Observed 95% $\text{CL}_\text{S}$ upper limits on the production cross-section times acceptance times branching ratio to jets, $\sigma \cdot A \cdot \text{BR}$, of Gaussian-shaped signals of 5%, 10%, and 15% width relative to their peak mass, $m_G$. Also included are the corresponding expected upper limits predicted for the case the $m_{jj}$ distribution is observed to be identical to the background prediction in each bin and the $1\sigma$ and $2\sigma$ envelopes of outcomes expected for Poisson fluctuations around the background expectation. Limits are derived from the J100 signal region.

Observed 95% $\text{CL}_\text{S}$ upper limits on the the value of the coupling to quarks, $g_q$, of the $Z^\prime$ model as a function of the resonance mass $m_{Z^\prime}$. Also included are the corresponding expected upper limits predicted for the case the $m_{jj}$ distribution is observed to be identical to the background prediction in each bin and the $1\sigma$ and $2\sigma$ envelopes of outcomes expected for Poisson fluctuations around the background expectation. Limits are derived from the J50 signal region.

Observed 95% $\text{CL}_\text{S}$ upper limits on the the value of the coupling to quarks, $g_q$, of the $Z^\prime$ model as a function of the resonance mass $m_{Z^\prime}$. Also included are the corresponding expected upper limits predicted for the case the $m_{jj}$ distribution is observed to be identical to the background prediction in each bin and the $1\sigma$ and $2\sigma$ envelopes of outcomes expected for Poisson fluctuations around the background expectation. Limits are derived from the J100 signal region.

Acceptance of simulated $Z^\prime$ signal events given the analysis event selection as a function of $m_{Z^\prime}$. The solid black line corresponds to the acceptance without a lower $m_{jj}$ requirement applied, the solid blue line includes the $m_{jj} > 344$ GeV requirement of the J50 signal region, and the solid red line includes the $m_{jj} > 481$ GeV requirement of the J100 signal region.

Numbers of events in each of the two considered datasets after consecutively applying the analysis selections.

Observed profile likelihood scans of $\kappa_\lambda$. The scans are performed by varying only the coupling modifier of interest, while all other relevant coupling modifiers are fixed to unity.

Expected profile likelihood scans of $\kappa_\lambda$. The scans are performed by varying only the coupling modifier of interest, while all other relevant coupling modifiers are fixed to unity.

Observed profile likelihood scans of $\kappa_{2V}$. The scans are performed by varying only the coupling modifier of interest, while all other relevant coupling modifiers are fixed to unity.

Expected profile likelihood scans of $\kappa_{2V}$. The scans are performed by varying only the coupling modifier of interest, while all other relevant coupling modifiers are fixed to unity.

Confidence level contours at 68% (solid line) and 95% (dashed line) in the $(\kappa_\lambda, \kappa_{2V})$ parameter space, when all other coupling modifiers are fixed to their SM predictions. The corresponding expected contours are shown by the inner and outer shaded regions The SM prediction is indicated by the star, while the best-fit value is denoted by the cross.

Confidence level contours at 68% (solid line) and 95% (dashed line) in the $(\kappa_\lambda, \kappa_{2V})$ parameter space, when all other coupling modifiers are fixed to their SM predictions. The corresponding expected contours are shown by the inner and outer shaded regions The SM prediction is indicated by the star, while the best-fit value is denoted by the cross.

Observed $m_{\gamma\gamma}$ distributions for the high-mass categories in Run 2. The lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed $m_{\gamma\gamma}$ distributions for the high-mass categories in Run 3. The lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed $m_{\gamma\gamma}$ distributions for the high-mass categories in Run 2. The lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed $m_{\gamma\gamma}$ distributions for the high-mass categories in Run 3. The lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed $m_{\gamma\gamma}$ distributions for the high-mass categories in Run 2. 3he lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed $m_{\gamma\gamma}$ distributions for the high-mass categories in Run 3. The lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed $m_{\gamma\gamma}$ distributions for the low-mass categories in Run 2. The lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed $m_{\gamma\gamma}$ distributions for the low-mass categories in Run 3. The lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed $m_{\gamma\gamma}$ distributions for the low-mass categories in Run 2. The lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed $m_{\gamma\gamma}$ distributions for the low-mass categories in Run 3. The lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed $m_{\gamma\gamma}$ distributions for the low-mass categories in Run 2. The lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed $m_{\gamma\gamma}$ distributions for the low-mass categories in Run 3. The lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed $m_{\gamma\gamma}$ distributions for the low-mass categories in Run 2. The lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed $m_{\gamma\gamma}$ distributions for the low-mass categories in Run 3. The lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed and expected profiled likelihood scans on $\kappa_\lambda$ for the low-mass (LM) and high-mass (HM) regions separately and for their combination. The scan is performed by floating the indicated parameter of interest while fixing all the others to their SM value.

Observed and expected profiled likelihood scans on $\kappa_\lambda$ for the low-mass (LM) and high-mass (HM) regions separately and for their combination. The scan is performed by floating the indicated parameter of interest while fixing all the others to their SM value.

Observed and expected profiled likelihood scans on $\kappa_\lambda$ for the low-mass (LM) and high-mass (HM) regions separately and for their combination. The scan is performed by floating the indicated parameter of interest while fixing all the others to their SM value.

Observed and expected profiled likelihood scans on $\kappa_\lambda$ for the low-mass (LM) and high-mass (HM) regions separately and for their combination. The scan is performed by floating the indicated parameter of interest while fixing all the others to their SM value.

Observed and expected profiled likelihood scans on $\kappa_\lambda$ for the low-mass (LM) and high-mass (HM) regions separately and for their combination. The scan is performed by floating the indicated parameter of interest while fixing all the others to their SM value.

Observed and expected profiled likelihood scans on $\kappa_\lambda$ for the low-mass (LM) and high-mass (HM) regions separately and for their combination. The scan is performed by floating the indicated parameter of interest while fixing all the others to their SM value.

The expected number of events (estimated by using simulation) from the SM HH signals and single Higgs boson production, and the expected number of events from the continuum background, evaluated in the 120 GeV < $m_{\gamma\gamma}$ < 130 GeV window in Run 3 for the different low-mass (LM) and high-mass (HM) categories. For comparison, the number of data events is also shown. The uncertainties in the HH signals and single Higgs boson backgrounds include the systematic uncertainties discussed in Section 6. Asymmetric uncertainties arise primarily from the theory calculation of the SM ggF HH cross section and the large uncertainty in the yield of single Higgs bosons produced in ggF events in association with heavy-flavour jets. The uncertainty in the continuum background is given by the sum in quadrature of the statistical uncertainty from the fit to the data and the spurious signal uncertainty.

Unfolded $R(\rho_{s})$ observable in the 2-to-3 measurement (normalized and divided by bin width). The parton level is defined with two stable top-quarks and a jet with $p_{T}>50$ GeV and $|\eta|<2.5$.

Covariance matrix for statistical effects of the measured $R(\rho_{s})$ observable after unfolding, for the 2-to-3 measurement (normalized)

Covariance matrix for statistical and systematic effects of the measured $R(\rho_{s})$ observable after unfolding, for the 2-to-3 measurement (normalized)

Impact of systematic uncertainties on the 2-to-3 unfolded observable. Values are given in percentage of bin content.

Central value and breakdown of the uncertainties affecting the top-quark pole mass extraction from the 2-to-3 unfolded observable.

