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CMS-HIG-20-007 ; CERN-EP-2022-021

Constraints on anomalous Higgs boson couplings to vector bosons and fermions from the production of Higgs bosons using the $\tau\tau$ final state

CMS Collaboration

10 May 2022

Phys. Rev. D 108 (2023) 032013

Abstract: A study of anomalous couplings of the Higgs boson to vector bosons and fermions is presented. The data were recorded by the CMS experiment at a center-of-mass energy of pp collisions at the LHC of 13 TeV and correspond to an integrated luminosity of 138 fb$^{-1}$. The study uses Higgs boson candidates produced mainly in gluon fusion or electroweak vector boson fusion at the LHC that subsequently decay to a pair of $\tau$ leptons. Matrix-element and machine-learning techniques were employed in a search for anomalous interactions. The results are combined with those from the four-lepton and two-photon decay channels to yield the most stringent constraints on anomalous Higgs boson couplings to date. The pure CP-odd scenario of the Higgs boson coupling to gluons is excluded at 2.4 standard deviations. The results are consistent with the standard model predictions.

Links: e-print arXiv:2205.05120 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ;

Figures
png pdf	Figure 1: Illustrations of H production in VBF ($\mathrm{q} {\mathrm{q} ^\prime}\to \mathrm{q} {\mathrm{q} ^\prime} \mathrm{H}$) (left) and VH ($\mathrm{q} \mathrm{\bar{q}} ^\prime \to \mathrm {V}^*\to \mathrm {V}\mathrm{H} \to \mathrm{q} {\mathrm{q} ^\prime} \mathrm{H}$) (right) in the rest frame of the H. The decay $\mathrm{H} \to \tau \tau$ is shown without illustrating the further decay chain. The incoming partons and fermions in the V decay are shown in brown and the intermediate or final-state particles are shown in red and green. The angles characterizing kinematic distributions are shown in blue and are defined in the respective rest frames [32,34]. The illustration for H production via ggH in association with two jets is identical to the VBF diagram, except with V=g.
png pdf	Figure 1-a: Illustration of H production in VBF ($\mathrm{q} {\mathrm{q} ^\prime}\to \mathrm{q} {\mathrm{q} ^\prime} \mathrm{H}$) in the rest frame of the H. The decay $\mathrm{H} \to \tau \tau$ is shown without illustrating the further decay chain. The incoming and outgoing partons are shown in brown and the intermediate or final-state particles are shown in red and green. The angles characterizing kinematic distributions are shown in blue and are defined in the respective rest frames [32,34]. The illustration for H production via ggH in association with two jets is identical to this diagram, except with V=g.
png pdf	Figure 1-b: Illustration of H production in VH ($\mathrm{q} \mathrm{\bar{q}} ^\prime \to \mathrm {V}^*\to \mathrm {V}\mathrm{H} \to \mathrm{q} {\mathrm{q} ^\prime} \mathrm{H}$) in the rest frame of the H. The decay $\mathrm{H} \to \tau \tau$ is shown without illustrating the further decay chain. The incoming partons and fermions in the V decay are shown in brown and the intermediate or final-state particles are shown in red and green. The angles characterizing kinematic distributions are shown in blue and are defined in the respective rest frames [32,34].
png pdf	Figure 2: The ${m_{\tau \tau}}$ (left) and ${p_{\mathrm {T}}}$ (right) distributions for H candidate di-$\tau$ lepton pairs in the VBF category. All events selected in the e$\mu$, e${\tau _\mathrm {h}}$, $\mu {\tau _\mathrm {h}}$, and ${\tau _\mathrm {h}} {\tau _\mathrm {h}}$ final states are included. The yields of the H processes are scaled to match 50 times the SM predictions. Only statistical uncertainties are shown.
png pdf	Figure 2-a: The ${m_{\tau \tau}}$ distribution for H candidate di-$\tau$ lepton pairs in the VBF category. All events selected in the e$\mu$, e${\tau _\mathrm {h}}$, $\mu {\tau _\mathrm {h}}$, and ${\tau _\mathrm {h}} {\tau _\mathrm {h}}$ final states are included. The yields of the H processes are scaled to match 50 times the SM predictions. Only statistical uncertainties are shown.
png pdf	Figure 2-b: The ${p_{\mathrm {T}}}$ distribution for H candidate di-$\tau$ lepton pairs in the VBF category. All events selected in the e$\mu$, e${\tau _\mathrm {h}}$, $\mu {\tau _\mathrm {h}}$, and ${\tau _\mathrm {h}} {\tau _\mathrm {h}}$ final states are included. The yields of the H processes are scaled to match 50 times the SM predictions. Only statistical uncertainties are shown.
png pdf	Figure 3: Examples of data and signal and background predictions for MELA and neural network discriminants in the ${\tau _\mathrm {h}} {\tau _\mathrm {h}}$ and $\mu {\tau _\mathrm {h}}$ channels. Events passing the selections outlined in Section 6 and allocated to the VBF category are included. The yields of the H processes are scaled to match 50 times the SM predictions. The uncertainty band includes statistical uncertainties and systematic uncertainties that affect the normalization of the background distribution. The expectation in the ratio panel is the sum of the estimated backgrounds and the SM H signal. For the ${\mathcal {D}_{0-}^{\mathrm{g} \mathrm{g} \mathrm{H}}}$ discriminant the distribution expected for a pseudoscalar H hypothesis (labeled "PS" in the legend) is overlaid to be compared to the SM signal. Similarly, for the ${\mathcal {D}_{\text{CP}}^{\mathrm{g} \mathrm{g} \mathrm{H}}}$ discriminant the distribution for a CP-violating scenario with the maximum-mixing between CP-even and CP-odd couplings (labeled "MM" in the legend) is shown.
png pdf	Figure 3-a: Data and signal and background predictions for the ${\mathcal {D}_{0-}^{\mathrm{g} \mathrm{g} \mathrm{H}}}$ discriminant in the ${\tau _\mathrm {h}} {\tau _\mathrm {h}}$ and $\mu {\tau _\mathrm {h}}$ channels. Events passing the selections outlined in Section 6 and allocated to the VBF category are included. The yields of the H processes are scaled to match 50 times the SM predictions. The uncertainty band includes statistical uncertainties and systematic uncertainties that affect the normalization of the background distribution. The expectation in the ratio panel is the sum of the estimated backgrounds and the SM H signal. The distribution expected for a pseudoscalar H hypothesis (labeled "PS" in the legend) is overlaid to be compared to the SM signal.
png pdf	Figure 3-b: Data and signal and background predictions for the ${\mathcal {D}_\mathrm {2jet}^\mathrm {VBF}}$ discriminant in the ${\tau _\mathrm {h}} {\tau _\mathrm {h}}$ and $\mu {\tau _\mathrm {h}}$ channels. Events passing the selections outlined in Section 6 and allocated to the VBF category are included. The yields of the H processes are scaled to match 50 times the SM predictions. The uncertainty band includes statistical uncertainties and systematic uncertainties that affect the normalization of the background distribution. The expectation in the ratio panel is the sum of the estimated backgrounds and the SM H signal.
png pdf	Figure 3-c: Data and signal and background predictions for the ${\mathcal {D}_{\text{CP}}^{\mathrm{g} \mathrm{g} \mathrm{H}}}$ discriminant in the ${\tau _\mathrm {h}} {\tau _\mathrm {h}}$ and $\mu {\tau _\mathrm {h}}$ channels. Events passing the selections outlined in Section 6 and allocated to the VBF category are included. The yields of the H processes are scaled to match 50 times the SM predictions. The uncertainty band includes statistical uncertainties and systematic uncertainties that affect the normalization of the background distribution. The expectation in the ratio panel is the sum of the estimated backgrounds and the SM H signal. The distribution for a CP-violating scenario with the maximum-mixing between CP-even and CP-odd couplings (labeled "MM" in the legend) is shown.
png pdf	Figure 3-d: Data and signal and background predictions for the ${\mathcal {D}_\mathrm {NN}}$ discriminant in the ${\tau _\mathrm {h}} {\tau _\mathrm {h}}$ and $\mu {\tau _\mathrm {h}}$ channels. Events passing the selections outlined in Section 6 and allocated to the VBF category are included. The yields of the H processes are scaled to match 50 times the SM predictions. The uncertainty band includes statistical uncertainties and systematic uncertainties that affect the normalization of the background distribution. The expectation in the ratio panel is the sum of the estimated backgrounds and the SM H signal.
