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CMS-EXO-16-048 ; CERN-EP-2017-294
Search for new physics in final states with an energetic jet or a hadronically decaying W or Z boson and transverse momentum imbalance at $\sqrt{s} = $ 13 TeV
Phys. Rev. D 97 (2018) 092005
Abstract: A search for new physics using events containing an imbalance in transverse momentum and one or more energetic jets arising from initial-state radiation or the hadronic decay of W or Z bosons is presented. A data sample of proton-proton collisions at $\sqrt{s} = $ 13 TeV, collected with the CMS detector at the LHC and corresponding to an integrated luminosity of 35.9 fb$^{-1}$, is used. The observed data are found to be in agreement with the expectation from standard model processes. The results are interpreted as limits on the dark matter production cross section in simplified models with vector, axial-vector, scalar, and pseudoscalar mediators. Interpretations in the context of fermion portal and nonthermal dark matter models are also provided. In addition, the results are interpreted in terms of invisible decays of the Higgs boson and set stringent limits on the fundamental Planck scale in the Arkani-Hamed, Dimopoulos, and Dvali model with large extra spatial dimensions.
Figures & Tables Summary References CMS Publications
Figures

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Figure 1:
Examples of Feynman diagrams of the main production mechanisms at the LHC of DM particles in association with a quark or gluon in the fermion portal model providing multijet (left) and monojet (middle, right) signatures.

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Figure 1-a:
Example of Feynman diagram of the one of the production mechanisms of DM particles in association with a quark or gluon in the fermion portal model providing a multijet signature.

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Figure 1-b:
Example of Feynman diagram of the one of the production mechanisms of DM particles in association with a quark or gluon in the fermion portal model providing a monojet signature.

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Figure 1-c:
Example of Feynman diagram of the one of the production mechanisms of DM particles in association with a quark or gluon in the fermion portal model providing a monojet signature.

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Figure 2:
Example of Feynman diagram of the main production mechanism at the LHC of DM particles in the nonthermal model resulting in the monojet final state. In this diagram, $\rm {d}$ and $\rm {d^{'}}$ represent different down-type quark generations.

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Figure 3:
Examples of Feynman diagrams of the main production mechanisms of gravitons at the LHC that provide monojet signatures in the ADD model.

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Figure 3-a:
Example of Feynman diagram of one of the main production mechanisms of gravitons at the LHC that provide monojet signatures in the ADD model.

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Figure 3-b:
Example of Feynman diagram of one of the main production mechanisms of gravitons at the LHC that provide monojet signatures in the ADD model.

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Figure 3-c:
Example of Feynman diagram of one of the main production mechanisms of gravitons at the LHC that provide monojet signatures in the ADD model.

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Figure 4:
Comparison between data and MC simulation for the $\mathrm{Z} (\ell \ell)$/$\gamma $+jets, $\mathrm{Z} (\ell \ell)$/$\mathrm{W} (\ell \nu)$, and $\mathrm{W} (\ell \nu)$/$\gamma $+jets ratios as a function of the hadronic recoil in the monojet category. In the lower panels, ratios of data with the pre-fit background prediction are shown. The gray bands include both the pre-fit systematic uncertainties and the statistical uncertainty in the simulation.

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Figure 4-a:
Comparison between data and MC simulation for the $\mathrm{Z} (\ell \ell)$/$\gamma $+jets ratio as a function of the hadronic recoil in the monojet category. In the lower panel, the ratio of data with the pre-fit background prediction is shown. The gray bands include both the pre-fit systematic uncertainties and the statistical uncertainty in the simulation.

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Figure 4-b:
Comparison between data and MC simulation for the $\mathrm{Z} (\ell \ell)$/$\mathrm{W} (\ell \nu)$ ratio as a function of the hadronic recoil in the monojet category. In the lower panel, the ratio of data with the pre-fit background prediction is shown. The gray bands include both the pre-fit systematic uncertainties and the statistical uncertainty in the simulation.

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Figure 4-c:
Comparison between data and MC simulation for the $\mathrm{W} (\ell \nu)$/$\gamma $+jets ratio as a function of the hadronic recoil in the monojet category. In the lower panel, the ratio of data with the pre-fit background prediction is shown. The gray bands include both the pre-fit systematic uncertainties and the statistical uncertainty in the simulation.

