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| CMS-HIG-19-009 ; CERN-EP-2021-054 | ||
| Constraints on anomalous Higgs boson couplings to vector bosons and fermions in its production and decay using the four-lepton final state | ||
| CMS Collaboration | ||
| 25 April 2021 | ||
| Phys. Rev. D 104 (2021) 052004 | ||
| Abstract: Studies of $CP$ violation and anomalous couplings of the Higgs boson to vector bosons and fermions are presented. The data were acquired by the CMS experiment at the LHC and correspond to an integrated luminosity of 137 fb$^{-1}$ at a proton-proton collision energy of 13 TeV. The kinematic effects in the Higgs boson's four-lepton decay $\mathrm{H}\to4\ell$ and its production in association with two jets, a vector boson, or top quarks are analyzed, using a full detector simulation and matrix element techniques to identify the production mechanisms and to increase sensitivity to the Higgs boson tensor structure of the interactions. A simultaneous measurement is performed of up to five Higgs boson couplings to electroweak vector bosons (HVV), two couplings to gluons (Hgg), and two couplings to top quarks (Htt). The $CP$ measurement in the Htt interaction is combined with the recent measurement in the $\mathrm{H}\to\gamma\gamma$ channel. The results are presented in the framework of anomalous couplings and are also interpreted in the framework of effective field theory, including the first study of $CP$ properties of the Htt and effective Hgg couplings from a simultaneous analysis of the gluon fusion and top-associated processes. The results are consistent with the standard model of particle physics. | ||
| Links: e-print arXiv:2104.12152 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; Physics Briefing ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Leading-order Feynman diagrams for the gluon fusion production mode (left) and $\mathrm{H} \to \mathrm{V} \mathrm{V} $ decay (right). |
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Figure 1-a:
Leading-order Feynman diagram for the gluon fusion production mode. |
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Figure 1-b:
Leading-order Feynman diagram for the $\mathrm{H} \to \mathrm{V} \mathrm{V} $ decay. |
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Figure 2:
Leading-order Feynman diagrams for the VBF (left) and VH (right) production modes. |
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Figure 2-a:
Leading-order Feynman diagram for the VBF production mode. |
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Figure 2-b:
Leading-order Feynman diagram for the VH production mode. |
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Figure 3:
Examples of leading-order Feynman diagrams for the ttH (left) and bbH (right) production modes. |
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Figure 3-a:
Example of leading-order Feynman diagram for the ttH production mode. |
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Figure 3-b:
Example of leading-order Feynman diagram for the bbH production mode. |
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Figure 4:
Examples of leading-order Feynman diagrams for the tH production mode. |
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Figure 4-a:
Example of leading-order Feynman diagram for the tH production mode. |
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Figure 4-b:
Example of leading-order Feynman diagram for the tH production mode. |
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Figure 5:
Leading-order Feynman diagrams for the $\mathrm{g} \mathrm{g} \to \mathrm{Z} \mathrm{H} $ production mode. |
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Figure 5-a:
Leading-order Feynman diagram for the $\mathrm{g} \mathrm{g} \to \mathrm{Z} \mathrm{H} $ production mode. |
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Figure 5-b:
Leading-order Feynman diagram for the $\mathrm{g} \mathrm{g} \to \mathrm{Z} \mathrm{H} $ production mode. |
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Figure 6:
Four-lepton invariant mass distribution of observed events (data points) and expectation from MC simulation or background estimates (histograms) in the region between 70 and 170 GeV [78]. The peaks from the Z and $\mathrm{H} \to 4\ell $ decays are visible near 91 and 125 GeV, respectively. |
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Figure 7:
The distributions of observed events (data points) and expectation (histograms) for $\max\left (\mathcal {D}_\mathrm {2jet}^{{\mathrm {VBF}},i} \right)$ (middle) and $\max\left (\mathcal {D}_\mathrm {2jet}^{{\mathrm{W} \mathrm{H}},i},\mathcal {D}_\mathrm {2jet}^{{\mathrm{Z} \mathrm{H}},i} \right)$ (right), where maximum is evaluated over the the SM and the four anomalous coupling hypotheses $i$, described in the legend (left). Only events with at least two reconstructed jets are shown, and the requirement $ {{\mathcal {D}}_{\text {bkg}}} > $ 0.7 is applied in order to enhance the signal contribution over the background, where ${{\mathcal {D}}_{\text {bkg}}}$ is calculated using decay information only. The expectation is shown for the total distribution, including background and all production mechanisms of the H boson, and for the VBF (middle) and VH (right) signals, which are enhanced in the region above 0.5, indicated with the vertical dashed line. |
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Figure 7-a:
Legend of the figure. |
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Figure 7-b:
The distribution of observed events (data points) and expectation (histograms) for $\max\left (\mathcal {D}_\mathrm {2jet}^{{\mathrm {VBF}},i} \right)$, where maximum is evaluated over the the SM and the four anomalous coupling hypotheses $i$, described in the legend (Fig. 6-a). Only events with at least two reconstructed jets are shown, and the requirement $ {{\mathcal {D}}_{\text {bkg}}} > $ 0.7 is applied in order to enhance the signal contribution over the background, where ${{\mathcal {D}}_{\text {bkg}}}$ is calculated using decay information only. The expectation is shown for the total distribution, including background and all production mechanisms of the H boson, and for the VBF signal, which is enhanced in the region above 0.5, indicated with the vertical dashed line. |
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Figure 7-c:
The distribution of observed events (data points) and expectation (histograms) for $\max\left (\mathcal {D}_\mathrm {2jet}^{{\mathrm{W} \mathrm{H}},i},\mathcal {D}_\mathrm {2jet}^{{\mathrm{Z} \mathrm{H}},i} \right)$, where maximum is evaluated over the the SM and the four anomalous coupling hypotheses $i$, described in the legend (Fig. 6-a). Only events with at least two reconstructed jets are shown, and the requirement $ {{\mathcal {D}}_{\text {bkg}}} > $ 0.7 is applied in order to enhance the signal contribution over the background, where ${{\mathcal {D}}_{\text {bkg}}}$ is calculated using decay information only. The expectation is shown for the total distribution, including background and all production mechanisms of the H boson, and for the VH signals, which are enhanced in the region above 0.5, indicated with the vertical dashed line. |
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Figure 8:
Four topologies of the H boson production and decay: gluon or EW vector boson fusion $ {\mathrm{q} \mathrm{q}} \to \mathrm{V} _1\mathrm{V} _2 ({\mathrm{q} \mathrm{q}}) \to \mathrm{H} ({\mathrm{q} \mathrm{q}}) \to ({\mathrm{V} \mathrm{V}}) ({\mathrm{q} \mathrm{q}})$ (upper left); associated production $ {\mathrm{q} \mathrm{q}} \to \mathrm{V} \to \mathrm{V} \mathrm{H} \to (\mathrm {ff})\ ({\mathrm{V} \mathrm{V}})$ (upper right); H boson production in association with the top quarks ttH or tH (lower left); and four-lepton decay $\mathrm{H} \to {\mathrm{V} \mathrm{V}} \to 4\ell $ where the incoming gluons gg indicate the collision axis (lower right), and which proceeds either with or without associated particles. The incoming partons are shown in brown and the intermediate or final-state particles are shown in red and green. The angles characterizing kinematic distributions are shown in blue and are defined in the respective rest frames [29,31,32]. The subsequent top quark decay is not shown. See Ref. [32] for details. |
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Figure 8-a:
Topology for gluon or EW vector boson fusion H boson production, $ {\mathrm{q} \mathrm{q}} \to \mathrm{V} _1\mathrm{V} _2 ({\mathrm{q} \mathrm{q}}) \to \mathrm{H} ({\mathrm{q} \mathrm{q}}) \to ({\mathrm{V} \mathrm{V}}) ({\mathrm{q} \mathrm{q}})$. The incoming partons are shown in brown. The intermediate or final-state particles are shown in red and green. The angles characterizing kinematic distributions are shown in blue and are defined in the respective rest frames [29,31,32]. See Ref. [32] for details. |
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Figure 8-b:
Topology for associated H boson production $ {\mathrm{q} \mathrm{q}} \to \mathrm{V} \to \mathrm{V} \mathrm{H} \to (\mathrm {ff})\ ({\mathrm{V} \mathrm{V}})$. The incoming partons are shown in brown. The intermediate or final-state particles are shown in red and green. The angles characterizing kinematic distributions are shown in blue and are defined in the respective rest frames [29,31,32]. See Ref. [32] for details. |
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Figure 8-c:
Topology for four-lepton decay $\mathrm{H} \to {\mathrm{V} \mathrm{V}} \to 4\ell $. The incoming partons in brown indicate the collision axis. The intermediate or final-state particles are shown in red and green. The angles characterizing kinematic distributions are shown in blue and are defined in the respective rest frames [29,31,32]. The subsequent top quark decay is not shown. See Ref. [32] for details. |
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Figure 8-d:
Topology for four-lepton decay $\mathrm{H} \to {\mathrm{V} \mathrm{V}} \to 4\ell $ where the incoming gluons gg in brown indicate the collision axis. The intermediate or final-state particles are shown in red and green. The angles characterizing kinematic distributions are shown in blue and are defined in the respective rest frames [29,31,32]. See Ref. [32] for details. |
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Figure 9:
Distribution of the ${\mathcal {D}}_{\text {bkg}}$ (left) and $ \mathcal {D}_{\text {0-}}^{{{\mathrm{t} \mathrm{\bar{t}} \mathrm{H}}}}$ (right), discriminants in the sum of the ttH-leptonic and ttH-hadronic categories in Scheme 1. The latter distribution is shown with the requirement $ {{\mathcal {D}}_{\text {bkg}}} > $ 0.2 in order to enhance the signal over the background contribution. |
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Figure 9-a:
Distribution of the ${\mathcal {D}}_{\text {bkg}}$ discriminant in the sum of the ttH-leptonic and ttH-hadronic categories in Scheme 1. |
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Figure 9-b:
Distribution of the $ \mathcal {D}_{\text {0-}}^{{{\mathrm{t} \mathrm{\bar{t}} \mathrm{H}}}}$ discriminant in the sum of the ttH-leptonic and ttH-hadronic categories in Scheme 1. The distribution is shown with the requirement $ {{\mathcal {D}}_{\text {bkg}}} > $ 0.2 in order to enhance the signal over the background contribution. |
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Figure 10:
Distribution of the ${{\mathcal {D}}_{\text {bkg}}}$ (left), $\mathcal {D}_\text {0-}^{{\mathrm{g} \mathrm{g} \mathrm{H}}}$ (middle), and $\mathcal {D}_{\text {CP}}^{{\mathrm{g} \mathrm{g} \mathrm{H}}}$ (right) discriminants in the VBF-2jet category in Scheme 1. The latter two distributions are shown with the requirement $ {{\mathcal {D}}_{\text {bkg}}} > $ 0.2 in order to enhance the signal over the background contribution. |
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Figure 10-a:
Distribution of the ${{\mathcal {D}}_{\text {bkg}}}$ discriminant in the VBF-2jet category in Scheme 1. |
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Figure 10-b:
Distribution of the $\mathcal {D}_\text {0-}^{{\mathrm{g} \mathrm{g} \mathrm{H}}}$ discriminant in the VBF-2jet category in Scheme 1. The distribution is shown with the requirement $ {{\mathcal {D}}_{\text {bkg}}} > $ 0.2 in order to enhance the signal over the background contribution. |
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Figure 10-c:
Distribution of the $\mathcal {D}_{\text {CP}}^{{\mathrm{g} \mathrm{g} \mathrm{H}}}$ discriminant in the VBF-2jet category in Scheme 1. The distribution is shown with the requirement $ {{\mathcal {D}}_{\text {bkg}}} > $ 0.2 in order to enhance the signal over the background contribution. |
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Figure 11:
Distributions of events in the observables used in categorization Scheme 2. The first seven plots are in the Untagged category: The upper left plot shows ${{\mathcal {D}}_{\text {bkg}}}$. The rest of the distributions are shown with the requirement $ {{\mathcal {D}}_{\text {bkg}}} > $ 0.7 in order to enhance the signal over the background contribution: $\mathcal {D}_{0-}^{\text {dec}}$ (upper middle), $\mathcal {D}_{0h+}^{\text {dec}}$ (upper right), $\mathcal {D}_{\Lambda 1}^{\text {dec}}$ (middle left), $\mathcal {D}_{\Lambda 1}^{\mathrm{Z} \gamma, \text {dec}}$ (middle middle), $\mathcal {D}_{\mathrm {CP}}^{\text {dec}}$, and $\mathcal {D}_\text {int}^{\text {dec}}$. The last two plots are shown in the Boosted category: ${{\mathcal {D}}_{\text {bkg}}}$ (lower middle) and $ {p_{\mathrm {T}}} ^{4\ell}$ with the requirement $ {{\mathcal {D}}_{\text {bkg}}} > $ 0.7 and overflow events included in the last bin (lower right). Observed data, background expectation, and five signal models are shown in the plots, as indicated in the legend of Fig. 7. In several cases, a sixth signal model with a mixture of the SM and BSM couplings is shown and is indicated in the legend explicitly. |
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Figure 11-a:
Distribution of events for ${{\mathcal {D}}_{\text {bkg}}}$ in the Untagged category. Observed data, background expectation, and five signal models are shown in the plot, as indicated in the legend of Fig. 7. |
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Figure 11-b:
Distribution of events for $\mathcal {D}_{0-}^{\text {dec}}$ in the Untagged category, with the requirement $ {{\mathcal {D}}_{\text {bkg}}} > $ 0.7 in order to enhance the signal over the background contribution. Observed data, background expectation, and five signal models are shown in the plot, as indicated in the legend of Fig. 7. |
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Figure 11-c:
Distribution of events for $\mathcal {D}_{0h+}^{\text {dec}}$ in the Untagged category, with the requirement $ {{\mathcal {D}}_{\text {bkg}}} > $ 0.7 in order to enhance the signal over the background contribution. Observed data, background expectation, and five signal models are shown in the plot, as indicated in the legend of Fig. 7. A sixth signal model with a mixture of the SM and BSM couplings is shown and is indicated in the legend explicitly. |
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Figure 11-d:
Distribution of events for $\mathcal {D}_{\Lambda 1}^{\text {dec}}$ in the Untagged category, with the requirement $ {{\mathcal {D}}_{\text {bkg}}} > $ 0.7 in order to enhance the signal over the background contribution. Observed data, background expectation, and five signal models are shown in the plot, as indicated in the legend of Fig. 7. A sixth signal model with a mixture of the SM and BSM couplings is shown and is indicated in the legend explicitly. |
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Figure 11-e:
Distribution of events for $\mathcal {D}_{\Lambda 1}^{\mathrm{Z} \gamma, \text {dec}}$ in the Boosted category, with the requirement $ {{\mathcal {D}}_{\text {bkg}}} > $ 0.7 and overflow events included in the last bin (lower right). Observed data, background expectation, and five signal models are shown in the plot, as indicated in the legend of Fig. 7. |
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Figure 11-f:
Distribution of events for $\mathcal {D}_{\mathrm {CP}}^{\text {dec}}$ in the Untagged category, with the requirement $ {{\mathcal {D}}_{\text {bkg}}} > $ 0.7 in order to enhance the signal over the background contribution. Observed data, background expectation, and five signal models are shown in the plot, as indicated in the legend of Fig. 7. A sixth signal model with a mixture of the SM and BSM couplings is shown and is indicated in the legend explicitly. |
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Figure 11-g:
Distribution of events for $\mathcal {D}_\text {int}^{\text {dec}}$ in the Untagged category, with the requirement $ {{\mathcal {D}}_{\text {bkg}}} > $ 0.7 in order to enhance the signal over the background contribution. Observed data, background expectation, and five signal models are shown in the plot, as indicated in the legend of Fig. 7. A sixth signal model with a mixture of the SM and BSM couplings is shown and is indicated in the legend explicitly. |
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Figure 11-h:
Distribution of events for ${{\mathcal {D}}_{\text {bkg}}}$ in the Boosted category, with the requirement $ {{\mathcal {D}}_{\text {bkg}}} > $ 0.7. Observed data, background expectation, and five signal models are shown in the plot, as indicated in the legend of Fig. 7. |
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Figure 11-i:
Distribution of events for $ {p_{\mathrm {T}}} ^{4\ell}$ in the Boosted category, with the requirement $ {{\mathcal {D}}_{\text {bkg}}} > $ 0.7. The overflow events included in the last bin. Observed data, background expectation, and five signal models are shown in the plot, as indicated in the legend of Fig. 7. |
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Figure 12:
Distributions of events in the observables used in categorization Scheme 2. The first seven plots are in the VBF-2jet category: The upper left plot shows ${{\mathcal {D}}_{\text {bkg}}^{\mathrm {EW}}}$. The rest of the distributions are shown with the requirement $ {{\mathcal {D}}_{\text {bkg}}^{\mathrm {EW}}} > $ 0.2 in order to enhance the signal over the background contribution: $\mathcal {D}_{0-}^{\text {VBF}+\text {dec}}$ (upper middle), $\mathcal {D}_{0h+}^{\text {VBF}+\text {dec}}$ (upper right), $\mathcal {D}_{\Lambda 1}^{\text {VBF}+\text {dec}}$ (middle left), $\mathcal {D}_{\Lambda 1}^{\mathrm{Z} \gamma, \text {VBF}+\text {dec}}$ (middle middle), $\mathcal {D}_{\mathrm {CP}}^{\text {VBF}}$, and $\mathcal {D}_\text {int}^{\text {VBF}}$. The last two plots are shown in the VBF-1jet category: ${{\mathcal {D}}_{\text {bkg}}}$ (lower middle) and $ {p_{\mathrm {T}}} ^{4\ell}$ with the requirement $ {{\mathcal {D}}_{\text {bkg}}} > $ 0.7 and overflow events included in the last bin (lower right). Observed data, background expectation, and five signal models are shown in the plots, as indicated in the legend of Fig. 7. In several cases, a sixth signal model with a mixture of the SM and BSM couplings is shown and is indicated in the legend explicitly. |
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Figure 12-a:
Distribution of events for ${{\mathcal {D}}_{\text {bkg}}^{\mathrm {EW}}}$ in the VBF-2jet category. Observed data, background expectation, and five signal models are shown in the plots, as indicated in the legend of Fig. 7. |
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Figure 12-b:
Distribution of events for $\mathcal {D}_{0-}^{\text {VBF}+\text {dec}}$ in the VBF-2jet category with the requirement $ {{\mathcal {D}}_{\text {bkg}}^{\mathrm {EW}}} > $ 0.2 in order to enhance the signal over the background contribution. Observed data, background expectation, and five signal models are shown in the plots, as indicated in the legend of Fig. 7. |
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Figure 12-c:
Distribution of events for $\mathcal {D}_{0h+}^{\text {VBF}+\text {dec}}$ in the VBF-2jet category with the requirement $ {{\mathcal {D}}_{\text {bkg}}^{\mathrm {EW}}} > $ 0.2 in order to enhance the signal over the background contribution. Observed data, background expectation, and five signal models are shown in the plots, as indicated in the legend of Fig. 7. |
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Figure 12-d:
Distribution of events for $\mathcal {D}_{\Lambda 1}^{\text {VBF}+\text {dec}}$ in the VBF-2jet category with the requirement $ {{\mathcal {D}}_{\text {bkg}}^{\mathrm {EW}}} > $ 0.2 in order to enhance the signal over the background contribution. Observed data, background expectation, and five signal models are shown in the plots, as indicated in the legend of Fig. 7. |
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Figure 12-e:
Distribution of events for $\mathcal {D}_{\Lambda 1}^{\mathrm{Z} \gamma, \text {VBF}+\text {dec}}$ in the VBF-1jet category with the requirement $ {{\mathcal {D}}_{\text {bkg}}} > $ 0.7. Observed data, background expectation, and five signal models are shown in the plots, as indicated in the legend of Fig. 7. |
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Figure 12-f:
Distribution of events for $\mathcal {D}_{\mathrm {CP}}^{\text {VBF}}$ in the VBF-1jet category with the requirement $ {{\mathcal {D}}_{\text {bkg}}} > $ 0.7. Observed data, background expectation, and five signal models are shown in the plots, as indicated in the legend of Fig. 7. A sixth signal model with a mixture of the SM and BSM couplings is shown and is indicated in the legend explicitly. |
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Figure 12-g:
Distribution of events for $\mathcal {D}_\text {int}^{\text {VBF}}$ in the VBF-2jet category with the requirement $ {{\mathcal {D}}_{\text {bkg}}^{\mathrm {EW}}} > $ 0.2 in order to enhance the signal over the background contribution. Observed data, background expectation, and five signal models are shown in the plots, as indicated in the legend of Fig. 7. A sixth signal model with a mixture of the SM and BSM couplings is shown and is indicated in the legend explicitly. |
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Figure 12-h:
Distribution of events for ${{\mathcal {D}}_{\text {bkg}}}$ in the VBF-1jet category with the requirement $ {{\mathcal {D}}_{\text {bkg}}} > $ 0.7. Observed data, background expectation, and five signal models are shown in the plots, as indicated in the legend of Fig. 7. |
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Figure 12-i:
Distribution of events for $ {p_{\mathrm {T}}} ^{4\ell}$ in the VBF-1jet category with the requirement $ {{\mathcal {D}}_{\text {bkg}}} > $ 0.7. The overflow events included in the last bin. Observed data, background expectation, and five signal models are shown in the plots, as indicated in the legend of Fig. 7. |
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Figure 13:
Distributions of events in the observables used in categorization Scheme 2. The first seven plots are in the VH-hadronic category: The upper left plot shows ${{\mathcal {D}}_{\text {bkg}}^{\mathrm {EW}}}$. The rest of the distributions are shown with the requirement $ {{\mathcal {D}}_{\text {bkg}}^{\mathrm {EW}}} > $ 0.2 in order to enhance the signal over the background contribution: $\mathcal {D}_{0-}^{{\mathrm{V} \mathrm{H}} +\text {dec}}$ (upper middle); $\mathcal {D}_{0h+}^{{\mathrm{V} \mathrm{H}} +\text {dec}}$ (upper right); $\mathcal {D}_{\Lambda 1}^{{\mathrm{V} \mathrm{H}} +\text {dec}}$ (middle left); $\mathcal {D}_{\Lambda 1}^{\mathrm{Z} \gamma, VH +\text {dec}}$ (middle middle); $\mathcal {D}_{\mathrm {CP}}^{{\mathrm{V} \mathrm{H}}}$, and $\mathcal {D}_\text {int}^{{\mathrm{V} \mathrm{H}}}$. The last two plots are shown in the VH-leptonic category: ${{\mathcal {D}}_{\text {bkg}}}$ (lower middle) and $ {p_{\mathrm {T}}} ^{4\ell}$ with the requirement $ {{\mathcal {D}}_{\text {bkg}}} > $ 0.7 and overflow events included in the last bin (lower right). Observed data, background expectation, and five signal models are shown in the plots as indicated in the legend of Fig. 7. In several cases, a sixth signal model with a mixture of the SM and BSM couplings is shown and is indicated in the legend explicitly. |
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Figure 13-a:
Distribution of events for ${{\mathcal {D}}_{\text {bkg}}^{\mathrm {EW}}}$ in the VH-hadronic category. Observed data, background expectation, and five signal models are shown in the plots as indicated in the legend of Fig. 7. |
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Figure 13-b:
Distribution of events for $\mathcal {D}_{0-}^{{\mathrm{V} \mathrm{H}} +\text {dec}}$ in the VH-hadronic category with the requirement $ {{\mathcal {D}}_{\text {bkg}}^{\mathrm {EW}}} > $ 0.2 in order to enhance the signal over the background contribution. Observed data, background expectation, and five signal models are shown in the plots as indicated in the legend of Fig. 7. |
