Best fit values of $\sigma(gg\to H\to ZZ)$, $\sigma_i/\sigma_{gg\mathrm{F}}$, and $\mathrm{B}^f/\mathrm{B}^{ZZ}$ relative to their SM prediction from the combined analysis of the $\sqrt{s}$=7 and 8 TeV data. The results are shown for the combination of ATLAS and CMS, and also separately for each experiment, together with their total uncertainties and their breakdown into the four components described in the text. The expected uncertainties in the measurements are also shown.

Best fit values of $\sigma(gg\to H\to WW)$, $\sigma_i/\sigma_{gg\mathrm{F}}$, and $\mathrm{B}^f/\mathrm{B}^{WW}$ from the combined analysis of the $\sqrt{s}$=7 and 8 TeV data. The values involving cross sections are given for $\sqrt{s}$=8 TeV, assuming the SM values for $\sigma_i(7 \mathrm{TeV})/\sigma_i(8 \mathrm{TeV})$. The results are shown for the combination of ATLAS and CMS, and also separately for each experiment, together with their total uncertainties and their breakdown into the four components described in the text. The expected uncertainties in the measurements are also shown.

Best fit values of $\sigma(gg\to H\to WW)$, $\sigma_i/\sigma_{gg\mathrm{F}}$, and $\mathrm{B}^f/\mathrm{B}^{WW}$ relative to their SM prediction from the combined analysis of the $\sqrt{s}$=7 and 8 TeV data. The results are shown for the combination of ATLAS and CMS, and also separately for each experiment, together with their total uncertainties and their breakdown into the four components described in the text. The expected uncertainties in the measurements are also shown.

Best fit values of $\kappa_{gZ}= \kappa_{g}\cdot\kappa_{Z} / \kappa_{H}$ and of the ratios of coupling modifiers, as defined in the most generic parameterisation described in the context of the $\kappa$ framework, from the combined analysis of the $\sqrt{s}$=7 and 8 TeV data. The results are shown for the combination of ATLAS and CMS and also separately for each experiment, together with their total uncertainties and their breakdown into the four components described in the text. The uncertainties in $\lambda_{tg}$ and $\lambda_{WZ}$, for which a negative solution is allowed, are calculated around the overall best fit value. The expected total uncertainties in the measurements are also shown. For those parameters with no sensitivity to the sign, only the absolute values are shown.

Measured global signal strength $\mu$ and its total uncertainty, together with the breakdown of the uncertainty into its four components as defined in the text. The results are shown for the combination of ATLAS and CMS, and separately for each experiment. The expected uncertainty, with its breakdown, is also shown.

Measured signal strengths $\mu$ and their total uncertainties for different Higgs boson production processes. The results are shown for the combination of ATLAS and CMS, and separately for each experiment, for the combined $\sqrt{s}$=7 and 8 TeV data. The expected uncertainties in the measurements are also displayed. These results are obtained assuming that the Higgs boson branching fractions are the same as in the SM.

Measured signal strengths $\mu$ and their total uncertainties for different Higgs boson decay channels. The results are shown for the combination of ATLAS and CMS, and separately for each experiment, for the combined $\sqrt{s}$=7 and 8 TeV data. The expected uncertainties in the measurements are also displayed. These results are obtained assuming that the Higgs boson production process cross sections at $\sqrt{s}$ = 7 and 8 TeV are the same as in the SM.

Results of the ten-parameter fit of $\mu_F^f = \mu_{gg\mathrm{F}+ttH}^f$ and $\mu_V^f = \mu_{\mathrm{VBF}+VH}^f$ for each of the five decay channels. The results are shown for the combination of ATLAS and CMS, together with their measured and expected uncertainties. The measured results are also shown separately for each experiment.

Results of the six-parameter fit of the global ratio $\mu_V/\mu_F = \mu_{\mathrm{VBF}+VH}/\mu_{gg\mathrm{F}+ttH}$ together with $\mu_F^f$ for each of the five decay channels. The results are shown for the combination of ATLAS and CMS, together with their measured and expected uncertainties. The measured results are also shown separately for each experiment.

Fit results allowing BSM loop couplings, assuming that $|\kappa_{V}| \le$ 1, where $\kappa_{V}$ denotes $\kappa_{Z}$ or $\kappa_{W}$, and that $\mathrm{B_{BSM}} \ge$ 0. The results for the combination of ATLAS and CMS are reported with their measured and expected uncertainties. Also shown are the results from each experiment. For the parameters with both signs allowed, the other 1$\sigma$ interval is shown on a second line. For those parameters with no sensitivity to the sign, only the absolute values are shown.

Fit results allowing BSM loop couplings, assuming that there are no additional BSM contributions to the Higgs boson width, i.e. $\mathrm{B_{BSM}}=0$. The results for the combination of ATLAS and CMS are reported with their measured and expected uncertainties. Also shown are the results from each experiment. For the parameters with both signs allowed, the other 1$\sigma$ interval is shown on a second line. When a parameter is constrained and reaches a boundary, namely $\mathrm{B_{BSM}}$ = 0, the uncertainty is not indicated. For those parameters with no sensitivity to the sign, only the absolute values are shown.

Fit results for the parameterisation assuming the absence of BSM particles in the loops ($\mathrm{B_{BSM}}$=0). The results with their measured and expected uncertainties are reported for the combination of ATLAS and CMS, together with the individual results from each experiment. For the parameters with both signs allowed, the other 1$\sigma$ CL interval is shown on a second line. When a parameter is constrained and reaches a boundary, namely $|\kappa_\mu|$ = 0, the uncertainty is not indicated. For those parameters with no sensitivity to the sign, only the absolute values are shown.

Summary of fit results for a parameterisation probing the ratios of coupling modifiers for up-type versus down-type fermions. The results for the combination of ATLAS and CMS are reported together with their measured and expected uncertainties. Also shown are the results from each experiment. The parameter $\kappa_{uu}$ is positive definite since $\kappa_H$ is always assumed to be positive. For the parameter $\lambda_{du}$, for which both signs are allowed, the other 1$\sigma$ CL interval is shown on a second line. Negative values for the parameter $\lambda_{Vu}$ are excluded by more than 4$\sigma$.

Summary of fit results for a parameterisation probing the ratios of coupling modifiers for leptons versus quarks. The results for the combination of ATLAS and CMS are reported together with their measured and expected uncertainties. Also shown are the results from each experiment. The parameter $\kappa_{qq}$ is positive definite since $\kappa_H$ is always assumed to be positive. For the parameter $\lambda_{lq}$, for which there is no sensitivity to the sign, only the absolute values are shown. Negative values for the parameter $\lambda_{Vq}$ are excluded by more than 4$\sigma$.

Correlation matrix obtained from the fit combining the ATLAS and CMS data using the generic parameterisation with 23 parameters, $\sigma_i\cdot\mathrm{B}^f$ for each specific channel $i\to H\to f$. Only 20 parameters are shown because the other three, corresponding to the $H\to ZZ$ decay channel for the $WH$, $ZH$, and $ttH$ production processes, are not measured with a meaningful precision.

Correlation matrix obtained from the fit combining the ATLAS and CMS data using the generic parameterisation with nine parameters, $\sigma(gg\to H\to ZZ)$, $\sigma_i/\sigma_{gg\mathrm{F}}$, and $\mathrm{B}^f/\mathrm{B}^{ZZ}$.

Correlation matrix obtained from the fit combining the ATLAS and CMS data using the generic parameterisation with seven parameters, $\kappa_{gZ}=\kappa_{g}\cdot\kappa_{Z} / \kappa_{H}$ and the ratios of coupling modifiers.

Expected correlation matrix obtained from the fit combining ATLAS and CMS pre-fit Asimov data sets using the generic parameterisation with 23 parameters, $\sigma_i\cdot\mathrm{B}^f$ for each specific channel $i\to H\to f$. Only 20 parameters are shown because the other three, corresponding to the $H\to ZZ$ decay channel for the $WH$, $ZH$, and $ttH$ production processes, are not measured with a meaningful precision.

Expected correlation matrix obtained from the fit combining ATLAS and CMS pre-fit Asimov data sets using the generic parameterisation with nine parameters, $\sigma(gg\to H\to ZZ)$, $\sigma_i/\sigma_{gg\mathrm{F}}$, and $\mathrm{B}^f/\mathrm{B}^{ZZ}$.

Expected correlation matrix obtained from the fit combining ATLAS and CMS pre-fit Asimov data sets using the generic parameterisation with seven parameters, $\kappa_{gZ}=\kappa_{g}\cdot\kappa_{Z} / \kappa_{H}$ and the ratios of coupling modifiers.

ATLAS+CMS combined best-fit and 68% and 95% CL negative log-likelihood contours in the ($\kappa_{g}$,$\kappa_{\gamma}$) plane.

ATLAS best-fit and 68% and 95% CL negative log-likelihood contours in the ($\kappa_{g}$,$\kappa_{\gamma}$) plane.

CMS best-fit and 68% and 95% CL negative log-likelihood contours in the ($\kappa_{g}$,$\kappa_{\gamma}$) plane.

Best-fit and 68% and 95% CL negative log-likelihood contours in the ($\kappa_{F}$,$\kappa_{V}$) plane.

Best-fit and 68% CL negative log-likelihood contour in the ($\kappa_{F}$,$\kappa_{V}$) plane for the $H\rightarrow\gamma\gamma$ channel.