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Figure 5:
Comparison between data and MC simulation in the $\gamma $+jets control sample before and after performing the simultaneous fit across all the control samples and the signal region assuming the absence of any signal. The left plot shows the monojet category and the right plot shows the mono-V category. The hadronic recoil $ {p_{\mathrm {T}}} $ in $\gamma $+jets events is used as a proxy for $ {{p_{\mathrm {T}}} ^\text {miss}} $ in the signal region. The last bin includes all events with hadronic recoil $ {p_{\mathrm {T}}} $ larger than 1250 (750) GeV in the monojet (mono-V) category. In the lower panels, ratios of data with the pre-fit background prediction (red open points) and post-fit background prediction (blue full points) are shown for both the monojet and mono-V categories. The gray band in the lower panel indicates the post-fit uncertainty after combining all the systematic uncertainties. Finally, the distribution of the pulls, defined as the difference between data and the post-fit background prediction relative to the quadrature sum of the post-fit uncertainty in the prediction and statistical uncertainty in data, are also shown in the lowest panel.

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Figure 5-a:
Comparison between data and MC simulation in the $\gamma $+jets control sample before and after performing the simultaneous fit across all the control samples and the signal region assuming the absence of any signal. The plot shows the monojet category. The hadronic recoil $ {p_{\mathrm {T}}} $ in $\gamma $+jets events is used as a proxy for $ {{p_{\mathrm {T}}} ^\text {miss}} $ in the signal region. The last bin includes all events with hadronic recoil $ {p_{\mathrm {T}}} $ larger than 1250 (750) GeV in the monojet category. In the lower panel, the ratio of data with the pre-fit background prediction (red open points) and post-fit background prediction (blue full points) is shown. The gray band in the lower panel indicates the post-fit uncertainty after combining all the systematic uncertainties. Finally, the distribution of the pulls, defined as the difference between data and the post-fit background prediction relative to the quadrature sum of the post-fit uncertainty in the prediction and statistical uncertainty in data, are also shown in the lowest panel.

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Figure 5-b:
Comparison between data and MC simulation in the $\gamma $+jets control sample before and after performing the simultaneous fit across all the control samples and the signal region assuming the absence of any signal. The plot shows the mono-V category. The hadronic recoil $ {p_{\mathrm {T}}} $ in $\gamma $+jets events is used as a proxy for $ {{p_{\mathrm {T}}} ^\text {miss}} $ in the signal region. The last bin includes all events with hadronic recoil $ {p_{\mathrm {T}}} $ larger than 1250 (750) GeV in the mono-V category. In the lower panel, the ratio of data with the pre-fit background prediction (red open points) and post-fit background prediction (blue full points) is shown. The gray band in the lower panel indicates the post-fit uncertainty after combining all the systematic uncertainties. Finally, the distribution of the pulls, defined as the difference between data and the post-fit background prediction relative to the quadrature sum of the post-fit uncertainty in the prediction and statistical uncertainty in data, are also shown in the lowest panel.

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Figure 6:
Comparison between data and MC simulation in the dimuon (upper row) and dielectron (lower row) control samples before and after performing the simultaneous fit across all the control samples and the signal region assuming the absence of any signal. Plots correspond to the monojet (left) and mono-V (right) categories, respectively, in the dilepton control sample. The hadronic recoil $ {p_{\mathrm {T}}} $ in dilepton events is used as a proxy for $ {{p_{\mathrm {T}}} ^\text {miss}} $ in the signal region. The other backgrounds include top quark, diboson, and W+jets processes. The description of the lower panels is the same as in Fig. 5.

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Figure 6-a:
Comparison between data and MC simulation in the dimuon control sample before and after performing the simultaneous fit across all the control samples and the signal region assuming the absence of any signal. The plot corresponds to the monojet category. The hadronic recoil $ {p_{\mathrm {T}}} $ in dilepton events is used as a proxy for $ {{p_{\mathrm {T}}} ^\text {miss}} $ in the signal region. The other backgrounds include top quark, diboson, and W+jets processes.

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Figure 6-b:
Comparison between data and MC simulation in the dimuon control sample before and after performing the simultaneous fit across all the control samples and the signal region assuming the absence of any signal. The plot corresponds to the mono-V category. The hadronic recoil $ {p_{\mathrm {T}}} $ in dilepton events is used as a proxy for $ {{p_{\mathrm {T}}} ^\text {miss}} $ in the signal region. The other backgrounds include top quark, diboson, and W+jets processes.

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Figure 6-c:
Comparison between data and MC simulation in the dielectron control sample before and after performing the simultaneous fit across all the control samples and the signal region assuming the absence of any signal. The plot corresponds to the monojet category. The hadronic recoil $ {p_{\mathrm {T}}} $ in dilepton events is used as a proxy for $ {{p_{\mathrm {T}}} ^\text {miss}} $ in the signal region. The other backgrounds include top quark, diboson, and W+jets processes.