png pdf	Figure 4: The observed and predicted 2D distribution of (${\mathcal {D}_{0-}^{\mathrm{g} \mathrm{g} \mathrm{H}}}$, ${\mathcal {D}_\mathrm {NN}}$) before the fit to data in the most sensitive VBF category region with 0.3 $< {\mathcal {D}_\mathrm {2jet}^\mathrm {VBF}} <$ 0.7 in the ${\tau _\mathrm {h}} {\tau _\mathrm {h}}$ channel. The total H signal, including VBF, ggH, and VH processes, is shown stacked on top of the background in the solid red histogram. The ggH signal for the CP-even (CP-odd) scenario is also shown overlain by the red (blue) line. Only the statistical uncertainties are included in the uncertainty band.
png pdf	Figure 5: Observed and predicted 2D distributions after the fit to data in the VBF high-${m_{\mathrm {jj}}}$ boosted category in the ${\tau _\mathrm {h}} {\tau _\mathrm {h}}$ channel. The total H signal, including VBF, ggH, and VH processes, is shown stacked on top of the background in the solid red histogram. The ggH signal for the CP-even (CP-odd) scenario is also shown overlain by the red (blue) line. The uncertainty band accounts for all sources of systematic uncertainty in the signal and background predictions. The expectation in the ratio panel is the sum of the estimated backgrounds and the best fit signal.
png pdf	Figure 6: Observed (solid) and expected (dashed) likelihood scans of ${f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}}$ obtained with the MELA method (left) and the ${\Delta \phi _{\mathrm {jj}}}$ method used as a cross check (right).
png pdf	Figure 6-a: Observed (solid) and expected (dashed) likelihood scans of ${f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}}$ obtained with the MELA method.
png pdf	Figure 6-b: Observed (solid) and expected (dashed) likelihood scans of ${f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}}$ obtained with the ${\Delta \phi _{\mathrm {jj}}}$ method used as a cross check.
png pdf	Figure 7: Observed (solid) and expected (dashed) likelihood scans of ${\alpha ^{\mathrm{H} \mathrm {ff}}}$ (in degrees) obtained with the MELA method (left) and the ${\Delta \phi _{\mathrm {jj}}}$ method used as a cross check (right).
png pdf	Figure 7-a: Observed (solid) and expected (dashed) likelihood scans of ${\alpha ^{\mathrm{H} \mathrm {ff}}}$ (in degrees) obtained with the MELA method.
png pdf	Figure 7-b: Observed (solid) and expected (dashed) likelihood scans of ${\alpha ^{\mathrm{H} \mathrm {ff}}}$ (in degrees) obtained with the ${\Delta \phi _{\mathrm {jj}}}$ method used as a cross check.
png pdf	Figure 8: The observed and predicted 3D distribution of (${\mathcal {D}_{0-}}, {\mathcal {D}_\mathrm {NN}}$, ${\mathcal {D}_\mathrm {2jet}^\mathrm {VBF}}$) before the fit to data in the ${\tau _\mathrm {h}} {\tau _\mathrm {h}}$ channel for the most sensitive VBF category. The total H signal, including VBF, ggH, and VH processes, is shown stacked on top of the background in the solid red histogram. The VBF+ VH signal for the CP-even (CP-odd) scenario is also shown overlain by the red (blue) line. Only the statistical uncertainties are included in the uncertainty band.
png pdf	Figure 9: Observed (solid) and expected (dashed) likelihood scans of ${f_{a3}}$ (upper left), ${f_{a2}}$ (upper right), ${f_{\Lambda 1}}$ (lower left), and ${f_{\Lambda 1}^{\mathrm{Z} \gamma}}$ (lower right) in Approach 1 (${a_i^{\mathrm{W} \mathrm{W}}=a_i^{\mathrm{Z} \mathrm{Z}}}$).
png pdf	Figure 9-a: Observed (solid) and expected (dashed) likelihood scans of ${f_{a3}} in Approach 1 (${a_i^{\mathrm{W} \mathrm{W}}=a_i^{\mathrm{Z} \mathrm{Z}}}$).
png pdf	Figure 9-b: Observed (solid) and expected (dashed) likelihood scans of ${f_{a2}}$ in Approach 1 (${a_i^{\mathrm{W} \mathrm{W}}=a_i^{\mathrm{Z} \mathrm{Z}}}$).
png pdf	Figure 9-c: Observed (solid) and expected (dashed) likelihood scans of ${f_{\Lambda 1}}$ in Approach 1 (${a_i^{\mathrm{W} \mathrm{W}}=a_i^{\mathrm{Z} \mathrm{Z}}}$).
png pdf	Figure 9-d: Observed (solid) and expected (dashed) likelihood scans of ${f_{\Lambda 1}^{\mathrm{Z} \gamma}}$ in Approach 1 (${a_i^{\mathrm{W} \mathrm{W}}=a_i^{\mathrm{Z} \mathrm{Z}}}$).
png pdf	Figure 10: Observed (solid) and expected (dashed) likelihood scans of ${f_{a3}}$ in Approach 2.
png pdf	Figure 11: Observed (solid) and expected (dashed) likelihood scans of ${f_{a3}}$ (upper left), ${f_{a2}}$ (upper right), ${f_{\Lambda 1}}$ (lower left), and ${f_{\Lambda 1}^{\mathrm{Z} \gamma}}$ (lower right) in Approach 1 ($a_i^{\mathrm{W} \mathrm{W}}$ = $a_i^{\mathrm{Z} \mathrm{Z}}$) obtained with the combination of results using the ${\mathrm{H} \to \tau \tau}$ and ${\mathrm{H} \to 4\ell}$ [21] decay channels.
png pdf	Figure 11-a: Observed (solid) and expected (dashed) likelihood scans of ${f_{a3}}$ in Approach 1 ($a_i^{\mathrm{W} \mathrm{W}}$ = $a_i^{\mathrm{Z} \mathrm{Z}}$) obtained with the combination of results using the ${\mathrm{H} \to \tau \tau}$ and ${\mathrm{H} \to 4\ell}$ [21] decay channels.
png pdf	Figure 11-b: Observed (solid) and expected (dashed) likelihood scans of ${f_{a2}}$ in Approach 1 ($a_i^{\mathrm{W} \mathrm{W}}$ = $a_i^{\mathrm{Z} \mathrm{Z}}$) obtained with the combination of results using the ${\mathrm{H} \to \tau \tau}$ and ${\mathrm{H} \to 4\ell}$ [21] decay channels.
png pdf	Figure 11-c: Observed (solid) and expected (dashed) likelihood scans of ${f_{\Lambda 1}}$ in Approach 1 ($a_i^{\mathrm{W} \mathrm{W}}$ = $a_i^{\mathrm{Z} \mathrm{Z}}$) obtained with the combination of results using the ${\mathrm{H} \to \tau \tau}$ and ${\mathrm{H} \to 4\ell}$ [21] decay channels.
png pdf	Figure 11-d: Observed (solid) and expected (dashed) likelihood scans of ${f_{\Lambda 1}^{\mathrm{Z} \gamma}}$ in Approach 1 ($a_i^{\mathrm{W} \mathrm{W}}$ = $a_i^{\mathrm{Z} \mathrm{Z}}$) obtained with the combination of results using the ${\mathrm{H} \to \tau \tau}$ and ${\mathrm{H} \to 4\ell}$ [21] decay channels.
png pdf	Figure 12: Observed (solid) and expected (dashed) likelihood scans of ${f_{a3}}$ in Approach 2 (defined in Section 2) obtained with the combination of results using the ${\mathrm{H} \to \tau \tau}$ and ${\mathrm{H} \to 4\ell}$ [21] decay channels.
png pdf	Figure 13: Left: the observed (solid) and expected (dashed) likelihood scans of ${f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}}$ obtained with the combination of results using the ${\mathrm{H} \to \tau \tau}$ and ${\mathrm{H} \to 4\ell}$ [21] decay channels. Right: The observed (solid) and expected (dashed) likelihood scans of ${f_{\text{CP}}^{\mathrm{H} \mathrm{t} \mathrm{t}}}$ obtained with the combination of results using the ${\mathrm{H} \to \tau \tau}$, ${\mathrm{H} \to 4\ell}$ [21], and ${\mathrm{H} \to \gamma \gamma}$ [20] decay channels.
