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| CMS-PAS-HIG-19-009 | ||
| Constraints on anomalous Higgs boson couplings to vector bosons and fermions in production and decay in the $\mathrm{H}\to4\ell$ channel | ||
| CMS Collaboration | ||
| July 2020 | ||
| Abstract: Studies of CP-violation and anomalous couplings of the Higgs boson to vector bosons and fermions are presented. Kinematics of the Higgs boson's four-lepton decay and of its production in association with a vector boson, hadronic jets, or a top-quark pair are used. The data used in this study were acquired by the CMS experiment at the LHC and corresponds to an integrated luminosity of 137 fb$^{-1}$ at a center-of-mass energy of $\sqrt{s}= $ 13 TeV. A full detector simulation of all kinematic effects in the Higgs boson decay and associated particle production is performed. These effects are analyzed using matrix element techniques to identify the production mechanism and to increase sensitivity to the Higgs boson couplings. Simultaneous measurement of up to five HVV, two Hgg, and two Htt couplings is performed. The results are presented in the framework of anomalous coupling measurements and are also interpreted in the effective field theory framework, with SU(2)$\times$U(1) symmetry for the HVV couplings. | ||
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These preliminary results are superseded in this paper, PRD 104 (2021) 052004. The superseded preliminary plots can be found here. |
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| Figures & Tables | Summary | Additional Figures | References | CMS Publications |
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| Figures | |
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Figure 1:
The distributions of events for $\max (\mathcal {D}_\mathrm {2jet}^{{\mathrm {VBF}},i} )$ (middle) and $\max (\mathcal {D}_\mathrm {2jet}^{{\mathrm{W} \mathrm{H}},i},\mathcal {D}_\mathrm {2jet}^{{\mathrm{Z} \mathrm{H}},i} )$ (right). Only events with at least two reconstructed jets are shown, and the requirement $ {{\mathcal {D}}_{\text {bkg}}} > $ 0.7, where ${{\mathcal {D}}_{\text {bkg}}}$ is calculated using decay information only, is applied in order to enhance the signal contribution over the background. The VBF (middle) and VH (right) signal under the SM and the four pure anomalous hypotheses, as described in the legend (left), is enhanced in the region above 0.5, indicated with the vertical dashed line. |
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Figure 1-a:
Legend of Fig.1. |
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Figure 1-b:
The distribution of events for $\max (\mathcal {D}_\mathrm {2jet}^{{\mathrm {VBF}},i} )$. $\max (\mathcal {D}_\mathrm {2jet}^{{\mathrm{W} \mathrm{H}},i},\mathcal {D}_\mathrm {2jet}^{{\mathrm{Z} \mathrm{H}},i} )$. Only events with at least two reconstructed jets are shown, and the requirement $ {{\mathcal {D}}_{\text {bkg}}} > $ 0.7, where ${{\mathcal {D}}_{\text {bkg}}}$ is calculated using decay information only, is applied in order to enhance the signal contribution over the background. The VBF VH signal under the SM and the four pure anomalous hypotheses is enhanced in the region above 0.5, indicated with the vertical dashed line. |
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Figure 1-c:
The distribution of events for $\max (\mathcal {D}_\mathrm {2jet}^{{\mathrm {VBF}},i} )$. $\max (\mathcal {D}_\mathrm {2jet}^{{\mathrm{W} \mathrm{H}},i},\mathcal {D}_\mathrm {2jet}^{{\mathrm{Z} \mathrm{H}},i} )$. Only events with at least two reconstructed jets are shown, and the requirement $ {{\mathcal {D}}_{\text {bkg}}} > $ 0.7, where ${{\mathcal {D}}_{\text {bkg}}}$ is calculated using decay information only, is applied in order to enhance the signal contribution over the background. The VBF VH signal under the SM and the four pure anomalous hypotheses is enhanced in the region above 0.5, indicated with the vertical dashed line. |
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Figure 2:
Four topologies of the H boson production and decay: gluon or vector boson fusion $ {\mathrm{q} \mathrm{q}} \to {\mathrm {VV}} ({\mathrm{q} \mathrm{q}}) \to \mathrm{H} ({\mathrm{q} \mathrm{q}}) \to {\mathrm {VV}} ({\mathrm{q} \mathrm{q}})$ (top-left); associated production $ {\mathrm{q} \mathrm{q}} \to {\mathrm {V}} \to {\mathrm {V}} \mathrm{H} \to ({\mathrm {f}\mathrm {\overline {f}}})\ \mathrm{H} \to ({\mathrm {f}\mathrm {\overline {f}}})\ {\mathrm {VV}} $ (top-right); $ {\mathrm{t} \mathrm{\bar{t}} \mathrm{H}} $ or $ {\mathrm{t} \mathrm{H}} $ production in association with the top quarks (bottom-left); and decay $\mathrm{g} \mathrm{g} \to \mathrm{H} \to {\mathrm {VV}} \to 4\ell $ (bottom-right), 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 kinematics are shown in blue and are defined in the respective rest frames [43,52], while the subsequent top quark decay is not shown but should be included [61]. |
