Distribution of $m_{\mathrm{jjj}}$ for preselected events with $\mathrm{N}_{j}$ = 3

Distribution of $m_{\mathrm{j}}$ for preselected events with $\mathrm{N}_{j}$ = 3

Distribution of the deep-WH value of the highest-mass jet with 60 < $m_{\mathrm{j}}$ < 100 GeV for preselected events with $\mathrm{N}_{j}$ = 3

scale factors (SFs) for W, $t^{2}$, and q/g matched jets in the low-$m_{\mathrm{j}}$ and low-$p_{\mathrm{T}}$ (LL) bin, as functions of the deep-W discriminant value.

scale factors (SFs) for W, $t^{2}$, and q/g matched jets in the low-$m_{\mathrm{j}}$ and high-$p_{\mathrm{T}}$ (LH) bin, as functions of the deep-W discriminant value.

scale factors (SFs) for $t^{2}$, $t^{3,4}$, and q/g matched jets in the high-$m_{\mathrm{j}}$ and low-$p_{\mathrm{T}}$ (HL) bin, as functions of the deep-WH discriminant value.

scale factors (SFs) for $t^{2}$, $t^{3,4}$, and q/g matched jets in the high-$m_{\mathrm{j}}$ and high-$p_{\mathrm{T}}$ (HH) bin, as functions of the deep-WH discriminant value.

The deep-W discriminant of the jet with highest mass in the single-lepton sideband for LL samples.

The deep-W discriminant of the jet with highest mass in the single-lepton sideband for LH samples.

The deep-WH discriminant of the jet with highest mass in the single-lepton sideband for HL samples.

The deep-WH discriminant of the jet with highest mass in the single-lepton sideband for HH samples.

Comparison of the distribution of data and simulated backgrounds, as a function of the deep-W discriminant value for the highest-mass jet in CR1, after the scale factors have been applied.

Comparison of the distribution of data and simulated backgrounds, as a function of the deep-WH discriminant value for the highest-mass jet in CR2, after the scale factors have been applied.

Comparison of the distribution of data and simulated backgrounds, as a function of the deep-WH discriminant value for the highest-mass jet in CR3, after the scale factors have been applied.

Comparison of the distribution of data and simulated backgrounds, as a function of the deep-W discriminant value for the highest-mass jet in CR45, after the scale factors have been applied.

Comparison of the distribution of data and simulated backgrounds, as a function of the deep-W discriminant value for the highest-mass jet in CR6, after the scale factors have been applied.

The $m_{\mathrm{j}^{\mathrm{max}}}$ distributions for different jet types for SR1–3 events of the signal with $m_{\mathrm{W}_{\mathrm{KK}}}$ = 2.5 TeV, $m_{\mathrm{R}}$ = 0.2 TeV$ without deep-W (WH) constraints.

The deep-W distribution normalized to unity for the shown components of of the signal with $m_{\mathrm{W}_{\mathrm{KK}}}$ = 2.5 TeV, $m_{\mathrm{R}}$ = 0.2 TeV. The $t^{3,4}$ jets from the preselected sample, normalized to unity, are superimposed to compare shapes with the $R^{3q}$ and $R^{4q}$ distributions.

The deep-WH distribution normalized to unity for the shown components of of the signal with $m_{\mathrm{W}_{\mathrm{KK}}}$ = 2.5 TeV, $m_{\mathrm{R}}$ = 0.2 TeV. The $t^{3,4}$ jets from the preselected sample, normalized to unity, are superimposed to compare shapes with the $R^{3q}$ and $R^{4q}$ distributions.

The $m_{\mathrm{jj}}$ distribution for CR1 for data and simulation.

The $m_{\mathrm{jj}}$ distribution for CR2 for data and simulation.

The $m_{\mathrm{jj}}$ distribution for CR3 for data and simulation.

The $m_{\mathrm{jjj}}$ distribution for CR45 for data and simulation.

The $m_{\mathrm{jjj}}$ distribution for CR6 for data and simulation.

Post-fit distributions of the reconstructed triboson system ($m_{\mathrm{jj}}$) in data and simulation for SR1.

Post-fit distributions of the reconstructed triboson system ($m_{\mathrm{jj}}$) in data and simulation for SR2.

Post-fit distributions of the reconstructed triboson system ($m_{\mathrm{jj}}$) in data and simulation for SR3.

Post-fit distributions of the reconstructed triboson system ($m_{\mathrm{jjj}}$) in data and simulation for SR4.

Post-fit distributions of the reconstructed triboson system ($m_{\mathrm{jjj}}$) in data and simulation for SR5.

Post-fit distributions of the reconstructed triboson system ($m_{\mathrm{jjj}}$) in data and simulation for SR6.

Observed upper limits at $95\%$ CL on the signal cross section $\times$ branching fraction as functions of the $m_{\mathrm{W}_{\mathrm{KK}}}$ and $m_{\mathrm{R}}$ resonance masses.

Expected median lower limit contour on the $m_{\mathrm{W}_{\mathrm{KK}}}$ and $m_{\mathrm{R}}$ plane.

Expected $+ 1$ s.d. lower limit contour on the $m_{\mathrm{W}_{\mathrm{KK}}}$ and $m_{\mathrm{R}}$ plane.

Expected - 1 s.d. lower limit contour on the $m_{\mathrm{W}_{\mathrm{KK}}}$ and $m_{\mathrm{R}}$ plane.

Observed lower limit contour on the $m_{\mathrm{W}_{\mathrm{KK}}}$ and $m_{\mathrm{R}}$ plane.

The normalized distributions of the BDT input variable $D_{p_{\text{T}}}$ for the two highest $p_{\text{T}}$ jets from the simulated SM backgrounds and several signal models. Each sample's jet $p_{\text{T}}$ distribution is weighted to match a reference distribution (see text). The last bin of each histogram includes the overflow events.

The normalized BDT discriminator distribution for the two highest $p_{\text{T}}$ jets from the simulated SM backgrounds and several signal models.

The BDT ROC curves for the two highest $p_{\text{T}}$ jets, comparing the simulated SM backgrounds with one signal model with $m_{\text{Z}^{\prime}} = 3.1\,\text{TeV}$, $m_{\text{dark}} = 20\,\text{GeV}$, $r_{\text{inv}} = 0.3$, $\alpha_{\text{dark}} = \alpha_{\text{dark}}^{\text{peak}}$.

The BDT ROC curves for the two highest $p_{\text{T}}$ jets, comparing the simulated SM backgrounds with one signal model with $m_{\text{Z}^{\prime}} = 3.1\,\text{TeV}$, $m_{\text{dark}} = 20\,\text{GeV}$, $r_{\text{inv}} = 0.3$, $\alpha_{\text{dark}} = \alpha_{\text{dark}}^{\text{peak}}$.

The BDT ROC curves for the two highest $p_{\text{T}}$ jets, comparing the simulated SM backgrounds with one signal model with $m_{\text{Z}^{\prime}} = 3.1\,\text{TeV}$, $m_{\text{dark}} = 20\,\text{GeV}$, $r_{\text{inv}} = 0.3$, $\alpha_{\text{dark}} = \alpha_{\text{dark}}^{\text{peak}}$.

The BDT ROC curves for the two highest $p_{\text{T}}$ jets, comparing the simulated SM backgrounds with one signal model with $m_{\text{Z}^{\prime}} = 3.1\,\text{TeV}$, $m_{\text{dark}} = 20\,\text{GeV}$, $r_{\text{inv}} = 0.3$, $\alpha_{\text{dark}} = \alpha_{\text{dark}}^{\text{peak}}$.

The $m_{\text{T}}$ distribution for the high-$R_{\text{T}}$ signal region, comparing the observed data to the background prediction from the analytic fit ($g_{3}(x) = \exp(p_{1}x)x^{p_{2}(1+p_{3}\ln(x))}$, $x = m_{\text{T}}/\sqrt{s}$). The distributions from several example signal models, with cross sections corresponding to the observed limits, are superimposed.

The $m_{\text{T}}$ distribution for the low-$R_{\text{T}}$ signal region, comparing the observed data to the background prediction from the analytic fit ($g_{2}(x) = \exp(p_{1}x)x^{p_{2}}$, $x = m_{\text{T}}/\sqrt{s}$). The distributions from several example signal models, with cross sections corresponding to the observed limits, are superimposed.

