CMSB2G23002 ; CERNEP2024062  
Searches for Higgs boson production through decays of heavy resonances  
CMS Collaboration  
24 March 2024  
Submitted to Physics Reports  
Abstract: The discovery of the Higgs boson has led to new possible signatures for heavy resonance searches at the LHC. Since then, search channels including at least one Higgs boson plus another particle have formed an important part of the program of new physics searches. In this report, the status of these searches by the CMS Collaboration is reviewed. Searches are discussed for resonances decaying to two Higgs bosons, a Higgs and a vector boson, or a Higgs boson and another new resonance, with protonproton collision data collected at $ \sqrt{s}= $ 13 TeV in the years 20162018. A combination of the results of these searches is presented together with constraints on different beyondthestandard model scenarios, including scenarios with extended Higgs sectors, heavy vector bosons and extra dimensions. Studies are shown for the first time by CMS on the validity of the narrowwidth approximation in searches for the resonant production of a pair of Higgs bosons. The potential for a discovery at the High Luminosity LHC is also discussed.  
Links: eprint arXiv:2403.16926 [hepex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; 
Figures & Tables  Summary  Additional Figures  References  CMS Publications 

Figures  
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Figure 1:
Higgs boson production cross sections in the SM as a function of the collider centreofmass energy (left), and Higgs boson branching fractions in the SM as a function of the Higgs boson mass (right). Both figures are taken from Ref. [35]. 
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Figure 1a:
Higgs boson production cross sections in the SM as a function of the collider centreofmass energy (left), and Higgs boson branching fractions in the SM as a function of the Higgs boson mass (right). Both figures are taken from Ref. [35]. 
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Figure 1b:
Higgs boson production cross sections in the SM as a function of the collider centreofmass energy (left), and Higgs boson branching fractions in the SM as a function of the Higgs boson mass (right). Both figures are taken from Ref. [35]. 
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Figure 2:
Signal strength parameters extracted for various production modes $ \mu_i $, assuming the branching fractions $ \mathcal{B}^f = \mathcal{B}^\text{f}_\text{SM} $ (left), and decay channels $ \mu^\text{f} $, assuming the production cross sections as predicted by the SM (right). The thick and thin black lines indicate the one and two s.d. confidence intervals (labelled by SD in the figures), with the systematic and statistical components of the former indicated by the red and blue bands, respectively. The vertical dashed line at unity represents the values of $ \mu_i $ (resp. $ \mu^\text{f} $) in the SM. Taken from Ref [4]. 
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Figure 2a:
Signal strength parameters extracted for various production modes $ \mu_i $, assuming the branching fractions $ \mathcal{B}^f = \mathcal{B}^\text{f}_\text{SM} $ (left), and decay channels $ \mu^\text{f} $, assuming the production cross sections as predicted by the SM (right). The thick and thin black lines indicate the one and two s.d. confidence intervals (labelled by SD in the figures), with the systematic and statistical components of the former indicated by the red and blue bands, respectively. The vertical dashed line at unity represents the values of $ \mu_i $ (resp. $ \mu^\text{f} $) in the SM. Taken from Ref [4]. 
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Figure 2b:
Signal strength parameters extracted for various production modes $ \mu_i $, assuming the branching fractions $ \mathcal{B}^f = \mathcal{B}^\text{f}_\text{SM} $ (left), and decay channels $ \mu^\text{f} $, assuming the production cross sections as predicted by the SM (right). The thick and thin black lines indicate the one and two s.d. confidence intervals (labelled by SD in the figures), with the systematic and statistical components of the former indicated by the red and blue bands, respectively. The vertical dashed line at unity represents the values of $ \mu_i $ (resp. $ \mu^\text{f} $) in the SM. Taken from Ref [4]. 
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Figure 3:
Measurements of the coupling modifiers $ \kappa_{i} $, allowing both invisible and undetected decay modes, with the SM value used as an upper bound on both $ \kappa_\mathrm{W} $ and $ \kappa_\mathrm{Z} $. The thick and thin black lines indicate the $ \pm $1 and $ \pm $2 s.d. confidence intervals, respectively, with the systematic and statistical components of the $ \pm $1 s.d. interval indicated by the red and blue bands. The resulting branching fractions for invisible and undetected decay modes are also displayed. Taken from Ref. [4]. 
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Figure 4:
Leading order Feynman diagrams of Higgs boson pair production via gluon fusion. The left and middle parts of the figure show the ``triangle'' and ``box'' diagrams, respectively for nonresonant H production, as expected from the SM. The right part of the figure shows a diagram for H boson production through a new resonance of labeled as X. 
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Figure 4a:
Leading order Feynman diagrams of Higgs boson pair production via gluon fusion. The left and middle parts of the figure show the ``triangle'' and ``box'' diagrams, respectively for nonresonant H production, as expected from the SM. The right part of the figure shows a diagram for H boson production through a new resonance of labeled as X. 
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Figure 4b:
Leading order Feynman diagrams of Higgs boson pair production via gluon fusion. The left and middle parts of the figure show the ``triangle'' and ``box'' diagrams, respectively for nonresonant H production, as expected from the SM. The right part of the figure shows a diagram for H boson production through a new resonance of labeled as X. 
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Figure 4c:
Leading order Feynman diagrams of Higgs boson pair production via gluon fusion. The left and middle parts of the figure show the ``triangle'' and ``box'' diagrams, respectively for nonresonant H production, as expected from the SM. The right part of the figure shows a diagram for H boson production through a new resonance of labeled as X. 
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Figure 5:
Branching fractions of $ \mathrm{X}\to{\mathrm{H}\mathrm{H}} $ decays in 2HDMs of Type I (upper) and Type II (lower) in the $ \cos(\beta  \alpha) $$ \tan\beta $ plane for $ m_{\mathrm{X}} = $ 500 GeV (left) and in the $ m_{\mathrm{X}} $$ \tan\beta $ plane for $ \cos(\beta  \alpha) = $ 0.02 (right). The masses of all nonSMlike Higgs bosons are set to be the same, $ m_{\mathrm{X}} = m_{ {\mathrm{A}}} $, and $ m_{12}^2 = m_{{\mathrm{A}}}^2 \tan\beta/(1 + \tan^2\beta) $. The branching fractions have been calculated with 2HDMC v1.8.0 [55, 56]. 
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Figure 5a:
Branching fractions of $ \mathrm{X}\to{\mathrm{H}\mathrm{H}} $ decays in 2HDMs of Type I (upper) and Type II (lower) in the $ \cos(\beta  \alpha) $$ \tan\beta $ plane for $ m_{\mathrm{X}} = $ 500 GeV (left) and in the $ m_{\mathrm{X}} $$ \tan\beta $ plane for $ \cos(\beta  \alpha) = $ 0.02 (right). The masses of all nonSMlike Higgs bosons are set to be the same, $ m_{\mathrm{X}} = m_{ {\mathrm{A}}} $, and $ m_{12}^2 = m_{{\mathrm{A}}}^2 \tan\beta/(1 + \tan^2\beta) $. The branching fractions have been calculated with 2HDMC v1.8.0 [55, 56]. 
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Figure 5b:
Branching fractions of $ \mathrm{X}\to{\mathrm{H}\mathrm{H}} $ decays in 2HDMs of Type I (upper) and Type II (lower) in the $ \cos(\beta  \alpha) $$ \tan\beta $ plane for $ m_{\mathrm{X}} = $ 500 GeV (left) and in the $ m_{\mathrm{X}} $$ \tan\beta $ plane for $ \cos(\beta  \alpha) = $ 0.02 (right). The masses of all nonSMlike Higgs bosons are set to be the same, $ m_{\mathrm{X}} = m_{ {\mathrm{A}}} $, and $ m_{12}^2 = m_{{\mathrm{A}}}^2 \tan\beta/(1 + \tan^2\beta) $. The branching fractions have been calculated with 2HDMC v1.8.0 [55, 56]. 
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Figure 5c:
Branching fractions of $ \mathrm{X}\to{\mathrm{H}\mathrm{H}} $ decays in 2HDMs of Type I (upper) and Type II (lower) in the $ \cos(\beta  \alpha) $$ \tan\beta $ plane for $ m_{\mathrm{X}} = $ 500 GeV (left) and in the $ m_{\mathrm{X}} $$ \tan\beta $ plane for $ \cos(\beta  \alpha) = $ 0.02 (right). The masses of all nonSMlike Higgs bosons are set to be the same, $ m_{\mathrm{X}} = m_{ {\mathrm{A}}} $, and $ m_{12}^2 = m_{{\mathrm{A}}}^2 \tan\beta/(1 + \tan^2\beta) $. The branching fractions have been calculated with 2HDMC v1.8.0 [55, 56]. 
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Figure 5d:
Branching fractions of $ \mathrm{X}\to{\mathrm{H}\mathrm{H}} $ decays in 2HDMs of Type I (upper) and Type II (lower) in the $ \cos(\beta  \alpha) $$ \tan\beta $ plane for $ m_{\mathrm{X}} = $ 500 GeV (left) and in the $ m_{\mathrm{X}} $$ \tan\beta $ plane for $ \cos(\beta  \alpha) = $ 0.02 (right). The masses of all nonSMlike Higgs bosons are set to be the same, $ m_{\mathrm{X}} = m_{ {\mathrm{A}}} $, and $ m_{12}^2 = m_{{\mathrm{A}}}^2 \tan\beta/(1 + \tan^2\beta) $. The branching fractions have been calculated with 2HDMC v1.8.0 [55, 56]. 
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Figure 6:
Branching fraction of $ \mathrm{X}\to{\mathrm{H}\mathrm{H}} $ decays in the MSSM, for the hMSSM [57,58,59] (left) and the $ M^{125}_{\text{h,EFT}} $ [60] benchmarks, in the $ m_{{\mathrm{A}}} $$ \tan \beta $ plane. The branching fractions are taken from benchmark files produced by the MSSM subgroup of the LHC Higgs Working Group [61,62]. 
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Figure 6a:
Branching fraction of $ \mathrm{X}\to{\mathrm{H}\mathrm{H}} $ decays in the MSSM, for the hMSSM [57,58,59] (left) and the $ M^{125}_{\text{h,EFT}} $ [60] benchmarks, in the $ m_{{\mathrm{A}}} $$ \tan \beta $ plane. The branching fractions are taken from benchmark files produced by the MSSM subgroup of the LHC Higgs Working Group [61,62]. 
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Figure 6b:
Branching fraction of $ \mathrm{X}\to{\mathrm{H}\mathrm{H}} $ decays in the MSSM, for the hMSSM [57,58,59] (left) and the $ M^{125}_{\text{h,EFT}} $ [60] benchmarks, in the $ m_{{\mathrm{A}}} $$ \tan \beta $ plane. The branching fractions are taken from benchmark files produced by the MSSM subgroup of the LHC Higgs Working Group [61,62]. 
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Figure 7:
Localization of fields on the branes, in different types of the RandallSundrum (RS) model: RS1 (left) and bulkRS (right). The $ x $axis represents the 5th dimension with the Planck brane on the left and the TeV brane on the right. The $ y $axis is the probability density. Adapted from Ref. [28]. 
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Figure 7a:
Localization of fields on the branes, in different types of the RandallSundrum (RS) model: RS1 (left) and bulkRS (right). The $ x $axis represents the 5th dimension with the Planck brane on the left and the TeV brane on the right. The $ y $axis is the probability density. Adapted from Ref. [28]. 
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Figure 7b:
Localization of fields on the branes, in different types of the RandallSundrum (RS) model: RS1 (left) and bulkRS (right). The $ x $axis represents the 5th dimension with the Planck brane on the left and the TeV brane on the right. The $ y $axis is the probability density. Adapted from Ref. [28]. 
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Figure 8:
The decay branching fractions of an RS1 graviton (top left), bulk graviton (upper right), and radion (lower). Solid lines assume a fully elementary top quark, while the dashed lines ignore the coupling of the graviton to top quarks. Adapted from Ref. [28]. 
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Figure 8a:
The decay branching fractions of an RS1 graviton (top left), bulk graviton (upper right), and radion (lower). Solid lines assume a fully elementary top quark, while the dashed lines ignore the coupling of the graviton to top quarks. Adapted from Ref. [28]. 
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Figure 8b:
The decay branching fractions of an RS1 graviton (top left), bulk graviton (upper right), and radion (lower). Solid lines assume a fully elementary top quark, while the dashed lines ignore the coupling of the graviton to top quarks. Adapted from Ref. [28]. 
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Figure 8c:
The decay branching fractions of an RS1 graviton (top left), bulk graviton (upper right), and radion (lower). Solid lines assume a fully elementary top quark, while the dashed lines ignore the coupling of the graviton to top quarks. Adapted from Ref. [28]. 
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Figure 9:
Feynman diagrams for the production of Z' and W' bosons produced through the (left) DrellYan and (right) vector boson fusion process. The Z' (resp. W') boson subsequently decays into ZH and WH, respectively. 
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Figure 9a:
Feynman diagrams for the production of Z' and W' bosons produced through the (left) DrellYan and (right) vector boson fusion process. The Z' (resp. W') boson subsequently decays into ZH and WH, respectively. 
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Figure 9b:
Feynman diagrams for the production of Z' and W' bosons produced through the (left) DrellYan and (right) vector boson fusion process. The Z' (resp. W') boson subsequently decays into ZH and WH, respectively. 
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Figure 10:
Cross sections for (left) DrellYan production ($ \hat{\sigma}_{\mathrm{DY}} $) and (right) production through vector boson fusion ($ \hat{\sigma}_{\mathrm{ VBF}} $), as defined in Eqs. \eqrefeq:DY_HVT and \eqrefeq:VBF_HVT, for Z' and W' bosons in the heavy vector triplet (HVT) model B at $ \sqrt{s} = $ 13 TeV. Calculations are based on the work of Ref. [30]. 
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Figure 10a:
Cross sections for (left) DrellYan production ($ \hat{\sigma}_{\mathrm{DY}} $) and (right) production through vector boson fusion ($ \hat{\sigma}_{\mathrm{ VBF}} $), as defined in Eqs. \eqrefeq:DY_HVT and \eqrefeq:VBF_HVT, for Z' and W' bosons in the heavy vector triplet (HVT) model B at $ \sqrt{s} = $ 13 TeV. Calculations are based on the work of Ref. [30]. 
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Figure 10b:
Cross sections for (left) DrellYan production ($ \hat{\sigma}_{\mathrm{DY}} $) and (right) production through vector boson fusion ($ \hat{\sigma}_{\mathrm{ VBF}} $), as defined in Eqs. \eqrefeq:DY_HVT and \eqrefeq:VBF_HVT, for Z' and W' bosons in the heavy vector triplet (HVT) model B at $ \sqrt{s} = $ 13 TeV. Calculations are based on the work of Ref. [30]. 
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Figure 11:
Branching fractions for heavy vector triplet (HVT) bosons with masses of (upper) 1 and (lower) 2 TeV for values of the parameter $ g_\mathrm{F} $ corresponding to models (left) A and (right) B. The exact branching fractions of each model are indicated by the crossing points of the individual curves with the dashed vertical lines. Calculations are based on the work of Ref. [30]. 
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Figure 11a:
Branching fractions for heavy vector triplet (HVT) bosons with masses of (upper) 1 and (lower) 2 TeV for values of the parameter $ g_\mathrm{F} $ corresponding to models (left) A and (right) B. The exact branching fractions of each model are indicated by the crossing points of the individual curves with the dashed vertical lines. Calculations are based on the work of Ref. [30]. 
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Figure 11b:
Branching fractions for heavy vector triplet (HVT) bosons with masses of (upper) 1 and (lower) 2 TeV for values of the parameter $ g_\mathrm{F} $ corresponding to models (left) A and (right) B. The exact branching fractions of each model are indicated by the crossing points of the individual curves with the dashed vertical lines. Calculations are based on the work of Ref. [30]. 
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Figure 11c:
Branching fractions for heavy vector triplet (HVT) bosons with masses of (upper) 1 and (lower) 2 TeV for values of the parameter $ g_\mathrm{F} $ corresponding to models (left) A and (right) B. The exact branching fractions of each model are indicated by the crossing points of the individual curves with the dashed vertical lines. Calculations are based on the work of Ref. [30]. 
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Figure 11d:
Branching fractions for heavy vector triplet (HVT) bosons with masses of (upper) 1 and (lower) 2 TeV for values of the parameter $ g_\mathrm{F} $ corresponding to models (left) A and (right) B. The exact branching fractions of each model are indicated by the crossing points of the individual curves with the dashed vertical lines. Calculations are based on the work of Ref. [30]. 
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Figure 12:
(left) Branching fraction for the decay $ \mathrm{Z}^{'}\to\mathrm{Z}\mathrm{H} $, and (right) total width of the Z' boson, for a resonance with 2 TeV mass, for different values of the parameter $ g_\mathrm{F} $. Calculations are based the work of Ref. [30]. 