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Figure 2-a:
Topology of the gluon or vector boson fusion $ {\mathrm{q} \mathrm{q}} \to {\mathrm {VV}} ({\mathrm{q} \mathrm{q}}) \to \mathrm{H} ({\mathrm{q} \mathrm{q}}) \to {\mathrm {VV}} ({\mathrm{q} \mathrm{q}})$ process. The incoming partons are shown in brown and the intermediate or final state particles are shown in red and green. The angles characterizing kinematics are shown in blue and are defined in the respective rest frames [43,52]. |
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Figure 2-b:
Topology of the associated production $ {\mathrm{q} \mathrm{q}} \to {\mathrm {V}} \to {\mathrm {V}} \mathrm{H} \to ({\mathrm {f}\mathrm {\overline {f}}})\ \mathrm{H} \to ({\mathrm {f}\mathrm {\overline {f}}})\ {\mathrm {VV}} $ process. The incoming partons are shown in brown and the intermediate or final state particles are shown in red and green. The angles characterizing kinematics are shown in blue and are defined in the respective rest frames [43,52]. |
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Figure 2-c:
Topology of the $ {\mathrm{t} \mathrm{\bar{t}} \mathrm{H}} $ or $ {\mathrm{t} \mathrm{H}} $ processes. The incoming partons are shown in brown and the intermediate or final state particles are shown in red and green. The angles characterizing kinematics are shown in blue and are defined in the respective rest frames [43,52]. The subsequent top quark decays are not shown but should be included [61]. |
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Figure 2-d:
Topology of the $\mathrm{g} \mathrm{g} \to \mathrm{H} \to {\mathrm {VV}} \to 4\ell $ decay. The incoming partons are shown in brown and the intermediate or final state particles are shown in red and green. The angles characterizing kinematics are shown in blue and are defined in the respective rest frames [43,52]. |
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Figure 3:
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 ${\mathrm{t} \mathrm{\bar{t}} \mathrm{H}} $-leptonic and ${\mathrm{t} \mathrm{\bar{t}} \mathrm{H}} $-hadronic categories. The latter distribution is shown with the requirement $ {{\mathcal {D}}_{\text {bkg}}} > $ 0.2 in order to enhance signal over the background contribution. |
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Figure 3-a:
Distribution of the ${{\mathcal {D}}_{\text {bkg}}}$ discriminant in the sum of the ${\mathrm{t} \mathrm{\bar{t}} \mathrm{H}} $-leptonic and ${\mathrm{t} \mathrm{\bar{t}} \mathrm{H}} $-hadronic categories. |
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Figure 3-b:
Distribution of the$\mathcal {D}_\text {0-}^ {{\mathrm{t} \mathrm{\bar{t}} \mathrm{H}}}$ discriminant in the sum of the ${\mathrm{t} \mathrm{\bar{t}} \mathrm{H}} $-leptonic and ${\mathrm{t} \mathrm{\bar{t}} \mathrm{H}} $-hadronic categories. The distribution is shown with the requirement $ {{\mathcal {D}}_{\text {bkg}}} > $ 0.2 in order to enhance signal over the background contribution. |
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Figure 4:
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 signal over the background contribution. |
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Figure 4-a:
Distribution of the ${{\mathcal {D}}_{\text {bkg}}}$ discriminant in the VBF-2jet category in Scheme 1. |
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Figure 4-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 signal over the background contribution. |
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Figure 4-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 signal over the background contribution. |
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Figure 5:
Distributions of events in the observables used in categorization Scheme 2. The first seven plots are in the Untagged category: The top-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: $\mathcal {D}_{0-}^{\text {dec}}$ (top-middle), $\mathcal {D}_{0h+}^{\text {dec}}$ (top-right), $\mathcal {D}_{\lambda 1}^{\text {dec}}$ (middle-left), $\mathcal {D}_{\lambda 1}^{\mathrm{Z} \gamma, \text {dec}}$ (middle-middle), $\mathcal {D}_{CP}^{\text {dec}}$, and $\mathcal {D}_\text {int}^{\text {dec}}$. The last two plots are shown in the Boosted category: ${{\mathcal {D}}_{\text {bkg}}}$ (bottom-middle) and $ {p_{\mathrm {T}}} ^{4\ell}$, again with the requirement $ {{\mathcal {D}}_{\text {bkg}}} > $ 0.7 (bottom right). Observed data, background expectation, and five signal models are shown on the plots as indicated in the legend in Fig. 1 (left). 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 5-a:
Distribution of events in the ${{\mathcal {D}}_{\text {bkg}}}$ observable used in categorization Scheme 2, in the Untagged category. Observed data, background expectation, and five signal models are shown on the plots as indicated in the legend in Fig. 1-a. |
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Figure 5-b:
