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CMS-HIG-17-011 ; CERN-EP-2017-143

Constraints on anomalous Higgs boson couplings using production and decay information in the four-lepton final state

CMS Collaboration

3 July 2017

Phys. Lett. B 775 (2017) 1

Abstract: A search is performed for anomalous interactions of the recently discovered Higgs boson using matrix element techniques with the information from its decay to four leptons and from associated Higgs boson production with two quark jets in either vector boson fusion or associated production with a vector boson. The data were recorded by the CMS experiment at the LHC at a center-of-mass energy of 13 TeV and correspond to an integrated luminosity of 38.6 fb$^{-1}$. These data are combined with the data collected at center-of-mass energies of 7 and 8 TeV, corresponding to integrated luminosities of 5.1 and 19.7 fb$^{-1}$, respectively. All observations are consistent with the expectations for the standard model Higgs boson.

Links: e-print arXiv:1707.00541 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ;

Figures
png pdf	Figure 1: Illustration of H boson production and decay in three topologies: gluon fusion $\mathrm{g} \mathrm{g} \to \mathrm{ H } \to {\mathrm {V}} {\mathrm {V}} \to 4\ell$ (left); vector boson fusion ${\mathrm{ q } \mathrm{ q } } \to {\mathrm {V}} {\mathrm {V}} ( {\mathrm{ q } \mathrm{ q } } ) \to \mathrm{ H } ( {\mathrm{ q } \mathrm{ q } } ) \to {\mathrm {V}} {\mathrm {V}} ( {\mathrm{ q } \mathrm{ q } } )$ (middle); and associated production ${\mathrm{ q } \mathrm{ q } } \to {\mathrm {V}} \to {\mathrm {V}} \mathrm{ H } \to ( {\mathrm {ff}} )\mathrm{ H } \to ( {\mathrm {ff}} ) {\mathrm {V}} {\mathrm {V}}$ (right). In the latter two cases, the production and decay $\mathrm{ H } \to {\mathrm {V}} {\mathrm {V}}$ may be followed by the same four-lepton decay shown in the first case. The five angles shown in blue and the invariant masses of the two vector bosons shown in green fully characterize either the production or the decay chain. The angles are defined in either the H or V boson rest frames [26,33].
png pdf	Figure 1-a: Illustration of H boson production and decay in the gluon fusion topology, $\mathrm{g} \mathrm{g} \to \mathrm{ H } \to {\mathrm {V}} {\mathrm {V}} \to 4\ell$. The five angles shown in blue and the invariant masses of the two vector bosons shown in green fully characterize either the production or the decay chain. The angles are defined in either the H or V boson rest frames [26,33].
png pdf	Figure 1-b: Illustration of H boson production and decay in the vector boson fusion topology ${\mathrm{ q } \mathrm{ q } } \to {\mathrm {V}} {\mathrm {V}} ( {\mathrm{ q } \mathrm{ q } } ) \to \mathrm{ H } ( {\mathrm{ q } \mathrm{ q } } ) \to {\mathrm {V}} {\mathrm {V}} ( {\mathrm{ q } \mathrm{ q } } )$. The production and decay $\mathrm{ H } \to {\mathrm {V}} {\mathrm {V}}$ may be followed by the same four-lepton decay shown in Fig. 1-a. The five angles shown in blue and the invariant masses of the two vector bosons shown in green fully characterize either the production or the decay chain. The angles are defined in either the H or V boson rest frames [26,33].
png pdf	Figure 1-c: Illustration of H boson production and decay in the associated production topology ${\mathrm{ q } \mathrm{ q } } \to {\mathrm {V}} \to {\mathrm {V}} \mathrm{ H } \to ( {\mathrm {ff}} )\mathrm{ H } \to ( {\mathrm {ff}} ) {\mathrm {V}} {\mathrm {V}}$. The production and decay $\mathrm{ H } \to {\mathrm {V}} {\mathrm {V}}$ may be followed by the same four-lepton decay shown in Fig. 1-a. The five angles shown in blue and the invariant masses of the two vector bosons shown in green fully characterize either the production or the decay chain. The angles are defined in either the H or V boson rest frames [26,33].
png pdf	Figure 2: Distributions of $\mathcal {D}_\text {bkg}$ (a) for all events in Run 2; $\mathcal {D}_{0h+}$ (b), $\mathcal {D}_{\Lambda 1}$ (c) , $\mathcal {D}_{\Lambda 1}^{{\mathrm{ Z } } \gamma }$ (d), $\mathcal {D}_{0-}$ (e), and $\mathcal {D}_{CP}$ (h) for the untagged and 2015 events; $\mathcal {D}_{0-}$ in the VBF-jet (f) and ${\mathrm {V}} \mathrm{ H }$-jet (g) categories. The arrow in (a) indicates the requirement $\mathcal {D}_\text {bkg}>0.5$, used to suppress background on all other plots. Points with error bars show data and histograms show expectations for background and signal, as indicated in the legend in (a). The dashed lines show expectations for BSM hypotheses, as indicated in the individual legends.
png pdf	Figure 3: Observed (solid) and expected (dashed) likelihood scans of $f_{a3}\cos(\phi _{a3})$ (a), $f_{a2}\cos(\phi _{a2})$ (b), $f_{\Lambda 1}\cos(\phi _{\Lambda 1})$ (c), and $f_{\Lambda 1}^{{\mathrm{ Z } } \gamma }\cos(\phi _{\Lambda 1}^{{\mathrm{ Z } } \gamma })$ (d). Results of the Run 2 only and the combined Run 1 and Run 2 analyses are shown.
png pdf	Figure 3-a: Observed (solid) and expected (dashed) likelihood scans of $f_{a3}\cos(\phi _{a3})$. Results of the Run 2 only and the combined Run 1 and Run 2 analyses are shown.
png pdf	Figure 3-b: Observed (solid) and expected (dashed) likelihood scans of $f_{a2}\cos(\phi _{a2})$. Results of the Run 2 only and the combined Run 1 and Run 2 analyses are shown.
png pdf	Figure 3-c: Observed (solid) and expected (dashed) likelihood scans of $f_{\Lambda 1}\cos(\phi _{\Lambda 1})$. Results of the Run 2 only and the combined Run 1 and Run 2 analyses are shown.
png pdf	Figure 3-d: Observed (solid) and expected (dashed) likelihood scans of $f_{\Lambda 1}^{{\mathrm{ Z } } \gamma }\cos(\phi _{\Lambda 1}^{{\mathrm{ Z } } \gamma })$. Results of the Run 2 only and the combined Run 1 and Run 2 analyses are shown.