Best-fit and 68% CL negative log-likelihood contour in the ($\kappa_{F}$,$\kappa_{V}$) plane for the $H\rightarrow ZZ$ channel.

Best-fit and 68% CL negative log-likelihood contour in the ($\kappa_{F}$,$\kappa_{V}$) plane for the $H\rightarrow WW$ channel.

Best-fit and 68% CL negative log-likelihood contour in the ($\kappa_{F}$,$\kappa_{V}$) plane for the $H\rightarrow\tau\tau$ channel.

Best-fit and 68% CL negative log-likelihood contour in the ($\kappa_{F}$,$\kappa_{V}$) plane for the $H\rightarrow bb$ channel.

ATLAS best-fit and 68% and 95% CL negative log-likelihood contours in the ($\kappa_{F}$,$\kappa_{V}$) plane.

CMS best-fit and 68% and 95% CL negative log-likelihood contours in the ($\kappa_{F}$,$\kappa_{V}$) plane.

Best-fit and 68% CL negative log-likelihood contour in the ($\kappa_{F}$,$\kappa_{V}$) plane for the $H\rightarrow\gamma\gamma$ channel, assuming $\kappa_{F}>0$.

Best-fit and 68% CL negative log-likelihood contour in the ($\kappa_{F}$,$\kappa_{V}$) plane for the $H\rightarrow ZZ$ channel, assuming $\kappa_{F}>0$.

Best-fit and 68% CL negative log-likelihood contour in the ($\kappa_{F}$,$\kappa_{V}$) plane for the $H\rightarrow WW$ channel, assuming $\kappa_{F}>0$.

Best-fit and 68% CL negative log-likelihood contour in the ($\kappa_{F}$,$\kappa_{V}$) plane for the $H\rightarrow\tau\tau$ channel, assuming $\kappa_{F}>0$.

Best-fit and 68% CL negative log-likelihood contour in the ($\kappa_{F}$,$\kappa_{V}$) plane for the $H\rightarrow bb$ channel, assuming $\kappa_{F}>0$.

Best-fit and 68% and 95% CL negative log-likelihood contours in the ($\mu^{f}_{gg\mathrm{F}+ttH}$,$\mu^{f}_{\mathrm{VBF}+VH}$) plane for the $H\rightarrow\gamma\gamma$ channel.

Best-fit and 68% and 95% CL negative log-likelihood contours in the ($\mu^{f}_{gg\mathrm{F}+ttH}$,$\mu^{f}_{\mathrm{VBF}+VH}$) plane for the $H\rightarrow ZZ$ channel.

Best-fit and 68% and 95% CL negative log-likelihood contours in the ($\mu^{f}_{gg\mathrm{F}+ttH}$,$\mu^{f}_{\mathrm{VBF}+VH}$) plane for the $H\rightarrow WW$ channel.

Best-fit and 68% and 95% CL negative log-likelihood contours in the ($\mu^{f}_{gg\mathrm{F}+ttH}$,$\mu^{f}_{\mathrm{VBF}+VH}$) plane for the $H\rightarrow\tau\tau$ channel.

Best-fit and 68% and 95% CL negative log-likelihood contours in the ($\mu^{f}_{gg\mathrm{F}+ttH}$,$\mu^{f}_{\mathrm{VBF}+VH}$) plane for the $H\rightarrow bb$ channel.

Upper limits on $\mathcal{B}(H\rightarrow aa\rightarrow bb\mu\mu)$ at 95% CL including the BDT cut as a function of the signal mass.

Upper limits on $\mathcal{B}(H\rightarrow aa\rightarrow bb\mu\mu)$ at 95% CL without the BDT cut as a function of the signal mass.

The number of events when applying each cut in the analysis for $m_a$ = 16 GeV. The first row shows the approximate total number of events scaled to the theoretical signal cross-section and luminosity of the full Run 2 dataset, assuming $ \mathcal{B}(H\rightarrow aa\rightarrow bb\mu\mu)$ = 0.16%.

The number of events when applying each cut in the analysis for $m_a$ = 20 GeV. The first row shows the approximate total number of events scaled to the theoretical signal cross-section and luminosity of the full Run 2 dataset, assuming $ \mathcal{B}(H\rightarrow aa\rightarrow bb\mu\mu)$ = 0.16%.

The number of events when applying each cut in the analysis for $m_a$ = 30 GeV. The first row shows the approximate total number of events scaled to the theoretical signal cross-section and luminosity of the full Run 2 dataset, assuming $ \mathcal{B}(H\rightarrow aa\rightarrow bb\mu\mu)$ = 0.16%.

The number of events when applying each cut in the analysis for $m_a$ = 40 GeV. The first row shows the approximate total number of events scaled to the theoretical signal cross-section and luminosity of the full Run 2 dataset, assuming $ \mathcal{B}(H\rightarrow aa\rightarrow bb\mu\mu)$ = 0.16%.

The number of events when applying each cut in the analysis for $m_a$ = 50 GeV. The first row shows the approximate total number of events scaled to the theoretical signal cross-section and luminosity of the full Run 2 dataset, assuming $ \mathcal{B}(H\rightarrow aa\rightarrow bb\mu\mu)$ = 0.16%.

The number of events when applying each cut in the analysis for $m_a$ = 60 GeV. The first row shows the approximate total number of events scaled to the theoretical signal cross-section and luminosity of the full Run 2 dataset, assuming $ \mathcal{B}(H\rightarrow aa\rightarrow bb\mu\mu)$ = 0.16%.

The efficiency for simulated VBF events to pass each analysis cut.

The efficiency for simulated VH events to pass each analysis cut.

The efficiency for simulated ttH events to pass each analysis cut.

The fractional contribution of each production mode to a given analysis region around the Higgs boson peak, defined as 105 < mJ < 140 GeV. The fraction is given with respect to the total signal yield in the analysis region in question.

Signal acceptance times efficiency within the fiducial volume used in the fiducial region.

Signal acceptance times efficiency for the STXS volumes in the differential measurement. Along with the pTH requirements shown, |yH | < 2 is required. For events with pTH < 300 GeV, the acceptance times efficiency is less than 0.1 × 10−2.

Event yields and associated uncertainties after the global likelihood fit in the pT(H) > 450 GeV fiducial region. The total background yield can differ from the sum of the individual components due to rounding.

Event yields and associated uncertainties after the global likelihood fit of the differential regions. The total background yield can differ from the sum of the individual components due to rounding. The five STXS volumes are labeled pT0–pT4 corresponding to pTH < 300 GeV, 300 – 450 GeV, 450 – 650 GeV, 650 – 1000 GeV, and > 1000 GeV, respectively. The pT0 event yield is constrained to its SM value within the theoretical and experimental uncertainties and free parameters act independently on the remaining four volumes.

Negative log-likelihood contours corresponding to 68% and 95% CL in the ($\kappa_{V}$, $\kappa_{F}$) plane obtained from a combined fit, assuming no contributions from invisible or undetected non-SM Higgs boson decays.

Reduced coupling strength modifiers $\kappa_{F}\cdot m_{F}/\text{vev}$ for fermions ($F=t,\,b,\,\tau,\,\mu$) and $\sqrt{\kappa_{V}}\cdot m_{V}/\text{vev}$ for vector bosons as a function of their masses $m_{F}$ and $m_{V}$ with vev = 246 GeV. Fit scenario with $\kappa_{c}=\kappa_{t}$ (coloured circle markers) is shown. Loop-induced processes are assumed to have the SM structure, and Higgs boson decays to non-SM particles are not allowed. The $p$-value for compatibility of the combined measurement and the SM prediction is 56%. The lower panel shows the values of the coupling strength modifiers.

Reduced coupling strength modifiers $\kappa_{F}\cdot m_{F}/\text{vev}$ for fermions ($F=t,\,b,\,\tau,\,\mu$) and $\sqrt{\kappa_{V}}\cdot m_{V}/\text{vev}$ for vector bosons as a function of their masses $m_{F}$ and $m_{V}$ with vev = 246 GeV. Fit scenario with $\kappa_{c}$ left free-floating (grey cross markers) is shown. Loop-induced processes are assumed to have the SM structure, and Higgs boson decays to non-SM particles are not allowed. The $p$-value for compatibility of the combined measurement and the SM prediction is 65%. The lower panel shows the values of the coupling strength modifiers. The grey arrow points in the direction of the best-fit value and the grey uncertainty bar extends beyond the lower panel range.

Reduced coupling strength modifiers and their uncertainties per particle type with effective photon, $Z\gamma$ and gluon couplings. The scenario where $B_{inv.}=B_{u.}=0$ is assumed is shown as solid lines. The $p$-value for compatibility with the SM prediction is 61% in this case. The scenario where $B_{inv.}$ and $B_{u.}$ are allowed to contribute to the total Higgs boson decay width while assuming that $\kappa_{V}\le1$ and $B_{u.}\ge0$ is shown as dashed lines.

Reduced coupling strength modifiers and their uncertainties per particle type with effective photon, $Z\gamma$ and gluon couplings. The scenario where $B_{inv.}$ and $B_{u.}$ are allowed to contribute to the total Higgs boson decay width while assuming that $\kappa_{V}\le1$ and $B_{u.}\ge0$ is shown as dashed lines. The lower panel shows the 95% CL upper limits on $B_{inv.}$ and $B_{u.}$.