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Figure 13-c:
Distribution of events for $\mathcal {D}_{0h+}^{{\mathrm{V} \mathrm{H}} +\text {dec}}$ in the VH-hadronic category with the requirement $ {{\mathcal {D}}_{\text {bkg}}^{\mathrm {EW}}} > $ 0.2 in order to enhance the signal over the background contribution. Observed data, background expectation, and five signal models are shown in the plots as indicated in the legend of Fig. 7. |
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Figure 13-d:
Distribution of events for $\mathcal {D}_{\Lambda 1}^{{\mathrm{V} \mathrm{H}} +\text {dec}}$ in the VH-hadronic category with the requirement $ {{\mathcal {D}}_{\text {bkg}}^{\mathrm {EW}}} > $ 0.2 in order to enhance the signal over the background contribution. Observed data, background expectation, and five signal models are shown in the plots as indicated in the legend of Fig. 7. |
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Figure 13-e:
Distribution of events for $\mathcal {D}_{\Lambda 1}^{\mathrm{Z} \gamma, VH +\text {dec}}$ in the VH-hadronic category with the requirement $ {{\mathcal {D}}_{\text {bkg}}^{\mathrm {EW}}} > $ 0.2 in order to enhance the signal over the background contribution. Observed data, background expectation, and five signal models are shown in the plots as indicated in the legend of Fig. 7. |
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Figure 13-f:
Distribution of events for $\mathcal {D}_{\mathrm {CP}}^{{\mathrm{V} \mathrm{H}}}$ in the VH-hadronic category with the requirement $ {{\mathcal {D}}_{\text {bkg}}^{\mathrm {EW}}} > $ 0.2 in order to enhance the signal over the background contribution. Observed data, background expectation, and five signal models are shown in the plots as indicated in the legend of Fig. 7. A sixth signal model with a mixture of the SM and BSM couplings is shown and is indicated in the legend explicitly. |
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Figure 13-g:
Distribution of events for $\mathcal {D}_\text {int}^{{\mathrm{V} \mathrm{H}}}$ in the VH-hadronic category with the requirement $ {{\mathcal {D}}_{\text {bkg}}^{\mathrm {EW}}} > $ 0.2 in order to enhance the signal over the background contribution. Observed data, background expectation, and five signal models are shown in the plots as indicated in the legend of Fig. 7. A sixth signal model with a mixture of the SM and BSM couplings is shown and is indicated in the legend explicitly. |
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Figure 13-h:
Distribution of events for ${{\mathcal {D}}_{\text {bkg}}}$ in the VH-leptonic category with the requirement $ {{\mathcal {D}}_{\text {bkg}}} > $ 0.7. Observed data, background expectation, and five signal models are shown in the plots as indicated in the legend of Fig. 7. |
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Figure 13-i:
Distribution of events for $ {p_{\mathrm {T}}} ^{4\ell}$ in the VH-leptonic category with the requirement $ {{\mathcal {D}}_{\text {bkg}}} > $ 0.7. The overflow events included in the last bin. Observed data, background expectation, and five signal models are shown in the plots as indicated in the legend of Fig. 7. |
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Figure 14:
Constraints on the anomalous H boson couplings to gluons in the ggH process using the $\mathrm{H} \to 4\ell $ decay. Left: Observed (solid) and expected (dashed) likelihood scans of the $CP$-sensitive parameter $ {f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}} $. The dashed horizontal lines show 68 and 95% CL. Right: Observed confidence level intervals on the $c_{\mathrm{g} \mathrm{g}}$ and $\tilde{c}_{\mathrm{g} \mathrm{g}}$ couplings reinterpreted from the $ {f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}} $ and $\mu _{{\mathrm{g} \mathrm{g} \mathrm{H}}}$ measurement with $ {f_{a3}} $ and $ {\mu _{\mathrm{V}}} $ profiled, and with $\kappa _{\mathrm{t}}=\kappa _{\mathrm{b}}=1$. The dashed and solid lines show the 68 and 95% CL exclusion regions in two dimensions, respectively. |
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Figure 14-a:
Constraints on the anomalous H boson couplings to gluons in the ggH process using the $\mathrm{H} \to 4\ell $ decay. Left: Observed (solid) and expected (dashed) likelihood scans of the $CP$-sensitive parameter $ {f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}} $. The dashed horizontal lines show 68 and 95% CL. Right: Observed confidence level intervals on the $c_{\mathrm{g} \mathrm{g}}$ and $\tilde{c}_{\mathrm{g} \mathrm{g}}$ couplings reinterpreted from the $ {f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}} $ and $\mu _{{\mathrm{g} \mathrm{g} \mathrm{H}}}$ measurement with $ {f_{a3}} $ and $ {\mu _{\mathrm{V}}} $ profiled, and with $\kappa _{\mathrm{t}}=\kappa _{\mathrm{b}}=1$. The dashed and solid lines show the 68 and 95% CL exclusion regions in two dimensions, respectively. |
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Figure 14-b:
Constraints on the anomalous H boson couplings to gluons in the ggH process using the $\mathrm{H} \to 4\ell $ decay. Left: Observed (solid) and expected (dashed) likelihood scans of the $CP$-sensitive parameter $ {f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}} $. The dashed horizontal lines show 68 and 95% CL. Right: Observed confidence level intervals on the $c_{\mathrm{g} \mathrm{g}}$ and $\tilde{c}_{\mathrm{g} \mathrm{g}}$ couplings reinterpreted from the $ {f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}} $ and $\mu _{{\mathrm{g} \mathrm{g} \mathrm{H}}}$ measurement with $ {f_{a3}} $ and $ {\mu _{\mathrm{V}}} $ profiled, and with $\kappa _{\mathrm{t}}=\kappa _{\mathrm{b}}=1$. The dashed and solid lines show the 68 and 95% CL exclusion regions in two dimensions, respectively. |
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Figure 15:
Constraints on the anomalous H boson couplings to top quarks in the ttH and tH processes using the $\mathrm{H} \to \gamma \gamma $ [26] and $\mathrm{H} \to 4\ell $ decays. Left: Observed (solid) and expected (dashed) likelihood scans of $ {f_\mathrm {CP}^{{\mathrm{H} \text {tt}}}} $ in the ttH and tH processes in the $\mathrm{H} \to 4\ell $ (red), $\gamma \gamma $ (black), and combined (blue) channels, where the combination is done without relating the signal strengths in the two processes. The dashed horizontal lines show 68 and 95% CL. Right: Observed confidence level intervals on the $\kappa _{\mathrm{t}}$ and $\tilde\kappa _{\mathrm{t}}$ couplings reinterpreted from the $ {f_\mathrm {CP}^{{\mathrm{H} \text {tt}}}} $, $\mu _{{\mathrm{t} \mathrm{\bar{t}} \mathrm{H}}}$, and $ {\mu _{\mathrm{V}}} $ measurements in the combined fit of the $\mathrm{H} \to 4\ell $ and $\gamma \gamma $ channels, with the signal strengths in the two channels related through the couplings as discussed in text. The dashed and solid lines show the 68 and 95% CL exclusion regions in two dimensions, respectively. |
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Figure 15-a:
Constraints on the anomalous H boson couplings to top quarks in the ttH and tH processes using the $\mathrm{H} \to \gamma \gamma $ [26] and $\mathrm{H} \to 4\ell $ decays. Left: Observed (solid) and expected (dashed) likelihood scans of $ {f_\mathrm {CP}^{{\mathrm{H} \text {tt}}}} $ in the ttH and tH processes in the $\mathrm{H} \to 4\ell $ (red), $\gamma \gamma $ (black), and combined (blue) channels, where the combination is done without relating the signal strengths in the two processes. The dashed horizontal lines show 68 and 95% CL. Right: Observed confidence level intervals on the $\kappa _{\mathrm{t}}$ and $\tilde\kappa _{\mathrm{t}}$ couplings reinterpreted from the $ {f_\mathrm {CP}^{{\mathrm{H} \text {tt}}}} $, $\mu _{{\mathrm{t} \mathrm{\bar{t}} \mathrm{H}}}$, and $ {\mu _{\mathrm{V}}} $ measurements in the combined fit of the $\mathrm{H} \to 4\ell $ and $\gamma \gamma $ channels, with the signal strengths in the two channels related through the couplings as discussed in text. The dashed and solid lines show the 68 and 95% CL exclusion regions in two dimensions, respectively. |
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Figure 15-b:
Constraints on the anomalous H boson couplings to top quarks in the ttH and tH processes using the $\mathrm{H} \to \gamma \gamma $ [26] and $\mathrm{H} \to 4\ell $ decays. Left: Observed (solid) and expected (dashed) likelihood scans of $ {f_\mathrm {CP}^{{\mathrm{H} \text {tt}}}} $ in the ttH and tH processes in the $\mathrm{H} \to 4\ell $ (red), $\gamma \gamma $ (black), and combined (blue) channels, where the combination is done without relating the signal strengths in the two processes. The dashed horizontal lines show 68 and 95% CL. Right: Observed confidence level intervals on the $\kappa _{\mathrm{t}}$ and $\tilde\kappa _{\mathrm{t}}$ couplings reinterpreted from the $ {f_\mathrm {CP}^{{\mathrm{H} \text {tt}}}} $, $\mu _{{\mathrm{t} \mathrm{\bar{t}} \mathrm{H}}}$, and $ {\mu _{\mathrm{V}}} $ measurements in the combined fit of the $\mathrm{H} \to 4\ell $ and $\gamma \gamma $ channels, with the signal strengths in the two channels related through the couplings as discussed in text. The dashed and solid lines show the 68 and 95% CL exclusion regions in two dimensions, respectively. |
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Figure 16:
Constraints on the anomalous H boson couplings to top quarks in the ttH, tH, and ggH processes combined, assuming top quark dominance in the gluon fusion loop, using the $\mathrm{H} \to 4\ell $ and $\gamma \gamma $ decays. Observed (solid) and expected (dashed) likelihood scans of $ {f_\mathrm {CP}^{{\mathrm{H} \text {tt}}}} $ are shown in the ggH process with $\mathrm{H} \to 4\ell $ (black), ttH, tH, and ggH processes combined with $\mathrm{H} \to 4\ell $ (red), and in the ttH, tH, and ggH processes with $\mathrm{H} \to 4\ell $ and the ttH and tH processes with $\gamma \gamma $ combined (blue). Combination is done by relating the signal strengths in the three processes through the couplings in the loops in both production and decay, as discussed in the text. The dashed horizontal lines show 68 and 95% CL exclusion. |
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Figure 17:
Constraints on the anomalous H boson couplings $c_{\mathrm{g} \mathrm{g}}$, $\tilde{c}_{\mathrm{g} \mathrm{g}}$, $\kappa _\mathrm{t} $, and $\tilde\kappa _\mathrm{t} $ in the ttH, tH, and ggH processes combined, using the $\mathrm{H} \to 4\ell $ and $\gamma \gamma $ decays. The constraints are shown for the pairs of parameters: $c_{\mathrm{g} \mathrm{g}}$ and $\tilde{c}_{\mathrm{g} \mathrm{g}}$ (upper), $\kappa _\mathrm{t} $ and $\tilde\kappa _\mathrm{t} $ (middle), $\kappa _\mathrm{t} $ and $c_{\mathrm{g} \mathrm{g}}$ (lower), and with the other two parameters either profiled (left) or fixed to the SM expectation (right). The dashed and solid lines show the 68 and 95% CL exclusion regions in two dimensions, respectively. |
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Figure 17-a:
Constraints on the anomalous H boson couplings $c_{\mathrm{g} \mathrm{g}}$, $\tilde{c}_{\mathrm{g} \mathrm{g}}$, $\kappa _\mathrm{t} $, and $\tilde\kappa _\mathrm{t} $ in the ttH, tH, and ggH processes combined, using the $\mathrm{H} \to 4\ell $ and $\gamma \gamma $ decays. The constraints are shown for the pairs of parameters: $c_{\mathrm{g} \mathrm{g}}$ and $\tilde{c}_{\mathrm{g} \mathrm{g}}$ (upper), $\kappa _\mathrm{t} $ and $\tilde\kappa _\mathrm{t} $ (middle), $\kappa _\mathrm{t} $ and $c_{\mathrm{g} \mathrm{g}}$ (lower), and with the other two parameters either profiled (left) or fixed to the SM expectation (right). The dashed and solid lines show the 68 and 95% CL exclusion regions in two dimensions, respectively. |
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Figure 17-b:
Constraints on the anomalous H boson couplings $c_{\mathrm{g} \mathrm{g}}$, $\tilde{c}_{\mathrm{g} \mathrm{g}}$, $\kappa _\mathrm{t} $, and $\tilde\kappa _\mathrm{t} $ in the ttH, tH, and ggH processes combined, using the $\mathrm{H} \to 4\ell $ and $\gamma \gamma $ decays. The constraints are shown for the pairs of parameters: $c_{\mathrm{g} \mathrm{g}}$ and $\tilde{c}_{\mathrm{g} \mathrm{g}}$ (upper), $\kappa _\mathrm{t} $ and $\tilde\kappa _\mathrm{t} $ (middle), $\kappa _\mathrm{t} $ and $c_{\mathrm{g} \mathrm{g}}$ (lower), and with the other two parameters either profiled (left) or fixed to the SM expectation (right). The dashed and solid lines show the 68 and 95% CL exclusion regions in two dimensions, respectively. |
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Figure 17-c:
Constraints on the anomalous H boson couplings $c_{\mathrm{g} \mathrm{g}}$, $\tilde{c}_{\mathrm{g} \mathrm{g}}$, $\kappa _\mathrm{t} $, and $\tilde\kappa _\mathrm{t} $ in the ttH, tH, and ggH processes combined, using the $\mathrm{H} \to 4\ell $ and $\gamma \gamma $ decays. The constraints are shown for the pairs of parameters: $c_{\mathrm{g} \mathrm{g}}$ and $\tilde{c}_{\mathrm{g} \mathrm{g}}$ (upper), $\kappa _\mathrm{t} $ and $\tilde\kappa _\mathrm{t} $ (middle), $\kappa _\mathrm{t} $ and $c_{\mathrm{g} \mathrm{g}}$ (lower), and with the other two parameters either profiled (left) or fixed to the SM expectation (right). The dashed and solid lines show the 68 and 95% CL exclusion regions in two dimensions, respectively. |
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Figure 17-d:
Constraints on the anomalous H boson couplings $c_{\mathrm{g} \mathrm{g}}$, $\tilde{c}_{\mathrm{g} \mathrm{g}}$, $\kappa _\mathrm{t} $, and $\tilde\kappa _\mathrm{t} $ in the ttH, tH, and ggH processes combined, using the $\mathrm{H} \to 4\ell $ and $\gamma \gamma $ decays. The constraints are shown for the pairs of parameters: $c_{\mathrm{g} \mathrm{g}}$ and $\tilde{c}_{\mathrm{g} \mathrm{g}}$ (upper), $\kappa _\mathrm{t} $ and $\tilde\kappa _\mathrm{t} $ (middle), $\kappa _\mathrm{t} $ and $c_{\mathrm{g} \mathrm{g}}$ (lower), and with the other two parameters either profiled (left) or fixed to the SM expectation (right). The dashed and solid lines show the 68 and 95% CL exclusion regions in two dimensions, respectively. |
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Figure 17-e:
Constraints on the anomalous H boson couplings $c_{\mathrm{g} \mathrm{g}}$, $\tilde{c}_{\mathrm{g} \mathrm{g}}$, $\kappa _\mathrm{t} $, and $\tilde\kappa _\mathrm{t} $ in the ttH, tH, and ggH processes combined, using the $\mathrm{H} \to 4\ell $ and $\gamma \gamma $ decays. The constraints are shown for the pairs of parameters: $c_{\mathrm{g} \mathrm{g}}$ and $\tilde{c}_{\mathrm{g} \mathrm{g}}$ (upper), $\kappa _\mathrm{t} $ and $\tilde\kappa _\mathrm{t} $ (middle), $\kappa _\mathrm{t} $ and $c_{\mathrm{g} \mathrm{g}}$ (lower), and with the other two parameters either profiled (left) or fixed to the SM expectation (right). The dashed and solid lines show the 68 and 95% CL exclusion regions in two dimensions, respectively. |
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Figure 17-f:
Constraints on the anomalous H boson couplings $c_{\mathrm{g} \mathrm{g}}$, $\tilde{c}_{\mathrm{g} \mathrm{g}}$, $\kappa _\mathrm{t} $, and $\tilde\kappa _\mathrm{t} $ in the ttH, tH, and ggH processes combined, using the $\mathrm{H} \to 4\ell $ and $\gamma \gamma $ decays. The constraints are shown for the pairs of parameters: $c_{\mathrm{g} \mathrm{g}}$ and $\tilde{c}_{\mathrm{g} \mathrm{g}}$ (upper), $\kappa _\mathrm{t} $ and $\tilde\kappa _\mathrm{t} $ (middle), $\kappa _\mathrm{t} $ and $c_{\mathrm{g} \mathrm{g}}$ (lower), and with the other two parameters either profiled (left) or fixed to the SM expectation (right). The dashed and solid lines show the 68 and 95% CL exclusion regions in two dimensions, respectively. |
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Figure 18:
Observed (solid) and expected (dashed) likelihood scans of ${f_{a3}}$ (upper left), ${f_{a2}}$ (upper right), ${f_{\Lambda 1}}$ (lower left), and ${f_{\Lambda 1}^{\mathrm{Z} \gamma}}$ (lower right) in Approach 1 with the coupling relationship $a_i^{WW}=a_i^{ZZ}$. The results are shown for each coupling fraction separately with the other three anomalous coupling fractions either set to zero or left unconstrained in the fit. In all cases, the signal strength parameters have been left unconstrained. The dashed horizontal lines show the 68 and 95% CL regions. For better visibility of all features, the $x$ and $y$ axes are presented with variable scales. On the linear-scale $x$ axis, a zoom is applied in the range $-$0.03 to 0.03. The $y$ axis is shown in linear or logarithmic scale for values of $-2\ln\mathcal {L}$ below or above 11, respectively. |
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Figure 18-a:
