CMSB2G20009 ; CERNEP2022152  
Search for new heavy resonances decaying to WW, WZ, ZZ, WH, or ZH boson pairs in the alljets final state in protonproton collisions at $ \sqrt{s}= $ 13 TeV  
CMS Collaboration  
30 September 2022  
Phys. Lett. B 844 (2023) 137813  
Abstract: A search for new heavy resonances decaying to WW, WZ, ZZ, WH, or ZH boson pairs in the alljets final state is presented. The analysis is based on protonproton collision data recorded by the CMS detector in 20162018 at a centreofmass energy of 13 TeV at the CERN LHC, corresponding to an integrated luminosity of 138 fb$^{1}$. The search is sensitive to resonances with masses above 1.3 TeV, decaying to bosons that are highly Lorentzboosted such that each of the bosons forms a single largeradius jet. Machine learning techniques are employed to identify such jets. No significant excess over the estimated standard model background is observed. A maximum local significance of 3.6 standard deviations, corresponding to a global significance of 2.3 standard deviations, is observed at masses of 2.1 and 2.9 TeV. In a heavy vector triplet model, spin1 Z' and W' resonances with masses below 4.8 TeV are excluded at the 95% confidence level (CL). These limits are the most stringent to date. In a bulk graviton model, spin2 gravitons and spin0 radions with masses below 1.4 and 2.7 TeV, respectively, are excluded at 95% CL. Production of heavy resonances through vector boson fusion is constrained with upper cross section limits at 95% CL as low as 0.1 fb.  
Links: eprint arXiv:2210.00043 [hepex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; Physics Briefing ; CADI line (restricted) ; 
Figures & Tables  Summary  Additional Figures  References  CMS Publications 

Figures  
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Figure 1:
Feynman diagrams of the signal processes ggF or DY produced (upper) and VBF produced (lower): (left) graviton or radion decaying to WW or ZZ; (center) Z' and W' decaying to ZH and WH, respectively; (right) Z' and W' decaying to WW and WZ, respectively. 
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Figure 1a:
Example Feynman diagram of signal process: DY produced graviton or radion decaying to WW or ZZ. 
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Figure 1b:
Example Feynman diagram of signal process: DY produced Z' and W' decaying to ZH and WH, respectively. 
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Figure 1c:
Example Feynman diagram of signal process: DY produced Z' and W' decaying to WW and WZ, respectively. 
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Figure 1d:
Example Feynman diagram of signal process: VBF produced graviton or radion decaying to WW or ZZ. 
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Figure 1e:
Example Feynman diagram of signal process: VBF produced Z' and W' decaying to ZH and WH, respectively. 
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Figure 1f:
Example Feynman diagram of signal process: VBF produced Z' and W' decaying to WW and WZ, respectively. 
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Figure 2:
Distributions of $ m_\mathrm{jj}^{ \mathrm{AK8} } $ (left) and $ m_\text{jet1}^{ \mathrm{AK8} } $ (right) in the nominal QCD multijet simulation using PYTHIA 8 (black markers) and threedimensional templates (black solid line) in the DY/ggF VH HPHP category. Superimposed are the normalized up and down variations of five alternative shapes corresponding to shape nuisance parameters in the fit model. Each of the variations has a characteristic dependence on $ m_\text{jet}^{ \mathrm{AK8} } $ to allow the necessary flexibility in the fit for the template to adapt to the data. We also allow an overall variation of the rate in the fit. 
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Figure 2a:
Distribution of $ m_\mathrm{jj}^{ \mathrm{AK8} } $ in the nominal QCD multijet simulation using PYTHIA 8 (black markers) and threedimensional templates (black solid line) in the DY/ggF VH HPHP category. Superimposed are the normalized up and down variations of five alternative shapes corresponding to shape nuisance parameters in the fit model. Each of the variations has a characteristic dependence on $ m_\text{jet}^{ \mathrm{AK8} } $ to allow the necessary flexibility in the fit for the template to adapt to the data. We also allow an overall variation of the rate in the fit. 
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Figure 2b:
Distribution of $ m_\text{jet1}^{ \mathrm{AK8} } $ in the nominal QCD multijet simulation using PYTHIA 8 (black markers) and threedimensional templates (black solid line) in the DY/ggF VH HPHP category. Superimposed are the normalized up and down variations of five alternative shapes corresponding to shape nuisance parameters in the fit model. Each of the variations has a characteristic dependence on $ m_\text{jet}^{ \mathrm{AK8} } $ to allow the necessary flexibility in the fit for the template to adapt to the data. We also allow an overall variation of the rate in the fit. 
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Figure 3:
Comparison between the background postfit and the data distributions of $ m_\mathrm{jj}^{ \mathrm{AK8} } $ (left) and $ m_\text{jet1}^{ \mathrm{AK8} } $ (right) in the DY/ggF VH HPHP category. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are represented as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. An example of a signal distribution is overlaid, where the number of expected events is scaled by an arbitrary normalization factor of 20. Shown below each mass plot is the difference between the data and the fit divided by the statistical uncertainty in the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty in the background estimate fitted to the data divided by the statistical uncertainty in the data is shown as a band. 
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Figure 3a:
Comparison between the background postfit and the data distributions of $ m_\mathrm{jj}^{ \mathrm{AK8} } $ in the DY/ggF VH HPHP category. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are represented as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. An example of a signal distribution is overlaid, where the number of expected events is scaled by an arbitrary normalization factor of 20. Shown below the plot is the difference between the data and the fit divided by the statistical uncertainty in the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty in the background estimate fitted to the data divided by the statistical uncertainty in the data is shown as a band. 
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Figure 3b:
Comparison between the background postfit and the data distributions of $ m_\text{jet1}^{ \mathrm{AK8} } $ in the DY/ggF VH HPHP category. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are represented as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. An example of a signal distribution is overlaid, where the number of expected events is scaled by an arbitrary normalization factor of 20. Shown below the plot is the difference between the data and the fit divided by the statistical uncertainty in the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty in the background estimate fitted to the data divided by the statistical uncertainty in the data is shown as a band. 
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Figure 4:
Projections of the data and background postfit distributions onto the $ m_\mathrm{jj}^{ \mathrm{AK8} } $ dimension in regions enriched in background ($ m_\text{jet1}^{\mathrm{AK8}} < $ 65 or $ > $140 GeV, and $ m_\text{jet2}^{\mathrm{AK8}} < $ 65 or $ > $140 GeV), for the HPHP VH (left) and VV (right) DY/ggF categories. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are shown as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. Shown below each mass plot is the difference between the data and the fit divided by the statistical uncertainty in the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty in the background estimate fitted to the data divided by the statistical uncertainty in the data is shown as a band. 
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Figure 4a:
Projection of the data and background postfit distributions onto the $ m_\mathrm{jj}^{ \mathrm{AK8} } $ dimension in regions enriched in background ($ m_\text{jet1}^{\mathrm{AK8}} < $ 65 or $ > $140 GeV, and $ m_\text{jet2}^{\mathrm{AK8}} < $ 65 or $ > $140 GeV), for the HPHP VH DY/ggF category. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are shown as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. Shown below the plot is the difference between the data and the fit divided by the statistical uncertainty in the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty in the background estimate fitted to the data divided by the statistical uncertainty in the data is shown as a band. 
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Figure 4b:
Projection of the data and background postfit distributions onto the $ m_\mathrm{jj}^{ \mathrm{AK8} } $ dimension in regions enriched in background ($ m_\text{jet1}^{\mathrm{AK8}} < $ 65 or $ > $140 GeV, and $ m_\text{jet2}^{\mathrm{AK8}} < $ 65 or $ > $140 GeV), for the HPHP VV DY/ggF category. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are shown as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. Shown below the plot is the difference between the data and the fit divided by the statistical uncertainty in the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty in the background estimate fitted to the data divided by the statistical uncertainty in the data is shown as a band. 
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Figure 5:
Projections of data and background postfit distributions onto the $ m_\mathrm{jj}^{ \mathrm{AK8} } $ dimension in regions enriched in signal from DY/ggF VV ( 65 $ < m_\text{jet1}^{\mathrm{AK8}} < $ 105 GeV, 65 $ < m_\text{jet2}^{\mathrm{AK8}} < $ 105 GeV) for the HPHP VH (left) and VV (right) DY/ggF categories. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are shown as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. An example of a signal distribution is overlaid. Shown below each mass plot is the difference between the data and the fit divided by the statistical uncertainty in the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty in the background estimate fitted to the data divided by the statistical uncertainty in the data is shown as a band. 
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Figure 5a:
Projection of data and background postfit distributions onto the $ m_\mathrm{jj}^{ \mathrm{AK8} } $ dimension in regions enriched in signal from DY/ggF VV ( 65 $ < m_\text{jet1}^{\mathrm{AK8}} < $ 105 GeV, 65 $ < m_\text{jet2}^{\mathrm{AK8}} < $ 105 GeV) for the HPHP VH DY/ggF categories. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are shown as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. An example of a signal distribution is overlaid. Shown below the plot is the difference between the data and the fit divided by the statistical uncertainty in the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty in the background estimate fitted to the data divided by the statistical uncertainty in the data is shown as a band. 
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Figure 5b:
Projection of data and background postfit distributions onto the $ m_\mathrm{jj}^{ \mathrm{AK8} } $ dimension in regions enriched in signal from DY/ggF VV ( 65 $ < m_\text{jet1}^{\mathrm{AK8}} < $ 105 GeV, 65 $ < m_\text{jet2}^{\mathrm{AK8}} < $ 105 GeV) for the HPHP VV DY/ggF categories. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are shown as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. An example of a signal distribution is overlaid. Shown below the plot is the difference between the data and the fit divided by the statistical uncertainty in the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty in the background estimate fitted to the data divided by the statistical uncertainty in the data is shown as a band. 
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Figure 6:
Distributions of the difference between the data and the backgroundonly fit divided by the statistical uncertainty in the data. The total uncertainty in the background estimate fitted to data divided by the statistical uncertainty in the data is shown as a band. It should be noted that these two uncertainties are partially correlated. Three projections of the 3D phase space are shown in regions enriched in signal from DY/ggF VV (65 $ < m_\text{jet1}^{\mathrm{AK8}} < $ 105 GeV, 65 $ < m_\text{jet2}^{\mathrm{AK8}} < $ 105 GeV) (upper left), DY/ggF VH (65 $ < m_\text{jet1/2}^{\mathrm{AK8}} < $ 105 GeV, 110 $ < m_\text{jet2/1}^{\mathrm{AK8}} < $ 140 GeV) (upper right) and VBF VV/VH (65 $ < m_\text{jet1}^{\mathrm{AK8}} < $ 140 GeV, 65 $ < m_\text{jet2}^{\mathrm{AK8}} < $ 140 GeV) (lower). Examples of expected signal shapes added to the fit are overlaid, where the number of expected events is scaled by an arbitrary normalization factor stated in the legend. 
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Figure 6a:
Distribution of the difference between the data and the backgroundonly fit divided by the statistical uncertainty in the data. The total uncertainty in the background estimate fitted to data divided by the statistical uncertainty in the data is shown as a band. It should be noted that these two uncertainties are partially correlated. The projection of the 3D phase space is shown in the 65 $ < m_\text{jet1}^{\mathrm{AK8}} < $ 105 GeV, 65 $ < m_\text{jet2}^{\mathrm{AK8}} < $ 105 GeV region. Examples of expected signal shapes added to the fit are overlaid, where the number of expected events is scaled by an arbitrary normalization factor stated in the legend. 
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Figure 6b:
Distribution of the difference between the data and the backgroundonly fit divided by the statistical uncertainty in the data. The total uncertainty in the background estimate fitted to data divided by the statistical uncertainty in the data is shown as a band. It should be noted that these two uncertainties are partially correlated. The projection of the 3D phase space is shown in the DY/ggF VH (65 $ < m_\text{jet1/2}^{\mathrm{AK8}} < $ 105 GeV, 110 $ < m_\text{jet2/1}^{\mathrm{AK8}} < $ 140 GeV region. Examples of expected signal shapes added to the fit are overlaid, where the number of expected events is scaled by an arbitrary normalization factor stated in the legend. 
