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CMS-HIG-20-003 ; CERN-EP-2021-273
Search for invisible decays of the Higgs boson produced via vector boson fusion in proton-proton collisions at $\sqrt{s} = $ 13 TeV
Phys. Rev. D 105 (2022) 092007
Abstract: A search for invisible decays of the Higgs boson produced via vector boson fusion (VBF) has been performed with 101 fb$^{-1}$ of proton-proton collisions delivered by the LHC at $\sqrt{s} = $ 13 TeV and collected by the CMS detector in 2017 and 2018. The sensitivity to the VBF production mechanism is enhanced by constructing two analysis categories, one based on missing transverse momentum, and a second based on the properties of jets. In addition to control regions with Z and W boson candidate events, a highly populated control region, based on the production of a photon in association with jets, is used to constrain the dominant irreducible background from the invisible decay of a Z boson produced in association with jets. The results of this search are combined with all previous measurements in the VBF topology, based on data collected in 2012 (at $\sqrt{s} = $ 8 TeV), 2015, and 2016, corresponding to integrated luminosities of 19.7, 2.3, and 36.3 fb$^{-1}$, respectively. The observed (expected) upper limit on the invisible branching fraction of the Higgs boson is found to be 0.18 (0.10) at the 95% confidence level, assuming the standard model production cross section. The results are also interpreted in the context of Higgs-portal models.
Figures & Tables Summary References CMS Publications
Figures

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Figure 1:
Leading-order Feynman diagrams for the production of the Higgs boson in association with two jets from VBF (left), and representative leading-order Feynman diagrams for the production of a Z boson in association with two jets either through VBF production (middle) or strong production (right). Diagrams for the production of a W boson in association with two jets are similar.

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Figure 1-a:
Leading-order Feynman diagrams for the production of the Higgs boson in association with two jets from VBF (left), and representative leading-order Feynman diagrams for the production of a Z boson in association with two jets either through VBF production (middle) or strong production (right). Diagrams for the production of a W boson in association with two jets are similar.

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Figure 1-b:
Leading-order Feynman diagrams for the production of the Higgs boson in association with two jets from VBF (left), and representative leading-order Feynman diagrams for the production of a Z boson in association with two jets either through VBF production (middle) or strong production (right). Diagrams for the production of a W boson in association with two jets are similar.

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Figure 1-c:
Leading-order Feynman diagrams for the production of the Higgs boson in association with two jets from VBF (left), and representative leading-order Feynman diagrams for the production of a Z boson in association with two jets either through VBF production (middle) or strong production (right). Diagrams for the production of a W boson in association with two jets are similar.

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Figure 2:
Comparison of shapes of quantities related to the dijet pair. Shown are ${m_{\mathrm {jj}}}$ (upper), ${\Delta \eta _{\mathrm {jj}}}$ (lower left), and ${\Delta \phi _{\mathrm {jj}}}$ (lower right), as predicted by simulation, separating strong and VBF production for V+jets and signal processes.

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Figure 2-a:
Comparison of shapes of quantities related to the dijet pair. Shown are ${m_{\mathrm {jj}}}$ (upper), ${\Delta \eta _{\mathrm {jj}}}$ (lower left), and ${\Delta \phi _{\mathrm {jj}}}$ (lower right), as predicted by simulation, separating strong and VBF production for V+jets and signal processes.

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Figure 2-b:
Comparison of shapes of quantities related to the dijet pair. Shown are ${m_{\mathrm {jj}}}$ (upper), ${\Delta \eta _{\mathrm {jj}}}$ (lower left), and ${\Delta \phi _{\mathrm {jj}}}$ (lower right), as predicted by simulation, separating strong and VBF production for V+jets and signal processes.

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Figure 2-c:
Comparison of shapes of quantities related to the dijet pair. Shown are ${m_{\mathrm {jj}}}$ (upper), ${\Delta \eta _{\mathrm {jj}}}$ (lower left), and ${\Delta \phi _{\mathrm {jj}}}$ (lower right), as predicted by simulation, separating strong and VBF production for V+jets and signal processes.

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Figure 3:
The $\Delta \phi ({p_{\mathrm {T, trk}}^\text {miss}}, {{p_{\mathrm {T}}} ^\text {miss}})$ distribution in the SR with the additional requirement that the leading-$ {p_{\mathrm {T}}}$ jet passes 3 $ < {| \eta |} < $ 3.25. The 2017 and 2018 data are compared with the sum of the HF noise template and other backgrounds from simulation. The uncertainty band includes only statistical uncertainties in the simulation.

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Figure 4:
The $\min({\Delta \phi ({{\vec{p}}_{\mathrm {T}}^{\,\text {miss}}},\vec{p}_{\mathrm {T}}^{\,\text {jet}})})$ distribution in data from 2017 and 2018, and contributions from V+jets, diboson plus top quark processes, HF noise, and QCD multijet events for the MTR (left) and VTR (right) categories. The uncertainty band shows the uncertainty from the fit used to determine the normalization of the QCD multijet template in the corresponding SR. The yields from the 2017 and 2018 samples are summed and the correlations between their uncertainties are neglected.

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Figure 4-a:
The $\min({\Delta \phi ({{\vec{p}}_{\mathrm {T}}^{\,\text {miss}}},\vec{p}_{\mathrm {T}}^{\,\text {jet}})})$ distribution in data from 2017 and 2018, and contributions from V+jets, diboson plus top quark processes, HF noise, and QCD multijet events for the MTR (left) and VTR (right) categories. The uncertainty band shows the uncertainty from the fit used to determine the normalization of the QCD multijet template in the corresponding SR. The yields from the 2017 and 2018 samples are summed and the correlations between their uncertainties are neglected.

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Figure 4-b:
The $\min({\Delta \phi ({{\vec{p}}_{\mathrm {T}}^{\,\text {miss}}},\vec{p}_{\mathrm {T}}^{\,\text {jet}})})$ distribution in data from 2017 and 2018, and contributions from V+jets, diboson plus top quark processes, HF noise, and QCD multijet events for the MTR (left) and VTR (right) categories. The uncertainty band shows the uncertainty from the fit used to determine the normalization of the QCD multijet template in the corresponding SR. The yields from the 2017 and 2018 samples are summed and the correlations between their uncertainties are neglected.

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Figure 5:
Comparison between data and simulation for the Z($\ell \ell$)+jets / W($\ell \nu$)+jets (upper row) and $\gamma$+jets / Z($\ell \ell$)+jets (lower row) prefit and CR-postfit ratios, as functions of ${m_{\mathrm {jj}}}$, for the MTR category using the 2017 (left) and 2018 (right) event samples. The minor backgrounds in each CR are subtracted from the data using estimates from simulation. The grey bands include the theoretical and experimental systematic uncertainties listed in Table 3, as well as the statistical uncertainty in the simulation.

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Figure 5-a:
Comparison between data and simulation for the Z($\ell \ell$)+jets / W($\ell \nu$)+jets (upper row) and $\gamma$+jets / Z($\ell \ell$)+jets (lower row) prefit and CR-postfit ratios, as functions of ${m_{\mathrm {jj}}}$, for the MTR category using the 2017 (left) and 2018 (right) event samples. The minor backgrounds in each CR are subtracted from the data using estimates from simulation. The grey bands include the theoretical and experimental systematic uncertainties listed in Table 3, as well as the statistical uncertainty in the simulation.