png pdf	Figure 13-a: The observed (solid) and expected (dashed) likelihood scans of ${f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}}$ obtained with the combination of results using the ${\mathrm{H} \to \tau \tau}$ and ${\mathrm{H} \to 4\ell}$ [21] decay channels.
png pdf	Figure 13-b: The observed (solid) and expected (dashed) likelihood scans of ${f_{\text{CP}}^{\mathrm{H} \mathrm{t} \mathrm{t}}}$ obtained with the combination of results using the ${\mathrm{H} \to \tau \tau}$, ${\mathrm{H} \to 4\ell}$ [21], and ${\mathrm{H} \to \gamma \gamma}$ [20] decay channels.
png pdf	Figure 14: Observed (solid) and expected (dashed) likelihood scans of ${c_{\mathrm{g} \mathrm{g}}}$ (left) and ${\tilde{c}_{\mathrm{g} \mathrm{g}}}$ (right) with ${\kappa _\mathrm {t}}$ and ${\tilde{\kappa}}_\mathrm {t}$ profiled (upper) and fixed to SM expectation (lower) using the ${\mathrm{H} \to \tau \tau}$, ${\mathrm{H} \to 4\ell}$ [21], and ${\mathrm{H} \to \gamma \gamma}$ [20] decay channels.
png pdf	Figure 14-a: Observed (solid) and expected (dashed) likelihood scans of ${c_{\mathrm{g} \mathrm{g}}}$ with ${\kappa _\mathrm {t}}$ and ${\tilde{\kappa}}_\mathrm {t}$ profiled using the ${\mathrm{H} \to \tau \tau}$, ${\mathrm{H} \to 4\ell}$ [21], and ${\mathrm{H} \to \gamma \gamma}$ [20] decay channels.
png pdf	Figure 14-b: Observed (solid) and expected (dashed) likelihood scans of ${\tilde{c}_{\mathrm{g} \mathrm{g}}}$ with ${\kappa _\mathrm {t}}$ and ${\tilde{\kappa}}_\mathrm {t}$ fixed to SM expectation using the ${\mathrm{H} \to \tau \tau}$, ${\mathrm{H} \to 4\ell}$ [21], and ${\mathrm{H} \to \gamma \gamma}$ [20] decay channels.
png pdf	Figure 14-c: Observed (solid) and expected (dashed) likelihood scans of ${c_{\mathrm{g} \mathrm{g}}}$ with ${\kappa _\mathrm {t}}$ and ${\tilde{\kappa}}_\mathrm {t}$ profiled using the ${\mathrm{H} \to \tau \tau}$, ${\mathrm{H} \to 4\ell}$ [21], and ${\mathrm{H} \to \gamma \gamma}$ [20] decay channels.
png pdf	Figure 14-d: Observed (solid) and expected (dashed) likelihood scans of ${\tilde{c}_{\mathrm{g} \mathrm{g}}}$ with ${\kappa _\mathrm {t}}$ and ${\tilde{\kappa}}_\mathrm {t}$ fixed to SM expectation using the ${\mathrm{H} \to \tau \tau}$, ${\mathrm{H} \to 4\ell}$ [21], and ${\mathrm{H} \to \gamma \gamma}$ [20] decay channels.

Tables
png pdf	Table 1: Cross sections for the anomalous contributions ($\sigma _i$) used to define the fractional cross sections [21]. The $\sigma _i$ values are defined as the cross section computed with $a_{i}=$ 1 and all other couplings set to zero. All cross sections are given relative to the SM value ($\sigma _1$). 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 so as to keep all coefficients of similar order of magnitude.
png pdf	Table 2: List of discriminants for separating anomalous couplings from the SM contribution.
png pdf	Table 3: Kinematic selection requirements for the four di-$\tau$ decay channels. The trigger requirement is defined by a combination of trigger candidates with ${p_{\mathrm {T}}}$ over a given threshold, indicated inside parentheses in GeV. The pseudorapidity thresholds come from trigger and object reconstruction constraints. The ${p_{\mathrm {T}}}$ thresholds for the lepton selection are driven by the trigger requirements, except for the ${\tau _\mathrm {h}}$ candidate in the $\mu {\tau _\mathrm {h}}$ and e${\tau _\mathrm {h}}$ channels, and the sub-leading lepton in the e$\mu$ channel, where they have been optimized to increase the analysis sensitivity.
png pdf	Table 4: Sources of systematic uncertainties.
png pdf	Table 5: List of observables used in the MELA method.
png pdf	Table 6: List of observables used in the ${\Delta \phi _{\mathrm {jj}}}$ method.
png pdf	Table 7: Allowed 68% (central values with uncertainties) and 95% CL (in square brackets) intervals on anomalous Hgg coupling parameters using the ${\mathrm{H} \to \tau \tau}$ decay. The use of "-" indicates cases where no exclusion at the 95% CL was found. As indicated in the Table, the results are presented for the MELA method, as well as the ${\Delta \phi _{\mathrm {jj}}}$ method for comparison. The final results of this study are from the MELA method. The ${\alpha ^{\mathrm{H} \mathrm {ff}}}$ results are derived from ${f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}}$ following Eqs. (5), (6), and (10).
png pdf	Table 8: Allowed 68% (central values with uncertainties) and 95% CL (in square brackets) intervals on anomalous HVV coupling parameters using the ${\mathrm{H} \to \tau \tau}$ decay. Approaches 1 and 2 refer to the choice of the relationship between the $a_i^{\mathrm{W} \mathrm{W}}$ and $a_i^{\mathrm{Z} \mathrm{Z}}$ couplings, defined in Section 2. For the observed ${f_{a2}}$scan, there is a second region allowed at the 68% CL away from the best fit value. We use the union symbol ($\cup$) to display the additional allowed ${f_{a2}}$range in this case.
png pdf	Table 9: Allowed 68% (central values with uncertainties) and 95% CL (in square brackets) intervals on anomalous HVV coupling parameters using the ${\mathrm{H} \to \tau \tau}$ and ${\mathrm{H} \to 4\ell}$ [21] decay channels, using two approaches described in Section 2 that define the relationship between the $a_i^{\mathrm{W} \mathrm{W}}$ and $a_i^{\mathrm{Z} \mathrm{Z}}$ couplings.
png pdf	Table 10: Allowed 68% (central values with uncertainties) and 95% CL (in square brackets) intervals on ${f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}}$, from the combination of the ${\mathrm{H} \to \tau \tau}$ and ${\mathrm{H} \to 4\ell}$ [21] decay channels, and ${f_{\text{CP}}^{\mathrm{H} \mathrm{t} \mathrm{t}}}$, from the combination of the ${\mathrm{H} \to \tau \tau}$, ${\mathrm{H} \to 4\ell}$ [21], and ${\mathrm{H} \to \gamma \gamma}$ [20] decay channels.
png pdf	Table 11: Allowed 68% (central values with uncertainties) and 95% CL (in square brackets) intervals on ${c_{\mathrm{g} \mathrm{g}}}$ and ${\tilde{c}_{\mathrm{g} \mathrm{g}}}$ using the ${\mathrm{H} \to \tau \tau}$, ${\mathrm{H} \to 4\ell}$ [21], and ${\mathrm{H} \to \gamma \gamma}$ [20] decay channels. Results are presented for two scenarios: ${\kappa _\mathrm {t}}$ and ${\tilde{\kappa}}_\mathrm {t}$ profiled in the fit, and ${\kappa _\mathrm {t}}$ and ${\tilde{\kappa}}_\mathrm {t}$ fixed to the SM expectation. In instances where there is a second allowed region away from the best fit value at a given CL, we use the union symbol ($\cup$) to display the additional allowed ${\tilde{c}_{\mathrm{g} \mathrm{g}}} / {c_{\mathrm{g} \mathrm{g}}}$ range.