Unfolded number of events in the 2-to-7measurement (not normalized). The parton level is defined with two neutrinos, one electron and one muon of opposite electric charges, two $b$-jets and an additional jet (extrajet). The four-momentum of the sum of neutrinos has transverse component larger than 30 GeV. The $p_{T}$-leading lepton has $p_{T}>28$ GeV, while the sub-leading has $p_{T}>20$ GeV. The two $b$-jets with have $p_{T}>30$ GeV and the extrajet has $p^\text{extrajet}_{T}>60$ GeV. All the leptons and jets are separated by $\Delta R >0.4$ and have $|\eta|<2.5$.

Covariance matrix for statistical effects of the measured number of events after unfolding, for the 2-to-7 measurement (not normalized)

Covariance matrix for statistical and systematic effects of the measured number of events after unfolding, for the 2-to-7 measurement (not normalized)

Unfolded $R(\rho_{s})$ observable in the 2-to-7 measurement (normalized and divided by bin width). The parton level is defined with two neutrinos, one electron and one muon of opposite electric charges, two $b$-jets and an additional jet (extrajet). The four-momentum of the sum of neutrinos has transverse component larger than 30 GeV. The $p_{T}$-leading lepton has $p_{T}>28$ GeV, while the sub-leading has $p_{T}>20$ GeV. The two $b$-jets with have $p_{T}>30$ GeV and the extrajet has $p^\text{extrajet}_{T}>60$ GeV. All the leptons and jets are separated by $\Delta R >0.4$ and have $|\eta|<2.5$.

Covariance matrix for statistical effects of the measured $R(\rho_{s})$ observable after unfolding, for the 2-to-7 measurement (normalized)

Covariance matrix for statistical and systematic effects of the measured $R(\rho_{s})$ observable after unfolding, for the 2-to-7 measurement (normalized)

Impact of systematic uncertainties on the 2-to-7 unfolded observable. Values are given in percentage of bin content.

Central value and breakdown of the uncertainties affecting the top-quark pole mass extraction from the 2-to-7 unfolded observable.

Distributions of the VLQ-candidate mass, m_VLQ, in the (a&ndash;c) SRs, (d&ndash;f) W+jets CRs and (g&ndash;i) tt&#772; CRs after the fit to the background-only hypothesis. The columns correspond from left to right to the low-, middle-, and high-p_T^W bins in each region. Other includes remaining backgrounds from top quarks or that contain two W/Z bosons. The last bin includes overflow. Note: the 'Data' values in the table are normalized by the width of the bin to correspond to the number of events per 100 GeV

Distributions of the VLQ-candidate mass, m_VLQ, in the (a&ndash;c) SRs, (d&ndash;f) W+jets CRs and (g&ndash;i) tt&#772; CRs after the fit to the background-only hypothesis. The columns correspond from left to right to the low-, middle-, and high-p_T^W bins in each region. Other includes remaining backgrounds from top quarks or that contain two W/Z bosons. The last bin includes overflow. Note: the 'Data' values in the table are normalized by the width of the bin to correspond to the number of events per 100 GeV

Distributions of the VLQ-candidate mass, m_VLQ, in the (a&ndash;c) SRs, (d&ndash;f) W+jets CRs and (g&ndash;i) tt&#772; CRs after the fit to the background-only hypothesis. The columns correspond from left to right to the low-, middle-, and high-p_T^W bins in each region. Other includes remaining backgrounds from top quarks or that contain two W/Z bosons. The last bin includes overflow. Note: the 'Data' values in the table are normalized by the width of the bin to correspond to the number of events per 100 GeV

Distributions of the VLQ-candidate mass, m_VLQ, in the (a&ndash;c) SRs, (d&ndash;f) W+jets CRs and (g&ndash;i) tt&#772; CRs after the fit to the background-only hypothesis. The columns correspond from left to right to the low-, middle-, and high-p_T^W bins in each region. Other includes remaining backgrounds from top quarks or that contain two W/Z bosons. The last bin includes overflow. Note: the 'Data' values in the table are normalized by the width of the bin to correspond to the number of events per 100 GeV

Distributions of the VLQ-candidate mass, m_VLQ, in the (a&ndash;c) SRs, (d&ndash;f) W+jets CRs and (g&ndash;i) tt&#772; CRs after the fit to the background-only hypothesis. The columns correspond from left to right to the low-, middle-, and high-p_T^W bins in each region. Other includes remaining backgrounds from top quarks or that contain two W/Z bosons. The last bin includes overflow. Note: the 'Data' values in the table are normalized by the width of the bin to correspond to the number of events per 100 GeV

Distributions of the VLQ-candidate mass, m_VLQ, in the (a&ndash;c) SRs, (d&ndash;f) W+jets CRs and (g&ndash;i) tt&#772; CRs after the fit to the background-only hypothesis. The columns correspond from left to right to the low-, middle-, and high-p_T^W bins in each region. Other includes remaining backgrounds from top quarks or that contain two W/Z bosons. The last bin includes overflow. Note: the 'Data' values in the table are normalized by the width of the bin to correspond to the number of events per 100 GeV

Distributions of the VLQ-candidate mass, m_VLQ, in the W+jets VRs (a-f) and tt&#772; VRs (g-i) after the fit to the background-only hypothesis. The columns correspond from left to right to the low-, middle-, and high-p_T^W bins in each region. Other includes remaining backgrounds from top quarks or containing combinations having two W/Z bosons. Last bin includes overflow. Note: the 'Data' values in the table are normalized by the width of the bin to correspond to the number of events per 100 GeV

Distributions of the VLQ-candidate mass, m_VLQ, in the W+jets VRs (a-f) and tt&#772; VRs (g-i) after the fit to the background-only hypothesis. The columns correspond from left to right to the low-, middle-, and high-p_T^W bins in each region. Other includes remaining backgrounds from top quarks or containing combinations having two W/Z bosons. Last bin includes overflow. Note: the 'Data' values in the table are normalized by the width of the bin to correspond to the number of events per 100 GeV

Distributions of the VLQ-candidate mass, m_VLQ, in the W+jets VRs (a-f) and tt&#772; VRs (g-i) after the fit to the background-only hypothesis. The columns correspond from left to right to the low-, middle-, and high-p_T^W bins in each region. Other includes remaining backgrounds from top quarks or containing combinations having two W/Z bosons. Last bin includes overflow. Note: the 'Data' values in the table are normalized by the width of the bin to correspond to the number of events per 100 GeV

Distributions of the VLQ-candidate mass, m_VLQ, in the W+jets VRs (a-f) and tt&#772; VRs (g-i) after the fit to the background-only hypothesis. The columns correspond from left to right to the low-, middle-, and high-p_T^W bins in each region. Other includes remaining backgrounds from top quarks or containing combinations having two W/Z bosons. Last bin includes overflow. Note: the 'Data' values in the table are normalized by the width of the bin to correspond to the number of events per 100 GeV

Distributions of the VLQ-candidate mass, m_VLQ, in the W+jets VRs (a-f) and tt&#772; VRs (g-i) after the fit to the background-only hypothesis. The columns correspond from left to right to the low-, middle-, and high-p_T^W bins in each region. Other includes remaining backgrounds from top quarks or containing combinations having two W/Z bosons. Last bin includes overflow. Note: the 'Data' values in the table are normalized by the width of the bin to correspond to the number of events per 100 GeV

Distributions of the VLQ-candidate mass, m_VLQ, in the W+jets VRs (a-f) and tt&#772; VRs (g-i) after the fit to the background-only hypothesis. The columns correspond from left to right to the low-, middle-, and high-p_T^W bins in each region. Other includes remaining backgrounds from top quarks or containing combinations having two W/Z bosons. Last bin includes overflow. Note: the 'Data' values in the table are normalized by the width of the bin to correspond to the number of events per 100 GeV

Expected (background-only) and observed 95&percnt;&nbsp;CL upper limits on the VLQ coupling &kappa; as functions of the VLQ mass m_Q, for T-singlet (a) and Y-triplet (b) vector-like quarks. The green and yellow bands indicate the systematic uncertainties which are profiled in the fit for the observed upper limits. For the T-singlet model, the result of the latest ATLAS combination of searches for single vector-like top-quarks&nbsp; is overlaid; this includes the decay modes T&rarr;H t and T&rarr;Z t. These interpretations are limited to parameter combinations for which the model corrections are valid, by restricting the VLQ relative width to &Gamma;_Q/m_Q &lt; 0.5, as indicated by the grey dashed line.