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Figure 5-b:
Comparison between data and simulation for the Z($\ell \ell$)+jets / W($\ell \nu$)+jets (upper row) and $\gamma$+jets / Z($\ell \ell$)+jets (lower row) prefit and CR-postfit ratios, as functions of ${m_{\mathrm {jj}}}$, for the MTR category using the 2017 (left) and 2018 (right) event samples. The minor backgrounds in each CR are subtracted from the data using estimates from simulation. The grey bands include the theoretical and experimental systematic uncertainties listed in Table 3, as well as the statistical uncertainty in the simulation.

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Figure 5-c:
Comparison between data and simulation for the Z($\ell \ell$)+jets / W($\ell \nu$)+jets (upper row) and $\gamma$+jets / Z($\ell \ell$)+jets (lower row) prefit and CR-postfit ratios, as functions of ${m_{\mathrm {jj}}}$, for the MTR category using the 2017 (left) and 2018 (right) event samples. The minor backgrounds in each CR are subtracted from the data using estimates from simulation. The grey bands include the theoretical and experimental systematic uncertainties listed in Table 3, as well as the statistical uncertainty in the simulation.

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Figure 5-d:
Comparison between data and simulation for the Z($\ell \ell$)+jets / W($\ell \nu$)+jets (upper row) and $\gamma$+jets / Z($\ell \ell$)+jets (lower row) prefit and CR-postfit ratios, as functions of ${m_{\mathrm {jj}}}$, for the MTR category using the 2017 (left) and 2018 (right) event samples. The minor backgrounds in each CR are subtracted from the data using estimates from simulation. The grey bands include the theoretical and experimental systematic uncertainties listed in Table 3, as well as the statistical uncertainty in the simulation.

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Figure 6:
The postfit ${m_{\mathrm {jj}}}$ distributions in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the MTR category, showing the summed 2017 and 2018 data samples and the background processes. The background contributions are estimated from the fit to the data described in the text (S+B fit). The total background estimated from a fit assuming $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} =$ 0 (B-only fit) is also shown. The yields from the 2017 and 2018 samples are summed and the correlations between their uncertainties are neglected. The last bin of each distribution integrates events above the bin threshold divided by the bin width.

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Figure 6-a:
The postfit ${m_{\mathrm {jj}}}$ distributions in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the MTR category, showing the summed 2017 and 2018 data samples and the background processes. The background contributions are estimated from the fit to the data described in the text (S+B fit). The total background estimated from a fit assuming $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} =$ 0 (B-only fit) is also shown. The yields from the 2017 and 2018 samples are summed and the correlations between their uncertainties are neglected. The last bin of each distribution integrates events above the bin threshold divided by the bin width.

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Figure 6-b:
The postfit ${m_{\mathrm {jj}}}$ distributions in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the MTR category, showing the summed 2017 and 2018 data samples and the background processes. The background contributions are estimated from the fit to the data described in the text (S+B fit). The total background estimated from a fit assuming $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} =$ 0 (B-only fit) is also shown. The yields from the 2017 and 2018 samples are summed and the correlations between their uncertainties are neglected. The last bin of each distribution integrates events above the bin threshold divided by the bin width.

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Figure 6-c:
The postfit ${m_{\mathrm {jj}}}$ distributions in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the MTR category, showing the summed 2017 and 2018 data samples and the background processes. The background contributions are estimated from the fit to the data described in the text (S+B fit). The total background estimated from a fit assuming $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} =$ 0 (B-only fit) is also shown. The yields from the 2017 and 2018 samples are summed and the correlations between their uncertainties are neglected. The last bin of each distribution integrates events above the bin threshold divided by the bin width.

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Figure 6-d:
The postfit ${m_{\mathrm {jj}}}$ distributions in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the MTR category, showing the summed 2017 and 2018 data samples and the background processes. The background contributions are estimated from the fit to the data described in the text (S+B fit). The total background estimated from a fit assuming $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} =$ 0 (B-only fit) is also shown. The yields from the 2017 and 2018 samples are summed and the correlations between their uncertainties are neglected. The last bin of each distribution integrates events above the bin threshold divided by the bin width.

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Figure 7:
The postfit ${m_{\mathrm {jj}}}$ distribution in the photon CR for the MTR category, showing the summed 2017 and 2018 data samples and the background processes. The background contributions are estimated from the fit to the data described in the text (S+B fit). The total background estimated from a fit assuming $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} =$ 0 (B-only fit) is also shown. The yields from the 2017 and 2018 samples are summed and the correlations between their uncertainties are neglected. The last bin of each distribution integrates events above the bin threshold divided by the bin width.

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Figure 8:
Comparison between data and simulation for the Z($\ell \ell$)+jets / W($\ell \nu$)+jets prefit and CR-postfit ratios, as functions of ${m_{\mathrm {jj}}}$, for the VTR category in the 2017 (left) and 2018 (right) data samples. The minor backgrounds in each CR are subtracted from the data using estimates from simulation. The grey bands include the theoretical and experimental systematic uncertainties listed in Table 3, as well as the statistical uncertainty in the simulation.

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Figure 8-a:
Comparison between data and simulation for the Z($\ell \ell$)+jets / W($\ell \nu$)+jets prefit and CR-postfit ratios, as functions of ${m_{\mathrm {jj}}}$, for the VTR category in the 2017 (left) and 2018 (right) data samples. The minor backgrounds in each CR are subtracted from the data using estimates from simulation. The grey bands include the theoretical and experimental systematic uncertainties listed in Table 3, as well as the statistical uncertainty in the simulation.

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Figure 8-b:
Comparison between data and simulation for the Z($\ell \ell$)+jets / W($\ell \nu$)+jets prefit and CR-postfit ratios, as functions of ${m_{\mathrm {jj}}}$, for the VTR category in the 2017 (left) and 2018 (right) data samples. The minor backgrounds in each CR are subtracted from the data using estimates from simulation. The grey bands include the theoretical and experimental systematic uncertainties listed in Table 3, as well as the statistical uncertainty in the simulation.

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Figure 9:
The postfit ${m_{\mathrm {jj}}}$ distributions in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CRs for the VTR category, showing the summed 2017 and 2018 data samples and the SM background processes. The background contributions are estimated from the fit to the data described in the text (S+B fit). The total background estimated from a fit assuming $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} =$ 0 (B-only fit) is also shown. The yields from the 2017 and 2018 samples are summed and the correlations between their uncertainties are neglected. The last bin of each distribution integrates events above the bin threshold divided by the bin width.

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Figure 9-a:
The postfit ${m_{\mathrm {jj}}}$ distributions in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CRs for the VTR category, showing the summed 2017 and 2018 data samples and the SM background processes. The background contributions are estimated from the fit to the data described in the text (S+B fit). The total background estimated from a fit assuming $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} =$ 0 (B-only fit) is also shown. The yields from the 2017 and 2018 samples are summed and the correlations between their uncertainties are neglected. The last bin of each distribution integrates events above the bin threshold divided by the bin width.

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Figure 9-b:
The postfit ${m_{\mathrm {jj}}}$ distributions in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CRs for the VTR category, showing the summed 2017 and 2018 data samples and the SM background processes. The background contributions are estimated from the fit to the data described in the text (S+B fit). The total background estimated from a fit assuming $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} =$ 0 (B-only fit) is also shown. The yields from the 2017 and 2018 samples are summed and the correlations between their uncertainties are neglected. The last bin of each distribution integrates events above the bin threshold divided by the bin width.

