CMSHIG22008 ; CERNEP2024035  
Constraints on anomalous Higgs boson couplings from its production and decay using the WW channel in protonproton collisions at $ \sqrt{s} = $ 13 TeV  
CMS Collaboration  
1 March 2024  
Accepted for publication in Eur. Phys. J. C  
Abstract: A study of the anomalous couplings of the Higgs boson to vector bosons, including CPviolation effects, has been conducted using its production and decay in the WW channel. This analysis is performed on protonproton collision data collected with the CMS detector at the CERN LHC during 20162018 at a centerofmass energy of 13 TeV, and corresponds to an integrated luminosity of 138 fb$ ^{1} $. The differentflavor dilepton ($ \mathrm{e}\mu $) final state is analyzed, with dedicated categories targeting gluon fusion, electroweak vector boson fusion, and associated production with a W or Z boson. Kinematic information from associated jets is combined using matrix element techniques to increase the sensitivity to anomalous effects at the production vertex. A simultaneous measurement of four Higgs boson couplings to electroweak vector bosons is performed in the framework of a standard model effective field theory. All measurements are consistent with the expectations for the standard model Higgs boson and constraints are set on the fractional contribution of the anomalous couplings to the Higgs boson production cross section.  
Links: eprint arXiv:2403.00657 [hepex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; 
Figures  
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Figure 1:
Topologies of the Higgs boson production and decay for vector boson fusion $ \mathrm{q}{\mathrm{q}^\prime}\to \mathrm{q}{\mathrm{q}^\prime} \mathrm{H} $ (left), $ \mathrm{q}\bar{\mathrm{q}}^\prime\to \mathrm{V}\mathrm{H} $ (center), and gluon fusion with decay $ \mathrm{g}\mathrm{g} \to \mathrm{H} \to 2 \ell 2\nu $ (right). For the electroweak production topologies, the intermediate vector bosons and their decays are shown in green and the $ \mathrm{H} \to \mathrm{W}\mathrm{W} $ decay is marked in red. For the $ \mathrm{g}\mathrm{g} \to \mathrm{H} \to 2 \ell 2\nu $ topology, the W boson leptonic decays are shown in green. In all cases, the incoming particles are depicted in brown and the angles characterizing kinematic distributions are marked in blue. Five angles fully characterize the orientation of the production and decay chain and are defined in the suitable rest frames. 
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Figure 1a:
Topologies of the Higgs boson production and decay for vector boson fusion $ \mathrm{q}{\mathrm{q}^\prime}\to \mathrm{q}{\mathrm{q}^\prime} \mathrm{H} $ (left), $ \mathrm{q}\bar{\mathrm{q}}^\prime\to \mathrm{V}\mathrm{H} $ (center), and gluon fusion with decay $ \mathrm{g}\mathrm{g} \to \mathrm{H} \to 2 \ell 2\nu $ (right). For the electroweak production topologies, the intermediate vector bosons and their decays are shown in green and the $ \mathrm{H} \to \mathrm{W}\mathrm{W} $ decay is marked in red. For the $ \mathrm{g}\mathrm{g} \to \mathrm{H} \to 2 \ell 2\nu $ topology, the W boson leptonic decays are shown in green. In all cases, the incoming particles are depicted in brown and the angles characterizing kinematic distributions are marked in blue. Five angles fully characterize the orientation of the production and decay chain and are defined in the suitable rest frames. 
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Figure 1b:
Topologies of the Higgs boson production and decay for vector boson fusion $ \mathrm{q}{\mathrm{q}^\prime}\to \mathrm{q}{\mathrm{q}^\prime} \mathrm{H} $ (left), $ \mathrm{q}\bar{\mathrm{q}}^\prime\to \mathrm{V}\mathrm{H} $ (center), and gluon fusion with decay $ \mathrm{g}\mathrm{g} \to \mathrm{H} \to 2 \ell 2\nu $ (right). For the electroweak production topologies, the intermediate vector bosons and their decays are shown in green and the $ \mathrm{H} \to \mathrm{W}\mathrm{W} $ decay is marked in red. For the $ \mathrm{g}\mathrm{g} \to \mathrm{H} \to 2 \ell 2\nu $ topology, the W boson leptonic decays are shown in green. In all cases, the incoming particles are depicted in brown and the angles characterizing kinematic distributions are marked in blue. Five angles fully characterize the orientation of the production and decay chain and are defined in the suitable rest frames. 
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Figure 1c:
Topologies of the Higgs boson production and decay for vector boson fusion $ \mathrm{q}{\mathrm{q}^\prime}\to \mathrm{q}{\mathrm{q}^\prime} \mathrm{H} $ (left), $ \mathrm{q}\bar{\mathrm{q}}^\prime\to \mathrm{V}\mathrm{H} $ (center), and gluon fusion with decay $ \mathrm{g}\mathrm{g} \to \mathrm{H} \to 2 \ell 2\nu $ (right). For the electroweak production topologies, the intermediate vector bosons and their decays are shown in green and the $ \mathrm{H} \to \mathrm{W}\mathrm{W} $ decay is marked in red. For the $ \mathrm{g}\mathrm{g} \to \mathrm{H} \to 2 \ell 2\nu $ topology, the W boson leptonic decays are shown in green. In all cases, the incoming particles are depicted in brown and the angles characterizing kinematic distributions are marked in blue. Five angles fully characterize the orientation of the production and decay chain and are defined in the suitable rest frames. 