Distribution of events in the $\mathcal {D}_{0-}^{\text {dec}}$ observable used in categorization Scheme 2, in the Untagged category. The distribution is shown 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 on the plots as indicated in the legend in Fig. 1-a. |
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Figure 5-c:
Distribution of events in the $\mathcal {D}_{0h+}^{\text {dec}}$ observable used in categorization Scheme 2, in the Untagged category. The distribution is shown 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 on the plots as indicated in the legend in Fig. 1-a. 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 5-d:
Distribution of events in the $\mathcal {D}_{\lambda 1}^{\text {dec}}$ observable used in categorization Scheme 2, in the Untagged category. The distribution is shown 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 on the plots as indicated in the legend in Fig. 1-a. 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 5-e:
Distribution of events in the $\mathcal {D}_{\lambda 1}^{\mathrm{Z} \gamma, \text {dec}}$ observable used in categorization Scheme 2, in the Untagged category. The distribution is shown 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 on the plots as indicated in the legend in Fig. 1-a. |
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Figure 5-f:
Distribution of events in the $\mathcal {D}_{CP}^{\text {dec}}$ observable used in categorization Scheme 2, in the Untagged category. The distribution is shown 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 on the plots as indicated in the legend in Fig. 1-a. 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 5-g:
Distribution of events in the $\mathcal {D}_\text {int}^{\text {dec}}$ observable used in categorization Scheme 2, in the Untagged category. The distribution is shown 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 on the plots as indicated in the legend in Fig. 1-a. 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 5-h:
Distribution of events in the ${{\mathcal {D}}_{\text {bkg}}}$ observable used in categorization Scheme 2, in the Boosted category. Observed data, background expectation, and five signal models are shown on the plots as indicated in the legend in Fig. 1-a. |
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Figure 5-i:
Distribution of events in the $ {p_{\mathrm {T}}} ^{4\ell}$ observable used in categorization Scheme 2, in the Boosted category, with the requirement $ {{\mathcal {D}}_{\text {bkg}}} > $ 0.7. Observed data, background expectation, and five signal models are shown on the plots as indicated in the legend in Fig. 1-a. |
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Figure 6:
Distributions of events in the observables used in categorization Scheme 2. The first seven plots are in the VBF-2jet category: The top-left plot shows ${{\mathcal {D}}_{\text {bkg}}}$. The rest of the distributions are shown with the requirement $ {{\mathcal {D}}_{\text {bkg}}} > $ 0.2 in order to enhance the signal over the background contribution: $\mathcal {D}_{0-}^{\text {VBF}+\text {dec}}$ (top-middle), $\mathcal {D}_{0h+}^{\text {VBF}+\text {dec}}$ (top-right), $\mathcal {D}_{\lambda 1}^{\text {VBF}+\text {dec}}$ (middle-left), $\mathcal {D}_{\lambda 1}^{\mathrm{Z} \gamma, \text {VBF}+\text {dec}}$ (middle-middle), $\mathcal {D}_{CP}^{\text {VBF}}$, and $\mathcal {D}_\text {int}^{\text {VBF}}$. The last two plots are shown in the VBF-1jet category: ${{\mathcal {D}}_{\text {bkg}}}$ (bottom-middle) and $ {p_{\mathrm {T}}} ^{4\ell}$ with the requirement $ {{\mathcal {D}}_{\text {bkg}}} > $ 0.7 (bottom right). Observed data, background expectation, and five signal models are shown on the plots as indicated in the legend in Fig. 1 (left). 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 6-a:
Distribution of events in the ${{\mathcal {D}}_{\text {bkg}}}$ observable used in categorization Scheme 2, in the VBF-2jet category. Observed data, background expectation, and five signal models are shown on the plots as indicated in the legend in Fig. 1-a. |
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Figure 6-b:
Distribution of events in the $\mathcal {D}_{0-}^{\text {VBF}+\text {dec}}$ observable used in categorization Scheme 2, in the VBF-2jet category. The distribution is shown with the requirement $ {{\mathcal {D}}_{\text {bkg}}} > $ 0.2 in order to enhance the signal over the background contribution. Observed data, background expectation, and five signal models are shown on the plots as indicated in the legend in Fig. 1-a. |
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Figure 6-c:
Distribution of events in the $\mathcal {D}_{0h+}^{\text {VBF}+\text {dec}}$ observable used in categorization Scheme 2, in the VBF-2jet category. The distribution is shown with the requirement $ {{\mathcal {D}}_{\text {bkg}}} > $ 0.2 in order to enhance the signal over the background contribution. Observed data, background expectation, and five signal models are shown on the plots as indicated in the legend in Fig. 1-a. |