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Figure 9-c:
The postfit ${m_{\mathrm {jj}}}$ distributions in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CRs for the VTR category, showing the summed 2017 and 2018 data samples and the SM background processes. The background contributions are estimated from the fit to the data described in the text (S+B fit). The total background estimated from a fit assuming $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} =$ 0 (B-only fit) is also shown. The yields from the 2017 and 2018 samples are summed and the correlations between their uncertainties are neglected. The last bin of each distribution integrates events above the bin threshold divided by the bin width.

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Figure 9-d:
The postfit ${m_{\mathrm {jj}}}$ distributions in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CRs for the VTR category, showing the summed 2017 and 2018 data samples and the SM background processes. The background contributions are estimated from the fit to the data described in the text (S+B fit). The total background estimated from a fit assuming $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} =$ 0 (B-only fit) is also shown. The yields from the 2017 and 2018 samples are summed and the correlations between their uncertainties are neglected. The last bin of each distribution integrates events above the bin threshold divided by the bin width.

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Figure 10:
The observed ${m_{\mathrm {jj}}}$ distribution in the MTR (left) and VTR (right) SR compared with the postfit backgrounds, showing the summed 2017 and 2018 samples. The signal processes are scaled by the fitted value of ${{\mathcal {B}(\mathrm{H} \to \text {inv})}}$, shown in the legend. The background contributions are estimated from the fit to the data described in the text (S+B fit). The total background estimated from a fit assuming $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} =$ 0 (B-only fit) is also shown. The yields from the 2017 and 2018 samples are summed and the correlations between their uncertainties are neglected. The last bin of each distribution integrates events above the bin threshold divided by the bin width.

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Figure 10-a:
The observed ${m_{\mathrm {jj}}}$ distribution in the MTR (left) and VTR (right) SR compared with the postfit backgrounds, showing the summed 2017 and 2018 samples. The signal processes are scaled by the fitted value of ${{\mathcal {B}(\mathrm{H} \to \text {inv})}}$, shown in the legend. The background contributions are estimated from the fit to the data described in the text (S+B fit). The total background estimated from a fit assuming $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} =$ 0 (B-only fit) is also shown. The yields from the 2017 and 2018 samples are summed and the correlations between their uncertainties are neglected. The last bin of each distribution integrates events above the bin threshold divided by the bin width.

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Figure 10-b:
The observed ${m_{\mathrm {jj}}}$ distribution in the MTR (left) and VTR (right) SR compared with the postfit backgrounds, showing the summed 2017 and 2018 samples. The signal processes are scaled by the fitted value of ${{\mathcal {B}(\mathrm{H} \to \text {inv})}}$, shown in the legend. The background contributions are estimated from the fit to the data described in the text (S+B fit). The total background estimated from a fit assuming $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} =$ 0 (B-only fit) is also shown. The yields from the 2017 and 2018 samples are summed and the correlations between their uncertainties are neglected. The last bin of each distribution integrates events above the bin threshold divided by the bin width.

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Figure 11:
Observed and expected 95% CL upper limits on ${(\sigma _{\mathrm{H}}/\sigma _{\mathrm{H}}^{\mathrm {SM}}) {{\mathcal {B}(\mathrm{H} \to \text {inv})}}}$ for all data-taking years considered, as well as their combination, assuming an SM Higgs boson with a mass of 125.38 GeV.

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Figure 12:
Profile likelihood ratios, as functions of ${{\mathcal {B}(\mathrm{H} \to \text {inv})}}$. The observed likelihood scans are reported for the full combination of 2012-2018 data, as well as for the individual years. The expected results for the combination are obtained using an Asimov data set [71] with $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} =$ 0.

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Figure 13:
The 90% CL upper limits on the spin-independent DM-nucleon scattering cross section in Higgs-portal models, assuming a scalar (dashed orange) or fermion (dashed red) DM candidate. Limits are computed as functions of $m_{\mathrm {DM}}$ and are compared to those from the XENON1T [76], CRESST-II [77], CDMSlite [78], LUX [79], Panda-X 4T [80], and DarkSide-50 [81] experiments, which are shown as solid lines.

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Figure A1:
Trigger efficiency measured in data for the 2017 and 2018 samples, comparing the two sets of triggers used in the analysis (${{p_{\mathrm {T}}} ^\text {miss}} $-based in MTR, VBF jet-based in VTR). The lower thresholds are indicated by the vertical lines. The lower threshold of the MTR category also corresponds to the upper threshold applied in the VTR category.

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Figure A1-a:
Trigger efficiency measured in data for the 2017 and 2018 samples, comparing the two sets of triggers used in the analysis (${{p_{\mathrm {T}}} ^\text {miss}} $-based in MTR, VBF jet-based in VTR). The lower thresholds are indicated by the vertical lines. The lower threshold of the MTR category also corresponds to the upper threshold applied in the VTR category.

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Figure A1-b:
Trigger efficiency measured in data for the 2017 and 2018 samples, comparing the two sets of triggers used in the analysis (${{p_{\mathrm {T}}} ^\text {miss}} $-based in MTR, VBF jet-based in VTR). The lower thresholds are indicated by the vertical lines. The lower threshold of the MTR category also corresponds to the upper threshold applied in the VTR category.

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Figure A2:
Observed and expected 95% CL upper limits on ${(\sigma _{\mathrm{H}}/\sigma _{\mathrm{H}}^{\mathrm {SM}}) {{\mathcal {B}(\mathrm{H} \to \text {inv})}}}$ for both individual categories and all data-taking years, as well as their combination, assuming an SM Higgs boson with a mass of 125.38 GeV.

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Figure A3:
The observed ${m_{\mathrm {jj}}}$ distribution in the MTR SR compared to the postfit backgrounds, with the 2016, 2017, and 2018 samples. The signal processes are scaled by the fitted value of ${{\mathcal {B}(\mathrm{H} \to \text {inv})}}$, shown in the legend. The background contributions are estimated from the fit to the data described in the text (S+B fit) and the total background estimated from a fit assuming $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} =$ 0 (B-only fit) is also shown. The yields from the 2016, 2017, and 2018 samples are summed and the correlations between their uncertainties are neglected. The last bin of each distribution integrates events above the bin threshold divided by the bin width.

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Figure A4:
The ${m_{\mathrm {jj}}}$ distributions (prefit and CR-postfit) in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the MTR category, with the 2017 and 2018 samples. The yields from the 2017 and 2018 samples are summed and the correlations between their uncertainties are neglected.

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Figure A4-a:
The ${m_{\mathrm {jj}}}$ distributions (prefit and CR-postfit) in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the MTR category, with the 2017 and 2018 samples. The yields from the 2017 and 2018 samples are summed and the correlations between their uncertainties are neglected.

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Figure A4-b:
The ${m_{\mathrm {jj}}}$ distributions (prefit and CR-postfit) in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the MTR category, with the 2017 and 2018 samples. The yields from the 2017 and 2018 samples are summed and the correlations between their uncertainties are neglected.

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Figure A4-c:
The ${m_{\mathrm {jj}}}$ distributions (prefit and CR-postfit) in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the MTR category, with the 2017 and 2018 samples. The yields from the 2017 and 2018 samples are summed and the correlations between their uncertainties are neglected.