Expected (background-only) and observed 95&percnt;&nbsp;CL upper limits on the VLQ coupling &kappa; as functions of the VLQ mass m_Q, for T-singlet (a) and Y-triplet (b) vector-like quarks. The green and yellow bands indicate the systematic uncertainties which are profiled in the fit for the observed upper limits. For the T-singlet model, the result of the latest ATLAS combination of searches for single vector-like top-quarks&nbsp; is overlaid; this includes the decay modes T&rarr;H t and T&rarr;Z t. These interpretations are limited to parameter combinations for which the model corrections are valid, by restricting the VLQ relative width to &Gamma;_Q/m_Q &lt; 0.5, as indicated by the grey dashed line.

Exclusion limit (at 95&percnt; CL) for (a) T-singlet and (b) Y-triplet, expressed in terms of an upper limit on the VLQ relative width &Gamma;_Q/m_Q, within its validity range for the modelling used, as a function of the VLQ mass m_Q. This is an alternative presentation of the upper limit set in terms of the coupling &kappa; in Figure&nbsp;6. As can be seen by the fact the interference-included and signal-only exclusion curves overlap almost entirely, the effect of neglecting the interference is negligible for the vector-like Y-quark.

Exclusion limit (at 95&percnt; CL) for (a) T-singlet and (b) Y-triplet, expressed in terms of an upper limit on the VLQ relative width &Gamma;_Q/m_Q, within its validity range for the modelling used, as a function of the VLQ mass m_Q. This is an alternative presentation of the upper limit set in terms of the coupling &kappa; in Figure&nbsp;6. As can be seen by the fact the interference-included and signal-only exclusion curves overlap almost entirely, the effect of neglecting the interference is negligible for the vector-like Y-quark.

Data from Figure 2, panel d, upper panel, $v_{0}(p_{T})$ for $\eta_{gap}$ = 1, 0-5% Centrality

Data from Figure 2, panel d, lower panel, $v_{0}(p_{T})$ for $\eta_{gap}$ = 1, 50-60% Centrality

Data from Figure 3, panel a, $v_{0}(p_{T})$ for $p^{ref}_{T}$ = 0.5-2 GeV, 0-5% Centrality, $\eta_{gap}$=0

Data from Figure 3, panel a, $v_{0}(p_{T})$ for $p^{ref}_{T}$ = 0.5-2 GeV, 0-5% Centrality, $\eta_{gap}$=1

Data from Figure 3, panel a, $v_{0}(p_{T})$ for $p^{ref}_{T}$ = 0.5-2 GeV, 0-5% Centrality, $\eta_{gap}$=2

Data from Figure 3, panel a, $v_{0}(p_{T})$ for $p^{ref}_{T}$ = 0.5-2 GeV, 0-5% Centrality, $\eta_{gap}$=3

Data from Figure 3, panel b, $v_{0}(p_{T})$ for $p^{ref}_{T}$ = 0.5-2 GeV, 60-70% Centrality, $\eta_{gap}$=0

Data from Figure 3, panel b, $v_{0}(p_{T})$ for $p^{ref}_{T}$ = 0.5-2 GeV, 60-70% Centrality, $\eta_{gap}$=1

Data from Figure 3, panel b, $v_{0}(p_{T})$ for $p^{ref}_{T}$ = 0.5-2 GeV, 60-70% Centrality, $\eta_{gap}$=2

Data from Figure 3, panel b, $v_{0}(p_{T})$ for $p^{ref}_{T}$ = 0.5-2 GeV, 60-70% Centrality, $\eta_{gap}$=3

Data from Figure 4, panel a, $v_{0}(p_{T})$ for $p^{ref}_{T}$ = 0.5-2 GeV, $\eta_{gap}$=1, 0-5% Centrality

Data from Figure 4, panel a, $v_{0}(p_{T})$ for $p^{ref}_{T}$ = 0.5-2 GeV, $\eta_{gap}$=1, 5-10% Centrality

Data from Figure 4, panel a, $v_{0}(p_{T})$ for $p^{ref}_{T}$ = 0.5-2 GeV, $\eta_{gap}$=1, 10-20% Centrality

Data from Figure 4, panel a, $v_{0}(p_{T})$ for $p^{ref}_{T}$ = 0.5-2 GeV, $\eta_{gap}$=1, 20-30% Centrality

Data from Figure 4, panel a, $v_{0}(p_{T})$ for $p^{ref}_{T}$ = 0.5-2 GeV, $\eta_{gap}$=1, 30-40% Centrality

Data from Figure 4, panel a, $v_{0}(p_{T})$ for $p^{ref}_{T}$ = 0.5-2 GeV, $\eta_{gap}$=1, 40-50% Centrality

Data from Figure 4, panel a, $v_{0}(p_{T})$ for $p^{ref}_{T}$ = 0.5-2 GeV, $\eta_{gap}$=1, 50-60% Centrality

Data from Figure 4, panel a, $v_{0}(p_{T})$ for $p^{ref}_{T}$ = 0.5-2 GeV, $\eta_{gap}$=1, 60-70% Centrality

Data from Figure 4, panel b, $v_{0}(p_{T})/v_{0}$ for $p^{ref}_{T}$ = 0.5-2 GeV, $\eta_{gap}$=1, 0-5% Centrality

Data from Figure 4, panel b, $v_{0}(p_{T})/v_{0}$ for $p^{ref}_{T}$ = 0.5-2 GeV, $\eta_{gap}$=1, 5-10% Centrality

Data from Figure 4, panel b, $v_{0}(p_{T})/v_{0}$ for $p^{ref}_{T}$ = 0.5-2 GeV, $\eta_{gap}$=1, 10-20% Centrality

Data from Figure 4, panel b, $v_{0}(p_{T})/v_{0}$ for $p^{ref}_{T}$ = 0.5-2 GeV, $\eta_{gap}$=1, 20-30% Centrality

Data from Figure 4, panel b, $v_{0}(p_{T})/v_{0}$ for $p^{ref}_{T}$ = 0.5-2 GeV, $\eta_{gap}$=1, 30-40% Centrality

Data from Figure 4, panel b, $v_{0}(p_{T})/v_{0}$ for $p^{ref}_{T}$ = 0.5-2 GeV, $\eta_{gap}$=1, 40-50% Centrality

Data from Figure 4, panel b, $v_{0}(p_{T})/v_{0}$ for $p^{ref}_{T}$ = 0.5-2 GeV, $\eta_{gap}$=1, 50-60% Centrality