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Figure 12a:
(left) Branching fraction for the decay $ \mathrm{Z}^{'}\to\mathrm{Z}\mathrm{H} $, and (right) total width of the Z' boson, for a resonance with 2 TeV mass, for different values of the parameter $ g_\mathrm{F} $. Calculations are based the work of Ref. [30]. 
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Figure 12b:
(left) Branching fraction for the decay $ \mathrm{Z}^{'}\to\mathrm{Z}\mathrm{H} $, and (right) total width of the Z' boson, for a resonance with 2 TeV mass, for different values of the parameter $ g_\mathrm{F} $. Calculations are based the work of Ref. [30]. 
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Figure 13:
Search for $ \mathrm{X}\to\mathrm{V}\mathrm{H}(\mathrm{b}\mathrm{b}) $: Distributions of the $ m_{\mathrm{Z}\mathrm{H}}^{\text{T}} $ and $ m_{\mathrm{Z}\mathrm{H}} $ variables, as introduced in the text, in the (left) 0 $ \ell $ and (right) 2 $ \ell $ categories, in the 2 b tag signal region of the $ {\mathrm{A}} \to\mathrm{Z}\mathrm{H}(\mathrm{b}\mathrm{b}) $ analysis [108]. In the 2 $ \ell $ categories, the contributions of the 2 e and 2 $ \mu $ channels have been summed. The gray dotted line represents the sum of all background processes before the fit to data; the shaded area represents the postfit uncertainty. The hatched red histograms represent signal hypotheses for b quark associated X production corresponding to $ \sigma_{{\mathrm{A}} }\mathcal{B}({\mathrm{A}} \to\mathrm{Z}\mathrm{H}) \mathcal{B}(\mathrm{H}\to\mathrm{b}\mathrm{b})= $ 0.1 pb. The lower panels depict $ (N^\text{ data}N^\text{bkg})/\sigma $ in each bin, where $ \sigma $ refers to the statistical uncertainty in the given bin. Figure from Ref. [108]. 
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Figure 13a:
Search for $ \mathrm{X}\to\mathrm{V}\mathrm{H}(\mathrm{b}\mathrm{b}) $: Distributions of the $ m_{\mathrm{Z}\mathrm{H}}^{\text{T}} $ and $ m_{\mathrm{Z}\mathrm{H}} $ variables, as introduced in the text, in the (left) 0 $ \ell $ and (right) 2 $ \ell $ categories, in the 2 b tag signal region of the $ {\mathrm{A}} \to\mathrm{Z}\mathrm{H}(\mathrm{b}\mathrm{b}) $ analysis [108]. In the 2 $ \ell $ categories, the contributions of the 2 e and 2 $ \mu $ channels have been summed. The gray dotted line represents the sum of all background processes before the fit to data; the shaded area represents the postfit uncertainty. The hatched red histograms represent signal hypotheses for b quark associated X production corresponding to $ \sigma_{{\mathrm{A}} }\mathcal{B}({\mathrm{A}} \to\mathrm{Z}\mathrm{H}) \mathcal{B}(\mathrm{H}\to\mathrm{b}\mathrm{b})= $ 0.1 pb. The lower panels depict $ (N^\text{ data}N^\text{bkg})/\sigma $ in each bin, where $ \sigma $ refers to the statistical uncertainty in the given bin. Figure from Ref. [108]. 
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Figure 13b:
Search for $ \mathrm{X}\to\mathrm{V}\mathrm{H}(\mathrm{b}\mathrm{b}) $: Distributions of the $ m_{\mathrm{Z}\mathrm{H}}^{\text{T}} $ and $ m_{\mathrm{Z}\mathrm{H}} $ variables, as introduced in the text, in the (left) 0 $ \ell $ and (right) 2 $ \ell $ categories, in the 2 b tag signal region of the $ {\mathrm{A}} \to\mathrm{Z}\mathrm{H}(\mathrm{b}\mathrm{b}) $ analysis [108]. In the 2 $ \ell $ categories, the contributions of the 2 e and 2 $ \mu $ channels have been summed. The gray dotted line represents the sum of all background processes before the fit to data; the shaded area represents the postfit uncertainty. The hatched red histograms represent signal hypotheses for b quark associated X production corresponding to $ \sigma_{{\mathrm{A}} }\mathcal{B}({\mathrm{A}} \to\mathrm{Z}\mathrm{H}) \mathcal{B}(\mathrm{H}\to\mathrm{b}\mathrm{b})= $ 0.1 pb. The lower panels depict $ (N^\text{ data}N^\text{bkg})/\sigma $ in each bin, where $ \sigma $ refers to the statistical uncertainty in the given bin. Figure from Ref. [108]. 
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Figure 14:
Search for $ \mathrm{X}\to\mathrm{V}\mathrm{H}(\tau\tau) $: Distribution of the $ m_{\ell\ell\tau\tau}^{\mathrm{c}} $ variable, as introduced in the text, of the $ {\mathrm{A}} \to\mathrm{Z}\mathrm{H}(\tau\tau) $ analysis [107], after a fit of the backgroundonly hypothesis in all eight final states. While the fit is based on corresponding distributions, for each final state individually, these have been combined into a single distribution, for visualization purposes for this figure. Uncertainties include both statistical and systematic components. The expected contribution from the $ {\mathrm{A}}\to\mathrm{Z}\mathrm{H} $ signal process is shown for a pseudoscalar Higgs boson with $ m_{{\mathrm{A}}} = $ 300 GeV with the product of the cross section and branching fraction of 20 fb. Figure from Ref. [107]. 
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Figure 15:
Search for $ \mathrm{X}\to\mathrm{V}\mathrm{H}(\mathrm{b}\mathrm{b}) $: Distributions of (left) the jet soft drop mass of a boosted Higgs boson candidate, labeled $ m_{\mathrm{jet}} $, and (right) the mass of the X resonance candidate, labeled $ m_{\mathrm{WV}} $ in the $ \mathrm{W}(\ell\nu)\mathrm{H}(\mathrm{b}\mathrm{b}) $ channel. The notation $ m_{\mathrm{WV}} $ is used as a shorthand since the analysis also searches for resonances in the WW and WZ final states. Figures from Ref. [109]. 
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Figure 15a:
Search for $ \mathrm{X}\to\mathrm{V}\mathrm{H}(\mathrm{b}\mathrm{b}) $: Distributions of (left) the jet soft drop mass of a boosted Higgs boson candidate, labeled $ m_{\mathrm{jet}} $, and (right) the mass of the X resonance candidate, labeled $ m_{\mathrm{WV}} $ in the $ \mathrm{W}(\ell\nu)\mathrm{H}(\mathrm{b}\mathrm{b}) $ channel. The notation $ m_{\mathrm{WV}} $ is used as a shorthand since the analysis also searches for resonances in the WW and WZ final states. Figures from Ref. [109]. 
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Figure 15b:
Search for $ \mathrm{X}\to\mathrm{V}\mathrm{H}(\mathrm{b}\mathrm{b}) $: Distributions of (left) the jet soft drop mass of a boosted Higgs boson candidate, labeled $ m_{\mathrm{jet}} $, and (right) the mass of the X resonance candidate, labeled $ m_{\mathrm{WV}} $ in the $ \mathrm{W}(\ell\nu)\mathrm{H}(\mathrm{b}\mathrm{b}) $ channel. The notation $ m_{\mathrm{WV}} $ is used as a shorthand since the analysis also searches for resonances in the WW and WZ final states. Figures from Ref. [109]. 
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Figure 16:
Search for $ \mathrm{X}\to\mathrm{V}\mathrm{H}(\mathrm{b}\mathrm{b}) $: Distributions of (left) the jet soft drop mass of a boosted Higgs boson candidate, labeled $ m_{\text{j}\mathrm{H}} $, and (right) the mass or transverse mass of the X resonance candidate, labeled $ m_{\mathrm{X}} $ and $ m_{\mathrm{X}}^{\mathrm{T}} $, respectively, in the $ \mathrm{Z}(\ell\ell)\mathrm{H}(\mathrm{b}\mathrm{b}) $ (upper) and $ \mathrm{Z}(\nu\nu)\mathrm{H}(\mathrm{b}\mathrm{b}) $ channels (lower). The shaded area depicts a veto region excluded from the analysis to minimize the event overlap with dedicated searches in the VV decay channel. Figures from Ref. [110]. 
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Figure 16a:
Search for $ \mathrm{X}\to\mathrm{V}\mathrm{H}(\mathrm{b}\mathrm{b}) $: Distributions of (left) the jet soft drop mass of a boosted Higgs boson candidate, labeled $ m_{\text{j}\mathrm{H}} $, and (right) the mass or transverse mass of the X resonance candidate, labeled $ m_{\mathrm{X}} $ and $ m_{\mathrm{X}}^{\mathrm{T}} $, respectively, in the $ \mathrm{Z}(\ell\ell)\mathrm{H}(\mathrm{b}\mathrm{b}) $ (upper) and $ \mathrm{Z}(\nu\nu)\mathrm{H}(\mathrm{b}\mathrm{b}) $ channels (lower). The shaded area depicts a veto region excluded from the analysis to minimize the event overlap with dedicated searches in the VV decay channel. Figures from Ref. [110]. 
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Figure 16b:
Search for $ \mathrm{X}\to\mathrm{V}\mathrm{H}(\mathrm{b}\mathrm{b}) $: Distributions of (left) the jet soft drop mass of a boosted Higgs boson candidate, labeled $ m_{\text{j}\mathrm{H}} $, and (right) the mass or transverse mass of the X resonance candidate, labeled $ m_{\mathrm{X}} $ and $ m_{\mathrm{X}}^{\mathrm{T}} $, respectively, in the $ \mathrm{Z}(\ell\ell)\mathrm{H}(\mathrm{b}\mathrm{b}) $ (upper) and $ \mathrm{Z}(\nu\nu)\mathrm{H}(\mathrm{b}\mathrm{b}) $ channels (lower). The shaded area depicts a veto region excluded from the analysis to minimize the event overlap with dedicated searches in the VV decay channel. Figures from Ref. [110]. 
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Figure 16c:
Search for $ \mathrm{X}\to\mathrm{V}\mathrm{H}(\mathrm{b}\mathrm{b}) $: Distributions of (left) the jet soft drop mass of a boosted Higgs boson candidate, labeled $ m_{\text{j}\mathrm{H}} $, and (right) the mass or transverse mass of the X resonance candidate, labeled $ m_{\mathrm{X}} $ and $ m_{\mathrm{X}}^{\mathrm{T}} $, respectively, in the $ \mathrm{Z}(\ell\ell)\mathrm{H}(\mathrm{b}\mathrm{b}) $ (upper) and $ \mathrm{Z}(\nu\nu)\mathrm{H}(\mathrm{b}\mathrm{b}) $ channels (lower). The shaded area depicts a veto region excluded from the analysis to minimize the event overlap with dedicated searches in the VV decay channel. Figures from Ref. [110]. 
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Figure 16d:
Search for $ \mathrm{X}\to\mathrm{V}\mathrm{H}(\mathrm{b}\mathrm{b}) $: Distributions of (left) the jet soft drop mass of a boosted Higgs boson candidate, labeled $ m_{\text{j}\mathrm{H}} $, and (right) the mass or transverse mass of the X resonance candidate, labeled $ m_{\mathrm{X}} $ and $ m_{\mathrm{X}}^{\mathrm{T}} $, respectively, in the $ \mathrm{Z}(\ell\ell)\mathrm{H}(\mathrm{b}\mathrm{b}) $ (upper) and $ \mathrm{Z}(\nu\nu)\mathrm{H}(\mathrm{b}\mathrm{b}) $ channels (lower). The shaded area depicts a veto region excluded from the analysis to minimize the event overlap with dedicated searches in the VV decay channel. Figures from Ref. [110]. 
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Figure 17:
Search for $ \mathrm{X}\to\mathrm{V} $ (qq) $ \mathrm{H}(\mathrm{b}\mathrm{b}) $: Distributions of (left) the soft drop mass $ m_{\mathrm{SD}} $ variable, labelled as $ m_{\text{jet1}}^{\text{AK8}} $, and (right) the dijet mass $ m_{\mathrm{jj}}^{\mathrm{AK8}} $ in the $ \mathrm{V}(\mathrm{q}\mathrm{q})\mathrm{H}(\mathrm{b}\mathrm{b}) $ channel [111]. The individual contributions of the background model are shown by open histograms with different colours and line styles. The signal of a Z' boson with a mass of 3 TeV decaying via $ \mathrm{Z}\to\text{qq} $ and $ \mathrm{H}\to\mathrm{b}\mathrm{b} $ is also shown, by a green filled histogram. Figure from Ref. [111]. 
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Figure 17a:
Search for $ \mathrm{X}\to\mathrm{V} $ (qq) $ \mathrm{H}(\mathrm{b}\mathrm{b}) $: Distributions of (left) the soft drop mass $ m_{\mathrm{SD}} $ variable, labelled as $ m_{\text{jet1}}^{\text{AK8}} $, and (right) the dijet mass $ m_{\mathrm{jj}}^{\mathrm{AK8}} $ in the $ \mathrm{V}(\mathrm{q}\mathrm{q})\mathrm{H}(\mathrm{b}\mathrm{b}) $ channel [111]. The individual contributions of the background model are shown by open histograms with different colours and line styles. The signal of a Z' boson with a mass of 3 TeV decaying via $ \mathrm{Z}\to\text{qq} $ and $ \mathrm{H}\to\mathrm{b}\mathrm{b} $ is also shown, by a green filled histogram. Figure from Ref. [111]. 
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Figure 17b:
Search for $ \mathrm{X}\to\mathrm{V} $ (qq) $ \mathrm{H}(\mathrm{b}\mathrm{b}) $: Distributions of (left) the soft drop mass $ m_{\mathrm{SD}} $ variable, labelled as $ m_{\text{jet1}}^{\text{AK8}} $, and (right) the dijet mass $ m_{\mathrm{jj}}^{\mathrm{AK8}} $ in the $ \mathrm{V}(\mathrm{q}\mathrm{q})\mathrm{H}(\mathrm{b}\mathrm{b}) $ channel [111]. The individual contributions of the background model are shown by open histograms with different colours and line styles. The signal of a Z' boson with a mass of 3 TeV decaying via $ \mathrm{Z}\to\text{qq} $ and $ \mathrm{H}\to\mathrm{b}\mathrm{b} $ is also shown, by a green filled histogram. Figure from Ref. [111]. 
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Figure 18:
Search for $ \mathrm{X}\to\mathrm{H}(\mathrm{b}\mathrm{b})\mathrm{H}(\mathrm{W}\mathrm{W}) $: Distributions of the DNN output for events in the signal nodes of the (upper) SL and (lower) DL categories of the $ \mathrm{H}(\mathrm{b}\mathrm{b})\mathrm{H}(\mathrm{W} \mathrm{W}) $ analysis based on merged and resolved jets [112]. The distributions for a signal of a resonant radion with a mass of 400 GeV is also shown, by an open red histogram. Figure from Ref. [112]. 
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Figure 18a:
Search for $ \mathrm{X}\to\mathrm{H}(\mathrm{b}\mathrm{b})\mathrm{H}(\mathrm{W}\mathrm{W}) $: Distributions of the DNN output for events in the signal nodes of the (upper) SL and (lower) DL categories of the $ \mathrm{H}(\mathrm{b}\mathrm{b})\mathrm{H}(\mathrm{W} \mathrm{W}) $ analysis based on merged and resolved jets [112]. The distributions for a signal of a resonant radion with a mass of 400 GeV is also shown, by an open red histogram. Figure from Ref. [112]. 
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Figure 18b:
Search for $ \mathrm{X}\to\mathrm{H}(\mathrm{b}\mathrm{b})\mathrm{H}(\mathrm{W}\mathrm{W}) $: Distributions of the DNN output for events in the signal nodes of the (upper) SL and (lower) DL categories of the $ \mathrm{H}(\mathrm{b}\mathrm{b})\mathrm{H}(\mathrm{W} \mathrm{W}) $ analysis based on merged and resolved jets [112]. The distributions for a signal of a resonant radion with a mass of 400 GeV is also shown, by an open red histogram. Figure from Ref. [112]. 
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Figure 19:
Search for $ \mathrm{X}\to\mathrm{H}(\mathrm{b}\mathrm{b})\mathrm{H}(\mathrm{W}\mathrm{W}) $: Distributions of the $ m_{{\mathrm{H}\mathrm{H}}} $ variable, in the (left) SL and (right) DL categories of the $ \mathrm{H}(\mathrm{b}\mathrm{b})\mathrm{H}(\mathrm{W}\mathrm{W}) $ analysis with merged jets [113]. Expected signal distributions from a spin0 resonance with a mass of 1 or 3 TeV are also shown, by the open green and blue histograms. Figure from Ref. [113]. 