The $m_{\text{T}}$ distribution for the high-SVJ2 signal region, comparing the observed data to the background prediction from the analytic fit ($g_{2}(x) = \exp(p_{1}x)x^{p_{2}}$, $x = m_{\text{T}}/\sqrt{s}$). The distributions from several example signal models, with cross sections corresponding to the observed limits, are superimposed.

The $m_{\text{T}}$ distribution for the low-SVJ2 signal region, comparing the observed data to the background prediction from the analytic fit ($g_{2}(x) = \exp(p_{1}x)x^{p_{2}}$, $x = m_{\text{T}}/\sqrt{s}$). The distributions from several example signal models, with cross sections corresponding to the observed limits, are superimposed.

The 95% CL observed upper limits on the product of the cross section and branching fraction from the inclusive search for variations of the mediator mass and the dark hadron mass.

The expected exclusion for the nominal $\text{Z}^{\prime}$ cross section.

The expected exclusion for the nominal $\text{Z}^{\prime}$ cross section.

The observed exclusion for the nominal $\text{Z}^{\prime}$ cross section.

The observed exclusion for the nominal $\text{Z}^{\prime}$ cross section.

The lower 68% expected exclusion for the nominal $\text{Z}^{\prime}$ cross section.

The lower 68% expected exclusion for the nominal $\text{Z}^{\prime}$ cross section.

The upper 68% expected exclusion for the nominal $\text{Z}^{\prime}$ cross section.

The upper 68% expected exclusion for the nominal $\text{Z}^{\prime}$ cross section.

The lower 95% expected exclusion for the nominal $\text{Z}^{\prime}$ cross section.

The lower 95% expected exclusion for the nominal $\text{Z}^{\prime}$ cross section.

The upper 95% expected exclusion for the nominal $\text{Z}^{\prime}$ cross section.

The 95% CL observed upper limits on the product of the cross section and branching fraction from the inclusive search for variations of the mediator mass and the invisible fraction.

The expected exclusion for the nominal $\text{Z}^{\prime}$ cross section.

The observed exclusion for the nominal $\text{Z}^{\prime}$ cross section.

The lower 68% expected exclusion for the nominal $\text{Z}^{\prime}$ cross section.

The lower 68% expected exclusion for the nominal $\text{Z}^{\prime}$ cross section.

The upper 68% expected exclusion for the nominal $\text{Z}^{\prime}$ cross section.

The lower 95% expected exclusion for the nominal $\text{Z}^{\prime}$ cross section.

The upper 95% expected exclusion for the nominal $\text{Z}^{\prime}$ cross section.

The upper 95% expected exclusion for the nominal $\text{Z}^{\prime}$ cross section.

The 95% CL observed upper limits on the product of the cross section and branching fraction from the BDT-based search for variations of the mediator mass and the dark hadron mass.

The expected exclusion for the nominal $\text{Z}^{\prime}$ cross section.

The expected exclusion for the nominal $\text{Z}^{\prime}$ cross section.

The expected exclusion for the nominal $\text{Z}^{\prime}$ cross section.

The observed exclusion for the nominal $\text{Z}^{\prime}$ cross section.

The observed exclusion for the nominal $\text{Z}^{\prime}$ cross section.

The observed exclusion for the nominal $\text{Z}^{\prime}$ cross section.

The observed exclusion for the nominal $\text{Z}^{\prime}$ cross section.

The lower 68% expected exclusion for the nominal $\text{Z}^{\prime}$ cross section.

The lower 68% expected exclusion for the nominal $\text{Z}^{\prime}$ cross section.

The lower 68% expected exclusion for the nominal $\text{Z}^{\prime}$ cross section.

The upper 68% expected exclusion for the nominal $\text{Z}^{\prime}$ cross section.

The upper 68% expected exclusion for the nominal $\text{Z}^{\prime}$ cross section.

The upper 68% expected exclusion for the nominal $\text{Z}^{\prime}$ cross section.

The lower 95% expected exclusion for the nominal $\text{Z}^{\prime}$ cross section.

The lower 95% expected exclusion for the nominal $\text{Z}^{\prime}$ cross section.

The upper 95% expected exclusion for the nominal $\text{Z}^{\prime}$ cross section.

The upper 95% expected exclusion for the nominal $\text{Z}^{\prime}$ cross section.

The upper 95% expected exclusion for the nominal $\text{Z}^{\prime}$ cross section.

The 95% CL observed upper limits on the product of the cross section and branching fraction from the BDT-based search for variations of the mediator mass and the invisible fraction.

The expected exclusion for the nominal $\text{Z}^{\prime}$ cross section.

The expected exclusion for the nominal $\text{Z}^{\prime}$ cross section.

The expected exclusion for the nominal $\text{Z}^{\prime}$ cross section.

The observed exclusion for the nominal $\text{Z}^{\prime}$ cross section.

The observed exclusion for the nominal $\text{Z}^{\prime}$ cross section.

The lower 68% expected exclusion for the nominal $\text{Z}^{\prime}$ cross section.

The lower 68% expected exclusion for the nominal $\text{Z}^{\prime}$ cross section.

The lower 68% expected exclusion for the nominal $\text{Z}^{\prime}$ cross section.

The lower 68% expected exclusion for the nominal $\text{Z}^{\prime}$ cross section.

The upper 68% expected exclusion for the nominal $\text{Z}^{\prime}$ cross section.

The lower 95% expected exclusion for the nominal $\text{Z}^{\prime}$ cross section.

The lower 95% expected exclusion for the nominal $\text{Z}^{\prime}$ cross section.

The lower 95% expected exclusion for the nominal $\text{Z}^{\prime}$ cross section.

The lower 95% expected exclusion for the nominal $\text{Z}^{\prime}$ cross section.

The upper 95% expected exclusion for the nominal $\text{Z}^{\prime}$ cross section.

The 95% CL upper limits on the product of the cross section and branching fraction from the inclusive search for the $\alpha_{\text{dark}}$ variations.

The 95% CL upper limits on the product of the cross section and branching fraction from the BDT-based search for the $\alpha_{\text{dark}}$ variations.

The three two-dimensional signal model parameter scans.

Metrics representing the performance of the BDT for the benchmark signal model ($m_{\text{Z}^{\prime}} = 3.1\,\text{TeV}$, $m_{\text{dark}} = 20\,\text{GeV}$, $r_{\text{inv}} = 0.3$, $\alpha_{\text{dark}} = \alpha_{\text{dark}}^{\text{peak}}$), compared to each of the major SM background processes.

The range of effects on the signal yield for each systematic uncertainty and the total. Values less than 0.01% are rounded to 0.0%.

The normalized distribution of the variable $m_{\text{T}}$ for the simulated SM backgrounds and several signal models. The requirement on this variable is omitted, but all other preselection requirements are applied. The last bin of each histogram includes the overflow events.

The normalized distribution of the variable $\Delta\eta(\text{J}_{1},\text{J}_{2})$ for the simulated SM backgrounds and several signal models. The requirement on this variable is omitted, but all other preselection requirements are applied. The last bin of each histogram includes the overflow events.

The normalized distribution of the variable $p_{\text{T}}^{\text{miss}}$ for the simulated SM backgrounds and several signal models. The $R_{\text{T}}$ requirement is omitted, but all other preselection requirements are applied. The last bin of each histogram includes the overflow events.

The normalized distribution of the variable $N_{\text{e}}$ for the simulated SM backgrounds and several signal models. The requirement on this variable is omitted, but all other preselection requirements are applied. The last bin of each histogram includes the overflow events.

The normalized distribution of the variable $N_{\mu}$ for the simulated SM backgrounds and several signal models. The requirement on this variable is omitted, but all other preselection requirements are applied. The last bin of each histogram includes the overflow events.

The normalized distribution of $\Delta\eta(\text{J}_{1},\text{J}_{2})$ vs. $R_{\text{T}}$ for the simulated QCD background. The preselection requirements on both variables are omitted, but all other preselection requirements are applied.

The normalized distribution of $p_{\text{T}}^{\text{miss}}$ vs. $m_{\text{T}}$ for the simulated QCD background. All selection requirements are omitted, except for the requirement of two high-$p_{\text{T}}$ wide jets.