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Figure 6c:
Distribution of the difference between the data and the backgroundonly fit divided by the statistical uncertainty in the data. The total uncertainty in the background estimate fitted to data divided by the statistical uncertainty in the data is shown as a band. It should be noted that these two uncertainties are partially correlated. The projection of the 3D phase space is shown in the VBF VV/VH (65 $ < m_\text{jet1}^{\mathrm{AK8}} < $ 140 GeV, 65 $ < m_\text{jet2}^{\mathrm{AK8}} < $ 140 GeV region. Examples of expected signal shapes added to the fit are overlaid, where the number of expected events is scaled by an arbitrary normalization factor stated in the legend. 
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Figure 7:
Observed and expected 95% CL upper limits on the product of the production cross section ($ \sigma $) and the branching fraction, obtained after combining all categories with 138 fb$^{1}$ of data at $ \sqrt{s}= $ 13 TeV, for $ \text{Rad}\to\mathrm{V}\mathrm{V} $ (upper left), $ \mathrm{G}_{\text{bulk}}\to\mathrm{V}\mathrm{V} $ (upper right), HVT model B $ \mathrm{V}^\prime\to\mathrm{V}\mathrm{V} $+ VH (lower left), HVT model C $ \mathrm{V}^\prime\to\mathrm{V}\mathrm{V} $+ VH (lower right) signals. For each signal scenario the theoretical prediction and its uncertainty associated with the choice of PDF set is shown. 
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Figure 7a:
Observed and expected 95% CL upper limits on the product of the production cross section ($ \sigma $) and the branching fraction, obtained after combining all categories with 138 fb$^{1}$ of data at $ \sqrt{s}= $ 13 TeV, for $ \text{Rad}\to\mathrm{V}\mathrm{V} $ signals. The theoretical prediction and its uncertainty associated with the choice of PDF set is shown. 
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Figure 7b:
Observed and expected 95% CL upper limits on the product of the production cross section ($ \sigma $) and the branching fraction, obtained after combining all categories with 138 fb$^{1}$ of data at $ \sqrt{s}= $ 13 TeV, for $ \mathrm{G}_{\text{bulk}}\to\mathrm{V}\mathrm{V} $ signals. The theoretical prediction and its uncertainty associated with the choice of PDF set is shown. 
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Figure 7c:
Observed and expected 95% CL upper limits on the product of the production cross section ($ \sigma $) and the branching fraction, obtained after combining all categories with 138 fb$^{1}$ of data at $ \sqrt{s}= $ 13 TeV, for HVT model B $ \mathrm{V}^\prime\to\mathrm{V}\mathrm{V} $+ VH signals. The theoretical prediction and its uncertainty associated with the choice of PDF set is shown. 
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Figure 7d:
Observed and expected 95% CL upper limits on the product of the production cross section ($ \sigma $) and the branching fraction, obtained after combining all categories with 138 fb$^{1}$ of data at $ \sqrt{s}= $ 13 TeV, for HVT model C $ \mathrm{V}^\prime\to\mathrm{V}\mathrm{V} $+ VH signals. The theoretical prediction and its uncertainty associated with the choice of PDF set is shown. 
Tables  
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Table 1:
Summary of the event category definitions. The categories are listed from the highest to the lowest sensitivity in each production mode. The percentages correspond to the maximum misidentification rate associated with the high (HP) and low (LP) purity working points. 
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Table 2:
Summary of the exclusion limits on the resonance masses for the considered models. The numbers show the lower limit at 95% CL, with the exception of the ones given in parentheses quoting the ranges of exclusion. 
Summary 
A search has been presented for resonances with masses above 1.3 TeV that decay to WW, WZ, ZZ, WH, or ZH boson pairs. Each of the two boson decays is clustered into one largeradius jet, yielding a dijet final state from DrellYan and gluon fusion production, complemented by two additional jets for vector boson fusion production. The hadronic decays of H, W, and Z bosons are identified using machine learningbased jet taggers that reduce the background from quantum chromodynamics multijet production. No evidence of a departure from the expected background is found. A maximum local significance of 3.6 standard deviations from the standard model prediction, corresponding to a global significance of 2.3 standard deviations, is observed at masses of 2.1 and 2.9 TeV. Upper limits at 95% confidence level on the resonance production cross section are set as a function of the resonance mass. In a heavy vector triplet model, spin1 Z' and W' resonances with masses below 4.8 TeV are excluded. These limits are the most stringent to date. In a bulk graviton model, spin2 gravitons and spin0 radions with masses below 1.4 and 2.7 TeV, respectively, are excluded. Furthermore, the exclusive production of new heavy resonances through the vector boson fusion mode is constrained with upper cross section limits as low as 0.1 fb. 
Additional Figures  
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Additional Figure 1:
Example Feynman diagrams of signal processes: (top left) $ \mathrm{g} \mathrm{g} $ produced graviton or radion decaying to WW or ZZ; (top center) DY produced $ \mathrm{Z}^{'} $ and $ \mathrm{W^{'}} $ decaying to ZH and WH, respectively; (top right) VBF produced $ \mathrm{Z}^{'} $ and $ \mathrm{W^{'}} $ decaying to WW and WZ, respectively; (bottom left) VBF produced graviton or radion decaying to WW or ZZ; (bottom center) DY produced $ \mathrm{Z}^{'} $ and $ \mathrm{W^{'}} $ decaying to WW and WZ, respectively; (bottom right) VBF produced $ \mathrm{Z}^{'} $ and $ \mathrm{W^{'}} $ decaying to ZH and WH, respectively. The diagrams on the top are shown in the paper as well, and are included here for convenience. 
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Additional Figure 1a:
Example Feynman diagrams of signal processes: (top left) $ \mathrm{g} \mathrm{g} $ produced graviton or radion decaying to WW or ZZ; (top center) DY produced $ \mathrm{Z}^{'} $ and $ \mathrm{W^{'}} $ decaying to ZH and WH, respectively; (top right) VBF produced $ \mathrm{Z}^{'} $ and $ \mathrm{W^{'}} $ decaying to WW and WZ, respectively; (bottom left) VBF produced graviton or radion decaying to WW or ZZ; (bottom center) DY produced $ \mathrm{Z}^{'} $ and $ \mathrm{W^{'}} $ decaying to WW and WZ, respectively; (bottom right) VBF produced $ \mathrm{Z}^{'} $ and $ \mathrm{W^{'}} $ decaying to ZH and WH, respectively. The diagrams on the top are shown in the paper as well, and are included here for convenience. 
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Additional Figure 1b:
Example Feynman diagrams of signal processes: (top left) $ \mathrm{g} \mathrm{g} $ produced graviton or radion decaying to WW or ZZ; (top center) DY produced $ \mathrm{Z}^{'} $ and $ \mathrm{W^{'}} $ decaying to ZH and WH, respectively; (top right) VBF produced $ \mathrm{Z}^{'} $ and $ \mathrm{W^{'}} $ decaying to WW and WZ, respectively; (bottom left) VBF produced graviton or radion decaying to WW or ZZ; (bottom center) DY produced $ \mathrm{Z}^{'} $ and $ \mathrm{W^{'}} $ decaying to WW and WZ, respectively; (bottom right) VBF produced $ \mathrm{Z}^{'} $ and $ \mathrm{W^{'}} $ decaying to ZH and WH, respectively. The diagrams on the top are shown in the paper as well, and are included here for convenience. 
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Additional Figure 1c:
Example Feynman diagrams of signal processes: (top left) $ \mathrm{g} \mathrm{g} $ produced graviton or radion decaying to WW or ZZ; (top center) DY produced $ \mathrm{Z}^{'} $ and $ \mathrm{W^{'}} $ decaying to ZH and WH, respectively; (top right) VBF produced $ \mathrm{Z}^{'} $ and $ \mathrm{W^{'}} $ decaying to WW and WZ, respectively; (bottom left) VBF produced graviton or radion decaying to WW or ZZ; (bottom center) DY produced $ \mathrm{Z}^{'} $ and $ \mathrm{W^{'}} $ decaying to WW and WZ, respectively; (bottom right) VBF produced $ \mathrm{Z}^{'} $ and $ \mathrm{W^{'}} $ decaying to ZH and WH, respectively. The diagrams on the top are shown in the paper as well, and are included here for convenience. 
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Additional Figure 1d:
Example Feynman diagrams of signal processes: (top left) $ \mathrm{g} \mathrm{g} $ produced graviton or radion decaying to WW or ZZ; (top center) DY produced $ \mathrm{Z}^{'} $ and $ \mathrm{W^{'}} $ decaying to ZH and WH, respectively; (top right) VBF produced $ \mathrm{Z}^{'} $ and $ \mathrm{W^{'}} $ decaying to WW and WZ, respectively; (bottom left) VBF produced graviton or radion decaying to WW or ZZ; (bottom center) DY produced $ \mathrm{Z}^{'} $ and $ \mathrm{W^{'}} $ decaying to WW and WZ, respectively; (bottom right) VBF produced $ \mathrm{Z}^{'} $ and $ \mathrm{W^{'}} $ decaying to ZH and WH, respectively. The diagrams on the top are shown in the paper as well, and are included here for convenience. 
png pdf 
Additional Figure 1e:
Example Feynman diagrams of signal processes: (top left) $ \mathrm{g} \mathrm{g} $ produced graviton or radion decaying to WW or ZZ; (top center) DY produced $ \mathrm{Z}^{'} $ and $ \mathrm{W^{'}} $ decaying to ZH and WH, respectively; (top right) VBF produced $ \mathrm{Z}^{'} $ and $ \mathrm{W^{'}} $ decaying to WW and WZ, respectively; (bottom left) VBF produced graviton or radion decaying to WW or ZZ; (bottom center) DY produced $ \mathrm{Z}^{'} $ and $ \mathrm{W^{'}} $ decaying to WW and WZ, respectively; (bottom right) VBF produced $ \mathrm{Z}^{'} $ and $ \mathrm{W^{'}} $ decaying to ZH and WH, respectively. The diagrams on the top are shown in the paper as well, and are included here for convenience. 
png pdf 
Additional Figure 1f:
Example Feynman diagrams of signal processes: (top left) $ \mathrm{g} \mathrm{g} $ produced graviton or radion decaying to WW or ZZ; (top center) DY produced $ \mathrm{Z}^{'} $ and $ \mathrm{W^{'}} $ decaying to ZH and WH, respectively; (top right) VBF produced $ \mathrm{Z}^{'} $ and $ \mathrm{W^{'}} $ decaying to WW and WZ, respectively; (bottom left) VBF produced graviton or radion decaying to WW or ZZ; (bottom center) DY produced $ \mathrm{Z}^{'} $ and $ \mathrm{W^{'}} $ decaying to WW and WZ, respectively; (bottom right) VBF produced $ \mathrm{Z}^{'} $ and $ \mathrm{W^{'}} $ decaying to ZH and WH, respectively. The diagrams on the top are shown in the paper as well, and are included here for convenience. 
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Additional Figure 2:
Total signal efficiency including all event categories as a function of the resonance mass $M_{\mathrm{X}}$ for all DY/ggF (left) and VBF (right) signal models under consideration. The estimates from MC simulation (markers) are interpolated with a functional form (lines). 
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Additional Figure 2a:
Total signal efficiency including all event categories as a function of the resonance mass $M_{\mathrm{X}}$ for all DY/ggF (left) and VBF (right) signal models under consideration. The estimates from MC simulation (markers) are interpolated with a functional form (lines). 
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Additional Figure 2b:
Total signal efficiency including all event categories as a function of the resonance mass $M_{\mathrm{X}}$ for all DY/ggF (left) and VBF (right) signal models under consideration. The estimates from MC simulation (markers) are interpolated with a functional form (lines). 
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Additional Figure 3:
Signal efficiency in each of the categories as a function of the resonance mass $M_{\mathrm{X}}$ for all DY/ggF signal models under consideration. The estimates from MC simulation (markers) are interpolated with a functional form (lines). 
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Additional Figure 3a:
Signal efficiency in each of the categories as a function of the resonance mass $M_{\mathrm{X}}$ for all DY/ggF signal models under consideration. The estimates from MC simulation (markers) are interpolated with a functional form (lines). 
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Additional Figure 3b:
Signal efficiency in each of the categories as a function of the resonance mass $M_{\mathrm{X}}$ for all DY/ggF signal models under consideration. The estimates from MC simulation (markers) are interpolated with a functional form (lines). 