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Figure 6-d:
Comparison between data and MC simulation in the dielectron control sample before and after performing the simultaneous fit across all the control samples and the signal region assuming the absence of any signal. The plot corresponds to the mono-V category. The hadronic recoil $ {p_{\mathrm {T}}} $ in dilepton events is used as a proxy for $ {{p_{\mathrm {T}}} ^\text {miss}} $ in the signal region. The other backgrounds include top quark, diboson, and W+jets processes.

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Figure 7:
Comparison between data and MC simulation in the single-muon (upper row) and single-electron (lower row) control samples before and after performing the simultaneous fit across all the control samples and the signal region assuming the absence of any signal. Plots correspond to the monojet (left) and mono-V (right) categories, respectively, in the single-lepton control samples. The hadronic recoil $ {p_{\mathrm {T}}} $ in single-lepton events is used as a proxy for $ {{p_{\mathrm {T}}} ^\text {miss}} $ in the signal region. The other backgrounds include top quark, diboson, and QCD multijet processes. The description of the lower panels is the same as in Fig. 5.

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Figure 7-a:
Comparison between data and MC simulation in the single-muon control sample before and after performing the simultaneous fit across all the control samples and the signal region assuming the absence of any signal. The plot corresponds to the monojet category. The hadronic recoil $ {p_{\mathrm {T}}} $ in single-lepton events is used as a proxy for $ {{p_{\mathrm {T}}} ^\text {miss}} $ in the signal region. The other backgrounds include top quark, diboson, and QCD multijet processes.

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Figure 7-b:
Comparison between data and MC simulation in the single-muon control sample before and after performing the simultaneous fit across all the control samples and the signal region assuming the absence of any signal. The plot corresponds to the mono-V category. The hadronic recoil $ {p_{\mathrm {T}}} $ in single-lepton events is used as a proxy for $ {{p_{\mathrm {T}}} ^\text {miss}} $ in the signal region. The other backgrounds include top quark, diboson, and QCD multijet processes.

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Figure 7-c:
Comparison between data and MC simulation in the single-electron control sample before and after performing the simultaneous fit across all the control samples and the signal region assuming the absence of any signal. The plot corresponds to the monojet category. The hadronic recoil $ {p_{\mathrm {T}}} $ in single-lepton events is used as a proxy for $ {{p_{\mathrm {T}}} ^\text {miss}} $ in the signal region. The other backgrounds include top quark, diboson, and QCD multijet processes.

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Figure 7-d:
Comparison between data and MC simulation in the single-electron control sample before and after performing the simultaneous fit across all the control samples and the signal region assuming the absence of any signal. The plot corresponds to the mono-V category. The hadronic recoil $ {p_{\mathrm {T}}} $ in single-lepton events is used as a proxy for $ {{p_{\mathrm {T}}} ^\text {miss}} $ in the signal region. The other backgrounds include top quark, diboson, and QCD multijet processes.

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Figure 8:
Observed $ {{p_{\mathrm {T}}} ^\text {miss}} $ distribution in the monojet (left) and mono-V (right) signal regions compared with the post-fit background expectations for various SM processes. The last bin includes all events with $ {{p_{\mathrm {T}}} ^\text {miss}} > $ 1250 GeV for the monojet (mono-V) category. The expected background distributions are evaluated after performing a combined fit to the data in all the control samples, not including the signal region. Expected signal distributions for the 125 GeV Higgs boson decaying exclusively to invisible particles, and a 2 TeV axial-vector mediator decaying to 1 GeV DM particles, are overlaid. The description of the lower panels is the same as in Fig. 5.

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Figure 8-a:
Observed $ {{p_{\mathrm {T}}} ^\text {miss}} $ distribution in the monojet signal region compared with the post-fit background expectations for various SM processes. The last bin includes all events with $ {{p_{\mathrm {T}}} ^\text {miss}} > $ 1250 GeV for the monojet (mono-V) category. The expected background distributions are evaluated after performing a combined fit to the data in all the control samples, not including the signal region. Expected signal distributions for the 125 GeV Higgs boson decaying exclusively to invisible particles, and a 2 TeV axial-vector mediator decaying to 1 GeV DM particles, are overlaid.

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Figure 8-b:
Observed $ {{p_{\mathrm {T}}} ^\text {miss}} $ distribution in the mono-V signal region compared with the post-fit background expectations for various SM processes. The last bin includes all events with $ {{p_{\mathrm {T}}} ^\text {miss}} > $ 1250 GeV for the monojet (mono-V) category. The expected background distributions are evaluated after performing a combined fit to the data in all the control samples, not including the signal region. Expected signal distributions for the 125 GeV Higgs boson decaying exclusively to invisible particles, and a 2 TeV axial-vector mediator decaying to 1 GeV DM particles, are overlaid.