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Figure 19a:
Search for $ \mathrm{X}\to\mathrm{H}(\mathrm{b}\mathrm{b})\mathrm{H}(\mathrm{W}\mathrm{W}) $: Distributions of the $ m_{{\mathrm{H}\mathrm{H}}} $ variable, in the (left) SL and (right) DL categories of the $ \mathrm{H}(\mathrm{b}\mathrm{b})\mathrm{H}(\mathrm{W}\mathrm{W}) $ analysis with merged jets [113]. Expected signal distributions from a spin0 resonance with a mass of 1 or 3 TeV are also shown, by the open green and blue histograms. Figure from Ref. [113]. 
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Figure 19b:
Search for $ \mathrm{X}\to\mathrm{H}(\mathrm{b}\mathrm{b})\mathrm{H}(\mathrm{W}\mathrm{W}) $: Distributions of the $ m_{{\mathrm{H}\mathrm{H}}} $ variable, in the (left) SL and (right) DL categories of the $ \mathrm{H}(\mathrm{b}\mathrm{b})\mathrm{H}(\mathrm{W}\mathrm{W}) $ analysis with merged jets [113]. Expected signal distributions from a spin0 resonance with a mass of 1 or 3 TeV are also shown, by the open green and blue histograms. Figure from Ref. [113]. 
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Figure 20:
Search for $ \mathrm{X}\to\mathrm{H}\mathrm{H} $ in multilepton final states: Distributions of the BDT classifier output for events in the (left) 2 $ \ell\text{ss} $ and (right) 3 $ \ell $ categories of the $ \mathrm{H}(\mathrm{W}\mathrm{W}+\tau\tau)\mathrm{H}(\mathrm{W}\mathrm{W}+\tau\tau) $ analysis in multilepton final states [114]. The expected signal for a spin2 resonance with a mass of 750 GeV resonant HH signal is shown, by the open dashed histogram. The signal is normalized to a a cross section of 1\unitpb. The distributions of the estimated background processes and corresponding uncertainties are shown after a fit of the signal plus background hypothesis to the data. Figure from Ref. [114]. 
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Figure 20a:
Search for $ \mathrm{X}\to\mathrm{H}\mathrm{H} $ in multilepton final states: Distributions of the BDT classifier output for events in the (left) 2 $ \ell\text{ss} $ and (right) 3 $ \ell $ categories of the $ \mathrm{H}(\mathrm{W}\mathrm{W}+\tau\tau)\mathrm{H}(\mathrm{W}\mathrm{W}+\tau\tau) $ analysis in multilepton final states [114]. The expected signal for a spin2 resonance with a mass of 750 GeV resonant HH signal is shown, by the open dashed histogram. The signal is normalized to a a cross section of 1\unitpb. The distributions of the estimated background processes and corresponding uncertainties are shown after a fit of the signal plus background hypothesis to the data. Figure from Ref. [114]. 
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Figure 20b:
Search for $ \mathrm{X}\to\mathrm{H}\mathrm{H} $ in multilepton final states: Distributions of the BDT classifier output for events in the (left) 2 $ \ell\text{ss} $ and (right) 3 $ \ell $ categories of the $ \mathrm{H}(\mathrm{W}\mathrm{W}+\tau\tau)\mathrm{H}(\mathrm{W}\mathrm{W}+\tau\tau) $ analysis in multilepton final states [114]. The expected signal for a spin2 resonance with a mass of 750 GeV resonant HH signal is shown, by the open dashed histogram. The signal is normalized to a a cross section of 1\unitpb. The distributions of the estimated background processes and corresponding uncertainties are shown after a fit of the signal plus background hypothesis to the data. Figure from Ref. [114]. 
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Figure 21:
Search for $ \mathrm{X}\to{\mathrm{Y}}(\mathrm{b}\mathrm{b})\mathrm{H}(\tau\tau) $: Distributions of the NN output scores $ y_{i} $, in different event categories after NN classification, based on a training for a resonance X with $ m_{\mathrm{X}}= $ 500 GeV and a resonance Y with 100 $ \leq m_{{\mathrm{Y}}} < $ 150 GeV in the $ \mathrm{e}\tau_\mathrm{h} $ final state of the $ \mathrm{H}(\tau\tau){\mathrm{Y}}(\mathrm{b}\mathrm{b}) $ analysis [115]. Shown are the (left) $ \tau\tau $ and (right) signal categories. For these figures, the data of all years have been combined. The uncertainty bands correspond to the combination of statistical and systematic uncertainties after the fit of the signal plus background hypothesis for $ m_{\mathrm{X}}= $ 500 GeV and $ m_{{\mathrm{Y}}}= $ 110 GeV to the data. In the lower panels of the figures the (left) purity and (right) fraction of the expected signal over background yields for a signal with a cross section of 200 fb, as well as the ratio of the obtained yields in data over the expectation based on only the background model, are shown. Figure from Ref. [115]. 
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Figure 21a:
Search for $ \mathrm{X}\to{\mathrm{Y}}(\mathrm{b}\mathrm{b})\mathrm{H}(\tau\tau) $: Distributions of the NN output scores $ y_{i} $, in different event categories after NN classification, based on a training for a resonance X with $ m_{\mathrm{X}}= $ 500 GeV and a resonance Y with 100 $ \leq m_{{\mathrm{Y}}} < $ 150 GeV in the $ \mathrm{e}\tau_\mathrm{h} $ final state of the $ \mathrm{H}(\tau\tau){\mathrm{Y}}(\mathrm{b}\mathrm{b}) $ analysis [115]. Shown are the (left) $ \tau\tau $ and (right) signal categories. For these figures, the data of all years have been combined. The uncertainty bands correspond to the combination of statistical and systematic uncertainties after the fit of the signal plus background hypothesis for $ m_{\mathrm{X}}= $ 500 GeV and $ m_{{\mathrm{Y}}}= $ 110 GeV to the data. In the lower panels of the figures the (left) purity and (right) fraction of the expected signal over background yields for a signal with a cross section of 200 fb, as well as the ratio of the obtained yields in data over the expectation based on only the background model, are shown. Figure from Ref. [115]. 
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Figure 21b:
Search for $ \mathrm{X}\to{\mathrm{Y}}(\mathrm{b}\mathrm{b})\mathrm{H}(\tau\tau) $: Distributions of the NN output scores $ y_{i} $, in different event categories after NN classification, based on a training for a resonance X with $ m_{\mathrm{X}}= $ 500 GeV and a resonance Y with 100 $ \leq m_{{\mathrm{Y}}} < $ 150 GeV in the $ \mathrm{e}\tau_\mathrm{h} $ final state of the $ \mathrm{H}(\tau\tau){\mathrm{Y}}(\mathrm{b}\mathrm{b}) $ analysis [115]. Shown are the (left) $ \tau\tau $ and (right) signal categories. For these figures, the data of all years have been combined. The uncertainty bands correspond to the combination of statistical and systematic uncertainties after the fit of the signal plus background hypothesis for $ m_{\mathrm{X}}= $ 500 GeV and $ m_{{\mathrm{Y}}}= $ 110 GeV to the data. In the lower panels of the figures the (left) purity and (right) fraction of the expected signal over background yields for a signal with a cross section of 200 fb, as well as the ratio of the obtained yields in data over the expectation based on only the background model, are shown. Figure from Ref. [115]. 
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Figure 22:
Search for $ \mathrm{X}\to{\mathrm{Y}} $ (bb) $ \mathrm{H}(\gamma\gamma) $: Marginal distributions of the (left) $ m_{\gamma\gamma} $ and (right) $ m_{\mathrm{jj}} $ variables, in the highpurity SR (labeled ``CAT 0'') of the $ {\mathrm{Y}}(\mathrm{b}\mathrm{b})\mathrm{H}(\gamma\gamma) $ analysis [116]. The figure is shown, for a hypothesis of $ m_{\mathrm{X}}= $ 650 GeV and $ m_{{\mathrm{Y}}}= $ 90 GeV, for which the largest excess of events over the background model is observed. In the lower panels, the numbers of backgroundsubtracted events are shown after the fit of the background model to the data. Figure from Ref. [116]. 
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Figure 22a:
Search for $ \mathrm{X}\to{\mathrm{Y}} $ (bb) $ \mathrm{H}(\gamma\gamma) $: Marginal distributions of the (left) $ m_{\gamma\gamma} $ and (right) $ m_{\mathrm{jj}} $ variables, in the highpurity SR (labeled ``CAT 0'') of the $ {\mathrm{Y}}(\mathrm{b}\mathrm{b})\mathrm{H}(\gamma\gamma) $ analysis [116]. The figure is shown, for a hypothesis of $ m_{\mathrm{X}}= $ 650 GeV and $ m_{{\mathrm{Y}}}= $ 90 GeV, for which the largest excess of events over the background model is observed. In the lower panels, the numbers of backgroundsubtracted events are shown after the fit of the background model to the data. Figure from Ref. [116]. 
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Figure 22b:
Search for $ \mathrm{X}\to{\mathrm{Y}} $ (bb) $ \mathrm{H}(\gamma\gamma) $: Marginal distributions of the (left) $ m_{\gamma\gamma} $ and (right) $ m_{\mathrm{jj}} $ variables, in the highpurity SR (labeled ``CAT 0'') of the $ {\mathrm{Y}}(\mathrm{b}\mathrm{b})\mathrm{H}(\gamma\gamma) $ analysis [116]. The figure is shown, for a hypothesis of $ m_{\mathrm{X}}= $ 650 GeV and $ m_{{\mathrm{Y}}}= $ 90 GeV, for which the largest excess of events over the background model is observed. In the lower panels, the numbers of backgroundsubtracted events are shown after the fit of the background model to the data. Figure from Ref. [116]. 
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Figure 23:
Search for $ \mathrm{X}\to{\mathrm{Y}}(\mathrm{b}\mathrm{b})\mathrm{H}(\mathrm{b}\mathrm{b}) $: Distributions of the (left) softdrop mass of the boosted Y candidate, labeled $ M^{\mathrm{Y}}_\text{J} $, and (right) the dijet mass of the Y and H candidates, $ M_\text{JJ} $, in the highpurity SR of the $ {\mathrm{Y}}(\mathrm{b}\mathrm{b})\mathrm{H}(\mathrm{b}\mathrm{b}) $ analysis with two merged $ \mathrm{b}\mathrm{b} $ jets [117]. The distributions as expected for signals with three different values of $ m_{\mathrm{X}} $ and $ m_{{\mathrm{Y}}} $ (labeled $ M^\mathrm{X} $ and $ M^{\mathrm{Y}} $) are also shown. In the lower panels the statistical pull in each bin is displayed. Figure from Ref. [117]. 
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Figure 23a:
Search for $ \mathrm{X}\to{\mathrm{Y}}(\mathrm{b}\mathrm{b})\mathrm{H}(\mathrm{b}\mathrm{b}) $: Distributions of the (left) softdrop mass of the boosted Y candidate, labeled $ M^{\mathrm{Y}}_\text{J} $, and (right) the dijet mass of the Y and H candidates, $ M_\text{JJ} $, in the highpurity SR of the $ {\mathrm{Y}}(\mathrm{b}\mathrm{b})\mathrm{H}(\mathrm{b}\mathrm{b}) $ analysis with two merged $ \mathrm{b}\mathrm{b} $ jets [117]. The distributions as expected for signals with three different values of $ m_{\mathrm{X}} $ and $ m_{{\mathrm{Y}}} $ (labeled $ M^\mathrm{X} $ and $ M^{\mathrm{Y}} $) are also shown. In the lower panels the statistical pull in each bin is displayed. Figure from Ref. [117]. 
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Figure 23b:
Search for $ \mathrm{X}\to{\mathrm{Y}}(\mathrm{b}\mathrm{b})\mathrm{H}(\mathrm{b}\mathrm{b}) $: Distributions of the (left) softdrop mass of the boosted Y candidate, labeled $ M^{\mathrm{Y}}_\text{J} $, and (right) the dijet mass of the Y and H candidates, $ M_\text{JJ} $, in the highpurity SR of the $ {\mathrm{Y}}(\mathrm{b}\mathrm{b})\mathrm{H}(\mathrm{b}\mathrm{b}) $ analysis with two merged $ \mathrm{b}\mathrm{b} $ jets [117]. The distributions as expected for signals with three different values of $ m_{\mathrm{X}} $ and $ m_{{\mathrm{Y}}} $ (labeled $ M^\mathrm{X} $ and $ M^{\mathrm{Y}} $) are also shown. In the lower panels the statistical pull in each bin is displayed. Figure from Ref. [117]. 
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Figure 24:
Search for $ \mathrm{X}\to\mathrm{Z}\mathrm{H} $: Observed and expected 95% CL upper limits on the product of the cross section $ \sigma $ for the production of an $ {\mathrm{A}} $ boson, via gluongluon fusion and the branching fraction $ \mathcal{B} $ for the $ {\mathrm{A}}\to\mathrm{Z}\mathrm{H} $ decay. The limits are given in \unitpb as functions of $ m_{{\mathrm{A}}} $. The markers connected with solid lines (dashed lines) indicate the observed (expected) limits. The green (magenta) lines refer to the $ \mathrm{Z}(\ell\ell+\nu\nu)\mathrm{H}(\mathrm{b}\mathrm{b}) $ [108] ($ \mathrm{Z}(\ell\ell)\mathrm{H}(\tau\tau ) $ [107]) analysis. The red and blue solid lines indicate the product $ \sigma\mathcal{B} $ as expected by the 2HDM Type I and Type II models, respectively, for the parameters $ \tan\beta= $ 3 and $ \cos(\beta\alpha)= $ 0.1. The shaded areas associated with these predictions indicate the corresponding model uncertainties. The results and model predictions have been adapted from Refs. [108,107]. 
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Figure 25:
Search for $ \mathrm{X}\to\mathrm{W}\mathrm{H} $: Observed and expected 95% CL upper limits on the product of the cross section $ \sigma $ for the production of a W' spin1 resonance, via (left) DY production or (right) vector boson fusion and the branching fraction $ \mathcal{B} $ for the $ \mathrm{W^{'}}\to\mathrm{W}\mathrm{H} $ decay. The solid lines represent the observed and the dotted lines the expected limits. The theory predictions from the heavy vector triplet models A, B, and C are also shown. 
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Figure 25a:
Search for $ \mathrm{X}\to\mathrm{W}\mathrm{H} $: Observed and expected 95% CL upper limits on the product of the cross section $ \sigma $ for the production of a W' spin1 resonance, via (left) DY production or (right) vector boson fusion and the branching fraction $ \mathcal{B} $ for the $ \mathrm{W^{'}}\to\mathrm{W}\mathrm{H} $ decay. The solid lines represent the observed and the dotted lines the expected limits. The theory predictions from the heavy vector triplet models A, B, and C are also shown. 
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Figure 25b:
Search for $ \mathrm{X}\to\mathrm{W}\mathrm{H} $: Observed and expected 95% CL upper limits on the product of the cross section $ \sigma $ for the production of a W' spin1 resonance, via (left) DY production or (right) vector boson fusion and the branching fraction $ \mathcal{B} $ for the $ \mathrm{W^{'}}\to\mathrm{W}\mathrm{H} $ decay. The solid lines represent the observed and the dotted lines the expected limits. The theory predictions from the heavy vector triplet models A, B, and C are also shown. 
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Figure 26:
Search for $ \mathrm{X}\to\mathrm{Z}\mathrm{H} $: Observed and expected 95% CL upper limits on the product of the cross section $ \sigma $ for the production of a Z' spin1 resonance, via (left) DY production or (right) vector boson fusion and the branching fraction $ \mathcal{B} $ for the $ \mathrm{Z}^{'}\to\mathrm{Z}\mathrm{H} $ decay. The solid lines represent the observed and the dotted lines the expected limits. The theory predictions from the heavy vector triplet models A, B and C are also shown. 
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Figure 26a:
Search for $ \mathrm{X}\to\mathrm{Z}\mathrm{H} $: Observed and expected 95% CL upper limits on the product of the cross section $ \sigma $ for the production of a Z' spin1 resonance, via (left) DY production or (right) vector boson fusion and the branching fraction $ \mathcal{B} $ for the $ \mathrm{Z}^{'}\to\mathrm{Z}\mathrm{H} $ decay. The solid lines represent the observed and the dotted lines the expected limits. The theory predictions from the heavy vector triplet models A, B and C are also shown. 
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Figure 26b:
Search for $ \mathrm{X}\to\mathrm{Z}\mathrm{H} $: Observed and expected 95% CL upper limits on the product of the cross section $ \sigma $ for the production of a Z' spin1 resonance, via (left) DY production or (right) vector boson fusion and the branching fraction $ \mathcal{B} $ for the $ \mathrm{Z}^{'}\to\mathrm{Z}\mathrm{H} $ decay. The solid lines represent the observed and the dotted lines the expected limits. The theory predictions from the heavy vector triplet models A, B and C are also shown. 