The normalized distribution of $R_{\text{T}}$ vs. $m_{\text{T}}$ for the simulated QCD background. All selection requirements are omitted, except for the requirement of two high-$p_{\text{T}}$ wide jets.

The normalized distributions of the BDT input variable $\tau_{21}$ for the two highest $p_{\text{T}}$ wide jets from the simulated SM backgrounds and several signal models with varying $m_{\text{dark}}$ values. Each sample's jet $p_{\text{T}}$ distribution is weighted to match a reference distribution (see text). The last bin of each histogram includes the overflow events.

The normalized distributions of the BDT input variable $\tau_{32}$ for the two highest $p_{\text{T}}$ wide jets from the simulated SM backgrounds and several signal models with varying $m_{\text{dark}}$ values. Each sample's jet $p_{\text{T}}$ distribution is weighted to match a reference distribution (see text). The last bin of each histogram includes the overflow events.

The normalized distributions of the BDT input variable $N_{2}^{(1)}$ for the two highest $p_{\text{T}}$ wide jets from the simulated SM backgrounds and several signal models with varying $m_{\text{dark}}$ values. Each sample's jet $p_{\text{T}}$ distribution is weighted to match a reference distribution (see text). The last bin of each histogram includes the overflow events.

The normalized distributions of the BDT input variable $N_{3}^{(1)}$ for the two highest $p_{\text{T}}$ wide jets from the simulated SM backgrounds and several signal models with varying $m_{\text{dark}}$ values. Each sample's jet $p_{\text{T}}$ distribution is weighted to match a reference distribution (see text). The last bin of each histogram includes the overflow events.

The normalized distributions of the BDT input variable $g_{\text{jet}}$ for the two highest $p_{\text{T}}$ wide jets from the simulated SM backgrounds and several signal models with varying $r_{\text{inv}}$ values. Each sample's jet $p_{\text{T}}$ distribution is weighted to match a reference distribution (see text). The last bin of each histogram includes the overflow events.

The normalized distributions of the BDT input variable $\sigma_{\text{major}}$ for the two highest $p_{\text{T}}$ wide jets from the simulated SM backgrounds and several signal models with varying $r_{\text{inv}}$ values. Each sample's jet $p_{\text{T}}$ distribution is weighted to match a reference distribution (see text). The last bin of each histogram includes the overflow events.

The normalized distributions of the BDT input variable $\sigma_{\text{minor}}$ for the two highest $p_{\text{T}}$ wide jets from the simulated SM backgrounds and several signal models with varying $r_{\text{inv}}$ values. Each sample's jet $p_{\text{T}}$ distribution is weighted to match a reference distribution (see text). The last bin of each histogram includes the overflow events.

The normalized distributions of the BDT input variable $\Delta\phi(\vec{J},\vec{p}_{\text{T}}^{\text{miss}})$ for the two highest $p_{\text{T}}$ wide jets from the simulated SM backgrounds and several signal models with varying $r_{\text{inv}}$ values. Each sample's jet $p_{\text{T}}$ distribution is weighted to match a reference distribution (see text). The last bin of each histogram includes the overflow events.

The normalized distributions of the BDT input variable $f_{\text{h}^{\pm}}$ for the two highest $p_{\text{T}}$ wide jets from the simulated SM backgrounds and several signal models with varying $m_{\text{Z}^{\prime}}$ values. Each sample's jet $p_{\text{T}}$ distribution is weighted to match a reference distribution (see text). The last bin of each histogram includes the overflow events.

The normalized distributions of the BDT input variable $f_{\text{e}}$ for the two highest $p_{\text{T}}$ wide jets from the simulated SM backgrounds and several signal models with varying $m_{\text{Z}^{\prime}}$ values. Each sample's jet $p_{\text{T}}$ distribution is weighted to match a reference distribution (see text). The last bin of each histogram includes the overflow events.

The normalized distributions of the BDT input variable $f_{\mu}$ for the two highest $p_{\text{T}}$ wide jets from the simulated SM backgrounds and several signal models with varying $m_{\text{Z}^{\prime}}$ values. Each sample's jet $p_{\text{T}}$ distribution is weighted to match a reference distribution (see text). The last bin of each histogram includes the overflow events.

The normalized distributions of the BDT input variable $f_{\text{h}^{0}}$ for the two highest $p_{\text{T}}$ wide jets from the simulated SM backgrounds and several signal models with varying $m_{\text{Z}^{\prime}}$ values. Each sample's jet $p_{\text{T}}$ distribution is weighted to match a reference distribution (see text). The last bin of each histogram includes the overflow events.

The normalized distributions of the BDT input variable $f_{\gamma}$ for the two highest $p_{\text{T}}$ wide jets from the simulated SM backgrounds and several signal models with varying $m_{\text{Z}^{\prime}}$ values. Each sample's jet $p_{\text{T}}$ distribution is weighted to match a reference distribution (see text). The last bin of each histogram includes the overflow events.

The product of signal acceptance and efficiency in the high-$R_{\text{T}}$ signal region, for variations of the mediator mass and the dark hadron mass.

The product of signal acceptance and efficiency in the high-$R_{\text{T}}$ signal region, for variations of the mediator mass and the invisible fraction.

The product of signal acceptance and efficiency in the high-$R_{\text{T}}$ signal region, for variations of the mediator mass and the dark coupling strength.

The product of signal acceptance and efficiency in the low-$R_{\text{T}}$ signal region, for variations of the mediator mass and the dark hadron mass.

The product of signal acceptance and efficiency in the low-$R_{\text{T}}$ signal region, for variations of the mediator mass and the invisible fraction.

The product of signal acceptance and efficiency in the low-$R_{\text{T}}$ signal region, for variations of the mediator mass and the dark coupling strength.

The product of signal acceptance and efficiency in the high-SVJ2 signal region, for variations of the mediator mass and the dark hadron mass.

The product of signal acceptance and efficiency in the high-SVJ2 signal region, for variations of the mediator mass and the invisible fraction.

The product of signal acceptance and efficiency in the high-SVJ2 signal region, for variations of the mediator mass and the dark coupling strength.

The product of signal acceptance and efficiency in the low-SVJ2 signal region, for variations of the mediator mass and the dark hadron mass.

The product of signal acceptance and efficiency in the low-SVJ2 signal region, for variations of the mediator mass and the invisible fraction.

The product of signal acceptance and efficiency in the low-SVJ2 signal region, for variations of the mediator mass and the dark coupling strength.

Comparison of different the dijet mass $m_{\text{J}\text{J}}$, the transverse mass $m_{\text{T}}$, and the Monte Carlo (MC) mass $m_{\text{MC}}$ for a signal model with $m_{\text{Z}^{\prime}} = 2.1\,\text{TeV}$, $m_{\text{dark}} = 20\,\text{GeV}$, $r_{\text{inv}} = 0.3$, $\alpha_{\text{dark}} = \alpha_{\text{dark}}^{\text{peak}}$. No selection is applied, except that there must be at least two jets. $m_{\text{MC}}$ is computed by adding the generator-level four-vectors for invisible particles to the dijet system, to represent the achievable resolution if the invisible component were fully measured. The last bin of each histogram includes the overflow events.

$m_{\text{T}}$ distributions for signal models with different $m_{\text{dark}}$ values for the high-$R_{\text{T}}$ inclusive signal region.

$m_{\text{T}}$ distributions for signal models with different $m_{\text{dark}}$ values for the low-$R_{\text{T}}$ inclusive signal region.

$m_{\text{T}}$ distributions for signal models with different $r_{\text{inv}}$ values for the high-$R_{\text{T}}$ inclusive signal region.

$m_{\text{T}}$ distributions for signal models with different $r_{\text{inv}}$ values for the low-$R_{\text{T}}$ inclusive signal region.

$m_{\text{T}}$ distributions for signal models with different $\alpha_{\text{dark}}$ values for the high-$R_{\text{T}}$ inclusive signal region.

$m_{\text{T}}$ distributions for signal models with different $\alpha_{\text{dark}}$ values for the low-$R_{\text{T}}$ inclusive signal region.

The proportions of each SM background process in the high-$R_{\text{T}}$ signal region.

The proportions of each SM background process in the low-$R_{\text{T}}$ signal region.