Tables
png pdf	Table 1: Summary of the three production categories in the analysis of 2016 data. The discriminants $\mathcal {D}$ are calculated from Eqs.(4) and (5), as discussed in more detail in the text. For each analysis, the appropriate BSM model is considered in the definition of the categories: $f_{a3}=1$, $f_{a2}=1$, $f_{\Lambda 1}=1$, or $f^{{\mathrm{ Z } } \gamma }_{\Lambda 1}=1$. Three observables (abbreviated as obs.) are listed for each analysis and for each category. They are described in more detail later in the text.
png pdf	Table 2: The numbers of events expected for the SM (or $f_{a3}=1$, in parentheses) for different signal and background modes and the total observed numbers of events across the three $f_{a3}$ categories in 2016 and 2015 data.
png pdf	Table 3: Summary of allowed 68%CL (central values with uncertainties) and 95%CL (in square brackets) intervals on anomalous coupling parameters obtained from the combined Run 1 and Run 2 data analysis.

Summary

We study anomalous interactions of the H boson using novel techniques with a matrix element likelihood approach to simultaneously analyze the $\mathrm{ H }\to4\ell$ decay and associated production with two quark jets. Three categories of events are analyzed, targeting events produced in vector boson fusion, with an associated vector boson, and in gluon fusion, respectively. The data collected at a center-of-mass energy of 13 TeV in Run\,2 of the LHC are combined with the Run\,1 data, collected at 7 and 8 TeV. No deviations from the standard model are observed and constraints are set on the four anomalous $\mathrm{ H }{\mathrm{V}} {\mathrm{V}}$ contributions, including the CP-violation parameter $f_{a3}$, summarized in Table 3.

