non prompt $\psi(2S)$ $\lambda_\theta$

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_\lambda$ parameter for $b\bar{b}\gamma\gamma$.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_\lambda$ parameter for $b\bar{b}\ell\ell+E_\text{T}^{\text{miss}}$.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_\lambda$ parameter for Multilepton.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_\lambda$ parameter for combination.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_{2V}$ parameter for $b\bar{b}b\bar{b}$.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_{2V}$ parameter for $b\bar{b}\tau\tau$.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_{2V}$ parameter for $b\bar{b}\gamma\gamma$.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_{2V}$ parameter for $b\bar{b}\ell\ell+E_\text{T}^{\text{miss}}$.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_{2V}$ parameter for Multilepton.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_{2V}$ parameter for combination.

Observed and expected 95% CL upper limits on the signal strength for the inclusive ggF HH production from the bb̄τ⁺τ^-, bb̄γγ, bb̄bb̄, multilepton and bb̄ℓℓ+E_T^miss decay channels, and their statistical combination. When deriving the limit on μ_ggF^HH (μ_VBF^HH), the VBF (ggF) HH production cross-section is fixed to the SM predicted value for m_H=125 GeV. The expected limit, along with the ±1σ and ±2σ bands, is calculated under the assumption of no HH process and with all NPs profiled to the observed data.

Observed and expected 95% CL upper limits on the signal strength for the VBF HH production from the bb̄τ⁺τ^-, bb̄γγ, bb̄bb̄, multilepton and bb̄ℓℓ+E_T^miss decay channels, and their statistical combination. When deriving the limit on μ_ggF^HH (μ_VBF^HH), the VBF (ggF) HH production cross-section is fixed to the SM predicted value for m_H=125 GeV. The expected limit, along with the ±1σ and ±2σ bands, is calculated under the assumption of no HH process and with all NPs profiled to the observed data.

Observed and expected upper limits at 95% CL on the inclusive ggF and VBF HH production cross-section from the bb̄τ⁺τ^-, bb̄γγ, bb̄bb̄, multilepton and bb̄ℓℓ+E_T^miss decay channels, and their statistical combination. The Higgs boson mass is set to 125 GeV when deriving the predicted SM cross-section (red band). The expected limits, along with the ±1σ and ±2σ bands, are calculated under the assumption of no Higgs boson pair production and with all NPs profiled to the observed data.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_\lambda$ parameter for $b\bar{b}b\bar{b}$.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_\lambda$ parameter for $b\bar{b}\tau\tau$.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_\lambda$ parameter for $b\bar{b}\gamma\gamma$.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_\lambda$ parameter for $b\bar{b}\ell\ell+E_\text{T}^{\text{miss}}$.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_\lambda$ parameter for Multilepton.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_\lambda$ parameter for combination.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_{2V}$ parameter for $b\bar{b}b\bar{b}$.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_{2V}$ parameter for $b\bar{b}\tau\tau$.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_{2V}$ parameter for $b\bar{b}\gamma\gamma$.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_{2V}$ parameter for $b\bar{b}\ell\ell+E_\text{T}^{\text{miss}}$.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_{2V}$ parameter for Multilepton.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_{2V}$ parameter for combination.

Observed (solid lines) and expected (dashed lines) 95% CL exclusion limits on the HH production cross-sections of (a) the inclusive ggF and VBF processes as a function of κ_λ, for the bb̄γγ (purple), bb̄τ⁺τ^- (green), multilepton (cyan), bb̄bb̄ (blue) and bb̄ℓℓ+E_T^miss (brown) decay channels and their combination (black). The expected limits assume no HH production. The red line shows the theory prediction for the ggF and VBF HH production cross-section as a function of κ_λ. The bands surrounding the red cross-section lines indicate the theoretical uncertainties on the predicted cross-section.

