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Summary of the impact of different categories of systematic uncertainties on the background estimate in BDT bins, after the background-only fit. The individual uncertainties can be correlated and do not necessarily add in quadrature to equal the total background uncertainty.

Observed and expected exclusion limits at 95% CL on BR(H$\to\gamma\gamma_d$) as function of the $\gamma_d$ mass.

Background, data and signal yields in bins of BDT, in the SR and in the VV$\gamma$ CR, before the background-only fit. The expectations for the signal are shown for the massless dark photon and for dark photon mass values of 20 GeV and 40 GeV, assuming BR(H$\to\gamma\gamma_d$) = 5%. Uncertainties are statistical for data, while for backgrounds include statistical and systematic sources.

Number of events after each cut in SR for 139fb$^{-1}$ for ZH, H$\to\gamma\gamma_d$ considering BR=5% and massless dark photon. Generator-level filters are applied on the total events. Only the statistical uncertainty is shown.

Distribution of the BDT classifier response in data and for the expected SM background after the background-only fit, in the ee channel. The expectations for signal are also shown for the massless dark photon and for dark photon mass values of 20 GeV and 40 GeV, assuming BR(H$\to\gamma\gamma_d$) = 5%. Uncertainties shown are statistical for data, while for backgrounds include statistical and systematic sources.

Distribution of the BDT classifier response for data and for the expected SM background after the background-only fit, in the $\mu\mu$ channel. The expectations for signal are also shown for the massless dark photon and for dark photon mass values of 20 GeV and 40 GeV, assuming BR(H$\to\gamma\gamma_d$) = 5%. Uncertainties shown are statistical for data, while for backgrounds include statistical and systematic sources.

Distribution of jet girth of CMS data, SM multijet MC events, and various signal samples. Events are required to pass the trigger requirements and also have 4 jets with $p_\mathrm{T}>100\mathrm{GeV}$. The distribution from various processes have their total count normalized to 1.

Distribution of uGNN output score of CMS data, SM multijet MC events, and various signal samples. Events are required to pass the trigger requirements and also have 4 jets with $p_\mathrm{T}>100\mathrm{GeV}$. The distribution from various processes have their total count normalized to 1.

Distribution of aGNN output score of CMS data, SM multijet MC events, and various signal samples. Events are required to pass the trigger requirements and also have 4 jets with $p_\mathrm{T}>100\mathrm{GeV}$. The distribution from various processes have their total count normalized to 1.

Template fit of the DeepJet discriminator used to determine the b jet fraction of the non-EMJ tagged jets in data events that pass the 1-EMJ selection of the event selection criteria defined in the paper.

The EJ tagger misidentification probability for b quark jets and light jets as a function of jet $p_\mathrm{T}$ for the taggers u-tag 1, u-tag 2, and u-tag 3, as defined in the paper, evaluated using data and generator-level flavor information from simulated samples in events containing a high-$p_\mathrm{T}$ photon.

The EJ tagger misidentification probability for b quark jets and light jets as a function of jet $p_\mathrm{T}$ for the taggers uGNN tag 1, uGNN tag 2, and uGNN tag 3, as defined in the paper, evaluated using data and generator-level flavor information from simulated samples in events containing a high-$p_\mathrm{T}$ photon.

The EJ tagger misidentification probability for b quark jets and light jets as a function of jet $p_\mathrm{T}$ for the taggers u-tag 4 and u-tag 5, as defined in the paper, evaluated using data and generator-level flavor information from simulated samples in events containing a high-$p_\mathrm{T}$ photon.

The expected and observed 95% CL upper limits on the production cross section for various signal models in the unflavored scenario model-generic and GNN EMJ tagging methods.

The expected and observed 95% CL upper limits on the production cross section for various signal models in the flavor-aligned scenario model-generic and GNN EMJ tagging methods.

The observed yield of events in data satisfying the validation selection criteria with at least two jets passing the corresponding validation tag, and the estimation based on the misidentification rate calculated using validation events with exactly one jet passing the validation tagger scaled by the factor given in Equation (4) of the paper.

The estimated number of events from the background prediction based on control samples in data and the observed event yields.

