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CMS-EXO-22-015 ; CERN-EP-2024-049
Search for new physics with emerging jets in proton-proton collisions at $ \sqrt{s} = $ 13 TeV
Accepted for publication in J. High Energy Phys.
Abstract: A search for ``emerging jets'' produced in proton-proton collisions at a center-of-mass energy of 13 TeV is performed using data collected by the CMS experiment corresponding to an integrated luminosity of 138 fb$ ^{-1} $. This search examines a hypothetical dark quantum chromodynamics (QCD) sector that couples to the standard model (SM) through a scalar mediator. The scalar mediator decays into an SM quark and a dark sector quark. As the dark sector quark showers and hadronizes, it produces long-lived dark mesons that subsequently decay into SM particles, resulting in a jet, known as an emerging jet, with multiple displaced vertices. This search looks for pair production of the scalar mediator at the LHC, which yields events with two SM jets and two emerging jets at leading order. The results are interpreted using two dark sector models with different flavor structures, and exclude mediator masses up to 1950 (1850) GeV for an unflavored (flavor-aligned) dark QCD model. The unflavored results surpass a previous search for emerging jets by setting the most stringent mediator mass exclusion limits to date, while the flavor-aligned results provide the first direct mediator mass exclusion limits to date.
Figures & Tables Summary Additional Figures & Tables References CMS Publications
Figures

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Figure 1:
Feynman diagrams for pair production of dark mediator particles via gluon-gluon fusion (left) and quark-antiquark annihilation (right), with each mediator decaying to an SM quark and a dark quark.

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Figure 1-a:
Feynman diagrams for pair production of dark mediator particles via gluon-gluon fusion (left) and quark-antiquark annihilation (right), with each mediator decaying to an SM quark and a dark quark.

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Figure 1-b:
Feynman diagrams for pair production of dark mediator particles via gluon-gluon fusion (left) and quark-antiquark annihilation (right), with each mediator decaying to an SM quark and a dark quark.

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Figure 2:
Distributions of the jet variables $ \langle {d_{xy}} \rangle $ (left) and $ \alpha_\text{3D} $ with $ D_{N}^\text{max}= $ 4 (right) used for the model-agnostic EJ tagging that targets the unflavored dark sector models are shown for data (points), SM multijet simulation (gray line), and signal jets in simulation (colored lines). The sums of the entries are normalized to unity.

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Figure 2-a:
Distributions of the jet variables $ \langle {d_{xy}} \rangle $ (left) and $ \alpha_\text{3D} $ with $ D_{N}^\text{max}= $ 4 (right) used for the model-agnostic EJ tagging that targets the unflavored dark sector models are shown for data (points), SM multijet simulation (gray line), and signal jets in simulation (colored lines). The sums of the entries are normalized to unity.

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Figure 2-b:
Distributions of the jet variables $ \langle {d_{xy}} \rangle $ (left) and $ \alpha_\text{3D} $ with $ D_{N}^\text{max}= $ 4 (right) used for the model-agnostic EJ tagging that targets the unflavored dark sector models are shown for data (points), SM multijet simulation (gray line), and signal jets in simulation (colored lines). The sums of the entries are normalized to unity.

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Figure 3:
Distributions of the jet variables used for the model-agnostic EJ tagging targeting flavor-aligned dark sector models for jets obtained in data (points), SM multijet simulation (gray line), and simulated signal jets (colored lines). The distribution of the number of tracks with $ d_{xy} > $ 10$^{-2.2}$ cm (jet girth) is shown on the left (right). The sums of the entries are normalized to unity.

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Figure 3-a:
Distributions of the jet variables used for the model-agnostic EJ tagging targeting flavor-aligned dark sector models for jets obtained in data (points), SM multijet simulation (gray line), and simulated signal jets (colored lines). The distribution of the number of tracks with $ d_{xy} > $ 10$^{-2.2}$ cm (jet girth) is shown on the left (right). The sums of the entries are normalized to unity.

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Figure 3-b:
Distributions of the jet variables used for the model-agnostic EJ tagging targeting flavor-aligned dark sector models for jets obtained in data (points), SM multijet simulation (gray line), and simulated signal jets (colored lines). The distribution of the number of tracks with $ d_{xy} > $ 10$^{-2.2}$ cm (jet girth) is shown on the left (right). The sums of the entries are normalized to unity.

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Figure 4:
Distributions of the output score of the uGNN (left) and aGNN (right) for the data (points with error bars), SM multijet simulation (dark gray line), and signal simulation (colored lines). The signal distributions in the left (right) plot are generated from the unflavored (flavor-aligned) model. Bins are chosen to correspond to the jet selection criteria defined in Table 5. The sums of the entries are normalized to unity.

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Figure 4-a:
Distributions of the output score of the uGNN (left) and aGNN (right) for the data (points with error bars), SM multijet simulation (dark gray line), and signal simulation (colored lines). The signal distributions in the left (right) plot are generated from the unflavored (flavor-aligned) model. Bins are chosen to correspond to the jet selection criteria defined in Table 5. The sums of the entries are normalized to unity.

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Figure 4-b:
Distributions of the output score of the uGNN (left) and aGNN (right) for the data (points with error bars), SM multijet simulation (dark gray line), and signal simulation (colored lines). The signal distributions in the left (right) plot are generated from the unflavored (flavor-aligned) model. Bins are chosen to correspond to the jet selection criteria defined in Table 5. The sums of the entries are normalized to unity.

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Figure 5:
Template fit of the DEEPJET discriminator used to determine the b jet fraction of the non-EJ tagged jets for data events that pass the ``u-set validation'' selection criteria, except with the requirement on the number of EJ-tagged jets changed from 2 to 1. The lower panel shows the ratio of the number of jets in the data compared to the sum of the fitted template distributions.

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Figure 6:
The EJ tagger misidentification probability for b quark jets (red, orange) and light jets (light blue, dark blue) as a function of jet $ p_{\mathrm{T}} $ for the model-agnostic tagger ``u-tag 1'' (left) and the ML-based tagger ``uGNN tag 1'' (right), as defined in Tables 3 and 5, evaluated using data (red, dark blue) and generator-level flavor information from simulated samples (orange, light blue) in events containing a high-$ p_{\mathrm{T}} $ photon. The lower panel shows the pull, defined as the difference between the mistag rate calculated in simulation and mistag rate measured in data divided by the uncertainty measured in data.