Observed (solid lines) and expected (dashed lines) 95% CL exclusion limits on the HH production cross-sections of the VBF process as a function of κ_2V, for the bb̄γγ (purple), bb̄τ⁺τ^- (green), multilepton (cyan), bb̄bb̄ (blue) and bb̄ℓℓ+E_T^miss (brown) decay channels and their combination (black). The expected limits assume no VBF HH production. The ggF HH production cross-section is assumed to be as predicted by the SM. The ggF HH production cross-section is assumed to be as predicted by the SM. The red line shows the predicted VBF HH cross-section as a function of κ_2V. The bands surrounding the red cross-section lines indicate the theoretical uncertainties on the predicted cross-section.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $c_{gghh}$ parameter for $b\bar{b}b\bar{b}$.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $c_{gghh}$ parameter for $b\bar{b}\tau\tau$.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $c_{gghh}$ parameter for $b\bar{b}\gamma\gamma$.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $c_{gghh}$ parameter for combination.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $c_{gghh}$ parameter for $b\bar{b}b\bar{b}$.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $c_{gghh}$ parameter for $b\bar{b}\tau\tau$.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $c_{gghh}$ parameter for $b\bar{b}\gamma\gamma$.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $c_{gghh}$ parameter for combination.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $c_{tthh}$ parameter for $b\bar{b}b\bar{b}$.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $c_{tthh}$ parameter for $b\bar{b}\tau\tau$.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $c_{tthh}$ parameter for $b\bar{b}\gamma\gamma$.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $c_{tthh}$ parameter for combination.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $c_{tthh}$ parameter for $b\bar{b}b\bar{b}$.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $c_{tthh}$ parameter for $b\bar{b}\tau\tau$.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $c_{tthh}$ parameter for $b\bar{b}\gamma\gamma$.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $c_{tthh}$ parameter for combination.

Observed and expected 95% CL combined upper limits on the cross-section for the SM and seven BSM HEFT benchmarks (arXiv:2304.01968 [hep-ph]) in the ggF process, describing representative signal kinematics and m_HH shape features obtained by varying multiple HEFT coefficients. The expected limits from the bb̄τ⁺τ^-, bb̄γγ and bb̄bb̄ decay channels are presented as well. Theoretical predictions, estimated using specific sets of coefficient values defined in the benchmarks, are shown as red cross dots.

The product of detector acceptance and analysis selection efficiency in the muon channel as functions of the particle X mass. Three analysis requirements are applied consecutively: event reconstruction, HLT, and final signal selection. The product of detector acceptance and analysis selection efficiencies are shown at each stage in red, blue, and orange, respectively.

Background-only fit to data. The lower panel contains the pull distribution, defined as the difference between the data yield and the background prediction divided by their combined uncertainty (electron channel).

Background-only fit to data. The lower panel contains the pull distribution, defined as the difference between the data yield and the background prediction divided by their combined uncertainty (muon channel).

The systematic uncertainties affecting signal normalization (electron channel).

The systematic uncertainties affecting signal normalization (muon channel).

The 95% CL expected and observed limits on P P --> X --> W gamma as a function of the resonant mass with leptonic decays of W bosons (narrow width).

The 95% CL expected and observed limits on P P --> X --> W gamma as a function of the resonant mass with leptonic decays of W bosons (broad width).

The 95% CL expected and observed limits on P P --> X --> W gamma as a function of the resonant mass with both leptonic and hadronic decays of W bosons (narrow width).

The 95% CL expected and observed limits on P P --> X --> W gamma as a function of the resonant mass with both leptonic and hadronic decays of W bosons (broad width).

The observed local p-values for narrow resonance width hypotheses.

The observed local p-values for broad resonance width hypotheses.

Correlation matrix from inclusive and normalized cross section measurements

Fiducial cross sections for $N_j = 0, 1, \geq 2$ jets. The total uncertainty is reported.

Covariance Matrix from fiducial and normalized cross sections measurements (total, and one and two jet bin fractions).

<b>Note: in the paper, uncertainties are given in relative terms. The HEPData table contains absolute numbers. The original data file, containing relative uncertainties as in the paper, is available via the 'Resources' button above.</b> Differential cross sections, $d\sigma/d\Delta\phi$, in the $p_{T,jet}^{lead}$ region of $2.5 \;\mathrm{GeV} < p_{T,jet}^{lead} < 7 \;\mathrm{GeV}$ for $N_{jet} \geq 3$, as obtained from the data, ARIADNE MC simulations, and perturbative calculations at $\mathcal{O}(\alpha_{s})$ and $\mathcal{O}(\alpha_{s}^{2})$ accuracy. Other details are as in the caption to Table 1.

<b>Note: in the paper, uncertainties are given in relative terms. The HEPData table contains absolute numbers. The original data file, containing relative uncertainties as in the paper, is available via the 'Resources' button above.</b> Differential cross sections, $d\sigma/d\Delta\phi$, in the $p_{T,jet}^{lead}$ region of $7 \;\mathrm{GeV} < p_{T,jet}^{lead} < 12 \;\mathrm{GeV}$ for $N_{jet} \geq 1$, as obtained from the data, ARIADNE MC simulations, and perturbative calculations at $\mathcal{O}(\alpha_{s})$ and $\mathcal{O}(\alpha_{s}^{2})$ accuracy. Other details are as in the caption to Table 1.

