$r_{q}$, 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)

Observed and expected 95 % CL exclusion limits on $\tan\beta$ as a function of $m_{H^{\pm}}$, shown in the context of the mh125 scenario, for $m_{H^{\pm}}>150$ GeV and $(1 \leq \tan\beta \leq 60)$. The surrounding shaded bands correspond to the 1$\sigma$ and 2$\sigma$ confidence intervals around the expected limit.

Observed and expected 95 % CL exclusions on $\tan\beta$ as a function of $m_{H^{\pm}}$ derived from exclusion limits on $\mathrm{\cal{B}}(t\to bH^+)\times \mathrm{\cal{B}}(H^+ \to \tau \nu)$, for Type I 2HDM low mass scenario. The surrounding shaded bands correspond to the 1$\sigma$ and 2$\sigma$ confidence intervals around the expected limit.

Observed and expected 95 % CL exclusions on $\tan\beta$ as a function of $m_{H^{\pm}}$ derived from exclusion limits on $\mathrm{\cal{B}}(t\to bH^+)\times \mathrm{\cal{B}}(H^+ \to \tau \nu)$, for Lepton Specific 2HDM low mass scenario. The surrounding shaded bands correspond to the 1$\sigma$ and 2$\sigma$ confidence intervals around the expected limit.

The measured differential cross-sections and the predictions from the GM-VFNS calculation for the $D_s^\pm$ meson in bins of $p_T$ for $|\eta| < 2.5$. The statistical, systematic (excluding branching ratio) and branching ratio uncertainties are shown separately for data, while the total theory uncertainties are shown for GM-VFNS.

Inclusive $D^\pm$ meson production cross-sections in different fiducial volumes defined by $|\eta|<2.5$ and different $p_T$ regions. For the ATLAS measurements, the statistical, systematic (excluding branching ratio) and branching ratio uncertainties are shown separately; for the theoretical predictions, the total theoretical uncertainties are shown.

Inclusive $D_s^\pm$ meson production cross-sections in different fiducial volumes defined by $|\eta|<2.5$ and different $p_T$ regions. For the ATLAS measurements, the statistical, systematic (excluding branching ratio) and branching ratio uncertainties are shown separately; for the theoretical predictions, the total theoretical uncertainties are shown.

The distribution of the $p_\mathrm{T}{}_{\mu\mathrm{-had}}^\mathrm{col}$ in the VR. `$Z(\rightarrow\tau\tau)+\text{jets}$' represents the contributions from the signal process. `Diboson' indicates the contributions from $WW$, $WZ$, and $ZZ$ processes. `Top' represents the predicted contributions from the $t\bar{t}$, single-top-quark, and $tW$ processes. `Other' includes the contributions from the $Z(\rightarrow\ell\ell)$+jets, $W$+jets, and Higgs boson processes. The uncertainties shown include both statistical and systematic sources.

The distributions of $m_{\mu\mathrm{-had}}^\mathrm{col}$ corresponding to the SR selection criteria defined in the text. `$Z(\rightarrow\tau\tau)+\text{jets}$' represents the contributions from the signal process. `Diboson' indicates the contributions from $WW$, $WZ$, and $ZZ$ processes. `Top' represents the predicted contributions from the $t\bar{t}$, single-top-quark, and $tW$ processes. `Other' includes the contributions from the $Z(\rightarrow\ell\ell)$+jets, $W$+jets, and Higgs boson processes. The uncertainties shown include both statistical and systematic sources.

The distributions of $m_{\mu\mathrm{-had}}^\mathrm{col}$ corresponding to the SR_\text{std} selection criteria defined in the text. `$Z(\rightarrow\tau\tau)+\text{jets}$' represents the contributions from the signal process. `Diboson' indicates the contributions from $WW$, $WZ$, and $ZZ$ processes. `Top' represents the predicted contributions from the $t\bar{t}$, single-top-quark, and $tW$ processes. `Other' includes the contributions from the $Z(\rightarrow\ell\ell)$+jets, $W$+jets, and Higgs boson processes. The uncertainties shown include both statistical and systematic sources.