Distribution of event $H_\mathrm{T}$ of CMS data, SM multijet MC events, and various signal samples. Events are required to pass the trigger requirements and also have 4 jets with $p_\mathrm{T}>100\mathrm{GeV}$. The distribution from various processes have their total count normalized to 1.

Distribution of leading jet $p_\mathrm{T}$ of CMS data, SM multijet MC events, and various signal samples. Events are required to pass the trigger requirements and also have 4 jets with $p_\mathrm{T}>100\mathrm{GeV}$. The distribution from various processes have their total count normalized to 1.

Distribution of second leading jet $p_\mathrm{T}$ of CMS data, SM multijet MC events, and various signal samples. Events are required to pass the trigger requirements and also have 4 jets with $p_\mathrm{T}>100\mathrm{GeV}$. The distribution from various processes have their total count normalized to 1.

Distribution of third leading jet $p_\mathrm{T}$ of CMS data, SM multijet MC events, and various signal samples. Events are required to pass the trigger requirements and also have 4 jets with $p_\mathrm{T}>100\mathrm{GeV}$. The distribution from various processes have their total count normalized to 1.

Distribution of forth leading jet $p_\mathrm{T}$ of CMS data, SM multijet MC events, and various signal samples. Events are required to pass the trigger requirements and also have 4 jets with $p_\mathrm{T}>100\mathrm{GeV}$. The distribution from various processes have their total count normalized to 1.

Distribution of Track $d_{xy}$ of CMS data, SM multijet MC events, and various signal samples. Events are required to pass the trigger requirements and also have 4 jets with $p_\mathrm{T}>100\mathrm{GeV}$. The distribution from various processes have their total count normalized to 1.

Distribution of track $D_{N}$ of CMS data, SM multijet MC events, and various signal samples. Events are required to pass the trigger requirements and also have 4 jets with $p_\mathrm{T}>100\mathrm{GeV}$. The distribution from various processes have their total count normalized to 1.

Distribution of track $d_{xy}$ of CMS data, SM multijet MC events, and various signal samples. Events are required to pass the trigger requirements and also have 4 jets with $p_\mathrm{T}>100\mathrm{GeV}$. The distribution from various processes have their total count normalized to 1.

Distribution of jet $\overline{\tau}_{2/1}$ of CMS data, SM multijet MC events, and various signal samples. Events are required to pass the trigger requirements and also have 4 jets with $p_\mathrm{T}>100\mathrm{GeV}$. The distribution from various processes have their total count normalized to 1.

Distribution of $|\Delta\eta|$ between jet and tracks of CMS data, SM multijet MC events, and various signal samples. Events are required to pass the trigger requirements and also have 4 jets with $p_\mathrm{T}>100\mathrm{GeV}$. The distribution from various processes have their total count normalized to 1.

Distribution of $|\Delta\phi|$ between jet and tracks of CMS data, SM multijet MC events, and various signal samples. Events are required to pass the trigger requirements and also have 4 jets with $p_\mathrm{T}>100\mathrm{GeV}$. The distribution from various processes have their total count normalized to 1.

Distribution of track $d_{xy}$ of CMS data, SM multijet MC events, and various signal samples. Events are required to pass the trigger requirements and also have 4 jets with $p_\mathrm{T}>100\mathrm{GeV}$. The distribution from various processes have their total count normalized to 1.

Distribution of track $p_\mathrm{T}$ of CMS data, SM multijet MC events, and various signal samples. Events are required to pass the trigger requirements and also have 4 jets with $p_\mathrm{T}>100\mathrm{GeV}$. The distribution from various processes have their total count normalized to 1.

Distribution of track $d_{z}$ of CMS data, SM multijet MC events, and various signal samples. Events are required to pass the trigger requirements and also have 4 jets with $p_\mathrm{T}>100\mathrm{GeV}$. The distribution from various processes have their total count normalized to 1.

Distribution of track $p_\mathrm{T}$ fraction of CMS data, SM multijet MC events, and various signal samples. Events are required to pass the trigger requirements and also have 4 jets with $p_\mathrm{T}>100\mathrm{GeV}$. The distribution from various processes have their total count normalized to 1.