<b>Note: in the paper, uncertainties are given in relative terms. The HEPData table contains absolute numbers. The original data file, containing relative uncertainties as in the paper, is available via the 'Resources' button above.</b> Differential cross sections, $d\sigma/d\Delta\phi$, in the $p_{T,jet}^{lead}$ region of $7 \;\mathrm{GeV} < p_{T,jet}^{lead} < 12 \;\mathrm{GeV}$ for $N_{jet} \geq 2$, as obtained from the data, ARIADNE MC simulations, and perturbative calculations at $\mathcal{O}(\alpha_{s})$ and $\mathcal{O}(\alpha_{s}^{2})$ accuracy. Other details are as in the caption to Table 1.

<b>Note: in the paper, uncertainties are given in relative terms. The HEPData table contains absolute numbers. The original data file, containing relative uncertainties as in the paper, is available via the 'Resources' button above.</b> Differential cross sections, $d\sigma/d\Delta\phi$, in the $p_{T,jet}^{lead}$ region of $7 \;\mathrm{GeV} < p_{T,jet}^{lead} < 12 \;\mathrm{GeV}$ for $N_{jet} \geq 3$, as obtained from the data, ARIADNE MC simulations, and perturbative calculations at $\mathcal{O}(\alpha_{s})$ and $\mathcal{O}(\alpha_{s}^{2})$ accuracy. Other details are as in the caption to Table 1.

<b>Note: in the paper, uncertainties are given in relative terms. The HEPData table contains absolute numbers. The original data file, containing relative uncertainties as in the paper, is available via the 'Resources' button above.</b> Differential cross sections, $d\sigma/d\Delta\phi$, in the $p_{T,jet}^{lead}$ region of $12 \;\mathrm{GeV} < p_{T,jet}^{lead} < 30 \;\mathrm{GeV}$ for $N_{jet} \geq 1$, as obtained from the data, ARIADNE MC simulations, and perturbative calculations at $\mathcal{O}(\alpha_{s})$ and $\mathcal{O}(\alpha_{s}^{2})$ accuracy. Other details are as in the caption to Table 1.

<b>Note: in the paper, uncertainties are given in relative terms. The HEPData table contains absolute numbers. The original data file, containing relative uncertainties as in the paper, is available via the 'Resources' button above.</b> Differential cross sections, $d\sigma/d\Delta\phi$, in the $p_{T,jet}^{lead}$ region of $12 \;\mathrm{GeV} < p_{T,jet}^{lead} < 30 \;\mathrm{GeV}$ for $N_{jet} \geq 2$, as obtained from the data, ARIADNE MC simulations, and perturbative calculations at $\mathcal{O}(\alpha_{s})$ and $\mathcal{O}(\alpha_{s}^{2})$ accuracy. Other details are as in the caption to Table 1.

<b>Note: in the paper, uncertainties are given in relative terms. The HEPData table contains absolute numbers. The original data file, containing relative uncertainties as in the paper, is available via the 'Resources' button above.</b> Differential cross sections, $d\sigma/d\Delta\phi$, in the $p_{T,jet}^{lead}$ region of $12 \;\mathrm{GeV} < p_{T,jet}^{lead} < 30 \;\mathrm{GeV}$ for $N_{jet} \geq 3$, as obtained from the data, ARIADNE MC simulations, and perturbative calculations at $\mathcal{O}(\alpha_{s})$ and $\mathcal{O}(\alpha_{s}^{2})$ accuracy. Other details are as in the caption to Table 1.

<b>Note: in the paper, uncertainties are given in relative terms. The HEPData table contains absolute numbers. The original data file, containing relative uncertainties as in the paper, is available via the 'Resources' button above.</b> Differential cross sections, $d\sigma/d\Delta\phi$, in the $Q^{2}$ region of $10 \;\mathrm{GeV}^{2} < Q^{2} < 50 \;\mathrm{GeV}^{2}$ for $N_{jet} \geq 1$, as obtained from the data, ARIADNE MC simulations, and perturbative calculations at $\mathcal{O}(\alpha_{s})$ and $\mathcal{O}(\alpha_{s}^{2})$ accuracy. Other details are as in the caption to Table 1.