Observed and predicted Higgs boson production cross sections in different kinematic regions. The $p$-value for compatibility of the combined measurement and the SM prediction is 94%. Kinematic regions are defined separately for each production process, based on the jet multiplicity, the transverse momentum of the Higgs ($p_{T}^{H}$) and vector bosons ($p_{T}^{W}$ and $p_{T}^{Z}$) and the two-jet invariant mass ($m_{jj}$). The VH-enriched and VBF-enriched regions with the respective requirements of $m_{jj}\in[60, 120)$ GeV and $m_{jj}\notin[60, 120)$ GeV are enhanced in signal events from $VH$ and VBF productions, respectively.

Observed variations of −2 ln $\Lambda(\mu)$ as a function of $\mu$ with all systematic uncertainties included.

Observed variations of −2 ln $\Lambda(\mu)$ as a function of $\mu$ with with parameters describing theory uncertainties in background processes fixed to their best-fit values.

Observed variations of −2 ln $\Lambda(\mu)$ as a function of $\mu$ with parameters describing theory uncertainties in background and signal processes fixed to their best-fit values.

Observed variations of −2 ln $\Lambda(\mu)$ as a function of $\mu$ with all systematic uncertainties fixed to their best-fit values.

Cross sections for ggF, VBF, $WH$, $ZH$, $t\bar{t}H$ and $tH$ production modes. The cross sections are normalized to their SM predictions, measured assuming SM values for the decay branching fractions. The black error bars, blue boxes and yellow boxes show the total, systematic, and statistical uncertainties in the measurements, respectively. The gray bands indicate the theory uncertainties on the SM cross section predictions. The level of compatibility between the measurement and the SM prediction corresponds to a $p$-value of $p_{SM}=65\%$.

Correlation matrix from the measurement of ggF, VBF, $WH$, $ZH$, $ttH$ and $tH$ production cross sections without theory uncertainties.

Correlation matrix from the measurement of ggF, VBF, $WH$, $ZH$, $ttH$ and $tH$ production cross sections with the theory uncertainties.

Cross sections for ggF, VBF, $WH$, $ZH$, $t\bar{t}H+tH$ production modes, obtained without including the theory uncertainties on the predicted SM cross sections in the fit. The cross sections are normalized to their SM predictions, measured assuming SM values for the decay branching fractions. The black error bars, blue boxes and yellow boxes show the total, systematic, and statistical uncertainties in the measurements, respectively. The gray bands indicate the theory uncertainties on the SM cross section predictions. The level of compatibility between the measurement and the SM prediction corresponds to a $p$-value of $p_{SM}=89\%$.

Correlation matrix from the measurement of ggF, VBF, $WH$, $ZH$, $ttH+tH$ production cross sections without theory uncertainties.

Correlation matrix from the measurement of the branching fractions, assuming SM values for the decay production cross sections and no contributions from non-SM decays to the total Higgs boson decay width.

Correlation matrix from the measured values of the production cross sections times branching fractions of the Higgs boson, for the combinations in which sufficient sensitivity is provided by the input analyses.

Observed correlation matrix from the fit of $\kappa_{V}$ and $\kappa_{F}$ coupling modifiers. No contributions from non-SM invisible and undetected Higgs boson decays are allowed, i.e. $B_{inv.}=B_{u.}=0$.

Negative log-likelihood contour corresponding to 68% CL in the ($\kappa_{V}$, $\kappa_{F}$) plane, corresponding to $H\to\gamma\gamma$ decay, obtained from a combined fit, assuming no contributions from invisible or undetected non-SM Higgs boson decays.

Negative log-likelihood contour corresponding to 68% CL in the ($\kappa_{V}$, $\kappa_{F}$) plane, corresponding to $H\to ZZ$ decay, obtained from a combined fit, assuming no contributions from invisible or undetected non-SM Higgs boson decays.

Negative log-likelihood contour corresponding to 68% CL in the ($\kappa_{V}$, $\kappa_{F}$) plane, corresponding to $H\to\tau\tau$ decay, obtained from a combined fit, assuming no contributions from invisible or undetected non-SM Higgs boson decays.

Negative log-likelihood contour corresponding to 68% CL in the ($\kappa_{V}$, $\kappa_{F}$) plane, corresponding to $H\to WW$ decay, obtained from a combined fit, assuming no contributions from invisible or undetected non-SM Higgs boson decays.

Negative log-likelihood contour corresponding to 68% CL in the ($\kappa_{V}$, $\kappa_{F}$) plane, corresponding to $H\to bb$ decay, obtained from a combined fit, assuming no contributions from invisible or undetected non-SM Higgs boson decays.

Observed correlation matrix from the fit of $\kappa_{Z}$, $\kappa_{W}$, $\kappa_{b}$, $\kappa_{t}$, $\kappa_{\tau}$ and $\kappa_{\mu}$ coupling modifiers with $\kappa_{c}$ = $\kappa_{t}$ in the fit. All fitted parameters are assumed to be positive. No contributions from non-SM invisible and undetected Higgs boson decays are allowed, i.e. $B_{inv.}=B_{u.}=0$.

Observed correlation matrix from the fit of the $\kappa_{Z}$, $\kappa_{W}$, $\kappa_{b}$, $\kappa_{t}$, $\kappa_{\tau}$, $\kappa_{\mu}$ and effective photon, $Z \gamma$ and gluon coupling modifiers. No contributions from non-SM invisible and undetected Higgs boson decays are allowed, i.e. $B_{inv.}=B_{u.}=0$.

Coupling-strength modifiers and their uncertainties for the effective photon, $Z\gamma$ and gluon couplings as free parameters and all other coupling modifiers set to unity. The scenario where $B_{inv.}=B_{u.}=0$ is assumed is shown as solid lines. The $p$-value of the compatibility with the SM prediction is 63% in this case. The scenario where $B_{inv.}$ and $B_{u.}$ are allowed to contribute to the total Higgs width is shown as dashed lines, with the corresponding $p$-value of 49%. Both $B_{inv.}$ and $B_{u.}$ are allowed to take negative values in the latter case.

Coupling-strength modifiers and their uncertainties for the effective photon, $Z\gamma$ and gluon couplings as free parameters and all other coupling modifiers set to unity. The scenario where $B_{inv.}$ and $B_{u.}$ are allowed to contribute to the total Higgs width is shown as dashed lines, with the corresponding $p$-value of 49%. Both $B_{inv.}$ and $B_{u.}$ are allowed to take negative values. The lower pad shows the 95% CL upper limits on $B_{inv.}$ and $B_{u.}$.

Negative log-likelihood contours corresponding to 68% and 95% CL in the ($\kappa_{g}$, $\kappa_{\gamma}$) plane obtained from a combined fit of ($\kappa_{g}$, $\kappa_{\gamma}$ and $\kappa_{Z\gamma}$) .

Measured ratios of coupling modifiers. The red line indicates the SM value of unity for each parameter. The level of compatibility between the combined measurement and the SM prediction corresponds to a $p$-value of 71% with ten degrees of freedom.

Best-fit values and uncertainties for the cross sections in each measurement region, normalized to the SM predictions for the various parameters. The measurements assume SM branching fractions for all measured decays. The black error bars, blue boxes and yellow boxes show the total, systematic, and statistical uncertainties in the measurements, respectively. The gray bands show the theory uncertainties on the predictions. The level of compatibility between the combined measurement and the SM prediction corresponds to a $p$-value of 94%.

Correlation matrix for the measured values of the simplified template cross sections.

Expected negative log-likelihood scans as a function of $\kappa_{Z}$.

Observed negative log-likelihood scans as a function of $\kappa_{Z}$.

Expected negative log-likelihood scans as a function of $\kappa_{W}$.

Observed negative log-likelihood scans as a function of $\kappa_{W}$.

Expected negative log-likelihood scans as a function of $\kappa_{t}$.

Observed negative log-likelihood scans as a function of $\kappa_{t}$.

Expected negative log-likelihood scans as a function of $\kappa_{b}$.

Observed negative log-likelihood scans as a function of $\kappa_{b}$.

Expected negative log-likelihood scans as a function of $\kappa_{\tau}$.

Observed negative log-likelihood scans as a function of $\kappa_{\tau}$.

Expected negative log-likelihood scans as a function of $\kappa_{\mu}$.

Observed negative log-likelihood scans as a function of $\kappa_{\mu}$.

Expected negative log-likelihood scans as a function of $\kappa_{g}$.

Observed negative log-likelihood scans as a function of $\kappa_{g}$.

Expected negative log-likelihood scans as a function of $\kappa_{\gamma}$.

Observed negative log-likelihood scans as a function of $\kappa_{\gamma}$.

Expected negative log-likelihood scans as a function of $\kappa_{Z\gamma}$.

Observed negative log-likelihood scans as a function of $\kappa_{Z\gamma}$.

Expected negative log-likelihood scans as a function of $B_{inv.}$.

Observed negative log-likelihood scans as a function of $B_{inv.}$.

Expected negative log-likelihood scans as a function of $B_{u.}$.

Observed negative log-likelihood scans as a function of $B_{u.}$.

The acceptances of STXS stage 1.2 kinematic regions in the Higgs boson production processes.

The BDT distribution (with x-axis zoomed in) of the di-Higgs ggF signal for two different values of $\kappa_{\lambda}$ and the main backgrounds in the high mass region ($m^{*}_{b\bar{b}\gamma\gamma} > 350$ GeV). Distributions are normalized to unit area. The dotted lines denote the category boundaries. Events with a BDT score below 0.857 in the high mass region are discarded. The range of BDT scores is from 0.8 to 1.