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Figure 6-a:
The EJ tagger misidentification probability for b quark jets (red, orange) and light jets (light blue, dark blue) as a function of jet $ p_{\mathrm{T}} $ for the model-agnostic tagger ``u-tag 1'' (left) and the ML-based tagger ``uGNN tag 1'' (right), as defined in Tables 3 and 5, evaluated using data (red, dark blue) and generator-level flavor information from simulated samples (orange, light blue) in events containing a high-$ p_{\mathrm{T}} $ photon. The lower panel shows the pull, defined as the difference between the mistag rate calculated in simulation and mistag rate measured in data divided by the uncertainty measured in data.

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Figure 6-b:
The EJ tagger misidentification probability for b quark jets (red, orange) and light jets (light blue, dark blue) as a function of jet $ p_{\mathrm{T}} $ for the model-agnostic tagger ``u-tag 1'' (left) and the ML-based tagger ``uGNN tag 1'' (right), as defined in Tables 3 and 5, evaluated using data (red, dark blue) and generator-level flavor information from simulated samples (orange, light blue) in events containing a high-$ p_{\mathrm{T}} $ photon. The lower panel shows the pull, defined as the difference between the mistag rate calculated in simulation and mistag rate measured in data divided by the uncertainty measured in data.

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Figure 7:
The 95% CL upper limits on the production cross section for various signal models in the unflavored scenario (upper plots) and the flavor-aligned scenario (lower plots) with $ m_{\pi_{\text{dark}}}= $ 10 GeV using the model-agnostic (GNN) EJ tagging method, on the left (right). The red curve is the expected exclusion limit, with the band representing its 68% CL variation. The black curve is the observed limit. The dark blue dotted curves in the upper plots are the expected and observed limits previously obtained by CMS [20].

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Figure 7-a:
The 95% CL upper limits on the production cross section for various signal models in the unflavored scenario (upper plots) and the flavor-aligned scenario (lower plots) with $ m_{\pi_{\text{dark}}}= $ 10 GeV using the model-agnostic (GNN) EJ tagging method, on the left (right). The red curve is the expected exclusion limit, with the band representing its 68% CL variation. The black curve is the observed limit. The dark blue dotted curves in the upper plots are the expected and observed limits previously obtained by CMS [20].

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Figure 7-b:
The 95% CL upper limits on the production cross section for various signal models in the unflavored scenario (upper plots) and the flavor-aligned scenario (lower plots) with $ m_{\pi_{\text{dark}}}= $ 10 GeV using the model-agnostic (GNN) EJ tagging method, on the left (right). The red curve is the expected exclusion limit, with the band representing its 68% CL variation. The black curve is the observed limit. The dark blue dotted curves in the upper plots are the expected and observed limits previously obtained by CMS [20].

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Figure 7-c:
The 95% CL upper limits on the production cross section for various signal models in the unflavored scenario (upper plots) and the flavor-aligned scenario (lower plots) with $ m_{\pi_{\text{dark}}}= $ 10 GeV using the model-agnostic (GNN) EJ tagging method, on the left (right). The red curve is the expected exclusion limit, with the band representing its 68% CL variation. The black curve is the observed limit. The dark blue dotted curves in the upper plots are the expected and observed limits previously obtained by CMS [20].

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Figure 7-d:
The 95% CL upper limits on the production cross section for various signal models in the unflavored scenario (upper plots) and the flavor-aligned scenario (lower plots) with $ m_{\pi_{\text{dark}}}= $ 10 GeV using the model-agnostic (GNN) EJ tagging method, on the left (right). The red curve is the expected exclusion limit, with the band representing its 68% CL variation. The black curve is the observed limit. The dark blue dotted curves in the upper plots are the expected and observed limits previously obtained by CMS [20].

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Figure 8:
The 95% CL upper limits on the production cross section for various signal models in the unflavored scenario (upper plots) and the flavor-aligned scenario (lower plots) with $ m_{\pi_{\text{dark}}}= $ 20 GeV using the model-agnostic (GNN) EJ tagging method, on the left (right). The red curve is the expected exclusion limit, with the band representing its 68% CL variation. The black curve is the observed limit.

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Figure 8-a:
The 95% CL upper limits on the production cross section for various signal models in the unflavored scenario (upper plots) and the flavor-aligned scenario (lower plots) with $ m_{\pi_{\text{dark}}}= $ 20 GeV using the model-agnostic (GNN) EJ tagging method, on the left (right). The red curve is the expected exclusion limit, with the band representing its 68% CL variation. The black curve is the observed limit.

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Figure 8-b:
The 95% CL upper limits on the production cross section for various signal models in the unflavored scenario (upper plots) and the flavor-aligned scenario (lower plots) with $ m_{\pi_{\text{dark}}}= $ 20 GeV using the model-agnostic (GNN) EJ tagging method, on the left (right). The red curve is the expected exclusion limit, with the band representing its 68% CL variation. The black curve is the observed limit.

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Figure 8-c:
The 95% CL upper limits on the production cross section for various signal models in the unflavored scenario (upper plots) and the flavor-aligned scenario (lower plots) with $ m_{\pi_{\text{dark}}}= $ 20 GeV using the model-agnostic (GNN) EJ tagging method, on the left (right). The red curve is the expected exclusion limit, with the band representing its 68% CL variation. The black curve is the observed limit.

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Figure 8-d:
The 95% CL upper limits on the production cross section for various signal models in the unflavored scenario (upper plots) and the flavor-aligned scenario (lower plots) with $ m_{\pi_{\text{dark}}}= $ 20 GeV using the model-agnostic (GNN) EJ tagging method, on the left (right). The red curve is the expected exclusion limit, with the band representing its 68% CL variation. The black curve is the observed limit.

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Figure 9:
The 95% CL upper limits on the production cross section for various signal models in the flavor-aligned scenario with $ m_{\pi_{\text{dark}}}= $ 6 GeV using the model-agnostic (GNN) EJ tagging method, on the left (right). The red curve is the expected exclusion limit, with the band representing its 68% CL variation. The black curve is the observed limit.