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Figure 9:
Observed $ {{p_{\mathrm {T}}} ^\text {miss}} $ distribution in the monojet (left) and mono-V (right) signal regions compared with the post-fit background expectations for various SM processes. The last bin includes all events with $ {{p_{\mathrm {T}}} ^\text {miss}} > $ 1250 GeV for the monojet (mono-V) category. The expected background distributions are evaluated after performing a combined fit to the data in all the control samples, as well as in the signal region. The fit is performed assuming the absence of any signal. Expected signal distributions for the 125 GeV Higgs boson decaying exclusively to invisible particles, and a 2 TeV axial-vector mediator decaying to 1 GeV DM particles, are overlaid. The description of the lower panels is the same as in Fig. 5.

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Figure 9-a:
Observed $ {{p_{\mathrm {T}}} ^\text {miss}} $ distribution in the monojet signal region compared with the post-fit background expectations for various SM processes. The last bin includes all events with $ {{p_{\mathrm {T}}} ^\text {miss}} > $ 1250 GeV for the monojet (mono-V) category. The expected background distributions are evaluated after performing a combined fit to the data in all the control samples, as well as in the signal region. The fit is performed assuming the absence of any signal. Expected signal distributions for the 125 GeV Higgs boson decaying exclusively to invisible particles, and a 2 TeV axial-vector mediator decaying to 1 GeV DM particles, are overlaid.

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Figure 9-b:
Observed $ {{p_{\mathrm {T}}} ^\text {miss}} $ distribution in the mono-V signal region compared with the post-fit background expectations for various SM processes. The last bin includes all events with $ {{p_{\mathrm {T}}} ^\text {miss}} > $ 1250 GeV for the monojet (mono-V) category. The expected background distributions are evaluated after performing a combined fit to the data in all the control samples, as well as in the signal region. The fit is performed assuming the absence of any signal. Expected signal distributions for the 125 GeV Higgs boson decaying exclusively to invisible particles, and a 2 TeV axial-vector mediator decaying to 1 GeV DM particles, are overlaid.

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Figure 10:
Exclusion limits at 95%CL on $\mu =\sigma /\sigma _{\textrm {th}}$ in the $m_{\textrm {med}}$-$m_{\textrm {DM}}$ plane assuming vector (left) and axial-vector (right) mediators. The solid (dotted) red (black) line shows the contour for the observed (expected) exclusion. The solid contours around the observed limit and the dashed contours around the expected limit represent one standard deviation due to theoretical uncertainties in the signal cross section and the combination of the statistical and experimental systematic uncertainties, respectively. Constraints from the Planck satellite experiment [97] are shown as dark blue contours; in the shaded area DM is overabundant.

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Figure 10-a:
Exclusion limits at 95%CL on $\mu =\sigma /\sigma _{\textrm {th}}$ in the $m_{\textrm {med}}$-$m_{\textrm {DM}}$ plane assuming vector mediators. The solid (dotted) red (black) line shows the contour for the observed (expected) exclusion. The solid contours around the observed limit and the dashed contours around the expected limit represent one standard deviation due to theoretical uncertainties in the signal cross section and the combination of the statistical and experimental systematic uncertainties, respectively. Constraints from the Planck satellite experiment [97] are shown as dark blue contours; in the shaded area DM is overabundant.

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Figure 10-b:
Exclusion limits at 95%CL on $\mu =\sigma /\sigma _{\textrm {th}}$ in the $m_{\textrm {med}}$-$m_{\textrm {DM}}$ plane assuming axial-vector mediators. The solid (dotted) red (black) line shows the contour for the observed (expected) exclusion. The solid contours around the observed limit and the dashed contours around the expected limit represent one standard deviation due to theoretical uncertainties in the signal cross section and the combination of the statistical and experimental systematic uncertainties, respectively. Constraints from the Planck satellite experiment [97] are shown as dark blue contours; in the shaded area DM is overabundant.

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Figure 11:
Expected (dotted black line) and observed (solid black line) 95%CL upper limits on the signal strength $\mu =\sigma /\sigma _{\textrm {th}}$ as a function of the mediator mass for the scalar mediators (left) for $m_{\textrm {DM}} = $ 1 GeV. The horizontal red line denotes $\mu = $ 1. Exclusion limits at 95%CL on $\mu =\sigma /\sigma _{\textrm {th}}$ in the $m_{\textrm {med}}$-$m_{\textrm {DM}}$ plane assuming pseudoscalar mediators (right). The solid (dashed) red (back) line shows the contours for the observed (expected) exclusion. Constraints from the Planck satellite experiment [97] are shown with the dark blue contours; in the shaded area DM is overabundant.