Data from Figure 4, panel b, $v_{0}(p_{T})/v_{0}$ for $p^{ref}_{T}$ = 0.5-2 GeV, $\eta_{gap}$=1, 60-70% Centrality

Data from Figure 5, panel a, $v_{0}(p_{T})/v_{0}$ for $p^{ref}_{T}$ = 0.5-2 GeV, $\eta_{gap}$=1, 0-5% Centrality

Data from Figure 5, panel b, $v_{0}(p_{T})/v_{0}$ for $p^{ref}_{T}$ = 0.5-2 GeV, $\eta_{gap}$=1, 0-5% Centrality

Data from Appendix, Figure 6, panel a, $v_{0}(p_{T})$ for $p^{ref}_{T}$ = 0.5-2 GeV, $\eta_{gap}$ = 1, 0-5% Centrality

Data from Appendix, Figure 6, panel b, $v_{0}(p_{T})$ for $p^{ref}_{T}$ = 0.5-2 GeV, $\eta_{gap}$ = 1, 10-20% Centrality

Data from Appendix, Figure 6, panel c, $v_{0}(p_{T})$ for $p^{ref}_{T}$ = 0.5-2 GeV, $\eta_{gap}$ = 1, 30-40% Centrality

Data from Appendix, Figure 6, panel d, $v_{0}(p_{T})$ for $p^{ref}_{T}$ = 0.5-2 GeV, $\eta_{gap}$ = 1, 60-70% Centrality

Data from Appendix, Figure 7, Zero Crossing Point of $v_{0}(p_{T})$ for $\eta_{gap}$ = 1

Data from Appendix, Figure 7, $\left\langle [p_{T}]\right\rangle$ for $p_{T}$ range of 0.5-10 GeV, $\eta_{gap}$ = 1

Data from Appendix, Figure 8, panel a, Closure of Sum Rule 1 for $\eta_{gap}$ = 1

Data from Appendix, Figure 8, panel b, Closure of Sum Rule 2 for $\eta_{gap}$ = 1

Data from Appendix, Figure 9, panel a, $v_{0}$ vs $N_{ch}$ for $\eta_{gap}$ = 1

Data from Appendix, Figure 9, panel b, $v_{0} / v^{5\%}_{0}$ vs $N_{ch}$ for $\eta_{gap}$ = 1

Data from Appendix, Figure 10, panel a, $v_{0}\sqrt{N_{ch}}$ vs $N_{ch}$ for $\eta_{gap}$ = 1

Data from Appendix, Figure 10, panel b, $v_{0}\sqrt{N_{ch}}$ vs Centrality for $\eta_{gap}$ = 1

Data from Appendix, Figure 11, $v_{0}(p_{T})\,\sqrt{\left\langle N_{\mathrm{ch}}\right\rangle}$ for $p^{ref}_{T}$ = 0.5-2 GeV, $\eta_{gap}$ = 1, 0-5% Centrality

Data from Appendix, Figure 11, $v_{0}(p_{T})\,\sqrt{\left\langle N_{\mathrm{ch}}\right\rangle}$ for $p^{ref}_{T}$ = 0.5-2 GeV, $\eta_{gap}$ = 1, 5-10% Centrality

Data from Appendix, Figure 11, $v_{0}(p_{T})\,\sqrt{\left\langle N_{\mathrm{ch}}\right\rangle}$ for $p^{ref}_{T}$ = 0.5-2 GeV, $\eta_{gap}$ = 1, 10-20% Centrality

Data from Appendix, Figure 11, $v_{0}(p_{T})\,\sqrt{\left\langle N_{\mathrm{ch}}\right\rangle}$ for $p^{ref}_{T}$ = 0.5-2 GeV, $\eta_{gap}$ = 1, 20-30% Centrality

Data from Appendix, Figure 11, $v_{0}(p_{T})\,\sqrt{\left\langle N_{\mathrm{ch}}\right\rangle}$ for $p^{ref}_{T}$ = 0.5-2 GeV, $\eta_{gap}$ = 1, 30-40% Centrality

Data from Appendix, Figure 11, $v_{0}(p_{T})\,\sqrt{\left\langle N_{\mathrm{ch}}\right\rangle}$ for $p^{ref}_{T}$ = 0.5-2 GeV, $\eta_{gap}$ = 1, 40-50% Centrality

Data from Appendix, Figure 11, $v_{0}(p_{T})\,\sqrt{\left\langle N_{\mathrm{ch}}\right\rangle}$ for $p^{ref}_{T}$ = 0.5-2 GeV, $\eta_{gap}$ = 1, 50-60% Centrality

Data from Appendix, Figure 11, $v_{0}(p_{T})\,\sqrt{\left\langle N_{\mathrm{ch}}\right\rangle}$ for $p^{ref}_{T}$ = 0.5-2 GeV, $\eta_{gap}$ = 1, 60-70% Centrality

Data from Auxiliary, Figure 1, Top row, Left column, $v_{0}(p_{T})$ for $p^{ref}_{T}$ = 0.5-5 GeV, 0-5% Centrality, $\eta_{gap}$=0

Data from Auxiliary, Figure 1, Top row, Left column, $v_{0}(p_{T})$ for $p^{ref}_{T}$ = 0.5-5 GeV, 0-5% Centrality, $\eta_{gap}$=1

Data from Auxiliary, Figure 1, Top row, Left column, $v_{0}(p_{T})$ for $p^{ref}_{T}$ = 0.5-5 GeV, 0-5% Centrality, $\eta_{gap}$=2

Data from Auxiliary, Figure 1, Top row, Left column, $v_{0}(p_{T})$ for $p^{ref}_{T}$ = 0.5-5 GeV, 0-5% Centrality, $\eta_{gap}$=3

Data from Auxiliary, Figure 1, Top row, Right column, $v_{0}(p_{T})$ for $p^{ref}_{T}$ = 0.5-5 GeV, 60-70% Centrality, $\eta_{gap}$=0

Data from Auxiliary, Figure 1, Top row, Right column, $v_{0}(p_{T})$ for $p^{ref}_{T}$ = 0.5-5 GeV, 60-70% Centrality, $\eta_{gap}$=1

Data from Auxiliary, Figure 1, Top row, Right column, $v_{0}(p_{T})$ for $p^{ref}_{T}$ = 0.5-5 GeV, 60-70% Centrality, $\eta_{gap}$=2

Data from Auxiliary, Figure 1, Top row, Right column, $v_{0}(p_{T})$ for $p^{ref}_{T}$ = 0.5-5 GeV, 60-70% Centrality, $\eta_{gap}$=3

Data from Auxiliary, Figure 1, Bottom row, Left column, $v_{0}(p_{T})$ for $p^{ref}_{T}$ = 0.5-5 GeV, 0-5% Centrality, $\eta_{gap}$=0

Data from Auxiliary, Figure 1, Bottom row, Left column, $v_{0}(p_{T})$ for $p^{ref}_{T}$ = 0.5-5 GeV, 0-5% Centrality, $\eta_{gap}$=1

Data from Auxiliary, Figure 1, Bottom row, Left column, $v_{0}(p_{T})$ for $p^{ref}_{T}$ = 0.5-5 GeV, 0-5% Centrality, $\eta_{gap}$=2

Data from Auxiliary, Figure 1, Bottom row, Left column, $v_{0}(p_{T})$ for $p^{ref}_{T}$ = 0.5-5 GeV, 0-5% Centrality, $\eta_{gap}$=3