The distributions of $m_{\mu\mathrm{-had}}^\mathrm{col}$ corresponding to the SR_\text{tight} selection criteria defined in the text. `$Z(\rightarrow\tau\tau)+\text{jets}$' represents the contributions from the signal process. `Diboson' indicates the contributions from $WW$, $WZ$, and $ZZ$ processes. `Top' represents the predicted contributions from the $t\bar{t}$, single-top-quark, and $tW$ processes. `Other' includes the contributions from the $Z(\rightarrow\ell\ell)$+jets, $W$+jets, and Higgs boson processes. The uncertainties shown include both statistical and systematic sources.

The distributions of $m_{\mu\mathrm{-had}}^\mathrm{col}$ corresponding to the SR_\text{tight}^\text{std} selection criteria defined in the text. `$Z(\rightarrow\tau\tau)+\text{jets}$' represents the contributions from the signal process. `Diboson' indicates the contributions from $WW$, $WZ$, and $ZZ$ processes. `Top' represents the predicted contributions from the $t\bar{t}$, single-top-quark, and $tW$ processes. `Other' includes the contributions from the $Z(\rightarrow\ell\ell)$+jets, $W$+jets, and Higgs boson processes. The uncertainties shown include both statistical and systematic sources.

The distribution of $\Delta\phi^\mathrm{signed}_{\mu-MET}$ with all other event selection criteria applied in the SR; the straight lines indicate the positions of the selection requirements. `$Z(\rightarrow\tau\tau)+\text{jets}$' represents the contributions from the signal process. `Diboson' indicates the contributions from $WW$, $WZ$, and $ZZ$ processes. `Top' represents the predicted contributions from the $t\bar{t}$, single-top, and $tW$ processes. `Other' includes the contributions from the $Z(\rightarrow\ell\ell)$+jets, $W$+jets, and Higgs boson processes. The uncertainties shown include both statistical and systematic errors.

The distribution of $\Delta\phi^\mathrm{signed}_{\mu-MET}$ with all other event selection criteria applied in the VR; the straight lines indicate the positions of the selection requirements. `$Z(\rightarrow\tau\tau)+\text{jets}$' represents the contributions from the signal process. `Diboson' indicates the contributions from $WW$, $WZ$, and $ZZ$ processes. `Top' represents the predicted contributions from the $t\bar{t}$, single-top, and $tW$ processes. `Other' includes the contributions from the $Z(\rightarrow\ell\ell)$+jets, $W$+jets, and Higgs boson processes. The uncertainties shown include both statistical and systematic errors.

The distribution of the $m_{\mu\mathrm{-had}}^\mathrm{col}$ in the SR. `$Z(\rightarrow\tau\tau)+\text{jets}$' represents the contributions from the signal process. `Diboson' indicates the contributions from $WW$, $WZ$, and $ZZ$ processes. `Top' represents the predicted contributions from the $t\bar{t}$, single-top, and $tW$ processes. `Other' includes the contributions from the $Z(\rightarrow\ell\ell)$+jets, $W$+jets, and Higgs boson processes. The uncertainties shown include both statistical and systematic errors.

The distribution of the $m_{\mu\mathrm{-had}}^\mathrm{col}$ in the VR. `$Z(\rightarrow\tau\tau)+\text{jets}$' represents the contributions from the signal process. `Diboson' indicates the contributions from $WW$, $WZ$, and $ZZ$ processes. `Top' represents the predicted contributions from the $t\bar{t}$, single-top, and $tW$ processes. `Other' includes the contributions from the $Z(\rightarrow\ell\ell)$+jets, $W$+jets, and Higgs boson processes. The uncertainties shown include both statistical and systematic errors.