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Figure 27:
Search for $ \mathrm{X}\to\mathrm{H}\mathrm{H} $/$ {\mathrm{G}} \to\mathrm{H}\mathrm{H} $: Observed and expected 95% CL upper limits on the product of the cross section $ \sigma $ for the production of a (left) spin0 resonance X and (right) a spin2 resonance G, via gluongluon fusion and the branching fraction $ \mathcal{B} $ for the corresponding HH decay. The results of the individual analyses presented in this report and the result of their combined likelihood analysis are shown. The observed limits are indicated by markers connected with solid lines and the expected limits by dashed lines. 
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Figure 27a:
Search for $ \mathrm{X}\to\mathrm{H}\mathrm{H} $/$ {\mathrm{G}} \to\mathrm{H}\mathrm{H} $: Observed and expected 95% CL upper limits on the product of the cross section $ \sigma $ for the production of a (left) spin0 resonance X and (right) a spin2 resonance G, via gluongluon fusion and the branching fraction $ \mathcal{B} $ for the corresponding HH decay. The results of the individual analyses presented in this report and the result of their combined likelihood analysis are shown. The observed limits are indicated by markers connected with solid lines and the expected limits by dashed lines. 
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Figure 27b:
Search for $ \mathrm{X}\to\mathrm{H}\mathrm{H} $/$ {\mathrm{G}} \to\mathrm{H}\mathrm{H} $: Observed and expected 95% CL upper limits on the product of the cross section $ \sigma $ for the production of a (left) spin0 resonance X and (right) a spin2 resonance G, via gluongluon fusion and the branching fraction $ \mathcal{B} $ for the corresponding HH decay. The results of the individual analyses presented in this report and the result of their combined likelihood analysis are shown. The observed limits are indicated by markers connected with solid lines and the expected limits by dashed lines. 
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Figure 28:
Search for $ \mathrm{X}\to\mathrm{H}\mathrm{H} $/$ {\mathrm{G}} \to\mathrm{H}\mathrm{H} $: Observed and expected 95% CL upper limits on the product of the cross section $ \sigma $ for the production of a (left) spin0 resonance X and (right) a spin2 resonance G, via gluongluon fusion, and the branching fraction $ \mathcal{B} $ for the corresponding HH decay, as obtained from the combined likelihood analysis of all contributing individual analyses presented in this report and shown in Fig. 27. In addition to the limit from the combined likelihood analysis the 68 and 95% central intervals for the expected upper limits in the absence of a signal are shown as coloured bands. 
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Figure 28a:
Search for $ \mathrm{X}\to\mathrm{H}\mathrm{H} $/$ {\mathrm{G}} \to\mathrm{H}\mathrm{H} $: Observed and expected 95% CL upper limits on the product of the cross section $ \sigma $ for the production of a (left) spin0 resonance X and (right) a spin2 resonance G, via gluongluon fusion, and the branching fraction $ \mathcal{B} $ for the corresponding HH decay, as obtained from the combined likelihood analysis of all contributing individual analyses presented in this report and shown in Fig. 27. In addition to the limit from the combined likelihood analysis the 68 and 95% central intervals for the expected upper limits in the absence of a signal are shown as coloured bands. 
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Figure 28b:
Search for $ \mathrm{X}\to\mathrm{H}\mathrm{H} $/$ {\mathrm{G}} \to\mathrm{H}\mathrm{H} $: Observed and expected 95% CL upper limits on the product of the cross section $ \sigma $ for the production of a (left) spin0 resonance X and (right) a spin2 resonance G, via gluongluon fusion, and the branching fraction $ \mathcal{B} $ for the corresponding HH decay, as obtained from the combined likelihood analysis of all contributing individual analyses presented in this report and shown in Fig. 27. In addition to the limit from the combined likelihood analysis the 68 and 95% central intervals for the expected upper limits in the absence of a signal are shown as coloured bands. 
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Figure 29:
Search for $ \mathrm{X}\to{\mathrm{Y}}\mathrm{H} $: Observed and expected upper limits, at 95% CL, on the product of the cross section $ \sigma $ for the production of a resonance X via gluongluon fusion and the branching fraction $ \mathcal{B} $ for the $ \mathrm{X}\to{\mathrm{Y}}(\mathrm{b}\mathrm{b}) \mathrm{H} $ decay. For the branching fractions of the $ \mathrm{H}\to\tau\tau $, $ \mathrm{H}\to\gamma\gamma $ and $ \mathrm{H}\to\mathrm{b}\mathrm{b} $ decays, the SM values are assumed. The results derived from the individual analyses presented in this report and the result of their combined likelihood analysis are shown as functions of $ m_{{\mathrm{Y}}} $ and $ m_{\mathrm{X}} $ for $ m_{\mathrm{X}}\le $ 1 TeV. Observed limits are indicated by markers connected with solid lines, expected limits by dashed lines. For presentation purposes, the limits have been scaled in successive steps by two orders of magnitude, each. For each set of graphs, a black arrow points to the $ m_{\mathrm{X}} $ related legend. 
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Figure 30:
Search for $ \mathrm{X}\to{\mathrm{Y}}\mathrm{H} $: Observed and expected upper limits, at 95% CL, on the product of the cross section $ \sigma $ for the production of a resonance X via gluongluon fusion and the branching fraction $ \mathcal{B} $ for the $ \mathrm{X}\to{\mathrm{Y}}(\mathrm{b}\mathrm{b}) \mathrm{H} $ decay. For the branching fractions of the $ \mathrm{H}\to\tau\tau $ and $ \mathrm{H}\to\mathrm{b}\mathrm{b} $ decays, the SM values are assumed. The results derived from the individual analyses presented in this report and the result of their combined likelihood analysis are shown as functions of $ m_{{\mathrm{Y}}} $ and $ m_{\mathrm{X}} $ for $ m_{\mathrm{X}}\ge $ 1.2 TeV. Observed limits are indicated by markers connected with solid lines, expected limits by dashed lines. For presentation purposes, the limits have been scaled in successive steps by four orders of magnitude, each. For each set of graphs, a black arrow points to the $ m_{\mathrm{X}} $ related legend. 
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Figure 31:
Interpretation of the results from the searches for the $ \mathrm{X}\to{\mathrm{H}\mathrm{H}} $ decay, in the hMSSM model. In the upper part of the figure, the observed and expected exclusion contours at 95% CL, in the ($ m_{{\mathrm{A}}} $, $ \tan\beta $) plane, from the individual HH analyses presented in this report and their combined likelihood analysis are shown. In the lower part of the figure, a comparison of the region excluded by the combined likelihood analysis shown in the upper part of the figure with selected results from other searches for the production of heavy scalar bosons in the hMSSM, in $ \tau\tau $ [64], $ \mathrm{t} \overline{\mathrm{t}} $ [169] and WW [170] decays is shown. Also shown, are the results from one representative search for $ {\mathrm{A}}\to\mathrm{Z}\mathrm{H} $ [107] and indirect constraints obtained from measurements of the coupling strength of the observed H boson [47]. Results not marked by a club symbol are based on an integrated luminosity of 35.9 fb$^{1}$. 
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Figure 31a:
Interpretation of the results from the searches for the $ \mathrm{X}\to{\mathrm{H}\mathrm{H}} $ decay, in the hMSSM model. In the upper part of the figure, the observed and expected exclusion contours at 95% CL, in the ($ m_{{\mathrm{A}}} $, $ \tan\beta $) plane, from the individual HH analyses presented in this report and their combined likelihood analysis are shown. In the lower part of the figure, a comparison of the region excluded by the combined likelihood analysis shown in the upper part of the figure with selected results from other searches for the production of heavy scalar bosons in the hMSSM, in $ \tau\tau $ [64], $ \mathrm{t} \overline{\mathrm{t}} $ [169] and WW [170] decays is shown. Also shown, are the results from one representative search for $ {\mathrm{A}}\to\mathrm{Z}\mathrm{H} $ [107] and indirect constraints obtained from measurements of the coupling strength of the observed H boson [47]. Results not marked by a club symbol are based on an integrated luminosity of 35.9 fb$^{1}$. 
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Figure 31b:
Interpretation of the results from the searches for the $ \mathrm{X}\to{\mathrm{H}\mathrm{H}} $ decay, in the hMSSM model. In the upper part of the figure, the observed and expected exclusion contours at 95% CL, in the ($ m_{{\mathrm{A}}} $, $ \tan\beta $) plane, from the individual HH analyses presented in this report and their combined likelihood analysis are shown. In the lower part of the figure, a comparison of the region excluded by the combined likelihood analysis shown in the upper part of the figure with selected results from other searches for the production of heavy scalar bosons in the hMSSM, in $ \tau\tau $ [64], $ \mathrm{t} \overline{\mathrm{t}} $ [169] and WW [170] decays is shown. Also shown, are the results from one representative search for $ {\mathrm{A}}\to\mathrm{Z}\mathrm{H} $ [107] and indirect constraints obtained from measurements of the coupling strength of the observed H boson [47]. Results not marked by a club symbol are based on an integrated luminosity of 35.9 fb$^{1}$. 
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Figure 32:
Interpretation of the results from the searches for the $ \mathrm{X}\to{\mathrm{H}\mathrm{H}} $ decay, in the $ M^{125}_{\text{h,EFT}} $ benchmark scenario. In the upper part of the figure, the observed and expected exclusion contours at 95% CL are shown, in the ($ m_{{\mathrm{A}}} $, $ \tan\beta $) plane from the individual HH analyses presented in this report and their combined likelihood analysis. In the lower part of the figure, a comparison of the region excluded by the combined likelihood analysis shown in the upper part of the figure with selected results from other searches for the production of heavy scalar bosons in the $ M^{125}_{\text{h,EFT}} $ scenario, in $ \tau\tau $ [64], $ \mathrm{t} \overline{\mathrm{t}} $ [169] and WW [170] decays is shown. Also shown, are the results from one representative search for $ {\mathrm{A}}\to\mathrm{Z}\mathrm{H} $ [107]. The parameter region in which the mass of the lightest MSSM Higgs boson does not coincide with 125 GeV within a 3 GeV margin is indicated by the dark hatched area. Results not marked by a club symbol are based on an integrated luminosity of 35.9 fb$^{1}$. 
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Figure 32a:
Interpretation of the results from the searches for the $ \mathrm{X}\to{\mathrm{H}\mathrm{H}} $ decay, in the $ M^{125}_{\text{h,EFT}} $ benchmark scenario. In the upper part of the figure, the observed and expected exclusion contours at 95% CL are shown, in the ($ m_{{\mathrm{A}}} $, $ \tan\beta $) plane from the individual HH analyses presented in this report and their combined likelihood analysis. In the lower part of the figure, a comparison of the region excluded by the combined likelihood analysis shown in the upper part of the figure with selected results from other searches for the production of heavy scalar bosons in the $ M^{125}_{\text{h,EFT}} $ scenario, in $ \tau\tau $ [64], $ \mathrm{t} \overline{\mathrm{t}} $ [169] and WW [170] decays is shown. Also shown, are the results from one representative search for $ {\mathrm{A}}\to\mathrm{Z}\mathrm{H} $ [107]. The parameter region in which the mass of the lightest MSSM Higgs boson does not coincide with 125 GeV within a 3 GeV margin is indicated by the dark hatched area. Results not marked by a club symbol are based on an integrated luminosity of 35.9 fb$^{1}$. 
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Figure 32b:
Interpretation of the results from the searches for the $ \mathrm{X}\to{\mathrm{H}\mathrm{H}} $ decay, in the $ M^{125}_{\text{h,EFT}} $ benchmark scenario. In the upper part of the figure, the observed and expected exclusion contours at 95% CL are shown, in the ($ m_{{\mathrm{A}}} $, $ \tan\beta $) plane from the individual HH analyses presented in this report and their combined likelihood analysis. In the lower part of the figure, a comparison of the region excluded by the combined likelihood analysis shown in the upper part of the figure with selected results from other searches for the production of heavy scalar bosons in the $ M^{125}_{\text{h,EFT}} $ scenario, in $ \tau\tau $ [64], $ \mathrm{t} \overline{\mathrm{t}} $ [169] and WW [170] decays is shown. Also shown, are the results from one representative search for $ {\mathrm{A}}\to\mathrm{Z}\mathrm{H} $ [107]. The parameter region in which the mass of the lightest MSSM Higgs boson does not coincide with 125 GeV within a 3 GeV margin is indicated by the dark hatched area. Results not marked by a club symbol are based on an integrated luminosity of 35.9 fb$^{1}$. 
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Figure 33:
Interpretation of the results of the $ {\mathrm{A}}\to\mathrm{Z}\mathrm{H}(\mathrm{b}\mathrm{b}) $ analysis [108], in the (upper left) Type I, (upper right) Type II, (lower left) flipped, and (lower right) leptonspecific 2HDM models. In each case observed and expected exclusion contours at 95% CL, in the plane defined by $ \cos(\beta\alpha) $ and $ \tan\beta $, are shown. The excluded regions are represented by the shaded gray areas. The 68 and 95% central intervals of the expected exclusion contours in the absence of a signal are indicated by the green and yellow bands. Contours are derived from the projection on the corresponding 2HDM parameter space for $ m_{{\mathrm{A}}} = $ 300 GeV. The regions of parameter space where the natural width of the $ {\mathrm{A}} $ boson $ \Gamma_{\mathrm{A}} $ is comparable to or larger than the experimental resolution and thus the narrowwidth approximation is not valid are represented by hatched gray areas. Figure from Ref. [108]. 
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Figure 33a:
Interpretation of the results of the $ {\mathrm{A}}\to\mathrm{Z}\mathrm{H}(\mathrm{b}\mathrm{b}) $ analysis [108], in the (upper left) Type I, (upper right) Type II, (lower left) flipped, and (lower right) leptonspecific 2HDM models. In each case observed and expected exclusion contours at 95% CL, in the plane defined by $ \cos(\beta\alpha) $ and $ \tan\beta $, are shown. The excluded regions are represented by the shaded gray areas. The 68 and 95% central intervals of the expected exclusion contours in the absence of a signal are indicated by the green and yellow bands. Contours are derived from the projection on the corresponding 2HDM parameter space for $ m_{{\mathrm{A}}} = $ 300 GeV. The regions of parameter space where the natural width of the $ {\mathrm{A}} $ boson $ \Gamma_{\mathrm{A}} $ is comparable to or larger than the experimental resolution and thus the narrowwidth approximation is not valid are represented by hatched gray areas. Figure from Ref. [108]. 
