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.

Systematic covariance matrix for the differential cross-section distribution.

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

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.

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.

The measured $p_{\mathrm{T}}^{\mathrm{recoil}}$ distributions in the $Z\rightarrow\mu\mu$ control region, compared with the background predictions as estimated after the simultaneous, binned background-only fit to the data in the control regions. The last bin of the distribution contains overflows.

The measured $p_{\mathrm{T}}^{\mathrm{recoil}}$ distributions in the $Z\rightarrow ee$ control region, compared with the background predictions as estimated after the simultaneous, binned background-only fit to the data in the control regions. The last bin of the distribution contains overflows.

The measured $p_{\mathrm{T}}^{\mathrm{recoil}}$ distributions in the signal region, compared with the background predictions as estimated after the simultaneous, binned background-only fit to the data in the control regions. The last bin of the distribution contains overflows.

Product of acceptance and efficiency for pp->tbH(->Wh) as function of the charged Higgs boson mass for the resolved qqbb signal region.

Product of acceptance and efficiency for pp->tbH(->Wh) as function of the charged Higgs boson mass for the resolved lvbb signal region.

Product of acceptance and efficiency for pp->tbH(->Wh) as function of the charged Higgs boson mass for the merged lvbb signal region

Product of acceptance and efficiency for pp->tbH(->Wh) as function of the charged Higgs boson mass for the merged qqbb signal region

Distributions of the mWh observable in the low-purity signal regions of the resolved qqbb 5jex3bex event categories. The term ‘Others’ summarises events from tHjb, tWh, tttt, and SM Vh production. The distributions are presented after a background-only maximum-likelihood fit to data. The individual background uncertainty does not take into account the possible correlations between the nuisance parameter. The expected signal contribution assuming $m_{H^{\pm}}$ = 700 GeV, normalised to the expected limit of the cross-section times branching ratio ($\sigma_{sig}$ × B) of 0.064 pb, is shown as a dashed histogram.

Distributions of the mWh observable in the low-purity signal regions of the resolved qqbb 5jex4bin event categories. The term ‘Others’ summarises events from tHjb, tWh, tttt, and SM Vh production. The distributions are presented after a background-only maximum-likelihood fit to data. The individual background uncertainty does not take into account the possible correlations between the nuisance parameter. The expected signal contribution assuming $m_{H^{\pm}}$ = 700 GeV, normalised to the expected limit of the cross-section times branching ratio ($\sigma_{sig}$ × B) of 0.064 pb, is shown as a dashed histogram.

Distributions of the mWh observable in the low-purity signal regions of the resolved qqbb 6jin3bex event categories. The term ‘Others’ summarises events from tHjb, tWh, tttt, and SM Vh production. The distributions are presented after a background-only maximum-likelihood fit to data. The individual background uncertainty does not take into account the possible correlations between the nuisance parameter. The expected signal contribution assuming $m_{H^{\pm}}$ = 700 GeV, normalised to the expected limit of the cross-section times branching ratio ($\sigma_{sig}$ × B) of 0.064 pb, is shown as a dashed histogram.

Distributions of the mWh observable in the low-purity signal regions of the resolved qqbb 6jin4bin event categories. The term ‘Others’ summarises events from tHjb, tWh, tttt, and SM Vh production. The distributions are presented after a background-only maximum-likelihood fit to data. The individual background uncertainty does not take into account the possible correlations between the nuisance parameter. The expected signal contribution assuming $m_{H^{\pm}}$ = 700 GeV, normalised to the expected limit of the cross-section times branching ratio ($\sigma_{sig}$ × B) of 0.064 pb, is shown as a dashed histogram.

Distributions of the mWh observable in the high-purity signal regions of the resolved qqbb 5jex3bex event categories. The term ‘Others’ summarises events from tHjb, tWh, tttt, and SM Vh production. The distributions are presented after a background-only maximum-likelihood fit to data. The individual background uncertainty does not take into account the possible correlations between the nuisance parameter. The expected signal contribution assuming $m_{H^{\pm}}$ = 700 GeV, normalised to the expected limit of the cross-section times branching ratio ($\sigma_{sig}$ × B) of 0.064 pb, is shown as a dashed histogram.

Distributions of the mWh observable in the high-purity signal regions of the resolved qqbb 5jex4bin event categories. The term ‘Others’ summarises events from tHjb, tWh, tttt, and SM Vh production. The distributions are presented after a background-only maximum-likelihood fit to data. The individual background uncertainty does not take into account the possible correlations between the nuisance parameter. The expected signal contribution assuming $m_{H^{\pm}}$ = 700 GeV, normalised to the expected limit of the cross-section times branching ratio ($\sigma_{sig}$ × B) of 0.064 pb, is shown as a dashed histogram.