The proportions of each SM background process in the high-SVJ2 signal region.

The proportions of each SM background process in the low-SVJ2 signal region.

The 95% CL expected upper limits on the product of the cross section and branching fraction from the inclusive search for variations of the mediator mass and the dark hadron mass.

The 95% CL expected upper limits on the product of the cross section and branching fraction from the inclusive search for variations of the mediator mass and the invisible fraction.

The 95% CL expected upper limits on the product of the cross section and branching fraction from the BDT-based search for variations of the mediator mass and the dark hadron mass.

The 95% CL expected upper limits on the product of the cross section and branching fraction from the BDT-based search for variations of the mediator mass and the invisible fraction.

Relative efficiencies in % for each step of the event selection process for the major background processes. Statistical uncertainties, at most 1.8%, are omitted. The line "Efficiency [%]" is the absolute efficiency after the final selection. The subsequent lines show the efficiency for each signal region, relative to the final selection.

Relative efficiencies in % for each step of the event selection process for signals with $m_{\text{Z}^{\prime}} = 2.1\,\text{TeV}$, varying $m_{\text{dark}}$ values, $r_{\text{inv}} = 0.3$, and $\alpha_{\text{dark}} = \alpha_{\text{dark}}^{\text{peak}}$. Statistical uncertainties, at most 0.5%, are omitted. The line "Efficiency [%]" is the absolute efficiency after the final selection. The subsequent lines show the efficiency for each signal region, relative to the final selection.

Relative efficiencies in % for each step of the event selection process for signals with $m_{\text{Z}^{\prime}} = 3.1\,\text{TeV}$, varying $m_{\text{dark}}$ values, $r_{\text{inv}} = 0.3$, and $\alpha_{\text{dark}} = \alpha_{\text{dark}}^{\text{peak}}$. Statistical uncertainties, at most 0.4%, are omitted. The line "Efficiency [%]" is the absolute efficiency after the final selection. The subsequent lines show the efficiency for each signal region, relative to the final selection.

Relative efficiencies in % for each step of the event selection process for signals with $m_{\text{Z}^{\prime}} = 4.1\,\text{TeV}$, varying $m_{\text{dark}}$ values, $r_{\text{inv}} = 0.3$, and $\alpha_{\text{dark}} = \alpha_{\text{dark}}^{\text{peak}}$. Statistical uncertainties, at most 0.4%, are omitted. The line "Efficiency [%]" is the absolute efficiency after the final selection. The subsequent lines show the efficiency for each signal region, relative to the final selection.

Relative efficiencies in % for each step of the event selection process for signals with $m_{\text{Z}^{\prime}} = 2.1\,\text{TeV}$, $m_{\text{dark}} = 20\,\text{GeV}$, varying $r_{\text{inv}}$ values, and $\alpha_{\text{dark}} = \alpha_{\text{dark}}^{\text{peak}}$. Statistical uncertainties, at most 2.6%, are omitted. The line "Efficiency [%]" is the absolute efficiency after the final selection. The subsequent lines show the efficiency for each signal region, relative to the final selection.

Relative efficiencies in % for each step of the event selection process for signals with $m_{\text{Z}^{\prime}} = 3.1\,\text{TeV}$, $m_{\text{dark}} = 20\,\text{GeV}$, varying $r_{\text{inv}}$ values, and $\alpha_{\text{dark}} = \alpha_{\text{dark}}^{\text{peak}}$. Statistical uncertainties, at most 1.2%, are omitted. The line "Efficiency [%]" is the absolute efficiency after the final selection. The subsequent lines show the efficiency for each signal region, relative to the final selection.

Relative efficiencies in % for each step of the event selection process for signals with $m_{\text{Z}^{\prime}} = 4.1\,\text{TeV}$, $m_{\text{dark}} = 20\,\text{GeV}$, varying $r_{\text{inv}}$ values, and $\alpha_{\text{dark}} = \alpha_{\text{dark}}^{\text{peak}}$. Statistical uncertainties, at most 0.9%, are omitted. The line "Efficiency [%]" is the absolute efficiency after the final selection. The subsequent lines show the efficiency for each signal region, relative to the final selection.

Relative efficiencies in % for each step of the event selection process for signals with $m_{\text{Z}^{\prime}} = 2.1\,\text{TeV}$, $m_{\text{dark}} = 20\,\text{GeV}$, $r_{\text{inv}} = 0.3$, and varying $\alpha_{\text{dark}}$ values. Statistical uncertainties, at most 0.4%, are omitted. The line "Efficiency [%]" is the absolute efficiency after the final selection. The subsequent lines show the efficiency for each signal region, relative to the final selection.

Relative efficiencies in % for each step of the event selection process for signals with $m_{\text{Z}^{\prime}} = 3.1\,\text{TeV}$, $m_{\text{dark}} = 20\,\text{GeV}$, $r_{\text{inv}} = 0.3$, and varying $\alpha_{\text{dark}}$ values. Statistical uncertainties, at most 0.4%, are omitted. The line "Efficiency [%]" is the absolute efficiency after the final selection. The subsequent lines show the efficiency for each signal region, relative to the final selection.

Relative efficiencies in % for each step of the event selection process for signals with $m_{\text{Z}^{\prime}} = 4.1\,\text{TeV}$, $m_{\text{dark}} = 20\,\text{GeV}$, $r_{\text{inv}} = 0.3$, and varying $\alpha_{\text{dark}}$ values. Statistical uncertainties, at most 0.4%, are omitted. The line "Efficiency [%]" is the absolute efficiency after the final selection. The subsequent lines show the efficiency for each signal region, relative to the final selection.

Normalized differential cross section distribution as a function of the leading b jet transverse momentum for the Z + >= 1 b jet events

Differential cross section distribution as a function of the leading b jet absolute pseudorapidity for the Z + >= 1 b jet events

Normalized differential cross section distribution as a function of the leading b jet absolute pseudorapidity for the Z + >= 1 b jet events

Differential cross section distribution as a function of the leading b jet transverse momentum for Z +>= 1 b jet events

Normalized differential cross section distribution as a function of azimuthal difference between Z boson and the leading b jet for the Z + >= 1 b jet events

Differential cross section distribution as a function of the rapidity difference between Z boson and the leading b jet for the Z + >= 1 b jet events

Normalized differential cross section distribution as a function of the rapidity difference between Z boson and the leading b jet for the Z + >= 1 b jet events

Differential cross section distribution as a function of the angular separation between the Z boson and the leading b jet for the Z + >= 1 b jet events

Normalized differential cross section distribution as a function of the angular separation between the Z boson and the leading b jet for the Z + >= 1 b jet events

Differential cross section distribution as a function of the leading b jet transverse momentum for the Z + >= 2 b jet events

Normalized differential cross section distribution as a function of the leading b jet transverse momentum for the Z + >= 2 b jet events

Differential cross section distribution as a function of the leading b jet absolute pseudorapidity

Normalized differential cross section distribution as a function of the leading b jet absolute pseudorapidity

Differential cross section distribution as a function of the subleading b jet transverse momentum for the Z + >= 2 b jet events

Normalized differential cross section distribution as a function of the subleading b jet transverse momentum for the Z + >= 2 b jet events

Differential cross section distribution as a function of the Z boson transverse momentum for the Z + >= 2 b jet events

Normalized differential cross section distribution as a function of the Z boson transverse momentum for the Z + >= 2 b jet events

Differential cross section as a function of the angular separation between two b jets for the Z + >= 2 b jet events

Normalized differential cross section as a function of the angular separtion between two b jets for the Z + >= 2 b jet events

Differential cross section as a function of the minimum angular separation between the Z boson and two b jets for the Z + >= 2 b jet events

Normalized differential cross section as a function of the minimum angular separation between the Z boson and two b jets for the Z + >= 2 b jet events

Differential cross section as a function of the asymmetry of the Z + >= 2 b jets system

Normalized differential cross section as a function of the asymmetry of the Z + >= 2 b jets system

Differential cross section as a function of the invariant mass of two b jets for the Z + >= 2 b jet events

Normalized differential cross section as a function of the invariant mass of two b jets for the Z + >= 2 b jet events

Differential cross section as a function of the invariant mass of the Z boson and two b jets for the Z + >= 2 b jet events

Normalized differential cross section as a function of invariant mass of the Z boson and two b jets for the Z + >= 2 b jet events

Distributions of the cross section ratios as a function of the leading b jet transverse momentum

Distributions of the cross section ratios as a function of the leading b jet absolute pseudorapidity

Excluded signal cross section at $95\%$ CL for Hut coupling. Each jet category and their combination are shown separately.