Summary

A study is presented of anomalous interactions of the Higgs boson (H) with vector bosons, including violation, using its associated production with two hadronic jets in gluon fusion (ggH), vector boson fusion (VBF), and associated production with a vector boson, and a subsequent decay to a pair of $\tau$ leptons. Constraints have been set on the CP-violating effects in ggH production in terms of the effective cross section ratio ${f_{a3}^{\mathrm{g}\mathrm{g}\mathrm{H}}}$, or equivalently the effective mixing angle ${\alpha^{\mathrm{H}\mathrm{ff}}}$, using matrix element techniques. The ggH production analysis results in the most stringent limits on violation in ggH production to date. In the VBF production analysis, constraints on the CP-violating parameter ${f_{a3}}$ and on the CP-conserving parameters ${f_{a2}}$, ${f_{\Lambda 1}}$, and ${f_{\Lambda 1}^{\mathrm{Z}\gamma}}$ have been set using matrix element techniques. Further constraints were obtained in the combination of the $\mathrm{H} \to \tau \tau$, $\mathrm{H} \to 4\ell$, and $\mathrm{H} \to \gamma\gamma$ channels. The combination improves the limits on the anomalous coupling parameters typically by about 20-50%. The analysis excludes the pure CP-odd scenario of the Higgs coupling to gluons with a significance of 2.4 standard deviations.

Additional Figures
png pdf	Additional Figure 1: Observed and predicted 2D distributions after the fit to data to extract the ggH anomalous coupling parameters using the $\Delta \phi _{\mathrm {jj}}$ method for the VBF high-$m_{\mathrm {jj}}$ boosted category in the $\mu {\tau _\mathrm {h}}$ channel. The uncertainty band accounts for all sources of systematic uncertainty on the signal and background predictions. The expectation in the ratio panel is the sum of the estimated backgrounds and the best fit signal. In total 12 $\Delta \phi _{\mathrm {jj}}$ bins are used with boundaries that range from $-$3.2 to 3.2. Since the physical range of $\Delta \phi _{\mathrm {jj}}$ is between ${\pm} \pi$, the first and last bins actually only include events with 8/3 $< |\Delta \phi _{\mathrm {jj}}| < \pi$, however, the bin range is extended to $\pm$3.2 in the plot for visualisation.
png pdf	Additional Figure 2: Observed and predicted 2D distributions after the fit to data to extract the ggH anomalous coupling parameters using the $\Delta \phi _{\mathrm {jj}}$ method for the VBF high-$m_{\mathrm {jj}}$ boosted category in the e${\tau _\mathrm {h}}$ channel. The uncertainty band accounts for all sources of systematic uncertainty on the signal and background predictions. The expectation in the ratio panel is the sum of the estimated backgrounds and the best fit signal. In total 12 $\Delta \phi _{\mathrm {jj}}$ bins are used with boundaries that range from $-$3.2 to 3.2. Since the physical range of $\Delta \phi _{\mathrm {jj}}$ is between ${\pm} \pi$, the first and last bins actually only include events with 8/3 $< |\Delta \phi _{\mathrm {jj}}| < \pi$, however, the bin range is extended to $\pm$3.2 in the plot for visualisation.
png pdf	Additional Figure 3: Observed and predicted 2D distributions after the fit to data to extract the ggH anomalous coupling parameters using the $\Delta \phi _{\mathrm {jj}}$ method for the VBF high-$m_{\mathrm {jj}}$ boosted category in the e$\mu$ channel. The uncertainty band accounts for all sources of systematic uncertainty on the signal and background predictions. The expectation in the ratio panel is the sum of the estimated backgrounds and the best fit signal. In total 12 $\Delta \phi _{\mathrm {jj}}$ bins are used with boundaries that range from $-$3.2 to 3.2. Since the physical range of $\Delta \phi _{\mathrm {jj}}$ is between ${\pm} \pi$, the first and last bins actually only include events with 8/3 $< |\Delta \phi _{\mathrm {jj}}| < \pi$, however, the bin range is extended to $\pm$3.2 in the plot for visualisation.
png pdf	Additional Figure 4: Observed and predicted 2D distributions after the fit to data to extract the ggH anomalous coupling parameters using the $\Delta \phi _{\mathrm {jj}}$ method for the VBF high-$m_{\mathrm {jj}}$ category in the $\mu {\tau _\mathrm {h}}$ channel. The uncertainty band accounts for all sources of systematic uncertainty on the signal and background predictions. The expectation in the ratio panel is the sum of the estimated backgrounds and the best fit signal. In total 12 $\Delta \phi _{\mathrm {jj}}$ bins are used with boundaries that range from $-$3.2 to 3.2. Since the physical range of $\Delta \phi _{\mathrm {jj}}$ is between ${\pm} \pi$, the first and last bins actually only include events with 8/3 $< |\Delta \phi _{\mathrm {jj}}| < \pi$, however, the bin range is extended to $\pm$3.2 in the plot for visualisation.
png pdf	Additional Figure 5: Observed and predicted 2D distributions after the fit to data to extract the ggH anomalous coupling parameters using the $\Delta \phi _{\mathrm {jj}}$ method for the VBF high-$m_{\mathrm {jj}}$ category in the ${\tau _\mathrm {h}} {\tau _\mathrm {h}}$ channel. The uncertainty band accounts for all sources of systematic uncertainty on the signal and background predictions. The expectation in the ratio panel is the sum of the estimated backgrounds and the best fit signal. In total 12 $\Delta \phi _{\mathrm {jj}}$ bins are used with boundaries that range from $-$3.2 to 3.2. Since the physical range of $\Delta \phi _{\mathrm {jj}}$ is between ${\pm} \pi$, the first and last bins actually only include events with 8/3 $< |\Delta \phi _{\mathrm {jj}}| < \pi$, however, the bin range is extended to $\pm$3.2 in the plot for visualisation.
png pdf	Additional Figure 6: Observed and predicted 2D distributions after the fit to data to extract the ggH anomalous coupling parameters using the $\Delta \phi _{\mathrm {jj}}$ method for the VBF high-$m_{\mathrm {jj}}$ category in the e${\tau _\mathrm {h}}$ channel. The uncertainty band accounts for all sources of systematic uncertainty on the signal and background predictions. The expectation in the ratio panel is the sum of the estimated backgrounds and the best fit signal. In total 12 $\Delta \phi _{\mathrm {jj}}$ bins are used with boundaries that range from $-$3.2 to 3.2. Since the physical range of $\Delta \phi _{\mathrm {jj}}$ is between ${\pm} \pi$, the first and last bins actually only include events with 8/3 $< |\Delta \phi _{\mathrm {jj}}| < \pi$, however, the bin range is extended to $\pm$3.2 in the plot for visualisation.
png pdf	Additional Figure 7: Observed and predicted 2D distributions after the fit to data to extract the ggH anomalous coupling parameters using the $\Delta \phi _{\mathrm {jj}}$ method for the VBF high-$m_{\mathrm {jj}}$ category in the e$\mu$ channel. The uncertainty band accounts for all sources of systematic uncertainty on the signal and background predictions. The expectation in the ratio panel is the sum of the estimated backgrounds and the best fit signal. In total 12 $\Delta \phi _{\mathrm {jj}}$ bins are used with boundaries that range from $-$3.2 to 3.2. Since the physical range of $\Delta \phi _{\mathrm {jj}}$ is between ${\pm} \pi$, the first and last bins actually only include events with 8/3 $< |\Delta \phi _{\mathrm {jj}}| < \pi$, however, the bin range is extended to $\pm$3.2 in the plot for visualisation.
png pdf	Additional Figure 8: Observed and predicted 2D distributions after the fit to data to extract the ggH anomalous coupling parameters using the $\Delta \phi _{\mathrm {jj}}$ method for the VBF low-$m_{\mathrm {jj}}$ boosted category in the $\mu {\tau _\mathrm {h}}$ channel. The uncertainty band accounts for all sources of systematic uncertainty on the signal and background predictions. The expectation in the ratio panel is the sum of the estimated backgrounds and the best fit signal. In total 12 $\Delta \phi _{\mathrm {jj}}$ bins are used with boundaries that range from $-$3.2 to 3.2. Since the physical range of $\Delta \phi _{\mathrm {jj}}$ is between ${\pm} \pi$, the first and last bins actually only include events with 8/3 $< |\Delta \phi _{\mathrm {jj}}| < \pi$, however, the bin range is extended to $\pm$3.2 in the plot for visualisation.
