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| CMS-EXO-19-020 ; CERN-EP-2021-252 | ||
| Search for resonant production of strongly coupled dark matter in proton-proton collisions at 13 TeV | ||
| CMS Collaboration | ||
| 21 December 2021 | ||
| JHEP 06 (2022) 156 | ||
| Abstract: The first collider search for dark matter arising from a strongly coupled hidden sector is presented and uses a data sample corresponding to 138 fb$^{-1}$, collected with the CMS detector at the CERN LHC, at $\sqrt{s} = $ 13 TeV. The hidden sector is hypothesized to couple to the standard model (SM) via a heavy leptophobic Z' mediator produced as a resonance in proton-proton collisions. The mediator decay results in two "semivisible'' jets, containing both visible matter and invisible dark matter. The final state therefore includes moderate missing energy aligned with one of the jets, a signature ignored by most dark matter searches. No structure in the dijet transverse mass spectra compatible with the signal is observed. Assuming the Z' boson has a universal coupling of 0.25 to the SM quarks, an inclusive search, relevant to any model that exhibits this kinematic behavior, excludes mediator masses of 1.5-4.0 TeV at 95% confidence level, depending on the other signal model parameters. To enhance the sensitivity of the search for this particular class of hidden sector models, a boosted decision tree (BDT) is trained using jet substructure variables to distinguish between semivisible jets and SM jets from background processes. When the BDT is employed to identify each jet in the dijet system as semivisible, the mediator mass exclusion increases to 5.1 TeV, for wider ranges of the other signal model parameters. These limits exclude a wide range of strongly coupled hidden sector models for the first time. | ||
| Links: e-print arXiv:2112.11125 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; | ||
| Figures & Tables | Summary | Additional Figures & Tables | References | CMS Publications |
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| Figures | |
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Figure 1:
Feynman diagram of leading-order resonant production of dark quarks through a Z' mediator. The relevant couplings to SM quarks and dark quarks, ${g_{\mathrm{q}}}$ and ${g_{{\chi}}}$, are indicated at the labeled vertices. |
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Figure 2:
The normalized distributions of the characteristic variables ${R_{\mathrm {T}}}$ and ${\Delta \phi _{\text {min}}}$ for the simulated SM backgrounds and several signal models. For each variable, the requirement on that variable is omitted, but all other preselection requirements are applied. The black (red) vertical dotted line indicates the preselection (final selection) requirement on the variable, if any. The blue vertical dotted line indicates the boundary between different signal regions. The last bin of each histogram includes the overflow events. |
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Figure 2-a:
The normalized distribution of ${R_{\mathrm {T}}}$ for the simulated SM backgrounds and several signal models. The requirement on that variable is omitted, but all other preselection requirements are applied. The black (red) vertical dotted line indicates the preselection (final selection) requirement on the variable, if any. The blue vertical dotted line indicates the boundary between different signal regions. The last bin includes the overflow events. |
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Figure 2-b:
The normalized distribution of ${\Delta \phi _{\text {min}}}$ for the simulated SM backgrounds and several signal models. The requirement on that variable is omitted, but all other preselection requirements are applied. The black (red) vertical dotted line indicates the preselection (final selection) requirement on the variable, if any. The blue vertical dotted line indicates the boundary between different signal regions. The last bin includes the overflow events. |
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Figure 3:
The normalized distributions of the BDT input variables ${m_{\mathrm {SD}}}$ and ${D_{{p_{\mathrm {T}}}}}$ for the two highest ${p_{\mathrm {T}}}$ jets from the simulated SM backgrounds and several signal models. Each sample's jet ${p_{\mathrm {T}}}$ distribution is weighted to match a reference distribution (see text). The last bin of each histogram includes the overflow events. |
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Figure 3-a:
The normalized distribution of the BDT input variable ${m_{\mathrm {SD}}}$ for the two highest ${p_{\mathrm {T}}}$ jets from the simulated SM backgrounds and several signal models. Each sample's jet ${p_{\mathrm {T}}}$ distribution is weighted to match a reference distribution (see text). The last bin includes the overflow events. |
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Figure 3-b:
The normalized distribution of the BDT input variable ${D_{{p_{\mathrm {T}}}}}$ for the two highest ${p_{\mathrm {T}}}$ jets from the simulated SM backgrounds and several signal models. Each sample's jet ${p_{\mathrm {T}}}$ distribution is weighted to match a reference distribution (see text). The last bin includes the overflow events. |
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Figure 4:
Left: The normalized BDT discriminator distribution for the two highest ${p_{\mathrm {T}}}$ jets from the simulated SM backgrounds and several signal models. The discriminator WP of 0.55 is indicated as a dashed line. Right: The BDT ROC curves for the two highest ${p_{\mathrm {T}}}$ jets, comparing the simulated SM backgrounds with one signal model. The area under the ROC curve is listed in parentheses for each pairing. The discriminator WP of 0.55 is indicated on each curve as a filled circle. |
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Figure 4-a:
The normalized BDT discriminator distribution for the two highest ${p_{\mathrm {T}}}$ jets from the simulated SM backgrounds and several signal models. The discriminator WP of 0.55 is indicated as a dashed line. |