Additional Figures
png pdf	Additional Figure 1: Distributions of the $\mathcal {D}_{\rm bkg}$ kinematic discriminant in the $f_{a3}$ (a), $f_{a2}$ (b), $f_{\Lambda 1}$ (c), and $f_{\Lambda 1}^{{\mathrm{ Z } } \gamma }$ (d) analyses. The distributions are summed over all three categories. Points with error bars show data and histograms show expectations for background and SM or BSM signal as indicated in the legend.
png pdf	Additional Figure 1-a: Distributions of the $\mathcal {D}_{\rm bkg}$ kinematic discriminant in the $f_{a3}$ analysis. The distributions are summed over all three categories. Points with error bars show data and histograms show expectations for background and SM or BSM signal as indicated in the legend.
png pdf	Additional Figure 1-b: Distributions of the $\mathcal {D}_{\rm bkg}$ kinematic discriminant in the $f_{a2}$ analysis. The distributions are summed over all three categories. Points with error bars show data and histograms show expectations for background and SM or BSM signal as indicated in the legend.
png pdf	Additional Figure 1-c: Distributions of the $\mathcal {D}_{\rm bkg}$ kinematic discriminant in the $f_{\Lambda 1}$ analysis. The distributions are summed over all three categories. Points with error bars show data and histograms show expectations for background and SM or BSM signal as indicated in the legend.
png pdf	Additional Figure 1-d: Distributions of the $\mathcal {D}_{\rm bkg}$ kinematic discriminant in the $f_{\Lambda 1}^{{\mathrm{ Z } } \gamma }$ analysis. The distributions are summed over all three categories. Points with error bars show data and histograms show expectations for background and SM or BSM signal as indicated in the legend.
png pdf	Additional Figure 2: Distributions of kinematic discriminants in the $f_{a3}$ analysis: $\mathcal {D}_{\rm bkg}$ (a), (d), (g), $\mathcal {D}_{0-}$ (b), (e), (h), and $\mathcal {D}_{CP}$ (c), (f), (i). The decay or production information used in the $\mathcal {D}_{0-}$ and $\mathcal {D}_{CP}$ discriminants is reflected in the superscript label and depends on the tagging category. $f_{a3}^\text {VBF}$ and $f_{a3}^{\mathrm {V} \mathrm{ H } }$ are defined using Eq.(2) by analogy with $f_{a3}$, but using the cross sections for the VBF and VH processes, respectively. Three tagging categories are shown: VBF-jets (a)-(c), VH-jets (d)-(f), and untagged (g)-(i). Points with error bars show data and histograms show expectations for background and SM or BSM signal as indicated in the legend.
png pdf	Additional Figure 2-a: Distribution of the $\mathcal {D}_{\rm bkg}$ kinematic discriminant in the $f_{a3}$ analysis, in the VBF-jets tagging category. Points with error bars show data and histograms show expectations for background and SM or BSM signal as indicated in the legend.
png pdf	Additional Figure 2-b: Distribution of the $\mathcal {D}_{0-}$ kinematic discriminant in the $f_{a3}$ analysis, in the VBF-jets tagging category. Points with error bars show data and histograms show expectations for background and SM or BSM signal as indicated in the legend.
png pdf	Additional Figure 2-c: Distribution of the $\mathcal {D}_{CP}$ kinematic discriminant in the $f_{a3}$ analysis, in the VBF-jets tagging category. Points with error bars show data and histograms show expectations for background and SM or BSM signal as indicated in the legend.
png pdf	Additional Figure 2-d: Distribution of the $\mathcal {D}_{\rm bkg}$ kinematic discriminant in the $f_{a3}$ analysis, in the VH-jets tagging category. Points with error bars show data and histograms show expectations for background and SM or BSM signal as indicated in the legend.
png pdf	Additional Figure 2-e: Distribution of the $\mathcal {D}_{0-}$ kinematic discriminant in the $f_{a3}$ analysis, in the VH-jets tagging category. Points with error bars show data and histograms show expectations for background and SM or BSM signal as indicated in the legend.
png pdf	Additional Figure 2-f: Distribution of the $\mathcal {D}_{CP}$ kinematic discriminant in the $f_{a3}$ analysis, in the VH-jets tagging category. Points with error bars show data and histograms show expectations for background and SM or BSM signal as indicated in the legend.
png pdf	Additional Figure 2-g: Distribution of the $\mathcal {D}_{\rm bkg}$ kinematic discriminant in the $f_{a3}$ analysis, in the untagged tagging category. Points with error bars show data and histograms show expectations for background and SM or BSM signal as indicated in the legend.
png pdf	Additional Figure 2-h: Distribution of the $\mathcal {D}_{0-}$ kinematic discriminant in the $f_{a3}$ analysis, in the untagged tagging category. Points with error bars show data and histograms show expectations for background and SM or BSM signal as indicated in the legend.
png pdf	Additional Figure 2-i: Distribution of the $\mathcal {D}_{CP}$ kinematic discriminant in the $f_{a3}$ analysis, in the untagged tagging category. Points with error bars show data and histograms show expectations for background and SM or BSM signal as indicated in the legend.
png pdf	Additional Figure 3: Distributions of kinematic discriminants in the $f_{a2}$ analysis: $\mathcal {D}_{\rm bkg}$ (a), (d), (g), $\mathcal {D}_{0h+}$ (b), (e), (h) and $\mathcal {D}_\text {int}$ (c), (f), (i). The decay or production information used in the $\mathcal {D}_{0h+}$ and $\mathcal {D}_\text {int}$ discriminants is reflected in the superscript label and depends on the tagging category. $f_{a2}^\text {VBF}$ and $f_{a2}^{\mathrm {V} \mathrm{ H } }$ are defined using Eq.(2) by analogy with $f_{a2}$, but using the cross sections for the VBF and VH processes, respectively. Three tagging categories are shown: VBF-jets (a)-(c), VH-jets (d)-(f), and untagged (g)-(i). Points with error bars show data and histograms show expectations for background and SM or BSM signal as indicated in the legend.
png pdf	Additional Figure 3-a: Distribution of the $\mathcal {D}_{\rm bkg}$ kinematic discriminants in the $f_{a2}$ analysis, in the VBF-jets tagging category. Points with error bars show data and histograms show expectations for background and SM or BSM signal as indicated in the legend.
png pdf	Additional Figure 3-b: Distribution of the $\mathcal {D}_{0h+}$ kinematic discriminants in the $f_{a2}$ analysis, in the VBF-jets tagging category. Points with error bars show data and histograms show expectations for background and SM or BSM signal as indicated in the legend.
png pdf	Additional Figure 3-c: Distribution of the $\mathcal {D}_\text {int}$ kinematic discriminants in the $f_{a2}$ analysis, in the VBF-jets tagging category. Points with error bars show data and histograms show expectations for background and SM or BSM signal as indicated in the legend.
png pdf	Additional Figure 3-d: Distribution of the $\mathcal {D}_{\rm bkg}$ kinematic discriminants in the $f_{a2}$ analysis, in the VH-jets tagging category. Points with error bars show data and histograms show expectations for background and SM or BSM signal as indicated in the legend.
png pdf	Additional Figure 3-e: Distribution of the $\mathcal {D}_{0h+}$ kinematic discriminants in the $f_{a2}$ analysis, in the VH-jets tagging category. Points with error bars show data and histograms show expectations for background and SM or BSM signal as indicated in the legend.
png pdf	Additional Figure 3-f: Distribution of the $\mathcal {D}_\text {int}$ kinematic discriminants in the $f_{a2}$ analysis, in the VH-jets tagging category. Points with error bars show data and histograms show expectations for background and SM or BSM signal as indicated in the legend.
png pdf	Additional Figure 3-g: Distribution of the $\mathcal {D}_{\rm bkg}$ kinematic discriminants in the $f_{a2}$ analysis, in the untagged tagging category. Points with error bars show data and histograms show expectations for background and SM or BSM signal as indicated in the legend.
png pdf	Additional Figure 3-h: Distribution of the $\mathcal {D}_{0h+}$ kinematic discriminants in the $f_{a2}$ analysis, in the untagged tagging category. Points with error bars show data and histograms show expectations for background and SM or BSM signal as indicated in the legend.
png pdf	Additional Figure 3-i: Distribution of the $\mathcal {D}_\text {int}$ kinematic discriminants in the $f_{a2}$ analysis, in the untagged tagging category. Points with error bars show data and histograms show expectations for background and SM or BSM signal as indicated in the legend.