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Figure 6-d:
Distribution of events in the $\mathcal {D}_{\lambda 1}^{\text {VBF}+\text {dec}}$ observable used in categorization Scheme 2, in the VBF-2jet category. The distribution is shown with the requirement $ {{\mathcal {D}}_{\text {bkg}}} > $ 0.2 in order to enhance the signal over the background contribution. Observed data, background expectation, and five signal models are shown on the plots as indicated in the legend in Fig. 1-a. |
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Figure 6-e:
Distribution of events in the $\mathcal {D}_{\lambda 1}^{\mathrm{Z} \gamma, \text {VBF}+\text {dec}}$ observable used in categorization Scheme 2, in the VBF-2jet category. The distribution is shown with the requirement $ {{\mathcal {D}}_{\text {bkg}}} > $ 0.2 in order to enhance the signal over the background contribution. Observed data, background expectation, and five signal models are shown on the plots as indicated in the legend in Fig. 1-a. |
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Figure 6-f:
Distribution of events in the $\mathcal {D}_{CP}^{\text {VBF}}$ observable used in categorization Scheme 2, in the VBF-2jet category. The distribution is shown with the requirement $ {{\mathcal {D}}_{\text {bkg}}} > $ 0.2 in order to enhance the signal over the background contribution. Observed data, background expectation, and five signal models are shown on the plots as indicated in the legend in Fig. 1-a. 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 6-g:
Distribution of events in the $\mathcal {D}_\text {int}^{\text {VBF}}$ observable used in categorization Scheme 2, in the VBF-2jet category. The distribution is shown with the requirement $ {{\mathcal {D}}_{\text {bkg}}} > $ 0.2 in order to enhance the signal over the background contribution. Observed data, background expectation, and five signal models are shown on the plots as indicated in the legend in Fig. 1-a. 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 6-h:
Distribution of events in the ${{\mathcal {D}}_{\text {bkg}}}$ observable used in categorization Scheme 2, in the VBF-1jet category. Observed data, background expectation, and five signal models are shown on the plots as indicated in the legend in Fig. 1-a. |
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Figure 6-i:
Distribution of events in the $ {p_{\mathrm {T}}} ^{4\ell}$ observable used in categorization Scheme 2, in the VBF-1jet category, with the requirement $ {{\mathcal {D}}_{\text {bkg}}} > $ 0.7. Observed data, background expectation, and five signal models are shown on the plots as indicated in the legend in Fig. 1-a. |
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Figure 7:
Distributions of events in the observables used in categorization Scheme 2. The first seven plots are in the VH-hadronic category: The top-left plot shows ${{\mathcal {D}}_{\text {bkg}}}$. The rest of the distributions are shown with the requirement $ {{\mathcal {D}}_{\text {bkg}}} > $ 0.2 in order to enhance the signal over the background contribution: $\mathcal {D}_{0-}^{{{\mathrm {V}} \mathrm{H}} +\text {dec}}$ (top-middle), $\mathcal {D}_{0h+}^{{{\mathrm {V}} \mathrm{H}} +\text {dec}}$ (top-right), $\mathcal {D}_{\lambda 1}^{{{\mathrm {V}} \mathrm{H}} +\text {dec}}$ (middle-left), $\mathcal {D}_{\lambda 1}^{\mathrm{Z} \gamma, {{\mathrm {V}} \mathrm{H}} +\text {dec}}$ (middle-middle), $\mathcal {D}_{CP}^{{{\mathrm {V}} \mathrm{H}}}$, and $\mathcal {D}_\text {int}^{{{\mathrm {V}} \mathrm{H}}}$. The last two plots are shown in the VH-leptonic category: ${{\mathcal {D}}_{\text {bkg}}}$ (bottom-middle) and $ {p_{\mathrm {T}}} ^{4\ell}$ with the requirement $ {{\mathcal {D}}_{\text {bkg}}} > $ 0.7 (bottom right). Observed data, background expectation, and five signal models are shown on the plots as indicated in the legend in Fig. 1 (left). 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 7-a:
Distribution of events in the ${{\mathcal {D}}_{\text {bkg}}}$ observable used in categorization Scheme 2, in the VH-hadronic category. Observed data, background expectation, and five signal models are shown on the plots as indicated in the legend in Fig. 1-a. |
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Figure 7-b:
Distribution of events in the $\mathcal {D}_{0-}^{{{\mathrm {V}} \mathrm{H}} +\text {dec}}$ observable used in categorization Scheme 2, in the VH-hadronic category. The distribution is shown with the requirement $ {{\mathcal {D}}_{\text {bkg}}} > $ 0.2 in order to enhance the signal over the background contribution. Observed data, background expectation, and five signal models are shown on the plots as indicated in the legend in Fig. 1-a. |
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Figure 7-c:
Distribution of events in the $\mathcal {D}_{0h+}^{{{\mathrm {V}} \mathrm{H}} +\text {dec}}$ observable used in categorization Scheme 2, in the VH-hadronic category. The distribution is shown with the requirement $ {{\mathcal {D}}_{\text {bkg}}} > $ 0.2 in order to enhance the signal over the background contribution. Observed data, background expectation, and five signal models are shown on the plots as indicated in the legend in Fig. 1-a. |
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Figure 7-d:
Distribution of events in the $\mathcal {D}_{\lambda 1}^{{{\mathrm {V}} \mathrm{H}} +\text {dec}}$ observable used in categorization Scheme 2, in the VH-hadronic category. The distribution is shown with the requirement $ {{\mathcal {D}}_{\text {bkg}}} > $ 0.2 in order to enhance the signal over the background contribution. Observed data, background expectation, and five signal models are shown on the plots as indicated in the legend in Fig. 1-a. |
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Figure 7-e:
Distribution of events in the $\mathcal {D}_{\lambda 1}^{\mathrm{Z} \gamma, {{\mathrm {V}} \mathrm{H}} +\text {dec}}$ observable used in categorization Scheme 2, in the VH-hadronic category. The distribution is shown with the requirement $ {{\mathcal {D}}_{\text {bkg}}} > $ 0.2 in order to enhance the signal over the background contribution. Observed data, background expectation, and five signal models are shown on the plots as indicated in the legend in Fig. 1-a. |
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Figure 7-f:
Distribution of events in the $\mathcal {D}_{CP}^{{{\mathrm {V}} \mathrm{H}}}$ observable used in categorization Scheme 2, in the VH-hadronic category. The distribution is shown with the requirement $ {{\mathcal {D}}_{\text {bkg}}} > $ 0.2 in order to enhance the signal over the background contribution. Observed data, background expectation, and five signal models are shown on the plots as indicated in the legend in Fig. 1-a. 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 7-g:
Distribution of events in the $\mathcal {D}_\text {int}^{{{\mathrm {V}} \mathrm{H}}}$ observable used in categorization Scheme 2, in the VH-hadronic category. The distribution is shown with the requirement $ {{\mathcal {D}}_{\text {bkg}}} > $ 0.2 in order to enhance the signal over the background contribution. Observed data, background expectation, and five signal models are shown on the plots as indicated in the legend in Fig. 1-a. 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 7-h:
Distribution of events in the ${{\mathcal {D}}_{\text {bkg}}}$ observable used in categorization Scheme 2, in the VH-leptonic category. Observed data, background expectation, and five signal models are shown on the plots as indicated in the legend in Fig. 1-a. |
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Figure 7-i:
Distribution of events in the $ {p_{\mathrm {T}}} ^{4\ell}$ observable used in categorization Scheme 2, in the VH-leptonic category, with the requirement $ {{\mathcal {D}}_{\text {bkg}}} > $ 0.7. Observed data, background expectation, and five signal models are shown on the plots as indicated in the legend in Fig. 1-a. |
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Figure 8:
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 $c_{gg}$ and $\tilde{c}_{gg}$ 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. The dashed and solid lines show the 68% and 95% CL exclusion regions in two dimensions, respectively. |
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Figure 8-a:
Constraints on the anomalous H boson couplings to gluons in the ggH process using the $\mathrm{H} \to 4\ell $ decay. 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. |
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Figure 8-b:
Constraints on the anomalous H boson couplings to gluons in the ggH process using the $\mathrm{H} \to 4\ell $ decay. Observed confidence level intervals on the $c_{gg}$ and $\tilde{c}_{gg}$ 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. The dashed and solid lines show the 68% and 95% CL exclusion regions in two dimensions, respectively. |
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Figure 9:
Constraints on the anomalous H boson couplings to top quarks in the ${\mathrm{t} \mathrm{\bar{t}} \mathrm{H}} $ process using the $\mathrm{H} \to 4\ell $ and $\gamma \gamma $ decays. Left: Observed (solid) and expected (dashed) likelihood scans of $ {f_\mathrm {CP}^{{\mathrm{H} \text {tt}}}} $ in the ${\mathrm{t} \mathrm{\bar{t}} \mathrm{H}} $ process 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}}}} $ and $\mu _{{\mathrm{t} \mathrm{\bar{t}} \mathrm{H}}}$ measurements in the combined fit of the $\mathrm{H} \to 4\ell $ and $\gamma \gamma $ channels, with the signal strength $\mu _{{\mathrm{t} \mathrm{\bar{t}} \mathrm{H}}}$ 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 9-a:
Constraints on the anomalous H boson couplings to top quarks in the ${\mathrm{t} \mathrm{\bar{t}} \mathrm{H}} $ process 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}}}} $ in the ${\mathrm{t} \mathrm{\bar{t}} \mathrm{H}} $ process 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. |