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Figure 33b:
Interpretation of the results of the $ {\mathrm{A}}\to\mathrm{Z}\mathrm{H}(\mathrm{b}\mathrm{b}) $ analysis [108], in the (upper left) Type I, (upper right) Type II, (lower left) flipped, and (lower right) leptonspecific 2HDM models. In each case observed and expected exclusion contours at 95% CL, in the plane defined by $ \cos(\beta\alpha) $ and $ \tan\beta $, are shown. The excluded regions are represented by the shaded gray areas. The 68 and 95% central intervals of the expected exclusion contours in the absence of a signal are indicated by the green and yellow bands. Contours are derived from the projection on the corresponding 2HDM parameter space for $ m_{{\mathrm{A}}} = $ 300 GeV. The regions of parameter space where the natural width of the $ {\mathrm{A}} $ boson $ \Gamma_{\mathrm{A}} $ is comparable to or larger than the experimental resolution and thus the narrowwidth approximation is not valid are represented by hatched gray areas. Figure from Ref. [108]. 
png pdf 
Figure 33c:
Interpretation of the results of the $ {\mathrm{A}}\to\mathrm{Z}\mathrm{H}(\mathrm{b}\mathrm{b}) $ analysis [108], in the (upper left) Type I, (upper right) Type II, (lower left) flipped, and (lower right) leptonspecific 2HDM models. In each case observed and expected exclusion contours at 95% CL, in the plane defined by $ \cos(\beta\alpha) $ and $ \tan\beta $, are shown. The excluded regions are represented by the shaded gray areas. The 68 and 95% central intervals of the expected exclusion contours in the absence of a signal are indicated by the green and yellow bands. Contours are derived from the projection on the corresponding 2HDM parameter space for $ m_{{\mathrm{A}}} = $ 300 GeV. The regions of parameter space where the natural width of the $ {\mathrm{A}} $ boson $ \Gamma_{\mathrm{A}} $ is comparable to or larger than the experimental resolution and thus the narrowwidth approximation is not valid are represented by hatched gray areas. Figure from Ref. [108]. 
png pdf 
Figure 33d:
Interpretation of the results of the $ {\mathrm{A}}\to\mathrm{Z}\mathrm{H}(\mathrm{b}\mathrm{b}) $ analysis [108], in the (upper left) Type I, (upper right) Type II, (lower left) flipped, and (lower right) leptonspecific 2HDM models. In each case observed and expected exclusion contours at 95% CL, in the plane defined by $ \cos(\beta\alpha) $ and $ \tan\beta $, are shown. The excluded regions are represented by the shaded gray areas. The 68 and 95% central intervals of the expected exclusion contours in the absence of a signal are indicated by the green and yellow bands. Contours are derived from the projection on the corresponding 2HDM parameter space for $ m_{{\mathrm{A}}} = $ 300 GeV. The regions of parameter space where the natural width of the $ {\mathrm{A}} $ boson $ \Gamma_{\mathrm{A}} $ is comparable to or larger than the experimental resolution and thus the narrowwidth approximation is not valid are represented by hatched gray areas. Figure from Ref. [108]. 
png pdf 
Figure 34:
(Upper left) Observed and (upper right) expected upper limits at 95% CL, on the product of the cross section $ \sigma $ for the production of a resonance X via gluongluon fusion and the branching fraction $ \mathcal{B} $ for the $ \mathrm{X}\to{\mathrm{Y}}(\mathrm{b}\mathrm{b})\mathrm{H} $ decay, as obtained from a combined likelihood analysis of the individual analyses presented in this report and shown in Fig. 29. The results are presented in a plane defined by $ m_{\mathrm{X}} $ and $ m_{{\mathrm{Y}}} $. The limits have been evaluated in discrete steps corresponding to the centers of the boxes. The numbers in the boxes are given in fb. The corresponding maximally allowed values of $ \sigma\mathcal{B} $ in the NMSSM are also shown for comparison (lower plot), as adapted from Ref. [193]. 
png pdf 
Figure 34a:
(Upper left) Observed and (upper right) expected upper limits at 95% CL, on the product of the cross section $ \sigma $ for the production of a resonance X via gluongluon fusion and the branching fraction $ \mathcal{B} $ for the $ \mathrm{X}\to{\mathrm{Y}}(\mathrm{b}\mathrm{b})\mathrm{H} $ decay, as obtained from a combined likelihood analysis of the individual analyses presented in this report and shown in Fig. 29. The results are presented in a plane defined by $ m_{\mathrm{X}} $ and $ m_{{\mathrm{Y}}} $. The limits have been evaluated in discrete steps corresponding to the centers of the boxes. The numbers in the boxes are given in fb. The corresponding maximally allowed values of $ \sigma\mathcal{B} $ in the NMSSM are also shown for comparison (lower plot), as adapted from Ref. [193]. 
png pdf 
Figure 34b:
(Upper left) Observed and (upper right) expected upper limits at 95% CL, on the product of the cross section $ \sigma $ for the production of a resonance X via gluongluon fusion and the branching fraction $ \mathcal{B} $ for the $ \mathrm{X}\to{\mathrm{Y}}(\mathrm{b}\mathrm{b})\mathrm{H} $ decay, as obtained from a combined likelihood analysis of the individual analyses presented in this report and shown in Fig. 29. The results are presented in a plane defined by $ m_{\mathrm{X}} $ and $ m_{{\mathrm{Y}}} $. The limits have been evaluated in discrete steps corresponding to the centers of the boxes. The numbers in the boxes are given in fb. The corresponding maximally allowed values of $ \sigma\mathcal{B} $ in the NMSSM are also shown for comparison (lower plot), as adapted from Ref. [193]. 
png pdf 
Figure 34c:
(Upper left) Observed and (upper right) expected upper limits at 95% CL, on the product of the cross section $ \sigma $ for the production of a resonance X via gluongluon fusion and the branching fraction $ \mathcal{B} $ for the $ \mathrm{X}\to{\mathrm{Y}}(\mathrm{b}\mathrm{b})\mathrm{H} $ decay, as obtained from a combined likelihood analysis of the individual analyses presented in this report and shown in Fig. 29. The results are presented in a plane defined by $ m_{\mathrm{X}} $ and $ m_{{\mathrm{Y}}} $. The limits have been evaluated in discrete steps corresponding to the centers of the boxes. The numbers in the boxes are given in fb. The corresponding maximally allowed values of $ \sigma\mathcal{B} $ in the NMSSM are also shown for comparison (lower plot), as adapted from Ref. [193]. 
png pdf 
Figure 35:
Observed and expected limits, at 95% CL, on the parameters of models with warped extra dimensions, as obtained from the $ \mathrm{X}\to\mathrm{H}\mathrm{H} $ analyses presented in this report and their combined likelihood analysis. Shown are lower limits (left) on the bulk radion ultraviolet cutoff parameter $ \Lambda_{\mathrm{R}} $, as a function of the radion mass $ m_{{\mathrm{R}} } $, and upper limits (right) on the parameter $ \tilde{k} $ of the spin2 bulk graviton G, as a function of $ m_{{\mathrm{G}} } $. Excluded areas are indicated by the direction of the hatching along the exclusion contours. 
png pdf 
Figure 35a:
Observed and expected limits, at 95% CL, on the parameters of models with warped extra dimensions, as obtained from the $ \mathrm{X}\to\mathrm{H}\mathrm{H} $ analyses presented in this report and their combined likelihood analysis. Shown are lower limits (left) on the bulk radion ultraviolet cutoff parameter $ \Lambda_{\mathrm{R}} $, as a function of the radion mass $ m_{{\mathrm{R}} } $, and upper limits (right) on the parameter $ \tilde{k} $ of the spin2 bulk graviton G, as a function of $ m_{{\mathrm{G}} } $. Excluded areas are indicated by the direction of the hatching along the exclusion contours. 
png pdf 
Figure 35b:
Observed and expected limits, at 95% CL, on the parameters of models with warped extra dimensions, as obtained from the $ \mathrm{X}\to\mathrm{H}\mathrm{H} $ analyses presented in this report and their combined likelihood analysis. Shown are lower limits (left) on the bulk radion ultraviolet cutoff parameter $ \Lambda_{\mathrm{R}} $, as a function of the radion mass $ m_{{\mathrm{R}} } $, and upper limits (right) on the parameter $ \tilde{k} $ of the spin2 bulk graviton G, as a function of $ m_{{\mathrm{G}} } $. Excluded areas are indicated by the direction of the hatching along the exclusion contours. 
png pdf 
Figure 36:
Observed and expected limits, at 95% CL, on the parameters of models with warped extra dimensions, as obtained from the combined likelihood analysis of the individual $ \mathrm{X}\to\mathrm{H}\mathrm{H} $ analyses presented in this report and shown in Fig. 35. The exclusion contours obtained from the combined likelihood analysis are compared to similar exclusions obtained from individual searches in the decays $ \mathrm{Z}(\ell\ell)\mathrm{Z}(\mathrm{q}\mathrm{q}/\nu\nu/\ell\ell) $ [195], $ \mathrm{W}(\ell\nu)\mathrm{W}(\ell\nu/\mathrm{q}\mathrm{q}) $ [170], $ \mathrm{W}(\ell\nu)\mathrm{W}(\mathrm{q}\mathrm{q}) $ [109], $ \mathrm{V}(\mathrm{q}\mathrm{q})\mathrm{V}(\mathrm{q}\mathrm{q}) $ [111], and $ \mathrm{Z}(\nu\nu)\mathrm{Z}(\mathrm{q}\mathrm{q}) $ [196], in case of the radion interpretation, and from individual searches in the decays $ \mathrm{Z}(\mathrm{q}\mathrm{q})\mathrm{Z}(\ell\ell) $ [197], $ \mathrm{V}(\mathrm{q}\mathrm{q})\mathrm{V}(\mathrm{q}\mathrm{q}) $ [111], $ \mathrm{Z}(\nu\nu)\mathrm{Z}(\mathrm{q}\mathrm{q}) $ [196], and $ \mathrm{W}(\ell\nu)\mathrm{W}(\mathrm{q}\mathrm{q}) $ [109], in the case of the graviton interpretation. Excluded areas are indicated by the direction of the hatching along the exclusion contours. 
png pdf 
Figure 36a:
Observed and expected limits, at 95% CL, on the parameters of models with warped extra dimensions, as obtained from the combined likelihood analysis of the individual $ \mathrm{X}\to\mathrm{H}\mathrm{H} $ analyses presented in this report and shown in Fig. 35. The exclusion contours obtained from the combined likelihood analysis are compared to similar exclusions obtained from individual searches in the decays $ \mathrm{Z}(\ell\ell)\mathrm{Z}(\mathrm{q}\mathrm{q}/\nu\nu/\ell\ell) $ [195], $ \mathrm{W}(\ell\nu)\mathrm{W}(\ell\nu/\mathrm{q}\mathrm{q}) $ [170], $ \mathrm{W}(\ell\nu)\mathrm{W}(\mathrm{q}\mathrm{q}) $ [109], $ \mathrm{V}(\mathrm{q}\mathrm{q})\mathrm{V}(\mathrm{q}\mathrm{q}) $ [111], and $ \mathrm{Z}(\nu\nu)\mathrm{Z}(\mathrm{q}\mathrm{q}) $ [196], in case of the radion interpretation, and from individual searches in the decays $ \mathrm{Z}(\mathrm{q}\mathrm{q})\mathrm{Z}(\ell\ell) $ [197], $ \mathrm{V}(\mathrm{q}\mathrm{q})\mathrm{V}(\mathrm{q}\mathrm{q}) $ [111], $ \mathrm{Z}(\nu\nu)\mathrm{Z}(\mathrm{q}\mathrm{q}) $ [196], and $ \mathrm{W}(\ell\nu)\mathrm{W}(\mathrm{q}\mathrm{q}) $ [109], in the case of the graviton interpretation. Excluded areas are indicated by the direction of the hatching along the exclusion contours. 
png pdf 
Figure 36b:
Observed and expected limits, at 95% CL, on the parameters of models with warped extra dimensions, as obtained from the combined likelihood analysis of the individual $ \mathrm{X}\to\mathrm{H}\mathrm{H} $ analyses presented in this report and shown in Fig. 35. The exclusion contours obtained from the combined likelihood analysis are compared to similar exclusions obtained from individual searches in the decays $ \mathrm{Z}(\ell\ell)\mathrm{Z}(\mathrm{q}\mathrm{q}/\nu\nu/\ell\ell) $ [195], $ \mathrm{W}(\ell\nu)\mathrm{W}(\ell\nu/\mathrm{q}\mathrm{q}) $ [170], $ \mathrm{W}(\ell\nu)\mathrm{W}(\mathrm{q}\mathrm{q}) $ [109], $ \mathrm{V}(\mathrm{q}\mathrm{q})\mathrm{V}(\mathrm{q}\mathrm{q}) $ [111], and $ \mathrm{Z}(\nu\nu)\mathrm{Z}(\mathrm{q}\mathrm{q}) $ [196], in case of the radion interpretation, and from individual searches in the decays $ \mathrm{Z}(\mathrm{q}\mathrm{q})\mathrm{Z}(\ell\ell) $ [197], $ \mathrm{V}(\mathrm{q}\mathrm{q})\mathrm{V}(\mathrm{q}\mathrm{q}) $ [111], $ \mathrm{Z}(\nu\nu)\mathrm{Z}(\mathrm{q}\mathrm{q}) $ [196], and $ \mathrm{W}(\ell\nu)\mathrm{W}(\mathrm{q}\mathrm{q}) $ [109], in the case of the graviton interpretation. Excluded areas are indicated by the direction of the hatching along the exclusion contours. 
png pdf 
Figure 37:
Observed upper limits, at 95% CL, on the DrellYan production cross section of (upper) W', (middle) Z', and (lower) combined $ \mathrm{V}^{\prime} $ spin1 resonances assuming branching fractions of the heavy vector triplet models (left) A and (right) B. The theory predictions from these models are also shown. Results from the VH [109,110,111] and VV channels [109,111,197,196], as well as results from dijet [201], $ \mathrm{t}\mathrm{b} $ [199], $ \ell\ell $ [198], and $ \ell\nu $ [200] final states are also shown, for comparison. 
png pdf 
Figure 37a:
Observed upper limits, at 95% CL, on the DrellYan production cross section of (upper) W', (middle) Z', and (lower) combined $ \mathrm{V}^{\prime} $ spin1 resonances assuming branching fractions of the heavy vector triplet models (left) A and (right) B. The theory predictions from these models are also shown. Results from the VH [109,110,111] and VV channels [109,111,197,196], as well as results from dijet [201], $ \mathrm{t}\mathrm{b} $ [199], $ \ell\ell $ [198], and $ \ell\nu $ [200] final states are also shown, for comparison. 
png pdf 
Figure 37b:
Observed upper limits, at 95% CL, on the DrellYan production cross section of (upper) W', (middle) Z', and (lower) combined $ \mathrm{V}^{\prime} $ spin1 resonances assuming branching fractions of the heavy vector triplet models (left) A and (right) B. The theory predictions from these models are also shown. Results from the VH [109,110,111] and VV channels [109,111,197,196], as well as results from dijet [201], $ \mathrm{t}\mathrm{b} $ [199], $ \ell\ell $ [198], and $ \ell\nu $ [200] final states are also shown, for comparison. 
png pdf 
Figure 37c:
Observed upper limits, at 95% CL, on the DrellYan production cross section of (upper) W', (middle) Z', and (lower) combined $ \mathrm{V}^{\prime} $ spin1 resonances assuming branching fractions of the heavy vector triplet models (left) A and (right) B. The theory predictions from these models are also shown. Results from the VH [109,110,111] and VV channels [109,111,197,196], as well as results from dijet [201], $ \mathrm{t}\mathrm{b} $ [199], $ \ell\ell $ [198], and $ \ell\nu $ [200] final states are also shown, for comparison. 
png pdf 
Figure 37d:
Observed upper limits, at 95% CL, on the DrellYan production cross section of (upper) W', (middle) Z', and (lower) combined $ \mathrm{V}^{\prime} $ spin1 resonances assuming branching fractions of the heavy vector triplet models (left) A and (right) B. The theory predictions from these models are also shown. Results from the VH [109,110,111] and VV channels [109,111,197,196], as well as results from dijet [201], $ \mathrm{t}\mathrm{b} $ [199], $ \ell\ell $ [198], and $ \ell\nu $ [200] final states are also shown, for comparison. 
png pdf 
Figure 37e:
Observed upper limits, at 95% CL, on the DrellYan production cross section of (upper) W', (middle) Z', and (lower) combined $ \mathrm{V}^{\prime} $ spin1 resonances assuming branching fractions of the heavy vector triplet models (left) A and (right) B. The theory predictions from these models are also shown. Results from the VH [109,110,111] and VV channels [109,111,197,196], as well as results from dijet [201], $ \mathrm{t}\mathrm{b} $ [199], $ \ell\ell $ [198], and $ \ell\nu $ [200] final states are also shown, for comparison. 
png pdf 
Figure 37f:
Observed upper limits, at 95% CL, on the DrellYan production cross section of (upper) W', (middle) Z', and (lower) combined $ \mathrm{V}^{\prime} $ spin1 resonances assuming branching fractions of the heavy vector triplet models (left) A and (right) B. The theory predictions from these models are also shown. Results from the VH [109,110,111] and VV channels [109,111,197,196], as well as results from dijet [201], $ \mathrm{t}\mathrm{b} $ [199], $ \ell\ell $ [198], and $ \ell\nu $ [200] final states are also shown, for comparison. 
png pdf 
Figure 38:
Observed upper limits, at 95% CL, on the $ \mathrm{V}^{\prime} $ couplings $ g_\mathrm{F} $ and $ g_{\mathrm{H}} $ within the HVT model for $ \mathrm{V}^{\prime} $ masses of (upper left) 1, (upper right) 2, (lower left) 3, and (lower right) 4 TeV, from DY production, derived from VH channels of Refs. [109,110,111] discussed in this report. Excluded areas are indicated by the direction of the shading along the exclusion contours. The dotted lines denote coupling values above which the relative width of the resonance, $ \Gamma_{\mathrm{V}^{\prime}} /m_{V^{\prime}} $, exceeds 4 and 10%, respectively, implying that the narrow width approximation no longer applies. The couplings corresponding to the heavy vector triplet models A and B are indicated by cross markers. 
png pdf 
Figure 38a:
Observed upper limits, at 95% CL, on the $ \mathrm{V}^{\prime} $ couplings $ g_\mathrm{F} $ and $ g_{\mathrm{H}} $ within the HVT model for $ \mathrm{V}^{\prime} $ masses of (upper left) 1, (upper right) 2, (lower left) 3, and (lower right) 4 TeV, from DY production, derived from VH channels of Refs. [109,110,111] discussed in this report. Excluded areas are indicated by the direction of the shading along the exclusion contours. The dotted lines denote coupling values above which the relative width of the resonance, $ \Gamma_{\mathrm{V}^{\prime}} /m_{V^{\prime}} $, exceeds 4 and 10%, respectively, implying that the narrow width approximation no longer applies. The couplings corresponding to the heavy vector triplet models A and B are indicated by cross markers. 
