainty of the data and MC simulation, respectively. Each lined signal histogram is normalized to the background yield. |
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Figure 2-a:
The distribution of the two most contributing variables for the (upper) two-track and (lower) single-track models: (upper left) $ \Delta v/\Delta R $, (upper right) $ \alpha_{\text{track}} $, (lower left) $ E/p $, and (lower right) \dXIn\phi. The signal samples are displayed according to the resonance masses that match the model. The vertical bar and shaded band represent the statistical uncertainty of the data and MC simulation, respectively. Each lined signal histogram is normalized to the background yield. |
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Figure 2-b:
The distribution of the two most contributing variables for the (upper) two-track and (lower) single-track models: (upper left) $ \Delta v/\Delta R $, (upper right) $ \alpha_{\text{track}} $, (lower left) $ E/p $, and (lower right) \dXIn\phi. The signal samples are displayed according to the resonance masses that match the model. The vertical bar and shaded band represent the statistical uncertainty of the data and MC simulation, respectively. Each lined signal histogram is normalized to the background yield. |
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Figure 2-c:
The distribution of the two most contributing variables for the (upper) two-track and (lower) single-track models: (upper left) $ \Delta v/\Delta R $, (upper right) $ \alpha_{\text{track}} $, (lower left) $ E/p $, and (lower right) \dXIn\phi. The signal samples are displayed according to the resonance masses that match the model. The vertical bar and shaded band represent the statistical uncertainty of the data and MC simulation, respectively. Each lined signal histogram is normalized to the background yield. |
png pdf |
Figure 2-d:
The distribution of the two most contributing variables for the (upper) two-track and (lower) single-track models: (upper left) $ \Delta v/\Delta R $, (upper right) $ \alpha_{\text{track}} $, (lower left) $ E/p $, and (lower right) \dXIn\phi. The signal samples are displayed according to the resonance masses that match the model. The vertical bar and shaded band represent the statistical uncertainty of the data and MC simulation, respectively. Each lined signal histogram is normalized to the background yield. |
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Figure 3:
The BDT score distributions of the (left) two-track and (right) single-track models. The signal samples are displayed according to the resonance masses that match the model. The vertical bar and shaded band represent the statistical uncertainty of the data and MC simulation, respectively. Each lined signal histogram is normalized to the background yield. |
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Figure 3-a:
The BDT score distributions of the (left) two-track and (right) single-track models. The signal samples are displayed according to the resonance masses that match the model. The vertical bar and shaded band represent the statistical uncertainty of the data and MC simulation, respectively. Each lined signal histogram is normalized to the background yield. |
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Figure 3-b:
The BDT score distributions of the (left) two-track and (right) single-track models. The signal samples are displayed according to the resonance masses that match the model. The vertical bar and shaded band represent the statistical uncertainty of the data and MC simulation, respectively. Each lined signal histogram is normalized to the background yield. |
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Figure 4:
The signal dielectron selection efficiency as a function of $ \Delta R $. The vertical error bar represents the statistical uncertainty. An equal number of signal events with $ m_{\mathrm{X}} = $ 250, 750, 2000 GeV and $ m_{\mathrm{Y}} = $ 1, 10 GeV are used for each mass point to incorporate dielectrons with various $ \Delta R $. The ID efficiencies include the effects of all prerequisite selections. For instance, the $ \mathrm{e}_{\mathrm{ME}} $ ID efficiency with two tracks (purple) includes the efficiency of the track selection described in Table 1 (yellow). The total dielectron efficiency is a sum of the two-track (purple) and single-track (brown) $ \mathrm{e}_{\mathrm{ME}} $ ID efficiencies, and the standard reconstruction efficiency of two electrons (gray). |
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Figure 5:
The nominal dielectron mass distribution of $ \mathrm{J}/\psi $ candidates in the $ {\mathrm{B}} $ Parking dataset with $ E_{\mathrm{T}}^{5\times5} > $ 30 GeV that pass or fail the two-track $ \mathrm{e}_{\mathrm{ME}} $ ID. The dielectron mass is reconstructed using the tracks of electron candidates. |
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Figure 6:
The efficiency and SF for the two-track model as a function of (left) $ E_{\mathrm{T}}^{5\times5} $ and (right) $ L_{xy} $ with $ E_{\mathrm{T}}^{5\times5} > $ 30 GeV. The vertical bar shows the statistical and systematic uncertainties from the alternative fits, summed in quadrature. The shaded band depicts the $ \mathrm{CI}_{0.95} $. The red and gray dashed lines depict the constant and first-order polynomial fits, respectively. |
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Figure 6-a:
The efficiency and SF for the two-track model as a function of (left) $ E_{\mathrm{T}}^{5\times5} $ and (right) $ L_{xy} $ with $ E_{\mathrm{T}}^{5\times5} > $ 30 GeV. The vertical bar shows the statistical and systematic uncertainties from the alternative fits, summed in quadrature. The shaded band depicts the $ \mathrm{CI}_{0.95} $. The red and gray dashed lines depict the constant and first-order polynomial fits, respectively. |
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Figure 6-b:
The efficiency and SF for the two-track model as a function of (left) $ E_{\mathrm{T}}^{5\times5} $ and (right) $ L_{xy} $ with $ E_{\mathrm{T}}^{5\times5} > $ 30 GeV. The vertical bar shows the statistical and systematic uncertainties from the alternative fits, summed in quadrature. The shaded band depicts the $ \mathrm{CI}_{0.95} $. The red and gray dashed lines depict the constant and first-order polynomial fits, respectively. |
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Figure 7:
The nominal Z boson candidate mass distribution in data using $ \mu^{+}\mu^{-}\gamma $ events with $ E_{\mathrm{T}}^{5\times5} > $ 20 GeV. The passing and failing regions represent the Z boson candidate mass distributions with $ \mathrm{e}_{\mathrm{ME}} $ candidates that pass or fail the $ \mathrm{e}_{\mathrm{ME}} $ ID. |
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Figure 8:
The efficiency and SF as a function of (left) $ E_{\mathrm{T}}^{5\times5} $ and (right) $ d_{0} $ for the single-track model. The vertical bar shows the statistical and systematic uncertainties from the alternative fits, summed in quadrature. The shaded band depicts the $ \mathrm{CI}_{0.95} $. The red and gray dashed lines depict the constant and first-order polynomial fits, respectively. |
png pdf |
Figure 8-a:
The efficiency and SF as a function of (left) $ E_{\mathrm{T}}^{5\times5} $ and (right) $ d_{0} $ for the single-track model. The vertical bar shows the statistical and systematic uncertainties from the alternative fits, summed in quadrature. The shaded band depicts the $ \mathrm{CI}_{0.95} $. The red and gray dashed lines depict the constant and first-order polynomial fits, respectively. |
png pdf |
Figure 8-b:
The efficiency and SF as a function of (left) $ E_{\mathrm{T}}^{5\times5} $ and (right) $ d_{0} $ for the single-track model. The vertical bar shows the statistical and systematic uncertainties from the alternative fits, summed in quadrature. The shaded band depicts the $ \mathrm{CI}_{0.95} $. The red and gray dashed lines depict the constant and first-order polynomial fits, respectively. |
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Figure 9:
The distribution of the invariant mass between the $ \mathrm{U}_{5\times5} $ cluster and the kaon candidate with $ E_{\mathrm{T}}^{5\times5} > $ 30 GeV. The vertical bar shows the statistical uncertainty. The signal (background) contribution is modeled with a Crystal Ball (exponential) function, represented with a red (blue) line. The inset on top right illustrates the mass distribution in a $ {\mathrm{B}^{\pm}}\to\mathrm{J}/\psi\mathrm{K^{\pm}}\to\mathrm{e}^+\mathrm{e}^-\mathrm{K^{\pm}} $ MC sample. |
| Tables | |
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Table 1:
Secondary track selection criteria |
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Table 2:
List of variables used to train the two-track model |
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Table 3:
List of variables used to train the single-track model |
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Table 4:
Selection criteria for the $ \mathrm{J}/\psi\to\mathrm{e}^+\mathrm{e}^- $ control region. |
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Table 5:
Selection criteria for the $ \mathrm{Z}\to\mu^{+}\mu^{-}\gamma $ control region. |
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Table 6:
Selection criteria (in addition to Table 4) for the $ {\mathrm{B}^{\pm}}\to\mathrm{J}/\psi\mathrm{K^{\pm}}\to\mathrm{e}^+\mathrm{e}^-\mathrm{K^{\pm}} $ control region. |
| Summary |
| Theories of beyond the standard model physics predict light bosons that subsequently decay into a dielectron ($ \mathrm{e}^+\mathrm{e}^- $). In such models, the light boson can be significantly boosted, and the standard clustering and reconstruction algorithm may fail to resolve the dielectron. The CMS standard electron reconstruction resolves about 5--40% of $ \mathrm{e}^+\mathrm{e}^- $ pairs when separated by $ \Delta R $ of 0.02--0.04, corresponding to 1--2 Moli\`ere radii, where $ \Delta R $ is defined as $ \Delta R\equiv\sqrt{\smash[b]{(\Delta\eta)^{2}+(\Delta\phi)^{2}}} $. Moreover, high Lorentz boosts can lead to the absence of either of the electron tracks due to shared hits in the inner tracker. Therefore, novel algorithms to identify merged electrons ($ \mathrm{e}_{\mathrm{ME}} $) are developed for the single-track and two-track cases, respectively. The two-track model is trained using a boosted decision tree based on the geometrical compatibility between the merged cluster and the electron tracks. The default clustering algorithm in the electromagnetic calorimeter does not capture all energy deposits from $ \mathrm{e}_{\mathrm{ME}} $ candidates. A cluster consisting of a union of the 5 $ \times $ 5 matrices of lead tungstate crystals around the two electron tracks ($ \mathrm{U}_{5\times5} $) is used to estimate the energy of the $ \mathrm{e}_{\mathrm{ME}} $ instead of the default cluster for the two-track case. The $ \mathrm{U}_{5\times5} $ cluster's energy scale and resolution in data are measured with $ {\mathrm{B}^{\pm}}\to\mathrm{J}/\psi\mathrm{K^{\pm}}\to\mathrm{e}^+\mathrm{e}^-\mathrm{K^{\pm}} $ decays by reconstructing the invariant mass of the $ \mathrm{U}_{5\times5} $ cluster and a track, and found to be consistent with that of the simulation. The two-track model shows about 75% efficiency for the $ \mathrm{e}^+\mathrm{e}^- $ pairs with two reconstructed tracks separated by $ \Delta R\simeq $ 0.01. The efficiency in data is validated using boosted $ \mathrm{J}/\psi $ mesons decaying into $ \mathrm{e}^+\mathrm{e}^- $. The single-track model targets $ \mathrm{e}^+\mathrm{e}^- $ pairs with an extreme Lorentz boost ($ \gamma_{\mathrm{L}} > $ 200), and is mainly based on the ratio between the energy of the merged cluster and the reconstructed electron track. Its efficiency is about 50% for the $ \mathrm{e}^+\mathrm{e}^- $ pairs with a single reconstructed track at $ \Delta R\simeq $ 0.001. The $ \mathrm{Z}\to\mu^{+}\mu^{-}\gamma $ events, where the final-state radiation photon becomes the $ \mathrm{e}^+\mathrm{e}^- $ pair with a single-reconstructed track, are used to assess the efficiency in data, which is found to be 60%. |
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