The $BDT_{tot}$ score for the benchmark signal $m_{X}$ = 300 GeV and for the main backgrounds. Distributions are normalized to unit area. The dotted line denotes the event selection threshold. Events with a $BDT_{tot}$ score below 0.85 for $m_{X}$ = 300 GeV are discarded.

The $BDT_{tot}$ score for the benchmark signal $m_{X}$ = 500 GeV and for the main backgrounds. Distributions are normalized to unit area. The dotted line denotes the event selection threshold. Events with a $BDT_{tot}$ score below 0.75 for $m_{X}$ = 500 GeV are discarded.

Distributions of $m_{\gamma\gamma}$ in high mass BDT tight category for the nonresonant $HH$ search. The data-derived fractions of nonresonant $\gamma\gamma$, $\gamma$-jet or jet-$\gamma$, and dijet background are applied and the total background is normalized to the data sideband.

Distributions of $m_{\gamma\gamma}$ in high mass BDT loose category for the nonresonant $HH$ search. The data-derived fractions of nonresonant $\gamma\gamma$, $\gamma$-jet or jet-$\gamma$, and dijet background are applied and the total background is normalized to the data sideband.

Distributions of $m_{\gamma\gamma}$ in low mass BDT tight category for the nonresonant $HH$ search. The data-derived fractions of nonresonant $\gamma\gamma$, $\gamma$-jet or jet-$\gamma$, and dijet background are applied and the total background is normalized to the data sideband.

Distributions of $m_{\gamma\gamma}$ in low mass BDT loose category for the nonresonant $HH$ search. The data-derived fractions of nonresonant $\gamma\gamma$, $\gamma$-jet or jet-$\gamma$, and dijet background are applied and the total background is normalized to the data sideband.

Distributions of $m_{\gamma\gamma}$ for the selections used for the resonance mass point $m_{X}$ = 300 GeV for the resonant search. The data-derived fractions of nonresonant $\gamma\gamma$, $\gamma$-jet or jet-$\gamma$, and dijet background are applied and the total background is normalized to the data sideband. The scalar resonance signal is scaled to a total production cross section $\sigma(pp \rightarrow X \rightarrow HH)$ = 370 fb.

Distributions of $m_{\gamma\gamma}$ for the selections used for the resonance mass point $m_{X}$ = 500 GeV for the resonant search. The data-derived fractions of nonresonant $\gamma\gamma$, $\gamma$-jet or jet-$\gamma$, and dijet background are applied and the total background is normalized to the data sideband. The scalar resonance signal is scaled to a total production cross section $\sigma(pp \rightarrow X \rightarrow HH)$ = 67 fb.

The number of data events observed in the 120 GeV < $m_{\gamma\gamma}$ < 130 GeV window, the number of $HH$ signal events expected for $\kappa_{\lambda}$ = 1 and for $\kappa_{\lambda}$ = 10, and events expected for single Higgs boson production (estimated using MC simulation), as well as for continuum background. For the single Higgs boson, Rest includes VBF, $WH$, $tHqb$, and $tHW$. The values are obtained from a fit of the Asimov data set generated under the SM signal-plus-background hypothesis, $\kappa_{\lambda}$ = 1. The continuum background component of the Asimov data set is obtained from the fit of the data sideband. The uncertainties in $HH$ signals and single Higgs boson background include the systematic uncertainties discussed in Section 6. The uncertainty in the continuum background is given by the sum in quadrature of the statistical uncertainty from the fit to the data and the spurious-signal uncertainty.

Observed and expected limits at 95% CL on the cross section of nonresonant Higgs boson pair production as a function of the Higgs boson self-coupling modifier $\kappa_{\lambda}= \lambda_{HHH}/\lambda^{\textrm{SM}}_{HHH}$. The expected constraints on $\kappa_{\lambda}$ are obtained with a background hypothesis excluding $pp \rightarrow HH$ production. The $\pm 1\sigma$ and $\pm 2\sigma$ variations about the expected limit due to statistical and systematic uncertainties are also shown. The theory prediction curve represents the scenario where all parameters and couplings are set to their SM values except for $\kappa_{\lambda}$. The uncertainty band of the theory prediction curve shows the cross-section uncertainty.

Values of the negative log-profile-likelihood ratio ($-2ln\Lambda$) as a function of $\kappa_{\lambda}$ evaluated for the combination of all the categories of the nonresonant search. The coupling of the Higgs boson to fermions and gauge bosons is set to SM values in the profile likelihood calculation. The Asimov data set is generated under the SM signal-plus-background hypothesis, $\kappa_{\lambda}$= 1. All systematic uncertainties, including the theoretical uncertainties in the di-Higgs boson production cross section, are included. The intersections of the solid curves and the horizontal dashed lines indicate the 1$\sigma$ and 2$\sigma$ confidence-level intervals.

The number of events observed in the 120 < $m_{\gamma\gamma}$ < 130 GeV window in data, the number of events expected for scalar resonance signals of masses $m_{X}$ = 300 GeV and $m_{X}$ = 500 GeV assuming a total production cross section $\sigma(pp \rightarrow X \rightarrow HH)$ equal to the observed exclusion limits of Figure 15, and events expected for SM $HH$ and single Higgs boson production (estimated using MC simulation), as well as for continuum background. The values are obtained from a fit of the Asimov data set generated under the signal-plus-background hypothesis. The continuum background component of the Asimov data set is obtained from the fit of the data sideband. The uncertainties in the resonant signals and the SM $HH$ and single-Higgs-boson backgrounds include the systematic uncertainties discussed in Section 6. The uncertainty in the continuum background is given by the sum in quadrature of the statistical uncertainty from the fit to the data and the spurious-signal uncertainty.

Observed and expected limits at 95% CL on the production cross section of a narrow-width scalar resonance $X$ as a function of the mass $m_{X}$ of the hypothetical scalar particle. The black solid line represents the observed upper limits. The dashed line represents the expected upper limits. The $\pm 1\sigma$ and $\pm 2\sigma$ variations about the expected limit due to statistical and systematic uncertainties are also shown.

Breakdown of the dominant systematic uncertainties. The impact of the uncertainties is defined according to the statistical analysis described in Section 7. It corresponds to the relative variation of the expected upper limit on the cross section when re-evaluating the profile likelihood ratio after fixing the nuisance parameter in question to its best-fit value, while all remaining nuisance parameters remain free to float. The impact is shown in %. Only systematic uncertainties with an impact of at least 0.2% are shown. Uncertainties of the "Norm. + Shape" type affect both the normalization and the parameters of the functional form. The rest of the uncertainties affect only the yields.

Cutflow for nonresonant di-Higgs ggF signal sample, yields are normalized to 139 $fb^{-1}$.

Cutflow for resonant signal sample, with $m_{X}$ = 300 GeV, yields are normalized to 139 $fb^{-1}$.

Cutflow for resonant signal sample, with $m_{X}$ = 500 GeV, yields are normalized to 139 $fb^{-1}$.

Comparison of $m_{b\bar{b}}$ distributions when applying the specific b-jet energy calibration and the nominal jet energy calibration. The distributions are fitted using a Bukin function, and the values of the peak position, resolution and the relative improvement are reported in the legend.

Fit results of $m_{b\bar{b}}$ distributions when applying the specific b-jet energy calibration and the nominal jet energy calibration. The distributions are fitted using a Bukin function, and the values of the peak position, resolution and the relative improvement are reported in the legend.

The relative amount (purity) of expected events from SM $HH$ and single Higgs boson production processes for each of the four categories of the nonresonant search. The Higgs boson pair production with $k_{\lambda} = 1$ is considered as signal in (a), while the case with $k_{\lambda} = 10$ is considered as signal in (b).

The expected significance in each of the four categories of the nonresonant search. The Higgs boson pair production with $k_{\lambda} = 1$ is considered as signal in (a), while the case with $k_{\lambda} = 10$ is considered as signal in (b). The single Higgs boson processes and the di-photon continuum spectrum are considered as background.

Spurious signal result for the exponential pdf for the various ggF nonresonant di-Higgs categories. In each category, the spurious signal value ($n_{sp}$) and its ratio to the expected statistical error ($Z_{spur}$) from data are shown.

Spurious signal result for the exponential pdf as function of the resonant di-Higgs signal mass. The spurious signal value and its ratio to the expected statistical error from data are shown.

Distributions of the signal efficiency as a function of $\kappa_{\lambda}$, for the di-Higgs boson ggF nonresonant production mode. The range of $\kappa_{\lambda}$ in the table is from -10 to 10.

Distributions of the signal efficiency as a function of $\kappa_{\lambda}$, for the di-Higgs boson VBF nonresonant production mode. The range of $\kappa_{\lambda}$ in the table is from -10 to 10.