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Figure 9-a:
The 95% CL upper limits on the production cross section for various signal models in the flavor-aligned scenario with $ m_{\pi_{\text{dark}}}= $ 6 GeV using the model-agnostic (GNN) EJ tagging method, on the left (right). The red curve is the expected exclusion limit, with the band representing its 68% CL variation. The black curve is the observed limit.

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Figure 9-b:
The 95% CL upper limits on the production cross section for various signal models in the flavor-aligned scenario with $ m_{\pi_{\text{dark}}}= $ 6 GeV using the model-agnostic (GNN) EJ tagging method, on the left (right). The red curve is the expected exclusion limit, with the band representing its 68% CL variation. The black curve is the observed limit.
Tables

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Table 1:
Model parameters for the unflavored model.

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Table 2:
Parameters used for the flavor-aligned model. In order to probe a range of lifetimes, the values of $ \kappa_0 $ listed in columns 3--7 are tuned to give the desired $ c\tau_{\pi_{\text{dark}}}^{\text{max}} $ values of 5, 25, 45, 100, and 500 mm. In addition, samples were made with fixed $ \kappa_0= $ 1, with a resultant value of $ c\tau_{\pi_{\text{dark}}}^{\text{max}} $ that depends on the other model parameters.

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Table 3:
Emerging jet selection criteria for the model-agnostic analysis designed for the unflavored scenario. The validation regions are discussed in Section 5.4. The symbols in parentheses indicate a minimum ($> $) or maximum ($<$) requirement.

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Table 4:
Emerging jet selection criteria for the model-agnostic analysis designed for the flavor-aligned scenario. The validation tag is described in Section 5.4. The symbols in parentheses indicate a minimum ($> $) or maximum ($<$) requirement.

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Table 5:
The GNN score range used to identify a jet as an EJ. The uGNN (aGNN) tag indicates that the tagger uses the output score of the GNN trained on the unflavored (flavor-aligned) simulated signal samples. The validation tags are described in Section 5.4.

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Table 6:
Event selection criteria used for the analysis. The validation selection criteria are described in Section 5.4.

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Table 7:
The observed yield of events in data satisfying the validation selection criteria with at least two jets passing the corresponding validation tag, and the estimation based on the misidentification rate calculated using validation events with exactly one jet passing the validation tagger scaled by the factor given in Eq. (4). The statistical and systematic uncertainties are reported for the estimated yields.

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Table 8:
Mean and standard deviation (std.) of the relative uncertainty calculated on the unflavored and flavor-aligned samples, by source, in percent.

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Table 9:
The estimated number of events from the background prediction based on control samples in data and the observed event yields. Statistical and systematic uncertainties in the estimated background are provided.
Summary
A search for emerging jet signatures arising from a strongly interacting dark sector produced in proton-proton collisions has been presented, using data corresponding to an integrated luminosity of 138 fb$ ^{-1} $ at $ \sqrt{s}= $ 13 TeV. The signal model contains a family of dark quarks that couple to the standard model (SM) quarks via a scalar mediator $ \text{X}_{\text{dark}} $. Dark pions ($ \pi_{\text{dark}} $) with a significant lifetime ($ c\tau_{\pi_{\text{dark}}} $) are produced by the hadronization of the dark quarks; these then decay to SM particles at vertices displaced from the proton-proton interaction point. As the scalar mediator is assumed to be produced in pairs, and each decays to an SM quark and a dark quark, the signature of this process is two SM jets plus two jets of particles with constituents emerging from displaced vertices. Both unflavored and flavor-aligned couplings between the SM quarks and the dark quarks are examined in the search. Events are selected using either a traditional cut-based approach or a graph neural network to identify emerging jets, in combination with other event-level selection criteria. The overall selection requirements are optimized for each coupling scenario and for different combinations of the mediator particle mass, dark pion mass, and dark pion lifetime. No excess of events beyond the SM expectations is found, and the observed 95% confidence level exclusion limits agree with the expected limits. For the unflavored model, dark mediator masses $ m_{\text{X}_{\text{dark}}} < $ 1950 GeV are excluded for $ c\tau_{\pi_{\text{dark}}}\approx$ 100 mm and $ m_{\pi_{\text{dark}}}= $ 10 GeV, while the flavor-aligned model result excludes $ m_{\text{X}_{\text{dark}}} < $ 1850 GeV at $ c\tau_{\pi_{\text{dark}}}^{\text{max}}\approx$ 500 mm for $ m_{\pi_{\text{dark}}}= $ 10 GeV. This result surpasses the previous search for emerging jets in the unflavored scenario, increasing the experimental limit of the dark mediator particle by $ {\approx} $ 500 GeV to set the most stringent limits to date, and provides the first direct exclusion of the flavor-aligned scenario.
Additional Figures

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Additional Figure 1:
Example of $ H_{\mathrm{T}} $ distribution of events in CMS data (points), SM multijet events from simulation (gray line), and various signal samples with varying dark mediator masses (colored lines) for events that pass the trigger requirements and also have 4 jets with $ p_{\mathrm{T}} > $ 100 GeV. The distribution from various processes have their total event count normalized to 1.

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Additional Figure 2:
Example of jet $ p_{\mathrm{T}} $ distributions of events in CMS data (points), SM multijet events from simulation (gray line), and various signal samples with varying dark mediator masses (colored lines) for events that pass the trigger requirements and also have 4 jets with $ p_{\mathrm{T}} > $ 100 GeV. The leading jet $ p_{\mathrm{T}} $ distribution is shown in the top right plot, the second leading jet $ p_{\mathrm{T}} $ in the top left, the third leading jet $ p_{\mathrm{T}} $ in the bottom left, and the forth leading jet $ p_{\mathrm{T}} $ in the bottom right. The distribution from various processes have their total event count normalized to 1.

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Additional Figure 2-a:
Example of jet $ p_{\mathrm{T}} $ distributions of events in CMS data (points), SM multijet events from simulation (gray line), and various signal samples with varying dark mediator masses (colored lines) for events that pass the trigger requirements and also have 4 jets with $ p_{\mathrm{T}} > $ 100 GeV. The leading jet $ p_{\mathrm{T}} $ distribution is shown in the top right plot, the second leading jet $ p_{\mathrm{T}} $ in the top left, the third leading jet $ p_{\mathrm{T}} $ in the bottom left, and the forth leading jet $ p_{\mathrm{T}} $ in the bottom right. The distribution from various processes have their total event count normalized to 1.