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Additional Figure 3c:
Signal efficiency in each of the categories as a function of the resonance mass $M_{\mathrm{X}}$ for all DY/ggF signal models under consideration. The estimates from MC simulation (markers) are interpolated with a functional form (lines). 
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Additional Figure 3d:
Signal efficiency in each of the categories as a function of the resonance mass $M_{\mathrm{X}}$ for all DY/ggF signal models under consideration. The estimates from MC simulation (markers) are interpolated with a functional form (lines). 
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Additional Figure 3e:
Signal efficiency in each of the categories as a function of the resonance mass $M_{\mathrm{X}}$ for all DY/ggF signal models under consideration. The estimates from MC simulation (markers) are interpolated with a functional form (lines). 
png pdf 
Additional Figure 3f:
Signal efficiency in each of the categories as a function of the resonance mass $M_{\mathrm{X}}$ for all DY/ggF signal models under consideration. The estimates from MC simulation (markers) are interpolated with a functional form (lines). 
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Additional Figure 3g:
Signal efficiency in each of the categories as a function of the resonance mass $M_{\mathrm{X}}$ for all DY/ggF signal models under consideration. The estimates from MC simulation (markers) are interpolated with a functional form (lines). 
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Additional Figure 3h:
Signal efficiency in each of the categories as a function of the resonance mass $M_{\mathrm{X}}$ for all DY/ggF signal models under consideration. The estimates from MC simulation (markers) are interpolated with a functional form (lines). 
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Additional Figure 3i:
Signal efficiency in each of the categories as a function of the resonance mass $M_{\mathrm{X}}$ for all DY/ggF signal models under consideration. The estimates from MC simulation (markers) are interpolated with a functional form (lines). 
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Additional Figure 3j:
Signal efficiency in each of the categories as a function of the resonance mass $M_{\mathrm{X}}$ for all DY/ggF signal models under consideration. The estimates from MC simulation (markers) are interpolated with a functional form (lines). 
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Additional Figure 4:
Signal efficiency in each of the categories as a function of the resonance mass $M_{\mathrm{X}}$ for all VBF signal models under consideration. The estimates from MC simulation (markers) are interpolated with a functional form (lines). 
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Additional Figure 4a:
Signal efficiency in each of the categories as a function of the resonance mass $M_{\mathrm{X}}$ for all VBF signal models under consideration. The estimates from MC simulation (markers) are interpolated with a functional form (lines). 
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Additional Figure 4b:
Signal efficiency in each of the categories as a function of the resonance mass $M_{\mathrm{X}}$ for all VBF signal models under consideration. The estimates from MC simulation (markers) are interpolated with a functional form (lines). 
png pdf 
Additional Figure 4c:
Signal efficiency in each of the categories as a function of the resonance mass $M_{\mathrm{X}}$ for all VBF signal models under consideration. The estimates from MC simulation (markers) are interpolated with a functional form (lines). 
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Additional Figure 4d:
Signal efficiency in each of the categories as a function of the resonance mass $M_{\mathrm{X}}$ for all VBF signal models under consideration. The estimates from MC simulation (markers) are interpolated with a functional form (lines). 
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Additional Figure 4e:
Signal efficiency in each of the categories as a function of the resonance mass $M_{\mathrm{X}}$ for all VBF signal models under consideration. The estimates from MC simulation (markers) are interpolated with a functional form (lines). 
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Additional Figure 4f:
Signal efficiency in each of the categories as a function of the resonance mass $M_{\mathrm{X}}$ for all VBF signal models under consideration. The estimates from MC simulation (markers) are interpolated with a functional form (lines). 
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Additional Figure 4g:
Signal efficiency in each of the categories as a function of the resonance mass $M_{\mathrm{X}}$ for all VBF signal models under consideration. The estimates from MC simulation (markers) are interpolated with a functional form (lines). 
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Additional Figure 4h:
Signal efficiency in each of the categories as a function of the resonance mass $M_{\mathrm{X}}$ for all VBF signal models under consideration. The estimates from MC simulation (markers) are interpolated with a functional form (lines). 
png pdf 
Additional Figure 4i:
Signal efficiency in each of the categories as a function of the resonance mass $M_{\mathrm{X}}$ for all VBF signal models under consideration. The estimates from MC simulation (markers) are interpolated with a functional form (lines). 
png pdf 
Additional Figure 4j:
Signal efficiency in each of the categories as a function of the resonance mass $M_{\mathrm{X}}$ for all VBF signal models under consideration. The estimates from MC simulation (markers) are interpolated with a functional form (lines). 
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Additional Figure 5:
Left: Selection requirement on the $ \mathrm{q}\overline{\mathrm{q}} $ discriminator to obtain a 5% misidentification rate in QCD multijet simulation as a function of jet $ p_{\mathrm{T}} $ and $ \rho=2\ln(m_\text{jet}^{\mathrm{AK8}}/p_{\mathrm{T}}) $. Right: Difference in the requirement to be applied on the $ \mathrm{q}\overline{\mathrm{q}} $ tagger to obtain a 5% background misidentification rate between the nominal and a smoothed version of this histogram. 
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Additional Figure 5a:
Left: Selection requirement on the $ \mathrm{q}\overline{\mathrm{q}} $ discriminator to obtain a 5% misidentification rate in QCD multijet simulation as a function of jet $ p_{\mathrm{T}} $ and $ \rho=2\ln(m_\text{jet}^{\mathrm{AK8}}/p_{\mathrm{T}}) $. Right: Difference in the requirement to be applied on the $ \mathrm{q}\overline{\mathrm{q}} $ tagger to obtain a 5% background misidentification rate between the nominal and a smoothed version of this histogram. 
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Additional Figure 5b:
Left: Selection requirement on the $ \mathrm{q}\overline{\mathrm{q}} $ discriminator to obtain a 5% misidentification rate in QCD multijet simulation as a function of jet $ p_{\mathrm{T}} $ and $ \rho=2\ln(m_\text{jet}^{\mathrm{AK8}}/p_{\mathrm{T}}) $. Right: Difference in the requirement to be applied on the $ \mathrm{q}\overline{\mathrm{q}} $ tagger to obtain a 5% background misidentification rate between the nominal and a smoothed version of this histogram. 
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Additional Figure 6:
Displays of an event with a reconstructed dijet invariant mass $ m_\mathrm{jj}^{\mathrm{AK8}}= $ 2.94 TeV in the DY/ggF VV HPHP category, with $ m_\text{jet1}^{\mathrm{AK8}}= $ 82 GeV and $ m_\text{jet2}^{\mathrm{AK8}}= $ 86 GeV, consistent with a WW, WZ or ZZ signal hypothesis. Reconstructed tracks are indicated as lines. Energy deposits in the electromagnetic and hadronic calorimeter are indicated as green and blue bars, respectively. The two leading AK8 jets have $ p_{\mathrm{T}}= $ 1.47 TeV, $ \eta= $ 0.27 and $ p_{\mathrm{T}}= $ 1.45 TeV, $ \eta= $ 0.17. 
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Additional Figure 6a:
Displays of an event with a reconstructed dijet invariant mass $ m_\mathrm{jj}^{\mathrm{AK8}}= $ 2.94 TeV in the DY/ggF VV HPHP category, with $ m_\text{jet1}^{\mathrm{AK8}}= $ 82 GeV and $ m_\text{jet2}^{\mathrm{AK8}}= $ 86 GeV, consistent with a WW, WZ or ZZ signal hypothesis. Reconstructed tracks are indicated as lines. Energy deposits in the electromagnetic and hadronic calorimeter are indicated as green and blue bars, respectively. The two leading AK8 jets have $ p_{\mathrm{T}}= $ 1.47 TeV, $ \eta= $ 0.27 and $ p_{\mathrm{T}}= $ 1.45 TeV, $ \eta= $ 0.17. 
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Additional Figure 6b:
Displays of an event with a reconstructed dijet invariant mass $ m_\mathrm{jj}^{\mathrm{AK8}}= $ 2.94 TeV in the DY/ggF VV HPHP category, with $ m_\text{jet1}^{\mathrm{AK8}}= $ 82 GeV and $ m_\text{jet2}^{\mathrm{AK8}}= $ 86 GeV, consistent with a WW, WZ or ZZ signal hypothesis. Reconstructed tracks are indicated as lines. Energy deposits in the electromagnetic and hadronic calorimeter are indicated as green and blue bars, respectively. The two leading AK8 jets have $ p_{\mathrm{T}}= $ 1.47 TeV, $ \eta= $ 0.27 and $ p_{\mathrm{T}}= $ 1.45 TeV, $ \eta= $ 0.17. 
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Additional Figure 7:
Projections of PYTHIA8 MC simulation of the QCD multijet background distribution onto the $ m_\text{jet1}^{\mathrm{AK8}} $ (left), $ m_\text{jet2}^{\mathrm{AK8}} $ (middle), and $ m_\mathrm{jj}^{\mathrm{AK8}} $ (right) dimensions are compared to the nominal QCD background template and the five alternate shapes added to the fit as shape nuisance parameters for the VH HPHP (upper) and VV HPHP (lower) categories. 
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Additional Figure 7a:
Projections of PYTHIA8 MC simulation of the QCD multijet background distribution onto the $ m_\text{jet1}^{\mathrm{AK8}} $ (left), $ m_\text{jet2}^{\mathrm{AK8}} $ (middle), and $ m_\mathrm{jj}^{\mathrm{AK8}} $ (right) dimensions are compared to the nominal QCD background template and the five alternate shapes added to the fit as shape nuisance parameters for the VH HPHP (upper) and VV HPHP (lower) categories. 
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Additional Figure 7b:
Projections of PYTHIA8 MC simulation of the QCD multijet background distribution onto the $ m_\text{jet1}^{\mathrm{AK8}} $ (left), $ m_\text{jet2}^{\mathrm{AK8}} $ (middle), and $ m_\mathrm{jj}^{\mathrm{AK8}} $ (right) dimensions are compared to the nominal QCD background template and the five alternate shapes added to the fit as shape nuisance parameters for the VH HPHP (upper) and VV HPHP (lower) categories. 
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Additional Figure 7c:
Projections of PYTHIA8 MC simulation of the QCD multijet background distribution onto the $ m_\text{jet1}^{\mathrm{AK8}} $ (left), $ m_\text{jet2}^{\mathrm{AK8}} $ (middle), and $ m_\mathrm{jj}^{\mathrm{AK8}} $ (right) dimensions are compared to the nominal QCD background template and the five alternate shapes added to the fit as shape nuisance parameters for the VH HPHP (upper) and VV HPHP (lower) categories. 
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Additional Figure 7d:
Projections of PYTHIA8 MC simulation of the QCD multijet background distribution onto the $ m_\text{jet1}^{\mathrm{AK8}} $ (left), $ m_\text{jet2}^{\mathrm{AK8}} $ (middle), and $ m_\mathrm{jj}^{\mathrm{AK8}} $ (right) dimensions are compared to the nominal QCD background template and the five alternate shapes added to the fit as shape nuisance parameters for the VH HPHP (upper) and VV HPHP (lower) categories. 
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Additional Figure 8:
Projections of PYTHIA8 MC simulation of the QCD multijet background distribution onto the $ m_\text{jet1}^{\mathrm{AK8}} $ (left), $ m_\text{jet2}^{\mathrm{AK8}} $ (middle), and $ m_\mathrm{jj}^{\mathrm{AK8}} $ (right) dimensions are compared to the nominal QCD background template and the five alternate shapes added to the fit as shape nuisance parameters for the VH LPHP (upper), VH HPLP (middle), and VV HPLP (lower) categories. 
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Additional Figure 8a:
Projections of PYTHIA8 MC simulation of the QCD multijet background distribution onto the $ m_\text{jet1}^{\mathrm{AK8}} $ (left), $ m_\text{jet2}^{\mathrm{AK8}} $ (middle), and $ m_\mathrm{jj}^{\mathrm{AK8}} $ (right) dimensions are compared to the nominal QCD background template and the five alternate shapes added to the fit as shape nuisance parameters for the VH LPHP (upper), VH HPLP (middle), and VV HPLP (lower) categories. 