Values of the negative log-profile-likelihood ($-2ln\Lambda$) as a function of $\kappa_{\lambda}$ evaluated for the combination of all the categories of the nonresonant search. The coupling of the Higgs boson to fermions and gauge bosons is set to SM values in the profile likelihood calculation. The Asimov data set is generated under the SM signal-plus-background hypothesis, $\kappa_{\lambda}$= 1. All systematic uncertainties, including the theoretical uncertainties on the di-Higgs boson production cross section, are included. The intersections of the solid curves and the horizontal dashed lines indicate the 1$\sigma$ and 2$\sigma$ confidence level intervals. The best fit value corresponds to $\kappa_{\lambda}$ = $2.8^{+2.0}_{-2.2}(^{+3.8}_{-4.3})$ for the 1$\sigma$(2$\sigma$) confidence interval. The expected value corresponds to $\kappa_{\lambda}$ = $1.0^{+5.5}_{-2.4}(^{+7.3}_{-4.2})$ for the 1$\sigma$(2$\sigma$) confidence interval. The dashed curves represent values of the negative log-profile-likelihood where the Higgs boson branching fractions and the cross section of the production modes are varied as a function of $\kappa_{\lambda}$. In this case,the best fit value corresponds to $\kappa_{\lambda}$ = $2.7^{+2.0}_{-2.2}(^{+3.8}_{-4.3})$ and the expected value corresponds to $\kappa_{\lambda}$ = $1.0^{+5.4}_{-2.5}(^{+7.3}_{-4.3})$ for the 1$\sigma$(2$\sigma$) confidence interval.

Minimum BDT value of the events passing the selection criteria of the resonant search. The combined BDT score is formed using as coefficients $C_{1}$ = 0.65 and $C_{2}$ = 1 − $C_{1}$. The selection efficiency for the resonant $X \rightarrow HH$ signal is also shown.

The 95% CL limits on the effective coupling constants. The scale of new physics is set to $\Lambda = 1$ TeV.

The 95% CL limits on the branching fractions. The scale of new physics is set to $\Lambda = 1$ TeV.

The pre-fit distribution of the NN discriminant for the FCNC $tu\gamma$ LH signal scaled to 10 times the observed limit and all SM backgrounds as well as measured data in the SR. The last bin of the distribution contains the overflow and the first bin also contains the underflow. The uncertainty band includes both the statistical and systematic uncertainties in the background prediction.

The pre-fit distribution of the photon transverse momentum for SM backgrounds as well as measured data in the $t\bar{t}\gamma$ CR. The last bin of the distribution contains the overflow. The uncertainty band includes both the statistical and systematic uncertainties in the background prediction.

The pre-fit distribution of the photon transverse momentum for the all SM backgrounds as well as measured data in the $W\gamma$+jets CR. The last bin of the distribution contains the overflow. The uncertainty band includes both the statistical and systematic uncertainties in the background prediction.

Pre-fit distribution of the reconstructed Higgs boson candidate $p_T^H$ for the dilepton $SR^{\geq 4j}_{\geq 4b}$ signal region. The dashed line shows the ${t\bar {t}H}$ signal distribution normalised to the total background prediction. The uncertainty band includes all uncertainties and their correlations, except for the uncertainty in the $k({t\bar {t}+{\geq }1b})$ normalisation factor which is not defined pre-fit. The last bin includes the overflow.

Pre-fit distribution of the reconstructed Higgs boson candidate $p_T^H$ for the single-lepton resolved $SR^{\geq 6j}_{\geq 4b}$ signal region. The dashed line shows the ${t\bar {t}H}$ signal distribution normalised to the total background prediction. The uncertainty band includes all uncertainties and their correlations, except for the uncertainty in the $k({t\bar {t}+{\geq }1b})$ normalisation factor which is not defined pre-fit. The last bin includes the overflow.

Pre-fit distribution of the reconstructed Higgs boson candidate $p_T^H$ for the single-lepton boosted ${{SR}_{{boosted}}}$ signal region. The dashed line shows the ${t\bar {t}H}$ signal distribution normalised to the total background prediction. The uncertainty band includes all uncertainties and their correlations, except for the uncertainty in the $k({t\bar {t}+{\geq }1b})$ normalisation factor which is not defined pre-fit. The last bin includes the overflow.

Comparison of predicted and observed event yields in each of the control and signal regions in the dilepton channel after the fit to the data. The uncertainty band includes all uncertainties and their correlations.

Comparison of predicted and observed event yields in each of the control and signal regions in the single-lepton channels after the fit to the data. The uncertainty band includes all uncertainties and their correlations.

Comparison between data and prediction for the BDT discriminant in the dilepton SRs after the inclusive fit to the data for $0\le p_T^H<120$ GeV. The ${t\bar {t}H}$ signal yield (solid red) is normalised to the fitted $\mu $ value from the inclusive fit. The dashed line shows the ${t\bar {t}H}$ signal distribution normalised to the total background prediction. The uncertainty band includes all uncertainties and their correlations.

Comparison between data and prediction for the BDT discriminant in the dilepton SRs after the inclusive fit to the data for $120\le p_T^H<200$ GeV. The ${t\bar {t}H}$ signal yield (solid red) is normalised to the fitted $\mu $ value from the inclusive fit. The dashed line shows the ${t\bar {t}H}$ signal distribution normalised to the total background prediction. The uncertainty band includes all uncertainties and their correlations.

Comparison between data and prediction for the BDT discriminant in the dilepton SRs after the inclusive fit to the data for $200\le p_T^H<300$ GeV. The ${t\bar {t}H}$ signal yield (solid red) is normalised to the fitted $\mu $ value from the inclusive fit. The dashed line shows the ${t\bar {t}H}$ signal distribution normalised to the total background prediction. The uncertainty band includes all uncertainties and their correlations.

Comparison between data and prediction for the BDT discriminant in the dilepton SRs after the inclusive fit to the data for $p_{{T}}^{H}\ge 300$ GeV. The ${t\bar {t}H}$ signal yield (solid red) is normalised to the fitted $\mu $ value from the inclusive fit. The dashed line shows the ${t\bar {t}H}$ signal distribution normalised to the total background prediction. The uncertainty band includes all uncertainties and their correlations.

Comparison between data and prediction for the BDT discriminant in the single-lepton resolved SRs after the inclusive fit to the data for $0\le p_T^H<120$ GeV. The ${t\bar {t}H}$ signal yield (solid red) is normalised to the fitted $\mu $ value from the inclusive fit. The dashed line shows the ${t\bar {t}H}$ signal distribution normalised to the total background prediction. The uncertainty band includes all uncertainties and their correlations.

Comparison between data and prediction for the BDT discriminant in the single-lepton resolved SRs after the inclusive fit to the data for $120\le p_T^H<200$ GeV. The ${t\bar {t}H}$ signal yield (solid red) is normalised to the fitted $\mu $ value from the inclusive fit. The dashed line shows the ${t\bar {t}H}$ signal distribution normalised to the total background prediction. The uncertainty band includes all uncertainties and their correlations.

Comparison between data and prediction for the BDT discriminant in the single-lepton resolved SRs after the inclusive fit to the data for $200\le p_T^H<300$ GeV. The ${t\bar {t}H}$ signal yield (solid red) is normalised to the fitted $\mu $ value from the inclusive fit. The dashed line shows the ${t\bar {t}H}$ signal distribution normalised to the total background prediction. The uncertainty band includes all uncertainties and their correlations.

Comparison between data and prediction for the BDT discriminant in the single-lepton resolved SRs after the inclusive fit to the data for $300\le p_T^H<450$ GeV. The ${t\bar {t}H}$ signal yield (solid red) is normalised to the fitted $\mu $ value from the inclusive fit. The dashed line shows the ${t\bar {t}H}$ signal distribution normalised to the total background prediction. The uncertainty band includes all uncertainties and their correlations.

Comparison between data and prediction for the BDT discriminant in the single-lepton resolved SRs after the inclusive fit to the data for $p_{{T}}^{H}\ge 450$ GeV (yield only). The ${t\bar {t}H}$ signal yield (solid red) is normalised to the fitted $\mu $ value from the inclusive fit. The dashed line shows the ${t\bar {t}H}$ signal distribution normalised to the total background prediction. The uncertainty band includes all uncertainties and their correlations.

Comparison between data and prediction for the BDT discriminant in the single-lepton boosted SRs after the inclusive fit to the data for $300\le p_T^H<450$ GeV. The ${t\bar {t}H}$ signal yield (solid red) is normalised to the fitted $\mu $ value from the inclusive fit. The dashed line shows the ${t\bar {t}H}$ signal distribution normalised to the total background prediction. The uncertainty band includes all uncertainties and their correlations.

Comparison between data and prediction for the BDT discriminant in the single-lepton boosted SRs after the inclusive fit to the data for $p_{{T}}^{H}\ge 450$ GeV. The ${t\bar {t}H}$ signal yield (solid red) is normalised to the fitted $\mu $ value from the inclusive fit. The dashed line shows the ${t\bar {t}H}$ signal distribution normalised to the total background prediction. The uncertainty band includes all uncertainties and their correlations.

Comparison between data and prediction for ${\Delta R^{{avg}}_{bb}}$ after the inclusive fit to the data in the single-lepton $CR^{5j}_{{\geq}4b\ lo}$ control region. The ${t\bar {t}H}$ signal yield (solid red) is normalised to the fitted $\mu $ value from the inclusive fit. The dashed line shows the ${t\bar {t}H}$ signal distribution normalised to the total background prediction. The uncertainty band includes all uncertainties and their correlations. The first (last) bin includes the underflow (overflow).