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Additional Figure 2-b:
Example of jet $ p_{\mathrm{T}} $ distributions of events in CMS data (points), SM multijet events from simulation (gray line), and various signal samples with varying dark mediator masses (colored lines) for events that pass the trigger requirements and also have 4 jets with $ p_{\mathrm{T}} > $ 100 GeV. The leading jet $ p_{\mathrm{T}} $ distribution is shown in the top right plot, the second leading jet $ p_{\mathrm{T}} $ in the top left, the third leading jet $ p_{\mathrm{T}} $ in the bottom left, and the forth leading jet $ p_{\mathrm{T}} $ in the bottom right. The distribution from various processes have their total event count normalized to 1.

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Additional Figure 2-c:
Example of jet $ p_{\mathrm{T}} $ distributions of events in CMS data (points), SM multijet events from simulation (gray line), and various signal samples with varying dark mediator masses (colored lines) for events that pass the trigger requirements and also have 4 jets with $ p_{\mathrm{T}} > $ 100 GeV. The leading jet $ p_{\mathrm{T}} $ distribution is shown in the top right plot, the second leading jet $ p_{\mathrm{T}} $ in the top left, the third leading jet $ p_{\mathrm{T}} $ in the bottom left, and the forth leading jet $ p_{\mathrm{T}} $ in the bottom right. The distribution from various processes have their total event count normalized to 1.

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Additional Figure 2-d:
Example of jet $ p_{\mathrm{T}} $ distributions of events in CMS data (points), SM multijet events from simulation (gray line), and various signal samples with varying dark mediator masses (colored lines) for events that pass the trigger requirements and also have 4 jets with $ p_{\mathrm{T}} > $ 100 GeV. The leading jet $ p_{\mathrm{T}} $ distribution is shown in the top right plot, the second leading jet $ p_{\mathrm{T}} $ in the top left, the third leading jet $ p_{\mathrm{T}} $ in the bottom left, and the forth leading jet $ p_{\mathrm{T}} $ in the bottom right. The distribution from various processes have their total event count normalized to 1.

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Additional Figure 3:
Example distributions of track-level variables that is used to calculate the tagging EJs produced in unflavored signal models for CMS data (points), SM multijet events from simulation (gray line), and various signal samples with varying dark pion lifetime (colored lines). The distribution of track $ d_{xy} $ ($ D_{N} $) is shown on the left (right). Distributions for various processes have their total track count normalized to 1.

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Additional Figure 3-a:
Example distributions of track-level variables that is used to calculate the tagging EJs produced in unflavored signal models for CMS data (points), SM multijet events from simulation (gray line), and various signal samples with varying dark pion lifetime (colored lines). The distribution of track $ d_{xy} $ ($ D_{N} $) is shown on the left (right). Distributions for various processes have their total track count normalized to 1.

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Additional Figure 3-b:
Example distributions of track-level variables that is used to calculate the tagging EJs produced in unflavored signal models for CMS data (points), SM multijet events from simulation (gray line), and various signal samples with varying dark pion lifetime (colored lines). The distribution of track $ d_{xy} $ ($ D_{N} $) is shown on the left (right). Distributions for various processes have their total track count normalized to 1.

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Additional Figure 4:
Example distributions of variables that is used to calculate the tagging EJs produced in flavor-aligned signal models for CMS data (points), SM multijet events from simulation (gray line), and various signal samples with varying dark pion lifetime (colored lines). The distribution of the $ d_{xy} $ of tracks ($\bar{\tau}_{2/1}$ of jets) is shown on the left (right). Distributions for various processes have their total count normalized to 1.

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Additional Figure 4-a:
Example distributions of variables that is used to calculate the tagging EJs produced in flavor-aligned signal models for CMS data (points), SM multijet events from simulation (gray line), and various signal samples with varying dark pion lifetime (colored lines). The distribution of the $ d_{xy} $ of tracks ($\bar{\tau}_{2/1}$ of jets) is shown on the left (right). Distributions for various processes have their total count normalized to 1.

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Additional Figure 4-b:
Example distributions of variables that is used to calculate the tagging EJs produced in flavor-aligned signal models for CMS data (points), SM multijet events from simulation (gray line), and various signal samples with varying dark pion lifetime (colored lines). The distribution of the $ d_{xy} $ of tracks ($\bar{\tau}_{2/1}$ of jets) is shown on the left (right). Distributions for various processes have their total count normalized to 1.

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Additional Figure 5:
Example distributions of track variables that is used to as coordinate inputs of the GNN used for EJ tagging for CMS data (points), SM multijet events from simulation (gray line), and various signal samples (colored lines). The distribution of $ |\Delta\eta| $ ($ |\Delta\phi| $) between the jet and associated tracks is shown on the left (right). Distributions for various processes have their total count normalized to 1.

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Additional Figure 5-a:
Example distributions of track variables that is used to as coordinate inputs of the GNN used for EJ tagging for CMS data (points), SM multijet events from simulation (gray line), and various signal samples (colored lines). The distribution of $ |\Delta\eta| $ ($ |\Delta\phi| $) between the jet and associated tracks is shown on the left (right). Distributions for various processes have their total count normalized to 1.

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Additional Figure 5-b:
Example distributions of track variables that is used to as coordinate inputs of the GNN used for EJ tagging for CMS data (points), SM multijet events from simulation (gray line), and various signal samples (colored lines). The distribution of $ |\Delta\eta| $ ($ |\Delta\phi| $) between the jet and associated tracks is shown on the left (right). Distributions for various processes have their total count normalized to 1.

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Additional Figure 6:
Example distributions of track variables that is used to as inputs of the GNN used for EJ tagging for CMS data (points), SM multijet events from simulation (gray line), and various signal samples (colored lines). The distribution of $ d_{xy} $ ($ d_{z} $) is shown on the top left (bottom left), while the distribution of the track $ p_{\mathrm{T}} $ ($ p_{\mathrm{T}}^\text{track}/\sum_{\text{track}}p_{\mathrm{T}}^{\text{track}} $) is shown on the top right (bottom right). Distributions for various processes have their total count normalized to 1.