png pdf	Additional Figure 9: Observed and predicted 2D distributions after the fit to data to extract the ggH anomalous coupling parameters using the $\Delta \phi _{\mathrm {jj}}$ method for the VBF low-$m_{\mathrm {jj}}$ boosted category in the ${\tau _\mathrm {h}} {\tau _\mathrm {h}}$ channel. The uncertainty band accounts for all sources of systematic uncertainty on the signal and background predictions. The expectation in the ratio panel is the sum of the estimated backgrounds and the best fit signal. In total 12 $\Delta \phi _{\mathrm {jj}}$ bins are used with boundaries that range from $-$3.2 to 3.2. Since the physical range of $\Delta \phi _{\mathrm {jj}}$ is between ${\pm} \pi$, the first and last bins actually only include events with 8/3 $< |\Delta \phi _{\mathrm {jj}}| < \pi$, however, the bin range is extended to $\pm$3.2 in the plot for visualisation.
png pdf	Additional Figure 10: Observed and predicted 2D distributions after the fit to data to extract the ggH anomalous coupling parameters using the $\Delta \phi _{\mathrm {jj}}$ method for the VBF low-$m_{\mathrm {jj}}$ boosted category in the e${\tau _\mathrm {h}}$ channel. The uncertainty band accounts for all sources of systematic uncertainty on the signal and background predictions. The expectation in the ratio panel is the sum of the estimated backgrounds and the best fit signal. In total 12 $\Delta \phi _{\mathrm {jj}}$ bins are used with boundaries that range from $-$3.2 to 3.2. Since the physical range of $\Delta \phi _{\mathrm {jj}}$ is between ${\pm} \pi$, the first and last bins actually only include events with 8/3 $< |\Delta \phi _{\mathrm {jj}}| < \pi$, however, the bin range is extended to $\pm$3.2 in the plot for visualisation.
png pdf	Additional Figure 11: Observed and predicted 2D distributions after the fit to data to extract the ggH anomalous coupling parameters using the $\Delta \phi _{\mathrm {jj}}$ method for the VBF low-$m_{\mathrm {jj}}$ boosted category in the e$\mu$ channel. The uncertainty band accounts for all sources of systematic uncertainty on the signal and background predictions. The expectation in the ratio panel is the sum of the estimated backgrounds and the best fit signal. In total 12 $\Delta \phi _{\mathrm {jj}}$ bins are used with boundaries that range from $-$3.2 to 3.2. Since the physical range of $\Delta \phi _{\mathrm {jj}}$ is between ${\pm} \pi$, the first and last bins actually only include events with 8/3 $< |\Delta \phi _{\mathrm {jj}}| < \pi$, however, the bin range is extended to $\pm$3.2 in the plot for visualisation.
png pdf	Additional Figure 12: Observed and predicted 2D distributions after the fit to data to extract the ggH anomalous coupling parameters using the $\Delta \phi _{\mathrm {jj}}$ method for the VBF low-$m_{\mathrm {jj}}$ category in the $\mu {\tau _\mathrm {h}}$ channel. The uncertainty band accounts for all sources of systematic uncertainty on the signal and background predictions. The expectation in the ratio panel is the sum of the estimated backgrounds and the best fit signal. In total 12 $\Delta \phi _{\mathrm {jj}}$ bins are used with boundaries that range from $-$3.2 to 3.2. Since the physical range of $\Delta \phi _{\mathrm {jj}}$ is between ${\pm} \pi$, the first and last bins actually only include events with 8/3 $< |\Delta \phi _{\mathrm {jj}}| < \pi$, however, the bin range is extended to $\pm$3.2 in the plot for visualisation.
png pdf	Additional Figure 13: Observed and predicted 2D distributions after the fit to data to extract the ggH anomalous coupling parameters using the $\Delta \phi _{\mathrm {jj}}$ method for the VBF low-$m_{\mathrm {jj}}$ category in the ${\tau _\mathrm {h}} {\tau _\mathrm {h}}$ channel. The uncertainty band accounts for all sources of systematic uncertainty on the signal and background predictions. The expectation in the ratio panel is the sum of the estimated backgrounds and the best fit signal. In total 12 $\Delta \phi _{\mathrm {jj}}$ bins are used with boundaries that range from $-$3.2 to 3.2. Since the physical range of $\Delta \phi _{\mathrm {jj}}$ is between ${\pm} \pi$, the first and last bins actually only include events with 8/3 $< |\Delta \phi _{\mathrm {jj}}| < \pi$, however, the bin range is extended to $\pm$3.2 in the plot for visualisation.
png pdf	Additional Figure 14: Observed and predicted 2D distributions after the fit to data to extract the ggH anomalous coupling parameters using the $\Delta \phi _{\mathrm {jj}}$ method for the VBF low-$m_{\mathrm {jj}}$ category in the e${\tau _\mathrm {h}}$ channel. The uncertainty band accounts for all sources of systematic uncertainty on the signal and background predictions. The expectation in the ratio panel is the sum of the estimated backgrounds and the best fit signal. In total 12 $\Delta \phi _{\mathrm {jj}}$ bins are used with boundaries that range from $-$3.2 to 3.2. Since the physical range of $\Delta \phi _{\mathrm {jj}}$ is between ${\pm} \pi$, the first and last bins actually only include events with 8/3 $< |\Delta \phi _{\mathrm {jj}}| < \pi$, however, the bin range is extended to $\pm$3.2 in the plot for visualisation.
png pdf	Additional Figure 15: Observed and predicted 2D distributions after the fit to data to extract the ggH anomalous coupling parameters using the $\Delta \phi _{\mathrm {jj}}$ method for the VBF low-$m_{\mathrm {jj}}$ category in the e$\mu$ channel. The uncertainty band accounts for all sources of systematic uncertainty on the signal and background predictions. The expectation in the ratio panel is the sum of the estimated backgrounds and the best fit signal. In total 12 $\Delta \phi _{\mathrm {jj}}$ bins are used with boundaries that range from $-$3.2 to 3.2. Since the physical range of $\Delta \phi _{\mathrm {jj}}$ is between ${\pm} \pi$, the first and last bins actually only include events with 8/3 $< |\Delta \phi _{\mathrm {jj}}| < \pi$, however, the bin range is extended to $\pm$3.2 in the plot for visualisation.
png pdf	Additional Figure 16: Observed and predicted 2D distributions after the fit to data to extract the ggH anomalous coupling parameters using the $\Delta \phi _{\mathrm {jj}}$ method for the boosted category in the $\mu {\tau _\mathrm {h}}$ channel. The uncertainty band accounts for all sources of systematic uncertainty on the signal and background predictions. The expectation in the ratio panel is the sum of the estimated backgrounds and the best fit signal.
png pdf	Additional Figure 17: Observed and predicted 2D distributions after the fit to data to extract the ggH anomalous coupling parameters using the $\Delta \phi _{\mathrm {jj}}$ method for the boosted category in the ${\tau _\mathrm {h}} {\tau _\mathrm {h}}$ channel. The uncertainty band accounts for all sources of systematic uncertainty on the signal and background predictions. The expectation in the ratio panel is the sum of the estimated backgrounds and the best fit signal.
png pdf	Additional Figure 18: Observed and predicted 2D distributions after the fit to data to extract the ggH anomalous coupling parameters using the $\Delta \phi _{\mathrm {jj}}$ method for the boosted category in the e${\tau _\mathrm {h}}$ channel. The uncertainty band accounts for all sources of systematic uncertainty on the signal and background predictions. The expectation in the ratio panel is the sum of the estimated backgrounds and the best fit signal.
png pdf	Additional Figure 19: Observed and predicted 2D distributions after the fit to data to extract the ggH anomalous coupling parameters using the $\Delta \phi _{\mathrm {jj}}$ method for the boosted category in the e$\mu$ channel. The uncertainty band accounts for all sources of systematic uncertainty on the signal and background predictions. The expectation in the ratio panel is the sum of the estimated backgrounds and the best fit signal.
png pdf	Additional Figure 20: Observed and predicted $m_{\tau \tau}$ distributions after the fit to data to extract the ggH anomalous coupling parameters using the $\Delta \phi _{\mathrm {jj}}$ method for the 0-jet category in the $\mu {\tau _\mathrm {h}}$ channel. The uncertainty band accounts for all sources of systematic uncertainty on the signal and background predictions. The expectation in the ratio panel is the sum of the estimated backgrounds and the best fit signal.