Comparison between data and prediction for ${\Delta R^{{avg}}_{bb}}$ after the inclusive fit to the data in the single-lepton $CR^{5j}_{{\geq}4b\ hi}$ control region. The ${t\bar {t}H}$ signal yield (solid red) is normalised to the fitted $\mu $ value from the inclusive fit. The dashed line shows the ${t\bar {t}H}$ signal distribution normalised to the total background prediction. The uncertainty band includes all uncertainties and their correlations. The first (last) bin includes the underflow (overflow).

Post-fit yields of signal ($S$) and total background ($B$) as a function of $\log (S/B)$, compared with data. Final-discriminant bins in all dilepton and single-lepton analysis regions are combined into bins of $\log (S/B)$, with the signal normalised to the SM prediction used for the computation of $\log (S/B)$. The signal is then shown normalised to the best-fit value and the SM prediction. The lower frame reports the ratio of data to background, and this is compared with the expected ${t\bar {t}H}$-signal-plus-background yield divided by the background-only yield for the best-fit signal strength (solid red line) and the SM prediction (dashed orange line).

Comparison between data and prediction for the reconstruction BDT score for the Higgs boson candidate identified using Higgs boson information, after the inclusive fit to the data in the dilepton resolved channel for $0\le p_T^H<120$ GeV. The ${t\bar {t}H}$ signal yield (solid red) is normalised to the fitted $\mu $ value from the inclusive fit. The dashed line shows the ${t\bar {t}H}$ signal distribution normalised to the total background prediction. The uncertainty band includes all uncertainties and their correlations.

Comparison between data and prediction for the average $\Delta \eta $ between $b$-tagged jets, after the inclusive fit to the data in the dilepton resolved channel for $0\le p_T^H<120$ GeV. The ${t\bar {t}H}$ signal yield (solid red) is normalised to the fitted $\mu $ value from the inclusive fit. The dashed line shows the ${t\bar {t}H}$ signal distribution normalised to the total background prediction. The uncertainty band includes all uncertainties and their correlations.

Comparison between data and prediction for the likelihood discriminant, after the inclusive fit to the data in the single-lepton resolved channel for $0\le p_T^H<120$ GeV. The ${t\bar {t}H}$ signal yield (solid red) is normalised to the fitted $\mu $ value from the inclusive fit. The dashed line shows the ${t\bar {t}H}$ signal distribution normalised to the total background prediction. The uncertainty band includes all uncertainties and their correlations.

Comparison between data and prediction for the average $\Delta R$ for all possible combinations of $b$-tagged jet pairs, after the inclusive fit to the data in the single-lepton resolved channel for $0\le p_T^H<120$ GeV. The ${t\bar {t}H}$ signal yield (solid red) is normalised to the fitted $\mu $ value from the inclusive fit. The dashed line shows the ${t\bar {t}H}$ signal distribution normalised to the total background prediction. The uncertainty band includes all uncertainties and their correlations.

Comparison between data and prediction for the DNN $P(H)$ output for the Higgs boson candidate after the inclusive fit to the data in the single-lepton boosted channel for $300\le p_T^H<450$ GeV. The ${t\bar {t}H}$ signal yield (solid red) is normalised to the fitted $\mu $ value from the inclusive fit. The dashed line shows the ${t\bar {t}H}$ signal distribution normalised to the total background prediction. The uncertainty band includes all uncertainties and their correlations.

Comparison between data and prediction for the DNN $P(H)$ output for the Higgs boson candidate after the inclusive fit to the data in the single-lepton boosted channel for $p_{{T}}^{H}\ge 450$ GeV. The ${t\bar {t}H}$ signal yield (solid red) is normalised to the fitted $\mu $ value from the inclusive fit. The dashed line shows the ${t\bar {t}H}$ signal distribution normalised to the total background prediction. The uncertainty band includes all uncertainties and their correlations.

Post-fit distribution of the reconstructed Higgs boson candidate mass for the dilepton $SR^{\geq 4j}_{\geq 4b}$ signal region. The ${t\bar {t}H}$ signal yield (solid red) is normalised to the fitted $\mu $ value from the inclusive fit. The dashed line shows the ${t\bar {t}H}$ signal distribution normalised to the total background prediction. The uncertainty band includes all uncertainties and their correlations. The first (last) bin includes the underflow (overflow).

Post-fit distribution of the reconstructed Higgs boson candidate mass for the single-lepton resolved $SR^{\geq 6j}_{\geq 4b}$ signal region. The ${t\bar {t}H}$ signal yield (solid red) is normalised to the fitted $\mu $ value from the inclusive fit. The dashed line shows the ${t\bar {t}H}$ signal distribution normalised to the total background prediction. The uncertainty band includes all uncertainties and their correlations. The first (last) bin includes the underflow (overflow).

Post-fit distribution of the reconstructed Higgs boson candidate mass for the single-lepton boosted ${{SR}_{{boosted}}}$ signal region. The ${t\bar {t}H}$ signal yield (solid red) is normalised to the fitted $\mu $ value from the inclusive fit. The dashed line shows the ${t\bar {t}H}$ signal distribution normalised to the total background prediction. The uncertainty band includes all uncertainties and their correlations. The first (last) bin includes the underflow (overflow).

Fitted values of the ${t\bar {t}H}$ signal strength parameter in the individual channels and in the inclusive signal-strength measurement.

Ranking of the 20 nuisance parameters with the largest post-fit impact on $\mu $ in the fit. Nuisance parameters corresponding to statistical uncertainties in the simulated event samples are not included. The empty blue rectangles correspond to the pre-fit impact on $\mu $ and the filled blue ones to the post-fit impact on $\mu $, both referring to the upper scale. The impact of each nuisance parameter, $\Delta \mu $, is computed by comparing the nominal best-fit value of $\mu $ with the result of the fit when fixing the considered nuisance parameter to its best-fit value, $\hat{\theta }$, shifted by its pre-fit (post-fit) uncertainties $\pm \Delta \theta $ ($\pm \Delta \hat{\theta }$). The black points show the pulls of the nuisance parameters relative to their nominal values, $\theta _0$. These pulls and their relative post-fit errors, $\Delta \hat{\theta }/\Delta \theta $, refer to the lower scale. The `ljets' (`dilep') label refers to the single-lepton (dilepton) channel.

Pre-fit distribution of the number of jets in the dilepton $SR^{\geq 4j}_{\geq 4b}$ signal region. The ${t\bar {t}H}$ signal yield (solid red) is normalised to the Standard Model expectation. The dashed line shows the ${t\bar {t}H}$ signal distribution normalised to the total background prediction. The uncertainty band includes all uncertainties and their correlations, except the uncertainty in the $k({t\bar {t}+{\geq }1b})$ normalisation factor that is not defined pre-fit.

Pre-fit distribution of the number of jets in the single-lepton resolved $SR^{\geq 6j}_{\geq 4b}$ signal region. The ${t\bar {t}H}$ signal yield (solid red) is normalised to the Standard Model expectation. The dashed line shows the ${t\bar {t}H}$ signal distribution normalised to the total background prediction. The uncertainty band includes all uncertainties and their correlations, except the uncertainty in the $k({t\bar {t}+{\geq }1b})$ normalisation factor that is not defined pre-fit.

Pre-fit distribution of the number of jets in the single-lepton boosted ${{SR}_{{boosted}}}$ signal region. The ${t\bar {t}H}$ signal yield (solid red) is normalised to the Standard Model expectation. The dashed line shows the ${t\bar {t}H}$ signal distribution normalised to the total background prediction. The uncertainty band includes all uncertainties and their correlations, except the uncertainty in the $k({t\bar {t}+{\geq }1b})$ normalisation factor that is not defined pre-fit.

Post-fit distribution of the number of jets in the dilepton $SR^{\geq 4j}_{\geq 4b}$ signal region. The ${t\bar {t}H}$ signal yield (solid red) is normalised to the fitted $\mu $ value from the inclusive fit. The dashed line shows the ${t\bar {t}H}$ signal distribution normalised to the total background prediction. The uncertainty band includes all uncertainties and their correlations.

Post-fit distribution of the number of jets in the single-lepton resolved $SR^{\geq 6j}_{\geq 4b}$ signal region. The ${t\bar {t}H}$ signal yield (solid red) is normalised to the fitted $\mu $ value from the inclusive fit. The dashed line shows the ${t\bar {t}H}$ signal distribution normalised to the total background prediction. The uncertainty band includes all uncertainties and their correlations.

Post-fit distribution of the number of jets in the single-lepton boosted ${{SR}_{{boosted}}}$ signal region. The ${t\bar {t}H}$ signal yield (solid red) is normalised to the fitted $\mu $ value from the inclusive fit. The dashed line shows the ${t\bar {t}H}$ signal distribution normalised to the total background prediction. The uncertainty band includes all uncertainties and their correlations.

Post-fit distribution of the reconstructed Higgs boson candidate $p_T^H$ for the dilepton $SR^{\geq 4j}_{\geq 4b}$ signal region. The ${t\bar {t}H}$ signal yield (solid red) is normalised to the fitted $\mu $ value from the inclusive fit. The dashed line shows the ${t\bar {t}H}$ signal distribution normalised to the total background prediction. The uncertainty band includes all uncertainties and their correlations. The last bin includes the overflow.

Post-fit distribution of the reconstructed Higgs boson candidate $p_T^H$ for the single-lepton resolved $SR^{\geq 6j}_{\geq 4b}$ signal region. The ${t\bar {t}H}$ signal yield (solid red) is normalised to the fitted $\mu $ value from the inclusive fit. The dashed line shows the ${t\bar {t}H}$ signal distribution normalised to the total background prediction. The uncertainty band includes all uncertainties and their correlations. The last bin includes the overflow.