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Additional Figure 6-a:
Example distributions of track variables that is used to as inputs of the GNN used for EJ tagging for CMS data (points), SM multijet events from simulation (gray line), and various signal samples (colored lines). The distribution of $ d_{xy} $ ($ d_{z} $) is shown on the top left (bottom left), while the distribution of the track $ p_{\mathrm{T}} $ ($ p_{\mathrm{T}}^\text{track}/\sum_{\text{track}}p_{\mathrm{T}}^{\text{track}} $) is shown on the top right (bottom right). Distributions for various processes have their total count normalized to 1.

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Additional Figure 6-b:
Example distributions of track variables that is used to as inputs of the GNN used for EJ tagging for CMS data (points), SM multijet events from simulation (gray line), and various signal samples (colored lines). The distribution of $ d_{xy} $ ($ d_{z} $) is shown on the top left (bottom left), while the distribution of the track $ p_{\mathrm{T}} $ ($ p_{\mathrm{T}}^\text{track}/\sum_{\text{track}}p_{\mathrm{T}}^{\text{track}} $) is shown on the top right (bottom right). Distributions for various processes have their total count normalized to 1.

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Additional Figure 6-c:
Example distributions of track variables that is used to as inputs of the GNN used for EJ tagging for CMS data (points), SM multijet events from simulation (gray line), and various signal samples (colored lines). The distribution of $ d_{xy} $ ($ d_{z} $) is shown on the top left (bottom left), while the distribution of the track $ p_{\mathrm{T}} $ ($ p_{\mathrm{T}}^\text{track}/\sum_{\text{track}}p_{\mathrm{T}}^{\text{track}} $) is shown on the top right (bottom right). Distributions for various processes have their total count normalized to 1.

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Additional Figure 6-d:
Example distributions of track variables that is used to as inputs of the GNN used for EJ tagging for CMS data (points), SM multijet events from simulation (gray line), and various signal samples (colored lines). The distribution of $ d_{xy} $ ($ d_{z} $) is shown on the top left (bottom left), while the distribution of the track $ p_{\mathrm{T}} $ ($ p_{\mathrm{T}}^\text{track}/\sum_{\text{track}}p_{\mathrm{T}}^{\text{track}} $) is shown on the top right (bottom right). Distributions for various processes have their total count normalized to 1.

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Additional Figure 7:
The mistag rate of the a-tag 1 (left) and aGNN tag 1 (right) EJ tagger evaluated in data and $ \gamma $+jets events from simulation as a function of jet $ p_{\mathrm{T}} $.

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Additional Figure 7-a:
The mistag rate of the a-tag 1 (left) and aGNN tag 1 (right) EJ tagger evaluated in data and $ \gamma $+jets events from simulation as a function of jet $ p_{\mathrm{T}} $.

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Additional Figure 7-b:
The mistag rate of the a-tag 1 (left) and aGNN tag 1 (right) EJ tagger evaluated in data and $ \gamma $+jets events from simulation as a function of jet $ p_{\mathrm{T}} $.

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Additional Figure 8:
Signal acceptance of signal models in the unflavored scenario with $ m_{\pi_\text{dark}}= $ 10 GeV with EJ tagging performed using the model-agnostic method, using the CMS detector configuration of 2016 pre-APV configuration fixes (top left), 2016 post-APV configuration fixes (top right), 2017 (bottom left) and 2018 (bottom right). The number in each box represents which cutset is being applied to each EJ sample; changes in cutsets in consecutive EJ samples can cause dips in efficiency as each cutset is optimized to maximize signal acceptance and background rejection.

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Additional Figure 8-a:
Signal acceptance of signal models in the unflavored scenario with $ m_{\pi_\text{dark}}= $ 10 GeV with EJ tagging performed using the model-agnostic method, using the CMS detector configuration of 2016 pre-APV configuration fixes (top left), 2016 post-APV configuration fixes (top right), 2017 (bottom left) and 2018 (bottom right). The number in each box represents which cutset is being applied to each EJ sample; changes in cutsets in consecutive EJ samples can cause dips in efficiency as each cutset is optimized to maximize signal acceptance and background rejection.

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Additional Figure 8-b:
Signal acceptance of signal models in the unflavored scenario with $ m_{\pi_\text{dark}}= $ 10 GeV with EJ tagging performed using the model-agnostic method, using the CMS detector configuration of 2016 pre-APV configuration fixes (top left), 2016 post-APV configuration fixes (top right), 2017 (bottom left) and 2018 (bottom right). The number in each box represents which cutset is being applied to each EJ sample; changes in cutsets in consecutive EJ samples can cause dips in efficiency as each cutset is optimized to maximize signal acceptance and background rejection.

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Additional Figure 8-c:
Signal acceptance of signal models in the unflavored scenario with $ m_{\pi_\text{dark}}= $ 10 GeV with EJ tagging performed using the model-agnostic method, using the CMS detector configuration of 2016 pre-APV configuration fixes (top left), 2016 post-APV configuration fixes (top right), 2017 (bottom left) and 2018 (bottom right). The number in each box represents which cutset is being applied to each EJ sample; changes in cutsets in consecutive EJ samples can cause dips in efficiency as each cutset is optimized to maximize signal acceptance and background rejection.

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Additional Figure 8-d:
Signal acceptance of signal models in the unflavored scenario with $ m_{\pi_\text{dark}}= $ 10 GeV with EJ tagging performed using the model-agnostic method, using the CMS detector configuration of 2016 pre-APV configuration fixes (top left), 2016 post-APV configuration fixes (top right), 2017 (bottom left) and 2018 (bottom right). The number in each box represents which cutset is being applied to each EJ sample; changes in cutsets in consecutive EJ samples can cause dips in efficiency as each cutset is optimized to maximize signal acceptance and background rejection.