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Figure 2:
The $ \mathcal{D}_{0} $ discriminant in the VBF (left) and Resolved VH (right) production channels for a number of VBF (left) and VH (right) signal hypotheses. Pure $ a_1 $ ($ f_{a3} = $ 0) and $ a_3 $ ($ f_{a3} = $ 1) HVV signal hypotheses are shown along with a mixed coupling hypothesis ($ f_{a3} = $ 0.5). All distributions are normalized to unity. 
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Figure 2a:
The $ \mathcal{D}_{0} $ discriminant in the VBF (left) and Resolved VH (right) production channels for a number of VBF (left) and VH (right) signal hypotheses. Pure $ a_1 $ ($ f_{a3} = $ 0) and $ a_3 $ ($ f_{a3} = $ 1) HVV signal hypotheses are shown along with a mixed coupling hypothesis ($ f_{a3} = $ 0.5). All distributions are normalized to unity. 
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Figure 2b:
The $ \mathcal{D}_{0} $ discriminant in the VBF (left) and Resolved VH (right) production channels for a number of VBF (left) and VH (right) signal hypotheses. Pure $ a_1 $ ($ f_{a3} = $ 0) and $ a_3 $ ($ f_{a3} = $ 1) HVV signal hypotheses are shown along with a mixed coupling hypothesis ($ f_{a3} = $ 0.5). All distributions are normalized to unity. 
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Figure 3:
Observed and predicted distributions after fitting the data for $ [\mathcal{D}_\text{VBF}, m_{\ell\ell}, \mathcal{D}_{0+}] $ in the VBF channel (upper), and for $ [m_{\ell\ell}, \mathcal{D}_{0+}] $ in the Resolved VH (lower left) and Boosted VH (lower right) channels. For the VBF channel, the $ \mathcal{D}_{\text{int}} < $ 0.4 (left) and $ \mathcal{D}_{\text{int}} > $ 0.4 (right) categories are shown. The predicted Higgs boson signal is shown stacked on top of the background distributions. For the fit, the $ a_{1} $ and $ a_2 $ HVV coupling contributions are included. The corresponding pure $ a_{1} $ ($ f_{a2} = $ 0) and $ a_2 $ ($ f_{a2} = $ 1) signal hypotheses are also shown superimposed, their yields correspond to the predicted number of SM signal events scaled by an arbitrary factor to improve visibility. The uncertainty band corresponds to the total systematic uncertainty. The lower panel in each figure shows the ratio of the number of events observed to the total prediction. 
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Figure 3a:
Observed and predicted distributions after fitting the data for $ [\mathcal{D}_\text{VBF}, m_{\ell\ell}, \mathcal{D}_{0+}] $ in the VBF channel (upper), and for $ [m_{\ell\ell}, \mathcal{D}_{0+}] $ in the Resolved VH (lower left) and Boosted VH (lower right) channels. For the VBF channel, the $ \mathcal{D}_{\text{int}} < $ 0.4 (left) and $ \mathcal{D}_{\text{int}} > $ 0.4 (right) categories are shown. The predicted Higgs boson signal is shown stacked on top of the background distributions. For the fit, the $ a_{1} $ and $ a_2 $ HVV coupling contributions are included. The corresponding pure $ a_{1} $ ($ f_{a2} = $ 0) and $ a_2 $ ($ f_{a2} = $ 1) signal hypotheses are also shown superimposed, their yields correspond to the predicted number of SM signal events scaled by an arbitrary factor to improve visibility. The uncertainty band corresponds to the total systematic uncertainty. The lower panel in each figure shows the ratio of the number of events observed to the total prediction. 
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Figure 3b:
Observed and predicted distributions after fitting the data for $ [\mathcal{D}_\text{VBF}, m_{\ell\ell}, \mathcal{D}_{0+}] $ in the VBF channel (upper), and for $ [m_{\ell\ell}, \mathcal{D}_{0+}] $ in the Resolved VH (lower left) and Boosted VH (lower right) channels. For the VBF channel, the $ \mathcal{D}_{\text{int}} < $ 0.4 (left) and $ \mathcal{D}_{\text{int}} > $ 0.4 (right) categories are shown. The predicted Higgs boson signal is shown stacked on top of the background distributions. For the fit, the $ a_{1} $ and $ a_2 $ HVV coupling contributions are included. The corresponding pure $ a_{1} $ ($ f_{a2} = $ 0) and $ a_2 $ ($ f_{a2} = $ 1) signal hypotheses are also shown superimposed, their yields correspond to the predicted number of SM signal events scaled by an arbitrary factor to improve visibility. The uncertainty band corresponds to the total systematic uncertainty. The lower panel in each figure shows the ratio of the number of events observed to the total prediction. 
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Figure 3c:
Observed and predicted distributions after fitting the data for $ [\mathcal{D}_\text{VBF}, m_{\ell\ell}, \mathcal{D}_{0+}] $ in the VBF channel (upper), and for $ [m_{\ell\ell}, \mathcal{D}_{0+}] $ in the Resolved VH (lower left) and Boosted VH (lower right) channels. For the VBF channel, the $ \mathcal{D}_{\text{int}} < $ 0.4 (left) and $ \mathcal{D}_{\text{int}} > $ 0.4 (right) categories are shown. The predicted Higgs boson signal is shown stacked on top of the background distributions. For the fit, the $ a_{1} $ and $ a_2 $ HVV coupling contributions are included. The corresponding pure $ a_{1} $ ($ f_{a2} = $ 0) and $ a_2 $ ($ f_{a2} = $ 1) signal hypotheses are also shown superimposed, their yields correspond to the predicted number of SM signal events scaled by an arbitrary factor to improve visibility. The uncertainty band corresponds to the total systematic uncertainty. The lower panel in each figure shows the ratio of the number of events observed to the total prediction. 