png pdf 
Figure 38b:
Observed upper limits, at 95% CL, on the $ \mathrm{V}^{\prime} $ couplings $ g_\mathrm{F} $ and $ g_{\mathrm{H}} $ within the HVT model for $ \mathrm{V}^{\prime} $ masses of (upper left) 1, (upper right) 2, (lower left) 3, and (lower right) 4 TeV, from DY production, derived from VH channels of Refs. [109,110,111] discussed in this report. Excluded areas are indicated by the direction of the shading along the exclusion contours. The dotted lines denote coupling values above which the relative width of the resonance, $ \Gamma_{\mathrm{V}^{\prime}} /m_{V^{\prime}} $, exceeds 4 and 10%, respectively, implying that the narrow width approximation no longer applies. The couplings corresponding to the heavy vector triplet models A and B are indicated by cross markers. 
png pdf 
Figure 38c:
Observed upper limits, at 95% CL, on the $ \mathrm{V}^{\prime} $ couplings $ g_\mathrm{F} $ and $ g_{\mathrm{H}} $ within the HVT model for $ \mathrm{V}^{\prime} $ masses of (upper left) 1, (upper right) 2, (lower left) 3, and (lower right) 4 TeV, from DY production, derived from VH channels of Refs. [109,110,111] discussed in this report. Excluded areas are indicated by the direction of the shading along the exclusion contours. The dotted lines denote coupling values above which the relative width of the resonance, $ \Gamma_{\mathrm{V}^{\prime}} /m_{V^{\prime}} $, exceeds 4 and 10%, respectively, implying that the narrow width approximation no longer applies. The couplings corresponding to the heavy vector triplet models A and B are indicated by cross markers. 
png pdf 
Figure 38d:
Observed upper limits, at 95% CL, on the $ \mathrm{V}^{\prime} $ couplings $ g_\mathrm{F} $ and $ g_{\mathrm{H}} $ within the HVT model for $ \mathrm{V}^{\prime} $ masses of (upper left) 1, (upper right) 2, (lower left) 3, and (lower right) 4 TeV, from DY production, derived from VH channels of Refs. [109,110,111] discussed in this report. Excluded areas are indicated by the direction of the shading along the exclusion contours. The dotted lines denote coupling values above which the relative width of the resonance, $ \Gamma_{\mathrm{V}^{\prime}} /m_{V^{\prime}} $, exceeds 4 and 10%, respectively, implying that the narrow width approximation no longer applies. The couplings corresponding to the heavy vector triplet models A and B are indicated by cross markers. 
png pdf 
Figure 39:
Observed upper limits, at 95% CL, on the $ \mathrm{V}^{\prime} $ couplings $ g_\mathrm{F} $ and $ g_{\mathrm{H}} $ within the HVT model for $ \mathrm{V}^{\prime} $ masses of (upper left) 1, (upper right) 2, (lower left) 3, and (lower right) 4 TeV, from DY production, derived from VH channels of Refs. [109,110,111] discussed in this report and the VV channels of Refs.[109,111,197,196], as well as results from dijet [201], $ \mathrm{t}\mathrm{b} $ [199], as well as results from dijet [201], $ \mathrm{t}\mathrm{b} $ [199], $ \ell\ell $ [198] and $ \ell\nu $ [200] final states. Excluded areas are indicated by the direction of the shading along the exclusion contours. The dotted lines denote coupling values above which the relative width of the resonance, $ \Gamma_{\mathrm{V}^{\prime}}/m_{V^{\prime}} $, exceeds 4 and 10%, respectively, implying that the narrow width approximation no longer applies. The couplings corresponding to the heavy vector triplet models A and B are indicated by cross markers. 
png pdf 
Figure 39a:
Observed upper limits, at 95% CL, on the $ \mathrm{V}^{\prime} $ couplings $ g_\mathrm{F} $ and $ g_{\mathrm{H}} $ within the HVT model for $ \mathrm{V}^{\prime} $ masses of (upper left) 1, (upper right) 2, (lower left) 3, and (lower right) 4 TeV, from DY production, derived from VH channels of Refs. [109,110,111] discussed in this report and the VV channels of Refs.[109,111,197,196], as well as results from dijet [201], $ \mathrm{t}\mathrm{b} $ [199], as well as results from dijet [201], $ \mathrm{t}\mathrm{b} $ [199], $ \ell\ell $ [198] and $ \ell\nu $ [200] final states. Excluded areas are indicated by the direction of the shading along the exclusion contours. The dotted lines denote coupling values above which the relative width of the resonance, $ \Gamma_{\mathrm{V}^{\prime}}/m_{V^{\prime}} $, exceeds 4 and 10%, respectively, implying that the narrow width approximation no longer applies. The couplings corresponding to the heavy vector triplet models A and B are indicated by cross markers. 
png pdf 
Figure 39b:
Observed upper limits, at 95% CL, on the $ \mathrm{V}^{\prime} $ couplings $ g_\mathrm{F} $ and $ g_{\mathrm{H}} $ within the HVT model for $ \mathrm{V}^{\prime} $ masses of (upper left) 1, (upper right) 2, (lower left) 3, and (lower right) 4 TeV, from DY production, derived from VH channels of Refs. [109,110,111] discussed in this report and the VV channels of Refs.[109,111,197,196], as well as results from dijet [201], $ \mathrm{t}\mathrm{b} $ [199], as well as results from dijet [201], $ \mathrm{t}\mathrm{b} $ [199], $ \ell\ell $ [198] and $ \ell\nu $ [200] final states. Excluded areas are indicated by the direction of the shading along the exclusion contours. The dotted lines denote coupling values above which the relative width of the resonance, $ \Gamma_{\mathrm{V}^{\prime}}/m_{V^{\prime}} $, exceeds 4 and 10%, respectively, implying that the narrow width approximation no longer applies. The couplings corresponding to the heavy vector triplet models A and B are indicated by cross markers. 
png pdf 
Figure 39c:
Observed upper limits, at 95% CL, on the $ \mathrm{V}^{\prime} $ couplings $ g_\mathrm{F} $ and $ g_{\mathrm{H}} $ within the HVT model for $ \mathrm{V}^{\prime} $ masses of (upper left) 1, (upper right) 2, (lower left) 3, and (lower right) 4 TeV, from DY production, derived from VH channels of Refs. [109,110,111] discussed in this report and the VV channels of Refs.[109,111,197,196], as well as results from dijet [201], $ \mathrm{t}\mathrm{b} $ [199], as well as results from dijet [201], $ \mathrm{t}\mathrm{b} $ [199], $ \ell\ell $ [198] and $ \ell\nu $ [200] final states. Excluded areas are indicated by the direction of the shading along the exclusion contours. The dotted lines denote coupling values above which the relative width of the resonance, $ \Gamma_{\mathrm{V}^{\prime}}/m_{V^{\prime}} $, exceeds 4 and 10%, respectively, implying that the narrow width approximation no longer applies. The couplings corresponding to the heavy vector triplet models A and B are indicated by cross markers. 
png pdf 
Figure 39d:
Observed upper limits, at 95% CL, on the $ \mathrm{V}^{\prime} $ couplings $ g_\mathrm{F} $ and $ g_{\mathrm{H}} $ within the HVT model for $ \mathrm{V}^{\prime} $ masses of (upper left) 1, (upper right) 2, (lower left) 3, and (lower right) 4 TeV, from DY production, derived from VH channels of Refs. [109,110,111] discussed in this report and the VV channels of Refs.[109,111,197,196], as well as results from dijet [201], $ \mathrm{t}\mathrm{b} $ [199], as well as results from dijet [201], $ \mathrm{t}\mathrm{b} $ [199], $ \ell\ell $ [198] and $ \ell\nu $ [200] final states. Excluded areas are indicated by the direction of the shading along the exclusion contours. The dotted lines denote coupling values above which the relative width of the resonance, $ \Gamma_{\mathrm{V}^{\prime}}/m_{V^{\prime}} $, exceeds 4 and 10%, respectively, implying that the narrow width approximation no longer applies. The couplings corresponding to the heavy vector triplet models A and B are indicated by cross markers. 
png pdf 
Figure 40:
Obseved upper limits, at 95% CL, on the coupling $ g_{\mathrm{H}} $ within the heavy vector triplet model, as a function of the $ \mathrm{V}^{\prime} $ mass. The limits are shown for the vecotr boson fusion production mode in the context of model C, in which $ g_\mathrm{F} = $ 0. The results are shown (left) for the WH and ZH analyses of Refs. [109,110,111], individually, and for a combination with the WZ final states of Refs. [196,111,109] (right), where the WH and ZH results from allhadronic final states have been combined with the corresponding VV channels. The dotted lines denote coupling values above which the relative width of the resonance, $ \Gamma_{\mathrm{V}^{\prime}}/m_{V^{\prime}} $, exceeds 4 and 10%, respectively, implying the narrow width approximation no longer applies. 
png pdf 
Figure 40a:
Obseved upper limits, at 95% CL, on the coupling $ g_{\mathrm{H}} $ within the heavy vector triplet model, as a function of the $ \mathrm{V}^{\prime} $ mass. The limits are shown for the vecotr boson fusion production mode in the context of model C, in which $ g_\mathrm{F} = $ 0. The results are shown (left) for the WH and ZH analyses of Refs. [109,110,111], individually, and for a combination with the WZ final states of Refs. [196,111,109] (right), where the WH and ZH results from allhadronic final states have been combined with the corresponding VV channels. The dotted lines denote coupling values above which the relative width of the resonance, $ \Gamma_{\mathrm{V}^{\prime}}/m_{V^{\prime}} $, exceeds 4 and 10%, respectively, implying the narrow width approximation no longer applies. 
png pdf 
Figure 40b:
Obseved upper limits, at 95% CL, on the coupling $ g_{\mathrm{H}} $ within the heavy vector triplet model, as a function of the $ \mathrm{V}^{\prime} $ mass. The limits are shown for the vecotr boson fusion production mode in the context of model C, in which $ g_\mathrm{F} = $ 0. The results are shown (left) for the WH and ZH analyses of Refs. [109,110,111], individually, and for a combination with the WZ final states of Refs. [196,111,109] (right), where the WH and ZH results from allhadronic final states have been combined with the corresponding VV channels. The dotted lines denote coupling values above which the relative width of the resonance, $ \Gamma_{\mathrm{V}^{\prime}}/m_{V^{\prime}} $, exceeds 4 and 10%, respectively, implying the narrow width approximation no longer applies. 
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Figure 41:
Contours of the variable $ R_{\text{int}} $ as defined in Eq. (13) and discussed in the text, in the ($ \sin\alpha $, $ \lambda_{\mathrm{H}\mathrm{H}\mathrm{X}} $) plane for the singlet model with $ k_{\lambda} = $ 1 and different resonance masses $ m_{\mathrm{X}} $ between (upper left) 280 and (lower right) 800 GeV. Contours are shown for $ R_{\text{int}} $ values of (dashed blue) $$0.2, (solid blue) $$0.1, (solid green) $ + $0.1, and (dashed green) $ + $0.2. Regions that are excluded, at 95% CL, from the combined likelihood analysis of the HH analyses presented in this report are indicated by red filled areas. Dashed black lines indicate constant relative widths of 5, 10, and 20%. 
png pdf 
Figure 42:
Expected differential cross sections for HH production, as a function of $ m_{{\mathrm{H}\mathrm{H}}} $, for the realsinglet model with $ m_{\mathrm{X}} = $ 280 GeV and $ \Gamma_{\mathrm{X}}/m_{\mathrm{X}} = 5% $. The parameters $ \sin\alpha $ and $ \lambda_{\mathrm{H}\mathrm{H}\mathrm{X}} $ have been chosen such that (upper row) $ R_{\text{int}}=\pm 10% $ and (lower row) $ R_{\text{int}}=\pm 20% $, for (left) negative and (right) positive values of $ R_{\text{int}} $. The total cross section for HH production $ \sigma^{\text{full}} $ (red line, labelled as $ \sigma_{\text{full}} $) is compared to the cross sections $ \sigma^{\text{ resonantonly}} $ (blue line, labelled as $ \sigma_{\text{res}} $) and $ \sigma^{ \text{nonresonant}} $ (green line, labelled as $ \sigma_{\text{nores}} $) considering only resonant and nonresonant production. In the lower panels the ratio of $ \sigma^{\text{full}} $ over $ (\sigma^{\text{resonantonly}}+\sigma^{ \text{nonresonant}}) $ is shown. 
png pdf 
Figure 42a:
Expected differential cross sections for HH production, as a function of $ m_{{\mathrm{H}\mathrm{H}}} $, for the realsinglet model with $ m_{\mathrm{X}} = $ 280 GeV and $ \Gamma_{\mathrm{X}}/m_{\mathrm{X}} = 5% $. The parameters $ \sin\alpha $ and $ \lambda_{\mathrm{H}\mathrm{H}\mathrm{X}} $ have been chosen such that (upper row) $ R_{\text{int}}=\pm 10% $ and (lower row) $ R_{\text{int}}=\pm 20% $, for (left) negative and (right) positive values of $ R_{\text{int}} $. The total cross section for HH production $ \sigma^{\text{full}} $ (red line, labelled as $ \sigma_{\text{full}} $) is compared to the cross sections $ \sigma^{\text{ resonantonly}} $ (blue line, labelled as $ \sigma_{\text{res}} $) and $ \sigma^{ \text{nonresonant}} $ (green line, labelled as $ \sigma_{\text{nores}} $) considering only resonant and nonresonant production. In the lower panels the ratio of $ \sigma^{\text{full}} $ over $ (\sigma^{\text{resonantonly}}+\sigma^{ \text{nonresonant}}) $ is shown. 
png pdf 
Figure 42b:
Expected differential cross sections for HH production, as a function of $ m_{{\mathrm{H}\mathrm{H}}} $, for the realsinglet model with $ m_{\mathrm{X}} = $ 280 GeV and $ \Gamma_{\mathrm{X}}/m_{\mathrm{X}} = 5% $. The parameters $ \sin\alpha $ and $ \lambda_{\mathrm{H}\mathrm{H}\mathrm{X}} $ have been chosen such that (upper row) $ R_{\text{int}}=\pm 10% $ and (lower row) $ R_{\text{int}}=\pm 20% $, for (left) negative and (right) positive values of $ R_{\text{int}} $. The total cross section for HH production $ \sigma^{\text{full}} $ (red line, labelled as $ \sigma_{\text{full}} $) is compared to the cross sections $ \sigma^{\text{ resonantonly}} $ (blue line, labelled as $ \sigma_{\text{res}} $) and $ \sigma^{ \text{nonresonant}} $ (green line, labelled as $ \sigma_{\text{nores}} $) considering only resonant and nonresonant production. In the lower panels the ratio of $ \sigma^{\text{full}} $ over $ (\sigma^{\text{resonantonly}}+\sigma^{ \text{nonresonant}}) $ is shown. 
png pdf 
Figure 42c:
Expected differential cross sections for HH production, as a function of $ m_{{\mathrm{H}\mathrm{H}}} $, for the realsinglet model with $ m_{\mathrm{X}} = $ 280 GeV and $ \Gamma_{\mathrm{X}}/m_{\mathrm{X}} = 5% $. The parameters $ \sin\alpha $ and $ \lambda_{\mathrm{H}\mathrm{H}\mathrm{X}} $ have been chosen such that (upper row) $ R_{\text{int}}=\pm 10% $ and (lower row) $ R_{\text{int}}=\pm 20% $, for (left) negative and (right) positive values of $ R_{\text{int}} $. The total cross section for HH production $ \sigma^{\text{full}} $ (red line, labelled as $ \sigma_{\text{full}} $) is compared to the cross sections $ \sigma^{\text{ resonantonly}} $ (blue line, labelled as $ \sigma_{\text{res}} $) and $ \sigma^{ \text{nonresonant}} $ (green line, labelled as $ \sigma_{\text{nores}} $) considering only resonant and nonresonant production. In the lower panels the ratio of $ \sigma^{\text{full}} $ over $ (\sigma^{\text{resonantonly}}+\sigma^{ \text{nonresonant}}) $ is shown. 
png pdf 
Figure 42d:
Expected differential cross sections for HH production, as a function of $ m_{{\mathrm{H}\mathrm{H}}} $, for the realsinglet model with $ m_{\mathrm{X}} = $ 280 GeV and $ \Gamma_{\mathrm{X}}/m_{\mathrm{X}} = 5% $. The parameters $ \sin\alpha $ and $ \lambda_{\mathrm{H}\mathrm{H}\mathrm{X}} $ have been chosen such that (upper row) $ R_{\text{int}}=\pm 10% $ and (lower row) $ R_{\text{int}}=\pm 20% $, for (left) negative and (right) positive values of $ R_{\text{int}} $. The total cross section for HH production $ \sigma^{\text{full}} $ (red line, labelled as $ \sigma_{\text{full}} $) is compared to the cross sections $ \sigma^{\text{ resonantonly}} $ (blue line, labelled as $ \sigma_{\text{res}} $) and $ \sigma^{ \text{nonresonant}} $ (green line, labelled as $ \sigma_{\text{nores}} $) considering only resonant and nonresonant production. In the lower panels the ratio of $ \sigma^{\text{full}} $ over $ (\sigma^{\text{resonantonly}}+\sigma^{ \text{nonresonant}}) $ is shown. 