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Figure 4-b:
The BDT ROC curves for the two highest ${p_{\mathrm {T}}}$ jets, comparing the simulated SM backgrounds with one signal model. The area under the ROC curve is listed in parentheses for each pairing. The discriminator WP of 0.55 is indicated on each curve as a filled circle. |
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Figure 5:
The ${m_{\mathrm {T}}}$ distribution for the high-${R_{\mathrm {T}}}$ (left) and low-${R_{\mathrm {T}}}$ (right) signal regions, comparing the observed data to the background prediction from the analytic fit (${g_{3}(x) = \exp(p_1 x) x^{p_2 (1 + p_3 \ln(x))}}$, ${g_{2}(x) = \exp(p_1 x) x^{p_2}}$, ${x = {m_{\mathrm {T}}} /\,\sqrt {\smash [b]{s}}}$). The lower panel shows the difference between the observation and the prediction divided by the statistical uncertainty in the observation (${\sigma _{\text {exp}}}$). The distributions from several example signal models, with cross sections corresponding to the observed limits, are superimposed. |
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Figure 5-a:
The ${m_{\mathrm {T}}}$ distribution for the high-${R_{\mathrm {T}}}$ signal region, comparing the observed data to the background prediction from the analytic fit (${g_{3}(x) = \exp(p_1 x) x^{p_2 (1 + p_3 \ln(x))}}$, ${x = {m_{\mathrm {T}}} /\,\sqrt {\smash [b]{s}}}$). The lower panel shows the difference between the observation and the prediction divided by the statistical uncertainty in the observation (${\sigma _{\text {exp}}}$). The distributions from several example signal models, with cross sections corresponding to the observed limits, are superimposed. |
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Figure 5-b:
The ${m_{\mathrm {T}}}$ distribution for the low-${R_{\mathrm {T}}}$ signal region, comparing the observed data to the background prediction from the analytic fit (${g_{2}(x) = \exp(p_1 x) x^{p_2}}$, ${x = {m_{\mathrm {T}}} /\,\sqrt {\smash [b]{s}}}$). The lower panel shows the difference between the observation and the prediction divided by the statistical uncertainty in the observation (${\sigma _{\text {exp}}}$). The distributions from several example signal models, with cross sections corresponding to the observed limits, are superimposed. |
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Figure 6:
The ${m_{\mathrm {T}}}$ distribution for the high-SVJ2 (left) and low-SVJ2 (right) signal regions, comparing the observed data to the background prediction from the analytic fit (${g_{2}(x) = \exp(p_1 x) x^{p_2}}$, ${x = {m_{\mathrm {T}}} /\,\sqrt {\smash [b]{s}}}$). The lower panel shows the difference between the observation and the prediction divided by the statistical uncertainty in the observation (${\sigma _{\text {exp}}}$). The distributions from several example signal models, with cross sections corresponding to the observed limits, are superimposed. |
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Figure 6-a:
The ${m_{\mathrm {T}}}$ distribution for the high-SVJ2 signal region, comparing the observed data to the background prediction from the analytic fit (${g_{2}(x) = \exp(p_1 x) x^{p_2}}$, ${x = {m_{\mathrm {T}}} /\,\sqrt {\smash [b]{s}}}$). The lower panel shows the difference between the observation and the prediction divided by the statistical uncertainty in the observation (${\sigma _{\text {exp}}}$). The distributions from several example signal models, with cross sections corresponding to the observed limits, are superimposed. |
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Figure 6-b:
The ${m_{\mathrm {T}}}$ distribution for the low-SVJ2 signal region, comparing the observed data to the background prediction from the analytic fit (${g_{2}(x) = \exp(p_1 x) x^{p_2}}$, ${x = {m_{\mathrm {T}}} /\,\sqrt {\smash [b]{s}}}$). The lower panel shows the difference between the observation and the prediction divided by the statistical uncertainty in the observation (${\sigma _{\text {exp}}}$). The distributions from several example signal models, with cross sections corresponding to the observed limits, are superimposed. |
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Figure 7:
The 95% CL upper limits on the product of the cross section and branching fraction from the inclusive search, for variations of pairs of the signal model parameters. In the upper plots, the filled region indicates the observed upper limit. The solid black curves indicate the observed exclusions for the nominal Z' cross section, while the solid red curves indicate the expected exclusions, and the dashed lines indicate the regions containing 68 and 95% of the distributions of expected exclusions. In the upper left plot, the regions between the respective pairs of lines or below the inner 95% dashed line are excluded. In the upper right plot, the regions inside the circles are excluded. The lower plot shows the ${\alpha _{\text {dark}}}$ variation as multiple curves in one dimension, because there are only three parameter values considered. The black, blue, and red solid lines show the observed upper limits for each variation, while the dashed lines show the expected limits. The inner (green) and outer (yellow) bands indicate the regions containing 68 and 95%, respectively, of the distributions of expected limits. The purple solid line labeled "Theoretical'' represents the nominal Z' cross section. |
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Figure 7-a:
The 95% CL upper limits on the product of the cross section and branching fraction from the inclusive search, for variations of pairs of the signal model parameters. The filled region indicates the observed upper limit. The solid black curves indicate the observed exclusions for the nominal Z' cross section, while the solid red curves indicate the expected exclusions, and the dashed lines indicate the regions containing 68 and 95% of the distributions of expected exclusions. The regions between the respective pairs of lines or below the inner 95% dashed line are excluded. |
