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| CMS-PAS-EXO-20-010 | ||
| Search for inelastic dark matter in events with two displaced muons and missing transverse momentum in proton-proton collisions at $ \sqrt{s} = $ 13 TeV | ||
| CMS Collaboration | ||
| 3 March 2023 | ||
| Abstract: A search is presented for dark matter in events with a pair of displaced muons and missing transverse momentum. The analysis is performed using 138 fb$ ^{-1} $ of proton-proton collision data at 13 TeV center-of-mass energy produced by the LHC and collected with the CMS detector from 2016 to 2018. No significant excess is observed over the predicted background. Upper limits are set on the product of the inelastically coupled dark matter production cross section and the decay branching fraction. This is the first search for inelastic dark matter performed at a hadron collider. | ||
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Links:
CDS record (PDF) ;
Physics Briefing ;
CADI line (restricted) ;
These preliminary results are superseded in this paper, PRL 132 (2024) 041802. The superseded preliminary plots can be found here. |
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| Figures & Tables | Summary | Additional Figures & Tables | References | CMS Publications |
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| Figures | |
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Figure 1:
Feynman diagram of inelastic dark matter production and decay in proton-proton collisions. The heavy dark matter state $ \chi_2 $ can be long-lived. |
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Figure 2:
Reconstruction efficiency of standard (blue) and displaced (red) reconstruction algorithms as a function of transverse vertex displacement $ v_{xy} $ in the central region of the detector ($ |\eta| < $ 1.2), for a representative signal sample. The two dashed gray lines denote the end of the fiducial tracker and muon chamber regions, respectively. |
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Figure 3:
Two-dimensional exclusion surfaces for $ \Delta = 0.1 \, m_1 $ (left) and $ \Delta = 0.4 \, m_1 $ (right), as a function of $ m_1 $ and $ y $ (see text). Filled histograms denote observed limits on the product of the dark matter production cross section and decay branching fraction, while dashed lines denote excluded regions at 95% CL, with one-sigma bands. Regions above the lines are excluded, depending on the $ \alpha_D $ hypothesis: $ \alpha_D = \alpha_{EM} $ (blue) or $ \alpha_D = $ 0.1 (magenta). |
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Figure 3-a:
Two-dimensional exclusion surfaces for $ \Delta = 0.1 \, m_1 $, as a function of $ m_1 $ and $ y $ (see text). Filled histograms denote observed limits on the product of the dark matter production cross section and decay branching fraction, while dashed lines denote excluded regions at 95% CL, with one-sigma bands. Regions above the lines are excluded, depending on the $ \alpha_D $ hypothesis: $ \alpha_D = \alpha_{EM} $ (blue) or $ \alpha_D = $ 0.1 (magenta). |
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Figure 3-b:
Two-dimensional exclusion surfaces for $ \Delta = 0.4 \, m_1 $, as a function of $ m_1 $ and $ y $ (see text). Filled histograms denote observed limits on the product of the dark matter production cross section and decay branching fraction, while dashed lines denote excluded regions at 95% CL, with one-sigma bands. Regions above the lines are excluded, depending on the $ \alpha_D $ hypothesis: $ \alpha_D = \alpha_{EM} $ (blue) or $ \alpha_D = $ 0.1 (magenta). |
| Tables | |
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Table 1:
Definition of ABCD bins and yields in data, per match category. The total signal systematic uncertainty averaged over all years is approximately 20%, 30%, and 40% for the 0-, 1-, and 2-match categories respectively (see supplemental material for a breakdown). The predicted yield in bin D is based on the assumption of zero signal. |
| Summary |