<b>Note: in the paper, uncertainties are given in relative terms. The HEPData table contains absolute numbers. The original data file, containing relative uncertainties as in the paper, is available via the 'Resources' button above.</b> Differential cross sections, $d\sigma/d\Delta\phi$, in the $Q^{2}$ region of $10 \;\mathrm{GeV}^{2} < Q^{2} < 50 \;\mathrm{GeV}^{2}$ for $N_{jet} \geq 2$, as obtained from the data, ARIADNE MC simulations, and perturbative calculations at $\mathcal{O}(\alpha_{s})$ and $\mathcal{O}(\alpha_{s}^{2})$ accuracy. Other details are as in the caption to Table 1.

<b>Note: in the paper, uncertainties are given in relative terms. The HEPData table contains absolute numbers. The original data file, containing relative uncertainties as in the paper, is available via the 'Resources' button above.</b> Differential cross sections, $d\sigma/d\Delta\phi$, in the $Q^{2}$ region of $10 \;\mathrm{GeV}^{2} < Q^{2} < 50 \;\mathrm{GeV}^{2}$ for $N_{jet} \geq 3$, as obtained from the data, ARIADNE MC simulations, and perturbative calculations at $\mathcal{O}(\alpha_{s})$ and $\mathcal{O}(\alpha_{s}^{2})$ accuracy. Other details are as in the caption to Table 1.

<b>Note: in the paper, uncertainties are given in relative terms. The HEPData table contains absolute numbers. The original data file, containing relative uncertainties as in the paper, is available via the 'Resources' button above.</b> Differential cross sections, $d\sigma/d\Delta\phi$, in the $Q^{2}$ region of $50 \;\mathrm{GeV}^{2} < Q^{2} < 100 \;\mathrm{GeV}^{2}$ for $N_{jet} \geq 1$, as obtained from the data, ARIADNE MC simulations, and perturbative calculations at $\mathcal{O}(\alpha_{s})$ and $\mathcal{O}(\alpha_{s}^{2})$ accuracy. Other details are as in the caption to Table 1.

<b>Note: in the paper, uncertainties are given in relative terms. The HEPData table contains absolute numbers. The original data file, containing relative uncertainties as in the paper, is available via the 'Resources' button above.</b> Differential cross sections, $d\sigma/d\Delta\phi$, in the $Q^{2}$ region of $50 \;\mathrm{GeV}^{2} < Q^{2} < 100 \;\mathrm{GeV}^{2}$ for $N_{jet} \geq 2$, as obtained from the data, ARIADNE MC simulations, and perturbative calculations at $\mathcal{O}(\alpha_{s})$ and $\mathcal{O}(\alpha_{s}^{2})$ accuracy. Other details are as in the caption to Table 1.

<b>Note: in the paper, uncertainties are given in relative terms. The HEPData table contains absolute numbers. The original data file, containing relative uncertainties as in the paper, is available via the 'Resources' button above.</b> Differential cross sections, $d\sigma/d\Delta\phi$, in the $Q^{2}$ region of $50 \;\mathrm{GeV}^{2} < Q^{2} < 100 \;\mathrm{GeV}^{2}$ for $N_{jet} \geq 3$, as obtained from the data, ARIADNE MC simulations, and perturbative calculations at $\mathcal{O}(\alpha_{s})$ and $\mathcal{O}(\alpha_{s}^{2})$ accuracy. Other details are as in the caption to Table 1.

<b>Note: in the paper, uncertainties are given in relative terms. The HEPData table contains absolute numbers. The original data file, containing relative uncertainties as in the paper, is available via the 'Resources' button above.</b> Differential cross sections, $d\sigma/d\Delta\phi$, in the $Q^{2}$ region of $100 \;\mathrm{GeV}^{2} < Q^{2} < 350 \;\mathrm{GeV}^{2}$ for $N_{jet} \geq 1$, as obtained from the data, ARIADNE MC simulations, and perturbative calculations at $\mathcal{O}(\alpha_{s})$ and $\mathcal{O}(\alpha_{s}^{2})$ accuracy. Other details are as in the caption to Table 1.

<b>Note: in the paper, uncertainties are given in relative terms. The HEPData table contains absolute numbers. The original data file, containing relative uncertainties as in the paper, is available via the 'Resources' button above.</b> Differential cross sections, $d\sigma/d\Delta\phi$, in the $Q^{2}$ region of $100 \;\mathrm{GeV}^{2} < Q^{2} < 350 \;\mathrm{GeV}^{2}$ for $N_{jet} \geq 2$, as obtained from the data, ARIADNE MC simulations, and perturbative calculations at $\mathcal{O}(\alpha_{s})$ and $\mathcal{O}(\alpha_{s}^{2})$ accuracy. Other details are as in the caption to Table 1.