Data from Auxiliary, Figure 1, Bottom row, Right column, $v_{0}(p_{T})$ for $p^{ref}_{T}$ = 0.5-5 GeV, 60-70% Centrality, $\eta_{gap}$=0

Data from Auxiliary, Figure 1, Bottom row, Right column, $v_{0}(p_{T})$ for $p^{ref}_{T}$ = 0.5-5 GeV, 60-70% Centrality, $\eta_{gap}$=1

Data from Auxiliary, Figure 1, Bottom row, Right column, $v_{0}(p_{T})$ for $p^{ref}_{T}$ = 0.5-5 GeV, 60-70% Centrality, $\eta_{gap}$=2

Data from Auxiliary, Figure 1, Bottom row, Right column, $v_{0}(p_{T})$ for $p^{ref}_{T}$ = 0.5-5 GeV, 60-70% Centrality, $\eta_{gap}$=3

Data from Auxiliary, Figure 2, $v_{0}(p_{T})$ For $\eta_{gap}$ = 0, and 0-5% Centrality

Data from Auxiliary, Figure 2, $v_{0}(p_{T})$ For $\eta_{gap}$ = 0, and 5-10% Centrality

Data from Auxiliary, Figure 2, $v_{0}(p_{T})$ For $\eta_{gap}$ = 0, and 10-20% Centrality

Data from Auxiliary, Figure 2, $v_{0}(p_{T})$ For $\eta_{gap}$ = 0, and 20-30% Centrality

Data from Auxiliary, Figure 2, $v_{0}(p_{T})$ For $\eta_{gap}$ = 0, and 30-40% Centrality

Data from Auxiliary, Figure 2, $v_{0}(p_{T})$ For $\eta_{gap}$ = 0, and 40-50% Centrality

Data from Auxiliary, Figure 2, $v_{0}(p_{T})$ For $\eta_{gap}$ = 0, and 50-60% Centrality

Data from Auxiliary, Figure 2, $v_{0}(p_{T})$ For $\eta_{gap}$ = 0, and 60-70% Centrality

Data from Auxiliary, Figure 3, $v_{0}(p_{T})$ For $\eta_{gap}$ = 1, and 0-5% Centrality

Data from Auxiliary, Figure 3, $v_{0}(p_{T})$ For $\eta_{gap}$ = 1, and 5-10% Centrality

Data from Auxiliary, Figure 3, $v_{0}(p_{T})$ For $\eta_{gap}$ = 1, and 10-20% Centrality

Data from Auxiliary, Figure 3, $v_{0}(p_{T})$ For $\eta_{gap}$ = 1, and 20-30% Centrality

Data from Auxiliary, Figure 3, $v_{0}(p_{T})$ For $\eta_{gap}$ = 1, and 30-40% Centrality

Data from Auxiliary, Figure 3, $v_{0}(p_{T})$ For $\eta_{gap}$ = 1, and 40-50% Centrality

Data from Auxiliary, Figure 3, $v_{0}(p_{T})$ For $\eta_{gap}$ = 1, and 50-60% Centrality

Data from Auxiliary, Figure 3, $v_{0}(p_{T})$ For $\eta_{gap}$ = 1, and 60-70% Centrality

Data from Auxiliary, Figure 4, $v_{0}(p_{T})$ For $\eta_{gap}$ = 2, and 0-5% Centrality

Data from Auxiliary, Figure 4, $v_{0}(p_{T})$ For $\eta_{gap}$ = 2, and 5-10% Centrality

Data from Auxiliary, Figure 4, $v_{0}(p_{T})$ For $\eta_{gap}$ = 2, and 10-20% Centrality

Data from Auxiliary, Figure 4, $v_{0}(p_{T})$ For $\eta_{gap}$ = 2, and 20-30% Centrality

Data from Auxiliary, Figure 4, $v_{0}(p_{T})$ For $\eta_{gap}$ = 2, and 30-40% Centrality

Data from Auxiliary, Figure 4, $v_{0}(p_{T})$ For $\eta_{gap}$ = 2, and 40-50% Centrality

Data from Auxiliary, Figure 4, $v_{0}(p_{T})$ For $\eta_{gap}$ = 2, and 50-60% Centrality

Data from Auxiliary, Figure 4, $v_{0}(p_{T})$ For $\eta_{gap}$ = 2, and 60-70% Centrality

Data from Auxiliary, Figure 5, $v_{0}(p_{T})$ For $\eta_{gap}$ = 3, and 0-5% Centrality

Data from Auxiliary, Figure 5, $v_{0}(p_{T})$ For $\eta_{gap}$ = 3, and 5-10% Centrality

Data from Auxiliary, Figure 5, $v_{0}(p_{T})$ For $\eta_{gap}$ = 3, and 10-20% Centrality

Data from Auxiliary, Figure 5, $v_{0}(p_{T})$ For $\eta_{gap}$ = 3, and 20-30% Centrality

Data from Auxiliary, Figure 5, $v_{0}(p_{T})$ For $\eta_{gap}$ = 3, and 30-40% Centrality

Data from Auxiliary Figure 5, $v_{0}(p_{T})$ For $\eta_{gap}$ = 3, and 40-50% Centrality

Data from Auxiliary Figure 5, $v_{0}(p_{T})$ For $\eta_{gap}$ = 3, and 50-60% Centrality

Data from Auxiliary Figure 5, $v_{0}(p_{T})$ For $\eta_{gap}$ = 3, and 60-70% Centrality

VLL &quot;4321&quot; cross-sections at NLO order of accuracy obtained by MadGraph.

SUSY RPV LQD higgsino cross-sections at NLO + NLL order of accuracy obtained by Resummino.

SUSY RPV LQD wino cross-sections at NLO + NLL order of accuracy obtained by Resummino.

Cutflow of the selection requirements for VLL signals with m_VLL =600, 900, and 1200 GeV. The yields correspond to an integrated luminosity of 126 fb^-1 (140 fb^-1) for the BJET (MST and MSDT) signal regions. The first row refers to unweighted event yields, while the yields presented in other rows are computed after applying event weights according to the selected object reconstruction and identification efficiency scale factors. Dashes (–&ndash;) refer to requirements that are not applicable.

The expected acceptance times efficiency (including object identification and reconstruction, trigger selection, and event selection) for VLL signal as a function of m_VLL for the combined signal regions as well as for three individual signal region categories: 1&tau;_had &ge;3b MST, 1&tau;_had &ge;3b BJET and &ge;2&tau;_had &ge;3b MSDT. The region 1&tau;_had &ge;3b MST refers to the combination of 1&tau;_had 3b MST and 1&tau;_had &ge;4b MST signal regions, while the region 1&tau;_had &ge;3b BJET refers to the combination of 1&tau;_had 3b BJET and 1&tau;_had &ge;4b BJET signal regions.