Distributions of the mWh observable in the high-purity signal regions of the resolved qqbb 6jin3bex event categories. The term ‘Others’ summarises events from tHjb, tWh, tttt, and SM Vh production. The distributions are presented after a background-only maximum-likelihood fit to data. The individual background uncertainty does not take into account the possible correlations between the nuisance parameter. The expected signal contribution assuming $m_{H^{\pm}}$ = 700 GeV, normalised to the expected limit of the cross-section times branching ratio ($\sigma_{sig}$ × B) of 0.064 pb, is shown as a dashed histogram.

Distributions of the mWh observable in the high-purity signal regions of the resolved qqbb 6jin4bin event categories. The term ‘Others’ summarises events from tHjb, tWh, tttt, and SM Vh production. The distributions are presented after a background-only maximum-likelihood fit to data. The individual background uncertainty does not take into account the possible correlations between the nuisance parameter. The expected signal contribution assuming $m_{H^{\pm}}$ = 700 GeV, normalised to the expected limit of the cross-section times branching ratio ($\sigma_{sig}$ × B) of 0.064 pb, is shown as a dashed histogram.

Distributions of the mWh observable in the signal regions of the resolved lvbb 5jex3bex event categories. The term ‘Others’ summarises events from tHjb, tWh, tttt, and SM Vh production. The distributions are presented after a background-only maximum-likelihood fit to data. The individual background uncertainty does not take into account the possible correlations between the nuisance parameter. The expected signal contribution assuming $m_{H^{\pm}}$ = 700 GeV, normalised to the expected limit of the cross-section times branching ratio ($\sigma_{sig}$ × B) of 0.064 pb, is shown as a dashed histogram.

Distributions of the mWh observable in the signal regions of the resolved lvbb 5jex4bin event categories. The term ‘Others’ summarises events from tHjb, tWh, tttt, and SM Vh production. The distributions are presented after a background-only maximum-likelihood fit to data. The individual background uncertainty does not take into account the possible correlations between the nuisance parameter. The expected signal contribution assuming $m_{H^{\pm}}$ = 700 GeV, normalised to the expected limit of the cross-section times branching ratio ($\sigma_{sig}$ × B) of 0.064 pb, is shown as a dashed histogram.

Distributions of the mWh observable in the signal regions of the resolved lvbb 6jin3bex event categories. The term ‘Others’ summarises events from tHjb, tWh, tttt, and SM Vh production. The distributions are presented after a background-only maximum-likelihood fit to data. The individual background uncertainty does not take into account the possible correlations between the nuisance parameter. The expected signal contribution assuming $m_{H^{\pm}}$ = 700 GeV, normalised to the expected limit of the cross-section times branching ratio ($\sigma_{sig}$ × B) of 0.064 pb, is shown as a dashed histogram.

Distributions of the mWh observable in the signal regions of the resolved lvbb 6jin4bin event categories. The term ‘Others’ summarises events from tHjb, tWh, tttt, and SM Vh production. The distributions are presented after a background-only maximum-likelihood fit to data. The individual background uncertainty does not take into account the possible correlations between the nuisance parameter. The expected signal contribution assuming $m_{H^{\pm}}$ = 700 GeV, normalised to the expected limit of the cross-section times branching ratio ($\sigma_{sig}$ × B) of 0.064 pb, is shown as a dashed histogram.

The mWh distributions in the Low-NN-score SRs of the merged qqbb 0b event categories. The term ‘Others’ summarises events from tHjb, tWh, tttt, and SM Vh production. The background prediction is shown after a background-only maximum-likelihood fit to data. The individual background uncertainty does not take into account the possible correlations between the nuisance parameter. The expected signal contributions assuming $m_{H^{\pm}}$ = 900 GeV and $m_{H^{\pm}}$ = 2000 GeV, normalised the expected limit of the cross-section times branching ratio ($\sigma_{sig}$ × B) values of 0.036 pb and 2.7 fb respectively, are shown as dashed histograms.

The mWh distributions in the Low-NN-score SRs of the merged qqbb 1b event categories. The term ‘Others’ summarises events from tHjb, tWh, tttt, and SM Vh production. The background prediction is shown after a background-only maximum-likelihood fit to data. The individual background uncertainty does not take into account the possible correlations between the nuisance parameter. The expected signal contributions assuming $m_{H^{\pm}}$ = 900 GeV and $m_{H^{\pm}}$ = 2000 GeV, normalised the expected limit of the cross-section times branching ratio ($\sigma_{sig}$ × B) values of 0.036 pb and 2.7 fb respectively, are shown as dashed histograms.

The mWh distributions in the High-NN-score SRs of the merged qqbb 0b event categories. The term ‘Others’ summarises events from tHjb, tWh, tttt, and SM Vh production. The background prediction is shown after a background-only maximum-likelihood fit to data. The individual background uncertainty does not take into account the possible correlations between the nuisance parameter. The expected signal contributions assuming $m_{H^{\pm}}$ = 900 GeV and $m_{H^{\pm}}$ = 2000 GeV, normalised the expected limit of the cross-section times branching ratio ($\sigma_{sig}$ × B) values of 0.036 pb and 2.7 fb respectively, are shown as dashed histograms.