png pdf	Additional Figure 4: Distributions of kinematic discriminants in the $f_{\Lambda 1}$ analysis: $\mathcal {D}_{\rm bkg}$ (a), (d), (g), $\mathcal {D}_{\Lambda 1}$ (b), (e), (h). and $\mathcal {D}_{0h+}$ (c), (f), (i). The decay or production information used in the $\mathcal {D}_{\Lambda 1}$ and $\mathcal {D}_{0h+}$ discriminants is reflected in the superscript label and depends on the tagging category. $f_{\Lambda 1}^\text {VBF}$ and $f_{\Lambda 1}^{\mathrm {V} \mathrm{ H } }$ are defined using Eq.(2) by analogy with $f_{\Lambda 1}$, but using the cross sections for the VBF and VH processes, respectively. Three tagging categories are shown: VBF-jets (a)-(c), VH-jets (d)-(f), and untagged (g)-(i). Points with error bars show data and histograms show expectations for background and SM or BSM signal as indicated in the legend.
png pdf	Additional Figure 4-a: Distribution of the $\mathcal {D}_{\rm bkg}$ kinematic discriminant in the $f_{\Lambda 1}$ analysis, in the VBF-jets tagging category. Points with error bars show data and histograms show expectations for background and SM or BSM signal as indicated in the legend.
png pdf	Additional Figure 4-b: Distribution of the $\mathcal {D}_{\Lambda 1}$ kinematic discriminant in the $f_{\Lambda 1}$ analysis, in the VBF-jets tagging category. Points with error bars show data and histograms show expectations for background and SM or BSM signal as indicated in the legend.
png pdf	Additional Figure 4-c: Distribution of the $\mathcal {D}_{0h+}$ kinematic discriminant in the $f_{\Lambda 1}$ analysis, in the VBF-jets tagging category. Points with error bars show data and histograms show expectations for background and SM or BSM signal as indicated in the legend.
png pdf	Additional Figure 4-d: Distribution of the $\mathcal {D}_{\rm bkg}$ kinematic discriminant in the $f_{\Lambda 1}$ analysis, in the VH-jets tagging category. Points with error bars show data and histograms show expectations for background and SM or BSM signal as indicated in the legend.
png pdf	Additional Figure 4-e: Distribution of the $\mathcal {D}_{\Lambda 1}$ kinematic discriminant in the $f_{\Lambda 1}$ analysis, in the VH-jets tagging category. Points with error bars show data and histograms show expectations for background and SM or BSM signal as indicated in the legend.
png pdf	Additional Figure 4-f: Distribution of the $\mathcal {D}_{0h+}$ kinematic discriminant in the $f_{\Lambda 1}$ analysis, in the VH-jets tagging category. Points with error bars show data and histograms show expectations for background and SM or BSM signal as indicated in the legend.
png pdf	Additional Figure 4-g: Distribution of the $\mathcal {D}_{\rm bkg}$ kinematic discriminant in the $f_{\Lambda 1}$ analysis, in the untagged tagging category. Points with error bars show data and histograms show expectations for background and SM or BSM signal as indicated in the legend.
png pdf	Additional Figure 4-h: Distribution of the $\mathcal {D}_{\Lambda 1}$ kinematic discriminant in the $f_{\Lambda 1}$ analysis, in the untagged tagging category. Points with error bars show data and histograms show expectations for background and SM or BSM signal as indicated in the legend.
png pdf	Additional Figure 4-i: Distribution of the $\mathcal {D}_{0h+}$ kinematic discriminant in the $f_{\Lambda 1}$ analysis, in the untagged tagging category. Points with error bars show data and histograms show expectations for background and SM or BSM signal as indicated in the legend.
png pdf	Additional Figure 5: Distributions of kinematic discriminants in the $f_{\Lambda 1}^{{\mathrm{ Z } } \gamma }$ analysis: $\mathcal {D}_{\rm bkg}$ (a), (d), (g), $\mathcal {D}_{\Lambda 1}^{{\mathrm{ Z } } \gamma }$ (b), (e), (h), and $\mathcal {D}_{0h+}$ (c), (f), (i). The decay or production information used in the $\mathcal {D}_{\Lambda 1}^{{\mathrm{ Z } } \gamma }$ and $\mathcal {D}_{0h+}$ discriminants is reflected in the superscript label and depends on the tagging category. Three tagging categories are shown: VBF-jets (a)-(c), VH-jets (d)-(f), and untagged (g)-(i). Points with error bars show data and histograms show expectations for background and SM or BSM signal as indicated in the legend.
png pdf	Additional Figure 5-a: Distribution of the $\mathcal {D}_{\rm bkg}$ kinematic discriminant in the $f_{\Lambda 1}^{{\mathrm{ Z } } \gamma }$ analysis, in the VBF-jets tagging category. Points with error bars show data and histograms show expectations for background and SM or BSM signal as indicated in the legend.
png pdf	Additional Figure 5-b: Distribution of the $\mathcal {D}_{\Lambda 1}^{{\mathrm{ Z } } \gamma }$ kinematic discriminant in the $f_{\Lambda 1}^{{\mathrm{ Z } } \gamma }$ analysis, in the VBF-jets tagging category. Points with error bars show data and histograms show expectations for background and SM or BSM signal as indicated in the legend.
png pdf	Additional Figure 5-c: Distribution of the $\mathcal {D}_{0h+}$ kinematic discriminant in the $f_{\Lambda 1}^{{\mathrm{ Z } } \gamma }$ analysis, in the VBF-jets tagging category. Points with error bars show data and histograms show expectations for background and SM or BSM signal as indicated in the legend.
png pdf	Additional Figure 5-d: Distribution of the $\mathcal {D}_{\rm bkg}$ kinematic discriminant in the $f_{\Lambda 1}^{{\mathrm{ Z } } \gamma }$ analysis, in the VH-jets tagging category. Points with error bars show data and histograms show expectations for background and SM or BSM signal as indicated in the legend.
png pdf	Additional Figure 5-e: Distribution of the $\mathcal {D}_{\Lambda 1}^{{\mathrm{ Z } } \gamma }$ kinematic discriminant in the $f_{\Lambda 1}^{{\mathrm{ Z } } \gamma }$ analysis, in the VH-jets tagging category. Points with error bars show data and histograms show expectations for background and SM or BSM signal as indicated in the legend.
png pdf	Additional Figure 5-f: Distribution of the $\mathcal {D}_{0h+}$ kinematic discriminant in the $f_{\Lambda 1}^{{\mathrm{ Z } } \gamma }$ analysis, in the VH-jets tagging category. Points with error bars show data and histograms show expectations for background and SM or BSM signal as indicated in the legend.
png pdf	Additional Figure 5-g: Distribution of the $\mathcal {D}_{\rm bkg}$ kinematic discriminant in the $f_{\Lambda 1}^{{\mathrm{ Z } } \gamma }$ analysis, in the untagged tagging category. Points with error bars show data and histograms show expectations for background and SM or BSM signal as indicated in the legend.
png pdf	Additional Figure 5-h: Distribution of the $\mathcal {D}_{\Lambda 1}^{{\mathrm{ Z } } \gamma }$ kinematic discriminant in the $f_{\Lambda 1}^{{\mathrm{ Z } } \gamma }$ analysis, in the untagged tagging category. Points with error bars show data and histograms show expectations for background and SM or BSM signal as indicated in the legend.
png pdf	Additional Figure 5-i: Distribution of the $\mathcal {D}_{0h+}$ kinematic discriminant in the $f_{\Lambda 1}^{{\mathrm{ Z } } \gamma }$ analysis, in the untagged tagging category. Points with error bars show data and histograms show expectations for background and SM or BSM signal as indicated in the legend.
png pdf	Additional Figure 6: Animated distributions of the $\mathcal {D}_{\rm bkg}$ kinematic discriminant in the $f_{a3}$ (a), $f_{a2}$ (b), $f_{\Lambda 1}$ (c), and $f_{\Lambda 1}^{{\mathrm{ Z } } \gamma }$ (d) analyses. The distributions are summed over all three categories. Points with error bars show data and histograms show expectations for background and SM or BSM signal as indicated in the legend. The animations scan $f_{ai}$ to illustrate how the expected signal distributions change as a function of $f_{ai}$. For each value of $f_{ai}$, the signal strengths for Higgs production through couplings to fermions $\mu _f$ and bosons $\mu _V$ are set to their best-fit values. The values of $f_{ai}$, $f_{ai}^\text {VBF}$, and $f_{ai}^{\mathrm {V} \mathrm{ H } }$ are recorded on the plots, along with the negative log likelihood. $f_{ai}^\text {VBF}$ and $f_{ai}^{\mathrm {V} \mathrm{ H } }$ are defined using Eq.(2) by analogy with $f_{ai}$, but using the cross sections for the VBF and VH processes, respectively.
png pdf	Additional Figure 12: Summary of allowed confidence level intervals on anomalous coupling parameters in HVV interactions under the assumption that all the coupling ratios are real ($\phi _{ai}^{\mathrm {V} \mathrm {V} }=0$ or $\pi$). The HZZ+HWW coupling limits assume that $a_{i}^{{\mathrm{ Z } } {\mathrm{ Z } } }=a_{i}^{\mathrm{ W } \mathrm{ W } }$, and the $f_{\Lambda Q}$ limits assume that the Higgs boson width is $4.1 MeV$. The expected 68% and 95% CL regions are shown as green and yellow bands. The observed constraints at 68% and 95% CL are shown as points with errors and the excluded hatched regions. The limits on $f_{a2,3}^{{\mathrm{ Z } } \gamma ,\gamma \gamma }$ are from Ref. [13], and the limits on $f_{\Lambda Q}$ are from Ref. [15].