png pdf	Additional Figure 21: Observed and predicted $m_{\tau \tau}$ distributions after the fit to data to extract the ggH anomalous coupling parameters using the $\Delta \phi _{\mathrm {jj}}$ method for the 0-jet category in the ${\tau _\mathrm {h}} {\tau _\mathrm {h}}$ channel. The uncertainty band accounts for all sources of systematic uncertainty on the signal and background predictions. The expectation in the ratio panel is the sum of the estimated backgrounds and the best fit signal.
png pdf	Additional Figure 22: Observed and predicted $m_{\tau \tau}$ distributions after the fit to data to extract the ggH anomalous coupling parameters using the $\Delta \phi _{\mathrm {jj}}$ method for the 0-jet category in the e${\tau _\mathrm {h}}$ channel. The uncertainty band accounts for all sources of systematic uncertainty on the signal and background predictions. The expectation in the ratio panel is the sum of the estimated backgrounds and the best fit signal.
png pdf	Additional Figure 23: Observed and predicted $m_{\tau \tau}$ distributions after the fit to data to extract the ggH anomalous coupling parameters using the $\Delta \phi _{\mathrm {jj}}$ method for the VBF 0-jet category in the e$\mu$ channel. The uncertainty band accounts for all sources of systematic uncertainty on the signal and background predictions. The expectation in the ratio panel is the sum of the estimated backgrounds and the best fit signal.
png pdf	Additional Figure 24: Generator-level $\Delta \phi _{\mathrm {jj}}$ distributions for ggH+2j events with $m_{\mathrm {jj}} >$ 500 GeV. The distributions are shown for a scalar Higgs ($f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}=$ 0) in red, a pseudoscalar Higgs ($f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}=$ 1) in blue, and for a CP-violating scenario with maximum-mixing between CP-even and CP-odd couplings ($f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}=$ 0.5) in green.
png pdf	Additional Figure 25: The $\Delta \phi _{\mathrm {jj}}$ distribution for all channels combined. Events were collected from all years and $m_{\tau \tau}$ bins in the four VBF signal categories. The non- $\mathrm{H} \rightarrow \tau \tau$ background is subtracted from the data. The events are reweighed by $A\,S/(S+B)$, in which $S$ and $B$ are the ggH signal and background rates, respectively, and $A$ is a measure for the average asymmetry between the scalar ($f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}=$ 0) and pseudoscalar ($f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}=$ 1) distributions. The definition of the value of $A$ per bin is $|N(f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}=0) - N(f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}=1)|/|N(f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}=0) + N(f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}=1)|$ where $N(f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}=0)$ and $N(f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}=1)$ are the expected scalar and pseudoscalar events per bin respectively, and $A$ is normalised to the total number of bins. The scalar ggH distribution is depicted in red, while the pseudoscalar ggH is displayed in blue; both are shown stacked on top of the scalar ($f_{a3}=$ 0) $\mathrm{q} \mathrm{q} \mathrm{H}$ (VBF+$\mathrm{V} \mathrm{H}$) distribution shown by the dashed magenta line. In the predictions, the rate parameters are taken from their best fit values. The grey uncertainty band indicates the uncertainty on the subtracted background component. In total 12 $\Delta \phi _{\mathrm {jj}}$ bins are used with boundaries that range from $-$3.2 to 3.2. Since the physical range of $\Delta \phi _{\mathrm {jj}}$ is between ${\pm} \pi$, the first and last bins actually only include events with 8/3 $< |\Delta \phi _{\mathrm {jj}}| < \pi$, however, the bin range is extended to $\pm$3.2 in the plot for visualisation.
png pdf	Additional Figure 26: The $\Delta \phi _{\mathrm {jj}}$ distribution for all channels combined. Events were collected from all years and $m_{\tau \tau}$ bins in the VBF high-$m_{\mathrm {jj}}$ boosted category. The non- $\mathrm{H} \rightarrow \tau \tau$ background is subtracted from the data. The events are reweighed by $A\,S/(S+B)$, in which $S$ and $B$ are the ggH signal and background rates, respectively, and $A$ is a measure for the average asymmetry between the scalar ($f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}=$ 0) and pseudoscalar ($f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}=$ 1) distributions. The definition of the value of $A$ per bin is $|N(f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}=0) - N(f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}=1)|/|N(f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}=0) + N(f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}=1)|$ where $N(f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}=0)$ and $N(f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}=1)$ are the expected scalar and pseudoscalar events per bin respectively, and $A$ is normalised to the total number of bins. The scalar ggH distribution is depicted in red, while the pseudoscalar ggH is displayed in blue; both are shown stacked on top of the scalar ($f_{a3}=$ 0) $\mathrm{q} \mathrm{q} \mathrm{H}$ (VBF+$\mathrm{V} \mathrm{H}$) distribution shown by the dashed magenta line. In the predictions, the rate parameters are taken from their best fit values. The grey uncertainty band indicates the uncertainty on the subtracted background component. In total 12 $\Delta \phi _{\mathrm {jj}}$ bins are used with boundaries that range from $-$3.2 to 3.2. Since the physical range of $\Delta \phi _{\mathrm {jj}}$ is between ${\pm} \pi$, the first and last bins actually only include events with 8/3 $< |\Delta \phi _{\mathrm {jj}}| < \pi$, however, the bin range is extended to $\pm$3.2 in the plot for visualisation.
png pdf	Additional Figure 27: The $\Delta \phi _{\mathrm {jj}}$ distribution for all channels combined. Events were collected from all years and $m_{\tau \tau}$ bins in the VBF high-$m_{\mathrm {jj}}$ category. The non- $\mathrm{H} \rightarrow \tau \tau$ background is subtracted from the data. The events are reweighed by $A\,S/(S+B)$, in which $S$ and $B$ are the ggH signal and background rates, respectively, and $A$ is a measure for the average asymmetry between the scalar ($f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}=$ 0) and pseudoscalar ($f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}=$ 1) distributions. The definition of the value of $A$ per bin is $|N(f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}=0) - N(f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}=1)|/|N(f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}=0) + N(f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}=1)|$ where $N(f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}=0)$ and $N(f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}=1)$ are the expected scalar and pseudoscalar events per bin respectively, and $A$ is normalised to the total number of bins. The scalar ggH distribution is depicted in red, while the pseudoscalar ggH is displayed in blue; both are shown stacked on top of the scalar ($f_{a3}=$ 0) $\mathrm{q} \mathrm{q} \mathrm{H}$ (VBF+$\mathrm{V} \mathrm{H}$) distribution shown by the dashed magenta line. In the predictions, the rate parameters are taken from their best fit values. The grey uncertainty band indicates the uncertainty on the subtracted background component. In total 12 $\Delta \phi _{\mathrm {jj}}$ bins are used with boundaries that range from $-$3.2 to 3.2. Since the physical range of $\Delta \phi _{\mathrm {jj}}$ is between ${\pm} \pi$, the first and last bins actually only include events with 8/3 $< |\Delta \phi _{\mathrm {jj}}| < \pi$, however, the bin range is extended to $\pm$3.2 in the plot for visualisation.
png pdf	Additional Figure 28: The $\Delta \phi _{\mathrm {jj}}$ distribution for all channels combined. Events were collected from all years and $m_{\tau \tau}$ bins in the VBF low-$m_{\mathrm {jj}}$ boosted category. The non- $\mathrm{H} \rightarrow \tau \tau$ background is subtracted from the data. The events are reweighed by $A\,S/(S+B)$, in which $S$ and $B$ are the ggH signal and background rates, respectively, and $A$ is a measure for the average asymmetry between the scalar ($f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}=$ 0) and pseudoscalar ($f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}=$ 1) distributions. The definition of the value of $A$ per bin is $|N(f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}=0) - N(f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}=1)|/|N(f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}=0) + N(f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}=1)|$ where $N(f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}=0)$ and $N(f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}=1)$ are the expected scalar and pseudoscalar events per bin respectively, and $A$ is normalised to the total number of bins. The scalar ggH distribution is depicted in red, while the pseudoscalar ggH is displayed in blue; both are shown stacked on top of the scalar ($f_{a3}=$ 0) $\mathrm{q} \mathrm{q} \mathrm{H}$ (VBF+$\mathrm{V} \mathrm{H}$) distribution shown by the dashed magenta line. In the predictions, the rate parameters are taken from their best fit values. The grey uncertainty band indicates the uncertainty on the subtracted background component. In total 12 $\Delta \phi _{\mathrm {jj}}$ bins are used with boundaries that range from $-$3.2 to 3.2. Since the physical range of $\Delta \phi _{\mathrm {jj}}$ is between ${\pm} \pi$, the first and last bins actually only include events with 8/3 $< |\Delta \phi _{\mathrm {jj}}| < \pi$, however, the bin range is extended to $\pm$3.2 in the plot for visualisation.