| In summary, a search was presented for inelastically-coupled dark matter with a unique final-state signature including a soft, displaced muon pair collimated with $ {\vec p}_{\mathrm{T}}^{\,\text{miss}} $. Proton-proton collisions at 13 TeV center-of-mass energy produced at the LHC and collected by CMS from 2016 to 2018 were analyzed, totaling 138 fb$ ^{-1} $ of data. The striking nature of the signal provides various handles that were exploited to enhance the sensitivity to the benchmark model. A data-driven background estimation strategy based on a modified ABCD method was used to predict the background. No significant excess is observed over SM expectations. Upper limits are set on the product of the dark matter production cross section and decay branching fraction into muons as a function of dark matter mass $ m_1 $ and $ y \equiv \epsilon^2 \, \alpha_D \, (m_1/m_{A'})^4 $. This is the first search for inelastic dark matter at a hadron collider. |
| Additional Figures | |
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Additional Figure 1:
(Upper left) Observed distribution in data of $\Delta\phi_{\mu\mu}^{\text{MET}}$ vs. min-$d_{xy}$ in the 0-match category. (Upper right) Observed distribution in data of vs. vs. min-$d_{xy}$ in the 1-match category. (Lower center) Observed distribution in data of $I^{\text{rel}}_{\text{PF}}$ vs. min-$d_{xy}$ in the 2-match category. |
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Additional Figure 1-a:
Observed distribution in data of $\Delta\phi_{\mu\mu}^{\text{MET}}$ vs. min-$d_{xy}$ in the 0-match category. |
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Additional Figure 1-b:
Observed distribution in data of vs. vs. min-$d_{xy}$ in the 1-match category. (Lower center) Observed distribution in data of $I^{\text{rel}}_{\text{PF}}$ vs. min-$d_{xy}$ in the 2-match category. |
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Additional Figure 1-c:
(Upper left) Observed distribution in data of $\Delta\phi_{\mu\mu}^{\text{MET}}$ vs. min-$d_{xy}$ in the 0-match category. (Upper right) Observed distribution in data of vs. vs. min-$d_{xy}$ in the 1-match category. (Lower center) Observed distribution in data of $I^{\text{rel}}_{\text{PF}}$ vs. min-$d_{xy}$ in the 2-match category. |
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Additional Figure 2:
Observed distributions in data (black points) of min-$d_{xy}$ (right panels), $\Delta\phi_{\mu\mu}^{\text{MET}}$ (upper left panel), and $I^{\text{rel}}_{\text{PF}}$ (middle and lower left panels), overlaid with the background prediction extracted from data in an orthogonal control region (filled red histogram). Benchmark signal hypotheses are also shown. |
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Additional Figure 2-a:
Observed distribution in data (black points) of $\Delta\phi_{\mu\mu}^{\text{MET}}$ (0 muon matched), overlaid with the background prediction extracted from data in an orthogonal control region (filled red histogram). Benchmark signal hypotheses are also shown. |
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Additional Figure 2-b:
Observed distribution in data (black points) of min-$d_{xy}$ (0 muon matched), overlaid with the background prediction extracted from data in an orthogonal control region (filled red histogram). Benchmark signal hypotheses are also shown. |
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Additional Figure 2-c:
Observed distribution in data (black points) of $I^{\text{rel}}_{\text{PF}}$ (1 muon matched), overlaid with the background prediction extracted from data in an orthogonal control region (filled red histogram). Benchmark signal hypotheses are also shown. |
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Additional Figure 2-d:
Observed distribution in data (black points) of min-$d_{xy}$ (1 muon matched), overlaid with the background prediction extracted from data in an orthogonal control region (filled red histogram). Benchmark signal hypotheses are also shown. |
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Additional Figure 2-e:
Observed distribution in data (black points) of $I^{\text{rel}}_{\text{PF}}$ (2 muon matched), overlaid with the background prediction extracted from data in an orthogonal control region (filled red histogram). Benchmark signal hypotheses are also shown. |
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Additional Figure 2-f:
Observed distribution in data (black points) of min-$d_{xy}$ (2 muon2 matched), overlaid with the background prediction extracted from data in an orthogonal control region (filled red histogram). Benchmark signal hypotheses are also shown. |
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Additional Figure 3:
The observed and expected upper limits at 95% CL on the product of $ A' $ production cross section and $ \chi_2 \to \chi_1 \mu^+\mu^- $ branching fraction for an inelastic dark matter model with mass splitting $ \Delta = 0.1 \, m_1 $, shown as a function of $ m_1 $. The one (two) standard deviation variation in the expected limit is shown in the inner green (outer yellow) band. The blue and magenta dashed lines represent the theoretically predicted cross sections, assuming $ \alpha_D = \alpha_{EM} $ and $ \alpha_D = $ 0.1, respectively. Clockwise from the upper left: $ c\tau = $ 1 mm; $ c\tau = $ 10 mm; $ c\tau = $ 1000 mm; $ c\tau = $ 100 mm. |
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Additional Figure 3-a:
The observed and expected upper limits at 95% CL on the product of $ A' $ production cross section and $ \chi_2 \to \chi_1 \mu^+\mu^- $ branching fraction for an inelastic dark matter model with mass splitting $ \Delta = 0.1 \, m_1 $, shown as a function of $ m_1 $. The one (two) standard deviation variation in the expected limit is shown in the inner green (outer yellow) band. The blue and magenta dashed lines represent the theoretically predicted cross sections, assuming $ \alpha_D = \alpha_{EM} $ and $ \alpha_D = $ 0.1, respectively. $ c\tau = $ 1 mm. |
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Additional Figure 3-b:
The observed and expected upper limits at 95% CL on the product of $ A' $ production cross section and $ \chi_2 \to \chi_1 \mu^+\mu^- $ branching fraction for an inelastic dark matter model with mass splitting $ \Delta = 0.1 \, m_1 $, shown as a function of $ m_1 $. The one (two) standard deviation variation in the expected limit is shown in the inner green (outer yellow) band. The blue and magenta dashed lines represent the theoretically predicted cross sections, assuming $ \alpha_D = \alpha_{EM} $ and $ \alpha_D = $ 0.1, respectively. $ c\tau = $ 10 mm. |
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Additional Figure 3-c:
The observed and expected upper limits at 95% CL on the product of $ A' $ production cross section and $ \chi_2 \to \chi_1 \mu^+\mu^- $ branching fraction for an inelastic dark matter model with mass splitting $ \Delta = 0.1 \, m_1 $, shown as a function of $ m_1 $. The one (two) standard deviation variation in the expected limit is shown in the inner green (outer yellow) band. The blue and magenta dashed lines represent the theoretically predicted cross sections, assuming $ \alpha_D = \alpha_{EM} $ and $ \alpha_D = $ 0.1, respectively. $ c\tau = $ 1000 mm. |
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Additional Figure 3-d:
The observed and expected upper limits at 95% CL on the product of $ A' $ production cross section and $ \chi_2 \to \chi_1 \mu^+\mu^- $ branching fraction for an inelastic dark matter model with mass splitting $ \Delta = 0.1 \, m_1 $, shown as a function of $ m_1 $. The one (two) standard deviation variation in the expected limit is shown in the inner green (outer yellow) band. The blue and magenta dashed lines represent the theoretically predicted cross sections, assuming $ \alpha_D = \alpha_{EM} $ and $ \alpha_D = $ 0.1, respectively. $ c\tau = $ 100 mm. |
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Additional Figure 4:
The observed and expected upper limits at 95% CL on the product of $ A' $ production cross section and $ \chi_2 \to \chi_1 \mu^+\mu^- $ branching fraction for an inelastic dark matter model with mass splitting $ \Delta = 0.4 \, m_1 $, shown as a function of $ m_1 $. The one (two) standard deviation variation in the expected limit is shown in the inner green (outer yellow) band. The blue and magenta dashed lines represent the theoretically predicted cross sections, assuming $ \alpha_D = \alpha_{EM} $ and $ \alpha_D = $ 0.1, respectively. Clockwise from the upper left: $ c\tau = $ 1 mm; $ c\tau = $ 10 mm; $ c\tau = $ 1000 mm; $ c\tau = $ 100 mm. |
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Additional Figure 4-a:
The observed and expected upper limits at 95% CL on the product of $ A' $ production cross section and $ \chi_2 \to \chi_1 \mu^+\mu^- $ branching fraction for an inelastic dark matter model with mass splitting $ \Delta = 0.4 \, m_1 $, shown as a function of $ m_1 $. The one (two) standard deviation variation in the expected limit is shown in the inner green (outer yellow) band. The blue and magenta dashed lines represent the theoretically predicted cross sections, assuming $ \alpha_D = \alpha_{EM} $ and $ \alpha_D = $ 0.1, respectively. $ c\tau = $ 1 mm. |
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Additional Figure 4-b:
The observed and expected upper limits at 95% CL on the product of $ A' $ production cross section and $ \chi_2 \to \chi_1 \mu^+\mu^- $ branching fraction for an inelastic dark matter model with mass splitting $ \Delta = 0.4 \, m_1 $, shown as a function of $ m_1 $. The one (two) standard deviation variation in the expected limit is shown in the inner green (outer yellow) band. The blue and magenta dashed lines represent the theoretically predicted cross sections, assuming $ \alpha_D = \alpha_{EM} $ and $ \alpha_D = $ 0.1, respectively. $ c\tau = $ 10 mm. |
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Additional Figure 4-c:
The observed and expected upper limits at 95% CL on the product of $ A' $ production cross section and $ \chi_2 \to \chi_1 \mu^+\mu^- $ branching fraction for an inelastic dark matter model with mass splitting $ \Delta = 0.4 \, m_1 $, shown as a function of $ m_1 $. The one (two) standard deviation variation in the expected limit is shown in the inner green (outer yellow) band. The blue and magenta dashed lines represent the theoretically predicted cross sections, assuming $ \alpha_D = \alpha_{EM} $ and $ \alpha_D = $ 0.1, respectively. $ c\tau = $ 10000 mm. |
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Additional Figure 4-d:
The observed and expected upper limits at 95% CL on the product of $ A' $ production cross section and $ \chi_2 \to \chi_1 \mu^+\mu^- $ branching fraction for an inelastic dark matter model with mass splitting $ \Delta = 0.4 \, m_1 $, shown as a function of $ m_1 $. The one (two) standard deviation variation in the expected limit is shown in the inner green (outer yellow) band. The blue and magenta dashed lines represent the theoretically predicted cross sections, assuming $ \alpha_D = \alpha_{EM} $ and $ \alpha_D = $ 0.1, respectively. $ c\tau = $ 100 mm. |
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Additional Figure 5:
The observed and expected upper limits at 95% CL on the product of $ A' $ production cross section and $ \chi_2 \to \chi_1 \mu^+\mu^- $ branching fraction for an inelastic dark matter model with varying $ m_1 $ and $ \Delta $, shown as a function of $ c\tau $. The one (two) standard deviation variation in the expected limit is shown in the inner green (outer yellow) band. The blue and magenta dashed lines represent the theoretically predicted cross sections, assuming $ \alpha_D = \alpha_{EM} $ and $ \alpha_D = $ 0.1, respectively. Clockwise from the upper left: $ m_1 = $ 3 GeV, $ \Delta = 0.1 \, m_1 $; $ m_1 = $ 20 GeV, $ \Delta = 0.1 \, m_1 $; $ m_1 = $ 60 GeV, $ \Delta = 0.4 \, m_1 $; $ m_1 = $ 60 GeV, $ \Delta = 0.1 \, m_1 $. |
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Additional Figure 5-a:
The observed and expected upper limits at 95% CL on the product of $ A' $ production cross section and $ \chi_2 \to \chi_1 \mu^+\mu^- $ branching fraction for an inelastic dark matter model with varying $ m_1 $ and $ \Delta $, shown as a function of $ c\tau $. The one (two) standard deviation variation in the expected limit is shown in the inner green (outer yellow) band. The blue and magenta dashed lines represent the theoretically predicted cross sections, assuming $ \alpha_D = \alpha_{EM} $ and $ \alpha_D = $ 0.1, respectively. $ m_1 = $ 3 GeV, $ \Delta = 0.1 \, m_1 $. |
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Additional Figure 5-b:
The observed and expected upper limits at 95% CL on the product of $ A' $ production cross section and $ \chi_2 \to \chi_1 \mu^+\mu^- $ branching fraction for an inelastic dark matter model with varying $ m_1 $ and $ \Delta $, shown as a function of $ c\tau $. The one (two) standard deviation variation in the expected limit is shown in the inner green (outer yellow) band. The blue and magenta dashed lines represent the theoretically predicted cross sections, assuming $ \alpha_D = \alpha_{EM} $ and $ \alpha_D = $ 0.1, respectively. $ m_1 = $ 20 GeV, $ \Delta = 0.1 \, m_1 $. |