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Figure 3d:
Observed and predicted distributions after fitting the data for $ [\mathcal{D}_\text{VBF}, m_{\ell\ell}, \mathcal{D}_{0+}] $ in the VBF channel (upper), and for $ [m_{\ell\ell}, \mathcal{D}_{0+}] $ in the Resolved VH (lower left) and Boosted VH (lower right) channels. For the VBF channel, the $ \mathcal{D}_{\text{int}} < $ 0.4 (left) and $ \mathcal{D}_{\text{int}} > $ 0.4 (right) categories are shown. The predicted Higgs boson signal is shown stacked on top of the background distributions. For the fit, the $ a_{1} $ and $ a_2 $ HVV coupling contributions are included. The corresponding pure $ a_{1} $ ($ f_{a2} = $ 0) and $ a_2 $ ($ f_{a2} = $ 1) signal hypotheses are also shown superimposed, their yields correspond to the predicted number of SM signal events scaled by an arbitrary factor to improve visibility. The uncertainty band corresponds to the total systematic uncertainty. The lower panel in each figure shows the ratio of the number of events observed to the total prediction. 
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Figure 4:
Observed and predicted distributions after fitting the data for $ [\mathcal{D}_\text{VBF}, m_{\ell\ell}, \mathcal{D}_{0}] $ in the VBF channel (upper), and for $ [m_{\ell\ell}, \mathcal{D}_{0}] $ in the Resolved VH (middle) and Boosted VH (lower) channels. For each channel, the $ \mathcal{D}_{CP} < $ 0 (left) and $ \mathcal{D}_{CP} > $ 0 (right) categories are shown. For the fit, the $ a_{1} $ and $ a_3 $ HVV coupling contributions are included. More details are given in the caption of Fig. 3. 
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Figure 4a:
Observed and predicted distributions after fitting the data for $ [\mathcal{D}_\text{VBF}, m_{\ell\ell}, \mathcal{D}_{0}] $ in the VBF channel (upper), and for $ [m_{\ell\ell}, \mathcal{D}_{0}] $ in the Resolved VH (middle) and Boosted VH (lower) channels. For each channel, the $ \mathcal{D}_{CP} < $ 0 (left) and $ \mathcal{D}_{CP} > $ 0 (right) categories are shown. For the fit, the $ a_{1} $ and $ a_3 $ HVV coupling contributions are included. More details are given in the caption of Fig. 3. 
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Figure 4b:
Observed and predicted distributions after fitting the data for $ [\mathcal{D}_\text{VBF}, m_{\ell\ell}, \mathcal{D}_{0}] $ in the VBF channel (upper), and for $ [m_{\ell\ell}, \mathcal{D}_{0}] $ in the Resolved VH (middle) and Boosted VH (lower) channels. For each channel, the $ \mathcal{D}_{CP} < $ 0 (left) and $ \mathcal{D}_{CP} > $ 0 (right) categories are shown. For the fit, the $ a_{1} $ and $ a_3 $ HVV coupling contributions are included. More details are given in the caption of Fig. 3. 
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Figure 4c:
Observed and predicted distributions after fitting the data for $ [\mathcal{D}_\text{VBF}, m_{\ell\ell}, \mathcal{D}_{0}] $ in the VBF channel (upper), and for $ [m_{\ell\ell}, \mathcal{D}_{0}] $ in the Resolved VH (middle) and Boosted VH (lower) channels. For each channel, the $ \mathcal{D}_{CP} < $ 0 (left) and $ \mathcal{D}_{CP} > $ 0 (right) categories are shown. For the fit, the $ a_{1} $ and $ a_3 $ HVV coupling contributions are included. More details are given in the caption of Fig. 3. 
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Figure 4d:
Observed and predicted distributions after fitting the data for $ [\mathcal{D}_\text{VBF}, m_{\ell\ell}, \mathcal{D}_{0}] $ in the VBF channel (upper), and for $ [m_{\ell\ell}, \mathcal{D}_{0}] $ in the Resolved VH (middle) and Boosted VH (lower) channels. For each channel, the $ \mathcal{D}_{CP} < $ 0 (left) and $ \mathcal{D}_{CP} > $ 0 (right) categories are shown. For the fit, the $ a_{1} $ and $ a_3 $ HVV coupling contributions are included. More details are given in the caption of Fig. 3. 
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Figure 4e:
Observed and predicted distributions after fitting the data for $ [\mathcal{D}_\text{VBF}, m_{\ell\ell}, \mathcal{D}_{0}] $ in the VBF channel (upper), and for $ [m_{\ell\ell}, \mathcal{D}_{0}] $ in the Resolved VH (middle) and Boosted VH (lower) channels. For each channel, the $ \mathcal{D}_{CP} < $ 0 (left) and $ \mathcal{D}_{CP} > $ 0 (right) categories are shown. For the fit, the $ a_{1} $ and $ a_3 $ HVV coupling contributions are included. More details are given in the caption of Fig. 3. 
