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| CMS-PAS-EXO-19-020 | ||
| Search for resonant production of strongly-coupled dark matter in proton-proton collisions at 13 TeV | ||
| CMS Collaboration | ||
| August 2021 | ||
| Abstract: The first collider search for dark matter arising from a strongly-coupled hidden sector is presented, using a data sample corresponding to 137 fb$^{-1}$ collected with the CMS detector at the CERN LHC at a center-of-mass energy of 13 TeV. The hidden sector is hypothesized to couple to the standard model (SM) via a heavy leptophobic Z' mediator. The resonant production and decay of such a mediator in proton-proton collisions would result in two "semi-visible'' jets, which contain both visible matter and invisible dark matter. This would lead to moderate missing energy aligned with one of the jets, a signature ignored by most dark matter searches. The observed dijet transverse mass spectrum is smoothly falling, as expected from the SM; no structure compatible with the signal is observed. Assuming the same couplings as the SM Z boson, mediator masses up to 3.9 TeV are excluded at 95% confidence level, depending on the other signal model parameters. To enhance the sensitivity of the search for this particular class of models, a boosted decision tree (BDT) is trained using jet substructure variables to distinguish between semi-visible jets and standard model jets from background processes. When the BDT is employed to select events with jets identified as semi-visible, the mediator mass exclusion increases to 5.1 TeV, for wider ranges of the other signal model parameters. | ||
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Links:
CDS record (PDF) ;
CADI line (restricted) ;
These preliminary results are superseded in this paper, Submitted to JHEP. The superseded preliminary plots can be found here. |
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| Figures | |
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Figure 1:
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. |
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Figure 2-a:
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. |
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Figure 2-b:
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. |
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Figure 3:
The normalized distributions of the BDT input variables ${m_{\text {SD}}}$ and ${p_{\text {T}}D}$ for the two highest-${p_{\mathrm {T}}}$ jets from the simulated SM backgrounds and several signal models. The jet ${p_{\mathrm {T}}}$ distributions are weighted so that all samples have matching distributions. |
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Figure 3-a:
The normalized distributions of the BDT input variables ${m_{\text {SD}}}$ and ${p_{\text {T}}D}$ for the two highest-${p_{\mathrm {T}}}$ jets from the simulated SM backgrounds and several signal models. The jet ${p_{\mathrm {T}}}$ distributions are weighted so that all samples have matching distributions. |
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Figure 3-b:
The normalized distributions of the BDT input variables ${m_{\text {SD}}}$ and ${p_{\text {T}}D}$ for the two highest-${p_{\mathrm {T}}}$ jets from the simulated SM backgrounds and several signal models. The jet ${p_{\mathrm {T}}}$ distributions are weighted so that all samples have matching distributions. |
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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 for each pairing. The discriminator WP of 0.55 is indicated on each curve as a circle. |
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Figure 4-a:
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 for each pairing. The discriminator WP of 0.55 is indicated on each curve as a circle. |
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Figure 4-b:
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 for each pairing. The discriminator WP of 0.55 is indicated on each curve as a 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 (${g_{2}(x) = \exp(p_1 x) x^{p_2}}$, ${g_{3}(x) = \exp(p_1 x) x^{p_2 (1 + p_3 \log(x))}}$, ${x = {M_{\mathrm {T}}} /\,\sqrt {\smash [b]{s}}}$). The lower panel shows the difference between the observation and the prediction divided by the statistical uncertainty in the observation. 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-${R_{\mathrm {T}}}$ (left) and low-${R_{\mathrm {T}}}$ (right) signal regions, comparing the observed data to the background prediction from the analytic fit (${g_{2}(x) = \exp(p_1 x) x^{p_2}}$, ${g_{3}(x) = \exp(p_1 x) x^{p_2 (1 + p_3 \log(x))}}$, ${x = {M_{\mathrm {T}}} /\,\sqrt {\smash [b]{s}}}$). The lower panel shows the difference between the observation and the prediction divided by the statistical uncertainty in the observation. 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 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 (${g_{2}(x) = \exp(p_1 x) x^{p_2}}$, ${g_{3}(x) = \exp(p_1 x) x^{p_2 (1 + p_3 \log(x))}}$, ${x = {M_{\mathrm {T}}} /\,\sqrt {\smash [b]{s}}}$). The lower panel shows the difference between the observation and the prediction divided by the statistical uncertainty in the observation. 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. The distributions from several example signal models, with cross sections corresponding to the observed limits, are superimposed. |
png pdf |
Figure 6-a:
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. The distributions from several example signal models, with cross sections corresponding to the observed limits, are superimposed. |
png pdf |
Figure 6-b:
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. The distributions from several example signal models, with cross sections corresponding to the observed limits, are superimposed. |
png pdf |
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. 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. |
png pdf |
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. 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 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. |
png pdf |
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. 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 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. |
png pdf |
Figure 7-c:
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. 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. |
png pdf |
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 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. |
png pdf |
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. 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 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. |
png pdf |
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. 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 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. |
png pdf |
Figure 8-c:
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 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. |
| 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 given in bold text. |
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Table 2:
Summary of the selection requirements. |
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Table 3:
Metrics representing the performance of the BDT for the benchmark signal model ($ {m_{{{\mathrm{Z}}^{\prime}}}} = $ 3100 GeV, $ {m_{\text {dark}}} = $ 20 GeV, $ {r_{\text {inv}}} = $ 0.3, $ {\alpha _{\text {dark}}} = {{\alpha _{\text {dark}}} ^{\text {peak}}} $), compared to each of the major SM background processes. |
| Summary |
| We present the first collider search for resonant production of dark matter from a strongly-coupled hidden sector in the form of semi-visible jets. The search uses the full Run 2 proton-proton collision dataset collected by the CMS detector, which corresponds to an integrated luminosity of 137 fb$^{-1}$ at a center-of-mass energy of 13 TeV. The signal model introduces a dark sector with multiple flavors of dark quarks charged under a dark confining force, which 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 "semi-visible'' jets. The hidden sector communicates with the SM via a leptophobic Z' boson mediator. |
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