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Figure A4-d:
The ${m_{\mathrm {jj}}}$ distributions (prefit and CR-postfit) in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the MTR category, with the 2017 and 2018 samples. The yields from the 2017 and 2018 samples are summed and the correlations between their uncertainties are neglected.

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Figure A5:
The ${m_{\mathrm {jj}}}$ distributions (prefit and CR-postfit) in the photon CR for the MTR category, with the 2017 and 2018 samples. The yields from the 2017 and 2018 samples are summed and the correlations between their uncertainties are neglected.

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Figure A6:
The ${m_{\mathrm {jj}}}$ distributions (prefit and CR-postfit) in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the VTR category, with the 2017 and 2018 samples. The yields from the 2017 and 2018 samples are summed and the correlations between their uncertainties are neglected.

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Figure A6-a:
The ${m_{\mathrm {jj}}}$ distributions (prefit and CR-postfit) in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the VTR category, with the 2017 and 2018 samples. The yields from the 2017 and 2018 samples are summed and the correlations between their uncertainties are neglected.

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Figure A6-b:
The ${m_{\mathrm {jj}}}$ distributions (prefit and CR-postfit) in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the VTR category, with the 2017 and 2018 samples. The yields from the 2017 and 2018 samples are summed and the correlations between their uncertainties are neglected.

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Figure A6-c:
The ${m_{\mathrm {jj}}}$ distributions (prefit and CR-postfit) in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the VTR category, with the 2017 and 2018 samples. The yields from the 2017 and 2018 samples are summed and the correlations between their uncertainties are neglected.

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Figure A6-d:
The ${m_{\mathrm {jj}}}$ distributions (prefit and CR-postfit) in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the VTR category, with the 2017 and 2018 samples. The yields from the 2017 and 2018 samples are summed and the correlations between their uncertainties are neglected.

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Figure A7:
The observed ${m_{\mathrm {jj}}}$ distribution in the MTR (left) and VTR (right) SRs compared to the CR-postfit backgrounds, with the 2017 and 2018 samples. The yields from the 2017 and 2018 samples are summed and the correlations between their uncertainties are neglected. The signal processes are scaled by the fitted value of ${{\mathcal {B}(\mathrm{H} \to \text {inv})}}$, shown in the legend.

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Figure A7-a:
The observed ${m_{\mathrm {jj}}}$ distribution in the MTR (left) and VTR (right) SRs compared to the CR-postfit backgrounds, with the 2017 and 2018 samples. The yields from the 2017 and 2018 samples are summed and the correlations between their uncertainties are neglected. The signal processes are scaled by the fitted value of ${{\mathcal {B}(\mathrm{H} \to \text {inv})}}$, shown in the legend.

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Figure A7-b:
The observed ${m_{\mathrm {jj}}}$ distribution in the MTR (left) and VTR (right) SRs compared to the CR-postfit backgrounds, with the 2017 and 2018 samples. The yields from the 2017 and 2018 samples are summed and the correlations between their uncertainties are neglected. The signal processes are scaled by the fitted value of ${{\mathcal {B}(\mathrm{H} \to \text {inv})}}$, shown in the legend.

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Figure A8:
The ${m_{\mathrm {jj}}}$ distributions (prefit and CR-postfit) in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the MTR category, with the 2017 sample.

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Figure A8-a:
The ${m_{\mathrm {jj}}}$ distributions (prefit and CR-postfit) in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the MTR category, with the 2017 sample.

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Figure A8-b:
The ${m_{\mathrm {jj}}}$ distributions (prefit and CR-postfit) in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the MTR category, with the 2017 sample.

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Figure A8-c:
The ${m_{\mathrm {jj}}}$ distributions (prefit and CR-postfit) in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the MTR category, with the 2017 sample.

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Figure A8-d:
The ${m_{\mathrm {jj}}}$ distributions (prefit and CR-postfit) in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the MTR category, with the 2017 sample.

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Figure A9:
The ${m_{\mathrm {jj}}}$ postfit distributions in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the MTR category, with the 2017 sample. The background contributions are estimated from a fit to data in the SR and CRs allowing for the signal contribution to vary (S+B fit) and the total background estimated from a fit assuming $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} =$ 0 (B-only fit) is also shown.

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Figure A9-a:
The ${m_{\mathrm {jj}}}$ postfit distributions in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the MTR category, with the 2017 sample. The background contributions are estimated from a fit to data in the SR and CRs allowing for the signal contribution to vary (S+B fit) and the total background estimated from a fit assuming $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} =$ 0 (B-only fit) is also shown.

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Figure A9-b:
The ${m_{\mathrm {jj}}}$ postfit distributions in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the MTR category, with the 2017 sample. The background contributions are estimated from a fit to data in the SR and CRs allowing for the signal contribution to vary (S+B fit) and the total background estimated from a fit assuming $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} =$ 0 (B-only fit) is also shown.

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Figure A9-c:
The ${m_{\mathrm {jj}}}$ postfit distributions in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the MTR category, with the 2017 sample. The background contributions are estimated from a fit to data in the SR and CRs allowing for the signal contribution to vary (S+B fit) and the total background estimated from a fit assuming $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} =$ 0 (B-only fit) is also shown.

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Figure A9-d:
The ${m_{\mathrm {jj}}}$ postfit distributions in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the MTR category, with the 2017 sample. The background contributions are estimated from a fit to data in the SR and CRs allowing for the signal contribution to vary (S+B fit) and the total background estimated from a fit assuming $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} =$ 0 (B-only fit) is also shown.

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Figure A10:
The ${m_{\mathrm {jj}}}$ CR-postfit (left) and postfit (right) distributions in the photon CR for the MTR category, with the 2017 sample. In the right figure, the total background estimated from a fit assuming $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} =$ 0 (B-only fit) is also shown.

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Figure A10-a:
The ${m_{\mathrm {jj}}}$ CR-postfit (left) and postfit (right) distributions in the photon CR for the MTR category, with the 2017 sample. In the right figure, the total background estimated from a fit assuming $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} =$ 0 (B-only fit) is also shown.

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Figure A10-b:
The ${m_{\mathrm {jj}}}$ CR-postfit (left) and postfit (right) distributions in the photon CR for the MTR category, with the 2017 sample. In the right figure, the total background estimated from a fit assuming $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} =$ 0 (B-only fit) is also shown.

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Figure A11:
The observed ${m_{\mathrm {jj}}}$ distribution in the MTR prefit (left) and postfit (right) SR compared to the postfit backgrounds, with the 2017 samples. The signal processes are scaled by the fitted value of ${{\mathcal {B}(\mathrm{H} \to \text {inv})}}$, shown in the legend.

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Figure A11-a:
The observed ${m_{\mathrm {jj}}}$ distribution in the MTR prefit (left) and postfit (right) SR compared to the postfit backgrounds, with the 2017 samples. The signal processes are scaled by the fitted value of ${{\mathcal {B}(\mathrm{H} \to \text {inv})}}$, shown in the legend.

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Figure A11-b:
The observed ${m_{\mathrm {jj}}}$ distribution in the MTR prefit (left) and postfit (right) SR compared to the postfit backgrounds, with the 2017 samples. The signal processes are scaled by the fitted value of ${{\mathcal {B}(\mathrm{H} \to \text {inv})}}$, shown in the legend.

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Figure A12:
The ${m_{\mathrm {jj}}}$ distributions (prefit and CR-postfit) in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the MTR category, with the 2018 sample.