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Additional Figure 8b:
Projections of PYTHIA8 MC simulation of the QCD multijet background distribution onto the $ m_\text{jet1}^{\mathrm{AK8}} $ (left), $ m_\text{jet2}^{\mathrm{AK8}} $ (middle), and $ m_\mathrm{jj}^{\mathrm{AK8}} $ (right) dimensions are compared to the nominal QCD background template and the five alternate shapes added to the fit as shape nuisance parameters for the VH LPHP (upper), VH HPLP (middle), and VV HPLP (lower) categories. 
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Additional Figure 8c:
Projections of PYTHIA8 MC simulation of the QCD multijet background distribution onto the $ m_\text{jet1}^{\mathrm{AK8}} $ (left), $ m_\text{jet2}^{\mathrm{AK8}} $ (middle), and $ m_\mathrm{jj}^{\mathrm{AK8}} $ (right) dimensions are compared to the nominal QCD background template and the five alternate shapes added to the fit as shape nuisance parameters for the VH LPHP (upper), VH HPLP (middle), and VV HPLP (lower) categories. 
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Additional Figure 8d:
Projections of PYTHIA8 MC simulation of the QCD multijet background distribution onto the $ m_\text{jet1}^{\mathrm{AK8}} $ (left), $ m_\text{jet2}^{\mathrm{AK8}} $ (middle), and $ m_\mathrm{jj}^{\mathrm{AK8}} $ (right) dimensions are compared to the nominal QCD background template and the five alternate shapes added to the fit as shape nuisance parameters for the VH LPHP (upper), VH HPLP (middle), and VV HPLP (lower) categories. 
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Additional Figure 8e:
Projections of PYTHIA8 MC simulation of the QCD multijet background distribution onto the $ m_\text{jet1}^{\mathrm{AK8}} $ (left), $ m_\text{jet2}^{\mathrm{AK8}} $ (middle), and $ m_\mathrm{jj}^{\mathrm{AK8}} $ (right) dimensions are compared to the nominal QCD background template and the five alternate shapes added to the fit as shape nuisance parameters for the VH LPHP (upper), VH HPLP (middle), and VV HPLP (lower) categories. 
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Additional Figure 8f:
Projections of PYTHIA8 MC simulation of the QCD multijet background distribution onto the $ m_\text{jet1}^{\mathrm{AK8}} $ (left), $ m_\text{jet2}^{\mathrm{AK8}} $ (middle), and $ m_\mathrm{jj}^{\mathrm{AK8}} $ (right) dimensions are compared to the nominal QCD background template and the five alternate shapes added to the fit as shape nuisance parameters for the VH LPHP (upper), VH HPLP (middle), and VV HPLP (lower) categories. 
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Additional Figure 8g:
Projections of PYTHIA8 MC simulation of the QCD multijet background distribution onto the $ m_\text{jet1}^{\mathrm{AK8}} $ (left), $ m_\text{jet2}^{\mathrm{AK8}} $ (middle), and $ m_\mathrm{jj}^{\mathrm{AK8}} $ (right) dimensions are compared to the nominal QCD background template and the five alternate shapes added to the fit as shape nuisance parameters for the VH LPHP (upper), VH HPLP (middle), and VV HPLP (lower) categories. 
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Additional Figure 8h:
Projections of PYTHIA8 MC simulation of the QCD multijet background distribution onto the $ m_\text{jet1}^{\mathrm{AK8}} $ (left), $ m_\text{jet2}^{\mathrm{AK8}} $ (middle), and $ m_\mathrm{jj}^{\mathrm{AK8}} $ (right) dimensions are compared to the nominal QCD background template and the five alternate shapes added to the fit as shape nuisance parameters for the VH LPHP (upper), VH HPLP (middle), and VV HPLP (lower) categories. 
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Additional Figure 8i:
Projections of PYTHIA8 MC simulation of the QCD multijet background distribution onto the $ m_\text{jet1}^{\mathrm{AK8}} $ (left), $ m_\text{jet2}^{\mathrm{AK8}} $ (middle), and $ m_\mathrm{jj}^{\mathrm{AK8}} $ (right) dimensions are compared to the nominal QCD background template and the five alternate shapes added to the fit as shape nuisance parameters for the VH LPHP (upper), VH HPLP (middle), and VV HPLP (lower) categories. 
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Additional Figure 9:
Comparison between the background postfit and the data distributions of $ m_\text{jet1}^{\mathrm{AK8}} $ (left), $ m_\text{jet2}^{\mathrm{AK8}} $ (middle) and $ m_\mathrm{jj}^{\mathrm{AK8}} $ (right) in the DY/ggF VH HPHP (upper) and VV HPHP (lower) categories. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are shown as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. An example of a signal distribution is overlaid, where the number of expected events is scaled by an arbitrary normalization factor. Shown below each mass plot is the difference between the data and the fit divided by the statistical uncertainty of the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty on the background estimate fitted to the data divided by the statistical uncertainty of the data is shown as a band. 
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Additional Figure 9a:
Comparison between the background postfit and the data distributions of $ m_\text{jet1}^{\mathrm{AK8}} $ (left), $ m_\text{jet2}^{\mathrm{AK8}} $ (middle) and $ m_\mathrm{jj}^{\mathrm{AK8}} $ (right) in the DY/ggF VH HPHP (upper) and VV HPHP (lower) categories. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are shown as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. An example of a signal distribution is overlaid, where the number of expected events is scaled by an arbitrary normalization factor. Shown below each mass plot is the difference between the data and the fit divided by the statistical uncertainty of the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty on the background estimate fitted to the data divided by the statistical uncertainty of the data is shown as a band. 
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Additional Figure 9b:
Comparison between the background postfit and the data distributions of $ m_\text{jet1}^{\mathrm{AK8}} $ (left), $ m_\text{jet2}^{\mathrm{AK8}} $ (middle) and $ m_\mathrm{jj}^{\mathrm{AK8}} $ (right) in the DY/ggF VH HPHP (upper) and VV HPHP (lower) categories. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are shown as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. An example of a signal distribution is overlaid, where the number of expected events is scaled by an arbitrary normalization factor. Shown below each mass plot is the difference between the data and the fit divided by the statistical uncertainty of the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty on the background estimate fitted to the data divided by the statistical uncertainty of the data is shown as a band. 
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Additional Figure 9c:
Comparison between the background postfit and the data distributions of $ m_\text{jet1}^{\mathrm{AK8}} $ (left), $ m_\text{jet2}^{\mathrm{AK8}} $ (middle) and $ m_\mathrm{jj}^{\mathrm{AK8}} $ (right) in the DY/ggF VH HPHP (upper) and VV HPHP (lower) categories. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are shown as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. An example of a signal distribution is overlaid, where the number of expected events is scaled by an arbitrary normalization factor. Shown below each mass plot is the difference between the data and the fit divided by the statistical uncertainty of the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty on the background estimate fitted to the data divided by the statistical uncertainty of the data is shown as a band. 
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Additional Figure 9d:
Comparison between the background postfit and the data distributions of $ m_\text{jet1}^{\mathrm{AK8}} $ (left), $ m_\text{jet2}^{\mathrm{AK8}} $ (middle) and $ m_\mathrm{jj}^{\mathrm{AK8}} $ (right) in the DY/ggF VH HPHP (upper) and VV HPHP (lower) categories. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are shown as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. An example of a signal distribution is overlaid, where the number of expected events is scaled by an arbitrary normalization factor. Shown below each mass plot is the difference between the data and the fit divided by the statistical uncertainty of the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty on the background estimate fitted to the data divided by the statistical uncertainty of the data is shown as a band. 
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Additional Figure 10:
Comparison between the background postfit and the data distributions of $ m_\text{jet1}^{\mathrm{AK8}} $ (left), $ m_\text{jet2}^{\mathrm{AK8}} $ (middle) and $ m_\mathrm{jj}^{\mathrm{AK8}} $ (right) in the DY/ggF VH LPHP (upper), DY/ggF VH HPLP (middle), and DY/ggF VV HPLP (lower) categories. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are shown as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. An example of a signal distribution is overlaid, where the number of expected events is scaled by an arbitrary normalization factor. Shown below each mass plot is the difference between the data and the fit divided by the statistical uncertainty in the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty in the background estimate fitted to the data divided by the statistical uncertainty in the data is shown as a band. 
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Additional Figure 10a:
Comparison between the background postfit and the data distributions of $ m_\text{jet1}^{\mathrm{AK8}} $ (left), $ m_\text{jet2}^{\mathrm{AK8}} $ (middle) and $ m_\mathrm{jj}^{\mathrm{AK8}} $ (right) in the DY/ggF VH LPHP (upper), DY/ggF VH HPLP (middle), and DY/ggF VV HPLP (lower) categories. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are shown as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. An example of a signal distribution is overlaid, where the number of expected events is scaled by an arbitrary normalization factor. Shown below each mass plot is the difference between the data and the fit divided by the statistical uncertainty in the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty in the background estimate fitted to the data divided by the statistical uncertainty in the data is shown as a band. 
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Additional Figure 10b:
Comparison between the background postfit and the data distributions of $ m_\text{jet1}^{\mathrm{AK8}} $ (left), $ m_\text{jet2}^{\mathrm{AK8}} $ (middle) and $ m_\mathrm{jj}^{\mathrm{AK8}} $ (right) in the DY/ggF VH LPHP (upper), DY/ggF VH HPLP (middle), and DY/ggF VV HPLP (lower) categories. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are shown as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. An example of a signal distribution is overlaid, where the number of expected events is scaled by an arbitrary normalization factor. Shown below each mass plot is the difference between the data and the fit divided by the statistical uncertainty in the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty in the background estimate fitted to the data divided by the statistical uncertainty in the data is shown as a band. 
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Additional Figure 10c:
Comparison between the background postfit and the data distributions of $ m_\text{jet1}^{\mathrm{AK8}} $ (left), $ m_\text{jet2}^{\mathrm{AK8}} $ (middle) and $ m_\mathrm{jj}^{\mathrm{AK8}} $ (right) in the DY/ggF VH LPHP (upper), DY/ggF VH HPLP (middle), and DY/ggF VV HPLP (lower) categories. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are shown as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. An example of a signal distribution is overlaid, where the number of expected events is scaled by an arbitrary normalization factor. Shown below each mass plot is the difference between the data and the fit divided by the statistical uncertainty in the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty in the background estimate fitted to the data divided by the statistical uncertainty in the data is shown as a band. 
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Additional Figure 10d:
Comparison between the background postfit and the data distributions of $ m_\text{jet1}^{\mathrm{AK8}} $ (left), $ m_\text{jet2}^{\mathrm{AK8}} $ (middle) and $ m_\mathrm{jj}^{\mathrm{AK8}} $ (right) in the DY/ggF VH LPHP (upper), DY/ggF VH HPLP (middle), and DY/ggF VV HPLP (lower) categories. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are shown as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. An example of a signal distribution is overlaid, where the number of expected events is scaled by an arbitrary normalization factor. Shown below each mass plot is the difference between the data and the fit divided by the statistical uncertainty in the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty in the background estimate fitted to the data divided by the statistical uncertainty in the data is shown as a band. 
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Additional Figure 10e:
Comparison between the background postfit and the data distributions of $ m_\text{jet1}^{\mathrm{AK8}} $ (left), $ m_\text{jet2}^{\mathrm{AK8}} $ (middle) and $ m_\mathrm{jj}^{\mathrm{AK8}} $ (right) in the DY/ggF VH LPHP (upper), DY/ggF VH HPLP (middle), and DY/ggF VV HPLP (lower) categories. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are shown as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. An example of a signal distribution is overlaid, where the number of expected events is scaled by an arbitrary normalization factor. Shown below each mass plot is the difference between the data and the fit divided by the statistical uncertainty in the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty in the background estimate fitted to the data divided by the statistical uncertainty in the data is shown as a band. 
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Additional Figure 10f:
Comparison between the background postfit and the data distributions of $ m_\text{jet1}^{\mathrm{AK8}} $ (left), $ m_\text{jet2}^{\mathrm{AK8}} $ (middle) and $ m_\mathrm{jj}^{\mathrm{AK8}} $ (right) in the DY/ggF VH LPHP (upper), DY/ggF VH HPLP (middle), and DY/ggF VV HPLP (lower) categories. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are shown as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. An example of a signal distribution is overlaid, where the number of expected events is scaled by an arbitrary normalization factor. Shown below each mass plot is the difference between the data and the fit divided by the statistical uncertainty in the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty in the background estimate fitted to the data divided by the statistical uncertainty in the data is shown as a band. 