png pdf	Additional Figure 29: The $\Delta \phi _{\mathrm {jj}}$ distribution for all channels combined. Events were collected from all years and $m_{\tau \tau}$ bins in the VBF low-$m_{\mathrm {jj}}$ category. The non- $\mathrm{H} \rightarrow \tau \tau$ background is subtracted from the data. The events are reweighed by $A\,S/(S+B)$, in which $S$ and $B$ are the ggH signal and background rates, respectively, and $A$ is a measure for the average asymmetry between the scalar ($f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}=$ 0) and pseudoscalar ($f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}=$ 1) distributions. The definition of the value of $A$ per bin is $|N(f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}=0) - N(f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}=1)|/|N(f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}=0) + N(f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}=1)|$ where $N(f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}=0)$ and $N(f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}=1)$ are the expected scalar and pseudoscalar events per bin respectively, and $A$ is normalised to the total number of bins. The scalar ggH distribution is depicted in red, while the pseudoscalar ggH is displayed in blue; both are shown stacked on top of the scalar ($f_{a3}=$ 0) $\mathrm{q} \mathrm{q} \mathrm{H}$ (VBF+$\mathrm{V} \mathrm{H}$) distribution shown by the dashed magenta line. In the predictions, the rate parameters are taken from their best fit values. The grey uncertainty band indicates the uncertainty on the subtracted background component. In total 12 $\Delta \phi _{\mathrm {jj}}$ bins are used with boundaries that range from $-$3.2 to 3.2. Since the physical range of $\Delta \phi _{\mathrm {jj}}$ is between ${\pm} \pi$, the first and last bins actually only include events with 8/3 $< |\Delta \phi _{\mathrm {jj}}| < \pi$, however, the bin range is extended to $\pm$3.2 in the plot for visualisation.
png pdf	Additional Figure 30: Observed (solid) and expected (dashed) likelihood scans of $\alpha _{\mathrm{g} \mathrm{g} \mathrm{H}}$ obtained with the MELA method. The $\alpha _{\mathrm{g} \mathrm{g} \mathrm{H}}$ parameter is defined as $\alpha _{\mathrm{g} \mathrm{g} \mathrm{H}}=\arctan(a_{3}^{\mathrm{g} \mathrm{g}}/a_{2}^{\mathrm{g} \mathrm{g}})$.
png pdf	Additional Figure 31: Observed (solid) and expected (dashed) likelihood scans of $\alpha _{\mathrm{g} \mathrm{g} \mathrm{H}}$ obtained with the $\Delta \phi _{\mathrm {jj}}$ method. The $\alpha _{\mathrm{g} \mathrm{g} \mathrm{H}}$ parameter is defined as $\alpha _{\mathrm{g} \mathrm{g} \mathrm{H}}=\arctan(a_{3}^{\mathrm{g} \mathrm{g}}/a_{2}^{\mathrm{g} \mathrm{g}})$.
png pdf	Additional Figure 32: Observed (solid) and expected (dashed) likelihood scans of $\alpha _{\mathrm{g} \mathrm{g} \mathrm{H}}$ obtained with the combination of results using the $\mathrm{H} \to \tau \tau$ (obtained with the MELA method) and $\mathrm{H} \to 4\ell$ decay channels.
png pdf	Additional Figure 33: Observed (solid) and expected (dashed) likelihood scans of $f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}$ obtained with the MELA (black) and $\Delta \phi _{\mathrm {jj}}$ (red) methods.
png pdf	Additional Figure 34: Observed (solid) and expected (dashed) likelihood scans of $\alpha ^{\mathrm{H} \mathrm {ff}}$ obtained with the MELA (black) and $\Delta \phi _{\mathrm {jj}}$ (red) methods.
png pdf	Additional Figure 35: Observed (solid) and expected (dashed) likelihood scans of $\alpha _{\mathrm{g} \mathrm{g} \mathrm{H}}$ obtained with the MELA (black) and $\Delta \phi _{\mathrm {jj}}$ (red) methods. The $\alpha _{\mathrm{g} \mathrm{g} \mathrm{H}}$ parameter is defined as $\alpha _{\mathrm{g} \mathrm{g} \mathrm{H}}=\arctan(a_{3}^{\mathrm{g} \mathrm{g}}/a_{2}^{\mathrm{g} \mathrm{g}})$.
png pdf	Additional Figure 36: Observed (solid) and expected (dashed) likelihood scans of $f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}$ obtained with the combination of results using the $\mathrm{H} \to \tau \tau$ (obtained with the MELA method) and $\mathrm{H} \to 4\ell$ decay channels.
png pdf	Additional Figure 37: Observed (solid) and expected (dashed) likelihood scans of $\alpha ^{\mathrm{H} \mathrm {ff}}$ obtained with the combination of results using the $\mathrm{H} \to \tau \tau$ (obtained with the MELA method) and $\mathrm{H} \to 4\ell$ decay channels.
png pdf	Additional Figure 38: Observed (solid) and expected (dashed) likelihood scans of $\alpha _{\mathrm{g} \mathrm{g} \mathrm{H}}$ obtained with the combination of results using the $\mathrm{H} \to \tau \tau$ (obtained with the MELA method) and $\mathrm{H} \to 4\ell$ decay channels.
png pdf	Additional Figure 39: Observed (solid) and expected (dashed) likelihood scans of $f_{\textit {CP}}^{\mathrm{H} \mathrm{t} \mathrm{t}}$ obtained with the combination of results using the $\mathrm{H} \to \tau \tau$ (obtained with the MELA method), $\mathrm{H} \to 4\ell$, and $\mathrm{H} \to \gamma \gamma$ decay channels.
png pdf	Additional Figure 40: Observed (solid) and expected (dashed) likelihood scans of $f_{a3}$ in Approach 1 obtained with the combination of results using the $\mathrm{H} \to \tau \tau$ and $\mathrm{H} \to 4\ell$ decay channels.
png pdf	Additional Figure 41: Observed (solid) and expected (dashed) likelihood scans of $f_{a2}$ in Approach 1 obtained with the combination of results using the $\mathrm{H} \to \tau \tau$ and $\mathrm{H} \to 4\ell$ decay channels.
png pdf	Additional Figure 42: Observed (solid) and expected (dashed) likelihood scans of $f_{\Lambda 1}$ in Approach 1 obtained with the combination of results using the $\mathrm{H} \to \tau \tau$ and $\mathrm{H} \to 4\ell$ decay channels.
png pdf	Additional Figure 43: Observed (solid) and expected (dashed) likelihood scans of $f_{\Lambda 1}^{\mathrm{Z} \gamma}$ in Approach 1 obtained with the combination of results using the $\mathrm{H} \to \tau \tau$ and $\mathrm{H} \to 4\ell$ decay channels.
png pdf	Additional Figure 44: Observed (solid) and expected (dashed) likelihood scans of $f_{a3}$ in Approach 2 obtained with the combination of results using the $\mathrm{H} \to \tau \tau$ and $\mathrm{H} \to 4\ell$ decay channels.
png pdf	Additional Figure 45: Observed (solid) and expected (dashed) likelihood scans of $f_{a3}$ in Approach 1 obtained with the combination of results using the $\mathrm{H} \to \tau \tau$ and $\mathrm{H} \to 4\ell$ decay channels.
png pdf	Additional Figure 46: Observed (solid) and expected (dashed) likelihood scans of $f_{a2}$ in Approach 1 obtained with the combination of results using the $\mathrm{H} \to \tau \tau$ and $\mathrm{H} \to 4\ell$ decay channels.