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Figure 4f:
Observed and predicted distributions after fitting the data for $ [\mathcal{D}_\text{VBF}, m_{\ell\ell}, \mathcal{D}_{0}] $ in the VBF channel (upper), and for $ [m_{\ell\ell}, \mathcal{D}_{0}] $ in the Resolved VH (middle) and Boosted VH (lower) channels. For each channel, the $ \mathcal{D}_{CP} < $ 0 (left) and $ \mathcal{D}_{CP} > $ 0 (right) categories are shown. For the fit, the $ a_{1} $ and $ a_3 $ HVV coupling contributions are included. More details are given in the caption of Fig. 3. 
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Figure 5:
Observed and predicted distributions after fitting the data for $ [\mathcal{D}_\text{VBF}, m_{\ell\ell}, \mathcal{D}_{\Lambda 1}] $ (upper left) and $ [\mathcal{D}_\text{VBF}, m_{\ell\ell}, \mathcal{D}_{\Lambda 1}^{\mathrm{Z}\gamma}] $ (upper right) in the VBF channel, and for $ [m_{\ell\ell}, \mathcal{D}_{\Lambda 1}] $ (left) and $ [m_{\ell\ell}, \mathcal{D}_{\Lambda 1}^{\mathrm{Z}\gamma}] $ (right) in the Resolved VH (middle) and Boosted VH (lower) channels. For the fits, the $ a_{1} $ and $ \kappa_1/(\Lambda_1)^2 $ (left) or $ a_{1} $ and $ \kappa_2^{\mathrm{Z}\gamma}/(\Lambda_1^{\mathrm{Z}\gamma})^2 $ (right) HVV coupling contributions are included. More details are given in the caption of Fig. 3. 
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Figure 5a:
Observed and predicted distributions after fitting the data for $ [\mathcal{D}_\text{VBF}, m_{\ell\ell}, \mathcal{D}_{\Lambda 1}] $ (upper left) and $ [\mathcal{D}_\text{VBF}, m_{\ell\ell}, \mathcal{D}_{\Lambda 1}^{\mathrm{Z}\gamma}] $ (upper right) in the VBF channel, and for $ [m_{\ell\ell}, \mathcal{D}_{\Lambda 1}] $ (left) and $ [m_{\ell\ell}, \mathcal{D}_{\Lambda 1}^{\mathrm{Z}\gamma}] $ (right) in the Resolved VH (middle) and Boosted VH (lower) channels. For the fits, the $ a_{1} $ and $ \kappa_1/(\Lambda_1)^2 $ (left) or $ a_{1} $ and $ \kappa_2^{\mathrm{Z}\gamma}/(\Lambda_1^{\mathrm{Z}\gamma})^2 $ (right) HVV coupling contributions are included. More details are given in the caption of Fig. 3. 
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Figure 5b:
Observed and predicted distributions after fitting the data for $ [\mathcal{D}_\text{VBF}, m_{\ell\ell}, \mathcal{D}_{\Lambda 1}] $ (upper left) and $ [\mathcal{D}_\text{VBF}, m_{\ell\ell}, \mathcal{D}_{\Lambda 1}^{\mathrm{Z}\gamma}] $ (upper right) in the VBF channel, and for $ [m_{\ell\ell}, \mathcal{D}_{\Lambda 1}] $ (left) and $ [m_{\ell\ell}, \mathcal{D}_{\Lambda 1}^{\mathrm{Z}\gamma}] $ (right) in the Resolved VH (middle) and Boosted VH (lower) channels. For the fits, the $ a_{1} $ and $ \kappa_1/(\Lambda_1)^2 $ (left) or $ a_{1} $ and $ \kappa_2^{\mathrm{Z}\gamma}/(\Lambda_1^{\mathrm{Z}\gamma})^2 $ (right) HVV coupling contributions are included. More details are given in the caption of Fig. 3. 
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Figure 5c:
Observed and predicted distributions after fitting the data for $ [\mathcal{D}_\text{VBF}, m_{\ell\ell}, \mathcal{D}_{\Lambda 1}] $ (upper left) and $ [\mathcal{D}_\text{VBF}, m_{\ell\ell}, \mathcal{D}_{\Lambda 1}^{\mathrm{Z}\gamma}] $ (upper right) in the VBF channel, and for $ [m_{\ell\ell}, \mathcal{D}_{\Lambda 1}] $ (left) and $ [m_{\ell\ell}, \mathcal{D}_{\Lambda 1}^{\mathrm{Z}\gamma}] $ (right) in the Resolved VH (middle) and Boosted VH (lower) channels. For the fits, the $ a_{1} $ and $ \kappa_1/(\Lambda_1)^2 $ (left) or $ a_{1} $ and $ \kappa_2^{\mathrm{Z}\gamma}/(\Lambda_1^{\mathrm{Z}\gamma})^2 $ (right) HVV coupling contributions are included. More details are given in the caption of Fig. 3. 