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Figure A12-a:
The ${m_{\mathrm {jj}}}$ distributions (prefit and CR-postfit) in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the MTR category, with the 2018 sample.

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Figure A12-b:
The ${m_{\mathrm {jj}}}$ distributions (prefit and CR-postfit) in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the MTR category, with the 2018 sample.

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Figure A12-c:
The ${m_{\mathrm {jj}}}$ distributions (prefit and CR-postfit) in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the MTR category, with the 2018 sample.

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Figure A12-d:
The ${m_{\mathrm {jj}}}$ distributions (prefit and CR-postfit) in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the MTR category, with the 2018 sample.

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Figure A13:
The ${m_{\mathrm {jj}}}$ postfit distributions in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the MTR category, with the 2018 sample. The background contributions are estimated from a fit to data in the SR and CRs allowing for the signal contribution to vary (S+B fit) and the total background estimated from a fit assuming $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} =$ 0 (B-only fit) is also shown.

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Figure A13-a:
The ${m_{\mathrm {jj}}}$ postfit distributions in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the MTR category, with the 2018 sample. The background contributions are estimated from a fit to data in the SR and CRs allowing for the signal contribution to vary (S+B fit) and the total background estimated from a fit assuming $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} =$ 0 (B-only fit) is also shown.

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Figure A13-b:
The ${m_{\mathrm {jj}}}$ postfit distributions in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the MTR category, with the 2018 sample. The background contributions are estimated from a fit to data in the SR and CRs allowing for the signal contribution to vary (S+B fit) and the total background estimated from a fit assuming $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} =$ 0 (B-only fit) is also shown.

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Figure A13-c:
The ${m_{\mathrm {jj}}}$ postfit distributions in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the MTR category, with the 2018 sample. The background contributions are estimated from a fit to data in the SR and CRs allowing for the signal contribution to vary (S+B fit) and the total background estimated from a fit assuming $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} =$ 0 (B-only fit) is also shown.

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Figure A13-d:
The ${m_{\mathrm {jj}}}$ postfit distributions in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the MTR category, with the 2018 sample. The background contributions are estimated from a fit to data in the SR and CRs allowing for the signal contribution to vary (S+B fit) and the total background estimated from a fit assuming $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} =$ 0 (B-only fit) is also shown.

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Figure A14:
The ${m_{\mathrm {jj}}}$ CR-postfit (left) and postfit (right) distributions in the photon CR for the MTR category, with the 2018 sample. In the right figure, the total background estimated from a fit assuming $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} =$ 0 (B-only fit) is also shown.

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Figure A14-a:
The ${m_{\mathrm {jj}}}$ CR-postfit (left) and postfit (right) distributions in the photon CR for the MTR category, with the 2018 sample. In the right figure, the total background estimated from a fit assuming $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} =$ 0 (B-only fit) is also shown.

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Figure A14-b:
The ${m_{\mathrm {jj}}}$ CR-postfit (left) and postfit (right) distributions in the photon CR for the MTR category, with the 2018 sample. In the right figure, the total background estimated from a fit assuming $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} =$ 0 (B-only fit) is also shown.

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Figure A15:
The observed ${m_{\mathrm {jj}}}$ distribution in the MTR prefit (left) and postfit (right) SR compared to the postfit backgrounds, with the 2018 samples. The signal processes are scaled by the fitted value of ${{\mathcal {B}(\mathrm{H} \to \text {inv})}}$, shown in the legend.

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Figure A15-a:
The observed ${m_{\mathrm {jj}}}$ distribution in the MTR prefit (left) and postfit (right) SR compared to the postfit backgrounds, with the 2018 samples. The signal processes are scaled by the fitted value of ${{\mathcal {B}(\mathrm{H} \to \text {inv})}}$, shown in the legend.

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Figure A15-b:
The observed ${m_{\mathrm {jj}}}$ distribution in the MTR prefit (left) and postfit (right) SR compared to the postfit backgrounds, with the 2018 samples. The signal processes are scaled by the fitted value of ${{\mathcal {B}(\mathrm{H} \to \text {inv})}}$, shown in the legend.

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Figure A16:
The ${m_{\mathrm {jj}}}$ distributions (prefit and CR-postfit) in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the VTR category, with the 2017 sample.

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Figure A16-a:
The ${m_{\mathrm {jj}}}$ distributions (prefit and CR-postfit) in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the VTR category, with the 2017 sample.

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Figure A16-b:
The ${m_{\mathrm {jj}}}$ distributions (prefit and CR-postfit) in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the VTR category, with the 2017 sample.

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Figure A16-c:
The ${m_{\mathrm {jj}}}$ distributions (prefit and CR-postfit) in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the VTR category, with the 2017 sample.

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Figure A16-d:
The ${m_{\mathrm {jj}}}$ distributions (prefit and CR-postfit) in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the VTR category, with the 2017 sample.

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Figure A17:
The ${m_{\mathrm {jj}}}$ postfit distributions in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the VTR category, with the 2017 sample. The background contributions are estimated from a fit to data in the SR and CRs allowing for the signal contribution to vary (S+B fit) and the total background estimated from a fit assuming $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} =$ 0 (B-only fit) is also shown.

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Figure A17-a:
The ${m_{\mathrm {jj}}}$ postfit distributions in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the VTR category, with the 2017 sample. The background contributions are estimated from a fit to data in the SR and CRs allowing for the signal contribution to vary (S+B fit) and the total background estimated from a fit assuming $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} =$ 0 (B-only fit) is also shown.

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Figure A17-b:
The ${m_{\mathrm {jj}}}$ postfit distributions in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the VTR category, with the 2017 sample. The background contributions are estimated from a fit to data in the SR and CRs allowing for the signal contribution to vary (S+B fit) and the total background estimated from a fit assuming $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} =$ 0 (B-only fit) is also shown.

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Figure A17-c:
The ${m_{\mathrm {jj}}}$ postfit distributions in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the VTR category, with the 2017 sample. The background contributions are estimated from a fit to data in the SR and CRs allowing for the signal contribution to vary (S+B fit) and the total background estimated from a fit assuming $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} =$ 0 (B-only fit) is also shown.

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Figure A17-d:
The ${m_{\mathrm {jj}}}$ postfit distributions in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the VTR category, with the 2017 sample. The background contributions are estimated from a fit to data in the SR and CRs allowing for the signal contribution to vary (S+B fit) and the total background estimated from a fit assuming $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} =$ 0 (B-only fit) is also shown.

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Figure A18:
The observed ${m_{\mathrm {jj}}}$ distribution in the VTR prefit (left) and postfit (right) SR compared to the postfit backgrounds, with the 2017 samples. The signal processes are scaled by the fitted value of ${{\mathcal {B}(\mathrm{H} \to \text {inv})}}$, shown in the legend.

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Figure A18-a:
The observed ${m_{\mathrm {jj}}}$ distribution in the VTR prefit (left) and postfit (right) SR compared to the postfit backgrounds, with the 2017 samples. The signal processes are scaled by the fitted value of ${{\mathcal {B}(\mathrm{H} \to \text {inv})}}$, shown in the legend.

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Figure A18-b:
The observed ${m_{\mathrm {jj}}}$ distribution in the VTR prefit (left) and postfit (right) SR compared to the postfit backgrounds, with the 2017 samples. The signal processes are scaled by the fitted value of ${{\mathcal {B}(\mathrm{H} \to \text {inv})}}$, shown in the legend.