$r_{q}$, Gluon jets, $500~\text{GeV} \leq p_T < 600~\text{GeV}$, Gluon $\eta$, Fig 5

$r_{q}$, Gluon jets, $600~\text{GeV} \leq p_T < 800~\text{GeV}$, Gluon $\eta$, Fig 5

$r_{q}$, Gluon jets, $800~\text{GeV} \leq p_T < 1200~\text{GeV}$, Gluon $\eta$, Fig 5

$r_{q}$, Gluon jets, $1200~\text{GeV} \leq p_T < 2500~\text{GeV}$, Gluon $\eta$, Fig 5

$r_{q}$, Quark jets, $240\text{GeV} \leq p_T < 300~\text{GeV}$, Quark $\eta$, Fig 5

$r_{q}$, Quark jets, $300~\text{GeV} \leq p_T < 400~\text{GeV}$, Quark $\eta$, Fig 5

$r_{q}$, Quark jets, $400~\text{GeV} \leq p_T < 500~\text{GeV}$, Quark $\eta$, Fig 5

$r_{q}$, Quark jets, $500~\text{GeV} \leq p_T < 600~\text{GeV}$, Quark $\eta$, Fig 5

$r_{q}$, Quark jets, $600~\text{GeV} \leq p_T < 800~\text{GeV}$, Quark $\eta$, Fig 5

$r_{q}$, Quark jets, $800~\text{GeV} \leq p_T < 1200~\text{GeV}$, Quark $\eta$, Fig 5

$r_{q}$, Quark jets, $1200~\text{GeV} \leq p_T < 2500~\text{GeV}$, Quark $\eta$, Fig 5

$r_{q}$, mixed, $240\text{GeV} \leq p_T < 300~\text{GeV}$, Central $\eta$, Fig 1

$r_{q}$, mixed, $240\text{GeV} \leq p_T < 300~\text{GeV}$, Forward $\eta$, Fig 1

$r_{q}$, mixed, $300~\text{GeV} \leq p_T < 400~\text{GeV}$, Central $\eta$, Fig 1

$r_{q}$, mixed, $300~\text{GeV} \leq p_T < 400~\text{GeV}$, Forward $\eta$, Fig 1

$r_{q}$, mixed, $400~\text{GeV} \leq p_T < 500~\text{GeV}$, Central $\eta$, Fig 1

$r_{q}$, mixed, $400~\text{GeV} \leq p_T < 500~\text{GeV}$, Forward $\eta$, Fig 1

$r_{q}$, mixed, $500~\text{GeV} \leq p_T < 600~\text{GeV}$, Central $\eta$, Fig 1

$r_{q}$, mixed, $500~\text{GeV} \leq p_T < 600~\text{GeV}$, Forward $\eta$, Fig 1

$r_{q}$, mixed, $600~\text{GeV} \leq p_T < 800~\text{GeV}$, Central $\eta$, Fig 1

$r_{q}$, mixed, $600~\text{GeV} \leq p_T < 800~\text{GeV}$, Forward $\eta$, Fig 1

$Moment1$, 240\text{GeV} \leq p_T < 800~\text{GeV}, Central $\eta$, Fig 2(a)

$Moment1$, 240\text{GeV} \leq p_T < 800~\text{GeV}, Forward $\eta$, Fig 2(b)

$Moment1$, 240\text{GeV} \leq p_T < 800~\text{GeV}, Gluon $\eta$, Fig 6(a)

$Moment1$, 240\text{GeV} \leq p_T < 800~\text{GeV}, Quark $\eta$, Fig 6(b)

$Moment2$, 240\text{GeV} \leq p_T < 800~\text{GeV}, Central $\eta$, Fig 2(a)

$Moment2$, 240\text{GeV} \leq p_T < 800~\text{GeV}, Forward $\eta$, Fig 2(b)

$Moment2$, 240\text{GeV} \leq p_T < 800~\text{GeV}, Gluon $\eta$, Fig 6(a)

$Moment2$, 240\text{GeV} \leq p_T < 800~\text{GeV}, Quark $\eta$, Fig 6(b)

$Moment3$, 240\text{GeV} \leq p_T < 800~\text{GeV}, Central $\eta$, Fig 2(a)

$Moment3$, 240\text{GeV} \leq p_T < 800~\text{GeV}, Forward $\eta$, Fig 2(b)

$Moment3$, 240\text{GeV} \leq p_T < 800~\text{GeV}, Gluon $\eta$, Fig 6(a)

$Moment3$, 240\text{GeV} \leq p_T < 800~\text{GeV}, Quark $\eta$, Fig 6(b)

$Moment4$, 240\text{GeV} \leq p_T < 800~\text{GeV}, Central $\eta$, Fig 2(a)

$Moment4$, 240\text{GeV} \leq p_T < 800~\text{GeV}, Forward $\eta$, Fig 2(b)

$Moment4$, 240\text{GeV} \leq p_T < 800~\text{GeV}, Gluon $\eta$, Fig 6(a)

$Moment4$, 240\text{GeV} \leq p_T < 800~\text{GeV}, Quark $\eta$, Fig 6(b)

$Moment5$, 240\text{GeV} \leq p_T < 800~\text{GeV}, Central $\eta$, Fig 2(a)

$Moment5$, 240\text{GeV} \leq p_T < 800~\text{GeV}, Forward $\eta$, Fig 2(b)

$Moment5$, 240\text{GeV} \leq p_T < 800~\text{GeV}, Gluon $\eta$, Fig 6(a)

$Moment5$, 240\text{GeV} \leq p_T < 800~\text{GeV}, Quark $\eta$, Fig 6(b)

$Moment6$, 240\text{GeV} \leq p_T < 800~\text{GeV}, Central $\eta$, Fig 2(a)

$Moment6$, 240\text{GeV} \leq p_T < 800~\text{GeV}, Forward $\eta$, Fig 2(b)

$Moment6$, 240\text{GeV} \leq p_T < 800~\text{GeV}, Gluon $\eta$, Fig 6(a)

$Moment6$, 240\text{GeV} \leq p_T < 800~\text{GeV}, Quark $\eta$, Fig 6(b)

$Cumulant4$, 240\text{GeV} \leq p_T < 800~\text{GeV}, Central $\eta$, Fig 3(a)

$Cumulant5$, 240\text{GeV} \leq p_T < 800~\text{GeV}, Central $\eta$, Fig 3(b)

$Cumulant6$, 240\text{GeV} \leq p_T < 800~\text{GeV}, Central $\eta$, Fig 3(c) and 3(d)

$Cumulant22$, 240\text{GeV} \leq p_T < 800~\text{GeV}, Central $\eta$, Fig 3(a)

$Cumulant23$, 240\text{GeV} \leq p_T < 800~\text{GeV}, Central $\eta$, Fig 3(b)

$Cumulant222$, 240\text{GeV} \leq p_T < 800~\text{GeV}, Central $\eta$, Fig 3(c)

$Cumulant33$, 240\text{GeV} \leq p_T < 800~\text{GeV}, Central $\eta$, Fig 3(d)

Values of the test statistic $t_{\kappa_{g,\mathrm{off-shell}}}$ as a function of $\kappa_{g,\mathrm{off-shell}}$ while profiling $\kappa_{V,\mathrm{off-shell}}$ obtained with an Asimov dataset and with data. The values with all nuisance parameters fixed at their best-fit values (stat-only) are added for comparison. The 68% and 95% confidence intervals obtained from the Neyman construction are also added.

Values of the test statistic $t_{\kappa_{V,\mathrm{off-shell}}}$ as a function of $\kappa_{V,\mathrm{off-shell}}$ while profiling $\kappa_{g,\mathrm{off-shell}}$ obtained with an Asimov dataset and with data. The values with all nuisance parameters fixed at their best-fit values (stat-only) are added for comparison. The 68% and 95% confidence intervals obtained from the Neyman construction are also added.