Post-fit distribution of the reconstructed Higgs boson candidate $p_T^H$ for the single-lepton boosted ${{SR}_{{boosted}}}$ signal region. The ${t\bar {t}H}$ signal yield (solid red) is normalised to the fitted $\mu $ value from the inclusive fit. The dashed line shows the ${t\bar {t}H}$ signal distribution normalised to the total background prediction. The uncertainty band includes all uncertainties and their correlations. The last bin includes the overflow.

Signal-strength measurements in the individual STXS ${\hat{p}_{{T}}^{H}}$ bins, as well as the inclusive signal strength.

95% CL simplified template cross-section upper limits in the individual STXS ${\hat{p}_{{T}}^{H}}$ bins, as well as the inclusive limit. The observed limits are shown (solid black lines), together with the expected limits both in the background-only hypothesis (dotted black lines) and in the SM hypothesis (dotted red lines). In the case of the expected limits in the background-only hypothesis, one- and two-standard-deviation uncertainty bands are also shown. The hatched uncertainty bands correspond to the theory uncertainty in the fiducial cross-section prediction in each bin.

The ratios $S/B$ (black solid line, referring to the vertical axis on the left) and $S/\sqrt{B}$ (red dashed line, referring to the vertical axis on the right) for each category in the inclusive analysis in the dilepton channel (left) and in the single-lepton channels (right), where $S$ ($B$) is the number of selected signal (background) events predicted by the simulation and normalised to a luminosity of 139 fb$^{-1}$ .

Comparison between data and prediction for the $\Delta R$ between the Higgs candidate and the ${t\bar {t}}$ candidate system, after the inclusive fit to the data in the dilepton resolved channel for $0\le p_T^H<120$ GeV. The ${t\bar {t}H}$ signal yield (solid red) is normalised to the fitted $\mu $ value from the inclusive fit. The dashed line shows the ${t\bar {t}H}$ signal distribution normalised to the total background prediction. The uncertainty band includes all uncertainties and their correlations.

Comparison between data and prediction for the number of $b$-tagged jet pairs with an invariant mass within 30 GeV of 125 GeV, after the inclusive fit to the data in the dilepton resolved channel for $0\le p_T^H<120$ GeV. The ${t\bar {t}H}$ signal yield (solid red) is normalised to the fitted $\mu $ value from the inclusive fit. The dashed line shows the ${t\bar {t}H}$ signal distribution normalised to the total background prediction. The uncertainty band includes all uncertainties and their correlations.

Comparison between data and prediction for the reconstruction BDT score for the Higgs boson candidate identified using Higgs boson information, after the inclusive fit to the data in the single-lepton resolved channel for $0\le p_T^H<120$ GeV. The ${t\bar {t}H}$ signal yield (solid red) is normalised to the fitted $\mu $ value from the inclusive fit. The dashed line shows the ${t\bar {t}H}$ signal distribution normalised to the total background prediction. The uncertainty band includes all uncertainties and their correlations.

Comparison between data and prediction for the $\Delta R$ between the two highest ${p_{{T}}}$ $b$-tagged jets, after the inclusive fit to the data in the single-lepton resolved channel for $0\le p_T^H<120$ GeV. The ${t\bar {t}H}$ signal yield (solid red) is normalised to the fitted $\mu $ value from the inclusive fit. The dashed line shows the ${t\bar {t}H}$ signal distribution normalised to the total background prediction. The uncertainty band includes all uncertainties and their correlations.

Comparison between data and prediction for the sum of $b$-tagging discriminants of jets from Higgs, hadronic top and leptonic top candidates, after the inclusive fit to the data in the single-lepton boosted channel for $300\le p_T^H<450$ GeV. The ${t\bar {t}H}$ signal yield (solid red) is normalised to the fitted $\mu $ value from the inclusive fit. The dashed line shows the ${t\bar {t}H}$ signal distribution normalised to the total background prediction. The uncertainty band includes all uncertainties and their correlations. The first (last) bin includes the underflow (overflow).

Comparison between data and prediction for the sum of $b$-tagging discriminants of jets from Higgs, hadronic top and leptonic top candidates, after the inclusive fit to the data in the single-lepton boosted channel for $p_{{T}}^{H}\ge 450$ GeV. The ${t\bar {t}H}$ signal yield (solid red) is normalised to the fitted $\mu $ value from the inclusive fit. The dashed line shows the ${t\bar {t}H}$ signal distribution normalised to the total background prediction. The uncertainty band includes all uncertainties and their correlations. The first (last) bin includes the underflow (overflow).

Comparison between data and prediction for the hadronic top candidate invariant mass, after the inclusive fit to the data in the single-lepton boosted channel for $300\le p_T^H<450$ GeV. The ${t\bar {t}H}$ signal yield (solid red) is normalised to the fitted $\mu $ value from the inclusive fit. The dashed line shows the ${t\bar {t}H}$ signal distribution normalised to the total background prediction. The uncertainty band includes all uncertainties and their correlations. The first (last) bin includes the underflow (overflow).

Comparison between data and prediction for the hadronic top candidate invariant mass, after the inclusive fit to the data in the single-lepton boosted channel for $p_{{T}}^{H}\ge 450$ GeV. The ${t\bar {t}H}$ signal yield (solid red) is normalised to the fitted $\mu $ value from the inclusive fit. The dashed line shows the ${t\bar {t}H}$ signal distribution normalised to the total background prediction. The uncertainty band includes all uncertainties and their correlations. The first (last) bin includes the underflow (overflow).

Comparison between data and prediction for the fraction of the sum of $b$-tagging discriminants of all jets not associated to the Higgs or hadronic top candidates, after the inclusive fit to the data in the single-lepton boosted channel for $300\le p_T^H<450$ GeV. The ${t\bar {t}H}$ signal yield (solid red) is normalised to the fitted $\mu $ value from the inclusive fit. The dashed line shows the ${t\bar {t}H}$ signal distribution normalised to the total background prediction. The uncertainty band includes all uncertainties and their correlations. The first (last) bin includes the underflow (overflow).

Comparison between data and prediction for the fraction of the sum of $b$-tagging discriminants of all jets not associated to the Higgs or hadronic top candidates, after the inclusive fit to the data in the single-lepton boosted channel for $p_{{T}}^{H}\ge 450$ GeV. The ${t\bar {t}H}$ signal yield (solid red) is normalised to the fitted $\mu $ value from the inclusive fit. The dashed line shows the ${t\bar {t}H}$ signal distribution normalised to the total background prediction. The uncertainty band includes all uncertainties and their correlations. The first (last) bin includes the underflow (overflow).

Ranking of the 20 nuisance parameters with the largest post-fit impact on $\mu $ in the STXS fit for $0\le {\hat{p}_{{T}}^{H}}<120$ GeV. Nuisance parameters corresponding to statistical uncertainties in the simulated event samples are not included. The empty blue rectangles correspond to the pre-fit impact on $\mu $ and the filled blue ones to the post-fit impact on $\mu $, both referring to the upper scale. The impact of each nuisance parameter, $\Delta \mu $, is computed by comparing the nominal best-fit value of $\mu $ with the result of the fit when fixing the considered nuisance parameter to its best-fit value, $\hat{\theta }$, shifted by its pre-fit (post-fit) uncertainties $\pm \Delta \theta $ ($\pm \Delta \hat{\theta }$). The black points show the pulls of the nuisance parameters relative to their nominal values, $\theta _0$. These pulls and their relative post-fit errors, $\Delta \hat{\theta }/\Delta \theta $, refer to the lower scale. For experimental uncertainties that are decomposed into several independent sources, NP X corresponds to the X$^{th}$ nuisance parameter, ordered by their impact on $\mu $. The `ljets' (`dilep') label refers to the single-lepton (dilepton) channel.

Ranking of the 20 nuisance parameters with the largest post-fit impact on $\mu $ in the STXS fit for $120\le {\hat{p}_{{T}}^{H}}<200$ GeV. Nuisance parameters corresponding to statistical uncertainties in the simulated event samples are not included. The empty blue rectangles correspond to the pre-fit impact on $\mu $ and the filled blue ones to the post-fit impact on $\mu $, both referring to the upper scale. The impact of each nuisance parameter, $\Delta \mu $, is computed by comparing the nominal best-fit value of $\mu $ with the result of the fit when fixing the considered nuisance parameter to its best-fit value, $\hat{\theta }$, shifted by its pre-fit (post-fit) uncertainties $\pm \Delta \theta $ ($\pm \Delta \hat{\theta }$). The black points show the pulls of the nuisance parameters relative to their nominal values, $\theta _0$. These pulls and their relative post-fit errors, $\Delta \hat{\theta }/\Delta \theta $, refer to the lower scale. For experimental uncertainties that are decomposed into several independent sources, NP X corresponds to the X$^{th}$ nuisance parameter, ordered by their impact on $\mu $. The `ljets' (`dilep') label refers to the single-lepton (dilepton) channel.