The mWh distributions in the High-NN-score SRs of the merged qqbb 1b event categories. The term ‘Others’ summarises events from tHjb, tWh, tttt, and SM Vh production. The background prediction is shown after a background-only maximum-likelihood fit to data. The individual background uncertainty does not take into account the possible correlations between the nuisance parameter. The expected signal contributions assuming $m_{H^{\pm}}$ = 900 GeV and $m_{H^{\pm}}$ = 2000 GeV, normalised the expected limit of the cross-section times branching ratio ($\sigma_{sig}$ × B) values of 0.036 pb and 2.7 fb respectively, are shown as dashed histograms.

The mWh distributions in the Low-NN-score SRs of the merged lvbb 0b event categories. The term ‘Others’ summarises events from tHjb, tWh, tttt, and SM Vh production. The background prediction is shown after a background-only maximum-likelihood fit to data. The individual background uncertainty does not take into account the possible correlations between the nuisance parameter. The expected signal contributions assuming $m_{H^{\pm}}$ = 900 GeV and $m_{H^{\pm}}$ = 2000 GeV, normalised the expected limit of the cross-section times branching ratio ($\sigma_{sig}$ × B) values of 0.036 pb and 2.7 fb respectively, are shown as dashed histograms.

The mWh distributions in the Low-NN-score SRs of the merged lvbb 1b event categories. The term ‘Others’ summarises events from tHjb, tWh, tttt, and SM Vh production. The background prediction is shown after a background-only maximum-likelihood fit to data. The individual background uncertainty does not take into account the possible correlations between the nuisance parameter. The expected signal contributions assuming $m_{H^{\pm}}$ = 900 GeV and $m_{H^{\pm}}$ = 2000 GeV, normalised the expected limit of the cross-section times branching ratio ($\sigma_{sig}$ × B) values of 0.036 pb and 2.7 fb respectively, are shown as dashed histograms.

The mWh distributions in the Medium-NN-score SRs of the merged lvbb 0b event categories. The term ‘Others’ summarises events from tHjb, tWh, tttt, and SM Vh production. The background prediction is shown after a background-only maximum-likelihood fit to data. The individual background uncertainty does not take into account the possible correlations between the nuisance parameter. The expected signal contributions assuming $m_{H^{\pm}}$ = 900 GeV and $m_{H^{\pm}}$ = 2000 GeV, normalised the expected limit of the cross-section times branching ratio ($\sigma_{sig}$ × B) values of 0.036 pb and 2.7 fb respectively, are shown as dashed histograms.

The mWh distributions in the Medium-NN-score SRs of the merged lvbb 1b event categories. The term ‘Others’ summarises events from tHjb, tWh, tttt, and SM Vh production. The background prediction is shown after a background-only maximum-likelihood fit to data. The individual background uncertainty does not take into account the possible correlations between the nuisance parameter. The expected signal contributions assuming $m_{H^{\pm}}$ = 900 GeV and $m_{H^{\pm}}$ = 2000 GeV, normalised the expected limit of the cross-section times branching ratio ($\sigma_{sig}$ × B) values of 0.036 pb and 2.7 fb respectively, are shown as dashed histograms.

The mWh distributions in the High-NN-score SRs of the merged lvbb 0b event categories. The term ‘Others’ summarises events from tHjb, tWh, tttt, and SM Vh production. The background prediction is shown after a background-only maximum-likelihood fit to data. The individual background uncertainty does not take into account the possible correlations between the nuisance parameter. The expected signal contributions assuming $m_{H^{\pm}}$ = 900 GeV and $m_{H^{\pm}}$ = 2000 GeV, normalised the expected limit of the cross-section times branching ratio ($\sigma_{sig}$ × B) values of 0.036 pb and 2.7 fb respectively, are shown as dashed histograms.

The mWh distributions in the High-NN-score SRs of the merged lvbb 1b event categories. The term ‘Others’ summarises events from tHjb, tWh, tttt, and SM Vh production. The background prediction is shown after a background-only maximum-likelihood fit to data. The individual background uncertainty does not take into account the possible correlations between the nuisance parameter. The expected signal contributions assuming $m_{H^{\pm}}$ = 900 GeV and $m_{H^{\pm}}$ = 2000 GeV, normalised the expected limit of the cross-section times branching ratio ($\sigma_{sig}$ × B) values of 0.036 pb and 2.7 fb respectively, are shown as dashed histograms.

Cutflow table for a few selected signal samples after applying the selection requirements of the resolved analysis. At the initial cut stage, all events from the tbH ± → W ± h(→ b b) production process (including those from the fully hadronic decay channel) are considered.

Cutflow table for a few selected signal samples after applying the selection requirements of the merged analysis. At the initial cut stage, all events from the tbH ± → W ± h(→ bb) production process (including those from the fully hadronic decay channel) are considered.