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Figure 7-b:
The 95% CL upper limits on the product of the cross section and branching fraction from the inclusive search, for variations of pairs of the signal model parameters. The filled region indicates the observed upper limit. The solid black curves indicate the observed exclusions for the nominal Z' cross section, while the solid red curves indicate the expected exclusions, and the dashed lines indicate the regions containing 68 and 95% of the distributions of expected exclusions. The regions inside the circles are excluded. |
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Figure 7-c:
The 95% CL upper limits on the product of the cross section and branching fraction from the inclusive search. The plot shows the ${\alpha _{\text {dark}}}$ variation as multiple curves in one dimension, because there are only three parameter values considered. The black, blue, and red solid lines show the observed upper limits for each variation, while the dashed lines show the expected limits. The inner (green) and outer (yellow) bands indicate the regions containing 68 and 95%, respectively, of the distributions of expected limits. The purple solid line labeled "Theoretical'' represents the nominal Z' cross section. |
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Figure 8:
The 95% CL upper limits on the product of the cross section and branching fraction from the BDT-based search, for variations of pairs of the signal model parameters. In the upper plots, the filled region indicates the observed upper limit. The solid black curves indicate the observed exclusions for the nominal Z' cross section, while the solid red curves indicate the expected exclusions, and the dashed lines indicate the regions containing 68 and 95% of the distributions of expected exclusions. The regions inside the circles are excluded. The lower plot shows the ${\alpha _{\text {dark}}}$ variation as multiple curves in one dimension, because there are only three parameter values considered. The black, blue, and red solid lines show the observed upper limits for each variation, while the dashed lines show the expected limits. The inner (green) and outer (yellow) bands indicate the regions containing 68 and 95%, respectively, of the distributions of expected limits. The purple solid line labeled "Theoretical'' represents the nominal Z' cross section. |
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Figure 8-a:
The 95% CL upper limits on the product of the cross section and branching fraction from the BDT-based search, for variations of pairs of the signal model parameters. The filled region indicates the observed upper limit. The solid black curves indicate the observed exclusions for the nominal Z' cross section, while the solid red curves indicate the expected exclusions, and the dashed lines indicate the regions containing 68 and 95% of the distributions of expected exclusions. The regions inside the circles are excluded. |
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Figure 8-b:
The 95% CL upper limits on the product of the cross section and branching fraction from the BDT-based search, for variations of pairs of the signal model parameters. The filled region indicates the observed upper limit. The solid black curves indicate the observed exclusions for the nominal Z' cross section, while the solid red curves indicate the expected exclusions, and the dashed lines indicate the regions containing 68 and 95% of the distributions of expected exclusions. The regions inside the circles are excluded. |
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Figure 8-c:
The 95% CL upper limits on the product of the cross section and branching fraction from the BDT-based search. The plot shows the ${\alpha _{\text {dark}}}$ variation as multiple curves in one dimension, because there are only three parameter values considered. The black, blue, and red solid lines show the observed upper limits for each variation, while the dashed lines show the expected limits. The inner (green) and outer (yellow) bands indicate the regions containing 68 and 95%, respectively, of the distributions of expected limits. The purple solid line labeled "Theoretical'' represents the nominal Z' cross section. |
| Tables | |
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Table 1:
The three two-dimensional signal model parameter scans. For each scan, the ranges of the parameters that are varied in that scan are indicated by dashes. |
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Table 2:
Summary of the preselection and final selection requirements. The symbol * indicates a selection applied only to the later portion of the 2018 data. |
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Table 3:
Metrics representing the performance of the BDT for the benchmark signal model ($ {m_{{{\mathrm{Z}}^{\prime}}}} = $ 3.1 TeV, $ {m_{\text {dark}}} = $ 20 GeV, $ {r_{\text {inv}}} = $ 0.3, $ {\alpha _{\text {dark}}} = \alpha {} _{\text {dark}} ^{\text {peak}} $), compared to each of the major SM background processes. |
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Table 4:
The range of effects on the signal yield for each systematic uncertainty and the total. Values less than 0.01% are rounded to 0.0%. |
| Summary |
|