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Figure 11-a:
Expected (dotted black line) and observed (solid black line) 95%CL upper limits on the signal strength $\mu =\sigma /\sigma _{\textrm {th}}$ as a function of the mediator mass for the scalar mediators for $m_{\textrm {DM}} = $ 1 GeV. The horizontal red line denotes $\mu = $ 1.

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Figure 11-b:
Exclusion limits at 95%CL on $\mu =\sigma /\sigma _{\textrm {th}}$ in the $m_{\textrm {med}}$-$m_{\textrm {DM}}$ plane assuming pseudoscalar mediators. The solid (dashed) red (back) line shows the contours for the observed (expected) exclusion. Constraints from the Planck satellite experiment [97] are shown with the dark blue contours; in the shaded area DM is overabundant.

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Figure 12:
Exclusion limits at 95%CL on $\mu =\sigma /\sigma _{\textrm {th}}$ in the $m_{\textrm {med}}$-$g_{\mathrm {q}}$ plane assuming vector (left) and axial-vector (right) mediators. The widths shown on the axis correspond to mediator masses above 400 GeV, where the top quark decay channel is fully open. For the mediator masses below the top quark decay channel threshold the width is 9% less. The solid (dotted) black line shows the contour for the observed (expected) exclusion. The solid red contours around the observed limit represent one standard deviation due to theoretical uncertainties in the signal cross section. Constraints from the Planck satellite experiment [97] are shown as dark blue contours; in the shaded area DM is overabundant.

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Figure 12-a:
Exclusion limits at 95%CL on $\mu =\sigma /\sigma _{\textrm {th}}$ in the $m_{\textrm {med}}$-$g_{\mathrm {q}}$ plane assuming vector mediators. The widths shown on the axis correspond to mediator masses above 400 GeV, where the top quark decay channel is fully open. For the mediator masses below the top quark decay channel threshold the width is 9% less. The solid (dotted) black line shows the contour for the observed (expected) exclusion. The solid red contours around the observed limit represent one standard deviation due to theoretical uncertainties in the signal cross section. Constraints from the Planck satellite experiment [97] are shown as dark blue contours; in the shaded area DM is overabundant.

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Figure 12-b:
Exclusion limits at 95%CL on $\mu =\sigma /\sigma _{\textrm {th}}$ in the $m_{\textrm {med}}$-$g_{\mathrm {q}}$ plane assuming axial-vector mediators. The widths shown on the axis correspond to mediator masses above 400 GeV, where the top quark decay channel is fully open. For the mediator masses below the top quark decay channel threshold the width is 9% less. The solid (dotted) black line shows the contour for the observed (expected) exclusion. The solid red contours around the observed limit represent one standard deviation due to theoretical uncertainties in the signal cross section. Constraints from the Planck satellite experiment [97] are shown as dark blue contours; in the shaded area DM is overabundant.

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Figure 13:
Exclusion limits at 90%CL in the $m_{\textrm {DM}}$ vs. $\sigma _{\textrm {SI/SD}}$ plane for vector (left) and axial-vector (right) mediator models. The solid red (dotted black) line shows the contour for the observed (expected) exclusion in this search. Limits from CDMSLite [102], LUX [103], XENON-1T [104], and CRESST-II [105] are shown for the vector mediator. Limits from Picasso [106], PICO-60 [107], IceCube [108], and Super-Kamiokande [109] are shown for the axial-vector mediator.

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Figure 13-a:
Exclusion limits at 90%CL in the $m_{\textrm {DM}}$ vs. $\sigma _{\textrm {SI/SD}}$ plane for the vector mediator model. The solid red (dotted black) line shows the contour for the observed (expected) exclusion in this search. Limits from CDMSLite [102], LUX [103], XENON-1T [104], and CRESST-II [105] are shown.

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Figure 13-b:
Exclusion limits at 90%CL in the $m_{\textrm {DM}}$ vs. $\sigma _{\textrm {SI/SD}}$ plane for the axial-vector mediator model. The solid red (dotted black) line shows the contour for the observed (expected) exclusion in this search. Limits from Picasso [106], PICO-60 [107], IceCube [108], and Super-Kamiokande [109] are shown .