Values of the test statistic $t_{\kappa_{H}}$ as a function of $\kappa_{H}=\Gamma_H/\Gamma_H^{\mathrm{SM}}$ obtained with an Asimov dataset and with data. The values with all nuisance parameters fixed at their best-fit values (stat-only) are added for comparison. The 68% and 95% confidence intervals obtained from the Neyman construction are also added.

Values of the test statistic $t_{R_{gg}}$ as a function of $R_{gg}=\kappa_{g,\mathrm{on-shell}}^2/\kappa_{g,\mathrm{off-shell}}^2$ while profiling $R_{VV}=\kappa_{V,\mathrm{on-shell}}^2/\kappa_{V,\mathrm{off-shell}}^2$ and fixing $\kappa_H=1$ obtained with an Asimov dataset and with data. The values with all nuisance parameters fixed at their best-fit values (stat-only) are added for comparison. The 68% and 95% confidence intervals obtained from the Neyman construction are also added.

Values of the test statistic $t_{R_{VV}}$ as a function of $R_{VV}=\kappa_{V,\mathrm{on-shell}}^2/\kappa_{V,\mathrm{off-shell}}^2$ while profiling $R_{gg}=\kappa_{g,\mathrm{on-shell}}^2/\kappa_{g,\mathrm{off-shell}}^2$ and fixing $\kappa_H=1$ obtained with an Asimov dataset and with data. The values with all nuisance parameters fixed at their best-fit values (stat-only) are added for comparison. The 68% and 95% confidence intervals obtained from the Neyman construction are also added.

Values of the test statistic $t_{\mu_{\mathrm{off-shell}}}$ assuming a single parameter of interest $\mu_{\mathrm{off-shell}}$ obtained with an Asimov dataset and with data when combining the $H^*\rightarrow ZZ\rightarrow 4\ell$ and $H^*\rightarrow ZZ\rightarrow 2\ell 2\nu$ decay channels. The values from the histogram-based analysis (Phys. Lett. B 846 (2023) 138223) are added for comparison. The 68% and 95% confidence intervals obtained from the Neyman construction are also added.

Values of the test statistic $t_{\kappa_{H}}$ as a function of $\kappa_{H}=\Gamma_H/\Gamma_H^{\mathrm{SM}}$ obtained with an Asimov dataset and with data in the $H^*\rightarrow ZZ\rightarrow 4\ell$ decay channel. The values from the histogram-based analysis (Phys. Lett. B 846 (2023) 138223) are added for comparison. The 68% and 95% confidence intervals obtained from the Neyman construction are also added.

Values of the test statistic $t_{\kappa_{H}}$ as a function of $\kappa_{H}=\Gamma_H/\Gamma_H^{\mathrm{SM}}$ obtained with an Asimov dataset and with data when combining the $H^*\rightarrow ZZ\rightarrow 4\ell$ and $H^*\rightarrow ZZ\rightarrow 2\ell 2\nu$ decay channels. The values from the histogram-based analysis (Phys. Lett. B 846 (2023) 138223) are added for comparison. The 68% and 95% confidence intervals obtained from the Neyman construction are also added.

Values of the test statistic $t_{R_{gg}}$ as a function of $R_{gg}$ while profiling $R_{VV}$ and fixing $\kappa_H=1$ obtained with an Asimov dataset and with data. The values from the histogram-based analysis (Phys. Lett. B 846 (2023) 138223) are added for comparison. The 68% and 95% confidence intervals obtained from the Neyman construction are also added.

Values of the test statistic $t_{R_{VV}}$ as a function of $R_{VV}$ while profiling $R_{gg}$ and fixing $\kappa_H=1$ obtained with an Asimov dataset and with data. The values from the histogram-based analysis (Phys. Lett. B 846 (2023) 138223) are added for comparison. The 68% and 95% confidence intervals obtained from the Neyman construction are also added.

The modified energy correlation function, for data, background (pre- and post-reweighting) and three $H\rightarrow Za$ signal hypotheses (for $a\rightarrow q\bar{q}/gg$ inclusively). Events are required to pass the complete event selection but not the classification NN requirement. The background normalization is set equal to that of the data for events passing the preselection and being in the $m_{\ell\ell j}$ 100-180 GeV region. The signal normalization assumes the SM Higgs boson inclusive production cross-section, $\mathcal{B}(H\to Za)=100\%$, and it is scaled up by a factor of 100. The error bars (hatched regions) represent the data (MC) sample's statistical uncertainty in the histograms and the ratio plots. Vertical arrows indicate data points that fall outside the displayed $y$-axis range.

$Z$ boson transverse momentum, for data, background (pre- and post-reweighting) and three $H\rightarrow Za$ signal hypotheses (for $a\rightarrow q\bar{q}/gg$ inclusively). Events are required to pass the complete event selection but not the classification NN requirement. The background normalization is set equal to that of the data for events passing the preselection and being in the $m_{\ell\ell j}$ 100-180 GeV region. The signal normalization assumes the SM Higgs boson inclusive production cross-section, $\mathcal{B}(H\to Za)=100\%$, and it is scaled up by a factor of 100. The error bars (hatched regions) represent the data (MC) sample's statistical uncertainty in the histograms and the ratio plots. Vertical arrows indicate data points that fall outside the displayed $y$-axis range.

$Z$ boson transverse momentum, for data, background (pre- and post-reweighting) and three $H\rightarrow Za$ signal hypotheses (for $a\rightarrow q\bar{q}/gg$ inclusively). Events are required to pass the complete event selection but not the classification NN requirement. The background normalization is set equal to that of the data for events passing the preselection and being in the $m_{\ell\ell j}$ 100-180 GeV region. The signal normalization assumes the SM Higgs boson inclusive production cross-section, $\mathcal{B}(H\to Za)=100\%$, and it is scaled up by a factor of 100. The error bars (hatched regions) represent the data (MC) sample's statistical uncertainty in the histograms and the ratio plots. Vertical arrows indicate data points that fall outside the displayed $y$-axis range.

Invariant mass of the lepton pair plus jet system, for data, background (pre- and post-reweighting) and three $H\rightarrow Za$ signal hypotheses (for $a\rightarrow q\bar{q}/gg$ inclusively). Events are required to pass the complete event selection but not the classification NN requirement. The background normalization is set equal to that of the data for events passing the preselection and being in the $m_{\ell\ell j}$ 100-180 GeV region. The signal normalization assumes the SM Higgs boson inclusive production cross-section, $\mathcal{B}(H\to Za)=100\%$, and it is scaled up by a factor of 100. The error bars (hatched regions) represent the data (MC) sample's statistical uncertainty in the histograms and the ratio plots. Vertical arrows indicate data points that fall outside the displayed $y$-axis range.

Invariant mass of the lepton pair plus jet system, for data, background (pre- and post-reweighting) and three $H\rightarrow Za$ signal hypotheses (for $a\rightarrow q\bar{q}/gg$ inclusively). Events are required to pass the complete event selection but not the classification NN requirement. The background normalization is set equal to that of the data for events passing the preselection and being in the $m_{\ell\ell j}$ 100-180 GeV region. The signal normalization assumes the SM Higgs boson inclusive production cross-section, $\mathcal{B}(H\to Za)=100\%$, and it is scaled up by a factor of 100. The error bars (hatched regions) represent the data (MC) sample's statistical uncertainty in the histograms and the ratio plots. Vertical arrows indicate data points that fall outside the displayed $y$-axis range.