We present the first collider search for resonant production of dark matter from a strongly coupled hidden sector. The search uses proton-proton collision data collected with the CMS detector in 2016-2018, corresponding to an integrated luminosity of 138 fb$^{-1}$ at a center-of-mass energy of 13 TeV. The signal model introduces a dark sector with multiple flavors of dark quarks that are charged under a dark confining force and form stable and unstable dark hadrons. The stable dark hadrons constitute dark matter candidates, while the unstable dark hadrons decay promptly to standard model (SM) quarks, forming collimated sprays of both invisible and visible particles known as "semivisible'' jets. The hidden sector communicates with the SM via a leptophobic Z' boson mediator. We consider variations in several parameters of the hidden sector signal model: the Z' mass, ${m_{Z'}} $; the dark hadron mass, ${m_{\text{dark}}} $; the fraction of stable, invisible dark hadrons, ${r_{\text{inv}}} $; and the running coupling of the dark force, ${\alpha_{\text{dark}}} $. We pursue a dual strategy to maximize both generality and sensitivity. The general version of the search, which uses only event-level kinematic variables, excludes models with 1.5 $ < {m_{Z'}} < $ 4.0 TeV and 0.07 $ < {r_{\text{inv}}} < $ 0.53 at 95% confidence level (CL), depending on the other signal model parameters. The more sensitive version of the search employs a boosted decision tree (BDT) to discriminate between signal and background jets. With the BDT-based search, the 95% CL exclusion limits extend to 1.5 $ < {m_{Z'}} < $ 5.1 TeV and 0.01 $ < {r_{\text{inv}}} < $ 0.77, for wider ranges of the other signal model parameters. Depending on the mediator mass, all variations considered for ${m_{\text{dark}}} $ and ${\alpha_{\text{dark}}} $ can be excluded. These improvements indicate the power of machine learning techniques to separate dark sector signals from large SM backgrounds. These results complement existing searches for dijet resonances and dark matter events with missing momentum and initial-state radiation. Existing strategies did not target strongly coupled hidden sector models, which produce events with jets aligned with moderate missing transverse momentum. Compared to standard dijet searches, the backgrounds are reduced and the resolution is improved by including missing momentum in the event selection and the resonance mass reconstruction, respectively. Events with jets aligned with missing momentum are explicitly rejected from other collider dark matter searches. In addition, the use of jet substructure provides a substantial increase in model-dependent sensitivity. As a result, a wide range of these models with intermediate ${r_{\text{inv}}} $ values are now excluded for the first time. |
| Additional Figures | |
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Additional Figure 1:
The normalized distributions of the variables ${m_{\mathrm {T}}}$, ${\Delta \eta ({\mathrm {J}} _{1}, {\mathrm {J}} _{2})}$, ${{p_{\mathrm {T}}} ^\text {miss}}$, ${N_{{\mathrm {e}}}}$, and ${N_{{{\mu}}}}$ for the simulated SM backgrounds and several signal models. For each variable, the requirement on that variable is omitted, but all other preselection requirements are applied. The ${R_{\mathrm {T}}}$ selection is omitted for the ${{p_{\mathrm {T}}} ^\text {miss}}$ distribution. The vertical dotted line indicates the preselection (final selection) requirement on the variable, if any. The last bin of each histogram includes the overflow events. |
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Additional Figure 1-a:
The normalized distribution of the variable ${m_{\mathrm {T}}}$ for the simulated SM backgrounds and several signal models. The requirement on that variable is omitted, but all other preselection requirements are applied. The vertical dotted line indicates the preselection (final selection) requirement on the variable. The last bin of each histogram includes the overflow events. |
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Additional Figure 1-b:
The normalized distribution of the variable ${\Delta \eta ({\mathrm {J}} _{1} {\mathrm {J}} _{2})}$ for the simulated SM backgrounds and several signal models. The requirement on that variable is omitted, but all other preselection requirements are applied. The vertical dotted line indicates the preselection (final selection) requirement on the variable. The last bin of each histogram includes the overflow events. |
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Additional Figure 1-c:
The normalized distribution of the variable ${{p_{\mathrm {T}}} ^\text {miss}}$ for the simulated SM backgrounds and several signal models. The requirement on that variable is omitted, but all other preselection requirements are applied. The ${R_{\mathrm {T}}}$ selection is omitted. The last bin of each histogram includes the overflow events. |
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Additional Figure 1-d:
The normalized distribution of the variable ${N_{{\mathrm {e}}}}$ for the simulated SM backgrounds and several signal models. The requirement on that variable is omitted, but all other preselection requirements are applied. The vertical dotted line indicates the preselection (final selection) requirement on the variable. The last bin of each histogram includes the overflow events. |
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Additional Figure 1-e:
The normalized distribution of the variable ${N_{{{\mu}}}}$ for the simulated SM backgrounds and several signal models. The requirement on that variable is omitted, but all other preselection requirements are applied. The vertical dotted line indicates the preselection (final selection) requirement on the variable. The last bin of each histogram includes the overflow events. |
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Additional Figure 2:
The normalized distribution of ${\Delta \eta ({\mathrm {J}} _{1}, {\mathrm {J}} _{2})}$ vs. ${R_{\mathrm {T}}}$ for the simulated QCD background. The preselection requirements on both variables are omitted, but all other preselection requirements are applied. The black dotted lines indicates the preselection requirements on the variables. |
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Additional Figure 3:
The normalized distributions of ${{p_{\mathrm {T}}} ^\text {miss}}$ vs. ${m_{\mathrm {T}}}$ and ${R_{\mathrm {T}}}$ vs. ${m_{\mathrm {T}}}$ for the simulated QCD background. All selection requirements are omitted, except for the requirement of two high-${p_{\mathrm {T}}}$ wide jets. |
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Additional Figure 3-a:
The normalized distributions of ${{p_{\mathrm {T}}} ^\text {miss}}$ vs. ${m_{\mathrm {T}}}$ for the simulated QCD background. All selection requirements are omitted, except for the requirement of two high-${p_{\mathrm {T}}}$ wide jets. |