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Additional Figure 10g:
Comparison between the background postfit and the data distributions of $ m_\text{jet1}^{\mathrm{AK8}} $ (left), $ m_\text{jet2}^{\mathrm{AK8}} $ (middle) and $ m_\mathrm{jj}^{\mathrm{AK8}} $ (right) in the DY/ggF VH LPHP (upper), DY/ggF VH HPLP (middle), and DY/ggF VV HPLP (lower) categories. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are shown as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. An example of a signal distribution is overlaid, where the number of expected events is scaled by an arbitrary normalization factor. Shown below each mass plot is the difference between the data and the fit divided by the statistical uncertainty in the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty in the background estimate fitted to the data divided by the statistical uncertainty in the data is shown as a band. 
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Additional Figure 10h:
Comparison between the background postfit and the data distributions of $ m_\text{jet1}^{\mathrm{AK8}} $ (left), $ m_\text{jet2}^{\mathrm{AK8}} $ (middle) and $ m_\mathrm{jj}^{\mathrm{AK8}} $ (right) in the DY/ggF VH LPHP (upper), DY/ggF VH HPLP (middle), and DY/ggF VV HPLP (lower) categories. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are shown as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. An example of a signal distribution is overlaid, where the number of expected events is scaled by an arbitrary normalization factor. Shown below each mass plot is the difference between the data and the fit divided by the statistical uncertainty in the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty in the background estimate fitted to the data divided by the statistical uncertainty in the data is shown as a band. 
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Additional Figure 10i:
Comparison between the background postfit and the data distributions of $ m_\text{jet1}^{\mathrm{AK8}} $ (left), $ m_\text{jet2}^{\mathrm{AK8}} $ (middle) and $ m_\mathrm{jj}^{\mathrm{AK8}} $ (right) in the DY/ggF VH LPHP (upper), DY/ggF VH HPLP (middle), and DY/ggF VV HPLP (lower) categories. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are shown as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. An example of a signal distribution is overlaid, where the number of expected events is scaled by an arbitrary normalization factor. Shown below each mass plot is the difference between the data and the fit divided by the statistical uncertainty in the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty in the background estimate fitted to the data divided by the statistical uncertainty in the data is shown as a band. 
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Additional Figure 11:
Comparison between the background postfit and the data distributions of $ m_\text{jet1}^{\mathrm{AK8}} $ (left), $ m_\text{jet2}^{\mathrm{AK8}} $ (middle) and $ m_\mathrm{jj}^{\mathrm{AK8}} $ (right) in the VBF VH HPHP (upper) and VBF VV HPHP (lower) categories. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are shown as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. An example of a signal distribution is overlaid, where the number of expected events is scaled by an arbitrary normalization factor. Shown below each mass plot is the difference between the data and the fit divided by the statistical uncertainty in the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty in the background estimate fitted to the data divided by the statistical uncertainty in the data is shown as a band. 
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Additional Figure 11a:
Comparison between the background postfit and the data distributions of $ m_\text{jet1}^{\mathrm{AK8}} $ (left), $ m_\text{jet2}^{\mathrm{AK8}} $ (middle) and $ m_\mathrm{jj}^{\mathrm{AK8}} $ (right) in the VBF VH HPHP (upper) and VBF VV HPHP (lower) categories. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are shown as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. An example of a signal distribution is overlaid, where the number of expected events is scaled by an arbitrary normalization factor. Shown below each mass plot is the difference between the data and the fit divided by the statistical uncertainty in the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty in the background estimate fitted to the data divided by the statistical uncertainty in the data is shown as a band. 
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Additional Figure 11b:
Comparison between the background postfit and the data distributions of $ m_\text{jet1}^{\mathrm{AK8}} $ (left), $ m_\text{jet2}^{\mathrm{AK8}} $ (middle) and $ m_\mathrm{jj}^{\mathrm{AK8}} $ (right) in the VBF VH HPHP (upper) and VBF VV HPHP (lower) categories. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are shown as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. An example of a signal distribution is overlaid, where the number of expected events is scaled by an arbitrary normalization factor. Shown below each mass plot is the difference between the data and the fit divided by the statistical uncertainty in the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty in the background estimate fitted to the data divided by the statistical uncertainty in the data is shown as a band. 
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Additional Figure 11c:
Comparison between the background postfit and the data distributions of $ m_\text{jet1}^{\mathrm{AK8}} $ (left), $ m_\text{jet2}^{\mathrm{AK8}} $ (middle) and $ m_\mathrm{jj}^{\mathrm{AK8}} $ (right) in the VBF VH HPHP (upper) and VBF VV HPHP (lower) categories. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are shown as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. An example of a signal distribution is overlaid, where the number of expected events is scaled by an arbitrary normalization factor. Shown below each mass plot is the difference between the data and the fit divided by the statistical uncertainty in the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty in the background estimate fitted to the data divided by the statistical uncertainty in the data is shown as a band. 
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Additional Figure 11d:
Comparison between the background postfit and the data distributions of $ m_\text{jet1}^{\mathrm{AK8}} $ (left), $ m_\text{jet2}^{\mathrm{AK8}} $ (middle) and $ m_\mathrm{jj}^{\mathrm{AK8}} $ (right) in the VBF VH HPHP (upper) and VBF VV HPHP (lower) categories. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are shown as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. An example of a signal distribution is overlaid, where the number of expected events is scaled by an arbitrary normalization factor. Shown below each mass plot is the difference between the data and the fit divided by the statistical uncertainty in the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty in the background estimate fitted to the data divided by the statistical uncertainty in the data is shown as a band. 
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Additional Figure 11e:
Comparison between the background postfit and the data distributions of $ m_\text{jet1}^{\mathrm{AK8}} $ (left), $ m_\text{jet2}^{\mathrm{AK8}} $ (middle) and $ m_\mathrm{jj}^{\mathrm{AK8}} $ (right) in the VBF VH HPHP (upper) and VBF VV HPHP (lower) categories. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are shown as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. An example of a signal distribution is overlaid, where the number of expected events is scaled by an arbitrary normalization factor. Shown below each mass plot is the difference between the data and the fit divided by the statistical uncertainty in the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty in the background estimate fitted to the data divided by the statistical uncertainty in the data is shown as a band. 
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Additional Figure 11f:
Comparison between the background postfit and the data distributions of $ m_\text{jet1}^{\mathrm{AK8}} $ (left), $ m_\text{jet2}^{\mathrm{AK8}} $ (middle) and $ m_\mathrm{jj}^{\mathrm{AK8}} $ (right) in the VBF VH HPHP (upper) and VBF VV HPHP (lower) categories. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are shown as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. An example of a signal distribution is overlaid, where the number of expected events is scaled by an arbitrary normalization factor. Shown below each mass plot is the difference between the data and the fit divided by the statistical uncertainty in the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty in the background estimate fitted to the data divided by the statistical uncertainty in the data is shown as a band. 
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Additional Figure 12:
Comparison between the background postfit and the data distributions of $ m_\text{jet1}^{\mathrm{AK8}} $ (left), $ m_\text{jet2}^{\mathrm{AK8}} $ (middle) and $ m_\mathrm{jj}^{\mathrm{AK8}} $ (right) in the VBF VH LPHP (upper), VBF VH HPLP (middle), and VBF VV HPLP (lower) categories. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are shown as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. An example of a signal distribution is overlaid, where the number of expected events is scaled by an arbitrary normalization factor. Shown below each mass plot is the difference between the data and the fit divided by the statistical uncertainty in the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty in the background estimate fitted to the data divided by the statistical uncertainty in the data is shown as a band. 
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Additional Figure 12a:
Comparison between the background postfit and the data distributions of $ m_\text{jet1}^{\mathrm{AK8}} $ (left), $ m_\text{jet2}^{\mathrm{AK8}} $ (middle) and $ m_\mathrm{jj}^{\mathrm{AK8}} $ (right) in the VBF VH LPHP (upper), VBF VH HPLP (middle), and VBF VV HPLP (lower) categories. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are shown as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. An example of a signal distribution is overlaid, where the number of expected events is scaled by an arbitrary normalization factor. Shown below each mass plot is the difference between the data and the fit divided by the statistical uncertainty in the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty in the background estimate fitted to the data divided by the statistical uncertainty in the data is shown as a band. 
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Additional Figure 12b:
Comparison between the background postfit and the data distributions of $ m_\text{jet1}^{\mathrm{AK8}} $ (left), $ m_\text{jet2}^{\mathrm{AK8}} $ (middle) and $ m_\mathrm{jj}^{\mathrm{AK8}} $ (right) in the VBF VH LPHP (upper), VBF VH HPLP (middle), and VBF VV HPLP (lower) categories. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are shown as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. An example of a signal distribution is overlaid, where the number of expected events is scaled by an arbitrary normalization factor. Shown below each mass plot is the difference between the data and the fit divided by the statistical uncertainty in the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty in the background estimate fitted to the data divided by the statistical uncertainty in the data is shown as a band. 
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Additional Figure 12c:
Comparison between the background postfit and the data distributions of $ m_\text{jet1}^{\mathrm{AK8}} $ (left), $ m_\text{jet2}^{\mathrm{AK8}} $ (middle) and $ m_\mathrm{jj}^{\mathrm{AK8}} $ (right) in the VBF VH LPHP (upper), VBF VH HPLP (middle), and VBF VV HPLP (lower) categories. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are shown as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. An example of a signal distribution is overlaid, where the number of expected events is scaled by an arbitrary normalization factor. Shown below each mass plot is the difference between the data and the fit divided by the statistical uncertainty in the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty in the background estimate fitted to the data divided by the statistical uncertainty in the data is shown as a band. 
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Additional Figure 12d:
Comparison between the background postfit and the data distributions of $ m_\text{jet1}^{\mathrm{AK8}} $ (left), $ m_\text{jet2}^{\mathrm{AK8}} $ (middle) and $ m_\mathrm{jj}^{\mathrm{AK8}} $ (right) in the VBF VH LPHP (upper), VBF VH HPLP (middle), and VBF VV HPLP (lower) categories. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are shown as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. An example of a signal distribution is overlaid, where the number of expected events is scaled by an arbitrary normalization factor. Shown below each mass plot is the difference between the data and the fit divided by the statistical uncertainty in the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty in the background estimate fitted to the data divided by the statistical uncertainty in the data is shown as a band. 
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Additional Figure 12e:
Comparison between the background postfit and the data distributions of $ m_\text{jet1}^{\mathrm{AK8}} $ (left), $ m_\text{jet2}^{\mathrm{AK8}} $ (middle) and $ m_\mathrm{jj}^{\mathrm{AK8}} $ (right) in the VBF VH LPHP (upper), VBF VH HPLP (middle), and VBF VV HPLP (lower) categories. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are shown as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. An example of a signal distribution is overlaid, where the number of expected events is scaled by an arbitrary normalization factor. Shown below each mass plot is the difference between the data and the fit divided by the statistical uncertainty in the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty in the background estimate fitted to the data divided by the statistical uncertainty in the data is shown as a band. 
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Additional Figure 12f:
Comparison between the background postfit and the data distributions of $ m_\text{jet1}^{\mathrm{AK8}} $ (left), $ m_\text{jet2}^{\mathrm{AK8}} $ (middle) and $ m_\mathrm{jj}^{\mathrm{AK8}} $ (right) in the VBF VH LPHP (upper), VBF VH HPLP (middle), and VBF VV HPLP (lower) categories. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are shown as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. An example of a signal distribution is overlaid, where the number of expected events is scaled by an arbitrary normalization factor. Shown below each mass plot is the difference between the data and the fit divided by the statistical uncertainty in the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty in the background estimate fitted to the data divided by the statistical uncertainty in the data is shown as a band. 