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Figure A19:
The ${m_{\mathrm {jj}}}$ distributions (prefit and CR-postfit) in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the VTR category, with the 2018 sample.

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Figure A19-a:
The ${m_{\mathrm {jj}}}$ distributions (prefit and CR-postfit) in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the VTR category, with the 2018 sample.

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Figure A19-b:
The ${m_{\mathrm {jj}}}$ distributions (prefit and CR-postfit) in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the VTR category, with the 2018 sample.

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Figure A19-c:
The ${m_{\mathrm {jj}}}$ distributions (prefit and CR-postfit) in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the VTR category, with the 2018 sample.

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Figure A19-d:
The ${m_{\mathrm {jj}}}$ distributions (prefit and CR-postfit) in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the VTR category, with the 2018 sample.

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Figure A20:
The ${m_{\mathrm {jj}}}$ postfit distributions in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the VTR category, with the 2018 sample. The background contributions are estimated from a fit to data in the SR and CRs allowing for the signal contribution to vary (S+B fit) and the total background estimated from a fit assuming $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} =$ 0 (B-only fit) is also shown.

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Figure A20-a:
The ${m_{\mathrm {jj}}}$ postfit distributions in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the VTR category, with the 2018 sample. The background contributions are estimated from a fit to data in the SR and CRs allowing for the signal contribution to vary (S+B fit) and the total background estimated from a fit assuming $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} =$ 0 (B-only fit) is also shown.

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Figure A20-b:
The ${m_{\mathrm {jj}}}$ postfit distributions in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the VTR category, with the 2018 sample. The background contributions are estimated from a fit to data in the SR and CRs allowing for the signal contribution to vary (S+B fit) and the total background estimated from a fit assuming $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} =$ 0 (B-only fit) is also shown.

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Figure A20-c:
The ${m_{\mathrm {jj}}}$ postfit distributions in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the VTR category, with the 2018 sample. The background contributions are estimated from a fit to data in the SR and CRs allowing for the signal contribution to vary (S+B fit) and the total background estimated from a fit assuming $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} =$ 0 (B-only fit) is also shown.

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Figure A20-d:
The ${m_{\mathrm {jj}}}$ postfit distributions in the dielectron (upper left), dimuon (upper right), single-electron (lower left), and single-muon (lower right) CR for the VTR category, with the 2018 sample. The background contributions are estimated from a fit to data in the SR and CRs allowing for the signal contribution to vary (S+B fit) and the total background estimated from a fit assuming $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} =$ 0 (B-only fit) is also shown.

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Figure A21:
The observed ${m_{\mathrm {jj}}}$ distribution in the VTR prefit (left) and postfit (right) SR compared to the postfit backgrounds, with the 2018 samples. The signal processes are scaled by the fitted value of ${{\mathcal {B}(\mathrm{H} \to \text {inv})}}$, shown in the legend.

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Figure A21-a:
The observed ${m_{\mathrm {jj}}}$ distribution in the VTR prefit (left) and postfit (right) SR compared to the postfit backgrounds, with the 2018 samples. The signal processes are scaled by the fitted value of ${{\mathcal {B}(\mathrm{H} \to \text {inv})}}$, shown in the legend.

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Figure A21-b:
The observed ${m_{\mathrm {jj}}}$ distribution in the VTR prefit (left) and postfit (right) SR compared to the postfit backgrounds, with the 2018 samples. The signal processes are scaled by the fitted value of ${{\mathcal {B}(\mathrm{H} \to \text {inv})}}$, shown in the legend.

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Figure A22:
Comparison between data and simulation for the Z(ee)+jets / W(e$\nu$)+jets (upper left), Z($\mu \mu$)+jets / W($\mu \nu$)+jets (upper right), $\gamma$+jets / Z(ee)+jets (lower left), and $\gamma$+jets / Z($\mu \mu$)+jets (lower right) prefit and CR-postfit ratios, as functions of ${m_{\mathrm {jj}}}$, for the MTR category 2017 samples. The minor backgrounds in each CR are subtracted from the data using estimates from simulation. The grey bands include the theoretical and experimental systematic uncertainties listed in Table 3, as well as the statistical uncertainty in the simulation.

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Figure A22-a:
Comparison between data and simulation for the Z(ee)+jets / W(e$\nu$)+jets (upper left), Z($\mu \mu$)+jets / W($\mu \nu$)+jets (upper right), $\gamma$+jets / Z(ee)+jets (lower left), and $\gamma$+jets / Z($\mu \mu$)+jets (lower right) prefit and CR-postfit ratios, as functions of ${m_{\mathrm {jj}}}$, for the MTR category 2017 samples. The minor backgrounds in each CR are subtracted from the data using estimates from simulation. The grey bands include the theoretical and experimental systematic uncertainties listed in Table 3, as well as the statistical uncertainty in the simulation.

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Figure A22-b:
Comparison between data and simulation for the Z(ee)+jets / W(e$\nu$)+jets (upper left), Z($\mu \mu$)+jets / W($\mu \nu$)+jets (upper right), $\gamma$+jets / Z(ee)+jets (lower left), and $\gamma$+jets / Z($\mu \mu$)+jets (lower right) prefit and CR-postfit ratios, as functions of ${m_{\mathrm {jj}}}$, for the MTR category 2017 samples. The minor backgrounds in each CR are subtracted from the data using estimates from simulation. The grey bands include the theoretical and experimental systematic uncertainties listed in Table 3, as well as the statistical uncertainty in the simulation.

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Figure A22-c:
Comparison between data and simulation for the Z(ee)+jets / W(e$\nu$)+jets (upper left), Z($\mu \mu$)+jets / W($\mu \nu$)+jets (upper right), $\gamma$+jets / Z(ee)+jets (lower left), and $\gamma$+jets / Z($\mu \mu$)+jets (lower right) prefit and CR-postfit ratios, as functions of ${m_{\mathrm {jj}}}$, for the MTR category 2017 samples. The minor backgrounds in each CR are subtracted from the data using estimates from simulation. The grey bands include the theoretical and experimental systematic uncertainties listed in Table 3, as well as the statistical uncertainty in the simulation.

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Figure A22-d:
Comparison between data and simulation for the Z(ee)+jets / W(e$\nu$)+jets (upper left), Z($\mu \mu$)+jets / W($\mu \nu$)+jets (upper right), $\gamma$+jets / Z(ee)+jets (lower left), and $\gamma$+jets / Z($\mu \mu$)+jets (lower right) prefit and CR-postfit ratios, as functions of ${m_{\mathrm {jj}}}$, for the MTR category 2017 samples. The minor backgrounds in each CR are subtracted from the data using estimates from simulation. The grey bands include the theoretical and experimental systematic uncertainties listed in Table 3, as well as the statistical uncertainty in the simulation.

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Figure A23:
Comparison between data and simulation for the Z(ee)+jets / W(e$\nu$)+jets (left) and Z($\mu \mu$)+jets / W($\mu \nu$)+jets (right) prefit and CR-postfit ratios, as functions of ${m_{\mathrm {jj}}}$, for the VTR category 2017 samples. The minor backgrounds in each CR are subtracted from the data using estimates from simulation. The grey bands include the theoretical and experimental systematic uncertainties listed in Table 3, as well as the statistical uncertainty in the simulation.