The distribution of the $p_\mathrm{T}$ of the $\tau_\mathrm{had}^{\mu\mkern-10mu\backslash}$ in the SR. `$Z(\rightarrow\tau\tau)+\text{jets}$' represents the contributions from the signal process. `Diboson' indicates the contributions from $WW$, $WZ$, and $ZZ$ processes. `Top' represents the predicted contributions from the $t\bar{t}$, single-top, and $tW$ processes. `Other' includes the contributions from the $Z(\rightarrow\ell\ell)$+jets, $W$+jets, and Higgs boson processes. The uncertainties shown include both statistical and systematic errors.

The distribution of the $p_\mathrm{T}$ of the $\tau_\mathrm{had}^{\mu\mkern-10mu\backslash}$ in the VR. `$Z(\rightarrow\tau\tau)+\text{jets}$' represents the contributions from the signal process. `Diboson' indicates the contributions from $WW$, $WZ$, and $ZZ$ processes. `Top' represents the predicted contributions from the $t\bar{t}$, single-top, and $tW$ processes. `Other' includes the contributions from the $Z(\rightarrow\ell\ell)$+jets, $W$+jets, and Higgs boson processes. The uncertainties shown include both statistical and systematic errors.

The distribution of the $p_\mathrm{T}$ of the muon removed from the $\tau_\mathrm{had}^{\mu\mkern-10mu\backslash}$ in the SR `$Z(\rightarrow\tau\tau)+\text{jets}$' represents the contributions from the signal process. `Diboson' indicates the contributions from $WW$, $WZ$, and $ZZ$ processes. `Top' represents the predicted contributions from the $t\bar{t}$, single-top, and $tW$ processes. `Other' includes the contributions from the $Z(\rightarrow\ell\ell)$+jets, $W$+jets, and Higgs boson processes. The uncertainties shown include both statistical and systematic errors.

The distribution of the $p_\mathrm{T}$ of the muon removed from the $\tau_\mathrm{had}^{\mu\mkern-10mu\backslash}$ in the VR `$Z(\rightarrow\tau\tau)+\text{jets}$' represents the contributions from the signal process. `Diboson' indicates the contributions from $WW$, $WZ$, and $ZZ$ processes. `Top' represents the predicted contributions from the $t\bar{t}$, single-top, and $tW$ processes. `Other' includes the contributions from the $Z(\rightarrow\ell\ell)$+jets, $W$+jets, and Higgs boson processes. The uncertainties shown include both statistical and systematic errors.

The distribution of the $p_\mathrm{T}$ of the leading jet in the SR. `$Z(\rightarrow\tau\tau)+\text{jets}$' represents the contributions from the signal process. `Diboson' indicates the contributions from $WW$, $WZ$, and $ZZ$ processes. `Top' represents the predicted contributions from the $t\bar{t}$, single-top, and $tW$ processes. `Other' includes the contributions from the $Z(\rightarrow\ell\ell)$+jets, $W$+jets, and Higgs boson processes. The uncertainties shown include both statistical and systematic errors.

The distribution of the $p_\mathrm{T}$ of the leading jet in the VR. `$Z(\rightarrow\tau\tau)+\text{jets}$' represents the contributions from the signal process. `Diboson' indicates the contributions from $WW$, $WZ$, and $ZZ$ processes. `Top' represents the predicted contributions from the $t\bar{t}$, single-top, and $tW$ processes. `Other' includes the contributions from the $Z(\rightarrow\ell\ell)$+jets, $W$+jets, and Higgs boson processes. The uncertainties shown include both statistical and systematic errors.