png pdf	Additional Figure 47: Observed (solid) and expected (dashed) likelihood scans of $f_{\Lambda 1}$ in Approach 1 obtained with the combination of results using the $\mathrm{H} \to \tau \tau$ and $\mathrm{H} \to 4\ell$ decay channels.
png pdf	Additional Figure 48: Observed (solid) and expected (dashed) likelihood scans of $f_{\Lambda 1}^{\mathrm{Z} \gamma}$ in Approach 1 obtained with the combination of results using the $\mathrm{H} \to \tau \tau$ and $\mathrm{H} \to 4\ell$ decay channels.
png pdf	Additional Figure 49: Observed (solid) and expected (dashed) likelihood scans of $f_{a3}$ in Approach 2 obtained with the combination of results using the $\mathrm{H} \to \tau \tau$ and $\mathrm{H} \to 4\ell$ decay channels.
png pdf	Additional Figure 50: A candidate ggH + 2 jet event in the $\mu {\tau _\mathrm {h}}$ final state, as seen in the $\rho$-$\phi$ plane. The $\mu$ candidate is shown in red, and the missing transverse momentum vector is indicated by the purple arrow. Three jets are visible as shown in yellow and cyan. The ${\tau _\mathrm {h}}$ candidate corresponds to the cyan colored jet. The two other jets have a CP-even-like topology (${| \Delta \phi _{\mathrm {jj}} |}\approx \pi$). The dijet pair have $\Delta \phi _{\mathrm {jj}}=0.94\pi$, ${| \Delta \eta _{jj} |}=3.23$, and $m_{\mathrm {jj}} =$ 510 GeV. The event was recorded during the 2018 data-taking period (event number, run, luminosity section = 366863438, 322356, 194).
png pdf	Additional Figure 51: A candidate ggH + 2 jet event in the $\mu {\tau _\mathrm {h}}$ final state, as seen in the $\rho$-$z$ plane. The $\mu$ candidate is shown in red, and the missing transverse momentum vector is indicated by the purple arrow. Three jets are visible as shown in yellow and cyan. The ${\tau _\mathrm {h}}$ candidate corresponds to the cyan colored jet. The two other jets have a CP-even-like topology (${| \Delta \phi _{\mathrm {jj}} |}\approx \pi$). The dijet pair have $\Delta \phi _{\mathrm {jj}}=0.94\pi$, ${| \Delta \eta _{jj} |}=3.23$, and $m_{\mathrm {jj}} =$ 510 GeV. The event was recorded during the 2018 data-taking period (event number, run, luminosity section = 366863438, 322356, 194).
png pdf	Additional Figure 52: A candidate ggH + 2 jet event in the $\mu {\tau _\mathrm {h}}$ final state, as seen in the $\rho$-$\phi$ plane. The $\mu$ candidate is shown in red, and the missing transverse momentum vector is indicated by the purple arrow. Three jets are visible as shown in yellow and cyan. The ${\tau _\mathrm {h}}$ candidate corresponds to the cyan colored jet. The two other jets have a CP-odd-like topology (${| \Delta \phi _{\mathrm {jj}} |}\approx \frac {\pi}{2}$). The dijet pair have $\Delta \phi _{\mathrm {jj}}=$ $-$0.47$\pi$, ${| \Delta \eta _{jj} |}=$ 5.24, and $m_{\mathrm {jj}} =$ 582 GeV. The event was recorded during the 2018 data-taking period (event number, run, luminosity section = 1219733368, 320917, 742).
png pdf	Additional Figure 53: A candidate ggH + 2 jet event in the $\mu {\tau _\mathrm {h}}$ final state, as seen in the $\rho$-$z$ plane. The $\mu$ candidate is shown in red, and the missing transverse momentum vector is indicated by the purple arrow. Three jets are visible as shown in yellow and cyan. The ${\tau _\mathrm {h}}$ candidate corresponds to the cyan colored jet. The two other jets have a CP-odd-like topology (${| \Delta \phi _{\mathrm {jj}} |}\approx \frac {\pi}{2}$). The dijet pair have $\Delta \phi _{\mathrm {jj}}=$ $-$0.47$\pi$, ${| \Delta \eta _{jj} |}=$ 5.24, and $m_{\mathrm {jj}} =$ 582 GeV. The event was recorded during the 2018 data-taking period (event number, run, luminosity section = 1219733368, 320917, 742).
png pdf	Additional Figure 54: Projection of the expected likelihood scan of $f_{a3}$ based on the Run 2 analysis to an integrated luminosity of 3 ab$^{-1}$ at $\sqrt {s} =$ 14 TeV. "Bin-by-bin" systematic uncertainties are ignored in the extrapolation. The other systematic uncertainties are adjusted to the scheme used for the YR18 HL-LHC projections (arXiv:1902.00134). The relationship between the $a_i^{\mathrm{W} \mathrm{W}}$ and $a_i^{\mathrm{Z} \mathrm{Z}}$ couplings is assumed to satisfy ${a_i^{\mathrm{W} \mathrm{W}}=a_i^{\mathrm{Z} \mathrm{Z}}}$ and ${\kappa _i^{\mathrm{Z} \mathrm{Z}}/(\Lambda _{1}^{\mathrm{Z} \mathrm{Z}})^2}$ = ${\kappa _i^{\mathrm{W} \mathrm{W}}/(\Lambda _{1}^{\mathrm{W} \mathrm{W}})^2}$ (Approach 1).
png pdf	Additional Figure 55: Projection of the expected likelihood scan of $f_{a3}$ based on the Run 2 analysis to an integrated luminosity of 3 ab$^{-1}$ at $\sqrt {s} =$ 14 TeV. "Bin-by-bin" systematic uncertainties are ignored in the extrapolation. The other systematic uncertainties are adjusted to the scheme used for the YR18 HL-LHC projections (arXiv:1902.00134). The expected likelihood scan of $f_{a3}$ is reinterpretetd with custodial and SU(2)$\times$U(1) symmetries in the relationships of anomalous couplings (Approach 2).
png pdf	Additional Figure 56: Projection of the expected likelihood scan of $f_{a3}^{\mathrm{g} \mathrm{g} \mathrm{H}}$ based on the Run 2 analysis to an integrated luminosity of 3 ab$^{-1}$ at $\sqrt {s} =$ 14 TeV. "Bin-by-bin" systematic uncertainties are ignored in the extrapolation. The other systematic uncertainties are adjusted to the scheme used for the YR18 HL-LHC projections (arXiv:1902.00134). The extrapolation is performed on the result obtained with the MELA method.

Additional Tables
png pdf	Additional Table 1: The expected and observed values of the signal strength modifiers that scale the ggH ($\mu _{\mathrm{g} \mathrm{g} \mathrm{H}}$) and VBF+$\mathrm{V} \mathrm{H}$ ($\mu _{\mathrm{q} \mathrm{q} \mathrm{H}}$) signals in the $\mathrm{H} \to \tau \tau$ final state. The best fit values are shown for each of the fits used to extract a given anomalous coupling parameter.
png pdf	Additional Table 2: Projections of allowed 68% (central values with uncertainties) and 95% CL (in square brackets) intervals on $f_{a3}$ and $f_{a3}^{\gamma\gamma\mathrm{H}}$ based on the Run 2 analysis to an integrated luminosity of 3 ab$^{-1}$ at $\sqrt{s}=$ 14 TeV. "Bin-by-bin" systematic uncertainties are ignored in the extrapolation. The other systematic uncertainties are adjusted to the scheme used for the YR18 HL-LHC projections (arXiv:1902.00134). Two different approaches are adopted for $f_{a3}$ scans to set the relationship between the $a_i^{\mathrm{W}\mathrm{W}}$ and $a_i^{\mathrm{Z}\mathrm{Z}}$ couplings: assuming ${a_i^{\mathrm{W}\mathrm{W}}=a_i^{\mathrm{Z}\mathrm{Z}}}$ and ${\kappa_i^{\mathrm{Z}\mathrm{Z}}/(\Lambda_{1}^{\mathrm{Z}\mathrm{Z}})^2}$ = ${\kappa_i^{\mathrm{W}\mathrm{W}}/(\Lambda_{1}^{\mathrm{W}\mathrm{W}})^2}$ (Approach 1) or considering custodial and SU(2)$\times$U(1) symmetries in the relationships of anomalous couplings (Approach 2).

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