Excluded signal cross section at $95\%$ CL for Hut coupling. Each jet category and their combination are shown separately.

Observed upper limits on the branching fractions $\mathcal{B}(\mathrm{t}\to\mathrm{Hu})$ and $\mathcal{B}(\mathrm{t}\to\mathrm{Hc})$ at $95\%$ CL.

Expected upper limits on the branching fractions $\mathcal{B}(\mathrm{t}\to\mathrm{Hu})$ and $\mathcal{B}(\mathrm{t}\to\mathrm{Hc})$ at $95\%$ CL.

Expected +1 standard deviation upper limits on the branching fractions $\mathcal{B}(\mathrm{t}\to\mathrm{Hu})$ and $\mathcal{B}(\mathrm{t}\to\mathrm{Hc})$ at $95\%$ CL.

Expected -1 standard deviation upper limits on the branching fractions $\mathcal{B}(\mathrm{t}\to\mathrm{Hu})$ and $\mathcal{B}(\mathrm{t}\to\mathrm{Hc})$ at $95\%$ CL.

Expected +2 standard deviation upper limits on the branching fractions $\mathcal{B}(\mathrm{t}\to\mathrm{Hu})$ and $\mathcal{B}(\mathrm{t}\to\mathrm{Hc})$ at $95\%$ CL.

Expected -2 standard deviation upper limits on the branching fractions $\mathcal{B}(\mathrm{t}\to\mathrm{Hu})$ and $\mathcal{B}(\mathrm{t}\to\mathrm{Hc})$ at $95\%$ CL.

Observed upper limits on the anomalous couplings $\kappa_{\mathrm{Hut}}$ and $\kappa_{\mathrm{Hut}}$ at $95\%$ CL.

Expected upper limits on the anomalous couplings $\kappa_{\mathrm{Hut}}$ and $\kappa_{\mathrm{Hut}}$ at $95\%$ CL.

Expected +1 standard deviation upper limits on the anomalous couplings $\kappa_{\mathrm{Hut}}$ and $\kappa_{\mathrm{Hut}}$ at $95\%$ CL.

Expected -1 standard deviation upper limits on the anomalous couplings $\kappa_{\mathrm{Hut}}$ and $\kappa_{\mathrm{Hut}}$ at $95\%$ CL.

Expected +2 standard deviation upper limits on the anomalous couplings $\kappa_{\mathrm{Hut}}$ and $\kappa_{\mathrm{Hut}}$ at $95\%$ CL.

Expected -2 standard deviation upper limits on the anomalous couplings $\kappa_{\mathrm{Hut}}$ and $\kappa_{\mathrm{Hut}}$ at $95\%$ CL.

Relative uncertainties on the measured fractional differential $p_{\mathrm{T}}^{\gamma}$ cross section.

Correlation matrix for the measured absolute differential $p_{\mathrm{T}}^{\gamma}$ cross section.

Correlation matrix for the measured fractional differential $p_{\mathrm{T}}^{\gamma}$ cross section.

Response matrix from the fiducial to the reconstructed bins of the differential $p_{\mathrm{T}}^{\gamma}$ cross section measurement.

Measured absolute differential $\eta^{\gamma}$ cross section, compared to the MG5_aMC+PY8, GENEVA, MATRIX and MCFM predictions. The differential cross sections $\sigma_{j}(\mathrm{pp}\rightarrow\mathrm{W}^{\pm}\gamma\rightarrow\ell^{\pm}\nu\gamma)$, where $\ell$ denotes all three lepton flavors, are measured in the following fiducial region: $p_{\mathrm{T}}^{\ell} > 30\,\mathrm{GeV}$, $|\eta^{\ell}| < 2.5$, $p_{\mathrm{T}}^{\gamma} > 30\,\mathrm{GeV}$, $|\eta^{\gamma}| < 2.5$, $p_{\mathrm{T}}^{\mathrm{miss}} > 40\,\mathrm{GeV}$, and $\Delta R(\ell, \gamma) > 0.7$. The leptons are dressed by adding the four-momenta of any photons with $\Delta R(\ell, \gamma) < 0.1$ to the four-momentum of the lepton. A smooth-cone photon isolation is also applied, with parameters $\delta_{0}=0.4$, $\epsilon=1.0$, and $n=1$.

Measured fractional differential $\eta^{\gamma}$ cross section, compared to the MG5_aMC+PY8, GENEVA, MATRIX and MCFM predictions. The differential cross sections $\sigma_{j}(\mathrm{pp}\rightarrow\mathrm{W}^{\pm}\gamma\rightarrow\ell^{\pm}\nu\gamma)$, where $\ell$ denotes all three lepton flavors, are measured in the following fiducial region: $p_{\mathrm{T}}^{\ell} > 30\,\mathrm{GeV}$, $|\eta^{\ell}| < 2.5$, $p_{\mathrm{T}}^{\gamma} > 30\,\mathrm{GeV}$, $|\eta^{\gamma}| < 2.5$, $p_{\mathrm{T}}^{\mathrm{miss}} > 40\,\mathrm{GeV}$, and $\Delta R(\ell, \gamma) > 0.7$. The leptons are dressed by adding the four-momenta of any photons with $\Delta R(\ell, \gamma) < 0.1$ to the four-momentum of the lepton. A smooth-cone photon isolation is also applied, with parameters $\delta_{0}=0.4$, $\epsilon=1.0$, and $n=1$.

Relative uncertainties on the measured absolute differential $\eta^{\gamma}$ cross section.

Relative uncertainties on the measured fractional differential $\eta^{\gamma}$ cross section.

Correlation matrix for the measured absolute differential $\eta^{\gamma}$ cross section.

Correlation matrix for the measured fractional differential $\eta^{\gamma}$ cross section.

Response matrix from the fiducial to the reconstructed bins of the differential $\eta^{\gamma}$ cross section measurement.

Measured absolute differential $\Delta R(\ell,\gamma)$ cross section, compared to the MG5_aMC+PY8, GENEVA, MATRIX and MCFM predictions. The differential cross sections $\sigma_{j}(\mathrm{pp}\rightarrow\mathrm{W}^{\pm}\gamma\rightarrow\ell^{\pm}\nu\gamma)$, where $\ell$ denotes all three lepton flavors, are measured in the following fiducial region: $p_{\mathrm{T}}^{\ell} > 30\,\mathrm{GeV}$, $|\eta^{\ell}| < 2.5$, $p_{\mathrm{T}}^{\gamma} > 30\,\mathrm{GeV}$, $|\eta^{\gamma}| < 2.5$, $p_{\mathrm{T}}^{\mathrm{miss}} > 40\,\mathrm{GeV}$, and $\Delta R(\ell, \gamma) > 0.7$. The leptons are dressed by adding the four-momenta of any photons with $\Delta R(\ell, \gamma) < 0.1$ to the four-momentum of the lepton. A smooth-cone photon isolation is also applied, with parameters $\delta_{0}=0.4$, $\epsilon=1.0$, and $n=1$.

Measured fractional differential $\Delta R(\ell,\gamma)$ cross section, compared to the MG5_aMC+PY8, GENEVA, MATRIX and MCFM predictions. The differential cross sections $\sigma_{j}(\mathrm{pp}\rightarrow\mathrm{W}^{\pm}\gamma\rightarrow\ell^{\pm}\nu\gamma)$, where $\ell$ denotes all three lepton flavors, are measured in the following fiducial region: $p_{\mathrm{T}}^{\ell} > 30\,\mathrm{GeV}$, $|\eta^{\ell}| < 2.5$, $p_{\mathrm{T}}^{\gamma} > 30\,\mathrm{GeV}$, $|\eta^{\gamma}| < 2.5$, $p_{\mathrm{T}}^{\mathrm{miss}} > 40\,\mathrm{GeV}$, and $\Delta R(\ell, \gamma) > 0.7$. The leptons are dressed by adding the four-momenta of any photons with $\Delta R(\ell, \gamma) < 0.1$ to the four-momentum of the lepton. A smooth-cone photon isolation is also applied, with parameters $\delta_{0}=0.4$, $\epsilon=1.0$, and $n=1$.