The distribution of the $\Delta{R}_{\tau\tau}^\mathrm{reco}$ between the muon and the $\tau_\mathrm{had}^{\mu\mkern-10mu\backslash}$ in the SR `$Z(\rightarrow\tau\tau)+\text{jets}$' represents the contributions from the signal process. `Diboson' indicates the contributions from $WW$, $WZ$, and $ZZ$ processes. `Top' represents the predicted contributions from the $t\bar{t}$, single-top, and $tW$ processes. `Other' includes the contributions from the $Z(\rightarrow\ell\ell)$+jets, $W$+jets, and Higgs boson processes. The uncertainties shown include both statistical and systematic errors.

The distribution of the $\Delta{R}_{\tau\tau}^\mathrm{reco}$ between the muon and the $\tau_\mathrm{had}^{\mu\mkern-10mu\backslash}$ in the VR `$Z(\rightarrow\tau\tau)+\text{jets}$' represents the contributions from the signal process. `Diboson' indicates the contributions from $WW$, $WZ$, and $ZZ$ processes. `Top' represents the predicted contributions from the $t\bar{t}$, single-top, and $tW$ processes. `Other' includes the contributions from the $Z(\rightarrow\ell\ell)$+jets, $W$+jets, and Higgs boson processes. The uncertainties shown include both statistical and systematic errors.

The distribution of the reconstructed $E_\mathrm{T}^\mathrm{miss}$ in the SR `$Z(\rightarrow\tau\tau)+\text{jets}$' represents the contributions from the signal process. `Diboson' indicates the contributions from $WW$, $WZ$, and $ZZ$ processes. `Top' represents the predicted contributions from the $t\bar{t}$, single-top, and $tW$ processes. `Other' includes the contributions from the $Z(\rightarrow\ell\ell)$+jets, $W$+jets, and Higgs boson processes. The uncertainties shown include both statistical and systematic errors.

The distribution of the reconstructed $E_\mathrm{T}^\mathrm{miss}$ in the VR `$Z(\rightarrow\tau\tau)+\text{jets}$' represents the contributions from the signal process. `Diboson' indicates the contributions from $WW$, $WZ$, and $ZZ$ processes. `Top' represents the predicted contributions from the $t\bar{t}$, single-top, and $tW$ processes. `Other' includes the contributions from the $Z(\rightarrow\ell\ell)$+jets, $W$+jets, and Higgs boson processes. The uncertainties shown include both statistical and systematic errors.

The observed and expected ($\pm2\sigma$) upper limits at 95% CL on the branching ratio for $H\rightarrow aa\rightarrow \gamma\gamma\tau\tau$ as a function of the resonance mass hypothesis $m_{a}$.

The polynomial parameterisation of the total signal selection efficiency as a function of $m_{a}$, defined as the fraction of the reconstructed and selected events out of the total number of events in the signal simulated samples.

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.

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.

Jet pairing efficiencies over the parameter space for the wide-width heavy resonance signals. The pairing efficiency is evaluated in the 6$b$ region when a correct pairing is possible — that is, the six leading jets are geometrically matched to truth-level b-quarks.

Distributions of scores for nonresDNN in 6b data and the background prediction after background-only fits to the observed data. The Low- and High-Score regions are included. Benchmark signal models (normalized to the background) are overlaid: SM HHH signal and non-resonant TRSM signal with $(m_X, m_S)=(400,200)$ GeV.

Distributions of scores for resDNN in 6b data and the background prediction after background-only fits to the observed data. The Low- and High-Score regions are included. A benchmark signal model (normalized to the background) is overlaid: resonant TRSM signal with $(m_X, m_S)=(500,350)$ GeV.

Distributions of scores for heavyresDNN in 6b data and the background prediction after background-only fits to the observed data. The Low- and High-Score regions are included. Benchmark signal models (normalized to the background) are overlaid: heavy-resonant signals with (mX, mS)=(900,325) GeV with a 1% or 20% width.

Expected 95% CL $HHH$ cross section upper limits for the phase space within the perturbative unitarity bounds of the TRSM signals. While the points were generated under Benchmark point 3 of the TRSM, they can also be interpreted in the DM-CPV model.