png pdf |
Additional Figure 5-c:
The observed and expected upper limits at 95% CL on the product of $ A' $ production cross section and $ \chi_2 \to \chi_1 \mu^+\mu^- $ branching fraction for an inelastic dark matter model with varying $ m_1 $ and $ \Delta $, shown as a function of $ c\tau $. The one (two) standard deviation variation in the expected limit is shown in the inner green (outer yellow) band. The blue and magenta dashed lines represent the theoretically predicted cross sections, assuming $ \alpha_D = \alpha_{EM} $ and $ \alpha_D = $ 0.1, respectively. $ m_1 = $ 60 GeV, $ \Delta = 0.4 \, m_1 $. |
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Additional Figure 5-d:
The observed and expected upper limits at 95% CL on the product of $ A' $ production cross section and $ \chi_2 \to \chi_1 \mu^+\mu^- $ branching fraction for an inelastic dark matter model with varying $ m_1 $ and $ \Delta $, shown as a function of $ c\tau $. The one (two) standard deviation variation in the expected limit is shown in the inner green (outer yellow) band. The blue and magenta dashed lines represent the theoretically predicted cross sections, assuming $ \alpha_D = \alpha_{EM} $ and $ \alpha_D = $ 0.1, respectively. $ m_1 = $ 60 GeV, $ \Delta = 0.1 \, m_1 $. |
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Additional Figure 6:
Signal efficiency of the simulated samples in the analysis, before splitting into muon match categories. Triangles denote the efficiency of filters imposed at generator level, while circles denote the total (generator filter plus selection) signal efficiency. The generator filters comprise the requirements: leading jet $ p_{\mathrm{T}} > $ 80 GeV and $ p_{\mathrm{T}}^\text{miss} > $ 80 GeV. |
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Additional Figure 6-a:
Signal efficiency of the simulated samples in the analysis, before splitting into muon match categories. Triangles denote the efficiency of filters imposed at generator level, while circles denote the total (generator filter plus selection) signal efficiency. The generator filters comprise the requirements: leading jet $ p_{\mathrm{T}} > $ 80 GeV and $ p_{\mathrm{T}}^\text{miss} > $ 80 GeV. |
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Additional Figure 6-b:
Signal efficiency of the simulated samples in the analysis, before splitting into muon match categories. Triangles denote the efficiency of filters imposed at generator level, while circles denote the total (generator filter plus selection) signal efficiency. The generator filters comprise the requirements: leading jet $ p_{\mathrm{T}} > $ 80 GeV and $ p_{\mathrm{T}}^\text{miss} > $ 80 GeV. |
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Additional Figure 7:
Signal efficiency versus generated $ \chi_2 p_{\mathrm{T}} $ and decay transverse position $ v_{xy} $ for an inelastic dark matter model with $ m_1 = $ 50 GeV and $ \Delta = 0.1 \, m_1 $, before splitting into muon match categories. Upper: $ \chi_2 |\eta| < $ 1.2. Lower: $ \chi_2 |\eta| > $ 1.2. The efficiency is calculated after application of generator filters. |
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Additional Figure 7-a:
Signal efficiency versus generated $ \chi_2 p_{\mathrm{T}} $ and decay transverse position $ v_{xy} $ for an inelastic dark matter model with $ m_1 = $ 50 GeV and $ \Delta = 0.1 \, m_1 $, before splitting into muon match categories. $ \chi_2 |\eta| < $ 1.2. The efficiency is calculated after application of generator filters. |
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Additional Figure 7-b:
Signal efficiency versus generated $ \chi_2 p_{\mathrm{T}} $ and decay transverse position $ v_{xy} $ for an inelastic dark matter model with $ m_1 = $ 50 GeV and $ \Delta = 0.1 \, m_1 $, before splitting into muon match categories. $ \chi_2 |\eta| > $ 1.2. The efficiency is calculated after application of generator filters. |
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Additional Figure 8:
Signal efficiency versus generated $ \chi_2 p_{\mathrm{T}} $ and decay transverse position $ v_{xy} $ for an inelastic dark matter model with $ m_1 = $ 50 GeV and $ \Delta = 0.4 \, m_1 $, before splitting into muon match categories. Upper: $ \chi_2 |\eta| < $ 1.2. Lower: $ \chi_2 |\eta| > $ 1.2. The efficiency is calculated after application of generator filters. |
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Additional Figure 8-a:
Signal efficiency versus generated $ \chi_2 p_{\mathrm{T}} $ and decay transverse position $ v_{xy} $ for an inelastic dark matter model with $ m_1 = $ 50 GeV and $ \Delta = 0.4 \, m_1 $, before splitting into muon match categories. Upper: $ \chi_2 |\eta| < $ 1.2. Lower: $ \chi_2 |\eta| > $ 1.2. The efficiency is calculated after application of generator filters. |
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Additional Figure 8-b:
Signal efficiency versus generated $ \chi_2 p_{\mathrm{T}} $ and decay transverse position $ v_{xy} $ for an inelastic dark matter model with $ m_1 = $ 50 GeV and $ \Delta = 0.4 \, m_1 $, before splitting into muon match categories. Upper: $ \chi_2 |\eta| < $ 1.2. Lower: $ \chi_2 |\eta| > $ 1.2. The efficiency is calculated after application of generator filters. |
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Additional Figure 9:
Signal efficiency versus generated $ \chi_2 p_{\mathrm{T}} $ and decay transverse position $ v_{xy} $ for an inelastic dark matter model with $ m_1 = $ 5 GeV and $ \Delta = 0.1 \, m_1 $, before splitting into muon match categories. Upper: $ \chi_2 |\eta| < $ 1.2. Lower: $ \chi_2 |\eta| > $ 1.2. The efficiency is calculated after application of generator filters. |
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Additional Figure 9-a:
Signal efficiency versus generated $ \chi_2 p_{\mathrm{T}} $ and decay transverse position $ v_{xy} $ for an inelastic dark matter model with $ m_1 = $ 5 GeV and $ \Delta = 0.1 \, m_1 $, before splitting into muon match categories. Upper: $ \chi_2 |\eta| < $ 1.2. Lower: $ \chi_2 |\eta| > $ 1.2. The efficiency is calculated after application of generator filters. |
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Additional Figure 9-b:
Signal efficiency versus generated $ \chi_2 p_{\mathrm{T}} $ and decay transverse position $ v_{xy} $ for an inelastic dark matter model with $ m_1 = $ 5 GeV and $ \Delta = 0.1 \, m_1 $, before splitting into muon match categories. Upper: $ \chi_2 |\eta| < $ 1.2. Lower: $ \chi_2 |\eta| > $ 1.2. The efficiency is calculated after application of generator filters. |
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Additional Figure 10:
Signal efficiency versus generated $ \chi_2 p_{\mathrm{T}} $ and decay transverse position $ v_{xy} $ for an inelastic dark matter model with $ m_1 = $ 5 GeV and $ \Delta = 0.4 \, m_1 $, before splitting into muon match categories. Upper: $ \chi_2 |\eta| < $ 1.2. Lower: $ \chi_2 |\eta| > $ 1.2. The efficiency is calculated after application of generator filters. |
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Additional Figure 10-a:
Signal efficiency versus generated $ \chi_2 p_{\mathrm{T}} $ and decay transverse position $ v_{xy} $ for an inelastic dark matter model with $ m_1 = $ 5 GeV and $ \Delta = 0.4 \, m_1 $, before splitting into muon match categories. Upper: $ \chi_2 |\eta| < $ 1.2. Lower: $ \chi_2 |\eta| > $ 1.2. The efficiency is calculated after application of generator filters. |
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Additional Figure 10-b:
Signal efficiency versus generated $ \chi_2 p_{\mathrm{T}} $ and decay transverse position $ v_{xy} $ for an inelastic dark matter model with $ m_1 = $ 5 GeV and $ \Delta = 0.4 \, m_1 $, before splitting into muon match categories. Upper: $ \chi_2 |\eta| < $ 1.2. Lower: $ \chi_2 |\eta| > $ 1.2. The efficiency is calculated after application of generator filters. |
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Additional Figure 11:
Fraction of events in each muon match category versus generated $ \chi_2 $ decay transverse position $ v_{xy} $ for an inelastic dark matter model with $ m_1 = $ 50 GeV and $ \Delta = 0.4 \, m_1 $. Left: $ \chi_2 |\eta| < $ 1.2. Right: $ \chi_2 |\eta| > $ 1.2. Other observables such as $ \Delta R(\mu\mu) $ have a subdominant impact on the matching distribution and are therefore not reported here. |