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Additional Figure 9:
Signal acceptance of signal models in the unflavored scenario with $ m_{\pi_\text{dark}}= $ 10 GeV with EJ tagging performed using the GNN method, for all CMS detector 2016--2018 eras combined. The number in each box represents which cutset is being applied to each EJ sample; changes in cutsets in consecutive EJ samples can cause dips in efficiency as each cutset is optimized to maximize signal acceptance and background rejection.

png pdf
Additional Figure 10:
Signal acceptance of signal models in the unflavored scenario with $ m_{\pi_\text{dark}}= $ 20 GeV with EJ tagging performed using the model-agnostic method, using the CMS detector configuration of 2016 pre-APV configuration fixes (top left), 2016 post-APV configuration fixes (top right), 2017 (bottom left) and 2018 (bottom right). The number in each box represents which cutset is being applied to each EJ sample; changes in cutsets in consecutive EJ samples can cause dips in efficiency as each cutset is optimized to maximize signal acceptance and background rejection.

png pdf
Additional Figure 10-a:
Signal acceptance of signal models in the unflavored scenario with $ m_{\pi_\text{dark}}= $ 20 GeV with EJ tagging performed using the model-agnostic method, using the CMS detector configuration of 2016 pre-APV configuration fixes (top left), 2016 post-APV configuration fixes (top right), 2017 (bottom left) and 2018 (bottom right). The number in each box represents which cutset is being applied to each EJ sample; changes in cutsets in consecutive EJ samples can cause dips in efficiency as each cutset is optimized to maximize signal acceptance and background rejection.

png pdf
Additional Figure 10-b:
Signal acceptance of signal models in the unflavored scenario with $ m_{\pi_\text{dark}}= $ 20 GeV with EJ tagging performed using the model-agnostic method, using the CMS detector configuration of 2016 pre-APV configuration fixes (top left), 2016 post-APV configuration fixes (top right), 2017 (bottom left) and 2018 (bottom right). The number in each box represents which cutset is being applied to each EJ sample; changes in cutsets in consecutive EJ samples can cause dips in efficiency as each cutset is optimized to maximize signal acceptance and background rejection.

png pdf
Additional Figure 10-c:
Signal acceptance of signal models in the unflavored scenario with $ m_{\pi_\text{dark}}= $ 20 GeV with EJ tagging performed using the model-agnostic method, using the CMS detector configuration of 2016 pre-APV configuration fixes (top left), 2016 post-APV configuration fixes (top right), 2017 (bottom left) and 2018 (bottom right). The number in each box represents which cutset is being applied to each EJ sample; changes in cutsets in consecutive EJ samples can cause dips in efficiency as each cutset is optimized to maximize signal acceptance and background rejection.

png pdf
Additional Figure 10-d:
Signal acceptance of signal models in the unflavored scenario with $ m_{\pi_\text{dark}}= $ 20 GeV with EJ tagging performed using the model-agnostic method, using the CMS detector configuration of 2016 pre-APV configuration fixes (top left), 2016 post-APV configuration fixes (top right), 2017 (bottom left) and 2018 (bottom right). The number in each box represents which cutset is being applied to each EJ sample; changes in cutsets in consecutive EJ samples can cause dips in efficiency as each cutset is optimized to maximize signal acceptance and background rejection.

png pdf
Additional Figure 11:
Signal acceptance of signal models in the unflavored scenario with $ m_{\pi_\text{dark}}= $ 20 GeV with EJ tagging performed using the GNN method, for all CMS detector 2016--2018 eras combined. The number in each box represents which cutset is being applied to each EJ sample; changes in cutsets in consecutive EJ samples can cause dips in efficiency as each cutset is optimized to maximize signal acceptance and background rejection.

png pdf
Additional Figure 12:
Signal acceptance of signal models in the flavor-aligned scenario with $ m_{\pi_\text{dark}}= $ 6 GeV with EJ tagging performed using the model-agnostic method, using the CMS detector configuration of 2016 pre-APV configuration fixes (top left), 2016 post-APV configuration fixes (top right), 2017 (bottom left) and 2018 (bottom right). The number in each box represents which cutset is being applied to each EJ sample; changes in cutsets in consecutive EJ samples can cause dips in efficiency as each cutset is optimized to maximize signal acceptance and background rejection.

png pdf
Additional Figure 12-a:
Signal acceptance of signal models in the flavor-aligned scenario with $ m_{\pi_\text{dark}}= $ 6 GeV with EJ tagging performed using the model-agnostic method, using the CMS detector configuration of 2016 pre-APV configuration fixes (top left), 2016 post-APV configuration fixes (top right), 2017 (bottom left) and 2018 (bottom right). The number in each box represents which cutset is being applied to each EJ sample; changes in cutsets in consecutive EJ samples can cause dips in efficiency as each cutset is optimized to maximize signal acceptance and background rejection.

png pdf
Additional Figure 12-b:
Signal acceptance of signal models in the flavor-aligned scenario with $ m_{\pi_\text{dark}}= $ 6 GeV with EJ tagging performed using the model-agnostic method, using the CMS detector configuration of 2016 pre-APV configuration fixes (top left), 2016 post-APV configuration fixes (top right), 2017 (bottom left) and 2018 (bottom right). The number in each box represents which cutset is being applied to each EJ sample; changes in cutsets in consecutive EJ samples can cause dips in efficiency as each cutset is optimized to maximize signal acceptance and background rejection.

png pdf
Additional Figure 12-c:
Signal acceptance of signal models in the flavor-aligned scenario with $ m_{\pi_\text{dark}}= $ 6 GeV with EJ tagging performed using the model-agnostic method, using the CMS detector configuration of 2016 pre-APV configuration fixes (top left), 2016 post-APV configuration fixes (top right), 2017 (bottom left) and 2018 (bottom right). The number in each box represents which cutset is being applied to each EJ sample; changes in cutsets in consecutive EJ samples can cause dips in efficiency as each cutset is optimized to maximize signal acceptance and background rejection.

png pdf
Additional Figure 12-d:
Signal acceptance of signal models in the flavor-aligned scenario with $ m_{\pi_\text{dark}}= $ 6 GeV with EJ tagging performed using the model-agnostic method, using the CMS detector configuration of 2016 pre-APV configuration fixes (top left), 2016 post-APV configuration fixes (top right), 2017 (bottom left) and 2018 (bottom right). The number in each box represents which cutset is being applied to each EJ sample; changes in cutsets in consecutive EJ samples can cause dips in efficiency as each cutset is optimized to maximize signal acceptance and background rejection.