Observed (solid) and expected (dashed) likelihood scans of ${f_{a3}}$ (upper left), ${f_{a2}}$ (upper right), ${f_{\Lambda 1}}$ (lower left), and ${f_{\Lambda 1}^{\mathrm{Z} \gamma}}$ (lower right) in Approach 1 with the coupling relationship $a_i^{WW}=a_i^{ZZ}$. The results are shown for each coupling fraction separately with the other three anomalous coupling fractions either set to zero or left unconstrained in the fit. In all cases, the signal strength parameters have been left unconstrained. The dashed horizontal lines show the 68 and 95% CL regions. For better visibility of all features, the $x$ and $y$ axes are presented with variable scales. On the linear-scale $x$ axis, a zoom is applied in the range $-$0.03 to 0.03. The $y$ axis is shown in linear or logarithmic scale for values of $-2\ln\mathcal {L}$ below or above 11, respectively. |
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Figure 18-b:
Observed (solid) and expected (dashed) likelihood scans of ${f_{a3}}$ (upper left), ${f_{a2}}$ (upper right), ${f_{\Lambda 1}}$ (lower left), and ${f_{\Lambda 1}^{\mathrm{Z} \gamma}}$ (lower right) in Approach 1 with the coupling relationship $a_i^{WW}=a_i^{ZZ}$. The results are shown for each coupling fraction separately with the other three anomalous coupling fractions either set to zero or left unconstrained in the fit. In all cases, the signal strength parameters have been left unconstrained. The dashed horizontal lines show the 68 and 95% CL regions. For better visibility of all features, the $x$ and $y$ axes are presented with variable scales. On the linear-scale $x$ axis, a zoom is applied in the range $-$0.03 to 0.03. The $y$ axis is shown in linear or logarithmic scale for values of $-2\ln\mathcal {L}$ below or above 11, respectively. |
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Figure 18-c:
Observed (solid) and expected (dashed) likelihood scans of ${f_{a3}}$ (upper left), ${f_{a2}}$ (upper right), ${f_{\Lambda 1}}$ (lower left), and ${f_{\Lambda 1}^{\mathrm{Z} \gamma}}$ (lower right) in Approach 1 with the coupling relationship $a_i^{WW}=a_i^{ZZ}$. The results are shown for each coupling fraction separately with the other three anomalous coupling fractions either set to zero or left unconstrained in the fit. In all cases, the signal strength parameters have been left unconstrained. The dashed horizontal lines show the 68 and 95% CL regions. For better visibility of all features, the $x$ and $y$ axes are presented with variable scales. On the linear-scale $x$ axis, a zoom is applied in the range $-$0.03 to 0.03. The $y$ axis is shown in linear or logarithmic scale for values of $-2\ln\mathcal {L}$ below or above 11, respectively. |
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Figure 18-d:
Observed (solid) and expected (dashed) likelihood scans of ${f_{a3}}$ (upper left), ${f_{a2}}$ (upper right), ${f_{\Lambda 1}}$ (lower left), and ${f_{\Lambda 1}^{\mathrm{Z} \gamma}}$ (lower right) in Approach 1 with the coupling relationship $a_i^{WW}=a_i^{ZZ}$. The results are shown for each coupling fraction separately with the other three anomalous coupling fractions either set to zero or left unconstrained in the fit. In all cases, the signal strength parameters have been left unconstrained. The dashed horizontal lines show the 68 and 95% CL regions. For better visibility of all features, the $x$ and $y$ axes are presented with variable scales. On the linear-scale $x$ axis, a zoom is applied in the range $-$0.03 to 0.03. The $y$ axis is shown in linear or logarithmic scale for values of $-2\ln\mathcal {L}$ below or above 11, respectively. |
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Figure 19:
Observed two-dimensional likelihood scans of the four coupling parameters ${f_{a3}}$, ${f_{a2}}$, ${f_{\Lambda 1}}$, and ${f_{\Lambda 1}^{\mathrm{Z} \gamma}}$ in Approach 1 with the coupling relationship $a_i^{WW}=a_i^{ZZ}$. In each case, the other two anomalous couplings along with the signal strength parameters have been left unconstrained. The 68 and 95% CL regions are presented as contours with dashed and solid black lines, respectively. The best fit values and the SM expectations are indicated by markers. |
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Figure 19-a:
Observed two-dimensional likelihood scans of the four coupling parameters ${f_{a3}}$, ${f_{a2}}$, ${f_{\Lambda 1}}$, and ${f_{\Lambda 1}^{\mathrm{Z} \gamma}}$ in Approach 1 with the coupling relationship $a_i^{WW}=a_i^{ZZ}$. In each case, the other two anomalous couplings along with the signal strength parameters have been left unconstrained. The 68 and 95% CL regions are presented as contours with dashed and solid black lines, respectively. The best fit values and the SM expectations are indicated by markers. |
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Figure 19-b:
Observed two-dimensional likelihood scans of the four coupling parameters ${f_{a3}}$, ${f_{a2}}$, ${f_{\Lambda 1}}$, and ${f_{\Lambda 1}^{\mathrm{Z} \gamma}}$ in Approach 1 with the coupling relationship $a_i^{WW}=a_i^{ZZ}$. In each case, the other two anomalous couplings along with the signal strength parameters have been left unconstrained. The 68 and 95% CL regions are presented as contours with dashed and solid black lines, respectively. The best fit values and the SM expectations are indicated by markers. |
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Figure 19-c:
Observed two-dimensional likelihood scans of the four coupling parameters ${f_{a3}}$, ${f_{a2}}$, ${f_{\Lambda 1}}$, and ${f_{\Lambda 1}^{\mathrm{Z} \gamma}}$ in Approach 1 with the coupling relationship $a_i^{WW}=a_i^{ZZ}$. In each case, the other two anomalous couplings along with the signal strength parameters have been left unconstrained. The 68 and 95% CL regions are presented as contours with dashed and solid black lines, respectively. The best fit values and the SM expectations are indicated by markers. |
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Figure 19-d:
Observed two-dimensional likelihood scans of the four coupling parameters ${f_{a3}}$, ${f_{a2}}$, ${f_{\Lambda 1}}$, and ${f_{\Lambda 1}^{\mathrm{Z} \gamma}}$ in Approach 1 with the coupling relationship $a_i^{WW}=a_i^{ZZ}$. In each case, the other two anomalous couplings along with the signal strength parameters have been left unconstrained. The 68 and 95% CL regions are presented as contours with dashed and solid black lines, respectively. The best fit values and the SM expectations are indicated by markers. |
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Figure 19-e:
Observed two-dimensional likelihood scans of the four coupling parameters ${f_{a3}}$, ${f_{a2}}$, ${f_{\Lambda 1}}$, and ${f_{\Lambda 1}^{\mathrm{Z} \gamma}}$ in Approach 1 with the coupling relationship $a_i^{WW}=a_i^{ZZ}$. In each case, the other two anomalous couplings along with the signal strength parameters have been left unconstrained. The 68 and 95% CL regions are presented as contours with dashed and solid black lines, respectively. The best fit values and the SM expectations are indicated by markers. |
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Figure 19-f:
Observed two-dimensional likelihood scans of the four coupling parameters ${f_{a3}}$, ${f_{a2}}$, ${f_{\Lambda 1}}$, and ${f_{\Lambda 1}^{\mathrm{Z} \gamma}}$ in Approach 1 with the coupling relationship $a_i^{WW}=a_i^{ZZ}$. In each case, the other two anomalous couplings along with the signal strength parameters have been left unconstrained. The 68 and 95% CL regions are presented as contours with dashed and solid black lines, respectively. The best fit values and the SM expectations are indicated by markers. |
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Figure 20:
Observed (solid) and expected (dashed) likelihood scans of ${f_{a3}}$ (upper left), ${f_{a2}}$ (upper right), and ${f_{\Lambda 1}}$ (lower) in Approach 2 within SMEFT with the symmetry relationship of couplings set in Eqs. (3-7). The results are shown for each coupling separately with the other anomalous coupling fractions either set to zero or left unconstrained in the fit. In all cases, the signal strength parameters have been left unconstrained. The dashed horizontal lines show the 68 and 95% CL regions. For better visibility of all features, the $x$ and $y$ axes are presented with variable scales. On the linear-scale $x$ axis, a zoom is applied in the range $-$0.03 to 0.03. The $y$ axis is shown in linear or logarithmic scale for values of $-2\ln\mathcal {L}$ below or above 11, respectively. |