Relative uncertainties on the measured absolute differential $\Delta R(\ell,\gamma)$ cross section.

Relative uncertainties on the measured fractional differential $\Delta R(\ell,\gamma)$ cross section.

Correlation matrix for the measured absolute differential $\Delta R(\ell,\gamma)$ cross section.

Correlation matrix for the measured fractional differential $\Delta R(\ell,\gamma)$ cross section.

Response matrix from the fiducial to the reconstructed bins of the differential $\Delta R(\ell,\gamma)$ cross section measurement.

Measured absolute differential $\Delta\eta(\ell,\gamma)$ cross section, compared to the MG5_aMC+PY8, GENEVA, MATRIX and MCFM predictions. The differential cross sections $\sigma_{j}(\mathrm{pp}\rightarrow\mathrm{W}^{\pm}\gamma\rightarrow\ell^{\pm}\nu\gamma)$, where $\ell$ denotes all three lepton flavors, are measured in the following fiducial region: $p_{\mathrm{T}}^{\ell} > 30\,\mathrm{GeV}$, $|\eta^{\ell}| < 2.5$, $p_{\mathrm{T}}^{\gamma} > 30\,\mathrm{GeV}$, $|\eta^{\gamma}| < 2.5$, $p_{\mathrm{T}}^{\mathrm{miss}} > 40\,\mathrm{GeV}$, and $\Delta R(\ell, \gamma) > 0.7$. The leptons are dressed by adding the four-momenta of any photons with $\Delta R(\ell, \gamma) < 0.1$ to the four-momentum of the lepton. A smooth-cone photon isolation is also applied, with parameters $\delta_{0}=0.4$, $\epsilon=1.0$, and $n=1$.

Measured fractional differential $\Delta\eta(\ell,\gamma)$ cross section, compared to the MG5_aMC+PY8, GENEVA, MATRIX and MCFM predictions. The differential cross sections $\sigma_{j}(\mathrm{pp}\rightarrow\mathrm{W}^{\pm}\gamma\rightarrow\ell^{\pm}\nu\gamma)$, where $\ell$ denotes all three lepton flavors, are measured in the following fiducial region: $p_{\mathrm{T}}^{\ell} > 30\,\mathrm{GeV}$, $|\eta^{\ell}| < 2.5$, $p_{\mathrm{T}}^{\gamma} > 30\,\mathrm{GeV}$, $|\eta^{\gamma}| < 2.5$, $p_{\mathrm{T}}^{\mathrm{miss}} > 40\,\mathrm{GeV}$, and $\Delta R(\ell, \gamma) > 0.7$. The leptons are dressed by adding the four-momenta of any photons with $\Delta R(\ell, \gamma) < 0.1$ to the four-momentum of the lepton. A smooth-cone photon isolation is also applied, with parameters $\delta_{0}=0.4$, $\epsilon=1.0$, and $n=1$.

Relative uncertainties on the measured absolute differential $\Delta \eta(\ell,\gamma)$ cross section.

Relative uncertainties on the measured fractional differential $\Delta \eta(\ell,\gamma)$ cross section.

Correlation matrix for the measured absolute differential $\Delta \eta(\ell,\gamma)$ cross section.

Correlation matrix for the measured fractional differential $\Delta \eta(\ell,\gamma)$ cross section.

Response matrix from the fiducial to the reconstructed bins of the differential $\Delta \eta(\ell,\gamma)$ cross section measurement.

Measured absolute differential $m_{\mathrm{T}}^{\mathrm{cluster}}$ cross section, compared to the MG5_aMC+PY8, GENEVA, MATRIX and MCFM predictions. The differential cross sections $\sigma_{j}(\mathrm{pp}\rightarrow\mathrm{W}^{\pm}\gamma\rightarrow\ell^{\pm}\nu\gamma)$, where $\ell$ denotes all three lepton flavors, are measured in the following fiducial region: $p_{\mathrm{T}}^{\ell} > 30\,\mathrm{GeV}$, $|\eta^{\ell}| < 2.5$, $p_{\mathrm{T}}^{\gamma} > 30\,\mathrm{GeV}$, $|\eta^{\gamma}| < 2.5$, $p_{\mathrm{T}}^{\mathrm{miss}} > 40\,\mathrm{GeV}$, and $\Delta R(\ell, \gamma) > 0.7$. The leptons are dressed by adding the four-momenta of any photons with $\Delta R(\ell, \gamma) < 0.1$ to the four-momentum of the lepton. A smooth-cone photon isolation is also applied, with parameters $\delta_{0}=0.4$, $\epsilon=1.0$, and $n=1$.

Measured fractional differential $m_{\mathrm{T}}^{\mathrm{cluster}}$ cross section, compared to the MG5_aMC+PY8, GENEVA, MATRIX and MCFM predictions. The differential cross sections $\sigma_{j}(\mathrm{pp}\rightarrow\mathrm{W}^{\pm}\gamma\rightarrow\ell^{\pm}\nu\gamma)$, where $\ell$ denotes all three lepton flavors, are measured in the following fiducial region: $p_{\mathrm{T}}^{\ell} > 30\,\mathrm{GeV}$, $|\eta^{\ell}| < 2.5$, $p_{\mathrm{T}}^{\gamma} > 30\,\mathrm{GeV}$, $|\eta^{\gamma}| < 2.5$, $p_{\mathrm{T}}^{\mathrm{miss}} > 40\,\mathrm{GeV}$, and $\Delta R(\ell, \gamma) > 0.7$. The leptons are dressed by adding the four-momenta of any photons with $\Delta R(\ell, \gamma) < 0.1$ to the four-momentum of the lepton. A smooth-cone photon isolation is also applied, with parameters $\delta_{0}=0.4$, $\epsilon=1.0$, and $n=1$.

Relative uncertainties on the measured absolute differential $m_{\mathrm{T}}^{\mathrm{cluster}}$ cross section.

Relative uncertainties on the measured fractional differential $m_{\mathrm{T}}^{\mathrm{cluster}}$ cross section.

Correlation matrix for the measured absolute differential $m_{\mathrm{T}}^{\mathrm{cluster}}$ cross section.

Correlation matrix for the measured fractional differential $m_{\mathrm{T}}^{\mathrm{cluster}}$ cross section.

Response matrix from the fiducial to the reconstructed bins of the differential $m_{\mathrm{T}}^{\mathrm{cluster}}$ cross section measurement.

Measured absolute differential $N_{\mathrm{jets}}$ cross section, compared to the MG5_aMC+PY8, GENEVA, MATRIX and MCFM predictions. The differential cross sections $\sigma_{j}(\mathrm{pp}\rightarrow\mathrm{W}^{\pm}\gamma\rightarrow\ell^{\pm}\nu\gamma)$, where $\ell$ denotes all three lepton flavors, are measured in the following fiducial region: $p_{\mathrm{T}}^{\ell} > 30\,\mathrm{GeV}$, $|\eta^{\ell}| < 2.5$, $p_{\mathrm{T}}^{\gamma} > 30\,\mathrm{GeV}$, $|\eta^{\gamma}| < 2.5$, $p_{\mathrm{T}}^{\mathrm{miss}} > 40\,\mathrm{GeV}$, and $\Delta R(\ell, \gamma) > 0.7$. The leptons are dressed by adding the four-momenta of any photons with $\Delta R(\ell, \gamma) < 0.1$ to the four-momentum of the lepton. A smooth-cone photon isolation is also applied, with parameters $\delta_{0}=0.4$, $\epsilon=1.0$, and $n=1$.