The EJ tagger misidentification probability for b quark jets and light jets as a function of jet $p_\mathrm{T}$ for the taggers a-tag 1, a-tag 2, a-tag 3, and a-tag 4, as defined in the paper, evaluated using data and generator-level flavor information from simulated samples in events containing a high-$p_\mathrm{T}$ photon.

The EJ tagger misidentification probability for b quark jets and light jets as a function of jet $p_\mathrm{T}$ for the taggers aGNN tag 1, aGNN tag 2, and aGNN tag 3, as defined in the paper, evaluated using data and generator-level flavor information from simulated samples in events containing a high-$p_\mathrm{T}$ photon.

Signal acceptance of signal models in the unflavored scenario with using the designated cut sets with the model agnostic and GNN EJ tagging methods.

Signal acceptance of signal models in the flavor-aligned scenario with using the designated cut sets with the model agnostic and GNN EJ tagging methods.

Tagging efficiency and its uncertainty of the taggers used to select signal jets in the unflavored scenario, as a function of the $p_\mathrm{T}$ and $|\eta|$ of the signal jet.

Tagging efficiency and its uncertainty of the taggers used to select signal jets in the unflavored scenario, as a function of the $p_\mathrm{T}$ and $|\eta|$ of the signal jet.

Tagging efficiency and its uncertainty of the taggers used to select signal jets in the unflavored scenario, as a function of the $p_\mathrm{T}$ and $|\eta|$ of the signal jet.

Tagging efficiency and its uncertainty of the taggers used to select signal jets in the unflavored scenario, as a function of the $p_\mathrm{T}$ and $|\eta|$ of the signal jet.

Tagging efficiency and its uncertainty of the taggers used to select signal jets in the unflavored scenario, as a function of the $p_\mathrm{T}$ and $|\eta|$ of the signal jet.

Tagging efficiency and its uncertainty of the taggers used to select signal jets in the unflavored scenario, as a function of the $p_\mathrm{T}$ and $|\eta|$ of the signal jet.

Tagging efficiency and its uncertainty of the taggers used to select signal jets in the unflavored scenario, as a function of the $p_\mathrm{T}$ and $|\eta|$ of the signal jet.

Tagging efficiency and its uncertainty of the taggers used to select signal jets in the unflavored scenario, as a function of the $p_\mathrm{T}$ and $|\eta|$ of the signal jet.

Tagging efficiency and its uncertainty of the taggers used to select signal jets in the unflavored scenario, as a function of the $p_\mathrm{T}$ and $|\eta|$ of the signal jet.

Tagging efficiency and its uncertainty of the taggers used to select signal jets in the unflavored scenario, as a function of the $p_\mathrm{T}$ and $|\eta|$ of the signal jet.

Tagging efficiency and its uncertainty of the taggers used to select signal jets in the flavor-aligned scenario, as a function of the $p_\mathrm{T}$ and $|\eta|$ of the signal jet.

Tagging efficiency and its uncertainty of the taggers used to select signal jets in the flavor-aligned scenario, as a function of the $p_\mathrm{T}$ and $|\eta|$ of the signal jet.

Tagging efficiency and its uncertainty of the taggers used to select signal jets in the flavor-aligned scenario, as a function of the $p_\mathrm{T}$ and $|\eta|$ of the signal jet.

Tagging efficiency and its uncertainty of the taggers used to select signal jets in the flavor-aligned scenario, as a function of the $p_\mathrm{T}$ and $|\eta|$ of the signal jet.

Tagging efficiency and its uncertainty of the taggers used to select signal jets in the flavor-aligned scenario, as a function of the $p_\mathrm{T}$ and $|\eta|$ of the signal jet.

Tagging efficiency and its uncertainty of the taggers used to select signal jets in the flavor-aligned scenario, as a function of the $p_\mathrm{T}$ and $|\eta|$ of the signal jet.

Tagging efficiency and its uncertainty of the taggers used to select signal jets in the flavor-aligned scenario, as a function of the $p_\mathrm{T}$ and $|\eta|$ of the signal jet.

Tagging efficiency and its uncertainty of the taggers used to select signal jets in the flavor-aligned scenario, as a function of the $p_\mathrm{T}$ and $|\eta|$ of the signal jet.