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Figure 20-a:
Observed (solid) and expected (dashed) likelihood scans of ${f_{a3}}$ (upper left), ${f_{a2}}$ (upper right), and ${f_{\Lambda 1}}$ (lower) in Approach 2 within SMEFT with the symmetry relationship of couplings set in Eqs. (3-7). The results are shown for each coupling separately with the other anomalous coupling fractions either set to zero or left unconstrained in the fit. In all cases, the signal strength parameters have been left unconstrained. The dashed horizontal lines show the 68 and 95% CL regions. For better visibility of all features, the $x$ and $y$ axes are presented with variable scales. On the linear-scale $x$ axis, a zoom is applied in the range $-$0.03 to 0.03. The $y$ axis is shown in linear or logarithmic scale for values of $-2\ln\mathcal {L}$ below or above 11, respectively. |
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Figure 20-b:
Observed (solid) and expected (dashed) likelihood scans of ${f_{a3}}$ (upper left), ${f_{a2}}$ (upper right), and ${f_{\Lambda 1}}$ (lower) in Approach 2 within SMEFT with the symmetry relationship of couplings set in Eqs. (3-7). The results are shown for each coupling separately with the other anomalous coupling fractions either set to zero or left unconstrained in the fit. In all cases, the signal strength parameters have been left unconstrained. The dashed horizontal lines show the 68 and 95% CL regions. For better visibility of all features, the $x$ and $y$ axes are presented with variable scales. On the linear-scale $x$ axis, a zoom is applied in the range $-$0.03 to 0.03. The $y$ axis is shown in linear or logarithmic scale for values of $-2\ln\mathcal {L}$ below or above 11, respectively. |
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Figure 20-c:
Observed (solid) and expected (dashed) likelihood scans of ${f_{a3}}$ (upper left), ${f_{a2}}$ (upper right), and ${f_{\Lambda 1}}$ (lower) in Approach 2 within SMEFT with the symmetry relationship of couplings set in Eqs. (3-7). The results are shown for each coupling separately with the other anomalous coupling fractions either set to zero or left unconstrained in the fit. In all cases, the signal strength parameters have been left unconstrained. The dashed horizontal lines show the 68 and 95% CL regions. For better visibility of all features, the $x$ and $y$ axes are presented with variable scales. On the linear-scale $x$ axis, a zoom is applied in the range $-$0.03 to 0.03. The $y$ axis is shown in linear or logarithmic scale for values of $-2\ln\mathcal {L}$ below or above 11, respectively. |
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Figure 21:
Observed (solid) and expected (dashed) constraints from a simultaneous fit of the SMEFT parameters $\delta c_\mathrm {z}$ (upper left), $c_\mathrm {zz}$ (upper right), $c_{\mathrm {z} \Box}$ (lower left), and $\tilde{c}_\mathrm {zz}$ (lower right) with the $c_{\mathrm{g} \mathrm{g}}$ and $\tilde{c}_{\mathrm{g} \mathrm{g}}$ couplings left unconstrained. |
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Figure 21-a:
Observed (solid) and expected (dashed) constraints from a simultaneous fit of the SMEFT parameters $\delta c_\mathrm {z}$ (upper left), $c_\mathrm {zz}$ (upper right), $c_{\mathrm {z} \Box}$ (lower left), and $\tilde{c}_\mathrm {zz}$ (lower right) with the $c_{\mathrm{g} \mathrm{g}}$ and $\tilde{c}_{\mathrm{g} \mathrm{g}}$ couplings left unconstrained. |
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Figure 21-b:
Observed (solid) and expected (dashed) constraints from a simultaneous fit of the SMEFT parameters $\delta c_\mathrm {z}$ (upper left), $c_\mathrm {zz}$ (upper right), $c_{\mathrm {z} \Box}$ (lower left), and $\tilde{c}_\mathrm {zz}$ (lower right) with the $c_{\mathrm{g} \mathrm{g}}$ and $\tilde{c}_{\mathrm{g} \mathrm{g}}$ couplings left unconstrained. |
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Figure 21-c:
Observed (solid) and expected (dashed) constraints from a simultaneous fit of the SMEFT parameters $\delta c_\mathrm {z}$ (upper left), $c_\mathrm {zz}$ (upper right), $c_{\mathrm {z} \Box}$ (lower left), and $\tilde{c}_\mathrm {zz}$ (lower right) with the $c_{\mathrm{g} \mathrm{g}}$ and $\tilde{c}_{\mathrm{g} \mathrm{g}}$ couplings left unconstrained. |
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Figure 21-d:
Observed (solid) and expected (dashed) constraints from a simultaneous fit of the SMEFT parameters $\delta c_\mathrm {z}$ (upper left), $c_\mathrm {zz}$ (upper right), $c_{\mathrm {z} \Box}$ (lower left), and $\tilde{c}_\mathrm {zz}$ (lower right) with the $c_{\mathrm{g} \mathrm{g}}$ and $\tilde{c}_{\mathrm{g} \mathrm{g}}$ couplings left unconstrained. |
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Figure 22:
Observed two-dimensional constraints from a simultaneous fit of the SMEFT parameters $\delta c_\mathrm {z}$, $c_\mathrm {zz}$, $c_{\mathrm {z} \Box}$, and $\tilde{c}_\mathrm {zz}$ with the $c_{\mathrm{g} \mathrm{g}}$ and $\tilde{c}_{\mathrm{g} \mathrm{g}}$ couplings left unconstrained. |
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Figure 22-a:
Observed two-dimensional constraints from a simultaneous fit of the SMEFT parameters $\delta c_\mathrm {z}$, $c_\mathrm {zz}$, $c_{\mathrm {z} \Box}$, and $\tilde{c}_\mathrm {zz}$ with the $c_{\mathrm{g} \mathrm{g}}$ and $\tilde{c}_{\mathrm{g} \mathrm{g}}$ couplings left unconstrained. |
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Figure 22-b:
Observed two-dimensional constraints from a simultaneous fit of the SMEFT parameters $\delta c_\mathrm {z}$, $c_\mathrm {zz}$, $c_{\mathrm {z} \Box}$, and $\tilde{c}_\mathrm {zz}$ with the $c_{\mathrm{g} \mathrm{g}}$ and $\tilde{c}_{\mathrm{g} \mathrm{g}}$ couplings left unconstrained. |
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Figure 22-c:
Observed two-dimensional constraints from a simultaneous fit of the SMEFT parameters $\delta c_\mathrm {z}$, $c_\mathrm {zz}$, $c_{\mathrm {z} \Box}$, and $\tilde{c}_\mathrm {zz}$ with the $c_{\mathrm{g} \mathrm{g}}$ and $\tilde{c}_{\mathrm{g} \mathrm{g}}$ couplings left unconstrained. |
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Figure 22-d:
Observed two-dimensional constraints from a simultaneous fit of the SMEFT parameters $\delta c_\mathrm {z}$, $c_\mathrm {zz}$, $c_{\mathrm {z} \Box}$, and $\tilde{c}_\mathrm {zz}$ with the $c_{\mathrm{g} \mathrm{g}}$ and $\tilde{c}_{\mathrm{g} \mathrm{g}}$ couplings left unconstrained. |
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Figure 22-e:
Observed two-dimensional constraints from a simultaneous fit of the SMEFT parameters $\delta c_\mathrm {z}$, $c_\mathrm {zz}$, $c_{\mathrm {z} \Box}$, and $\tilde{c}_\mathrm {zz}$ with the $c_{\mathrm{g} \mathrm{g}}$ and $\tilde{c}_{\mathrm{g} \mathrm{g}}$ couplings left unconstrained. |
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Figure 22-f:
Observed two-dimensional constraints from a simultaneous fit of the SMEFT parameters $\delta c_\mathrm {z}$, $c_\mathrm {zz}$, $c_{\mathrm {z} \Box}$, and $\tilde{c}_\mathrm {zz}$ with the $c_{\mathrm{g} \mathrm{g}}$ and $\tilde{c}_{\mathrm{g} \mathrm{g}}$ couplings left unconstrained. |
| Tables | |
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Table 1:
List of anomalous HVV couplings $a_i^{\mathrm{V} \mathrm{V}}$ considered, the corresponding measured cross section fractions $f_{ai}^{\mathrm{V} \mathrm{V}}$ defined in Eq. (18), and the translation coefficients $\alpha _{ii}/\alpha _{11}$ in this definition with the relationship $a_i^{\mathrm{Z} \mathrm{Z}}=a_i^{\mathrm{W} \mathrm{W}}$ (Approach 1), and with the SMEFT relationship according to Eqs. (3-7) (Approach 2). In the case of the $\kappa _1$ and $\kappa _2^{\mathrm{Z} \gamma}$ couplings, the numerical values $\Lambda _{1}=\Lambda _{1}^{\mathrm{Z} \gamma} = $ 100 GeV are adopted in this calculation to make the coefficients have the same order of magnitude. |
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Table 2:
The numbers of events expected in the SM for different H signal (sig) and background (bkg) contributions and the observed number of events in each category defined in Scheme 1 targeting Hff and Hgg anomalous couplings. The ttH signal expectation is quoted for the SM and anomalous coupling ($\kappa _{\mathrm{t}}=0$, $\tilde\kappa _{\mathrm{t}}=1.6$) scenario, both generated with the same cross section. |
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Table 3:
The numbers of events expected in the SM for different H signal (sig) and background (bkg) contributions and the observed number of events in each category defined in Scheme 2 targeting HVV anomalous couplings. The EW (VBF, WH, and ZH) signal expectation is quoted for the SM and four anomalous coupling ($a_3/a_2/\kappa _1/\kappa _2^{\mathrm{Z} \gamma}$) scenarios $f_{ai}=1$, all generated with the same total EW production cross section. |
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Table 4:
The list of kinematic observables used for category selection and fitting in categorization Schemes 1 and 2. Only the main features involving the kinematic discriminants in the category selection are listed, while complete details are given in Section 3. The Untagged category includes the events not selected in the other categories. |
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Table 5:
Constraints on the $ {f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}} $ and $ {f_\mathrm {CP}^{{\mathrm{H} \text {tt}}}} $ parameters with the best fit values and allowed $68%$ CL (quoted uncertainties) and 95% CL (within square brackets) intervals, limited to the physical range of $[-1, 1]$. The $ {f_\mathrm {CP}^{{\mathrm{H} \text {tt}}}} $ constraints obtained in this work are combined with those in the $\mathrm{H} \to \gamma \gamma $ channel [26]. The interpretation of the $ {f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}} $ result under the assumption of the top quark dominance in the gluon fusion loop are presented in terms of the $ {f_\mathrm {CP}^{{\mathrm{H} \text {tt}}}} $ parameter, where either ggH or its combination with tH and ttH results are shown. |
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Table 6:
Summary of constraints on the anomalous HVV coupling parameters with the best fit values and allowed 68 and 95% CL intervals. Three scenarios are shown for each parameter: with three other anomalous HVV couplings set to zero (first), with three other anomalous HVV couplings left unconstrained (second), in Approach 1 with the relationship $a_i^{WW}=a_i^{ZZ}$ in both cases; and with two other anomalous HVV couplings left unconstrained (third), in Approach 2 within SMEFT with the symmetry relationship of couplings set in Eqs. (3-7). The $ {f_{\Lambda 1}^{\mathrm{Z} \gamma}} $ parameter is not independent in the latter scenario. |
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Table 7:
The observed correlation coefficients of the signal strength ${\mu _{\mathrm{V}}}$ and the ${f_{a3}}$, ${f_{a2}}$, ${f_{\Lambda 1}}$ parameters in Approach 2 within SMEFT with the symmetry relationship of couplings set in Eqs. (3-7). |
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Table 8:
Summary of constraints on the Htt, Hgg, and HVV coupling parameters in the Higgs basis of SMEFT. The observed correlation coefficients are presented for the Htt & Hgg and HVV couplings in the fit configurations discussed in text and shown in Figs. 17 and 22, respectively. |
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Table 9:
Summary of constraints on the HVV coupling parameters in the Warsaw basis of SMEFT. For each coupling constraint reported, three other independent operators are left unconstrained, where only one of the three operators $c_{\mathrm{H} \mathrm{W}}$, $c_{\mathrm{H} \mathrm{W} \mathrm {B}}$, and $c_{\mathrm{H} \mathrm {B}}$ is independent, and only one of $c_{\mathrm{H} \tilde{\mathrm{W}}}$, $c_{\mathrm{H} \tilde{\mathrm{W}}\mathrm {B}}$, and $c_{\mathrm{H} \tilde{\mathrm {B}}}$ is independent. |
| Summary |
|
In this paper, a comprehensive study of $CP$-violation, anomalous couplings, and the tensor structure of H boson interactions with electroweak gauge bosons, gluons, and fermions, using all accessible production mechanisms and the ${\mathrm{H}\to4\ell} $ decay mode, is presented. The results are based on the 2016-2018 data from ${\mathrm{p}}{\mathrm{p}}$ collisions recorded with the CMS detector during Run 2 of the LHC, corresponding to an integrated luminosity of 137 fb$^{-1}$ at a center-of-mass energy of 13 TeV. These results significantly surpass our results from Run 1 [13] in both precision and extent of coverage. The improvements result not only from a significantly increased sample of H bosons, but also from a detailed analysis of kinematic distributions of the particles associated with the H boson production in addition to kinematic distributions in its decay. These results also surpass our earlier studies of on-shell production of the H boson in this decay channel with a partial Run 2 dataset [16,17]. The parameterization of the H boson production and decay processes is based on a scattering amplitude or, equivalently, an effective field theory Lagrangian, with operators up to dimension six. Additional symmetries and prior measurements allow us to reduce the number of independent parameters and make a connection to the standard model effective field theory (SMEFT) formulation. Dedicated Monte Carlo programs and matrix-element re-weighting techniques provide modeling of all kinematic effects in the production and decay of the H boson, with any variation of parameters of the scattering amplitude and with full simulation of detector effects. Each production process of the H boson is identified using the kinematic features of its associated particles. The matrix element likelihood approach (MELA) is employed to construct observables that are optimal for the measurement of the targeted anomalous couplings in each process, including $CP$-sensitive observables. A maximum likelihood fit allows a simultaneous measurement of up to five HVV, two Hgg, and two Htt couplings. For the first time, we present a complete dedicated study of $CP$ properties in the H boson coupling to gluons through a loop of heavy particles using the $CP$-sensitive observables, while separating the electroweak and strong boson fusion processes. An interpretation of the loop contribution is made both with and without an assumption of top quark dominance, which allows a new heavy particle to contribute. In both cases, combination with the $CP$-sensitive measurement of the Htt coupling in the ttH and tH processes allows either simultaneous or separate measurements of the two effective point-like Hgg couplings and the two Htt couplings, both $CP$-odd and $CP$-even. For the ttH and tH processes, results in the ${\mathrm{H}\to4\ell} $ channel are combined with those in the $\mathrm{H}\to\gamma\gamma$ channel [26]. This is the first comprehensive study of $CP$ properties in the Hgg and Htt couplings from a simultaneous measurement of the ggH, ttH, and tH processes. Also for the first time, we present the measurement of $CP$ properties and the tensor structure of the H boson 's interactions with two electroweak bosons with up to five parameters measured simultaneously. The HVV coupling is analyzed in VBF and VH production and in $\mathrm{H}\to{\mathrm{V}\mathrm{V}} \to4\ell$ decay. The measurements are performed with two approaches. In the first approach, more lenient symmetry considerations are applied, which allow a less restrictive interpretation of results. In the second approach, SU(2)$\times$U(1) symmetry is invoked and the formulation becomes equivalent to SMEFT. The operator basis is chosen to coincide with the couplings of the mass eigenstates, which allows us to minimize the number of independent parameters. A translation of the SMEFT results to the Warsaw basis is also presented for easier comparison with other results. In all cases, we first present results in terms of the total cross section of a process and the fractional contribution of each anomalous coupling. These results are further re-interpreted in terms of direct constraints on the couplings by applying certain assumptions about the H boson total width. Each of the measurements presented here is limited by statistical precision and is consistent with the expectations for the standard model Higgs boson. |
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