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Figure A23-a:
Comparison between data and simulation for the Z(ee)+jets / W(e$\nu$)+jets (left) and Z($\mu \mu$)+jets / W($\mu \nu$)+jets (right) prefit and CR-postfit ratios, as functions of ${m_{\mathrm {jj}}}$, for the VTR category 2017 samples. The minor backgrounds in each CR are subtracted from the data using estimates from simulation. The grey bands include the theoretical and experimental systematic uncertainties listed in Table 3, as well as the statistical uncertainty in the simulation.

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Figure A23-b:
Comparison between data and simulation for the Z(ee)+jets / W(e$\nu$)+jets (left) and Z($\mu \mu$)+jets / W($\mu \nu$)+jets (right) prefit and CR-postfit ratios, as functions of ${m_{\mathrm {jj}}}$, for the VTR category 2017 samples. The minor backgrounds in each CR are subtracted from the data using estimates from simulation. The grey bands include the theoretical and experimental systematic uncertainties listed in Table 3, as well as the statistical uncertainty in the simulation.

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Figure A24:
Comparison between data and simulation for the Z(ee)+jets / W(e$\nu$)+jets (upper left), Z($\mu \mu$)+jets / W($\mu \nu$)+jets (upper right), $\gamma$+jets / Z(ee)+jets (lower left), and $\gamma$+jets / Z($\mu \mu$)+jets (lower right) prefit and CR-postfit ratios, as functions of ${m_{\mathrm {jj}}}$, for the MTR category 2018 samples. The minor backgrounds in each CR are subtracted from the data using estimates from simulation. The grey bands include the theoretical and experimental systematic uncertainties listed in Table 3, as well as the statistical uncertainty in the simulation.

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Figure A24-a:
Comparison between data and simulation for the Z(ee)+jets / W(e$\nu$)+jets (upper left), Z($\mu \mu$)+jets / W($\mu \nu$)+jets (upper right), $\gamma$+jets / Z(ee)+jets (lower left), and $\gamma$+jets / Z($\mu \mu$)+jets (lower right) prefit and CR-postfit ratios, as functions of ${m_{\mathrm {jj}}}$, for the MTR category 2018 samples. The minor backgrounds in each CR are subtracted from the data using estimates from simulation. The grey bands include the theoretical and experimental systematic uncertainties listed in Table 3, as well as the statistical uncertainty in the simulation.

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Figure A24-b:
Comparison between data and simulation for the Z(ee)+jets / W(e$\nu$)+jets (upper left), Z($\mu \mu$)+jets / W($\mu \nu$)+jets (upper right), $\gamma$+jets / Z(ee)+jets (lower left), and $\gamma$+jets / Z($\mu \mu$)+jets (lower right) prefit and CR-postfit ratios, as functions of ${m_{\mathrm {jj}}}$, for the MTR category 2018 samples. The minor backgrounds in each CR are subtracted from the data using estimates from simulation. The grey bands include the theoretical and experimental systematic uncertainties listed in Table 3, as well as the statistical uncertainty in the simulation.

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Figure A24-c:
Comparison between data and simulation for the Z(ee)+jets / W(e$\nu$)+jets (upper left), Z($\mu \mu$)+jets / W($\mu \nu$)+jets (upper right), $\gamma$+jets / Z(ee)+jets (lower left), and $\gamma$+jets / Z($\mu \mu$)+jets (lower right) prefit and CR-postfit ratios, as functions of ${m_{\mathrm {jj}}}$, for the MTR category 2018 samples. The minor backgrounds in each CR are subtracted from the data using estimates from simulation. The grey bands include the theoretical and experimental systematic uncertainties listed in Table 3, as well as the statistical uncertainty in the simulation.

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Figure A24-d:
Comparison between data and simulation for the Z(ee)+jets / W(e$\nu$)+jets (upper left), Z($\mu \mu$)+jets / W($\mu \nu$)+jets (upper right), $\gamma$+jets / Z(ee)+jets (lower left), and $\gamma$+jets / Z($\mu \mu$)+jets (lower right) prefit and CR-postfit ratios, as functions of ${m_{\mathrm {jj}}}$, for the MTR category 2018 samples. The minor backgrounds in each CR are subtracted from the data using estimates from simulation. The grey bands include the theoretical and experimental systematic uncertainties listed in Table 3, as well as the statistical uncertainty in the simulation.

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Figure A25:
Comparison between data and simulation for the Z(ee)+jets / W(e$\nu$)+jets (left) and Z($\mu \mu$)+jets / W($\mu \nu$)+jets (right) prefit and CR-postfit ratios, as functions of ${m_{\mathrm {jj}}}$, for the VTR category 2018 samples. The minor backgrounds in each CR are subtracted from the data using estimates from simulation. The grey bands include the theoretical and experimental systematic uncertainties listed in Table 3, as well as the statistical uncertainty in the simulation.

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Figure A25-a:
Comparison between data and simulation for the Z(ee)+jets / W(e$\nu$)+jets (left) and Z($\mu \mu$)+jets / W($\mu \nu$)+jets (right) prefit and CR-postfit ratios, as functions of ${m_{\mathrm {jj}}}$, for the VTR category 2018 samples. The minor backgrounds in each CR are subtracted from the data using estimates from simulation. The grey bands include the theoretical and experimental systematic uncertainties listed in Table 3, as well as the statistical uncertainty in the simulation.

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Figure A25-b:
Comparison between data and simulation for the Z(ee)+jets / W(e$\nu$)+jets (left) and Z($\mu \mu$)+jets / W($\mu \nu$)+jets (right) prefit and CR-postfit ratios, as functions of ${m_{\mathrm {jj}}}$, for the VTR category 2018 samples. The minor backgrounds in each CR are subtracted from the data using estimates from simulation. The grey bands include the theoretical and experimental systematic uncertainties listed in Table 3, as well as the statistical uncertainty in the simulation.
Tables

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Table 1:
Selection applied in the 2017 and 2018 data sets to remove HF jets stemming from calorimeter noise.

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Table 2:
Summary of the kinematic selections used to define the SR for both the MTR and the VTR categories.

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Table 3:
Experimental and theoretical sources of systematic uncertainty in the V+jets transfer factors. The second column indicates which ratio a given source of uncertainty is applied to. The impact on ${m_{\mathrm {jj}}}$ is given in the 3rd column, as a single value if no dependence on ${m_{\mathrm {jj}}}$ is observed, or as a range. When a range is shown, the uncertainty increases with the value of ${m_{\mathrm {jj}}}$. The quoted uncertainty values represent the absolute value of the relative change in the transfer factor corresponding to a variation of ${\pm}$1 standard deviation in the systematic uncertainty, or equivalently to a variation of ${\pm}$1 in the corresponding nuisance parameter $\theta $ in Eq. (4).

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Table 4:
Expected event yields in each ${m_{\mathrm {jj}}}$ bin for the different background processes in the SR of the MTR category, summing the 2017 and 2018 samples. The background yields and the corresponding uncertainties are obtained after performing a combined fit across all of the CRs and the SR. The expected signal contributions for the Higgs boson, produced in the non-VBF and VBF modes, decaying to invisible particles with a branching fraction of $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} = $ 1, and the observed event yields are also reported. The yields from the 2017 and 2018 samples are summed and the correlations between their uncertainties are neglected.