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Figure 5d:
Observed and predicted distributions after fitting the data for $ [\mathcal{D}_\text{VBF}, m_{\ell\ell}, \mathcal{D}_{\Lambda 1}] $ (upper left) and $ [\mathcal{D}_\text{VBF}, m_{\ell\ell}, \mathcal{D}_{\Lambda 1}^{\mathrm{Z}\gamma}] $ (upper right) in the VBF channel, and for $ [m_{\ell\ell}, \mathcal{D}_{\Lambda 1}] $ (left) and $ [m_{\ell\ell}, \mathcal{D}_{\Lambda 1}^{\mathrm{Z}\gamma}] $ (right) in the Resolved VH (middle) and Boosted VH (lower) channels. For the fits, the $ a_{1} $ and $ \kappa_1/(\Lambda_1)^2 $ (left) or $ a_{1} $ and $ \kappa_2^{\mathrm{Z}\gamma}/(\Lambda_1^{\mathrm{Z}\gamma})^2 $ (right) HVV coupling contributions are included. More details are given in the caption of Fig. 3. 
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Figure 5e:
Observed and predicted distributions after fitting the data for $ [\mathcal{D}_\text{VBF}, m_{\ell\ell}, \mathcal{D}_{\Lambda 1}] $ (upper left) and $ [\mathcal{D}_\text{VBF}, m_{\ell\ell}, \mathcal{D}_{\Lambda 1}^{\mathrm{Z}\gamma}] $ (upper right) in the VBF channel, and for $ [m_{\ell\ell}, \mathcal{D}_{\Lambda 1}] $ (left) and $ [m_{\ell\ell}, \mathcal{D}_{\Lambda 1}^{\mathrm{Z}\gamma}] $ (right) in the Resolved VH (middle) and Boosted VH (lower) channels. For the fits, the $ a_{1} $ and $ \kappa_1/(\Lambda_1)^2 $ (left) or $ a_{1} $ and $ \kappa_2^{\mathrm{Z}\gamma}/(\Lambda_1^{\mathrm{Z}\gamma})^2 $ (right) HVV coupling contributions are included. More details are given in the caption of Fig. 3. 
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Figure 5f:
Observed and predicted distributions after fitting the data for $ [\mathcal{D}_\text{VBF}, m_{\ell\ell}, \mathcal{D}_{\Lambda 1}] $ (upper left) and $ [\mathcal{D}_\text{VBF}, m_{\ell\ell}, \mathcal{D}_{\Lambda 1}^{\mathrm{Z}\gamma}] $ (upper right) in the VBF channel, and for $ [m_{\ell\ell}, \mathcal{D}_{\Lambda 1}] $ (left) and $ [m_{\ell\ell}, \mathcal{D}_{\Lambda 1}^{\mathrm{Z}\gamma}] $ (right) in the Resolved VH (middle) and Boosted VH (lower) channels. For the fits, the $ a_{1} $ and $ \kappa_1/(\Lambda_1)^2 $ (left) or $ a_{1} $ and $ \kappa_2^{\mathrm{Z}\gamma}/(\Lambda_1^{\mathrm{Z}\gamma})^2 $ (right) HVV coupling contributions are included. More details are given in the caption of Fig. 3. 
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Figure 6:
Observed and predicted distributions after fitting the data for $ [m_{\mathrm{T}}, m_{\ell\ell}] $ in the 0 (left) and 1jet (right) ggH channels. For the fit, the $ a_{1} $ and $ a_3 \mathrm{H}\mathrm{V}\mathrm{V} $ coupling contributions are included. More details are given in the caption of Fig. 3. 
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Figure 6a:
Observed and predicted distributions after fitting the data for $ [m_{\mathrm{T}}, m_{\ell\ell}] $ in the 0 (left) and 1jet (right) ggH channels. For the fit, the $ a_{1} $ and $ a_3 \mathrm{H}\mathrm{V}\mathrm{V} $ coupling contributions are included. More details are given in the caption of Fig. 3. 
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Figure 6b:
Observed and predicted distributions after fitting the data for $ [m_{\mathrm{T}}, m_{\ell\ell}] $ in the 0 (left) and 1jet (right) ggH channels. For the fit, the $ a_{1} $ and $ a_3 \mathrm{H}\mathrm{V}\mathrm{V} $ coupling contributions are included. More details are given in the caption of Fig. 3. 
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Figure 7:
Observed and predicted distributions after fitting the data for $ [\mathcal{D}_\text{VBF} $, $ \mathcal{D}^{\mathrm{g}\mathrm{g}\mathrm{H}}_{0}] $ in the 2jet ggH channel. Both the $ \mathcal{D}^{\mathrm{g}\mathrm{g}\mathrm{H}}_{\text{CP}} < $ 0 (left) and $ \mathcal{D}^{\mathrm{g}\mathrm{g}\mathrm{H}}_{\text{CP}} > $ 0 (right) categories are shown. In this case, the VBF and ggH signals are shown separately. For the fit, the $ a_2^{\mathrm{g}\mathrm{g}} $ and $ a_3^{\mathrm{g}\mathrm{g}} $ coupling contributions are included. The corresponding pure $ a_2^{\mathrm{g}\mathrm{g}} $ ($ f_{a3}^{\mathrm{g}\mathrm{g}\mathrm{H}} = $ 0) and $ a_3^{\mathrm{g}\mathrm{g}} $ ($ f_{a3}^{\mathrm{g}\mathrm{g}\mathrm{H}} = $ 1) signal hypotheses are also shown superimposed, their yields correspond to the predicted number of SM signal events. More details are given in the caption of Fig. 3. 