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Additional Figure 11-a:
Fraction of events in each muon match category versus generated $ \chi_2 $ decay transverse position $ v_{xy} $ for an inelastic dark matter model with $ m_1 = $ 50 GeV and $ \Delta = 0.4 \, m_1 $. Left: $ \chi_2 |\eta| < $ 1.2. Right: $ \chi_2 |\eta| > $ 1.2. Other observables such as $ \Delta R(\mu\mu) $ have a subdominant impact on the matching distribution and are therefore not reported here. |
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Additional Figure 11-b:
Fraction of events in each muon match category versus generated $ \chi_2 $ decay transverse position $ v_{xy} $ for an inelastic dark matter model with $ m_1 = $ 50 GeV and $ \Delta = 0.4 \, m_1 $. Left: $ \chi_2 |\eta| < $ 1.2. Right: $ \chi_2 |\eta| > $ 1.2. Other observables such as $ \Delta R(\mu\mu) $ have a subdominant impact on the matching distribution and are therefore not reported here. |
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Additional Figure 12:
Fraction of events in each muon match category versus generated $ \chi_2 $ decay transverse position $ v_{xy} $ for an inelastic dark matter model with $ m_1 = $ 50 GeV and $ \Delta = 0.1 \, m_1 $. Left: $ \chi_2 |\eta| < $ 1.2. Right: $ \chi_2 |\eta| > $ 1.2. Other observables such as $ \Delta R(\mu\mu) $ have a subdominant impact on the matching distribution and are therefore not reported here. |
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Additional Figure 12-a:
Fraction of events in each muon match category versus generated $ \chi_2 $ decay transverse position $ v_{xy} $ for an inelastic dark matter model with $ m_1 = $ 50 GeV and $ \Delta = 0.1 \, m_1 $. Left: $ \chi_2 |\eta| < $ 1.2. Right: $ \chi_2 |\eta| > $ 1.2. Other observables such as $ \Delta R(\mu\mu) $ have a subdominant impact on the matching distribution and are therefore not reported here. |
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Additional Figure 12-b:
Fraction of events in each muon match category versus generated $ \chi_2 $ decay transverse position $ v_{xy} $ for an inelastic dark matter model with $ m_1 = $ 50 GeV and $ \Delta = 0.1 \, m_1 $. Left: $ \chi_2 |\eta| < $ 1.2. Right: $ \chi_2 |\eta| > $ 1.2. Other observables such as $ \Delta R(\mu\mu) $ have a subdominant impact on the matching distribution and are therefore not reported here. |
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Additional Figure 13:
Fraction of events in each muon match category versus generated $ \chi_2 $ decay transverse position $ v_{xy} $ for an inelastic dark matter model with $ m_1 = $ 5 GeV and $ \Delta = 0.4 \, m_1 $. Left: $ \chi_2 |\eta| < $ 1.2. Right: $ \chi_2 |\eta| > $ 1.2. Other observables such as $ \Delta R(\mu\mu) $ have a subdominant impact on the matching distribution and are therefore not reported here. |
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Additional Figure 13-a:
Fraction of events in each muon match category versus generated $ \chi_2 $ decay transverse position $ v_{xy} $ for an inelastic dark matter model with $ m_1 = $ 5 GeV and $ \Delta = 0.4 \, m_1 $. Left: $ \chi_2 |\eta| < $ 1.2. Right: $ \chi_2 |\eta| > $ 1.2. Other observables such as $ \Delta R(\mu\mu) $ have a subdominant impact on the matching distribution and are therefore not reported here. |
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Additional Figure 13-b:
Fraction of events in each muon match category versus generated $ \chi_2 $ decay transverse position $ v_{xy} $ for an inelastic dark matter model with $ m_1 = $ 5 GeV and $ \Delta = 0.4 \, m_1 $. Left: $ \chi_2 |\eta| < $ 1.2. Right: $ \chi_2 |\eta| > $ 1.2. Other observables such as $ \Delta R(\mu\mu) $ have a subdominant impact on the matching distribution and are therefore not reported here. |
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Additional Figure 14:
Fraction of events in each muon match category versus generated $ \chi_2 $ decay transverse position $ v_{xy} $ for an inelastic dark matter model with $ m_1 = $ 5 GeV and $ \Delta = 0.1 \, m_1 $. Left: $ \chi_2 |\eta| < $ 1.2. Right: $ \chi_2 |\eta| > $ 1.2. Other observables such as $ \Delta R(\mu\mu) $ have a subdominant impact on the matching distribution and are therefore not reported here. |