Regression NN output variable, for data, reweighted background, and three $H\rightarrow Za$ signal hypotheses ($a\rightarrow q\bar{q}/gg$ inclusively). Events are required to pass the complete event selection, including a $120<m_{\ell\ell j}<140$ GeV requirement, but not the classification NN output variable requirement. The background normalization is set equal to that of the data for events passing the preselection and being in the $m_{\ell\ell j}$ 100-180 GeV region. The signal normalization assumes the SM Higgs boson inclusive production cross-section, $\mathcal{B}(H\to Za)=100\%$, and it is scaled up by a factor of 100. The error bars (hatched regions) represent the data (MC) sample's statistical uncertainty in the histograms and the ratio plots. Vertical arrows indicate data points that fall outside the displayed $y$-axis range.

Regression NN output variable, for data, reweighted background, and three $H\rightarrow Za$ signal hypotheses ($a\rightarrow q\bar{q}/gg$ inclusively). Events are required to pass the complete event selection, including a $120<m_{\ell\ell j}<140$ GeV requirement, but not the classification NN output variable requirement. The background normalization is set equal to that of the data for events passing the preselection and being in the $m_{\ell\ell j}$ 100-180 GeV region. The signal normalization assumes the SM Higgs boson inclusive production cross-section, $\mathcal{B}(H\to Za)=100\%$, and it is scaled up by a factor of 100. The error bars (hatched regions) represent the data (MC) sample's statistical uncertainty in the histograms and the ratio plots. Vertical arrows indicate data points that fall outside the displayed $y$-axis range.

Classification NN output variable, for data, reweighted background, and three $H\rightarrow Za$ signal hypotheses ($a\rightarrow q\bar{q}/gg$ inclusively). Events are required to pass the complete event selection, including a $120<m_{\ell\ell j}<140$ GeV requirement, but not the classification NN output variable requirement. The background normalization is set equal to that of the data for events passing the preselection and being in the $m_{\ell\ell j}$ 100-180 GeV region. The signal normalization assumes the SM Higgs boson inclusive production cross-section, $\mathcal{B}(H\to Za)=100\%$, and it is scaled up by a factor of 100. The error bars (hatched regions) represent the data (MC) sample's statistical uncertainty in the histograms and the ratio plots. Vertical arrows indicate data points that fall outside the displayed $y$-axis range.

Classification NN output variable, for data, reweighted background, and three $H\rightarrow Za$ signal hypotheses ($a\rightarrow q\bar{q}/gg$ inclusively). Events are required to pass the complete event selection, including a $120<m_{\ell\ell j}<140$ GeV requirement, but not the classification NN output variable requirement. The background normalization is set equal to that of the data for events passing the preselection and being in the $m_{\ell\ell j}$ 100-180 GeV region. The signal normalization assumes the SM Higgs boson inclusive production cross-section, $\mathcal{B}(H\to Za)=100\%$, and it is scaled up by a factor of 100. The error bars (hatched regions) represent the data (MC) sample's statistical uncertainty in the histograms and the ratio plots. Vertical arrows indicate data points that fall outside the displayed $y$-axis range.

Invariant mass of the lepton pair plus jet system for data, reweighted background, and various signal hypotheses. Events are required to pass the complete event selection (preselection and classification NN requirement). The pre-fit background distribution is shown along with three $H\rightarrow Za$ signal hypotheses coming from the pure MC sample ($a\rightarrow q\bar{q}/gg$ inclusively). The background normalization is set equal to that of the data for events passing the preselection and being in the region 100-180 GeV. The error bars represent the data sample's statistical uncertainty and the grey bands represent the full background model uncertainty before the fit (assuming all the uncertainties are uncorrelated). The lower panel shows the ratio of the data to the pre-fit background prediction.

Invariant mass of the lepton pair plus jet system for data, reweighted background and its systematic uncertainties (only "up" variations are shown). Events are required to pass the complete event selection (preselection and classification NN requirement). The background normalization is set equal to that of the data for events passing this selection. The experimental uncertainty combines all the relevant jet uncertainties assuming they are completely uncorrelated. The error bars represent the data sample's statistical uncertainty and the grey bands represent the background statistical uncertainty. The lower panel shows the ratio of the data to the pre-fit background prediction.

Invariant mass of the lepton pair plus jet system for data, reweighted background, and 2.0 GeV signal hypotheses. Events are required to pass the complete event selection (preselection and classification NN requirement). The background shape and normalization come from the fit to the data. The signal includes only $gg$ decays, its shape comes from the fit, and it is normalized to $\mathcal{B}(H\rightarrow Za)=100\%$. The error bars represent the data sample's statistical uncertainty and the grey bands represent the full background model uncertainty after the fit. The lower panel shows the per-bin signal significance, $(N_\text{data}-N_\text{MC})\,\text{\Large{/}}\sqrt{\sigma_\text{data}^2+\sigma_\text{MC}^2}$. The post-fit background uncertainty is calculated from a fit under the background-only hypothesis. Vertical arrows indicate data points that fall outside the displayed $y$-axis range.

Invariant mass of the lepton pair plus jet system for data, reweighted background, and 0.5 GeV signal hypotheses. Events are required to pass the complete event selection (preselection and classification NN requirement). The background shape and normalization come from the fit to the data. The signal includes only $gg$ decays, its shape comes from the fit, and it is normalized to $\mathcal{B}(H\rightarrow Za)=100\%$. The error bars represent the data sample's statistical uncertainty and the grey bands represent the full background model uncertainty after the fit. The lower panel shows the per-bin signal significance, $(N_\text{data}-N_\text{MC})\,\text{\Large{/}}\sqrt{\sigma_\text{data}^2+\sigma_\text{MC}^2}$. The post-fit background uncertainty is calculated from a fit under the background-only hypothesis. Vertical arrows indicate data points that fall outside the displayed $y$-axis range.

Observed 95$\%$ CL upper limits on $\mathcal{B}(H \to Za)=100\%$ for $\mathcal{B}(a \to gg)=100\%$, and the expectation under the background-only hypothesis together with its $\pm1\sigma$ and $\pm2\sigma$ intervals. The weaker limits from the previous version of the analysis (PRL 125(2020) 221802) are also shown. Linear interpolation is used to set limits between the mass points for which MC signal samples were generated.

Observed 95$\%$ CL upper limits on $\mathcal{B}(H \to Za)=100\%$ for $\mathcal{B}(a \to gg)=100\%$, and the expectation under the background-only hypothesis together with its $\pm1\sigma$ and $\pm2\sigma$ intervals. The weaker limits from the previous version of the analysis (PRL 125(2020) 221802) are also shown. Linear interpolation is used to set limits between the mass points for which MC signal samples were generated.

Observed 95$\%$ confidence level upper limits on $\mathcal{B}(H \to Za)=100\%$ for $\mathcal{B}(a\rightarrow q\bar{q})=100\%$, and the expectation under the background-only hypothesis together with its $\pm1\sigma$ and $\pm2\sigma$ intervals. The weaker limits from the previous version of the analysis (PRL 125(2020) 221802) are also shown. Linear interpolation is used to set limits between the mass points for which MC signal samples were generated.

Observed 95$\%$ confidence level upper limits on $\mathcal{B}(H \to Za)=100\%$ for $\mathcal{B}(a\rightarrow q\bar{q})=100\%$, and the expectation under the background-only hypothesis together with its $\pm1\sigma$ and $\pm2\sigma$ intervals. The weaker limits from the previous version of the analysis (PRL 125(2020) 221802) are also shown. Linear interpolation is used to set limits between the mass points for which MC signal samples were generated.