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Additional Figure 12g:
Comparison between the background postfit and the data distributions of $ m_\text{jet1}^{\mathrm{AK8}} $ (left), $ m_\text{jet2}^{\mathrm{AK8}} $ (middle) and $ m_\mathrm{jj}^{\mathrm{AK8}} $ (right) in the VBF VH LPHP (upper), VBF VH HPLP (middle), and VBF VV HPLP (lower) categories. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are shown as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. An example of a signal distribution is overlaid, where the number of expected events is scaled by an arbitrary normalization factor. Shown below each mass plot is the difference between the data and the fit divided by the statistical uncertainty in the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty in the background estimate fitted to the data divided by the statistical uncertainty in the data is shown as a band. 
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Additional Figure 12h:
Comparison between the background postfit and the data distributions of $ m_\text{jet1}^{\mathrm{AK8}} $ (left), $ m_\text{jet2}^{\mathrm{AK8}} $ (middle) and $ m_\mathrm{jj}^{\mathrm{AK8}} $ (right) in the VBF VH LPHP (upper), VBF VH HPLP (middle), and VBF VV HPLP (lower) categories. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are shown as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. An example of a signal distribution is overlaid, where the number of expected events is scaled by an arbitrary normalization factor. Shown below each mass plot is the difference between the data and the fit divided by the statistical uncertainty in the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty in the background estimate fitted to the data divided by the statistical uncertainty in the data is shown as a band. 
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Additional Figure 12i:
Comparison between the background postfit and the data distributions of $ m_\text{jet1}^{\mathrm{AK8}} $ (left), $ m_\text{jet2}^{\mathrm{AK8}} $ (middle) and $ m_\mathrm{jj}^{\mathrm{AK8}} $ (right) in the VBF VH LPHP (upper), VBF VH HPLP (middle), and VBF VV HPLP (lower) categories. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are shown as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. An example of a signal distribution is overlaid, where the number of expected events is scaled by an arbitrary normalization factor. Shown below each mass plot is the difference between the data and the fit divided by the statistical uncertainty in the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty in the background estimate fitted to the data divided by the statistical uncertainty in the data is shown as a band. 
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Additional Figure 13:
Projections of data and background postfit distributions onto the $ m_\mathrm{jj}^{\mathrm{AK8}} $ dimension in regions enriched in signal from DY/ggF VV (65 $ < m_\text{jet1}^{\mathrm{AK8}} < $ 105 GeV, 65 $ < m_\text{jet2}^{\mathrm{AK8}} < $ 105 GeV) for the VH LPHP (left), VH HPLP (middle), and VV HPLP DY/ggF categories. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are shown as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. Shown below each mass plot is the difference between the data and the fit divided by the statistical uncertainty in the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty in the background estimate fitted to the data divided by the statistical uncertainty in the data is shown as a band. 
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Additional Figure 13a:
Projections of data and background postfit distributions onto the $ m_\mathrm{jj}^{\mathrm{AK8}} $ dimension in regions enriched in signal from DY/ggF VV (65 $ < m_\text{jet1}^{\mathrm{AK8}} < $ 105 GeV, 65 $ < m_\text{jet2}^{\mathrm{AK8}} < $ 105 GeV) for the VH LPHP (left), VH HPLP (middle), and VV HPLP DY/ggF categories. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are shown as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. Shown below each mass plot is the difference between the data and the fit divided by the statistical uncertainty in the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty in the background estimate fitted to the data divided by the statistical uncertainty in the data is shown as a band. 
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Additional Figure 13b:
Projections of data and background postfit distributions onto the $ m_\mathrm{jj}^{\mathrm{AK8}} $ dimension in regions enriched in signal from DY/ggF VV (65 $ < m_\text{jet1}^{\mathrm{AK8}} < $ 105 GeV, 65 $ < m_\text{jet2}^{\mathrm{AK8}} < $ 105 GeV) for the VH LPHP (left), VH HPLP (middle), and VV HPLP DY/ggF categories. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are shown as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. Shown below each mass plot is the difference between the data and the fit divided by the statistical uncertainty in the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty in the background estimate fitted to the data divided by the statistical uncertainty in the data is shown as a band. 
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Additional Figure 13c:
Projections of data and background postfit distributions onto the $ m_\mathrm{jj}^{\mathrm{AK8}} $ dimension in regions enriched in signal from DY/ggF VV (65 $ < m_\text{jet1}^{\mathrm{AK8}} < $ 105 GeV, 65 $ < m_\text{jet2}^{\mathrm{AK8}} < $ 105 GeV) for the VH LPHP (left), VH HPLP (middle), and VV HPLP DY/ggF categories. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are shown as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. Shown below each mass plot is the difference between the data and the fit divided by the statistical uncertainty in the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty in the background estimate fitted to the data divided by the statistical uncertainty in the data is shown as a band. 
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Additional Figure 14:
Projections of data and background postfit distributions onto the $ m_\mathrm{jj}^{\mathrm{AK8}} $ dimension in regions enriched in signal from DY/ggF VH (65 $ < m_\text{jet1/2}^{\mathrm{AK8}} < $ 105 GeV, 110 $ < m_\text{jet2/1}^{\mathrm{AK8}} < $ 140 GeV) for the HPHP (upper) and HPLP/LPHP (lower) DY/ggF categories. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are shown as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. Shown below each mass plot is the difference between the data and the fit divided by the statistical uncertainty in the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty in the background estimate fitted to the data divided by the statistical uncertainty in the data is shown as a band. 
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Additional Figure 14a:
Projections of data and background postfit distributions onto the $ m_\mathrm{jj}^{\mathrm{AK8}} $ dimension in regions enriched in signal from DY/ggF VH (65 $ < m_\text{jet1/2}^{\mathrm{AK8}} < $ 105 GeV, 110 $ < m_\text{jet2/1}^{\mathrm{AK8}} < $ 140 GeV) for the HPHP (upper) and HPLP/LPHP (lower) DY/ggF categories. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are shown as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. Shown below each mass plot is the difference between the data and the fit divided by the statistical uncertainty in the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty in the background estimate fitted to the data divided by the statistical uncertainty in the data is shown as a band. 
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Additional Figure 14b:
Projections of data and background postfit distributions onto the $ m_\mathrm{jj}^{\mathrm{AK8}} $ dimension in regions enriched in signal from DY/ggF VH (65 $ < m_\text{jet1/2}^{\mathrm{AK8}} < $ 105 GeV, 110 $ < m_\text{jet2/1}^{\mathrm{AK8}} < $ 140 GeV) for the HPHP (upper) and HPLP/LPHP (lower) DY/ggF categories. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are shown as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. Shown below each mass plot is the difference between the data and the fit divided by the statistical uncertainty in the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty in the background estimate fitted to the data divided by the statistical uncertainty in the data is shown as a band. 
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Additional Figure 14c:
Projections of data and background postfit distributions onto the $ m_\mathrm{jj}^{\mathrm{AK8}} $ dimension in regions enriched in signal from DY/ggF VH (65 $ < m_\text{jet1/2}^{\mathrm{AK8}} < $ 105 GeV, 110 $ < m_\text{jet2/1}^{\mathrm{AK8}} < $ 140 GeV) for the HPHP (upper) and HPLP/LPHP (lower) DY/ggF categories. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are shown as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. Shown below each mass plot is the difference between the data and the fit divided by the statistical uncertainty in the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty in the background estimate fitted to the data divided by the statistical uncertainty in the data is shown as a band. 
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Additional Figure 14d:
Projections of data and background postfit distributions onto the $ m_\mathrm{jj}^{\mathrm{AK8}} $ dimension in regions enriched in signal from DY/ggF VH (65 $ < m_\text{jet1/2}^{\mathrm{AK8}} < $ 105 GeV, 110 $ < m_\text{jet2/1}^{\mathrm{AK8}} < $ 140 GeV) for the HPHP (upper) and HPLP/LPHP (lower) DY/ggF categories. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are shown as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. Shown below each mass plot is the difference between the data and the fit divided by the statistical uncertainty in the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty in the background estimate fitted to the data divided by the statistical uncertainty in the data is shown as a band. 
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Additional Figure 14e:
Projections of data and background postfit distributions onto the $ m_\mathrm{jj}^{\mathrm{AK8}} $ dimension in regions enriched in signal from DY/ggF VH (65 $ < m_\text{jet1/2}^{\mathrm{AK8}} < $ 105 GeV, 110 $ < m_\text{jet2/1}^{\mathrm{AK8}} < $ 140 GeV) for the HPHP (upper) and HPLP/LPHP (lower) DY/ggF categories. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are shown as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. Shown below each mass plot is the difference between the data and the fit divided by the statistical uncertainty in the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty in the background estimate fitted to the data divided by the statistical uncertainty in the data is shown as a band. 
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Additional Figure 15:
Projections of data and background postfit distributions onto the $ m_\mathrm{jj}^{\mathrm{AK8}} $ dimension in regions enriched in signal from VBF VV/VH (65 $ < m_\text{jet1}^{\mathrm{AK8}} < $ 140 GeV, 65 $ < m_\text{jet2}^{\mathrm{AK8}} < $ 140 GeV) for the HPHP (upper) and HPLP/LPHP (lower) VBF categories. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are shown as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. Shown below each mass plot is the difference between the data and the fit divided by the statistical uncertainty in the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty in the background estimate fitted to the data divided by the statistical uncertainty in the data is shown as a band. 
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Additional Figure 15a:
Projections of data and background postfit distributions onto the $ m_\mathrm{jj}^{\mathrm{AK8}} $ dimension in regions enriched in signal from VBF VV/VH (65 $ < m_\text{jet1}^{\mathrm{AK8}} < $ 140 GeV, 65 $ < m_\text{jet2}^{\mathrm{AK8}} < $ 140 GeV) for the HPHP (upper) and HPLP/LPHP (lower) VBF categories. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are shown as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. Shown below each mass plot is the difference between the data and the fit divided by the statistical uncertainty in the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty in the background estimate fitted to the data divided by the statistical uncertainty in the data is shown as a band. 
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Additional Figure 15b:
Projections of data and background postfit distributions onto the $ m_\mathrm{jj}^{\mathrm{AK8}} $ dimension in regions enriched in signal from VBF VV/VH (65 $ < m_\text{jet1}^{\mathrm{AK8}} < $ 140 GeV, 65 $ < m_\text{jet2}^{\mathrm{AK8}} < $ 140 GeV) for the HPHP (upper) and HPLP/LPHP (lower) VBF categories. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are shown as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. Shown below each mass plot is the difference between the data and the fit divided by the statistical uncertainty in the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty in the background estimate fitted to the data divided by the statistical uncertainty in the data is shown as a band. 
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Additional Figure 15c:
Projections of data and background postfit distributions onto the $ m_\mathrm{jj}^{\mathrm{AK8}} $ dimension in regions enriched in signal from VBF VV/VH (65 $ < m_\text{jet1}^{\mathrm{AK8}} < $ 140 GeV, 65 $ < m_\text{jet2}^{\mathrm{AK8}} < $ 140 GeV) for the HPHP (upper) and HPLP/LPHP (lower) VBF categories. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are shown as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. Shown below each mass plot is the difference between the data and the fit divided by the statistical uncertainty in the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty in the background estimate fitted to the data divided by the statistical uncertainty in the data is shown as a band. 
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Additional Figure 15d:
Projections of data and background postfit distributions onto the $ m_\mathrm{jj}^{\mathrm{AK8}} $ dimension in regions enriched in signal from VBF VV/VH (65 $ < m_\text{jet1}^{\mathrm{AK8}} < $ 140 GeV, 65 $ < m_\text{jet2}^{\mathrm{AK8}} < $ 140 GeV) for the HPHP (upper) and HPLP/LPHP (lower) VBF categories. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are shown as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. Shown below each mass plot is the difference between the data and the fit divided by the statistical uncertainty in the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty in the background estimate fitted to the data divided by the statistical uncertainty in the data is shown as a band. 
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Additional Figure 15e:
Projections of data and background postfit distributions onto the $ m_\mathrm{jj}^{\mathrm{AK8}} $ dimension in regions enriched in signal from VBF VV/VH (65 $ < m_\text{jet1}^{\mathrm{AK8}} < $ 140 GeV, 65 $ < m_\text{jet2}^{\mathrm{AK8}} < $ 140 GeV) for the HPHP (upper) and HPLP/LPHP (lower) VBF categories. The background shape uncertainty is shown as a gray shaded band around the result of the maximum likelihood fit to the data under the backgroundonly assumption (gray solid line), and the statistical uncertainties in the data are shown as vertical bars. The various background components contributing to the total background fit are also shown with different line colors. Shown below each mass plot is the difference between the data and the fit divided by the statistical uncertainty in the data; the uncertainty bar represents the statistical uncertainty only. The total uncertainty in the background estimate fitted to the data divided by the statistical uncertainty in the data is shown as a band. 