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Additional Figure 14-a:
Fraction of events in each muon match category versus generated $ \chi_2 $ decay transverse position $ v_{xy} $ for an inelastic dark matter model with $ m_1 = $ 5 GeV and $ \Delta = 0.1 \, m_1 $. Left: $ \chi_2 |\eta| < $ 1.2. Right: $ \chi_2 |\eta| > $ 1.2. Other observables such as $ \Delta R(\mu\mu) $ have a subdominant impact on the matching distribution and are therefore not reported here. |
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Additional Figure 14-b:
Fraction of events in each muon match category versus generated $ \chi_2 $ decay transverse position $ v_{xy} $ for an inelastic dark matter model with $ m_1 = $ 5 GeV and $ \Delta = 0.1 \, m_1 $. Left: $ \chi_2 |\eta| < $ 1.2. Right: $ \chi_2 |\eta| > $ 1.2. Other observables such as $ \Delta R(\mu\mu) $ have a subdominant impact on the matching distribution and are therefore not reported here. |
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Additional Figure 15:
Measured distributions of min-$d_{xy}$ in the 0-match category (upper left), 1-match category (upper right), and 2-match category (lower) in the signal-enriched region of the ABCD plane. Events must pass $I^{\text{rel}}_{\text{PF}}$ requirements in the 1- and 2-match categories and the $\Delta\phi_{\mu\mu}^{\text{MET}}$ requirement in the 0-match category. The shapes of the background prediction (filled red histograms) are extracted from the remaining region of the ABCD plane and normalized to the signal-enriched yields. Benchmark signal hypotheses are also shown. Vertical dashed gray lines define the most signal-sensitive ABCD bins. The last bin contains the overflow events. |
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Additional Figure 15-a:
Measured distribution of min-$d_{xy}$ in the 0-match category in the signal-enriched region of the ABCD plane. Events must pass $\Delta\phi_{\mu\mu}^{\text{MET}}$ requirement. The shapes of the background prediction (filled red histograms) are extracted from the remaining region of the ABCD plane and normalized to the signal-enriched yields. Benchmark signal hypotheses are also shown. Vertical dashed gray lines define the most signal-sensitive ABCD bins. The last bin contains the overflow events. |
png pdf |
Additional Figure 15-b:
Measured distribution of min-$d_{xy}$ in the 1-match category in the signal-enriched region of the ABCD plane. Events must pass $I^{\text{rel}}_{\text{PF}}$ requirements. The shapes of the background prediction (filled red histograms) are extracted from the remaining region of the ABCD plane and normalized to the signal-enriched yields. Benchmark signal hypotheses are also shown. Vertical dashed gray lines define the most signal-sensitive ABCD bins. The last bin contains the overflow events. |
png pdf |
Additional Figure 15-c:
Measured distribution of min-$d_{xy}$ in the 2-match category in the signal-enriched region of the ABCD plane. Events must pass $I^{\text{rel}}_{\text{PF}}$ requirements. The shapes of the background prediction (filled red histograms) are extracted from the remaining region of the ABCD plane and normalized to the signal-enriched yields. Benchmark signal hypotheses are also shown. Vertical dashed gray lines define the most signal-sensitive ABCD bins. The last bin contains the overflow events. |
| Additional Tables | |
png pdf |
Additional Table 1:
Summary of the selection used to define the signal region. |
png pdf |
Additional Table 2:
Selection efficiencies for iDM with $ m_1 = $ 5 GeV and $ \Delta = 0.1 \, m_1 $. |
png pdf |
Additional Table 3:
Selection efficiencies for iDM with $ m_1 = $ 50 GeV and $ \Delta = 0.4 \, m_1 $. |
png pdf |
Additional Table 4:
Selection efficiencies for iDM with $ m_1 = $ 5 GeV and $ \Delta = 0.4 \, m_1 $. |
png pdf |
Additional Table 5:
Selection efficiencies for iDM with $ m_1 = $ 50 GeV and $ \Delta = 0.1 \, m_1 $. |
png pdf |
Additional Table 6:
Summary of the systematic uncertainties in the analysis. All uncertainties are applied to signal yields independently of the bin in the ABCD plane. |
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