png pdf 
Figure 43:
Expected differential cross sections for HH production, as a function of $ m_{{\mathrm{H}\mathrm{H}}} $ for the realsinglet model with $ m_{\mathrm{X}} = $ 500 GeV and $ \Gamma_{\mathrm{X}}/m_{\mathrm{X}} = 5% $. The parameters $ \sin\alpha $ and $ \lambda_{\mathrm{H}\mathrm{H}\mathrm{X}} $ have been chosen such that (upper row) $ R_{\text{int}}=\pm 10% $ and (lower row) $ R_{\text{int}}=\pm 20% $, for (left) negative and (right) positive values of $ R_{\text{int}} $. The total cross section for HH production $ \sigma^{\text{full}} $ (red line, labelled as $ \sigma_{\text{full}} $) is compared to the cross sections $ \sigma^{\text{ resonantonly}} $ (blue line, labelled as $ \sigma_{\text{res}} $) and $ \sigma^{ \text{nonresonant}} $ (green line, labelled as $ \sigma_{\text{nores}} $) considering only resonant and nonresonant production. In the lower panels the ratio of $ \sigma^{\text{full}} $ over $ (\sigma^{\text{resonantonly}}+\sigma^{ \text{nonresonant}}) $ is shown. 
png pdf 
Figure 43a:
Expected differential cross sections for HH production, as a function of $ m_{{\mathrm{H}\mathrm{H}}} $ for the realsinglet model with $ m_{\mathrm{X}} = $ 500 GeV and $ \Gamma_{\mathrm{X}}/m_{\mathrm{X}} = 5% $. The parameters $ \sin\alpha $ and $ \lambda_{\mathrm{H}\mathrm{H}\mathrm{X}} $ have been chosen such that (upper row) $ R_{\text{int}}=\pm 10% $ and (lower row) $ R_{\text{int}}=\pm 20% $, for (left) negative and (right) positive values of $ R_{\text{int}} $. The total cross section for HH production $ \sigma^{\text{full}} $ (red line, labelled as $ \sigma_{\text{full}} $) is compared to the cross sections $ \sigma^{\text{ resonantonly}} $ (blue line, labelled as $ \sigma_{\text{res}} $) and $ \sigma^{ \text{nonresonant}} $ (green line, labelled as $ \sigma_{\text{nores}} $) considering only resonant and nonresonant production. In the lower panels the ratio of $ \sigma^{\text{full}} $ over $ (\sigma^{\text{resonantonly}}+\sigma^{ \text{nonresonant}}) $ is shown. 
png pdf 
Figure 43b:
Expected differential cross sections for HH production, as a function of $ m_{{\mathrm{H}\mathrm{H}}} $ for the realsinglet model with $ m_{\mathrm{X}} = $ 500 GeV and $ \Gamma_{\mathrm{X}}/m_{\mathrm{X}} = 5% $. The parameters $ \sin\alpha $ and $ \lambda_{\mathrm{H}\mathrm{H}\mathrm{X}} $ have been chosen such that (upper row) $ R_{\text{int}}=\pm 10% $ and (lower row) $ R_{\text{int}}=\pm 20% $, for (left) negative and (right) positive values of $ R_{\text{int}} $. The total cross section for HH production $ \sigma^{\text{full}} $ (red line, labelled as $ \sigma_{\text{full}} $) is compared to the cross sections $ \sigma^{\text{ resonantonly}} $ (blue line, labelled as $ \sigma_{\text{res}} $) and $ \sigma^{ \text{nonresonant}} $ (green line, labelled as $ \sigma_{\text{nores}} $) considering only resonant and nonresonant production. In the lower panels the ratio of $ \sigma^{\text{full}} $ over $ (\sigma^{\text{resonantonly}}+\sigma^{ \text{nonresonant}}) $ is shown. 
png pdf 
Figure 43c:
Expected differential cross sections for HH production, as a function of $ m_{{\mathrm{H}\mathrm{H}}} $ for the realsinglet model with $ m_{\mathrm{X}} = $ 500 GeV and $ \Gamma_{\mathrm{X}}/m_{\mathrm{X}} = 5% $. The parameters $ \sin\alpha $ and $ \lambda_{\mathrm{H}\mathrm{H}\mathrm{X}} $ have been chosen such that (upper row) $ R_{\text{int}}=\pm 10% $ and (lower row) $ R_{\text{int}}=\pm 20% $, for (left) negative and (right) positive values of $ R_{\text{int}} $. The total cross section for HH production $ \sigma^{\text{full}} $ (red line, labelled as $ \sigma_{\text{full}} $) is compared to the cross sections $ \sigma^{\text{ resonantonly}} $ (blue line, labelled as $ \sigma_{\text{res}} $) and $ \sigma^{ \text{nonresonant}} $ (green line, labelled as $ \sigma_{\text{nores}} $) considering only resonant and nonresonant production. In the lower panels the ratio of $ \sigma^{\text{full}} $ over $ (\sigma^{\text{resonantonly}}+\sigma^{ \text{nonresonant}}) $ is shown. 
png pdf 
Figure 43d:
Expected differential cross sections for HH production, as a function of $ m_{{\mathrm{H}\mathrm{H}}} $ for the realsinglet model with $ m_{\mathrm{X}} = $ 500 GeV and $ \Gamma_{\mathrm{X}}/m_{\mathrm{X}} = 5% $. The parameters $ \sin\alpha $ and $ \lambda_{\mathrm{H}\mathrm{H}\mathrm{X}} $ have been chosen such that (upper row) $ R_{\text{int}}=\pm 10% $ and (lower row) $ R_{\text{int}}=\pm 20% $, for (left) negative and (right) positive values of $ R_{\text{int}} $. The total cross section for HH production $ \sigma^{\text{full}} $ (red line, labelled as $ \sigma_{\text{full}} $) is compared to the cross sections $ \sigma^{\text{ resonantonly}} $ (blue line, labelled as $ \sigma_{\text{res}} $) and $ \sigma^{ \text{nonresonant}} $ (green line, labelled as $ \sigma_{\text{nores}} $) considering only resonant and nonresonant production. In the lower panels the ratio of $ \sigma^{\text{full}} $ over $ (\sigma^{\text{resonantonly}}+\sigma^{ \text{nonresonant}}) $ is shown. 
png pdf 
Figure 44:
Expected upper limits at 95% CL, on the product of the cross section for the production of a spin0 resonance X and the branching fraction $ \mathcal{B}(\mathrm{X} \to\mathrm{H}\mathrm{H}) $, as functions of $ m_{\mathrm{X}} $ from the (upper left) $ \mathrm{b}\mathrm{b}\tau\tau $ [115], (upper right) $ \mathrm{b}\mathrm{b}\gamma\gamma $ [116], and (lower) $ \mathrm{b}\mathrm{b}\mathrm{b}\mathrm{b} $ with two merged $ \mathrm{b}\mathrm{b} $ jets [117] analyses discussed in this report, projected to an integrated luminosity of 3000 fb$ ^{1} $ under the assumption of different systematic uncertainty scenarios, as discussed in the text. All estimates include the anticipated statistical uncertainties. 
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Figure 44a:
Expected upper limits at 95% CL, on the product of the cross section for the production of a spin0 resonance X and the branching fraction $ \mathcal{B}(\mathrm{X} \to\mathrm{H}\mathrm{H}) $, as functions of $ m_{\mathrm{X}} $ from the (upper left) $ \mathrm{b}\mathrm{b}\tau\tau $ [115], (upper right) $ \mathrm{b}\mathrm{b}\gamma\gamma $ [116], and (lower) $ \mathrm{b}\mathrm{b}\mathrm{b}\mathrm{b} $ with two merged $ \mathrm{b}\mathrm{b} $ jets [117] analyses discussed in this report, projected to an integrated luminosity of 3000 fb$ ^{1} $ under the assumption of different systematic uncertainty scenarios, as discussed in the text. All estimates include the anticipated statistical uncertainties. 
png pdf 
Figure 44b:
Expected upper limits at 95% CL, on the product of the cross section for the production of a spin0 resonance X and the branching fraction $ \mathcal{B}(\mathrm{X} \to\mathrm{H}\mathrm{H}) $, as functions of $ m_{\mathrm{X}} $ from the (upper left) $ \mathrm{b}\mathrm{b}\tau\tau $ [115], (upper right) $ \mathrm{b}\mathrm{b}\gamma\gamma $ [116], and (lower) $ \mathrm{b}\mathrm{b}\mathrm{b}\mathrm{b} $ with two merged $ \mathrm{b}\mathrm{b} $ jets [117] analyses discussed in this report, projected to an integrated luminosity of 3000 fb$ ^{1} $ under the assumption of different systematic uncertainty scenarios, as discussed in the text. All estimates include the anticipated statistical uncertainties. 
png pdf 
Figure 44c:
Expected upper limits at 95% CL, on the product of the cross section for the production of a spin0 resonance X and the branching fraction $ \mathcal{B}(\mathrm{X} \to\mathrm{H}\mathrm{H}) $, as functions of $ m_{\mathrm{X}} $ from the (upper left) $ \mathrm{b}\mathrm{b}\tau\tau $ [115], (upper right) $ \mathrm{b}\mathrm{b}\gamma\gamma $ [116], and (lower) $ \mathrm{b}\mathrm{b}\mathrm{b}\mathrm{b} $ with two merged $ \mathrm{b}\mathrm{b} $ jets [117] analyses discussed in this report, projected to an integrated luminosity of 3000 fb$ ^{1} $ under the assumption of different systematic uncertainty scenarios, as discussed in the text. All estimates include the anticipated statistical uncertainties. 
png pdf 
Figure 45:
Expected upper limits at 95% CL, on the product of the cross section for the production of a spin0 resonance X and the branching fraction $ \mathcal{B}(\mathrm{X} \to\mathrm{H}\mathrm{H}) $, as a function of $ m_{\mathrm{X}} $, for an integrated luminosity of 3000 fb$ ^{1} $ and the combination of the three analyses shown in Fig. 44. Shown are the effects of the different systematic uncertainty scenarios (left), and the reach of the individual analyses for the S2 systematic scenario (right). All estimates include the anticipated statistical uncertainties. 
png pdf 
Figure 45a:
Expected upper limits at 95% CL, on the product of the cross section for the production of a spin0 resonance X and the branching fraction $ \mathcal{B}(\mathrm{X} \to\mathrm{H}\mathrm{H}) $, as a function of $ m_{\mathrm{X}} $, for an integrated luminosity of 3000 fb$ ^{1} $ and the combination of the three analyses shown in Fig. 44. Shown are the effects of the different systematic uncertainty scenarios (left), and the reach of the individual analyses for the S2 systematic scenario (right). All estimates include the anticipated statistical uncertainties. 
png pdf 
Figure 45b:
Expected upper limits at 95% CL, on the product of the cross section for the production of a spin0 resonance X and the branching fraction $ \mathcal{B}(\mathrm{X} \to\mathrm{H}\mathrm{H}) $, as a function of $ m_{\mathrm{X}} $, for an integrated luminosity of 3000 fb$ ^{1} $ and the combination of the three analyses shown in Fig. 44. Shown are the effects of the different systematic uncertainty scenarios (left), and the reach of the individual analyses for the S2 systematic scenario (right). All estimates include the anticipated statistical uncertainties. 
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Figure 46:
Expected discovery significance for a spin0 resonance X with $ m_{\mathrm{X}}= $ 1 TeV and cross sections of 1 and 10 fb, obtained for the combined likelihood analysis of the resonant HH searches as discussed in Section 5 and shown in Figs. 44 and 45, shown as function of the integrated luminosity. 
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Figure 47:
Expected exclusion contours at 95% CL, in the ($ \tan\beta $, $ m_{{\mathrm{A}}} $) plane of the (left) hMSSM and (right) $ M^{125}_{\text{h,EFT}} $ scenarios obtained from the combined likelihood analysis of the HH searches discussed in Section 4.1 and shown in Figs. 31 and 32, for different integrated luminosities and compared to the Run 2 result obtained at $ \sqrt{s}= $ 13 TeV. The projections assume $ \sqrt{s}= $ 14 TeV. 
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Figure 47a:
Expected exclusion contours at 95% CL, in the ($ \tan\beta $, $ m_{{\mathrm{A}}} $) plane of the (left) hMSSM and (right) $ M^{125}_{\text{h,EFT}} $ scenarios obtained from the combined likelihood analysis of the HH searches discussed in Section 4.1 and shown in Figs. 31 and 32, for different integrated luminosities and compared to the Run 2 result obtained at $ \sqrt{s}= $ 13 TeV. The projections assume $ \sqrt{s}= $ 14 TeV. 
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Figure 47b:
Expected exclusion contours at 95% CL, in the ($ \tan\beta $, $ m_{{\mathrm{A}}} $) plane of the (left) hMSSM and (right) $ M^{125}_{\text{h,EFT}} $ scenarios obtained from the combined likelihood analysis of the HH searches discussed in Section 4.1 and shown in Figs. 31 and 32, for different integrated luminosities and compared to the Run 2 result obtained at $ \sqrt{s}= $ 13 TeV. The projections assume $ \sqrt{s}= $ 14 TeV. 
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Figure 48:
Expected lower limit at 95% CL, on $ \Lambda_{\mathrm{R}} $ in the warped extra dimensions bulk scenario for the production of a radion R, as a function of $ m_{{\mathrm{R}} } $. The limits are derived from the combined likelihood analysis of the HH searches discussed in Section 4.2 and shown in Fig. 35, for different values of the integrated luminosity. Excluded areas are indicated by the direction of the hatching along the exclusion contours. 
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Figure 49:
Exclusion contours at 95% CL, in the ($ \sin\alpha $, $ \lambda_{\mathrm{H}\mathrm{H}\mathrm{X}} $) plane for $ k_{\lambda} = $ 1 in the realsinglet model. These contours are obtained from the combined likelihood analysis of the HH searches discussed in Section 4.1 for (upper left to lower right) $ m_{\mathrm{X}} = $ 280, 400, 500, 600, 700, and 1000 GeV. The expected limits from the Run 2 dataset have been projected to integrated luminosities of 300, 1000, and 3000 fb$ ^{1} $. Excluded areas are indicated by the direction of the hatching along the exclusion contours. 