png pdf
Additional Figure 13:
Signal acceptance of signal models in the flavor-aligned scenario with $ m_{\pi_\text{dark}}= $ 6 GeV with EJ tagging performed using the GNN method, for all CMS detector 2016--2018 eras combined. The number in each box represents which cutset is being applied to each EJ sample; changes in cutsets in consecutive EJ samples can cause dips in efficiency as each cutset is optimized to maximize signal acceptance and background rejection.

png pdf
Additional Figure 14:
Signal acceptance of signal models in the flavor-aligned scenario with $ m_{\pi_\text{dark}}= $ 10 GeV with EJ tagging performed using the model-agnostic method, using the CMS detector configuration of 2016 pre-APV configuration fixes (top left), 2016 post-APV configuration fixes (top right), 2017 (bottom left) and 2018 (bottom right). The number in each box represents which cutset is being applied to each EJ sample; changes in cutsets in consecutive EJ samples can cause dips in efficiency as each cutset is optimized to maximize signal acceptance and background rejection.

png pdf
Additional Figure 14-a:
Signal acceptance of signal models in the flavor-aligned scenario with $ m_{\pi_\text{dark}}= $ 10 GeV with EJ tagging performed using the model-agnostic method, using the CMS detector configuration of 2016 pre-APV configuration fixes (top left), 2016 post-APV configuration fixes (top right), 2017 (bottom left) and 2018 (bottom right). The number in each box represents which cutset is being applied to each EJ sample; changes in cutsets in consecutive EJ samples can cause dips in efficiency as each cutset is optimized to maximize signal acceptance and background rejection.

png pdf
Additional Figure 14-b:
Signal acceptance of signal models in the flavor-aligned scenario with $ m_{\pi_\text{dark}}= $ 10 GeV with EJ tagging performed using the model-agnostic method, using the CMS detector configuration of 2016 pre-APV configuration fixes (top left), 2016 post-APV configuration fixes (top right), 2017 (bottom left) and 2018 (bottom right). The number in each box represents which cutset is being applied to each EJ sample; changes in cutsets in consecutive EJ samples can cause dips in efficiency as each cutset is optimized to maximize signal acceptance and background rejection.

png pdf
Additional Figure 14-c:
Signal acceptance of signal models in the flavor-aligned scenario with $ m_{\pi_\text{dark}}= $ 10 GeV with EJ tagging performed using the model-agnostic method, using the CMS detector configuration of 2016 pre-APV configuration fixes (top left), 2016 post-APV configuration fixes (top right), 2017 (bottom left) and 2018 (bottom right). The number in each box represents which cutset is being applied to each EJ sample; changes in cutsets in consecutive EJ samples can cause dips in efficiency as each cutset is optimized to maximize signal acceptance and background rejection.

png pdf
Additional Figure 14-d:
Signal acceptance of signal models in the flavor-aligned scenario with $ m_{\pi_\text{dark}}= $ 10 GeV with EJ tagging performed using the model-agnostic method, using the CMS detector configuration of 2016 pre-APV configuration fixes (top left), 2016 post-APV configuration fixes (top right), 2017 (bottom left) and 2018 (bottom right). The number in each box represents which cutset is being applied to each EJ sample; changes in cutsets in consecutive EJ samples can cause dips in efficiency as each cutset is optimized to maximize signal acceptance and background rejection.

png pdf
Additional Figure 15:
Signal acceptance of signal models in the flavor-aligned scenario with $ m_{\pi_\text{dark}}= $ 10 GeV with EJ tagging performed using the GNN method, for all CMS detector 2016--2018 eras combined. The number in each box represents which cutset is being applied to each EJ sample; changes in cutsets in consecutive EJ samples can cause dips in efficiency as each cutset is optimized to maximize signal acceptance and background rejection.

png pdf
Additional Figure 16:
Signal acceptance of signal models in the flavor-aligned scenario with $ m_{\pi_\text{dark}}= $ 20 GeV with EJ tagging performed using the model-agnostic method, using the CMS detector configuration of 2016 pre-APV configuration fixes (top left), 2016 post-APV configuration fixes (top right), 2017 (bottom left) and 2018 (bottom right). The number in each box represents which cutset is being applied to each EJ sample; changes in cutsets in consecutive EJ samples can cause dips in efficiency as each cutset is optimized to maximize signal acceptance and background rejection.

png pdf
Additional Figure 16-a:
Signal acceptance of signal models in the flavor-aligned scenario with $ m_{\pi_\text{dark}}= $ 20 GeV with EJ tagging performed using the model-agnostic method, using the CMS detector configuration of 2016 pre-APV configuration fixes (top left), 2016 post-APV configuration fixes (top right), 2017 (bottom left) and 2018 (bottom right). The number in each box represents which cutset is being applied to each EJ sample; changes in cutsets in consecutive EJ samples can cause dips in efficiency as each cutset is optimized to maximize signal acceptance and background rejection.

png pdf
Additional Figure 16-b:
Signal acceptance of signal models in the flavor-aligned scenario with $ m_{\pi_\text{dark}}= $ 20 GeV with EJ tagging performed using the model-agnostic method, using the CMS detector configuration of 2016 pre-APV configuration fixes (top left), 2016 post-APV configuration fixes (top right), 2017 (bottom left) and 2018 (bottom right). The number in each box represents which cutset is being applied to each EJ sample; changes in cutsets in consecutive EJ samples can cause dips in efficiency as each cutset is optimized to maximize signal acceptance and background rejection.

png pdf
Additional Figure 16-c:
Signal acceptance of signal models in the flavor-aligned scenario with $ m_{\pi_\text{dark}}= $ 20 GeV with EJ tagging performed using the model-agnostic method, using the CMS detector configuration of 2016 pre-APV configuration fixes (top left), 2016 post-APV configuration fixes (top right), 2017 (bottom left) and 2018 (bottom right). The number in each box represents which cutset is being applied to each EJ sample; changes in cutsets in consecutive EJ samples can cause dips in efficiency as each cutset is optimized to maximize signal acceptance and background rejection.

png pdf
Additional Figure 16-d:
Signal acceptance of signal models in the flavor-aligned scenario with $ m_{\pi_\text{dark}}= $ 20 GeV with EJ tagging performed using the model-agnostic method, using the CMS detector configuration of 2016 pre-APV configuration fixes (top left), 2016 post-APV configuration fixes (top right), 2017 (bottom left) and 2018 (bottom right). The number in each box represents which cutset is being applied to each EJ sample; changes in cutsets in consecutive EJ samples can cause dips in efficiency as each cutset is optimized to maximize signal acceptance and background rejection.