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Additional Figure 3-b:
The normalized distributions of ${R_{\mathrm {T}}}$ vs. ${m_{\mathrm {T}}}$ for the simulated QCD background. All selection requirements are omitted, except for the requirement of two high-${p_{\mathrm {T}}}$ wide jets. |
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Additional Figure 4:
The normalized distributions of the BDT input variables ${\tau _{21}}$, ${\tau _{32}}$, ${N_{2}^{(1)}}$, and ${N_{3}^{(1)}}$ for the two highest ${p_{\mathrm {T}}}$ wide jets from the simulated SM backgrounds and several signal models with varying ${m_{\mathrm {dark}}}$ values. Each sample's jet ${p_{\mathrm {T}}}$ distribution is weighted to match a reference distribution (see text). The last bin of each histogram includes the overflow events. |
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Additional Figure 4-a:
The normalized distributions of the BDT input variable ${\tau _{21}}$ for the two highest ${p_{\mathrm {T}}}$ wide jets from the simulated SM backgrounds and several signal models with varying ${m_{\mathrm {dark}}}$ values. Each sample's jet ${p_{\mathrm {T}}}$ distribution is weighted to match a reference distribution (see text). The last bin of each histogram includes the overflow events. |
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Additional Figure 4-b:
The normalized distributions of the BDT input variable ${\tau _{32}}$ for the two highest ${p_{\mathrm {T}}}$ wide jets from the simulated SM backgrounds and several signal models with varying ${m_{\mathrm {dark}}}$ values. Each sample's jet ${p_{\mathrm {T}}}$ distribution is weighted to match a reference distribution (see text). The last bin of each histogram includes the overflow events. |
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Additional Figure 4-c:
The normalized distributions of the BDT input variable ${N_{2}^{(1)}}$ for the two highest ${p_{\mathrm {T}}}$ wide jets from the simulated SM backgrounds and several signal models with varying ${m_{\mathrm {dark}}}$ values. Each sample's jet ${p_{\mathrm {T}}}$ distribution is weighted to match a reference distribution (see text). The last bin of each histogram includes the overflow events. |
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Additional Figure 4-d:
The normalized distributions of the BDT input variable ${N_{3}^{(1)}}$ for the two highest ${p_{\mathrm {T}}}$ wide jets from the simulated SM backgrounds and several signal models with varying ${m_{\mathrm {dark}}}$ values. Each sample's jet ${p_{\mathrm {T}}}$ distribution is weighted to match a reference distribution (see text). The last bin of each histogram includes the overflow events. |
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Additional Figure 5:
The normalized distributions of the BDT input variables ${g_{\text {jet}}}$, ${\sigma _{\text {major}}}$, ${\sigma _{\text {minor}}}$, and $\Delta \phi (\vec{{\mathrm {J}}}, {\vec{p}_{\mathrm {T}}}^{\,\text {miss}})$ for the two highest ${p_{\mathrm {T}}}$ wide jets from the simulated SM backgrounds and several signal models with varying ${r_{\mathrm {inv}}}$ values. Each sample's jet ${p_{\mathrm {T}}}$ distribution is weighted to match a reference distribution (see text). The last bin of each histogram includes the overflow events. |
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Additional Figure 5-a:
The normalized distributions of the BDT input variable ${g_{\text {jet}}}$ for the two highest ${p_{\mathrm {T}}}$ wide jets from the simulated SM backgrounds and several signal models with varying ${r_{\mathrm {inv}}}$ values. Each sample's jet ${p_{\mathrm {T}}}$ distribution is weighted to match a reference distribution (see text). The last bin of each histogram includes the overflow events. |
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Additional Figure 5-b:
The normalized distributions of the BDT input variable ${\sigma _{\text {major}}}$ for the two highest ${p_{\mathrm {T}}}$ wide jets from the simulated SM backgrounds and several signal models with varying ${r_{\mathrm {inv}}}$ values. Each sample's jet ${p_{\mathrm {T}}}$ distribution is weighted to match a reference distribution (see text). The last bin of each histogram includes the overflow events. |
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Additional Figure 5-c:
The normalized distributions of the BDT input variable ${\sigma _{\text {minor}}}$ for the two highest ${p_{\mathrm {T}}}$ wide jets from the simulated SM backgrounds and several signal models with varying ${r_{\mathrm {inv}}}$ values. Each sample's jet ${p_{\mathrm {T}}}$ distribution is weighted to match a reference distribution (see text). The last bin of each histogram includes the overflow events. |
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Additional Figure 5-d:
The normalized distributions of the BDT input variable $\Delta \phi (\vec{{\mathrm {J}}}, {\vec{p}_{\mathrm {T}}}^{\,\text {miss}})$ for the two highest ${p_{\mathrm {T}}}$ wide jets from the simulated SM backgrounds and several signal models with varying ${r_{\mathrm {inv}}}$ values. Each sample's jet ${p_{\mathrm {T}}}$ distribution is weighted to match a reference distribution (see text). The last bin of each histogram includes the overflow events. |
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Additional Figure 6:
The normalized distributions of the BDT input variables $f_{{\mathrm {h}^{\pm}}}$, $f_{{\mathrm {e}}}$, $f_{{{\mu}}}$, $f_{{\mathrm {h}^{0}}}$, and $f_{\gamma}$ for the two highest ${p_{\mathrm {T}}}$ wide jets from the simulated SM backgrounds and several signal models with varying ${m_{{{{\mathrm {Z}}}^{\prime}}}}$ values. Each sample's jet ${p_{\mathrm {T}}}$ distribution is weighted to match a reference distribution (see text). The last bin of each histogram includes the overflow events. |
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Additional Figure 6-a:
The normalized distributions of the BDT input variables $f_{{\mathrm {h}^{\pm}}}$ or the two highest ${p_{\mathrm {T}}}$ wide jets from the simulated SM backgrounds and several signal models with varying ${m_{{{{\mathrm {Z}}}^{\prime}}}}$ values. Each sample's jet ${p_{\mathrm {T}}}$ distribution is weighted to match a reference distribution (see text). The last bin of each histogram includes the overflow events. |
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Additional Figure 6-b:
The normalized distributions of the BDT input variables $f_{{\mathrm {e}}}$ for the two highest ${p_{\mathrm {T}}}$ wide jets from the simulated SM backgrounds and several signal models with varying ${m_{{{{\mathrm {Z}}}^{\prime}}}}$ values. Each sample's jet ${p_{\mathrm {T}}}$ distribution is weighted to match a reference distribution (see text). The last bin of each histogram includes the overflow events. |
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Additional Figure 6-c:
The normalized distributions of the BDT input variables $f_{{{\mu}}}$ for the two highest ${p_{\mathrm {T}}}$ wide jets from the simulated SM backgrounds and several signal models with varying ${m_{{{{\mathrm {Z}}}^{\prime}}}}$ values. Each sample's jet ${p_{\mathrm {T}}}$ distribution is weighted to match a reference distribution (see text). The last bin of each histogram includes the overflow events. |
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Additional Figure 6-d:
The normalized distributions of the BDT input variables $f_{{\mathrm {h}^{0}}}$ for the two highest ${p_{\mathrm {T}}}$ wide jets from the simulated SM backgrounds and several signal models with varying ${m_{{{{\mathrm {Z}}}^{\prime}}}}$ values. Each sample's jet ${p_{\mathrm {T}}}$ distribution is weighted to match a reference distribution (see text). The last bin of each histogram includes the overflow events. |
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Additional Figure 6-e:
The normalized distributions of the BDT input variables $f_{\gamma}$ for the two highest ${p_{\mathrm {T}}}$ wide jets from the simulated SM backgrounds and several signal models with varying ${m_{{{{\mathrm {Z}}}^{\prime}}}}$ values. Each sample's jet ${p_{\mathrm {T}}}$ distribution is weighted to match a reference distribution (see text). The last bin of each histogram includes the overflow events. |
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Additional Figure 7:
The product of signal acceptance and efficiency in the high-${R_{\mathrm {T}}}$ signal region, for variations of pairs of the signal model parameters. |
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Additional Figure 7-a:
The product of signal acceptance and efficiency in the high-${R_{\mathrm {T}}}$ signal region, for variations of pairs of the signal model parameters. |
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Additional Figure 7-b:
The product of signal acceptance and efficiency in the high-${R_{\mathrm {T}}}$ signal region, for variations of pairs of the signal model parameters. |
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Additional Figure 7-c:
The product of signal acceptance and efficiency in the high-${R_{\mathrm {T}}}$ signal region, for variations of pairs of the signal model parameters. |
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Additional Figure 8:
The product of signal acceptance and efficiency in the low-${R_{\mathrm {T}}}$ signal region, for variations of pairs of the signal model parameters. |
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Additional Figure 8-a:
The product of signal acceptance and efficiency in the low-${R_{\mathrm {T}}}$ signal region, for variations of pairs of the signal model parameters. |
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Additional Figure 8-b:
The product of signal acceptance and efficiency in the low-${R_{\mathrm {T}}}$ signal region, for variations of pairs of the signal model parameters. |
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Additional Figure 8-c:
The product of signal acceptance and efficiency in the low-${R_{\mathrm {T}}}$ signal region, for variations of pairs of the signal model parameters. |
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Additional Figure 9:
The product of signal acceptance and efficiency in the high-SVJ2 signal region, for variations of pairs of the signal model parameters. |
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Additional Figure 9-a:
The product of signal acceptance and efficiency in the high-SVJ2 signal region, for variations of pairs of the signal model parameters. |
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Additional Figure 9-b:
The product of signal acceptance and efficiency in the high-SVJ2 signal region, for variations of pairs of the signal model parameters. |
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Additional Figure 9-c:
The product of signal acceptance and efficiency in the high-SVJ2 signal region, for variations of pairs of the signal model parameters. |
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Additional Figure 10:
The product of signal acceptance and efficiency in the low-SVJ2 signal region, for variations of pairs of the signal model parameters. |
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Additional Figure 10-a:
The product of signal acceptance and efficiency in the low-SVJ2 signal region, for variations of pairs of the signal model parameters. |
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Additional Figure 10-b:
The product of signal acceptance and efficiency in the low-SVJ2 signal region, for variations of pairs of the signal model parameters. |
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Additional Figure 10-c:
The product of signal acceptance and efficiency in the low-SVJ2 signal region, for variations of pairs of the signal model parameters. |
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Additional Figure 11:
Comparison of the dijet mass ${m_{{\mathrm {J}} {\mathrm {J}}}}$, the transverse mass ${m_{\mathrm {T}}}$, and the Monte Carlo (MC) mass ${m_{\mathrm {MC}}}$ for a signal model with ${m_{{{{\mathrm {Z}}}^{\prime}}}} = $ 2.1 TeV (shown as a dotted black line). No selection is applied, except that there must be at least two jets. ${m_{\mathrm {MC}}}$ is computed by adding the generator-level four-vectors for invisible particles to the dijet system, to represent the achievable resolution if the invisible component were fully measured. The last bin of each histogram includes the overflow events. |
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Additional Figure 12:
${m_{\mathrm {T}}}$ distributions for signal models with different ${m_{\mathrm {dark}}}$ values for the high-${R_{\mathrm {T}}}$ (left) and low-${R_{\mathrm {T}}}$ (right) inclusive signal regions. |
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Additional Figure 12-a:
${m_{\mathrm {T}}}$ distributions for signal models with different ${m_{\mathrm {dark}}}$ values for the high-${R_{\mathrm {T}}}$ inclusive signal region. |
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Additional Figure 12-b:
${m_{\mathrm {T}}}$ distributions for signal models with different ${m_{\mathrm {dark}}}$ values for the low-${R_{\mathrm {T}}}$ inclusive signal region. |
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Additional Figure 13:
${m_{\mathrm {T}}}$ distributions for signal models with different ${r_{\mathrm {inv}}}$ values for the low-${R_{\mathrm {T}}}$ inclusive signal region. |
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Additional Figure 13-a:
${m_{\mathrm {T}}}$ distributions for signal models with different ${r_{\mathrm {inv}}}$ values for the high-${R_{\mathrm {T}}}$ inclusive signal region. |
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Additional Figure 13-b:
${m_{\mathrm {T}}}$ distributions for signal models with different ${r_{\mathrm {inv}}}$ values for the low-${R_{\mathrm {T}}}$ inclusive signal region. |
png pdf |
Additional Figure 14:
${m_{\mathrm {T}}}$ distributions for signal models with different ${\alpha _{\mathrm {dark}}}$ values for thelow-${R_{\mathrm {T}}}$ inclusive signal region. |
png pdf root |
Additional Figure 14-a:
${m_{\mathrm {T}}}$ distributions for signal models with different ${\alpha _{\mathrm {dark}}}$ values for the high-${R_{\mathrm {T}}}$ inclusive signal region. |
png pdf root |
Additional Figure 14-b:
${m_{\mathrm {T}}}$ distributions for signal models with different ${\alpha _{\mathrm {dark}}}$ values for thelow-${R_{\mathrm {T}}}$ inclusive signal region. |
png pdf |
Additional Figure 15:
The proportions of each SM background process in the inclusive signal regions. |
png pdf root |
Additional Figure 15-a:
The proportions of each SM background process in the inclusive signal regions. |
png pdf root |
Additional Figure 15-b:
The proportions of each SM background process in the inclusive signal regions. |
png pdf |
Additional Figure 16:
The proportions of each SM background process in the BDT-based signal regions. |
png pdf root |
Additional Figure 16-a:
The proportions of each SM background process in the BDT-based signal regions. |
png pdf root |
Additional Figure 16-b:
The proportions of each SM background process in the BDT-based signal regions. |
png pdf |
Additional Figure 17:
The 95% CL upper limits on the product of the cross section and branching fraction from the inclusive search for variations of pairs of the signal model parameters. The filled region indicates the expected upper limit. The solid black curves indicate the observed exclusions for the nominal ${{{\mathrm {Z}}}^{\prime}}$ cross section, while the solid red curves indicate the expected exclusions, and the dashed lines indicate the regions containing 68 and 95% of the distributions of expected exclusions. In the left plot, the regions between the respective pairs of lines or below the inner 95% dashed line are excluded. In the right plot, the regions inside the circles are excluded. |
png pdf root |
Additional Figure 17-a:
The 95% CL upper limits on the product of the cross section and branching fraction from the inclusive search for variations of a pair of the signal model parameters. The filled region indicates the expected upper limit. The solid black curves indicate the observed exclusions for the nominal ${{{\mathrm {Z}}}^{\prime}}$ cross section, while the solid red curves indicate the expected exclusions, and the dashed lines indicate the regions containing 68 and 95% of the distributions of expected exclusions. The regions between the respective pairs of lines or below the inner 95% dashed line are excluded. |
png pdf root |
Additional Figure 17-b:
The 95% CL upper limits on the product of the cross section and branching fraction from the inclusive search for variations of a pair of the signal model parameters. The filled region indicates the expected upper limit. The solid black curves indicate the observed exclusions for the nominal ${{{\mathrm {Z}}}^{\prime}}$ cross section, while the solid red curves indicate the expected exclusions, and the dashed lines indicate the regions containing 68 and 95% of the distributions of expected exclusions. The regions inside the circles are excluded. |
png pdf |
Additional Figure 18:
The 95% CL upper limits on the product of the cross section and branching fraction from the BDT-based search for variations of pairs of the signal model parameters. The filled region indicates the expected upper limit. The solid black curves indicate the observed exclusions for the nominal ${{{\mathrm {Z}}}^{\prime}}$ cross section, while the solid red curves indicate the expected exclusions, and the dashed lines indicate the regions containing 68 and 95% of the distributions of expected exclusions. The regions inside the circles are excluded. |
png pdf root |
Additional Figure 18-a:
The 95% CL upper limits on the product of the cross section and branching fraction from the BDT-based search for variations of a pair of the signal model parameters. The filled region indicates the expected upper limit. The solid black curves indicate the observed exclusions for the nominal ${{{\mathrm {Z}}}^{\prime}}$ cross section, while the solid red curves indicate the expected exclusions, and the dashed lines indicate the regions containing 68 and 95% of the distributions of expected exclusions. The regions inside the circles are excluded. |