Additional Material: Animated Distributions

Additional Figure 6: Animated distributions of the $\mathcal {D}_{\rm bkg}$ kinematic discriminant in the $f_{a3}$ (a), $f_{a2}$ (b), $f_{\Lambda 1}$ (c), and $f_{\Lambda 1}^{{\mathrm{ Z } } \gamma }$ (d) analyses. The distributions are summed over all three categories. Points with error bars show data and histograms show expectations for background and SM or BSM signal as indicated in the legend. The animations scan $f_{ai}$ to illustrate how the expected signal distributions change as a function of $f_{ai}$. For each value of $f_{ai}$, the signal strengths for Higgs production through couplings to fermions $\mu _f$ and bosons $\mu _V$ are set to their best-fit values. The values of $f_{ai}$, $f_{ai}^\text {VBF}$, and $f_{ai}^{\mathrm {V} \mathrm{ H } }$ are recorded on the plots, along with the negative log likelihood. $f_{ai}^\text {VBF}$ and $f_{ai}^{\mathrm {V} \mathrm{ H } }$ are defined using Eq.(2) by analogy with $f_{ai}$, but using the cross sections for the VBF and VH processes, respectively.
animated gif	Additional Figure 6-a: Animated distribution of the $\mathcal {D}_{\rm bkg}$ kinematic discriminant in the $f_{a3}$ analysis. The distribution is summed over all three categories. Points with error bars show data and histograms show expectations for background and SM or BSM signal as indicated in the legend.
animated gif	Additional Figure 6-b: Animated distribution of the $\mathcal {D}_{\rm bkg}$ kinematic discriminant in the $f_{a2}$ analysis. The distribution is summed over all three categories. Points with error bars show data and histograms show expectations for background and SM or BSM signal as indicated in the legend.
animated gif	Additional Figure 6-c: Animated distribution of the $\mathcal {D}_{\rm bkg}$ kinematic discriminant in the $f_{\Lambda 1}$ analysis. The distribution is summed over all three categories. Points with error bars show data and histograms show expectations for background and SM or BSM signal as indicated in the legend.
animated gif	Additional Figure 6-d: Animated distribution of the $\mathcal {D}_{\rm bkg}$ kinematic discriminant in the $f_{\Lambda 1}^{{\mathrm{ Z } } \gamma }$ analysis. The distribution is summed over all three categories. Points with error bars show data and histograms show expectations for background and SM or BSM signal as indicated in the legend.