Tagging efficiency and its uncertainty of the taggers used to select signal jets in the flavor-aligned scenario, as a function of the $p_\mathrm{T}$ and $|\eta|$ of the signal jet.

Distribution of jet-associated tracks of jets in SM multijet processes that pass the basic kinematic selection, the uGNN tag 1 tagging criteria, and aGNN tag 1 EMJ tagging criteria as a function of $\Delta R$ between the jet and track of interest and $\mathrm{sign}(d_{xy})\cdot\ln\left( 1+\left\lvert\frac{d_{xy}}{1\mathrm{cm}}\right\rvert\right)$, with $d_{xy}$ being the transverse impact parameter of the track of interest.

Example cut flow used for selecting signals events using the u-set 4 selection criteria. Both background and MC events has been normalized to unity.

Example cut flow used for selecting signals events using the u-set 1 selection criteria. Both background and MC events has been normalized to unity.

Example cut flow used for selecting signals events using the u-set 2 selection criteria. Both background and MC events has been normalized to unity.

Example cut flow used for selecting signals events using the u-set 3 selection criteria. Both background and MC events has been normalized to unity.

Example cut flow used for selecting signals events using the u-set 5 selection criteria. Both background and MC events has been normalized to unity.

Example cut flow used for selecting signals events using the uGNN set 3 selection criteria. Both background and MC events has been normalized to unity.

Example cut flow used for selecting signals events using the uGNN set 1 selection criteria. Both background and MC events has been normalized to unity.

Example cut flow used for selecting signals events using the uGNN set 2 selection criteria. Both background and MC events has been normalized to unity.

Example cut flow used for selecting signals events using the a-set 3 selection criteria. Both background and MC events has been normalized to unity.

Example cut flow used for selecting signals events using the a-set 1 selection criteria. Both background and MC events has been normalized to unity.

Example cut flow used for selecting signals events using the a-set 2 selection criteria. Both background and MC events has been normalized to unity.

Example cut flow used for selecting signals events using the a-set 4 selection criteria. Both background and MC events has been normalized to unity.

Example cut flow used for selecting signals events using the a-set 5 selection criteria. Both background and MC events has been normalized to unity.

Example cut flow used for selecting signals events using the aGNN set 3 selection criteria. Both background and MC events has been normalized to unity.

Example cut flow used for selecting signals events using the aGNN set 1 selection criteria. Both background and MC events has been normalized to unity.

Example cut flow used for selecting signals events using the aGNN set 2 selection criteria. Both background and MC events has been normalized to unity.

Background-only-fit total covariance matrix for all channels and regions. Values are extracted from the Higgs Combine tool's fitDiagnostics option. Please see associated image ("fitRegions.pdf") for guide on region and channel setup.

Background-only-fit total covariance matrix for all channels and regions. Values are extracted from the Higgs Combine tool's fitDiagnostics option. Please see associated image ("fitRegions.pdf") for guide on region and channel setup.

Background-only-fit total covariance matrix for all channels and regions. Values are extracted from the Higgs Combine tool's fitDiagnostics option. Please see associated image ("fitRegions.pdf") for guide on region and channel setup.

The signal region is defined a an L-shaped band in the 2D collinear mass plane (min vs max collinear mass). The width of the band is chosen to be the value such that 90% of signal falls within the band for each taustar hypothesis mass

Observed upper limits on the cross section times branching fraction, as a function of the τ∗ mass, for single τ∗ production via a contact interaction in association with a SM τ. The dashed line shows the expected exclusion limit. The inner (green) band and the outer (yellow) band indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis.

Observed upper limits on the cross section times branching fraction, as a function of the τ∗ mass, for single τ∗ production via a contact interaction in association with a SM τ. The limits are shown for when the final states are treated as independent.

The number of observed events, and expected background and signal yields for each of the signal bins as a function of the τ* hypothesis mass. See Table 1 for the mass ranges considered for each point. The signal points shown are the pre-fit values assuming Λ=10 TeV

Observed signal yields in the 2-D mass plane for all final states. Of the two mass pairings, the minimum value is along the x-axis and the maximum value is along the y-axis. Expected yields are inclusive in the collinear mass and are shown only in tabular form.