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Figure 7a:
Observed and predicted distributions after fitting the data for $ [\mathcal{D}_\text{VBF} $, $ \mathcal{D}^{\mathrm{g}\mathrm{g}\mathrm{H}}_{0}] $ in the 2jet ggH channel. Both the $ \mathcal{D}^{\mathrm{g}\mathrm{g}\mathrm{H}}_{\text{CP}} < $ 0 (left) and $ \mathcal{D}^{\mathrm{g}\mathrm{g}\mathrm{H}}_{\text{CP}} > $ 0 (right) categories are shown. In this case, the VBF and ggH signals are shown separately. For the fit, the $ a_2^{\mathrm{g}\mathrm{g}} $ and $ a_3^{\mathrm{g}\mathrm{g}} $ coupling contributions are included. The corresponding pure $ a_2^{\mathrm{g}\mathrm{g}} $ ($ f_{a3}^{\mathrm{g}\mathrm{g}\mathrm{H}} = $ 0) and $ a_3^{\mathrm{g}\mathrm{g}} $ ($ f_{a3}^{\mathrm{g}\mathrm{g}\mathrm{H}} = $ 1) signal hypotheses are also shown superimposed, their yields correspond to the predicted number of SM signal events. More details are given in the caption of Fig. 3. 
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Figure 7b:
Observed and predicted distributions after fitting the data for $ [\mathcal{D}_\text{VBF} $, $ \mathcal{D}^{\mathrm{g}\mathrm{g}\mathrm{H}}_{0}] $ in the 2jet ggH channel. Both the $ \mathcal{D}^{\mathrm{g}\mathrm{g}\mathrm{H}}_{\text{CP}} < $ 0 (left) and $ \mathcal{D}^{\mathrm{g}\mathrm{g}\mathrm{H}}_{\text{CP}} > $ 0 (right) categories are shown. In this case, the VBF and ggH signals are shown separately. For the fit, the $ a_2^{\mathrm{g}\mathrm{g}} $ and $ a_3^{\mathrm{g}\mathrm{g}} $ coupling contributions are included. The corresponding pure $ a_2^{\mathrm{g}\mathrm{g}} $ ($ f_{a3}^{\mathrm{g}\mathrm{g}\mathrm{H}} = $ 0) and $ a_3^{\mathrm{g}\mathrm{g}} $ ($ f_{a3}^{\mathrm{g}\mathrm{g}\mathrm{H}} = $ 1) signal hypotheses are also shown superimposed, their yields correspond to the predicted number of SM signal events. More details are given in the caption of Fig. 3. 
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Figure 8:
Expected (dashed) and observed (solid) profiled likelihood on $ f_{a2} $ (upper left), $ f_{\Lambda 1} $ (upper right), $ f_{a3} $ (lower left), and $ f_{\Lambda 1}^{\mathrm{Z}\gamma} $ (lower right) using Approach 1. In each case, the signal strength modifiers are treated as free parameters. The dashed horizontal lines show the 68 and 95% CL regions. Axis scales are varied for $ f_{a2} $ and $ f_{\Lambda 1} $ to improve the visibility of important features. 
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Figure 8a:
Expected (dashed) and observed (solid) profiled likelihood on $ f_{a2} $ (upper left), $ f_{\Lambda 1} $ (upper right), $ f_{a3} $ (lower left), and $ f_{\Lambda 1}^{\mathrm{Z}\gamma} $ (lower right) using Approach 1. In each case, the signal strength modifiers are treated as free parameters. The dashed horizontal lines show the 68 and 95% CL regions. Axis scales are varied for $ f_{a2} $ and $ f_{\Lambda 1} $ to improve the visibility of important features. 
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Figure 8b:
Expected (dashed) and observed (solid) profiled likelihood on $ f_{a2} $ (upper left), $ f_{\Lambda 1} $ (upper right), $ f_{a3} $ (lower left), and $ f_{\Lambda 1}^{\mathrm{Z}\gamma} $ (lower right) using Approach 1. In each case, the signal strength modifiers are treated as free parameters. The dashed horizontal lines show the 68 and 95% CL regions. Axis scales are varied for $ f_{a2} $ and $ f_{\Lambda 1} $ to improve the visibility of important features. 
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Figure 8c:
Expected (dashed) and observed (solid) profiled likelihood on $ f_{a2} $ (upper left), $ f_{\Lambda 1} $ (upper right), $ f_{a3} $ (lower left), and $ f_{\Lambda 1}^{\mathrm{Z}\gamma} $ (lower right) using Approach 1. In each case, the signal strength modifiers are treated as free parameters. The dashed horizontal lines show the 68 and 95% CL regions. Axis scales are varied for $ f_{a2} $ and $ f_{\Lambda 1} $ to improve the visibility of important features. 
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Figure 8d:
Expected (dashed) and observed (solid) profiled likelihood on $ f_{a2} $ (upper left), $ f_{\Lambda 1} $ (upper right), $ f_{a3} $ (lower left), and $ f_{\Lambda 1}^{\mathrm{Z}\gamma} $ (lower right) using Approach 1. In each case, the signal strength modifiers are treated as free parameters. The dashed horizontal lines show the 68 and 95% CL regions. Axis scales are varied for $ f_{a2} $ and $ f_{\Lambda 1} $ to improve the visibility of important features. 