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Table 5:
Expected event yields in each ${m_{\mathrm {jj}}}$ bin for the different background processes in the SR of the VTR category, summing the 2017 and 2018 samples. The background yields and the corresponding uncertainties are obtained after performing a combined fit across all of the CRs and the SR. The expected signal contributions for the Higgs boson, produced in the non-VBF and VBF modes, decaying to invisible particles with a branching fraction of $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} = $ 1, and the observed event yields are also reported. The yields from the 2017 and 2018 samples are summed and the correlations between their uncertainties are neglected.

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Table 6:
The 95% CL upper limits on ${(\sigma _{\mathrm{H}}/\sigma _{\mathrm{H}}^{\mathrm {SM}}) {{\mathcal {B}(\mathrm{H} \to \text {inv})}}}$, assuming an SM Higgs boson with a mass of 125.38 GeV. The observed and median expected results are shown, along with the 68% and 95% interquartile ranges for each category and for the combinations.

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Table 7:
Uncertainty breakdown in ${{\mathcal {B}(\mathrm{H} \to \text {inv})}}$. The sources of uncertainty are separated into different groups. Observed and expected results are quoted for the full combination of 2012-2018 data. The expected results are obtained using an Asimov data set [71] with $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} =$ 0.

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Table A1:
Expected event yields in each ${m_{\mathrm {jj}}}$ bin for the different background processes in the SR of the MTR category, in the 2017 samples. The background yields and the corresponding uncertainties are obtained after performing a combined fit across all of the CRs and SR. The expected signal contributions for the Higgs boson, produced in the non-VBF and VBF modes, decaying to invisible particles with a branching fraction of $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} = $ 1, and the observed event yields are also reported.

png pdf
Table A2:
Expected event yields in each ${m_{\mathrm {jj}}}$ bin for the different background processes in the SR of the MTR category, in the 2018 samples. The background yields and the corresponding uncertainties are obtained after performing a combined fit across all of the CRs and SR. The expected signal contributions for the Higgs boson, produced in the non-VBF and VBF modes, decaying to invisible particles with a branching fraction of $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} = $ 1, and the observed event yields are also reported.

png pdf
Table A3:
Expected event yields in each ${m_{\mathrm {jj}}}$ bin for the different background processes in the SR of the MTR category, in the 2017 and 2018 samples. The background yields and the corresponding uncertainties are obtained after performing a combined fit across all of the CRs and SR. The expected signal contributions for the Higgs boson, produced in the non-VBF and VBF modes, decaying to invisible particles with a branching fraction of $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} = $ 1, and the observed event yields are also reported. The yields from the 2017 and 2018 samples are summed and the correlations between their uncertainties are neglected.

png pdf
Table A4:
Expected event yields in each ${m_{\mathrm {jj}}}$ bin for the different background processes in the SR of the VTR category, in the 2017 samples. The background yields and the corresponding uncertainties are obtained after performing a combined fit across all of the CRs and SR. The expected signal contributions for the Higgs boson, produced in the non-VBF and VBF modes, decaying to invisible particles with a branching fraction of $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} = $ 1, and the observed event yields are also reported.

png pdf
Table A5:
Expected event yields in each ${m_{\mathrm {jj}}}$ bin for the different background processes in the SR of the VTR category, in the 2018 samples. The background yields and the corresponding uncertainties are obtained after performing a combined fit across all of the CRs and SR. The expected signal contributions for the Higgs boson, produced in the non-VBF and VBF modes, decaying to invisible particles with a branching fraction of $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} = $ 1, and the observed event yields are also reported.

png pdf
Table A6:
Expected event yields in each ${m_{\mathrm {jj}}}$ bin for the different background processes in the SR of the VTR category, in the 2017 and 2018 samples. The background yields and the corresponding uncertainties are obtained after performing a combined fit across all of the CRs and SR. The expected signal contributions for the Higgs boson, produced in the non-VBF and VBF modes, decaying to invisible particles with a branching fraction of $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} = $ 1, and the observed event yields are also reported. The yields from the 2017 and 2018 samples are summed and the correlations between their uncertainties are neglected.

png pdf
Table A7:
Expected event yields in each ${m_{\mathrm {jj}}}$ bin for the different background processes in the SR of the MTR category, in the 2017 samples. The background yields and the corresponding uncertainties are obtained after performing a combined fit across all of the CRs and SR. The expected signal contributions for the Higgs boson, produced in the non-VBF and VBF modes, decaying to invisible particles with a branching fraction of $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} = $ 1, and the observed event yields are also reported.

png pdf
Table A8:
Expected event yields in each ${m_{\mathrm {jj}}}$ bin for the different background processes in the SR of the MTR category, in the 2018 samples. The background yields and the corresponding uncertainties are obtained after performing a combined fit across all of the CRs and SR. The expected signal contributions for the Higgs boson, produced in the non-VBF and VBF modes, decaying to invisible particles with a branching fraction of $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} = $ 1, and the observed event yields are also reported.

png pdf
Table A9:
Expected event yields in each ${m_{\mathrm {jj}}}$ bin for the different background processes in the SR of the VTR category, in the 2017 samples. The background yields and the corresponding uncertainties are obtained after performing a combined fit across all of the CRs and SR. The expected signal contributions for the Higgs boson, produced in the non-VBF and VBF modes, decaying to invisible particles with a branching fraction of $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} = $ 1, and the observed event yields are also reported.

png pdf
Table A10:
Expected event yields in each ${m_{\mathrm {jj}}}$ bin for the different background processes in the SR of the VTR category, in the 2018 samples. The background yields and the corresponding uncertainties are obtained after performing a combined fit across all of the CRs and SR. The expected signal contributions for the Higgs boson, produced in the non-VBF and VBF modes, decaying to invisible particles with a branching fraction of $ {{\mathcal {B}(\mathrm{H} \to \text {inv})}} = $ 1, and the observed event yields are also reported.
Summary
A search for the Higgs boson (H) decaying invisibly, produced in the vector boson fusion mode, is performed with 101 fb$^{-1}$ of proton-proton collisions delivered by the LHC at $\sqrt{s} = $ 13 TeV and collected by the CMS detector during 2017-2018. Building upon the previously published results, an additional category targeting events at lower Higgs boson transverse momentum is added. An additional highly populated control region, based on production of a photon associated with jets, is used to constrain the dominant irreducible background from invisible decays of a Z boson produced in association with jets. Compared with the strategy of the previously published analysis, these additions improve the expected limits by approximately 17%. The observed (expected) upper limit on the invisible branching fraction of the Higgs boson, ${{\mathcal{B}(\mathrm{H} \to \text{inv})}} $, is found to be 0.18 (0.12) at the 95% confidence level (CL), assuming the standard model production cross section. The results are combined with previous measurements in the vector boson fusion topology, for total integrated luminosities of 19.7 fb$^{-1}$ at $\sqrt{s} = $ 8 TeV and 140 fb$^{-1}$ at $\sqrt{s} = $ 13 TeV, yielding an observed (expected) upper limit of 0.18 (0.10) at the 95% CL. This is currently the most stringent limit on ${{\mathcal{B}(\mathrm{H} \to \text{inv})}} $. Finally, the results are interpreted in the context of Higgs-portal models. The 90% CL upper limits on the spin-independent dark-matter-nucleon scattering cross section obtained from the observed LHC data collected during 2012-2018 complement the direct detection experiments in the range of dark matter particle masses smaller than 12 (6) GeV, assuming a fermion (scalar) dark matter candidate.
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