Correlation matrix for the measured absolute differential $N_{\mathrm{jets}}$ cross section. The differential cross sections $\sigma_{j}(\mathrm{pp}\rightarrow\mathrm{W}^{\pm}\gamma\rightarrow\ell^{\pm}\nu\gamma)$, where $\ell$ denotes all three lepton flavors, are measured in the following fiducial region: $p_{\mathrm{T}}^{\ell} > 30\,\mathrm{GeV}$, $|\eta^{\ell}| < 2.5$, $p_{\mathrm{T}}^{\gamma} > 30\,\mathrm{GeV}$, $|\eta^{\gamma}| < 2.5$, $p_{\mathrm{T}}^{\mathrm{miss}} > 40\,\mathrm{GeV}$, and $\Delta R(\ell, \gamma) > 0.7$. The leptons are dressed by adding the four-momenta of any photons with $\Delta R(\ell, \gamma) < 0.1$ to the four-momentum of the lepton. A smooth-cone photon isolation is also applied, with parameters $\delta_{0}=0.4$, $\epsilon=1.0$, and $n=1$.

Response matrix from the fiducial to the reconstructed bins of the differential $N_{\mathrm{jets}}$ cross section measurement.

Relative uncertainties on the measured absolute differential $N_{\mathrm{jets}}$ cross section.

Measured absolute differential $\Delta\eta(\ell,\gamma)$ cross section, compared to the MG5_aMC+PY8, GENEVA, MATRIX and MCFM predictions. The differential cross sections $\sigma_{j}(\mathrm{pp}\rightarrow\mathrm{W}^{\pm}\gamma\rightarrow\ell^{\pm}\nu\gamma)$, where $\ell$ denotes all three lepton flavors, are measured in the following fiducial region: $p_{\mathrm{T}}^{\ell} > 30\,\mathrm{GeV}$, $|\eta^{\ell}| < 2.5$, $p_{\mathrm{T}}^{\gamma} > 30\,\mathrm{GeV}$, $|\eta^{\gamma}| < 2.5$, $p_{\mathrm{T}}^{\mathrm{miss}} > 40\,\mathrm{GeV}$, and $\Delta R(\ell, \gamma) > 0.7$. The leptons are dressed by adding the four-momenta of any photons with $\Delta R(\ell, \gamma) < 0.1$ to the four-momentum of the lepton. A smooth-cone photon isolation is also applied, with parameters $\delta_{0}=0.4$, $\epsilon=1.0$, and $n=1$. Requirements of $m_{\mathrm{T}}^{\mathrm{cluster}}>150\,\mathrm{GeV}$ and a veto on the presence of any jet with $p_{\mathrm{T}} > 30\,\mathrm{GeV}$ and $|\eta| < 2.5$ are applied in addition to the baseline selection.

Measured fractional differential $\Delta\eta(\ell,\gamma)$ cross section, compared to the MG5_aMC+PY8, GENEVA, MATRIX and MCFM predictions. The differential cross sections $\sigma_{j}(\mathrm{pp}\rightarrow\mathrm{W}^{\pm}\gamma\rightarrow\ell^{\pm}\nu\gamma)$, where $\ell$ denotes all three lepton flavors, are measured in the following fiducial region: $p_{\mathrm{T}}^{\ell} > 30\,\mathrm{GeV}$, $|\eta^{\ell}| < 2.5$, $p_{\mathrm{T}}^{\gamma} > 30\,\mathrm{GeV}$, $|\eta^{\gamma}| < 2.5$, $p_{\mathrm{T}}^{\mathrm{miss}} > 40\,\mathrm{GeV}$, and $\Delta R(\ell, \gamma) > 0.7$. The leptons are dressed by adding the four-momenta of any photons with $\Delta R(\ell, \gamma) < 0.1$ to the four-momentum of the lepton. A smooth-cone photon isolation is also applied, with parameters $\delta_{0}=0.4$, $\epsilon=1.0$, and $n=1$. Requirements of $m_{\mathrm{T}}^{\mathrm{cluster}}>150\,\mathrm{GeV}$ and a veto on the presence of any jet with $p_{\mathrm{T}} > 30\,\mathrm{GeV}$ and $|\eta| < 2.5$ are applied in addition to the baseline selection.

Relative uncertainties on the measured absolute differential $\Delta \eta(\ell,\gamma)$ cross section. Requirements of $m_{\mathrm{T}}^{\mathrm{cluster}}>150\,\mathrm{GeV}$ and a veto on the presence of any jet with $p_{\mathrm{T}} > 30\,\mathrm{GeV}$ and $|\eta| < 2.5$ are applied in addition to the baseline selection.

Relative uncertainties on the measured fractional differential $\Delta \eta(\ell,\gamma)$ cross section. Requirements of $m_{\mathrm{T}}^{\mathrm{cluster}}>150\,\mathrm{GeV}$ and a veto on the presence of any jet with $p_{\mathrm{T}} > 30\,\mathrm{GeV}$ and $|\eta| < 2.5$ are applied in addition to the baseline selection.

Correlation matrix for the measured absolute differential $\Delta \eta(\ell,\gamma)$ cross section. Requirements of $m_{\mathrm{T}}^{\mathrm{cluster}}>150\,\mathrm{GeV}$ and a veto on the presence of any jet with $p_{\mathrm{T}} > 30\,\mathrm{GeV}$ and $|\eta| < 2.5$ are applied in addition to the baseline selection.

Correlation matrix for the measured fractional differential $\Delta \eta(\ell,\gamma)$ cross section. Requirements of $m_{\mathrm{T}}^{\mathrm{cluster}}>150\,\mathrm{GeV}$ and a veto on the presence of any jet with $p_{\mathrm{T}} > 30\,\mathrm{GeV}$ and $|\eta| < 2.5$ are applied in addition to the baseline selection.

Response matrix from the fiducial to the reconstructed bins of the differential $\Delta \eta(\ell,\gamma)$ cross section measurement. Requirements of $m_{\mathrm{T}}^{\mathrm{cluster}}>150\,\mathrm{GeV}$ and a veto on the presence of any jet with $p_{\mathrm{T}} > 30\,\mathrm{GeV}$ and $|\eta| < 2.5$ are applied in addition to the baseline selection.

Fiducial cross section scaling terms as a function of $C_{3W}$ in all $p_{\mathrm{T}}^{\gamma} \times |\phi_{f}|$ bins. Values are given relative to the SM prediction.

Scans of the profile likelihood test statistic $q$ as a function of $C_{3W}$, given with and without the pure BSM term.

Scans of the profile likelihood test statistic $q$ as a function of $C_{3W}$, given with and without the pure BSM term.

Best-fit values of $C_{3W}$ and corresponding 95% CL confidence intervals as a function of the maximum $p_{\mathrm{T}}^{\gamma}$ bin included in the fit, with and without the pure BSM term.

Best-fit values of $C_{3W}$ and corresponding 95% CL confidence intervals as a function of the maximum $p_{\mathrm{T}}^{\gamma}$ bin included in the fit, with and without the binning in $|\phi_{f}|$.

Response matrix from the fiducial to the reconstructed bins of the differential $p_{\mathrm{T}}^{\gamma} \times |\phi_{f}|$ cross section measurement.

Measured double-differential $p_{\mathrm{T}}^{\gamma} \times |\phi_{f}|$ cross section, compared to the MG5_aMC+PY8 NLO prediction. The differential cross sections $\sigma_{j}(\mathrm{pp}\rightarrow\mathrm{W}^{\pm}\gamma\rightarrow\ell^{\pm}\nu\gamma)$, where $\ell$ denotes all three lepton flavors, are measured in the following fiducial region: $p_{\mathrm{T}}^{\ell} > 80\,\mathrm{GeV}$, $|\eta^{\ell}| < 2.5$, $p_{\mathrm{T}}^{\gamma} > 150\,\mathrm{GeV}$, $|\eta^{\gamma}| < 2.5$, $p_{\mathrm{T}}^{\mathrm{miss}} > 40\,\mathrm{GeV}$, and $\Delta R(\ell, \gamma) > 0.7$. The leptons are dressed by adding the four-momenta of any photons with $\Delta R(\ell, \gamma) < 0.1$ to the four-momentum of the lepton. A smooth-cone photon isolation is also applied, with parameters $\delta_{0}=0.4$, $\epsilon=1.0$, and $n=1$. A veto on the presence of any jet with $p_{\mathrm{T}} > 30\,\mathrm{GeV}$ and $|\eta| < 2.5$ is also applied for this result.