Additional Figure 7: Animated distributions of kinematic discriminants in the $f_{a3}$ analysis: $\mathcal {D}_{\rm bkg}$ (a), (d), (g), $\mathcal {D}_{0-}$ (b), (e), (h), and $\mathcal {D}_{CP}$ (c), (f), (i). The decay or production information used in the $\mathcal {D}_{0-}$ and $\mathcal {D}_{CP}$ discriminants is reflected in the superscript label and depends on the tagging category. Three tagging categories are shown: VBF-jets (a)-(c), VH-jets (d)-(f), and untagged (g)-(i). Points with error bars show data and histograms show expectations for background and signal as indicated in the legend. The animations scan $f_{a3}$ to illustrate how the expected signal distributions change as a function of $f_{a3}$. For each value of $f_{a3}$, the signal strengths for Higgs production through couplings to fermions $\mu _f$ and bosons $\mu _V$ are set to their best-fit values. The values of $f_{a3}$, $f_{a3}^\text {VBF}$, and $f_{a3}^{\mathrm {V} \mathrm{ H } }$ are recorded on the plots, along with the negative log likelihood. $f_{a3}^\text {VBF}$ and $f_{a3}^{\mathrm {V} \mathrm{ H } }$ are defined using Eq.(2) by analogy with $f_{a3}$, but using the cross sections for the VBF and VH processes, respectively.
animated gif	Additional Figure 7-a: Animated distributions of the $\mathcal {D}_{\rm bkg}$ kinematic discriminant in the $f_{a3}$ analysis, in the VBF-jets tagging category. Points with error bars show data and histograms show expectations for background and signal as indicated in the legend.
animated gif	Additional Figure 7-b: Animated distributions of the $\mathcal {D}_{0-}$ kinematic discriminant in the $f_{a3}$ analysis, in the VBF-jets tagging category. The decay or production information usedis reflected in the superscript label and depends on the tagging category. Points with error bars show data and histograms show expectations for background and signal as indicated in the legend.
animated gif	Additional Figure 7-c: Animated distributions of the $\mathcal {D}_{CP}$ kinematic discriminant in the $f_{a3}$ analysis, in the VBF-jets tagging category. The decay or production information used is reflected in the superscript label and depends on the tagging category. Points with error bars show data and histograms show expectations for background and signal as indicated in the legend.
animated gif	Additional Figure 7-d: Animated distributions of the $\mathcal {D}_{\rm bkg}$ kinematic discriminant in the $f_{a3}$ analysis, in the VH-jets tagging category. Points with error bars show data and histograms show expectations for background and signal as indicated in the legend.
animated gif	Additional Figure 7-e: Animated distributions of the $\mathcal {D}_{0-}$ kinematic discriminant in the $f_{a3}$ analysis, in the VH-jets tagging category. The decay or production information used is reflected in the superscript label and depends on the tagging category. Points with error bars show data and histograms show expectations for background and signal as indicated in the legend.
animated gif	Additional Figure 7-f: Animated distributions of the $\mathcal {D}_{CP}$ kinematic discriminant in the $f_{a3}$ analysis, in the VH-jets tagging category. The decay or production information used is reflected in the superscript label and depends on the tagging category. Points with error bars show data and histograms show expectations for background and signal as indicated in the legend.
animated gif	Additional Figure 7-g: Animated distributions of the $\mathcal {D}_{\rm bkg}$ kinematic discriminant in the $f_{a3}$ analysis, in the untagged tagging category. Points with error bars show data and histograms show expectations for background and signal as indicated in the legend.
animated gif	Additional Figure 7-h: Animated distributions of the $\mathcal {D}_{0-}$ kinematic discriminant in the $f_{a3}$ analysis, in the untagged tagging category. The decay or production information used is reflected in the superscript label and depends on the tagging category. Points with error bars show data and histograms show expectations for background and signal as indicated in the legend.
animated gif	Additional Figure 7-i: Animated distributions of the $\mathcal {D}_{CP}$ kinematic discriminant in the $f_{a3}$ analysis, in the untagged tagging category. Points with error bars show data and histograms show expectations for background and signal as indicated in the legend.

Additional Figure 8: Animated distributions of kinematic discriminants in the $f_{a2}$ analysis: $\mathcal {D}_{\rm bkg}$ (a), (d), (g), $\mathcal {D}_{0h+}$ (b), (e), (h), and $\mathcal {D}_\text {int}$ (c), (f), (i). The decay or production information used in the $\mathcal {D}_{0h+}$ and $\mathcal {D}_\text {int}$ discriminants is reflected in the superscript label and depends on the tagging category. Three tagging categories are shown: VBF-jets (a)-(c), VH-jets (d)-(f), and untagged (g)-(i). Points with error bars show data and histograms show expectations for background and signal as indicated in the legend. The animations scan $f_{a2}$ to illustrate how the expected signal distributions change as a function of $f_{a2}$. For each value of $f_{a2}$, the signal strengths for Higgs production through couplings to fermions $\mu _f$ and bosons $\mu _V$ are set to their best-fit values. The values of $f_{a2}$, $f_{a2}^\text {VBF}$, and $f_{a2}^{\mathrm {V} \mathrm{ H } }$ are recorded on the plots, along with the negative log likelihood. $f_{a2}^\text {VBF}$ and $f_{a2}^{\mathrm {V} \mathrm{ H } }$ are defined using Eq.(2) by analogy with $f_{a2}$, but using the cross sections for the VBF and VH processes, respectively.
animated gif	Additional Figure 8-a: Animated distributions of the $\mathcal {D}_{\rm bkg}$ kinematic discriminant in the $f_{a2}$ analysis, in the VBF-jets tagging category. Points with error bars show data and histograms show expectations for background and signal as indicated in the legend.
animated gif	Additional Figure 8-b: Animated distributions of the $\mathcal {D}_{0h+}$ kinematic discriminant in the $f_{a2}$ analysis, in the VBF-jets tagging category. The decay or production information used is reflected in the superscript label and depends on the tagging category. Points with error bars show data and histograms show expectations for background and signal as indicated in the legend.
animated gif	Additional Figure 8-c: Animated distributions of the $\mathcal {D}_\text {int}$ kinematic discriminant in the $f_{a2}$ analysis, in the VBF-jets tagging category. The decay or production information used is reflected in the superscript label and depends on the tagging category. Points with error bars show data and histograms show expectations for background and signal as indicated in the legend.
animated gif	Additional Figure 8-d: Animated distributions of the $\mathcal {D}_{\rm bkg}$ kinematic discriminant in the $f_{a2}$ analysis, in the VH-jets tagging category. Points with error bars show data and histograms show expectations for background and signal as indicated in the legend.
animated gif	Additional Figure 8-e: Animated distributions of the $\mathcal {D}_{0h+}$ kinematic discriminant in the $f_{a2}$ analysis, in the VH-jets tagging category. The decay or production information used is reflected in the superscript label and depends on the tagging category. Points with error bars show data and histograms show expectations for background and signal as indicated in the legend.
animated gif	Additional Figure 8-f: Animated distributions of the $\mathcal {D}_\text {int}$ kinematic discriminant in the $f_{a2}$ analysis, in the VH-jets tagging category. The decay or production information used is reflected in the superscript label and depends on the tagging category. Points with error bars show data and histograms show expectations for background and signal as indicated in the legend.
animated gif	Additional Figure 8-g: Animated distributions of the $\mathcal {D}_{\rm bkg}$ kinematic discriminant in the $f_{a2}$ analysis, in the untagged tagging category. Points with error bars show data and histograms show expectations for background and signal as indicated in the legend.
animated gif	Additional Figure 8-h: Animated distributions of the $\mathcal {D}_{0h+}$ kinematic discriminant in the $f_{a2}$ analysis, in the untagged tagging category. The decay or production information used is reflected in the superscript label and depends on the tagging category. Points with error bars show data and histograms show expectations for background and signal as indicated in the legend.
animated gif	Additional Figure 8-i: Animated distributions of the $\mathcal {D}_\text {int}$ kinematic discriminant in the $f_{a2}$ analysis, in the untagged tagging category. The decay or production information used is reflected in the superscript label and depends on the tagging category. Points with error bars show data and histograms show expectations for background and signal as indicated in the legend.