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Figure 9:
Expected (dashed) and observed (solid) profiled likelihood on $ f_{a2} $ (upper left), $ f_{\Lambda 1} $ (upper right) and $ f_{a3} $ (bottom) using Approach 2. The other two anomalous coupling cross section fractions are either fixed to zero (blue) or left floating in the fit (red). In each case, the signal strength modifiers are treated as free parameters. The dashed horizontal lines show the 68 and 95% CL regions. Axis scales are varied for $ f_{a2} $ and $ f_{\Lambda 1} $ to improve the visibility of important features. 
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Figure 9a:
Expected (dashed) and observed (solid) profiled likelihood on $ f_{a2} $ (upper left), $ f_{\Lambda 1} $ (upper right) and $ f_{a3} $ (bottom) using Approach 2. The other two anomalous coupling cross section fractions are either fixed to zero (blue) or left floating in the fit (red). In each case, the signal strength modifiers are treated as free parameters. The dashed horizontal lines show the 68 and 95% CL regions. Axis scales are varied for $ f_{a2} $ and $ f_{\Lambda 1} $ to improve the visibility of important features. 
png pdf 
Figure 9b:
Expected (dashed) and observed (solid) profiled likelihood on $ f_{a2} $ (upper left), $ f_{\Lambda 1} $ (upper right) and $ f_{a3} $ (bottom) using Approach 2. The other two anomalous coupling cross section fractions are either fixed to zero (blue) or left floating in the fit (red). In each case, the signal strength modifiers are treated as free parameters. The dashed horizontal lines show the 68 and 95% CL regions. Axis scales are varied for $ f_{a2} $ and $ f_{\Lambda 1} $ to improve the visibility of important features. 
png pdf 
Figure 9c:
Expected (dashed) and observed (solid) profiled likelihood on $ f_{a2} $ (upper left), $ f_{\Lambda 1} $ (upper right) and $ f_{a3} $ (bottom) using Approach 2. The other two anomalous coupling cross section fractions are either fixed to zero (blue) or left floating in the fit (red). In each case, the signal strength modifiers are treated as free parameters. The dashed horizontal lines show the 68 and 95% CL regions. Axis scales are varied for $ f_{a2} $ and $ f_{\Lambda 1} $ to improve the visibility of important features. 
png pdf 
Figure 10:
The observed correlation coefficients between HVV anomalous coupling cross section fractions and signal strength modifiers (left) and between SMEFT Higgs basis coupling parameters (right). 
png pdf 
Figure 10a:
The observed correlation coefficients between HVV anomalous coupling cross section fractions and signal strength modifiers (left) and between SMEFT Higgs basis coupling parameters (right). 
png pdf 
Figure 10b:
The observed correlation coefficients between HVV anomalous coupling cross section fractions and signal strength modifiers (left) and between SMEFT Higgs basis coupling parameters (right). 
png pdf 
Figure 11:
Expected (dashed) and observed (solid) profiled likelihood on the $ \delta c_\text{z} $ (upper left), $ c_{\text{z}\Box} $ (upper right), $ c_\text{zz} $ (lower left), and $ \tilde{c}_\text{zz} $ (lower right) couplings of the SMEFT Higgs basis. All four couplings are studied simultaneously. The dashed horizontal lines show the 68 and 95% CL regions. 
png pdf 
Figure 11a:
Expected (dashed) and observed (solid) profiled likelihood on the $ \delta c_\text{z} $ (upper left), $ c_{\text{z}\Box} $ (upper right), $ c_\text{zz} $ (lower left), and $ \tilde{c}_\text{zz} $ (lower right) couplings of the SMEFT Higgs basis. All four couplings are studied simultaneously. The dashed horizontal lines show the 68 and 95% CL regions. 
png pdf 
Figure 11b:
Expected (dashed) and observed (solid) profiled likelihood on the $ \delta c_\text{z} $ (upper left), $ c_{\text{z}\Box} $ (upper right), $ c_\text{zz} $ (lower left), and $ \tilde{c}_\text{zz} $ (lower right) couplings of the SMEFT Higgs basis. All four couplings are studied simultaneously. The dashed horizontal lines show the 68 and 95% CL regions. 
png pdf 
Figure 11c:
Expected (dashed) and observed (solid) profiled likelihood on the $ \delta c_\text{z} $ (upper left), $ c_{\text{z}\Box} $ (upper right), $ c_\text{zz} $ (lower left), and $ \tilde{c}_\text{zz} $ (lower right) couplings of the SMEFT Higgs basis. All four couplings are studied simultaneously. The dashed horizontal lines show the 68 and 95% CL regions. 
png pdf 
Figure 11d:
Expected (dashed) and observed (solid) profiled likelihood on the $ \delta c_\text{z} $ (upper left), $ c_{\text{z}\Box} $ (upper right), $ c_\text{zz} $ (lower left), and $ \tilde{c}_\text{zz} $ (lower right) couplings of the SMEFT Higgs basis. All four couplings are studied simultaneously. The dashed horizontal lines show the 68 and 95% CL regions. 
png pdf 
Figure 12:
Summary of constraints on the SMEFT Higgs (left) and Warsaw (right) basis coupling parameters with the best fit values and 68% CL uncertainties. For the Warsaw basis, only one of $ c_\text{HW} $, $ c_\text{HWB} $, and $ c_\text{HB} $ is independent, the same is also true for $ c_{\text{H}\tilde{\text{W}}} $, $ c_{\text{H}\tilde{\text{W}}\text{B}} $, and $ c_{\text{H}\tilde{\text{B}}} $. 