Observed signal yields in the 2-D mass plane for the ETauγ final state. Of the two mass pairings, the minimum value is along the x-axis and the maximum value is along the y-axis. Expected yields are inclusive in the collinear mass and are shown only in tabular form.

Observed signal yields in the 2-D mass plane for the MuTauγ final state. Of the two mass pairings, the minimum value is along the x-axis and the maximum value is along the y-axis. Expected yields are inclusive in the collinear mass and are shown only in tabular form.

Observed signal yields in the 2-D mass plane for the TauTauγ final state. Of the two mass pairings, the minimum value is along the x-axis and the maximum value is along the y-axis. Expected yields are inclusive in the collinear mass and are shown only in tabular form.

Distributions in $S_T$ in the SR for the electron channel, after a background-only fit to the data. The signal distributions are scaled to the cross section predicted by the theory. The hatched bands show the post-fit uncertainty band, combining all sources of uncertainty. The ratio of data to the background predictions is shown in the panels below the distributions.

Figure 3 (middle right): The $m^∗_{jjj}$ postfit spectra in the SR4a. The lower panel shows the pull distribution.

Figure 3 (lower): The $m^∗_{jjj}$ postfit spectra in the SR5a. The lower panel shows the pull distribution.

Figure 4 (upper left): The $m^∗_{jjj}$ postfit spectra in the SR1b. The lower panel shows the pull distribution.

Figure 4 (upper right): The $m^∗_{jjj}$ postfit spectra in the SR2b. The lower panel shows the pull distribution.

Figure 4 (middle left): The $m^∗_{jjj}$ postfit spectra in the SR3b. The lower panel shows the pull distribution.

Figure 4 (middle right): The $m^∗_{jjj}$ postfit spectra in the SR4b. The lower panel shows the pull distribution.

Figure 4 (lower): The $m^∗_{jjj}$ postfit spectra in the SR5b. The lower panel shows the pull distribution.

Figure 5. The upper limits on the production cross section times branching fraction $\sigma B$, at 95% CL, for the process $pp → g_{KK} → gR → gWW$. The black (red) line contour indicates the observed (expected) exclusion region of the gKK and R masses. The red dashed lines show the 68% CL band of the expected limit contour.

The black line contour indicates the observed exclusion region of the gKK and R masses.

The red line contour indicates the expected central exclusion region of the gKK and R masses.

The dashed red line contour indicates the +1 s.t.d. expected exclusion region of the gKK and R masses.

The dashed red line contour indicates the -1 s.t.d. expected exclusion region of the gKK and R masses.

Differential cross sections of Higgs boson production. See also HepData record of the original publication: https://www.hepdata.net/record/ins1851456

Covariance matrix for the differential cross sections of Higgs boson production

SMEFT parameterization for the differential cross sections of Higgs boson production, and for the Higgs boson decay widths

Differential cross sections of W Gamma production. See also HepData record of the original publication: https://www.hepdata.net/record/ins1978840

Covariance matrix for the differential cross sections of W Gamma production

SMEFT parameterization for the differential cross sections of W Gamma production

Differential cross sections of Z production. See also HepData record of the original publication: https://www.hepdata.net/record/ins1837084

Covariance matrix for the differential cross sections of Z production

SMEFT parameterization for the differential cross sections of Z production

Differential cross sections of WW production. See also HepData record of the original publication: https://www.hepdata.net/record/ins1814328

Covariance matrix for the differential cross sections of WW production

SMEFT parameterization for the differential cross sections of WW production

Differential cross sections of ttbar production. See also HepData record of the original publication: https://www.hepdata.net/record/ins1901295

Covariance matrix for the differential cross sections of ttbar production

SMEFT parameterization for the differential cross sections of ttbar production

Differential cross sections of inclusive jet production. See also HepData record of the original publication: https://www.hepdata.net/record/ins1972986

Covariance matrix for the differential cross sections of inclusive jet production

SMEFT parameterization for the differential cross sections of inclusive jet production

Measurements of electroweak precision observables

Covariance matrix for the electroweak precision observables

SMEFT parameterization for the electroweak precision observables