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Figure 14:
For the pseudoscalar mediator, limits are compared to the the velocity averaged DM annihilation cross section upper limits from Fermi-LAT [101]. There are no comparable limits from direct detection experiments, as the scattering cross section between DM particles and SM quarks is suppressed at nonrelativistic velocities for a pseudoscalar mediator [110,111].

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Figure 15:
The 95%CL expected (black dashed line) and observed (red solid line) upper limits on $\mu =\sigma /\sigma _{\rm {th}}$ in the context of the fermion portal DM model, for Dirac DM particles with coupling strengths to the up quark corresponding to $\lambda _{\rm {u}} = $ 1 in the $m_{\phi _{\rm {u}}}$-$m_\chi $ plane. Constraints from the Planck satellite experiment [97] are shown as dark blue contours; in the shaded area DM is overabundant.

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Figure 16:
Expected (black dashed line) and observed (red solid line) 95%CL upper limits on the signal strength $\mu =\sigma /\sigma _{\rm {th}}$, in the context of a nonthermal dark matter model. Results are reported in the $\lambda _1$-$\lambda _2$ plane, which represents the coupling strength of the interaction of the new scalar mediator with down-type quarks and DM with up-type quarks, respectively. Limits are shown for $m_{\rm X_1}$ of 1 TeV (left) and 2 TeV (right).

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Figure 16-a:
Expected (black dashed line) and observed (red solid line) 95%CL upper limits on the signal strength $\mu =\sigma /\sigma _{\rm {th}}$, in the context of a nonthermal dark matter model. Results are reported in the $\lambda _1$-$\lambda _2$ plane, which represents the coupling strength of the interaction of the new scalar mediator with down-type quarks and DM with up-type quarks, respectively. Limits are shown for $m_{\rm X_1}$ of 1 TeV.

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Figure 16-b:
Expected (black dashed line) and observed (red solid line) 95%CL upper limits on the signal strength $\mu =\sigma /\sigma _{\rm {th}}$, in the context of a nonthermal dark matter model. Results are reported in the $\lambda _1$-$\lambda _2$ plane, which represents the coupling strength of the interaction of the new scalar mediator with down-type quarks and DM with up-type quarks, respectively. Limits are shown for $m_{\rm X_1}$ of 2 TeV.

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Figure 17:
Expected (dotted line) and observed (solid line) 95%CL upper limits on the invisible branching fraction of the 125 GeV SM-like Higgs boson. Limits are shown for the monojet and mono-V categories separately, and also for their combination.

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Figure 18:
The 95%CL expected (dotted) and observed (solid) upper limits on the signal strength $\mu =\sigma /\sigma _{\rm {th}}$ for ADD graviton production (left), as a function of fundamental Planck scale ($M_{\mathrm {D}}$) for $n=$ 2, where $n$ is the number of extra spatial dimensions. The 95%CL expected (dotted) and observed (solid) lower limits (right) on $M_{\mathrm {D}}$ as a function of $n$ in the ADD model. The results are also compared to earlier ones obtained by the CMS Collaboration with data corresponding to an integrated luminosity of 19.7 fb$^{-1}$ at a centre-of-mass energy of 8 TeV [10] (blue points).

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Figure 18-a:
The 95%CL expected (dotted) and observed (solid) upper limits on the signal strength $\mu =\sigma /\sigma _{\rm {th}}$ for ADD graviton production, as a function of fundamental Planck scale ($M_{\mathrm {D}}$) for $n=$ 2, where $n$ is the number of extra spatial dimensions.

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Figure 18-b:
The 95%CL expected (dotted) and observed (solid) lower limits on $M_{\mathrm {D}}$ as a function of $n$ in the ADD model. The results are also compared to earlier ones obtained by the CMS Collaboration with data corresponding to an integrated luminosity of 19.7 fb$^{-1}$ at a centre-of-mass energy of 8 TeV [10] (blue points).

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Figure 19:
Comparison between data and Monte Carlo simulation of the $\mathrm{Z} (\mu \mu)$/$\gamma $+jets, $\mathrm{Z} (\mu \mu)$/$\mathrm{W} (\mu \nu)$ and $\mathrm{W} (\mu \nu)$/$\gamma $+jets ratios, as a function of boson $ {p_{\mathrm {T}}} $, in the monojet category. In the ratio panel, ratios of data with the pre-fit background prediction are shown. The gray bands include both the pre-fit systematic uncertainties and the statistical uncertainty in the simulation.

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Figure 19-a:
Comparison between data and Monte Carlo simulation of the $\mathrm{Z} (\mu \mu)$/$\gamma $+jets ratio, as a function of boson $ {p_{\mathrm {T}}} $, in the monojet category. In the ratio panel, the ratio of data with the pre-fit background prediction is shown. The gray bands include both the pre-fit systematic uncertainties and the statistical uncertainty in the simulation.