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Additional Figure 16:
Projection of the 3D phase space of the data onto the $ m_\mathrm{jj}^{\mathrm{AK8}} $$ m_\text{jet1}^{\mathrm{AK8}} $ plane for a selected region in $ m_\text{jet2}^{\mathrm{AK8}} $ enriched in signal from DY/ggF VV. Contours of the signal and background distributions after the background postfit are overlaid. The projections are shown for the HPHP VH (VV) DY/ggF category on the left (right). 
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Additional Figure 16a:
Projection of the 3D phase space of the data onto the $ m_\mathrm{jj}^{\mathrm{AK8}} $$ m_\text{jet1}^{\mathrm{AK8}} $ plane for a selected region in $ m_\text{jet2}^{\mathrm{AK8}} $ enriched in signal from DY/ggF VV. Contours of the signal and background distributions after the background postfit are overlaid. The projections are shown for the HPHP VH (VV) DY/ggF category on the left (right). 
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Additional Figure 16b:
Projection of the 3D phase space of the data onto the $ m_\mathrm{jj}^{\mathrm{AK8}} $$ m_\text{jet1}^{\mathrm{AK8}} $ plane for a selected region in $ m_\text{jet2}^{\mathrm{AK8}} $ enriched in signal from DY/ggF VV. Contours of the signal and background distributions after the background postfit are overlaid. The projections are shown for the HPHP VH (VV) DY/ggF category on the left (right). 
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Additional Figure 17:
Expected 95% CL\ upper limits on the product of the production cross section ($ \sigma $) and the branching fraction for a $ \mathrm{G}_{\text{bulk}}\to\mathrm{W}\mathrm{W} $ (left) and a $ \mathrm{G}_{\text{bulk}}\to\mathrm{Z}\mathrm{Z} $ (right) signal using 77.3 fb$ ^{1} $ of data collected in 2016+2017 obtained using the methods presented here (red solid line), compared to the result obtained with previous methods (black dashdotted line), published in EPJC 80 (2020) 237. The limit obtained combining data collected in 20162018 in this paper is also shown (blue dashed line). 
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Additional Figure 17a:
Expected 95% CL\ upper limits on the product of the production cross section ($ \sigma $) and the branching fraction for a $ \mathrm{G}_{\text{bulk}}\to\mathrm{W}\mathrm{W} $ (left) and a $ \mathrm{G}_{\text{bulk}}\to\mathrm{Z}\mathrm{Z} $ (right) signal using 77.3 fb$ ^{1} $ of data collected in 2016+2017 obtained using the methods presented here (red solid line), compared to the result obtained with previous methods (black dashdotted line), published in EPJC 80 (2020) 237. The limit obtained combining data collected in 20162018 in this paper is also shown (blue dashed line). 
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Additional Figure 17b:
Expected 95% CL\ upper limits on the product of the production cross section ($ \sigma $) and the branching fraction for a $ \mathrm{G}_{\text{bulk}}\to\mathrm{W}\mathrm{W} $ (left) and a $ \mathrm{G}_{\text{bulk}}\to\mathrm{Z}\mathrm{Z} $ (right) signal using 77.3 fb$ ^{1} $ of data collected in 2016+2017 obtained using the methods presented here (red solid line), compared to the result obtained with previous methods (black dashdotted line), published in EPJC 80 (2020) 237. The limit obtained combining data collected in 20162018 in this paper is also shown (blue dashed line). 
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Additional Figure 18:
Observed and expected 95% CL\ upper limits on the product of the production cross section ($ \sigma $) and the branching fraction, obtained after combining all categories with 138 fb$^{1}$ fb$ ^{1} $ of data at $ \sqrt{s}= $ 13 TeV, for $ \mathrm{G}_{\text{bulk}}\to\mathrm{W}\mathrm{W} $ (left) and $ \mathrm{G}_{\text{bulk}}\to\mathrm{Z}\mathrm{Z} $ (right) signals. In the upper panel the ggF production mode is shown while in the lower panel the VBF mode is presented. For each signal scenario the theoretical prediction (red line) and its uncertainty associated with the choice of PDF set (red hashed band) is shown. 
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Additional Figure 18a:
Observed and expected 95% CL\ upper limits on the product of the production cross section ($ \sigma $) and the branching fraction, obtained after combining all categories with 138 fb$^{1}$ fb$ ^{1} $ of data at $ \sqrt{s}= $ 13 TeV, for $ \mathrm{G}_{\text{bulk}}\to\mathrm{W}\mathrm{W} $ (left) and $ \mathrm{G}_{\text{bulk}}\to\mathrm{Z}\mathrm{Z} $ (right) signals. In the upper panel the ggF production mode is shown while in the lower panel the VBF mode is presented. For each signal scenario the theoretical prediction (red line) and its uncertainty associated with the choice of PDF set (red hashed band) is shown. 
png pdf 
Additional Figure 18b:
Observed and expected 95% CL\ upper limits on the product of the production cross section ($ \sigma $) and the branching fraction, obtained after combining all categories with 138 fb$^{1}$ fb$ ^{1} $ of data at $ \sqrt{s}= $ 13 TeV, for $ \mathrm{G}_{\text{bulk}}\to\mathrm{W}\mathrm{W} $ (left) and $ \mathrm{G}_{\text{bulk}}\to\mathrm{Z}\mathrm{Z} $ (right) signals. In the upper panel the ggF production mode is shown while in the lower panel the VBF mode is presented. For each signal scenario the theoretical prediction (red line) and its uncertainty associated with the choice of PDF set (red hashed band) is shown. 
png pdf 
Additional Figure 18c:
Observed and expected 95% CL\ upper limits on the product of the production cross section ($ \sigma $) and the branching fraction, obtained after combining all categories with 138 fb$^{1}$ fb$ ^{1} $ of data at $ \sqrt{s}= $ 13 TeV, for $ \mathrm{G}_{\text{bulk}}\to\mathrm{W}\mathrm{W} $ (left) and $ \mathrm{G}_{\text{bulk}}\to\mathrm{Z}\mathrm{Z} $ (right) signals. In the upper panel the ggF production mode is shown while in the lower panel the VBF mode is presented. For each signal scenario the theoretical prediction (red line) and its uncertainty associated with the choice of PDF set (red hashed band) is shown. 
png pdf 
Additional Figure 18d:
Observed and expected 95% CL\ upper limits on the product of the production cross section ($ \sigma $) and the branching fraction, obtained after combining all categories with 138 fb$^{1}$ fb$ ^{1} $ of data at $ \sqrt{s}= $ 13 TeV, for $ \mathrm{G}_{\text{bulk}}\to\mathrm{W}\mathrm{W} $ (left) and $ \mathrm{G}_{\text{bulk}}\to\mathrm{Z}\mathrm{Z} $ (right) signals. In the upper panel the ggF production mode is shown while in the lower panel the VBF mode is presented. For each signal scenario the theoretical prediction (red line) and its uncertainty associated with the choice of PDF set (red hashed band) is shown. 
png pdf 
Additional Figure 19:
Observed and expected 95% CL\ upper limits on the product of the production cross section ($ \sigma $) and the branching fraction, obtained after combining all categories with 138 fb$^{1}$ fb$ ^{1} $ of data at $ \sqrt{s}= $ 13 TeV, for $ \text{Rad} \to\mathrm{W}\mathrm{W} $ (left) and $ \text{Rad} \to\mathrm{Z}\mathrm{Z} $ (right) signals. In the upper panel the ggF production mode is shown while in the lower panel the VBF mode is presented. For each signal scenario the theoretical prediction (red line) and its uncertainty associated with the choice of PDF set (red hashed band) is shown. 
png pdf 
Additional Figure 19a:
Observed and expected 95% CL\ upper limits on the product of the production cross section ($ \sigma $) and the branching fraction, obtained after combining all categories with 138 fb$^{1}$ fb$ ^{1} $ of data at $ \sqrt{s}= $ 13 TeV, for $ \text{Rad} \to\mathrm{W}\mathrm{W} $ (left) and $ \text{Rad} \to\mathrm{Z}\mathrm{Z} $ (right) signals. In the upper panel the ggF production mode is shown while in the lower panel the VBF mode is presented. For each signal scenario the theoretical prediction (red line) and its uncertainty associated with the choice of PDF set (red hashed band) is shown. 
png pdf 
Additional Figure 19b:
Observed and expected 95% CL\ upper limits on the product of the production cross section ($ \sigma $) and the branching fraction, obtained after combining all categories with 138 fb$^{1}$ fb$ ^{1} $ of data at $ \sqrt{s}= $ 13 TeV, for $ \text{Rad} \to\mathrm{W}\mathrm{W} $ (left) and $ \text{Rad} \to\mathrm{Z}\mathrm{Z} $ (right) signals. In the upper panel the ggF production mode is shown while in the lower panel the VBF mode is presented. For each signal scenario the theoretical prediction (red line) and its uncertainty associated with the choice of PDF set (red hashed band) is shown. 
png pdf 
Additional Figure 19c:
Observed and expected 95% CL\ upper limits on the product of the production cross section ($ \sigma $) and the branching fraction, obtained after combining all categories with 138 fb$^{1}$ fb$ ^{1} $ of data at $ \sqrt{s}= $ 13 TeV, for $ \text{Rad} \to\mathrm{W}\mathrm{W} $ (left) and $ \text{Rad} \to\mathrm{Z}\mathrm{Z} $ (right) signals. In the upper panel the ggF production mode is shown while in the lower panel the VBF mode is presented. For each signal scenario the theoretical prediction (red line) and its uncertainty associated with the choice of PDF set (red hashed band) is shown. 
png pdf 
Additional Figure 19d:
Observed and expected 95% CL\ upper limits on the product of the production cross section ($ \sigma $) and the branching fraction, obtained after combining all categories with 138 fb$^{1}$ fb$ ^{1} $ of data at $ \sqrt{s}= $ 13 TeV, for $ \text{Rad} \to\mathrm{W}\mathrm{W} $ (left) and $ \text{Rad} \to\mathrm{Z}\mathrm{Z} $ (right) signals. In the upper panel the ggF production mode is shown while in the lower panel the VBF mode is presented. For each signal scenario the theoretical prediction (red line) and its uncertainty associated with the choice of PDF set (red hashed band) is shown. 
png pdf 
Additional Figure 20:
Observed and expected 95% CL\ upper limits on the product of the production cross section ($ \sigma $) and the branching fraction, obtained after combining all categories with 138 fb$^{1}$ fb$ ^{1} $ of data at $ \sqrt{s}= $ 13 TeV, for $ \mathrm{Z}^{'}\to\mathrm{W}\mathrm{W} $ (left) and $ \mathrm{W^{'}}\to\mathrm{W}\mathrm{Z} $ (right) signals. In the upper panel the DY production mode is shown while in the lower panel the VBF mode is presented. For each signal scenario the theoretical prediction (red line for $ c_{\mathrm{H}} = $ 1, blue line for $ c_{\mathrm{H}} = $ 3) and its uncertainty associated with the choice of PDF set (red and blue hashed bands) is shown. 
png pdf 
Additional Figure 20a:
Observed and expected 95% CL\ upper limits on the product of the production cross section ($ \sigma $) and the branching fraction, obtained after combining all categories with 138 fb$^{1}$ fb$ ^{1} $ of data at $ \sqrt{s}= $ 13 TeV, for $ \mathrm{Z}^{'}\to\mathrm{W}\mathrm{W} $ (left) and $ \mathrm{W^{'}}\to\mathrm{W}\mathrm{Z} $ (right) signals. In the upper panel the DY production mode is shown while in the lower panel the VBF mode is presented. For each signal scenario the theoretical prediction (red line for $ c_{\mathrm{H}} = $ 1, blue line for $ c_{\mathrm{H}} = $ 3) and its uncertainty associated with the choice of PDF set (red and blue hashed bands) is shown. 