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Figure 50:
Expected upper limits at 95% CL, on the product of the cross section $ \sigma $ for the production of a resonance X via gluongluon fusion and the branching fraction $ \mathcal{B} $ for the $ \mathrm{X}\to{\mathrm{Y}}(\mathrm{b}\mathrm{b})\mathrm{H} $ decay, as functions of $ m_{{\mathrm{Y}}} $, for $ m_{\mathrm{X}}\leq $ 1 TeV. For the branching fractions of the $ \mathrm{H}\to\tau\tau $, $ \mathrm{H}\to\gamma\gamma $ and $ \mathrm{H}\to\mathrm{b}\mathrm{b} $ decays, the SM values are assumed. The limits are obtained from the combined likelihood analysis of all analyses discussed in Section 3.3 and shown in Fig. 29, projected to an integrated luminosity of 3000 fb$ ^{1} $. Shown are the projections for the combined likelihood analysis for different systematic uncertainty scenarios (left), and the projections for the combined likelihood analysis and the individual contributing analyses assuming the S2 scenario (right). For presentation purposes, the limits have been scaled in successive steps by two orders of magnitude. For each set of graphs, a black arrow points to the $ m_{\mathrm{X}} $ related legend. 
png pdf 
Figure 50a:
Expected upper limits at 95% CL, on the product of the cross section $ \sigma $ for the production of a resonance X via gluongluon fusion and the branching fraction $ \mathcal{B} $ for the $ \mathrm{X}\to{\mathrm{Y}}(\mathrm{b}\mathrm{b})\mathrm{H} $ decay, as functions of $ m_{{\mathrm{Y}}} $, for $ m_{\mathrm{X}}\leq $ 1 TeV. For the branching fractions of the $ \mathrm{H}\to\tau\tau $, $ \mathrm{H}\to\gamma\gamma $ and $ \mathrm{H}\to\mathrm{b}\mathrm{b} $ decays, the SM values are assumed. The limits are obtained from the combined likelihood analysis of all analyses discussed in Section 3.3 and shown in Fig. 29, projected to an integrated luminosity of 3000 fb$ ^{1} $. Shown are the projections for the combined likelihood analysis for different systematic uncertainty scenarios (left), and the projections for the combined likelihood analysis and the individual contributing analyses assuming the S2 scenario (right). For presentation purposes, the limits have been scaled in successive steps by two orders of magnitude. For each set of graphs, a black arrow points to the $ m_{\mathrm{X}} $ related legend. 
png pdf 
Figure 50b:
Expected upper limits at 95% CL, on the product of the cross section $ \sigma $ for the production of a resonance X via gluongluon fusion and the branching fraction $ \mathcal{B} $ for the $ \mathrm{X}\to{\mathrm{Y}}(\mathrm{b}\mathrm{b})\mathrm{H} $ decay, as functions of $ m_{{\mathrm{Y}}} $, for $ m_{\mathrm{X}}\leq $ 1 TeV. For the branching fractions of the $ \mathrm{H}\to\tau\tau $, $ \mathrm{H}\to\gamma\gamma $ and $ \mathrm{H}\to\mathrm{b}\mathrm{b} $ decays, the SM values are assumed. The limits are obtained from the combined likelihood analysis of all analyses discussed in Section 3.3 and shown in Fig. 29, projected to an integrated luminosity of 3000 fb$ ^{1} $. Shown are the projections for the combined likelihood analysis for different systematic uncertainty scenarios (left), and the projections for the combined likelihood analysis and the individual contributing analyses assuming the S2 scenario (right). For presentation purposes, the limits have been scaled in successive steps by two orders of magnitude. For each set of graphs, a black arrow points to the $ m_{\mathrm{X}} $ related legend. 
png pdf 
Figure 51:
Expected upper limits at 95% CL, on the product of the cross section $ \sigma $ for the production of a resonance X via gluongluon fusion and the branching fraction $ \mathcal{B} $ for the $ \mathrm{X}\to{\mathrm{Y}}(\mathrm{b}\mathrm{b})\mathrm{H} $ decay, as functions of $ m_{{\mathrm{Y}}} $, for $ m_{\mathrm{X}}\geq $ 1.2 TeV. For the branching fractions of the $ \mathrm{H}\to\tau\tau $ and $ \mathrm{H}\to\mathrm{b}\mathrm{b} $ decays, the SM values are assumed. The limits are obtained from the combined likelihood analysis of all analyses discussed in Section 3.3 and shown in Fig. 30, projected to an integrated luminosity of 3000 fb$ ^{1} $. Shown are the projections for the combined likelihood analysis for different systematic uncertainty scenarios (left), and the projections for the combined likelihood analysis and the individual contributing analyses assuming the S2 scenario (right). For presentation purposes, the limits have been scaled in successive steps by four orders of magnitude. For each set of graphs, a black arrow points to the $ m_{\mathrm{X}} $ related legend. 
png pdf 
Figure 51a:
Expected upper limits at 95% CL, on the product of the cross section $ \sigma $ for the production of a resonance X via gluongluon fusion and the branching fraction $ \mathcal{B} $ for the $ \mathrm{X}\to{\mathrm{Y}}(\mathrm{b}\mathrm{b})\mathrm{H} $ decay, as functions of $ m_{{\mathrm{Y}}} $, for $ m_{\mathrm{X}}\geq $ 1.2 TeV. For the branching fractions of the $ \mathrm{H}\to\tau\tau $ and $ \mathrm{H}\to\mathrm{b}\mathrm{b} $ decays, the SM values are assumed. The limits are obtained from the combined likelihood analysis of all analyses discussed in Section 3.3 and shown in Fig. 30, projected to an integrated luminosity of 3000 fb$ ^{1} $. Shown are the projections for the combined likelihood analysis for different systematic uncertainty scenarios (left), and the projections for the combined likelihood analysis and the individual contributing analyses assuming the S2 scenario (right). For presentation purposes, the limits have been scaled in successive steps by four orders of magnitude. For each set of graphs, a black arrow points to the $ m_{\mathrm{X}} $ related legend. 
png pdf 
Figure 51b:
Expected upper limits at 95% CL, on the product of the cross section $ \sigma $ for the production of a resonance X via gluongluon fusion and the branching fraction $ \mathcal{B} $ for the $ \mathrm{X}\to{\mathrm{Y}}(\mathrm{b}\mathrm{b})\mathrm{H} $ decay, as functions of $ m_{{\mathrm{Y}}} $, for $ m_{\mathrm{X}}\geq $ 1.2 TeV. For the branching fractions of the $ \mathrm{H}\to\tau\tau $ and $ \mathrm{H}\to\mathrm{b}\mathrm{b} $ decays, the SM values are assumed. The limits are obtained from the combined likelihood analysis of all analyses discussed in Section 3.3 and shown in Fig. 30, projected to an integrated luminosity of 3000 fb$ ^{1} $. Shown are the projections for the combined likelihood analysis for different systematic uncertainty scenarios (left), and the projections for the combined likelihood analysis and the individual contributing analyses assuming the S2 scenario (right). For presentation purposes, the limits have been scaled in successive steps by four orders of magnitude. For each set of graphs, a black arrow points to the $ m_{\mathrm{X}} $ related legend. 
png pdf 
Figure 52:
Expected upper limits at 95 % CL on the product of the cross section $ \sigma $ for the production of a resonance X via gluongluon fusion and the branching fraction $ \mathcal{B} $ for the $ \mathrm{X}\to{\mathrm{Y}}(\mathrm{b}\mathrm{b})\mathrm{H} $ decay, as obtained from the combined likelihood analysis of the individual analyses presented in Section 3.3 and Figure 29. The results are shown in the plane spanned by $ m_{{\mathrm{Y}}} $ and $ m_{\mathrm{X}} $ for $ m_{\mathrm{X}}\le $ 1 TeV, and projected to an integrated luminosity of 3000 fb$ ^{1} $, assuming the S2 systematic uncertainty scenario. The numbers in the boxes are given in fb. 
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Figure 53:
Interpretation of the upper limits at 95% CL, on the product of the cross section $ \sigma $ for the production of a resonance X via gluongluon fusion and the branching fraction $ \mathcal{B} $ for the $ \mathrm{X}\to{\mathrm{Y}}(\mathrm{b}\mathrm{b})\mathrm{H} $ decay, obtained from the projections to an integrated luminosity of 3000 fb$ ^{1} $ of the (upper left) $ {\mathrm{Y}}(\mathrm{b}\mathrm{b})\mathrm{H}(\gamma\gamma) $ [116], (upper right) $ {\mathrm{Y}}(\mathrm{b}\mathrm{b})\mathrm{H}(\tau\tau) $ [115], and (lower row) $ {\mathrm{Y}}(\mathrm{b}\mathrm{b})\mathrm{H}(\mathrm{b}\mathrm{b}) $ [117] analyses, assuming the S2 systematic uncertainty scenario. The projected limits are mapped onto the ($ m_{\mathrm{X}} $, $ m_{{\mathrm{Y}}} $) plane, and compared with the maximally allowed cross sections of the NMSSM (left and upper right), and TRSM models (lower right) discussed in Section 4.1.3. The points indicate the available theory predictions. The mass dependences of both the projected experimental limits and the maximally allowed theory cross sections have been interpolated to obtain approximate exclusion contours. The NMSSM predictions based on NMSSMTOOLS version 5.6.2 are adapted from Ref. [193], whereas the TRSM is described in Ref. [12]. In both cases, the model predictions have been scaled to $ \sqrt{s}= $ 14 TeV. 
png pdf 
Figure 53a:
Interpretation of the upper limits at 95% CL, on the product of the cross section $ \sigma $ for the production of a resonance X via gluongluon fusion and the branching fraction $ \mathcal{B} $ for the $ \mathrm{X}\to{\mathrm{Y}}(\mathrm{b}\mathrm{b})\mathrm{H} $ decay, obtained from the projections to an integrated luminosity of 3000 fb$ ^{1} $ of the (upper left) $ {\mathrm{Y}}(\mathrm{b}\mathrm{b})\mathrm{H}(\gamma\gamma) $ [116], (upper right) $ {\mathrm{Y}}(\mathrm{b}\mathrm{b})\mathrm{H}(\tau\tau) $ [115], and (lower row) $ {\mathrm{Y}}(\mathrm{b}\mathrm{b})\mathrm{H}(\mathrm{b}\mathrm{b}) $ [117] analyses, assuming the S2 systematic uncertainty scenario. The projected limits are mapped onto the ($ m_{\mathrm{X}} $, $ m_{{\mathrm{Y}}} $) plane, and compared with the maximally allowed cross sections of the NMSSM (left and upper right), and TRSM models (lower right) discussed in Section 4.1.3. The points indicate the available theory predictions. The mass dependences of both the projected experimental limits and the maximally allowed theory cross sections have been interpolated to obtain approximate exclusion contours. The NMSSM predictions based on NMSSMTOOLS version 5.6.2 are adapted from Ref. [193], whereas the TRSM is described in Ref. [12]. In both cases, the model predictions have been scaled to $ \sqrt{s}= $ 14 TeV. 
png pdf 
Figure 53b:
Interpretation of the upper limits at 95% CL, on the product of the cross section $ \sigma $ for the production of a resonance X via gluongluon fusion and the branching fraction $ \mathcal{B} $ for the $ \mathrm{X}\to{\mathrm{Y}}(\mathrm{b}\mathrm{b})\mathrm{H} $ decay, obtained from the projections to an integrated luminosity of 3000 fb$ ^{1} $ of the (upper left) $ {\mathrm{Y}}(\mathrm{b}\mathrm{b})\mathrm{H}(\gamma\gamma) $ [116], (upper right) $ {\mathrm{Y}}(\mathrm{b}\mathrm{b})\mathrm{H}(\tau\tau) $ [115], and (lower row) $ {\mathrm{Y}}(\mathrm{b}\mathrm{b})\mathrm{H}(\mathrm{b}\mathrm{b}) $ [117] analyses, assuming the S2 systematic uncertainty scenario. The projected limits are mapped onto the ($ m_{\mathrm{X}} $, $ m_{{\mathrm{Y}}} $) plane, and compared with the maximally allowed cross sections of the NMSSM (left and upper right), and TRSM models (lower right) discussed in Section 4.1.3. The points indicate the available theory predictions. The mass dependences of both the projected experimental limits and the maximally allowed theory cross sections have been interpolated to obtain approximate exclusion contours. The NMSSM predictions based on NMSSMTOOLS version 5.6.2 are adapted from Ref. [193], whereas the TRSM is described in Ref. [12]. In both cases, the model predictions have been scaled to $ \sqrt{s}= $ 14 TeV. 
png pdf 
Figure 53c:
Interpretation of the upper limits at 95% CL, on the product of the cross section $ \sigma $ for the production of a resonance X via gluongluon fusion and the branching fraction $ \mathcal{B} $ for the $ \mathrm{X}\to{\mathrm{Y}}(\mathrm{b}\mathrm{b})\mathrm{H} $ decay, obtained from the projections to an integrated luminosity of 3000 fb$ ^{1} $ of the (upper left) $ {\mathrm{Y}}(\mathrm{b}\mathrm{b})\mathrm{H}(\gamma\gamma) $ [116], (upper right) $ {\mathrm{Y}}(\mathrm{b}\mathrm{b})\mathrm{H}(\tau\tau) $ [115], and (lower row) $ {\mathrm{Y}}(\mathrm{b}\mathrm{b})\mathrm{H}(\mathrm{b}\mathrm{b}) $ [117] analyses, assuming the S2 systematic uncertainty scenario. The projected limits are mapped onto the ($ m_{\mathrm{X}} $, $ m_{{\mathrm{Y}}} $) plane, and compared with the maximally allowed cross sections of the NMSSM (left and upper right), and TRSM models (lower right) discussed in Section 4.1.3. The points indicate the available theory predictions. The mass dependences of both the projected experimental limits and the maximally allowed theory cross sections have been interpolated to obtain approximate exclusion contours. The NMSSM predictions based on NMSSMTOOLS version 5.6.2 are adapted from Ref. [193], whereas the TRSM is described in Ref. [12]. In both cases, the model predictions have been scaled to $ \sqrt{s}= $ 14 TeV. 
png pdf 
Figure 53d:
Interpretation of the upper limits at 95% CL, on the product of the cross section $ \sigma $ for the production of a resonance X via gluongluon fusion and the branching fraction $ \mathcal{B} $ for the $ \mathrm{X}\to{\mathrm{Y}}(\mathrm{b}\mathrm{b})\mathrm{H} $ decay, obtained from the projections to an integrated luminosity of 3000 fb$ ^{1} $ of the (upper left) $ {\mathrm{Y}}(\mathrm{b}\mathrm{b})\mathrm{H}(\gamma\gamma) $ [116], (upper right) $ {\mathrm{Y}}(\mathrm{b}\mathrm{b})\mathrm{H}(\tau\tau) $ [115], and (lower row) $ {\mathrm{Y}}(\mathrm{b}\mathrm{b})\mathrm{H}(\mathrm{b}\mathrm{b}) $ [117] analyses, assuming the S2 systematic uncertainty scenario. The projected limits are mapped onto the ($ m_{\mathrm{X}} $, $ m_{{\mathrm{Y}}} $) plane, and compared with the maximally allowed cross sections of the NMSSM (left and upper right), and TRSM models (lower right) discussed in Section 4.1.3. The points indicate the available theory predictions. The mass dependences of both the projected experimental limits and the maximally allowed theory cross sections have been interpolated to obtain approximate exclusion contours. The NMSSM predictions based on NMSSMTOOLS version 5.6.2 are adapted from Ref. [193], whereas the TRSM is described in Ref. [12]. In both cases, the model predictions have been scaled to $ \sqrt{s}= $ 14 TeV. 
Tables  
png pdf 
Table 1:
Summary of all analyses discussed in Section 2. Note that the list of subchannels is not exhaustive in all cases. All analyses listed under YH also contribute to the HH measurements. 
png pdf 
Table 2:
Searches for resonant HH and YH production considered for the projection study. 
Summary 
The analyses searching for the production of the Higgs (H) boson through decays of heavy resonances, performed by the CMS Collaboration using the Run 2 data set, are reviewed. This review covers final states with two bosons with at least one an H boson, namely an H boson and a vector boson (VH), a pair of H bosons (HH), and an H boson joined by a new boson Y (YH), where V represents a W or a Z boson. The analyses cover a wide range of H boson decay modes, in particular, decays into photons, b quarks, $ \tau $ leptons, and W bosons. The Y boson is exclusively searched for in b quark final states. Topologies involving both resolved and merged jet objects are used to cover a wide range of the phase space. Multivariate methods are employed in various ways to improve the performance. The results are presented as summary plots which show the sensitivity of all channels in direct comparison. For the HH and YH final states, the results obtained by combining all decay channels are presented for the first time. The results are interpreted in the context of relevant beyondthestandard model scenarios for resonances decaying into VH, HH and YH final states. These include various extended Higgs sector models, warped extradimension models, and heavy vector triplet models. The results from resonant H boson production searches are compared with results from searches in other channels. While all presented analyses assume the validity of the narrowwidth approximation, a dedicated study of the impact of finite width and interference is performed for the first time in CMS for the real singlet extension of the standard model. This study shows the modification of the HH cross section and line shape in regions of the parameter space where the narrowwidth approximation is not valid anymore. The expected sensitivity of the analyses in the HH and YH final states is estimated for future data sets with integrated luminosities of 300, 1000, and 3000 fb$ ^{1} $, the last number corresponding to the baseline scenario of the HighLuminosity LHC (HLLHC) over its full lifetime. The expected upper limits for resonant HH production for the HLLHC scenario range from about 50 fb at a resonance mass of 300 GeV to nearly 0.01 fb for masses of 3 TeV and above. The exclusions in terms of $ \tan\beta $ in the hMSSM and $ M^{125}_{\text{h,EFT}} $ scenarios are expanded by almost a factor of two compared to the Run 2 data set. This review shows how the specific strengths of many different experimental signatures can be combined to chart very thoroughly the territory where resonant Higgs boson production might reveal beyond the standard model physics, and gives a promising outlook towards the achievement potential of future measurements in this sector. 
Additional Figures  
png pdf 
Additional Figure 1:
Observed and expected 95% CL upper limits on the product of the cross section $ \sigma $ for the production of a spin0 resonance X, via gluongluon fusion and the branching fraction $ \mathcal{B} $ for the decay into a pair of H bosons. The combined results of the CMS analyses are shown in red, while the combination from ATLAS [168] is shown in blue. The observed limits are indicated by markers connected with solid lines and the expected limits by dashed lines. 
png pdf 
Additional Figure 2:
Observed and expected upper limits at 95% CL, on the product of the cross section $ \sigma $ for the production of a resonance X via gluongluon fusion and the branching fraction $ \mathcal{B} $ for the $ \mathrm{X}\to{\mathrm{Y}}(\mathrm{b}\mathrm{b})\mathrm{H} $ decay, as obtained from a combined likelihood analysis of several individual channels. The results are presented as a function of $ m_{\mathrm{X}} $ for six values of $ m_{{\mathrm{Y}}} $. The corresponding maximally allowed values of $ \sigma\mathcal{B} $ in the NMSSM are also shown for comparison, as adapted from Ref. [193], which accounts for experimental constraints as defined in version 5.6.2 of the program NMSSMTOOLS. 
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