<b>Note: in the paper, uncertainties are given in relative terms. The HEPData table contains absolute numbers. The original data file, containing relative uncertainties as in the paper, is available via the 'Resources' button above.</b> Differential cross sections, $d\sigma/d\Delta\phi$, in the $Q^{2}$ region of $100 \;\mathrm{GeV}^{2} < Q^{2} < 350 \;\mathrm{GeV}^{2}$ for $N_{jet} \geq 3$, as obtained from the data, ARIADNE MC simulations, and perturbative calculations at $\mathcal{O}(\alpha_{s})$ and $\mathcal{O}(\alpha_{s}^{2})$ accuracy. Other details are as in the caption to Table 1.

QED correction factors for inclusive measurement, as estimated with RAPGAP.

QED correction factors for $2.5 \;\mathrm{GeV} < p_{T,jet}^{lead} < 7 \;\mathrm{GeV}$ and $N_{jet} \geq 1$, as estimated with RAPGAP.

QED correction factors for $2.5 \;\mathrm{GeV} < p_{T,jet}^{lead} < 7 \;\mathrm{GeV}$ and $N_{jet} \geq 2$, as estimated with RAPGAP.

QED correction factors for $2.5 \;\mathrm{GeV} < p_{T,jet}^{lead} < 7 \;\mathrm{GeV}$ and $N_{jet} \geq 3$, as estimated with RAPGAP.

QED correction factors for $7 \;\mathrm{GeV} < p_{T,jet}^{lead} < 12 \;\mathrm{GeV}$ and $N_{jet} \geq 1$, as estimated with RAPGAP.

QED correction factors for $7 \;\mathrm{GeV} < p_{T,jet}^{lead} < 12 \;\mathrm{GeV}$ and $N_{jet} \geq 2$, as estimated with RAPGAP.

QED correction factors for $7 \;\mathrm{GeV} < p_{T,jet}^{lead} < 12 \;\mathrm{GeV}$ and $N_{jet} \geq 3$, as estimated with RAPGAP.

QED correction factors for $12 \;\mathrm{GeV} < p_{T,jet}^{lead} < 30 \;\mathrm{GeV}$ and $N_{jet} \geq 1$, as estimated with RAPGAP.

QED correction factors for $12 \;\mathrm{GeV} < p_{T,jet}^{lead} < 30 \;\mathrm{GeV}$ and $N_{jet} \geq 2$, as estimated with RAPGAP.

QED correction factors for $12 \;\mathrm{GeV} < p_{T,jet}^{lead} < 30 \;\mathrm{GeV}$ and $N_{jet} \geq 3$, as estimated with RAPGAP.

QED correction factors for $10 \;\mathrm{GeV}^{2} < Q^{2} < 50 \;\mathrm{GeV}^{2}$ and $N_{jet} \geq 1$, as estimated with RAPGAP.

QED correction factors for $10 \;\mathrm{GeV}^{2} < Q^{2} < 50 \;\mathrm{GeV}^{2}$ and $N_{jet} \geq 2$, as estimated with RAPGAP.

QED correction factors for $10 \;\mathrm{GeV}^{2} < Q^{2} < 50 \;\mathrm{GeV}^{2}$ and $N_{jet} \geq 3$, as estimated with RAPGAP.

QED correction factors for $50 \;\mathrm{GeV}^{2} < Q^{2} < 100 \;\mathrm{GeV}^{2}$ and $N_{jet} \geq 1$, as estimated with RAPGAP.

QED correction factors for $50 \;\mathrm{GeV}^{2} < Q^{2} < 100 \;\mathrm{GeV}^{2}$ and $N_{jet} \geq 2$, as estimated with RAPGAP.

QED correction factors for $50 \;\mathrm{GeV}^{2} < Q^{2} < 100 \;\mathrm{GeV}^{2}$ and $N_{jet} \geq 3$, as estimated with RAPGAP.

QED correction factors for $100 \;\mathrm{GeV}^{2} < Q^{2} < 350 \;\mathrm{GeV}^{2}$ and $N_{jet} \geq 1$, as estimated with RAPGAP.

QED correction factors for $100 \;\mathrm{GeV}^{2} < Q^{2} < 350 \;\mathrm{GeV}^{2}$ and $N_{jet} \geq 2$, as estimated with RAPGAP.