Additional Figure 9: Animated distributions of kinematic discriminants in the $f_{\Lambda 1}$ analysis: $\mathcal {D}_{\rm bkg}$ (a), (d), (g), $\mathcal {D}_{\Lambda 1}$ (b), (e), (h), and $\mathcal {D}_{0h+}$ (c), (f), (i). The decay or production information used in the $\mathcal {D}_{\Lambda 1}$ and $\mathcal {D}_{0h+}$ discriminants is reflected in the superscript label and depends on the tagging category. Three tagging categories are shown: VBF-jets (a)-(c), VH-jets (d)-(f), and untagged (g)-(i). Points with error bars show data and histograms show expectations for background and signal as indicated in the legend. The animations scan $f_{\Lambda 1}$ to illustrate how the expected signal distributions change as a function of $f_{\Lambda 1}$. For each value of $f_{\Lambda 1}$, the signal strengths for Higgs production through couplings to fermions $\mu _f$ and bosons $\mu _V$ are set to their best-fit values. The values of $f_{\Lambda 1}$, $f_{\Lambda 1}^\text {VBF}$, and $f_{\Lambda 1}^{\mathrm {V} \mathrm{ H } }$ are recorded on the plots, along with the negative log likelihood. $f_{\Lambda 1}^\text {VBF}$ and $f_{\Lambda 1}^{\mathrm {V} \mathrm{ H } }$ are defined using Eq.(2) by analogy with $f_{\Lambda 1}$, but using the cross sections for the VBF and VH processes, respectively.
animated gif	Additional Figure 9-a: Animated distributions of the $\mathcal {D}_{\rm bkg}$ kinematic discriminant in the $f_{\Lambda 1}$ analysis, in the VBF-jets tagging category. Points with error bars show data and histograms show expectations for background and signal as indicated in the legend.
animated gif	Additional Figure 9-b: Animated distributions of the $\mathcal {D}_{\Lambda 1}$ kinematic discriminant in the $f_{\Lambda 1}$ analysis, in the VBF-jets tagging category.The decay or production information used is reflected in the superscript label and depends on the tagging category. Points with error bars show data and histograms show expectations for background and signal as indicated in the legend.
animated gif	Additional Figure 9-c: Animated distributions of the $\mathcal {D}_{0h+}$ kinematic discriminant in the $f_{\Lambda 1}$ analysis, in the VBF-jets tagging category.The decay or production information used is reflected in the superscript label and depends on the tagging category. Points with error bars show data and histograms show expectations for background and signal as indicated in the legend.
animated gif	Additional Figure 9-d: Animated distributions of the $\mathcal {D}_{\rm bkg}$ kinematic discriminant in the $f_{\Lambda 1}$ analysis, in the VH-jets tagging category. Points with error bars show data and histograms show expectations for background and signal as indicated in the legend.
animated gif	Additional Figure 9-e: Animated distributions of the $\mathcal {D}_{\Lambda 1}$ kinematic discriminant in the $f_{\Lambda 1}$ analysis, in the VH-jets tagging category.The decay or production information used is reflected in the superscript label and depends on the tagging category. Points with error bars show data and histograms show expectations for background and signal as indicated in the legend.
animated gif	Additional Figure 9-f: Animated distributions of the $\mathcal {D}_{0h+}$ kinematic discriminant in the $f_{\Lambda 1}$ analysis, in the VH-jets tagging category.The decay or production information used is reflected in the superscript label and depends on the tagging category. Points with error bars show data and histograms show expectations for background and signal as indicated in the legend.
animated gif	Additional Figure 9-g: Animated distributions of the $\mathcal {D}_{\rm bkg}$ kinematic discriminant in the $f_{\Lambda 1}$ analysis, in the untagged tagging category. Points with error bars show data and histograms show expectations for background and signal as indicated in the legend.
animated gif	Additional Figure 9-h: Animated distributions of the $\mathcal {D}_{\Lambda 1}$ kinematic discriminant in the $f_{\Lambda 1}$ analysis, in the untagged tagging category.The decay or production information used is reflected in the superscript label and depends on the tagging category. Points with error bars show data and histograms show expectations for background and signal as indicated in the legend.
animated gif	Additional Figure 9-i: Animated distributions of the $\mathcal {D}_{0h+}$ kinematic discriminant in the $f_{\Lambda 1}$ analysis, in the untagged tagging category.The decay or production information used is reflected in the superscript label and depends on the tagging category. Points with error bars show data and histograms show expectations for background and signal as indicated in the legend.