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Figure 19-b:
Comparison between data and Monte Carlo simulation of the $\mathrm{Z} (\mu \mu)$/$\mathrm{W} (\mu \nu)$ ratio, as a function of boson $ {p_{\mathrm {T}}} $, in the monojet category. In the ratio panel, the ratio of data with the pre-fit background prediction is shown. The gray bands include both the pre-fit systematic uncertainties and the statistical uncertainty in the simulation.

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Figure 19-c:
Comparison between data and Monte Carlo simulation of the $\mathrm{W} (\mu \nu)$/$\gamma $+jets ratio, as a function of boson $ {p_{\mathrm {T}}} $, in the monojet category. In the ratio panel, the ratio of data with the pre-fit background prediction is shown. The gray bands include both the pre-fit systematic uncertainties and the statistical uncertainty in the simulation.

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Figure 20:
Correlations between the predicted background yields in all the $ {E_{\mathrm {T}}^{\text {miss}}} $ bins of the monojet signal region. The boundaries of the $ {E_{\mathrm {T}}^{\text {miss}}} $ bins, expressed in GeV, are shown at the bottom and on the left.

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Figure 21:
Correlations between the predicted background yields in all the $ {E_{\mathrm {T}}^{\text {miss}}} $ bins of the mono-V signal region. The boundaries of the $ {E_{\mathrm {T}}^{\text {miss}}} $ bins, expressed in GeV, are shown at the bottom and on the left.

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Figure 22:
Exclusion limits at 95%CL on $\mu =\sigma /\sigma _{\textrm {th}}$ in the $m_{\textrm {med}}$-$m_{\textrm {DM}}$ plane assuming scalar mediators (left) allowing for vector boson couplings simulated at LO in QCD. The solid (dotted) red (black) line shows the contour for the observed (expected) exclusion. The solid contours around the observed limit and the dashed contours around the expected limit represent one standard deviation due to theoretical uncertainties in the signal cross section and the quadratic sum of the statistical and experimental systematic uncertainties, respectively. Expected and observed sensitivity of the previous CMS publication [14]are also presented. Results of the Planck satellite experiment [97] are shown as dark blue contours. In the shaded area DM is overabundant. Expected (dotted black line) and observed (solid black line) 95%CL upper limits on the signal strength $\mu $ as a function of the mediator mass for the spin-0 models (right).

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Figure 22-a:
Exclusion limits at 95%CL on $\mu =\sigma /\sigma _{\textrm {th}}$ in the $m_{\textrm {med}}$-$m_{\textrm {DM}}$ plane assuming scalar mediators allowing for vector boson couplings simulated at LO in QCD. The solid (dotted) red (black) line shows the contour for the observed (expected) exclusion. The solid contours around the observed limit and the dashed contours around the expected limit represent one standard deviation due to theoretical uncertainties in the signal cross section and the quadratic sum of the statistical and experimental systematic uncertainties, respectively. Expected and observed sensitivity of the previous CMS publication [14]are also presented. Results of the Planck satellite experiment [97] are shown as dark blue contours. In the shaded area DM is overabundant.

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Figure 22-b:
Expected (dotted black line) and observed (solid black line) 95%CL upper limits on the signal strength $\mu $ as a function of the mediator mass for the spin-0 models.

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Figure 23:
Exclusion limits at 95%CL on $\mu =\sigma /\sigma _{\textrm {th}}$ in the $m_{\textrm {med}}$-$m_{\textrm {DM}}$ plane assuming vector (left) and axial-vector (right) mediators where the the mono-V signal is simulated at LO in QCD. The solid (dotted) red (black) line shows the contour for the observed (expected) exclusion. The solid contours around the observed limit and the dashed contours around the expected limit represent one standard deviation due to theoretical uncertainties in the signal cross section and the quadratic sum of the statistical and experimental systematic uncertainties, respectively. Planck satellite experiment [97] are shown as dark blue contours. In the shaded area DM is overabundant.

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Figure 23-a:
Exclusion limits at 95%CL on $\mu =\sigma /\sigma _{\textrm {th}}$ in the $m_{\textrm {med}}$-$m_{\textrm {DM}}$ plane assuming vector mediators where the the mono-V signal is simulated at LO in QCD. The solid (dotted) red (black) line shows the contour for the observed (expected) exclusion. The solid contours around the observed limit and the dashed contours around the expected limit represent one standard deviation due to theoretical uncertainties in the signal cross section and the quadratic sum of the statistical and experimental systematic uncertainties, respectively. Planck satellite experiment [97] are shown as dark blue contours. In the shaded area DM is overabundant.