QED correction factors for $100 \;\mathrm{GeV}^{2} < Q^{2} < 350 \;\mathrm{GeV}^{2}$ and $N_{jet} \geq 3$, as estimated with RAPGAP.

The correlation matrix for the inclusive measurement. The azimuthal correlation angle $\Delta\phi$ of each lepton--leading-jet pair was assigned a bin ID between 0 to 59 segmented uniformly from 0 to $\pi$. This bin ID was offset by multiples of 60 based on the jet multiplicity so that the pair from a single jet event, as suggested by the MC simulation, was assigned a value between 0 to 59, dijet events were given 60 to 119, trijet 120 to 179, and four or more jets 180 to 239.

The correlation matrix for $2.5 \;\mathrm{GeV} < p_{T,jet}^{lead} < 7 \;\mathrm{GeV}$. Other details are as in the caption to Fig. 13.

The correlation matrix for $7 \;\mathrm{GeV} < p_{T,jet}^{lead} < 12 \;\mathrm{GeV}$. Other details are as in the caption to Fig. 13.

The correlation matrix for $12 \;\mathrm{GeV} < p_{T,jet}^{lead} < 30 \;\mathrm{GeV}$. Other details are as in the caption to Fig. 13.

The correlation matrix for $10 \;\mathrm{GeV}^{2} < Q^{2} < 50 \;\mathrm{GeV}^{2}$. Other details are as in the caption to Fig. 13.

The correlation matrix for $50 \;\mathrm{GeV}^{2} < Q^{2} < 100 \;\mathrm{GeV}^{2}$. Other details are as in the caption to Fig. 13.

The correlation matrix for $100 \;\mathrm{GeV}^{2} < Q^{2} < 350 \;\mathrm{GeV}^{2}$. Other details are as in the caption to Fig. 13.

Expected and observed exclusion limits at 95% CL in the asymptotic approximation, on the product of the production cross section and branching fraction into two photons for an additional SM-like Higgs boson, for the VBF plus VH processes, from the analysis of the combined data from 2016, 2017, and 2018.

Expected and observed exclusion limits at 95% CL in the asymptotic approximation, on the product of the production cross section and branching fraction into two photons for an additional SM-like Higgs boson, assuming 100% production via the VBF processes, from the analysis of the combined data from 2016, 2017, and 2018.

Expected and observed exclusion limits at 95% CL in the asymptotic approximation, on the product of the production cross section and branching fraction into two photons for an additional SM-like Higgs boson, assuming 100% production via the VH processes, from the analysis of the combined data from 2016, 2017, and 2018.

Histogram of the Hbb AK8 jet softdrop mass for data, simulated signal and background events, and the background yields estimated from data in region A.

Histogram of the Hbb AK8 jet softdrop mass for data and simulated signal and background events.

Histogram of $p_{T}(H) + p_{T}(W)$ at the LHE level.

The signal yield estimated by simulation, background yield predicted from data, and observed yield in the signal region.

Observed and expected BDT output in the signal region used for the extraction of the SM-like signal strength. The yields and uncertainties of the expected contributions are shown after the fit to the data. The rightmost bin includes the overflow.

Limits on the signal strength of SM VBS WH production

Observed and expected significance of the measurement of SM VBS WH production

95% confidence limits on the signal strength in the SM analysis

A scan of $-2\Delta\ln L$, where $L$ is the likelihood, for the SM analysis plotted as a function of the signal strength $\mu$ for the expected (red) and the observed (black) data.

The data, fitted signal, and background distributions for the VBS dijet mass in the $t\overline{t}$ control region of the SM analysis.

The data, fitted signal, and background distributions for the W+jets BDT score in the W+jets control region of the SM analysis.

Fitted SME coefficients and their uncertainties at 1$\sigma$ and 2$sigma$, measured in fits of single coefficients while the coefficients corresponding to the three other directions are left floating, within the $c_L$, $c_R$, $c$, and $d$ families. The error bar includes statistical and systematic uncertainties.

Uncertainty breakdown for SME fits of single coefficients while the coefficients corresponding to the three other directions are left floating, by splitting according to the treatment of time dependence:\ flat across sidereal time (flat luminosity component, background normalization, theory), correlated in sidereal time bins (trigger, luminosity stability and linearity, pileup, MC statistical uncertainty, single top quark decay in the SME), systematics uncorrelated in sidereal time bins (other experimental uncertainties), and statistical uncertainty.