Additional Figure 10: Animated distributions of kinematic discriminants in the $f_{\Lambda 1}^{{\mathrm{ Z } } \gamma }$ analysis: $\mathcal {D}_{\rm bkg}$ (a), (d), (g), $\mathcal {D}_{\Lambda 1}^{{\mathrm{ Z } } \gamma }$ (b), (e), (h), and $\mathcal {D}_{0h+}$ (c), (f), (i). The decay or production information used in the $\mathcal {D}_{\Lambda 1}^{{\mathrm{ Z } } \gamma }$ and $\mathcal {D}_{0h+}$ discriminants is reflected in the superscript label and depends on the tagging category. Three tagging categories are shown: VBF-jets (a)-(c), VH-jets (d)-(f), and untagged (g)-(i). Points with error bars show data and histograms show expectations for background and signal as indicated in the legend. The animations scan $f_{\Lambda 1}^{{\mathrm{ Z } } \gamma }$ to illustrate how the expected signal distributions change as a function of $f_{\Lambda 1}^{{\mathrm{ Z } } \gamma }$. For each value of $f_{\Lambda 1}^{{\mathrm{ Z } } \gamma }$, the signal strengths for Higgs production through couplings to fermions $\mu _f$ and bosons $\mu _V$ are set to their best-fit values. The values of $f_{\Lambda 1}^{{\mathrm{ Z } } \gamma }$, $f_{\Lambda 1}^{{\mathrm{ Z } } \gamma , \text {VBF}}$, and $f_{\Lambda 1}^{{\mathrm{ Z } } \gamma , \mathrm {V} \mathrm{ H } }$ are recorded on the plots, along with the negative log likelihood. $f_{\Lambda 1}^{{\mathrm{ Z } } \gamma , \text {VBF}}$ and $f_{\Lambda 1}^{{\mathrm{ Z } } \gamma , \mathrm {V} \mathrm{ H } }$ are defined using Eq.(2) by analogy with $f_{\Lambda 1}^{{\mathrm{ Z } } \gamma }$, but using the cross sections for the VBF and VH processes, respectively.
animated gif	Additional Figure 10-a: Animated distributions of the $\mathcal {D}_{\rm bkg}$ kinematic discriminant in the $f_{\Lambda 1}^{{\mathrm{ Z } } \gamma }$ analysis, in the VBF-jets tagging category. Points with error bars show data and histograms show expectations for background and signal as indicated in the legend.
animated gif	Additional Figure 10-b: Animated distributions of the $\mathcal {D}_{\Lambda 1}^{{\mathrm{ Z } } \gamma }$s kinematic discriminant in the $f_{\Lambda 1}^{{\mathrm{ Z } } \gamma }$ analysis, in the VBF-jets tagging category. The decay or production information used is reflected in the superscript label and depends on the tagging category. Points with error bars show data and histograms show expectations for background and signal as indicated in the legend.
animated gif	Additional Figure 10-c: Animated distributions of the $\mathcal {D}_{0h+}$ kinematic discriminant in the $f_{\Lambda 1}^{{\mathrm{ Z } } \gamma }$ analysis, in the VBF-jets tagging category. The decay or production information used is reflected in the superscript label and depends on the tagging category. Points with error bars show data and histograms show expectations for background and signal as indicated in the legend.
animated gif	Additional Figure 10-d: Animated distributions of the $\mathcal {D}_{\rm bkg}$ kinematic discriminant in the $f_{\Lambda 1}^{{\mathrm{ Z } } \gamma }$ analysis, in the VH-jets tagging category. Points with error bars show data and histograms show expectations for background and signal as indicated in the legend.
animated gif	Additional Figure 10-e: Animated distributions of the $\mathcal {D}_{\Lambda 1}^{{\mathrm{ Z } } \gamma }$s kinematic discriminant in the $f_{\Lambda 1}^{{\mathrm{ Z } } \gamma }$ analysis, in the VH-jets tagging category. The decay or production information used is reflected in the superscript label and depends on the tagging category. Points with error bars show data and histograms show expectations for background and signal as indicated in the legend.
animated gif	Additional Figure 10-f: Animated distributions of the $\mathcal {D}_{0h+}$ kinematic discriminant in the $f_{\Lambda 1}^{{\mathrm{ Z } } \gamma }$ analysis, in the VH-jets tagging category. The decay or production information used is reflected in the superscript label and depends on the tagging category. Points with error bars show data and histograms show expectations for background and signal as indicated in the legend.
animated gif	Additional Figure 10-g: Animated distributions of the $\mathcal {D}_{\rm bkg}$ kinematic discriminant in the $f_{\Lambda 1}^{{\mathrm{ Z } } \gamma }$ analysis, in the untagged tagging category. Points with error bars show data and histograms show expectations for background and signal as indicated in the legend.
animated gif	Additional Figure 10-h: Animated distributions of the $\mathcal {D}_{\Lambda 1}^{{\mathrm{ Z } } \gamma }$s kinematic discriminant in the $f_{\Lambda 1}^{{\mathrm{ Z } } \gamma }$ analysis, in the untagged tagging category. The decay or production information used is reflected in the superscript label and depends on the tagging category. Points with error bars show data and histograms show expectations for background and signal as indicated in the legend.
animated gif	Additional Figure 10-i: Animated distributions of the $\mathcal {D}_{0h+}$ kinematic discriminant in the $f_{\Lambda 1}^{{\mathrm{ Z } } \gamma }$ analysis, in the untagged tagging category. The decay or production information used is reflected in the superscript label and depends on the tagging category. Points with error bars show data and histograms show expectations for background and signal as indicated in the legend.

Additional Figure 11: Observed (solid) and expected (dashed) likelihood scans of $f_{a3}\cos(\phi _{a3})$ (a), $f_{a2}\cos(\phi _{a2})$ (b), $f_{\Lambda 1}\cos(\phi _{\Lambda 1})$ (c), and $f_{\Lambda 1}^{{\mathrm{ Z } } \gamma }\cos(\phi _{\Lambda 1}^{{\mathrm{ Z } } \gamma })$ (d). Results of the Run 2 only and the combined Run 1 and Run 2 analyses are shown. The marker follows the observed likelihood scan for the combined Run 1 and Run 2 analysis at the same speed as the animated discriminant distributions. The plots can be played simultaneously in order to better follow the animated distributions.
animated gif	Additional Figure 11-a: Observed (solid) and expected (dashed) likelihood scans of $f_{a3}\cos(\phi _{a3})$. Results of the Run 2 only and the combined Run 1 and Run 2 analyses are shown. The marker follows the observed likelihood scan for the combined Run 1 and Run 2 analysis at the same speed as the animated discriminant distributions.
animated gif	Additional Figure 11-b: Observed (solid) and expected (dashed) likelihood scans of $f_{a2}\cos(\phi _{a2})$. Results of the Run 2 only and the combined Run 1 and Run 2 analyses are shown. The marker follows the observed likelihood scan for the combined Run 1 and Run 2 analysis at the same speed as the animated discriminant distributions.
animated gif	Additional Figure 11-c: Observed (solid) and expected (dashed) likelihood scans of $f_{\Lambda 1}\cos(\phi _{\Lambda 1})$. Results of the Run 2 only and the combined Run 1 and Run 2 analyses are shown. The marker follows the observed likelihood scan for the combined Run 1 and Run 2 analysis at the same speed as the animated discriminant distributions.
animated gif	Additional Figure 11-d: Observed (solid) and expected (dashed) likelihood scans of $f_{\Lambda 1}^{{\mathrm{ Z } } \gamma }\cos(\phi _{\Lambda 1}^{{\mathrm{ Z } } \gamma })$. Results of the Run 2 only and the combined Run 1 and Run 2 analyses are shown. The marker follows the observed likelihood scan for the combined Run 1 and Run 2 analysis at the same speed as the animated discriminant distributions.

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