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Figure 23-b:
Exclusion limits at 95%CL on $\mu =\sigma /\sigma _{\textrm {th}}$ in the $m_{\textrm {med}}$-$m_{\textrm {DM}}$ plane assuming axial-vector mediators where the the mono-V signal is simulated at LO in QCD. The solid (dotted) red (black) line shows the contour for the observed (expected) exclusion. The solid contours around the observed limit and the dashed contours around the expected limit represent one standard deviation due to theoretical uncertainties in the signal cross section and the quadratic sum of the statistical and experimental systematic uncertainties, respectively. Planck satellite experiment [97] are shown as dark blue contours. In the shaded area DM is overabundant.
Tables

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Table 1:
Summary of the common selection requirements for mono-V and monojet categories.

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Table 2:
Summary of the selection requirements for the mono-V category. Events that fail the mono-V selection are assigned to the monojet category.

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Table 3:
Theoretical uncertainties considered in the V-jets and $\gamma $+jets processes, and their ratios. The correlation between each process and between the $ {p_{\mathrm {T}}} $ bins are described.

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Table 4:
Expected event yields in each $ {{p_{\mathrm {T}}} ^\text {miss}} $ bin for various background processes in the monojet signal region. The background yields and the corresponding uncertainties are obtained after performing a combined fit to data in all the control samples, excluding data in the signal region. The other backgrounds include QCD multijet and $\gamma $+jets processes.The expected signal contribution for a 2 TeV axial-vector mediator decaying to 1 GeV DM particles and the observed event yields in the monojet signal region are also reported.

png pdf
Table 5:
Expected event yields in each $ {{p_{\mathrm {T}}} ^\text {miss}} $ bin for various background processes in the mono-V signal region. The background yields and the corresponding uncertainties are obtained after performing a combined fit to data in all the control samples, but excluding data in the signal region. The other backgrounds include QCD multijet and $\gamma $+jets processes. The expected signal contribution for a 2 TeV axial-vector mediator decaying to 1 GeV DM particles and the observed event yields in the mono-V signal region are also reported.

png pdf
Table 6:
Expected and observed 95%CL upper limits on the invisible branching fraction of the Higgs boson. Limits are tabulated for the monojet and mono-V categories separately, and for their combination. The one standard deviation uncertainty range in the expected limits is listed. The expected composition of the production modes of a Higgs boson with a mass of 125 GeV is summarized, assuming SM production cross sections.

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Table 7:
Upper limits on the signal production cross section in the ADD model and lower limits on $M_{\mathrm {D}}$, both as functions of the number of extra spatial dimensions ($n$).

png pdf
Table 8:
Monte Carlo generators and perturbative order in QCD used for simulating various signal processes studied in this work, and in Ref. [14]
Summary
A search for dark matter (DM) particles, invisible decays of a standard-model-like (SM-like) Higgs boson, and extra spatial dimensions is presented using events with one or more energetic jets and large missing transverse momentum in proton-proton collisions recorded at $\sqrt{s} = $ 13 TeV, using a sample of data corresponding to an integrated luminosity of 35.9 fb$^{-1}$. Events are categorized based on whether jets are produced directly in hard scattering as initial-state radiation or originate from merged quarks from a decay of a highly Lorentz-boosted W or Z boson. No excess of events is observed compared to the SM background expectations in either of these two categories.

Limits are computed on the DM production cross section using simplified models in which DM production is mediated by spin-1 and spin-0 particles. Vector and axial-vector (pseudoscalar) mediators with masses up to 1.8 (0.4) TeV are excluded at 95% confidence level. Similarly, limits are also presented for the parameters of the fermion portal DM model and an exclusion up to 1.4 TeV on the mediator mass is observed at 95% confidence level. The first limits on the DM production at a particle collider in the nonthermal DM model are obtained and presented in the coupling strength plane. Furthermore, and observed (expected) 95% confidence level upper limit of 0.53 (0.40) is set for the invisible branching fraction of an SM-like 125 GeV Higgs boson, assuming the SM production cross section. Lower limits are also computed on the fundamental Planck scale $M_{\mathrm{D}}$ in the context of the Arkani-Hamed, Dimopoulos, and Dvali model with large extra spatial dimensions, which varies from 9.9 TeV for $n=$ 2 to 5.3 TeV for $n=$ 6 at 95% confidence level, where $n$ is the number of extra spatial dimensions. These limits provide the most stringent direct constraints on the fundamental Planck scale to date.
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