Observed 95% CL $HHH$ cross section upper limits for the phase space within the perturbative unitarity bounds of the TRSM signals. While the points were generated under Benchmark point 3 of the TRSM, they can also be interpreted in the DM-CPV model.

Expected 95% CL $HHH$ cross section upper limits for the narrow-width (1%) heavy resonance signals.

Expected 95% CL $HHH$ cross section upper limits for the wide-width (20%) heavy resonance signals.

Observed 95% CL $HHH$ cross section upper limits for the narrow-width (1%) heavy resonance signals.

Observed 95% CL $HHH$ cross section upper limits for the wide-width (20%) heavy resonance signals.

Expected 95% CL constraints on $\kappa_3$ and $\kappa_4$, the ratios of the Higgs tri-linear and quartic self-couplings to their predicted SM values.

Expected 68% CL constraints on $\kappa_3$ and $\kappa_4$, the ratios of the Higgs tri-linear and quartic self-couplings to their predicted SM values.

Observed 95% CL constraints on $\kappa_3$ and $\kappa_4$, the ratios of the Higgs tri-linear and quartic self-couplings to their predicted SM values.

Observed 68% CL constraints on $\kappa_3$ and $\kappa_4$, the ratios of the Higgs tri-linear and quartic self-couplings to their predicted SM values.

Unitarity limits, calculated in Eur. Phys. J. C 84 (2024) 366, are overlaid in the region bounded by the gray dashed line.

Overall acceptance x efficiency for events entering the 6$b$ region over the parameter space for the TRSM signals. Generator weights, and weights associated to pileup modeling corrections are applied. Jet trigger scale factors, NNJVT scale factors and scale factors associated to the $b$-tagging calibration are applied.

Overall acceptance x efficiency for events entering the 6$b$ region over the parameter space for the narrow-width heavy resonance signals. Generator weights, and weights associated to pileup modeling corrections are applied. Jet trigger scale factors, NNJVT scale factors and scale factors associated to the $b$-tagging calibration are applied.

Overall acceptance x efficiency for events entering the 6$b$ region over the parameter space for the wide-width heavy resonance signals. Generator weights, and weights associated to pileup modeling corrections are applied. Jet trigger scale factors, NNJVT scale factors and scale factors associated to the $b$-tagging calibration are applied.

Expected one-dimensional likelihood scan over the Higgs self-coupling modifier $\kappa_3$. Both of the modifiers are profiled in the profile-likelihood fit, and the likelihood scan keeps $\kappa_4$ fixed at one.

Observed one-dimensional likelihood scan over the Higgs self-coupling modifier $\kappa_3$. Both of the modifiers are profiled in the profile-likelihood fit, and the likelihood scan keeps $\kappa_4$ fixed at one.

Expected one-dimensional likelihood scan over the Higgs self-coupling modifier $\kappa_4$. Both of the modifiers are profiled in the profile-likelihood fit, and the likelihood scan keeps $\kappa_3$ fixed at one.

Observed one-dimensional likelihood scan over the Higgs self-coupling modifier $\kappa_4$. Both of the modifiers are profiled in the profile-likelihood fit, and the likelihood scan keeps $\kappa_3$ fixed at one.

Summary of the impact on the analysis of different sources of systematic uncertainty. The impact is estimated as the absolute value of the difference between the expected upper limit with all sources of uncertainty included and the upper limit with a subset of systematic uncertainties excluded. In the left-hand column, more heavily indented rows are a sub-category of the less indented row above.

Cutflow for selected signal points. Generator weights, and weights associated to pileup modeling corrections are applied from the second row onwards. These weight the SM events assuming the SM cross section, whilst the TRSM and Generic resonance events are weighted to 50 fb. Jet trigger scale factors are applied from the third row onwards. NNJVT scale factors are applied from the fourth row onwards. Scale factors associated to the b-tagging calibration are applied in the last three rows.