Measured double-differential $p_{\mathrm{T}}^{\gamma} \times |\phi_{f}|$ cross section, compared to the MG5_aMC+PY8 NLO prediction. This table gives the entries for the $(0,\pi/6)$ slice. The differential cross sections $\sigma_{j}(\mathrm{pp}\rightarrow\mathrm{W}^{\pm}\gamma\rightarrow\ell^{\pm}\nu\gamma)$, where $\ell$ denotes all three lepton flavors, are measured in the following fiducial region: $p_{\mathrm{T}}^{\ell} > 80\,\mathrm{GeV}$, $|\eta^{\ell}| < 2.5$, $p_{\mathrm{T}}^{\gamma} > 150\,\mathrm{GeV}$, $|\eta^{\gamma}| < 2.5$, $p_{\mathrm{T}}^{\mathrm{miss}} > 40\,\mathrm{GeV}$, and $\Delta R(\ell, \gamma) > 0.7$. The leptons are dressed by adding the four-momenta of any photons with $\Delta R(\ell, \gamma) < 0.1$ to the four-momentum of the lepton. A smooth-cone photon isolation is also applied, with parameters $\delta_{0}=0.4$, $\epsilon=1.0$, and $n=1$. A veto on the presence of any jet with $p_{\mathrm{T}} > 30\,\mathrm{GeV}$ and $|\eta| < 2.5$ is also applied for this result.

Measured double-differential $p_{\mathrm{T}}^{\gamma} \times |\phi_{f}|$ cross section, compared to the MG5_aMC+PY8 NLO prediction. This table gives the entries for the $(\pi/6,\pi/3)$ slice. The differential cross sections $\sigma_{j}(\mathrm{pp}\rightarrow\mathrm{W}^{\pm}\gamma\rightarrow\ell^{\pm}\nu\gamma)$, where $\ell$ denotes all three lepton flavors, are measured in the following fiducial region: $p_{\mathrm{T}}^{\ell} > 80\,\mathrm{GeV}$, $|\eta^{\ell}| < 2.5$, $p_{\mathrm{T}}^{\gamma} > 150\,\mathrm{GeV}$, $|\eta^{\gamma}| < 2.5$, $p_{\mathrm{T}}^{\mathrm{miss}} > 40\,\mathrm{GeV}$, and $\Delta R(\ell, \gamma) > 0.7$. The leptons are dressed by adding the four-momenta of any photons with $\Delta R(\ell, \gamma) < 0.1$ to the four-momentum of the lepton. A smooth-cone photon isolation is also applied, with parameters $\delta_{0}=0.4$, $\epsilon=1.0$, and $n=1$. A veto on the presence of any jet with $p_{\mathrm{T}} > 30\,\mathrm{GeV}$ and $|\eta| < 2.5$ is also applied for this result.

Measured double-differential $p_{\mathrm{T}}^{\gamma} \times |\phi_{f}|$ cross section, compared to the MG5_aMC+PY8 NLO prediction. This table gives the entries for the $(\pi/3,\pi/2)$ slice. The differential cross sections $\sigma_{j}(\mathrm{pp}\rightarrow\mathrm{W}^{\pm}\gamma\rightarrow\ell^{\pm}\nu\gamma)$, where $\ell$ denotes all three lepton flavors, are measured in the following fiducial region: $p_{\mathrm{T}}^{\ell} > 80\,\mathrm{GeV}$, $|\eta^{\ell}| < 2.5$, $p_{\mathrm{T}}^{\gamma} > 150\,\mathrm{GeV}$, $|\eta^{\gamma}| < 2.5$, $p_{\mathrm{T}}^{\mathrm{miss}} > 40\,\mathrm{GeV}$, and $\Delta R(\ell, \gamma) > 0.7$. The leptons are dressed by adding the four-momenta of any photons with $\Delta R(\ell, \gamma) < 0.1$ to the four-momentum of the lepton. A smooth-cone photon isolation is also applied, with parameters $\delta_{0}=0.4$, $\epsilon=1.0$, and $n=1$. A veto on the presence of any jet with $p_{\mathrm{T}} > 30\,\mathrm{GeV}$ and $|\eta| < 2.5$ is also applied for this result.

Correlation matrix for the measured absolute differential $p_{\mathrm{T}}^{\gamma} \times |\phi_{f}|$ cross section.

SR1 diboson invariant mass distribution in the resolved tagged category after fitting the signal and sideband regions using a signal (ALP linear ZZ) plus background model. The last bin includes events with diboson invariant masses up to 3000 GeV. The signal is normalized to the 95% CL cross section limit at $f_a$ = 3 TeV (the scale factor used in the original figure for better visibility is not applied here).

SR2 diboson invariant mass distribution in the boosted untagged category after fitting the signal and sideband regions using a signal (ALP chiral ZH) plus background model. The last bin includes events with diboson invariant masses up to 3000 GeV. The signal is normalized to the 95% CL cross section limit at $f_a$ = 3 TeV (the scale factor used in the original figure for better visibility is not applied here).

SR2 diboson invariant mass distribution in the boosted tagged category after fitting the signal and sideband regions using a signal (ALP chiral ZH) plus background model. The last bin includes events with diboson invariant masses up to 3000 GeV. The signal is normalized to the 95% CL cross section limit at $f_a$ = 3 TeV.

SR2 diboson invariant mass distribution in the resolved untagged category after fitting the signal and sideband regions using a signal (ALP chiral ZH) plus background model. The last bin includes events with diboson invariant masses up to 3000 GeV. The signal is normalized to the 95% CL cross section limit at $f_a$ = 3 TeV (the scale factor used in the original figure for better visibility is not applied here).

SR2 diboson invariant mass distribution in the resolved tagged category after fitting the signal and sideband regions using a signal (ALP chiral ZH) plus background model. The last bin includes events with diboson invariant masses up to 3000 GeV. The signal is normalized to the 95% CL cross section limit at $f_a$ = 3 TeV (the scale factor used in the original figure for better visibility is not applied here).

Observed and expected 95% CL upper limit on $\sigma \mathcal{B}$(G -> ZZ) as a function of the resonance mass, taking into account all statistical and systematic uncertainties. The electron and muon channels and the various categories used in the analysis are combined. The inner green band and the outer yellow band represent the 68 and 95% coverage of the expected limits in the background-only hypothesis.

Observed and expected 95% CL upper limit on $\sigma \mathcal{B}$(W' -> ZW) as a function of the resonance mass, taking into account all statistical and systematic uncertainties. The electron and muon channels and the various categories used in the analysis are combined. The inner green band and the outer yellow band represent the 68 and 95% coverage of the expected limits in the background-only hypothesis.

Observed and expected 95% CL upper limit on the product of the ALP coupling to gluons and the coupling to Z bosons as a function of the mass scale $f_a$ for ALP masses smaller than 100 GeV.

Observed and expected 95% CL upper limit on the product of the ALP coupling to gluons and the chiral $a_\widetilde{2D}$ coupling as a function of the mass scale $f_a$ for ALP masses smaller than 100 GeV.

Upper limits on the production cross section times branching fraction of the b* RH hypothesis at a 95% CL. Dashed colored lines show the expected limits from the l+jets and all-hadronic channels, where the latter start at resonance masses of 1.4 TeV. The observed and expected limits from the combination are shown as solid and dashed black lines, respectively. The green and yellow bands show the 68 and 95% confidence intervals on the combined expected limits.

Upper limits on the production cross section times branching fraction of the b* VL hypothesis at a 95% CL. Dashed colored lines show the expected limits from the l+jets and all-hadronic channels, where the latter start at resonance masses of 1.4 TeV. The observed and expected limits from the combination are shown as solid and dashed black lines, respectively. The green and yellow bands show the 68 and 95% confidence intervals on the combined expected limits.

Upper limits on the production cross section times branching fraction of the B+b hypothesis at a 95% CL. Dashed colored lines show the expected limits from the l+jets and all-hadronic channels, where the latter start at resonance masses of 1.4 TeV. The observed and expected limits from the combination are shown as solid and dashed black lines, respectively. The green and yellow bands show the 68 and 95% confidence intervals on the combined expected limits.

Upper limits on the production cross section times branching fraction of the B+t hypothesis at a 95% CL. Dashed colored lines show the expected limits from the l+jets and all-hadronic channels, where the latter start at resonance masses of 1.4 TeV. The observed and expected limits from the combination are shown as solid and dashed black lines, respectively. The green and yellow bands show the 68 and 95% confidence intervals on the combined expected limits.