png pdf root |
Additional Figure 18-b:
The 95% CL upper limits on the product of the cross section and branching fraction from the BDT-based search for variations of a pair of the signal model parameters. The filled region indicates the expected upper limit. The solid black curves indicate the observed exclusions for the nominal ${{{\mathrm {Z}}}^{\prime}}$ cross section, while the solid red curves indicate the expected exclusions, and the dashed lines indicate the regions containing 68 and 95% of the distributions of expected exclusions. The regions inside the circles are excluded. |
| Additional Tables | |
png pdf |
Additional Table 1:
Relative efficiencies in% for each step of the event selection process for the major background processes. Statistical uncertainties, at most 1.8%, are omitted. The line "Efficiency [%]'' is the absolute efficiency after the final selection. The subsequent lines show the efficiency for each signal region, relative to the final selection. |
png pdf |
Additional Table 2:
Relative efficiencies in% for each step of the event selection process for signals with $ {m_{{{{\mathrm {Z}}}^{\prime}}}} = $ 2.1 TeV, varying ${m_{\mathrm {dark}}}$ values, $ {r_{\mathrm {inv}}} = $ 0.3, and $ {\alpha _{\mathrm {dark}}} = {{\alpha _{\mathrm {dark}}} ^{\text {peak}}} $. Statistical uncertainties, at most 0.5%, are omitted. The line "Efficiency [%]'' is the absolute efficiency after the final selection. The subsequent lines show the efficiency for each signal region, relative to the final selection. |
png pdf |
Additional Table 3:
Relative efficiencies in% for each step of the event selection process for signals with $ {m_{{{{\mathrm {Z}}}^{\prime}}}} = $ 3.1 TeV, varying ${m_{\mathrm {dark}}}$ values, $ {r_{\mathrm {inv}}} = $ 0.3, and $ {\alpha _{\mathrm {dark}}} = {{\alpha _{\mathrm {dark}}} ^{\text {peak}}} $. Statistical uncertainties, at most 0.4%, are omitted. The line "Efficiency [%]'' is the absolute efficiency after the final selection. The subsequent lines show the efficiency for each signal region, relative to the final selection. |
png pdf |
Additional Table 4:
Relative efficiencies in% for each step of the event selection process for signals with $ {m_{{{{\mathrm {Z}}}^{\prime}}}} = $ 4.1 TeV, varying ${m_{\mathrm {dark}}}$ values, $ {r_{\mathrm {inv}}} = $ 0.3, and $ {\alpha _{\mathrm {dark}}} = {{\alpha _{\mathrm {dark}}} ^{\text {peak}}} $. Statistical uncertainties, at most 0.4%, are omitted. The line "Efficiency [%]'' is the absolute efficiency after the final selection. The subsequent lines show the efficiency for each signal region, relative to the final selection. |
png pdf |
Additional Table 5:
Relative efficiencies in% for each step of the event selection process for signals with $ {m_{{{{\mathrm {Z}}}^{\prime}}}} = $ 2.1 TeV, $ {m_{\mathrm {dark}}} = $ 20 GeV, varying ${r_{\mathrm {inv}}}$ values, and $ {\alpha _{\mathrm {dark}}} = {{\alpha _{\mathrm {dark}}} ^{\text {peak}}} $. Statistical uncertainties, at most 2.6%, are omitted. The line "Efficiency [%]'' is the absolute efficiency after the final selection. The subsequent lines show the efficiency for each signal region, relative to the final selection. |
png pdf |
Additional Table 6:
Relative efficiencies in% for each step of the event selection process for signals with $ {m_{{{{\mathrm {Z}}}^{\prime}}}} = $ 3.1 TeV, $ {m_{\mathrm {dark}}} = $ 20 GeV, varying ${r_{\mathrm {inv}}}$ values, and $ {\alpha _{\mathrm {dark}}} = {{\alpha _{\mathrm {dark}}} ^{\text {peak}}} $. Statistical uncertainties, at most 1.2%, are omitted. The line "Efficiency [%]'' is the absolute efficiency after the final selection. The subsequent lines show the efficiency for each signal region, relative to the final selection. |
png pdf |
Additional Table 7:
Relative efficiencies in% for each step of the event selection process for signals with $ {m_{{{{\mathrm {Z}}}^{\prime}}}} = $ 4.1 TeV, $ {m_{\mathrm {dark}}} = $ 20 GeV, varying ${r_{\mathrm {inv}}}$ values, and $ {\alpha _{\mathrm {dark}}} = {{\alpha _{\mathrm {dark}}} ^{\text {peak}}} $. Statistical uncertainties, at most 0.9%, are omitted. The line "Efficiency [%]'' is the absolute efficiency after the final selection. The subsequent lines show the efficiency for each signal region, relative to the final selection. |
png pdf |
Additional Table 8:
Relative efficiencies in% for each step of the event selection process for signals with $ {m_{{{{\mathrm {Z}}}^{\prime}}}} = $ 2.1 TeV, $ {m_{\mathrm {dark}}} = $ 20 GeV, $ {r_{\mathrm {inv}}} = $ 0.3, and varying ${\alpha _{\mathrm {dark}}}$ values. Statistical uncertainties, at most 0.4%, are omitted. The line "Efficiency [%]'' is the absolute efficiency after the final selection. The subsequent lines show the efficiency for each signal region, relative to the final selection. |
png pdf |
Additional Table 9:
Relative efficiencies in% for each step of the event selection process for signals with $ {m_{{{{\mathrm {Z}}}^{\prime}}}} = $ 3.1 TeV, $ {m_{\mathrm {dark}}} = $ 20 GeV, $ {r_{\mathrm {inv}}} = $ 0.3, and varying ${\alpha _{\mathrm {dark}}}$ values. Statistical uncertainties, at most 0.4%, are omitted. The line "Efficiency [%]'' is the absolute efficiency after the final selection. The subsequent lines show the efficiency for each signal region, relative to the final selection. |
png pdf |
Additional Table 10:
Relative efficiencies in% for each step of the event selection process for signals with $ {m_{{{{\mathrm {Z}}}^{\prime}}}} = $ 4.1 TeV, $ {m_{\mathrm {dark}}} = $ 20 GeV, $ {r_{\mathrm {inv}}} = $ 0.3, and varying ${\alpha _{\mathrm {dark}}}$ values. Statistical uncertainties, at most 0.4%, are omitted. The line "Efficiency [%]'' is the absolute efficiency after the final selection. The subsequent lines show the efficiency for each signal region, relative to the final selection. |
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