png pdf
Additional Figure 17:
Signal acceptance of signal models in the flavor-aligned scenario with $ m_{\pi_\text{dark}}= $ 20 GeV with EJ tagging performed using the GNN method, for all CMS detector 2016--2018 eras combined. The number in each box represents which cutset is being applied to each EJ sample; changes in cutsets in consecutive EJ samples can cause dips in efficiency as each cutset is optimized to maximize signal acceptance and background rejection.

png pdf
Additional Figure 18:
Template fit of the DEEPJET discriminator used to determine the b jet fraction of the non-EJ tagged jets in data events that pass the 1-EJ selection of the ``u-set 1'' (``a-set 1'') criteria on the left (right).

png pdf
Additional Figure 18-a:
Template fit of the DEEPJET discriminator used to determine the b jet fraction of the non-EJ tagged jets in data events that pass the 1-EJ selection of the ``u-set 1'' (``a-set 1'') criteria on the left (right).

png pdf
Additional Figure 18-b:
Template fit of the DEEPJET discriminator used to determine the b jet fraction of the non-EJ tagged jets in data events that pass the 1-EJ selection of the ``u-set 1'' (``a-set 1'') criteria on the left (right).

png pdf
Additional Figure 19:
Template fit of the DEEPJET discriminator used to determine the b jet fraction of the non-EJ tagged jets in data events that pass the 1-EJ selection of the ``uGNN set 1'' (``aGNN set 1'') criteria on the left (right).

png pdf
Additional Figure 19-a:
Template fit of the DEEPJET discriminator used to determine the b jet fraction of the non-EJ tagged jets in data events that pass the 1-EJ selection of the ``uGNN set 1'' (``aGNN set 1'') criteria on the left (right).

png pdf
Additional Figure 19-b:
Template fit of the DEEPJET discriminator used to determine the b jet fraction of the non-EJ tagged jets in data events that pass the 1-EJ selection of the ``uGNN set 1'' (``aGNN set 1'') criteria on the left (right).

png pdf
Additional Figure 20:
Comparison between the cut-based (model-agnostic) EJ tagging method with the unflavored (left) and flavor-aligned (right) GNN for 3 different EJ unflavored samples. The cut-based tagger performance is worse than the GNN in all 3 EJ samples.

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Additional Figure 20-a:
Comparison between the cut-based (model-agnostic) EJ tagging method with the unflavored (left) and flavor-aligned (right) GNN for 3 different EJ unflavored samples. The cut-based tagger performance is worse than the GNN in all 3 EJ samples.

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Additional Figure 20-b:
Comparison between the cut-based (model-agnostic) EJ tagging method with the unflavored (left) and flavor-aligned (right) GNN for 3 different EJ unflavored samples. The cut-based tagger performance is worse than the GNN in all 3 EJ samples.

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Additional Figure 21:
Performance of the GNN EJ tagger on different EJ unflavored samples. The GNN was trained on the $ m_{\pi_\text{dark}} = $ 10 and 20 GeV (green and red curves), but not 0.7 or 1 GeV (blue and orange curves), showing how the performance degrades when the tagger is applied to a sample outside what it is presented with at training.

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Additional Figure 22:
Fraction of jet-associated tracks of SM jets from simulation that pass the ``uGNN tag 1'' (aGNN tag 1) EJ tagging criteria shown on the top (bottom) as a function of $ \Delta R $ between the jet and track of interest and $ \text{sign}(d_{xy})\cdot\ln{(1+\lvert {d_{xy}}/{1\ \text{cm}}\rvert )} $, with $ d_{xy} $ being the transverse impact parameter of the track of interest.

png pdf
Additional Figure 22-a:
Fraction of jet-associated tracks of SM jets from simulation that pass the ``uGNN tag 1'' (aGNN tag 1) EJ tagging criteria shown on the top (bottom) as a function of $ \Delta R $ between the jet and track of interest and $ \text{sign}(d_{xy})\cdot\ln{(1+\lvert {d_{xy}}/{1\ \text{cm}}\rvert )} $, with $ d_{xy} $ being the transverse impact parameter of the track of interest.

png pdf
Additional Figure 22-b:
Fraction of jet-associated tracks of SM jets from simulation that pass the ``uGNN tag 1'' (aGNN tag 1) EJ tagging criteria shown on the top (bottom) as a function of $ \Delta R $ between the jet and track of interest and $ \text{sign}(d_{xy})\cdot\ln{(1+\lvert {d_{xy}}/{1\ \text{cm}}\rvert )} $, with $ d_{xy} $ being the transverse impact parameter of the track of interest.
Additional Tables

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Additional Table 1:
Example cut flow used for selecting signals events using the u-set 4 selection criteria. Simulated background and signal yields are normalized to unity. The example signal events are generated with $ m_{\text{X}_\text{dark}}= $ 1600 GeV and $ m_{\pi_\text{dark}}= $ 10 GeV in the unflavored scenario.

png pdf
Additional Table 2:
Example cut flow used for selecting signals events using the uGNN set 3 selection criteria. Simulated background and signal yields are normalized to unity. The example signal events are generated with $ m_{\text{X}_\text{dark}}= $ 1600 GeV and $ m_{\pi_\text{dark}}= $ 10 GeV in the unflavored scenario.

png pdf
Additional Table 3:
Example cut flow used for selecting signals events using the a-set 3 selection criteria. Simulated background and signal yields are normalized to unity. The example signal events are generated with $ m_{\text{X}_\text{dark}}= $ 1600 GeV and $ m_{\pi_\text{dark}}= $ 10 GeV in the flavor-aligned scenario.

png pdf
Additional Table 4:
Example cut flow used for selecting signals events using the aGNN set 3 selection criteria. Simulated background and signal yields are normalized to unity. The example signal events are generated with $ m_{\text{X}_\text{dark}}= $ 1600 GeV and $ m_{\pi_\text{dark}}= $ 10 GeV in the flavor-aligned scenario.
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Compact Muon Solenoid
LHC, CERN