png pdf 
Additional Figure 20b:
Observed and expected 95% CL\ upper limits on the product of the production cross section ($ \sigma $) and the branching fraction, obtained after combining all categories with 138 fb$^{1}$ fb$ ^{1} $ of data at $ \sqrt{s}= $ 13 TeV, for $ \mathrm{Z}^{'}\to\mathrm{W}\mathrm{W} $ (left) and $ \mathrm{W^{'}}\to\mathrm{W}\mathrm{Z} $ (right) signals. In the upper panel the DY production mode is shown while in the lower panel the VBF mode is presented. For each signal scenario the theoretical prediction (red line for $ c_{\mathrm{H}} = $ 1, blue line for $ c_{\mathrm{H}} = $ 3) and its uncertainty associated with the choice of PDF set (red and blue hashed bands) is shown. 
png pdf 
Additional Figure 20c:
Observed and expected 95% CL\ upper limits on the product of the production cross section ($ \sigma $) and the branching fraction, obtained after combining all categories with 138 fb$^{1}$ fb$ ^{1} $ of data at $ \sqrt{s}= $ 13 TeV, for $ \mathrm{Z}^{'}\to\mathrm{W}\mathrm{W} $ (left) and $ \mathrm{W^{'}}\to\mathrm{W}\mathrm{Z} $ (right) signals. In the upper panel the DY production mode is shown while in the lower panel the VBF mode is presented. For each signal scenario the theoretical prediction (red line for $ c_{\mathrm{H}} = $ 1, blue line for $ c_{\mathrm{H}} = $ 3) and its uncertainty associated with the choice of PDF set (red and blue hashed bands) is shown. 
png pdf 
Additional Figure 20d:
Observed and expected 95% CL\ upper limits on the product of the production cross section ($ \sigma $) and the branching fraction, obtained after combining all categories with 138 fb$^{1}$ fb$ ^{1} $ of data at $ \sqrt{s}= $ 13 TeV, for $ \mathrm{Z}^{'}\to\mathrm{W}\mathrm{W} $ (left) and $ \mathrm{W^{'}}\to\mathrm{W}\mathrm{Z} $ (right) signals. In the upper panel the DY production mode is shown while in the lower panel the VBF mode is presented. For each signal scenario the theoretical prediction (red line for $ c_{\mathrm{H}} = $ 1, blue line for $ c_{\mathrm{H}} = $ 3) and its uncertainty associated with the choice of PDF set (red and blue hashed bands) is shown. 
png pdf 
Additional Figure 21:
Observed and expected 95% CL\ upper limits on the product of the production cross section ($ \sigma $) and the branching fraction, obtained after combining all categories with 138 fb$^{1}$ fb$ ^{1} $ of data at $ \sqrt{s}= $ 13 TeV, for $ \mathrm{Z}^{'}\to\mathrm{Z}\mathrm{H} $ (left) and $ \mathrm{W^{'}}\to\mathrm{W}\mathrm{H} $ (right) signals. In the upper panel the DY production mode is shown while in the lower panel the VBF mode is presented. For each signal scenario the theoretical prediction (red line for $ c_{\mathrm{H}} = $ 1, blue line for $ c_{\mathrm{H}} = $ 3) and its uncertainty associated with the choice of PDF set (red and blue hashed bands) is shown. 
png pdf 
Additional Figure 21a:
Observed and expected 95% CL\ upper limits on the product of the production cross section ($ \sigma $) and the branching fraction, obtained after combining all categories with 138 fb$^{1}$ fb$ ^{1} $ of data at $ \sqrt{s}= $ 13 TeV, for $ \mathrm{Z}^{'}\to\mathrm{Z}\mathrm{H} $ (left) and $ \mathrm{W^{'}}\to\mathrm{W}\mathrm{H} $ (right) signals. In the upper panel the DY production mode is shown while in the lower panel the VBF mode is presented. For each signal scenario the theoretical prediction (red line for $ c_{\mathrm{H}} = $ 1, blue line for $ c_{\mathrm{H}} = $ 3) and its uncertainty associated with the choice of PDF set (red and blue hashed bands) is shown. 
png pdf 
Additional Figure 21b:
Observed and expected 95% CL\ upper limits on the product of the production cross section ($ \sigma $) and the branching fraction, obtained after combining all categories with 138 fb$^{1}$ fb$ ^{1} $ of data at $ \sqrt{s}= $ 13 TeV, for $ \mathrm{Z}^{'}\to\mathrm{Z}\mathrm{H} $ (left) and $ \mathrm{W^{'}}\to\mathrm{W}\mathrm{H} $ (right) signals. In the upper panel the DY production mode is shown while in the lower panel the VBF mode is presented. For each signal scenario the theoretical prediction (red line for $ c_{\mathrm{H}} = $ 1, blue line for $ c_{\mathrm{H}} = $ 3) and its uncertainty associated with the choice of PDF set (red and blue hashed bands) is shown. 
png pdf 
Additional Figure 21c:
Observed and expected 95% CL\ upper limits on the product of the production cross section ($ \sigma $) and the branching fraction, obtained after combining all categories with 138 fb$^{1}$ fb$ ^{1} $ of data at $ \sqrt{s}= $ 13 TeV, for $ \mathrm{Z}^{'}\to\mathrm{Z}\mathrm{H} $ (left) and $ \mathrm{W^{'}}\to\mathrm{W}\mathrm{H} $ (right) signals. In the upper panel the DY production mode is shown while in the lower panel the VBF mode is presented. For each signal scenario the theoretical prediction (red line for $ c_{\mathrm{H}} = $ 1, blue line for $ c_{\mathrm{H}} = $ 3) and its uncertainty associated with the choice of PDF set (red and blue hashed bands) is shown. 
png pdf 
Additional Figure 21d:
Observed and expected 95% CL\ upper limits on the product of the production cross section ($ \sigma $) and the branching fraction, obtained after combining all categories with 138 fb$^{1}$ fb$ ^{1} $ of data at $ \sqrt{s}= $ 13 TeV, for $ \mathrm{Z}^{'}\to\mathrm{Z}\mathrm{H} $ (left) and $ \mathrm{W^{'}}\to\mathrm{W}\mathrm{H} $ (right) signals. In the upper panel the DY production mode is shown while in the lower panel the VBF mode is presented. For each signal scenario the theoretical prediction (red line for $ c_{\mathrm{H}} = $ 1, blue line for $ c_{\mathrm{H}} = $ 3) and its uncertainty associated with the choice of PDF set (red and blue hashed bands) is shown. 
png pdf 
Additional Figure 22:
Observed and expected 95% CL\ upper limits on the product of the production cross section ($ \sigma $) and the branching fraction, obtained after combining all categories with 138 fb$^{1}$ fb$ ^{1} $ of data at $ \sqrt{s}= $ 13 TeV, for VBF produced $ \text{Rad} \to\mathrm{V}\mathrm{V} $ (left) and $ \mathrm{G}_{\text{bulk}}\to\mathrm{V}\mathrm{V} $ (right) signals. For each signal scenario the theoretical prediction (red line) and its uncertainty associated with the choice of PDF set (red hashed band) is shown. 
png pdf 
Additional Figure 22a:
Observed and expected 95% CL\ upper limits on the product of the production cross section ($ \sigma $) and the branching fraction, obtained after combining all categories with 138 fb$^{1}$ fb$ ^{1} $ of data at $ \sqrt{s}= $ 13 TeV, for VBF produced $ \text{Rad} \to\mathrm{V}\mathrm{V} $ (left) and $ \mathrm{G}_{\text{bulk}}\to\mathrm{V}\mathrm{V} $ (right) signals. For each signal scenario the theoretical prediction (red line) and its uncertainty associated with the choice of PDF set (red hashed band) is shown. 
png pdf 
Additional Figure 22b:
Observed and expected 95% CL\ upper limits on the product of the production cross section ($ \sigma $) and the branching fraction, obtained after combining all categories with 138 fb$^{1}$ fb$ ^{1} $ of data at $ \sqrt{s}= $ 13 TeV, for VBF produced $ \text{Rad} \to\mathrm{V}\mathrm{V} $ (left) and $ \mathrm{G}_{\text{bulk}}\to\mathrm{V}\mathrm{V} $ (right) signals. For each signal scenario the theoretical prediction (red line) and its uncertainty associated with the choice of PDF set (red hashed band) is shown. 
png pdf 
Additional Figure 23:
Observed and expected 95% CL\ upper limits on the product of the production cross section ($ \sigma $) and the branching fraction, obtained after combining all categories with 138 fb$^{1}$ fb$ ^{1} $ of data at $ \sqrt{s}= $ 13 TeV, for $ \mathrm{V}^\prime\to\mathrm{W}\mathrm{V} $ (upper) and $ \mathrm{V}^\prime\to\mathrm{V}\mathrm{H} $ (lower) signals. In the upper panel the DY production mode is shown while in the lower panel the VBF mode is presented. For each signal scenario the theoretical prediction (red line for $ c_{\mathrm{H}} = $ 1, blue line for $ c_{\mathrm{H}} = $ 3) and its uncertainty associated with the choice of PDF set (red and blue hashed bands) is shown. 
png pdf 
Additional Figure 23a:
Observed and expected 95% CL\ upper limits on the product of the production cross section ($ \sigma $) and the branching fraction, obtained after combining all categories with 138 fb$^{1}$ fb$ ^{1} $ of data at $ \sqrt{s}= $ 13 TeV, for $ \mathrm{V}^\prime\to\mathrm{W}\mathrm{V} $ (upper) and $ \mathrm{V}^\prime\to\mathrm{V}\mathrm{H} $ (lower) signals. In the upper panel the DY production mode is shown while in the lower panel the VBF mode is presented. For each signal scenario the theoretical prediction (red line for $ c_{\mathrm{H}} = $ 1, blue line for $ c_{\mathrm{H}} = $ 3) and its uncertainty associated with the choice of PDF set (red and blue hashed bands) is shown. 
png pdf 
Additional Figure 23b:
Observed and expected 95% CL\ upper limits on the product of the production cross section ($ \sigma $) and the branching fraction, obtained after combining all categories with 138 fb$^{1}$ fb$ ^{1} $ of data at $ \sqrt{s}= $ 13 TeV, for $ \mathrm{V}^\prime\to\mathrm{W}\mathrm{V} $ (upper) and $ \mathrm{V}^\prime\to\mathrm{V}\mathrm{H} $ (lower) signals. In the upper panel the DY production mode is shown while in the lower panel the VBF mode is presented. For each signal scenario the theoretical prediction (red line for $ c_{\mathrm{H}} = $ 1, blue line for $ c_{\mathrm{H}} = $ 3) and its uncertainty associated with the choice of PDF set (red and blue hashed bands) is shown. 
png pdf 
Additional Figure 23c:
Observed and expected 95% CL\ upper limits on the product of the production cross section ($ \sigma $) and the branching fraction, obtained after combining all categories with 138 fb$^{1}$ fb$ ^{1} $ of data at $ \sqrt{s}= $ 13 TeV, for $ \mathrm{V}^\prime\to\mathrm{W}\mathrm{V} $ (upper) and $ \mathrm{V}^\prime\to\mathrm{V}\mathrm{H} $ (lower) signals. In the upper panel the DY production mode is shown while in the lower panel the VBF mode is presented. For each signal scenario the theoretical prediction (red line for $ c_{\mathrm{H}} = $ 1, blue line for $ c_{\mathrm{H}} = $ 3) and its uncertainty associated with the choice of PDF set (red and blue hashed bands) is shown. 
png pdf 
Additional Figure 23d:
Observed and expected 95% CL\ upper limits on the product of the production cross section ($ \sigma $) and the branching fraction, obtained after combining all categories with 138 fb$^{1}$ fb$ ^{1} $ of data at $ \sqrt{s}= $ 13 TeV, for $ \mathrm{V}^\prime\to\mathrm{W}\mathrm{V} $ (upper) and $ \mathrm{V}^\prime\to\mathrm{V}\mathrm{H} $ (lower) signals. In the upper panel the DY production mode is shown while in the lower panel the VBF mode is presented. For each signal scenario the theoretical prediction (red line for $ c_{\mathrm{H}} = $ 1, blue line for $ c_{\mathrm{H}} = $ 3) and its uncertainty associated with the choice of PDF set (red and blue hashed bands) is shown. 
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