png pdf 
Figure 12a:
Summary of constraints on the SMEFT Higgs (left) and Warsaw (right) basis coupling parameters with the best fit values and 68% CL uncertainties. For the Warsaw basis, only one of $ c_\text{HW} $, $ c_\text{HWB} $, and $ c_\text{HB} $ is independent, the same is also true for $ c_{\text{H}\tilde{\text{W}}} $, $ c_{\text{H}\tilde{\text{W}}\text{B}} $, and $ c_{\text{H}\tilde{\text{B}}} $. 
png pdf 
Figure 12b:
Summary of constraints on the SMEFT Higgs (left) and Warsaw (right) basis coupling parameters with the best fit values and 68% CL uncertainties. For the Warsaw basis, only one of $ c_\text{HW} $, $ c_\text{HWB} $, and $ c_\text{HB} $ is independent, the same is also true for $ c_{\text{H}\tilde{\text{W}}} $, $ c_{\text{H}\tilde{\text{W}}\text{B}} $, and $ c_{\text{H}\tilde{\text{B}}} $. 
png pdf 
Figure 13:
Expected (dashed) and observed (solid) profiled likelihood on $ f_{a3}^{\mathrm{g}\mathrm{g}\mathrm{H}} $. The signal strength modifiers and the CPodd HVV anomalous coupling cross section fraction are treated as free parameters. The crossing of the observed likelihood with the dashed horizontal line shows the observed 68% CL region. 
Tables  
png pdf 
Table 1:
The cross sections ($ \sigma_i $) of the anomalous contributions ($ a_i $) relative to the SM value ($ \sigma_1 $) used to define the fractional cross sections $ f_{ai} $ for the Approach 1 and 2 coupling relationships. For the $ \kappa_{1} $ and $ \kappa_{2}^{\mathrm{Z}\gamma} $ couplings, the numerical values $ \Lambda_1 = \Lambda_1^{\mathrm{Z}\gamma} = $ 100 GeV are chosen to keep all coefficients of similar order of magnitude. 
png pdf 
Table 2:
Summary of the base selection criteria. 
png pdf 
Table 3:
Summary of the ggH, VBF, and VH production channels used for the HVV coupling study. 
png pdf 
Table 4:
Summary of ggH channel selections used for the Hgg coupling study. 
png pdf 
Table 5:
Summary of the $ \tau\tau $, top quark, and WW control region requirements. 
png pdf 
Table 6:
The kinematic observables used for the interference based categorization and for the final discriminants used in the fits to data to study the HVV and Hgg couplings. For each of the anomalous HVV couplings in Approach 1, we have a dedicated analysis in the VBF and VH channels. In Approach 2, we use one analysis to target all anomalous HVV couplings simultaneously. 
png pdf 
Table 7:
Summary of constraints on the anomalous HVV and Hgg coupling parameters with the best fit values and allowed 68 and 95% CL (in square brackets) intervals. For Approach 1, each $ f_{ai} $ is studied independently. For Approach 2, each $ f_{ai} $ is shown separately with the other two cross section fractions either fixed to zero or left floating in the fit. In each case, the signal strength modifiers are treated as free parameters. 
png pdf 
Table 8:
Summary of constraints on the SMEFT Higgs basis coupling parameters with the best fit values and 68% CL uncertainties. All four couplings are studied simultaneously. 
png pdf 
Table 9:
Summary of constraints on the SMEFT Warsaw basis coupling parameters with the best fit values and 68% CL uncertainties. Only one of $ c_\text{HW} $, $ c_\text{HWB} $, and $ c_\text{HB} $ is independent, the same is also true for $ c_{\text{H}\tilde{\text{W}}} $, $ c_{\text{H}\tilde{\text{W}}\text{B}} $, and $ c_{\text{H}\tilde{\text{B}}} $. Three independent fits to the data were performed with a different choice of four independent couplings in each. 
Summary 
This paper presents a study of the anomalous couplings of the Higgs boson (H) with vector bosons, including CP violating effects, using its associated production with hadronic jets in gluon fusion, electroweak vector boson fusion, and associated production with a W or Z boson, and its subsequent decay to a pair of W bosons. The results are based on the protonproton collision data set collected by the CMS detector at the LHC during 20162018, corresponding to an integrated luminosity of 138 fb$ ^{1} $ at a centerofmass energy of 13 TeV. The analysis targets the differentflavor dilepton ($ \mathrm{e}\mu $) final state, with kinematic information from associated jets combined using matrix element techniques to increase sensitivity to anomalous effects at the production vertex. Dedicated Monte Carlo simulation and matrix element reweighting provide modeling of all kinematic features in the production and decay of the Higgs boson with full simulation of detector effects. A simultaneous measurement of four Higgs boson couplings to electroweak vector bosons has been performed in the framework of a standard model effective field theory. All measurements are consistent with the expectations for the standard model Higgs boson and constraints are set on the fractional contribution of the anomalous couplings to the Higgs boson cross section. The most stringent constraints on the HVV anomalous coupling cross section fractions are at the per mille level. These results are in agreement with those obtained in the $ \mathrm{H}\to\mathrm{Z}\mathrm{Z} $ and $ \mathrm{H}\to\tau\tau $ channels, and also significantly surpass those of the previous $ \mathrm{H}\to\mathrm{W}\mathrm{W} $ anomalous coupling analysis from the CMS experiment in both scope and precision. 
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