Ranking of the 20 nuisance parameters with the largest post-fit impact on $\mu $ in the STXS fit for $200\le {\hat{p}_{{T}}^{H}}<300$ GeV. Nuisance parameters corresponding to statistical uncertainties in the simulated event samples are not included. The empty blue rectangles correspond to the pre-fit impact on $\mu $ and the filled blue ones to the post-fit impact on $\mu $, both referring to the upper scale. The impact of each nuisance parameter, $\Delta \mu $, is computed by comparing the nominal best-fit value of $\mu $ with the result of the fit when fixing the considered nuisance parameter to its best-fit value, $\hat{\theta }$, shifted by its pre-fit (post-fit) uncertainties $\pm \Delta \theta $ ($\pm \Delta \hat{\theta }$). The black points show the pulls of the nuisance parameters relative to their nominal values, $\theta _0$. These pulls and their relative post-fit errors, $\Delta \hat{\theta }/\Delta \theta $, refer to the lower scale. For experimental uncertainties that are decomposed into several independent sources, NP X corresponds to the X$^{th}$ nuisance parameter, ordered by their impact on $\mu $. The `ljets' (`dilep') label refers to the single-lepton (dilepton) channel.

Ranking of the 20 nuisance parameters with the largest post-fit impact on $\mu $ in the STXS fit for $300\le {\hat{p}_{{T}}^{H}}<450$ GeV. Nuisance parameters corresponding to statistical uncertainties in the simulated event samples are not included. The empty blue rectangles correspond to the pre-fit impact on $\mu $ and the filled blue ones to the post-fit impact on $\mu $, both referring to the upper scale. The impact of each nuisance parameter, $\Delta \mu $, is computed by comparing the nominal best-fit value of $\mu $ with the result of the fit when fixing the considered nuisance parameter to its best-fit value, $\hat{\theta }$, shifted by its pre-fit (post-fit) uncertainties $\pm \Delta \theta $ ($\pm \Delta \hat{\theta }$). The black points show the pulls of the nuisance parameters relative to their nominal values, $\theta _0$. These pulls and their relative post-fit errors, $\Delta \hat{\theta }/\Delta \theta $, refer to the lower scale. For experimental uncertainties that are decomposed into several independent sources, NP X corresponds to the X$^{th}$ nuisance parameter, ordered by their impact on $\mu $. The `ljets' (`dilep') label refers to the single-lepton (dilepton) channel.

Ranking of the 20 nuisance parameters with the largest post-fit impact on $\mu $ in the STXS fit for ${\hat{p}_{{T}}^{H}}\ge 450$ GeV. Nuisance parameters corresponding to statistical uncertainties in the simulated event samples are not included. The empty blue rectangles correspond to the pre-fit impact on $\mu $ and the filled blue ones to the post-fit impact on $\mu $, both referring to the upper scale. The impact of each nuisance parameter, $\Delta \mu $, is computed by comparing the nominal best-fit value of $\mu $ with the result of the fit when fixing the considered nuisance parameter to its best-fit value, $\hat{\theta }$, shifted by its pre-fit (post-fit) uncertainties $\pm \Delta \theta $ ($\pm \Delta \hat{\theta }$). The black points show the pulls of the nuisance parameters relative to their nominal values, $\theta _0$. These pulls and their relative post-fit errors, $\Delta \hat{\theta }/\Delta \theta $, refer to the lower scale. For experimental uncertainties that are decomposed into several independent sources, NP X corresponds to the X$^{th}$ nuisance parameter, ordered by their impact on $\mu $. The `ljets' (`dilep') label refers to the single-lepton (dilepton) channel.

95% confidence level upper limits on signal-strength measurements in the individual STXS ${\hat{p}_{{T}}^{H}}$ bins, as well as the inclusive signal-strength limit, after the fit used to extract multiple signal-strength parameters. The observed limits are shown (solid black lines), together with the expected limits both in the background-only hypothesis (dotted black lines) and in the SM hypothesis (dotted red lines). In the case of the expected limits in the background-only hypothesis, one- and two-standard-deviation uncertainty bands are also shown.

Post-fit correlation matrix (in percentages) between the $\mu $ values obtained in the STXS bins.

Performance of the Higgs boson reconstruction algorithms. For each row of `truth' ${\hat{p}_{{T}}^{H}}$, the matrix shows (in percentages) the fraction of Higgs boson candidates which are truth-matched to ${b\bar {b}}$ decays, with reconstructed $p_T^H$ in the various bins of the dilepton (left), single lepton resolved (middle) and boosted (right) channels.

Pre-fit event yields in the dilepton signal regions and control regions. All uncertainties are included except the $k({t\bar {t}+{\geq }1b})$ uncertainty that is not defined pre-fit. For the ${t\bar {t}H}$ signal, the pre-fit yield values correspond to the theoretical prediction and corresponding uncertainties. `Other sources' refers to s-channel, t-channel, $tW$, $tWZ$, $tZq$, $Z+$ jets and diboson events.

Post-fit event yields in the dilepton signal regions and control regions, after the inclusive fit in all channels. All uncertainties are included, taking into account correlations. For the ${t\bar {t}H}$ signal, the post-fit yield and uncertainties correspond to those in the inclusive signal-strength measurement. `Other sources' refers to s-channel, t-channel, $tW$, $tWZ$, $tZq$, $Z+$ jets and diboson events.

Pre-fit event yields in the single-lepton resolved and boosted signal regions and control regions. All uncertainties are included except the $k({t\bar {t}+{\geq }1b})$ uncertainty that is not defined pre-fit. For the ${t\bar {t}H}$ signal, the pre-fit yield values correspond to the theoretical prediction and corresponding uncertainties. `Other top sources' refers to s-channel, t-channel, $tWZ$ and $tZq$ events.

Post-fit event yields in the single-lepton resolved and boosted signal regions and control regions, after the inclusive fit in all channels. All uncertainties are included, taking into account correlations. For the ${t\bar {t}H}$ signal, the post-fit yield and uncertainties correspond to those in the inclusive signal-strength measurement. `Other top sources' refers to s-channel, t-channel, $tWZ$ and $tZq$ events.

Breakdown of the contributions to the uncertainties in $\mu$. The contributions from the different sources of uncertainty are evaluated after the fit. The $\Delta \mu $ values are obtained by repeating the fit after having fixed a certain set of nuisance parameters corresponding to a group of systematic uncertainties, and then evaluating $(\Delta \mu)^2$ by subtracting the resulting squared uncertainty of $\mu $ from its squared uncertainty found in the full fit. The same procedure is followed when quoting the effect of the ${t\bar {t}+{\geq }1b}$ normalisation. The total uncertainty is different from the sum in quadrature of the different components due to correlations between nuisance parameters existing in the fit.

Fraction (in percentages) of signal events, after SR and CR selections, originating from $b\bar {b}$, $WW$ and other remaining Higgs boson decay modes in the dilepton channel.

Fraction (in percentages) of signal events, after SR and CR selections, originating from $b\bar {b}$, $WW$ and other remaining Higgs boson decay modes in the single-lepton channels.

Predicted SM ${t\bar {t}H}$ cross-section in each of the five STXS ${\hat{p}_{{T}}^{H}}$ bins and signal acceptance times efficiency (including all event selection criteria) in each STXS bin as well as for the inclusive ${\hat{p}_{{T}}^{H}}$ range.

Number of expected signal events before the fit, after each selection requirement applied to enter the dilepton channel $SR^{\geq 4j}_{\geq 4b}$ region. All ${t\bar {t}H}$ signal events are included, regardless of the $H$ or ${t\bar {t}H}$ decay mode. All object corrections are applied, except for the initial number of events which is calculated using the NLO QCD+EW theoretical prediction. All quoted numbers are rounded to unity. More details on the selection criteria can be found in the text.

Number of expected signal events before the fit, after each selection requirement applied to enter the single-lepton channel resolved $SR^{\geq 6j}_{\geq 4b}$ region. All ${t\bar {t}H}$ signal events are included, regardless of the $H$ or ${t\bar {t}H}$ decay mode. All object corrections are applied, except for the initial number of events which is calculated using the NLO QCD+EW theoretical prediction. All quoted numbers are rounded to unity. More details on the selection criteria can be found in the text.

Number of expected signal events before the fit, after each selection requirement applied to enter the single-lepton channel boosted $SR_{boosted}$ region. All ${t\bar {t}H}$ signal events are included, regardless of the $H$ or ${t\bar {t}H}$ decay mode. All object corrections are applied, except for the initial number of events which is calculated using the NLO QCD+EW theoretical prediction. All quoted numbers are rounded to unity. More details on the selection criteria can be found in the text.

Observed and expected 95% CL lower limits on the $T$-quark mass as a function of the $T$-quark width-to-mass ratio and the branching fraction of the $T \rightarrow Ht$ decay ($\Gamma_{T}$ is the $T$-quark width).

Cutflow table listing the number of events passing each criterion for a $T$-quark hypothesis with a mass of 1.6 TeV and $\kappa_{T} = 0.5$. The initial signal event yield is the predicted number of $T$-quark events inclusive in the Higgs-boson and top-quark decays for 139 fb$^{-1}$.

Observed 95% CL upper limits on the single $T$-quark production cross-section as a function of the $T$-quark coupling $\kappa_{T}$ and $m_{T}$.

Expected 95% CL upper limits on the single $T$-quark production cross-section as a function of the $T$-quark coupling $\kappa_{T}$ and $m_{T}$.

Observed and expected 95% CL lower limits on the $T$-quark mass as a function of the $T$-quark width-to-mass ratio and the branching fraction of the $T \rightarrow Wb$ decay ($\Gamma_{T}$ is the $T$-quark width).