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Figure 9-b:
Constraints on the anomalous H boson couplings to top quarks in the ${\mathrm{t} \mathrm{\bar{t}} \mathrm{H}} $ process using the $\mathrm{H} \to 4\ell $ and $\gamma \gamma $ decays. 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}}}} $ and $\mu _{{\mathrm{t} \mathrm{\bar{t}} \mathrm{H}}}$ measurements in the combined fit of the $\mathrm{H} \to 4\ell $ and $\gamma \gamma $ channels, with the signal strength $\mu _{{\mathrm{t} \mathrm{\bar{t}} \mathrm{H}}}$ 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 10:
Constraints on the anomalous H boson couplings to top quarks in the ${\mathrm{t} \mathrm{\bar{t}} \mathrm{H}} $ and ggH processes combined, assuming top quark dominance in the gluon fusion loop, using the $\mathrm{H} \to 4\ell $ and $\gamma \gamma $ decays. Left: Observed (solid) and expected (dashed) likelihood scans of $ {f_\mathrm {CP}^{{\mathrm{H} \text {tt}}}} $ in the ggH process with $\mathrm{H} \to 4\ell $ (red), ${\mathrm{t} \mathrm{\bar{t}} \mathrm{H}} $ and ggH processes combined with $\mathrm{H} \to 4\ell $ (blue), and in the ${\mathrm{t} \mathrm{\bar{t}} \mathrm{H}} $ and ggH processes with $\mathrm{H} \to 4\ell $ and the ${\mathrm{t} \mathrm{\bar{t}} \mathrm{H}} $ process with $\gamma \gamma $ combined (black). 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. 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}}}} $ and signal strength measurements in the fit corresponding to the full combination of ${\mathrm{t} \mathrm{\bar{t}} \mathrm{H}} $ and ggH processes and the $\mathrm{H} \to 4\ell $ and $\gamma \gamma $ channels in the left plot. The dashed and solid lines show the 68 and 95% CL exclusion regions in two dimensions, respectively. |
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Figure 10-a:
Constraints on the anomalous H boson couplings to top quarks in the ${\mathrm{t} \mathrm{\bar{t}} \mathrm{H}} $ 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}}}} $ in the ggH process with $\mathrm{H} \to 4\ell $ (red), ${\mathrm{t} \mathrm{\bar{t}} \mathrm{H}} $ and ggH processes combined with $\mathrm{H} \to 4\ell $ (blue), and in the ${\mathrm{t} \mathrm{\bar{t}} \mathrm{H}} $ and ggH processes with $\mathrm{H} \to 4\ell $ and the ${\mathrm{t} \mathrm{\bar{t}} \mathrm{H}} $ process with $\gamma \gamma $ combined (black). 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. |
png pdf |
Figure 10-b:
Constraints on the anomalous H boson couplings to top quarks in the ${\mathrm{t} \mathrm{\bar{t}} \mathrm{H}} $ 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 confidence level intervals on the $\kappa _{\mathrm{t}}$ and $\tilde\kappa _{\mathrm{t}}$ couplings reinterpreted from the $ {f_\mathrm {CP}^{{\mathrm{H} \text {tt}}}} $ and signal strength measurements in the fit corresponding to the full combination of ${\mathrm{t} \mathrm{\bar{t}} \mathrm{H}} $ and ggH processes and the $\mathrm{H} \to 4\ell $ and $\gamma \gamma $ channels in the left plot. The dashed and solid lines show the 68 and 95% CL exclusion regions in two dimensions, respectively. |
png pdf |
Figure 11:
Observed (solid) and expected (dashed) likelihood scans of ${f_{a3}}$ (top left), ${f_{a2}}$ (top right), ${f_{\lambda 1}}$ (bottom left), and ${f_{\lambda 1}^{\mathrm{Z} \gamma}}$ (bottom right). 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. |
png pdf |
Figure 11-a:
Observed (solid) and expected (dashed) likelihood scans of ${f_{a3}}$. The results are shown with the other three anomalous coupling fractions either set to zero or left unconstrained in the fit. The signal strength parameters have been left unconstrained. The dashed horizontal lines show the 68% and 95% CL regions. |
png pdf |
Figure 11-b:
Observed (solid) and expected (dashed) likelihood scans of ${f_{a2}}$. The results are shown with the other three anomalous coupling fractions either set to zero or left unconstrained in the fit. The signal strength parameters have been left unconstrained. The dashed horizontal lines show the 68% and 95% CL regions. |
png pdf |
Figure 11-c:
Observed (solid) and expected (dashed) likelihood scans of ${f_{\lambda 1}}$. The results are shown with the other three anomalous coupling fractions either set to zero or left unconstrained in the fit. The signal strength parameters have been left unconstrained. The dashed horizontal lines show the 68% and 95% CL regions. |
png pdf |
Figure 11-d:
Observed (solid) and expected (dashed) likelihood scans of ${f_{\lambda 1}^{\mathrm{Z} \gamma}}$. The results are shown with the other three anomalous coupling fractions either set to zero or left unconstrained in the fit. The signal strength parameters have been left unconstrained. The dashed horizontal lines show the 68% and 95% CL regions. |
png pdf |
Figure 12:
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 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. |
png pdf |
Figure 12-a:
Observed two-dimensional likelihood scans of the coupling parameters ${f_{a3}}$ and ${f_{a2}}$. 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. |
png pdf |
Figure 12-b:
Observed two-dimensional likelihood scans of the coupling parameters ${f_{a3}}$ and ${f_{\lambda 1}}$. 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. |
png pdf |
Figure 12-c:
Observed two-dimensional likelihood scans of the coupling parameters ${f_{a3}}$ and ${f_{\lambda 1}^{\mathrm{Z} \gamma}}$. 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. |
png pdf |
Figure 12-d:
Observed two-dimensional likelihood scans of the coupling parameters ${f_{a2}}$ and ${f_{\lambda 1}}$. 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. |
png pdf |
Figure 12-e:
Observed two-dimensional likelihood scans of the coupling parameters ${f_{a2}}$ and ${f_{\lambda 1}^{\mathrm{Z} \gamma}}$. 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. |
png pdf |
Figure 12-f:
Observed two-dimensional likelihood scans of the coupling parameters ${f_{\lambda 1}}$ and ${f_{\lambda 1}^{\mathrm{Z} \gamma}}$. 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. |
png pdf |
Figure 13:
Observed (solid) and expected (dashed) likelihood scans of ${f_{a3}}$ (top left), ${f_{a2}}$ (top right), and ${f_{\lambda 1}}$ (bottom) with the EFT relationship of couplings set in Eqs. (4)-(8). 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. |
png pdf |
Figure 13-a:
Observed (solid) and expected (dashed) likelihood scans of ${f_{a3}}$, with the EFT relationship of couplings set in Eqs. (4)-(8). The results are shown with the other anomalous coupling fractions either set to zero or left unconstrained in the fit. The signal strength parameters have been left unconstrained. The dashed horizontal lines show the 68 and 95% CL regions. |
png pdf |
Figure 13-b:
Observed (solid) and expected (dashed) likelihood scans of ${f_{a2}}$, with the EFT relationship of couplings set in Eqs. (4)-(8). The results are shown with the other anomalous coupling fractions either set to zero or left unconstrained in the fit. The signal strength parameters have been left unconstrained. The dashed horizontal lines show the 68 and 95% CL regions. |
png pdf |
Figure 13-c:
Observed (solid) and expected (dashed) likelihood scans of ${f_{\lambda 1}}$, with the EFT relationship of couplings set in Eqs. (4)-(8). The results are shown with the other anomalous coupling fractions either set to zero or left unconstrained in the fit. The signal strength parameters have been left unconstrained. The dashed horizontal lines show the 68 and 95% CL regions. |
png pdf |
Figure 14:
Observed (solid) and expected (dashed) constraints from a simultaneous fit of EFT parameters $\delta c_z$ (top-left), $c_{zz}$ (top-right), $c_{z \Box}$ (bottom-left), and $\tilde{c}_{zz}$ (bottom-right) with the $c_{gg}$ and $\tilde{c}_{gg}$ couplings left unconstrained. |
png pdf |
Figure 14-a:
Observed (solid) and expected (dashed) constraints from a simultaneous fit of EFT parameters $\delta c_z$ (top-left), $c_{zz}$ (top-right), $c_{z \Box}$ (bottom-left), and $\tilde{c}_{zz}$ (bottom-right) with the $c_{gg}$ and $\tilde{c}_{gg}$ couplings left unconstrained. |
png pdf |
Figure 14-b:
Observed (solid) and expected (dashed) constraints from a simultaneous fit of EFT parameters $\delta c_z$ (top-left), $c_{zz}$ (top-right), $c_{z \Box}$ (bottom-left), and $\tilde{c}_{zz}$ (bottom-right) with the $c_{gg}$ and $\tilde{c}_{gg}$ couplings left unconstrained. |
png pdf |
Figure 14-c:
Observed (solid) and expected (dashed) constraints from a simultaneous fit of EFT parameters $\delta c_z$ (top-left), $c_{zz}$ (top-right), $c_{z \Box}$ (bottom-left), and $\tilde{c}_{zz}$ (bottom-right) with the $c_{gg}$ and $\tilde{c}_{gg}$ couplings left unconstrained. |
png pdf |
Figure 14-d:
Observed (solid) and expected (dashed) constraints from a simultaneous fit of EFT parameters $\delta c_z$ (top-left), $c_{zz}$ (top-right), $c_{z \Box}$ (bottom-left), and $\tilde{c}_{zz}$ (bottom-right) with the $c_{gg}$ and $\tilde{c}_{gg}$ couplings left unconstrained. |
png pdf |
Figure 15:
Observed two-dimensional constraints from a simultaneous fit of EFT parameters $\delta c_z$, $c_{zz}$, $c_{z \Box}$, and $\tilde{c}_{zz}$ with the $c_{gg}$ and $\tilde{c}_{gg}$ couplings left unconstrained. |
png pdf |
Figure 15-a:
Observed two-dimensional constraints from a simultaneous fit of EFT parameters $\delta c_z$, $c_{zz}$, $c_{z \Box}$, and $\tilde{c}_{zz}$ with the $c_{gg}$ and $\tilde{c}_{gg}$ couplings left unconstrained. |
png pdf |
Figure 15-b:
Observed two-dimensional constraints from a simultaneous fit of EFT parameters $\delta c_z$, $c_{zz}$, $c_{z \Box}$, and $\tilde{c}_{zz}$ with the $c_{gg}$ and $\tilde{c}_{gg}$ couplings left unconstrained. |
png pdf |
Figure 15-c:
Observed two-dimensional constraints from a simultaneous fit of EFT parameters $\delta c_z$, $c_{zz}$, $c_{z \Box}$, and $\tilde{c}_{zz}$ with the $c_{gg}$ and $\tilde{c}_{gg}$ couplings left unconstrained. |
png pdf |
Figure 15-d:
Observed two-dimensional constraints from a simultaneous fit of EFT parameters $\delta c_z$, $c_{zz}$, $c_{z \Box}$, and $\tilde{c}_{zz}$ with the $c_{gg}$ and $\tilde{c}_{gg}$ couplings left unconstrained. |
png pdf |
Figure 15-e:
Observed two-dimensional constraints from a simultaneous fit of EFT parameters $\delta c_z$, $c_{zz}$, $c_{z \Box}$, and $\tilde{c}_{zz}$ with the $c_{gg}$ and $\tilde{c}_{gg}$ couplings left unconstrained. |
png pdf |
Figure 15-f:
Observed two-dimensional constraints from a simultaneous fit of EFT parameters $\delta c_z$, $c_{zz}$, $c_{z \Box}$, and $\tilde{c}_{zz}$ with the $c_{gg}$ and $\tilde{c}_{gg}$ couplings left unconstrained. |
| Tables | |
png pdf |
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 relationship according to Eqs. (4-8) (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 considered to keep all coefficients of similar order of magnitude. |
png pdf |
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 ${\mathrm{t} \mathrm{\bar{t}} \mathrm{H}} $ signal expectation is quoted for the SM and anomalous ($\tilde\kappa _\mathrm {f}=$ 1.6) scenarios, both generated with the same cross section. |
png pdf |
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 anomalous ($a_3/a_2/\kappa _1/\kappa _2^{\mathrm{Z} \gamma}$) scenarios, all generated with the same total EW production cross section. |
png pdf |
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 Sec. 3. |
png pdf |
Table 5:
Observed and expected constraints on the CP-sensitive parameter $ {f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}} $ in the H boson couplings to gluons with the best-fit value and allowed 68% CL (quoted uncertainties) and 95% CL (within square brackets) intervals. |
png pdf |
Table 6:
Constraints on the $ {f_\mathrm {CP}^{{\mathrm{H} \text {tt}}}} $ parameter with the best-fit values and allowed 68% CL (quoted uncertainties) and 95% CL (within square brackets) intervals. The constraints obtained in this work are combined with those from our recent ${\mathrm{t} \mathrm{\bar{t}} \mathrm{H}} $ measurements in the $\mathrm{H} \to \gamma \gamma $ channel [26]. The interpretation of results from Table 5 under the assumption of the top quark dominance in the gluon fusion loop are presented as well, where either ggH or its combination with ${\mathrm{t} \mathrm{\bar{t}} \mathrm{H}} $ results are shown. |
png pdf |
Table 7:
Summary of constraints on the anomalous HVV coupling parameters with the best-fit values and allowed 68% CL 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 with the symmetry relationship of couplings set in Eqs. (4-8). The $ {f_{\lambda 1}^{\mathrm{Z} \gamma}} $ parameter is not independent in the latter scenario and can be derived following Eq. (8). |
png pdf |
Table 8:
Summary of constraints on the Htt, Hgg, Hff, and HVV coupling parameters in the Higgs basis of the EFT formalism. The observed correlation coefficients are presented for the Hgg, Htt, Hff, and HVV couplings in the fit configurations discussed in text and shown in Figs. 8, 9, 10, and 15, respectively. |
| Summary |
| We have presented studies of CP-violation and anomalous couplings of the Higgs boson to vector bosons and fermions using kinematics of the Higgs boson's four-lepton decay and of its production in association with a vector boson, hadronic jets, or a top-quark pair. Simultaneous measurement of up to five HVV, two Hgg, and two Htt couplings is performed and interpreted in the framework of effective field theory with the SU(2)$\times$U(1) symmetry of HVV interactions. Kinematic information from the decay and associated particles is combined using matrix element techniques to identify the production mechanism and increase sensitivity to the Higgs boson couplings. The data from the CMS experiment at the LHC corresponds to an integrated luminosity of 137 fb$^{-1}$ at a center-of-mass energy of $\sqrt{s}=$ 13 TeV. Each of the measurements presented here is still limited by statistical precision and is expected to improve further in future runs of the LHC. |
| Additional Figures | |
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Additional Figure 1:
Display of an $\mathrm {H}\to 4\mu $ event candidate in the $\mathrm {t\bar{t}H}$ topology, where the main distinguishing features of the top and anti-top quarks are the multiple hadronic jets, including a jet with a signature of the bottom quark. |
png pdf |
Additional Figure 2:
Display of an $\mathrm {H\to 2e2\mu} $ event candidate in the VBF topology, where the main distinguishing features are the two hadronic jets in the opposite forward regions. The VBF topology is a signature of both gluon fusion and electroweak boson fusion production mechanisms used for the study of anomalous Hgg and HVV couplings, respectively. |
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