The transverse-mass dependence of the correlation-strength parameter $\lambda$ in 30-40% centrality bin obtained from Lévy fits with Eq. (9).

The transverse-mass dependence of the correlation-strength parameter $\lambda$ in 40-50% centrality bin obtained from Lévy fits with Eq. (9).

The transverse-mass dependence of the correlation-strength parameter $\lambda$ in 50-60% centrality bin obtained from Lévy fits with Eq. (9).

The transverse-mass dependence of the Lévy-scale parameter $R$ in 0-10% centrality bin obtained from Lévy fits with Eq. (9).

The transverse-mass dependence of the Lévy-scale parameter $R$ in 10-20% centrality bin obtained from Lévy fits with Eq. (9).

The transverse-mass dependence of the Lévy-scale parameter $R$ in 20-30% centrality bin obtained from Lévy fits with Eq. (9).

The transverse-mass dependence of the Lévy-scale parameter $R$ in 30-40% centrality bin obtained from Lévy fits with Eq. (9).

The transverse-mass dependence of the Lévy-scale parameter $R$ in 40-50% centrality bin obtained from Lévy fits with Eq. (9).

The transverse-mass dependence of the Lévy-scale parameter $R$ in 50-60% centrality bin obtained from Lévy fits with Eq. (9).

The transverse-mass dependence of the Lévy-index of stability parameter $\alpha$ in 0-10% centrality bin obtained from Lévy fits with Eq. (9).

The transverse-mass dependence of the Lévy-index of stability parameter $\alpha$ in 10-20% centrality bin obtained from Lévy fits with Eq. (9).

The transverse-mass dependence of the Lévy-index of stability parameter $\alpha$ in 20-30% centrality bin obtained from Lévy fits with Eq. (9).

The transverse-mass dependence of the Lévy-index of stability parameter $\alpha$ in 30-40% centrality bin obtained from Lévy fits with Eq. (9).

The transverse-mass dependence of the Lévy-index of stability parameter $\alpha$ in 40-50% centrality bin obtained from Lévy fits with Eq. (9).

The transverse-mass dependence of the Lévy-index of stability parameter $\alpha$ in 50-60% centrality bin obtained from Lévy fits with Eq. (9).

The transverse-mass dependence of the normalized correlation-strength parameter $\lambda/\lambda_{\rm max}$ for 0-10% centrality intervals. For each centrality bin the data are fitted with the Gaussian function of Eq. (15). This parameterization can describe the data and is discussed in detail in Section VI B. The fit parameters with the statistic and systematic uncertainties are shown in Fig. 7.

The transverse-mass dependence of the normalized correlation-strength parameter $\lambda/\lambda_{\rm max}$ for 10-20% centrality intervals. For each centrality bin the data are fitted with the Gaussian function of Eq. (15). This parameterization can describe the data and is discussed in detail in Section VI B. The fit parameters with the statistic and systematic uncertainties are shown in Fig. 7.

The transverse-mass dependence of the normalized correlation-strength parameter $\lambda/\lambda_{\rm max}$ for 20-30% centrality intervals. For each centrality bin the data are fitted with the Gaussian function of Eq. (15). This parameterization can describe the data and is discussed in detail in Section VI B. The fit parameters with the statistic and systematic uncertainties are shown in Fig. 7.

The transverse-mass dependence of the normalized correlation-strength parameter $\lambda/\lambda_{\rm max}$ for 30-40% centrality intervals. For each centrality bin the data are fitted with the Gaussian function of Eq. (15). This parameterization can describe the data and is discussed in detail in Section VI B. The fit parameters with the statistic and systematic uncertainties are shown in Fig. 7.

The transverse-mass dependence of the normalized correlation-strength parameter $\lambda/\lambda_{\rm max}$ for 40-50% centrality interval. For each centrality bin the data are fitted with the Gaussian function of Eq. (15). This parameterization can describe the data and is discussed in detail in Section VI B. The fit parameters with the statistic and systematic uncertainties are shown in Fig. 7.

The transverse-mass dependence of the normalized correlation-strength parameter $\lambda/\lambda_{\rm max}$ for 50-60% centrality interval. For each centrality bin the data are fitted with the Gaussian function of Eq. (15). This parameterization can describe the data and is discussed in detail in Section VI B. The fit parameters with the statistic and systematic uncertainties are shown in Fig. 7.

The transverse-mass dependence of the inverse square of the Lévy-scale parameter $R$, shown in 0-10% centrality bin. The values and uncertainties of the A and B linear fit parameters with the statistic and systematic uncertainties are shown in Fig. 8.

The transverse-mass dependence of the inverse square of the Lévy-scale parameter $R$, shown in 10-20% centrality bin. The values and uncertainties of the A and B linear fit parameters with the statistic and systematic uncertainties are shown in Fig. 8.

The transverse-mass dependence of the inverse square of the Lévy-scale parameter $R$, shown in 20-30% centrality bin. The values and uncertainties of the A and B linear fit parameters with the statistic and systematic uncertainties are shown in Fig. 8.

The transverse-mass dependence of the inverse square of the Lévy-scale parameter $R$, shown in 30-40% centrality bin. The values and uncertainties of the A and B linear fit parameters with the statistic and systematic uncertainties are shown in Fig. 8.

The transverse-mass dependence of the inverse square of the Lévy-scale parameter $R$, shown in 40-50% centrality bin. The values and uncertainties of the A and B linear fit parameters with the statistic and systematic uncertainties are shown in Fig. 8.

The transverse-mass dependence of the inverse square of the Lévy-scale parameter $R$, shown in 50-60% centrality bin. The values and uncertainties of the A and B linear fit parameters with the statistic and systematic uncertainties are shown in Fig. 8.

The transverse-mass dependence of the $\widehat{R}$ parameter, shown in 0-10% centrality bin. The values and uncertainties of the linear fit parameters $\widehat{A}$ and $\widehat{B}$ with the statistic and systematic uncertainties are shown in Fig. 9

The transverse-mass dependence of the $\widehat{R}$ parameter, shown in 10-20% centrality bin. The values and uncertainties of the linear fit parameters $\widehat{A}$ and $\widehat{B}$ with the statistic and systematic uncertainties are shown in Fig. 9

The transverse-mass dependence of the $\widehat{R}$ parameter, shown in 20-30% centrality bin. The values and uncertainties of the linear fit parameters $\widehat{A}$ and $\widehat{B}$ with the statistic and systematic uncertainties are shown in Fig. 9

The transverse-mass dependence of the $\widehat{R}$ parameter, shown in 30-40% centrality bin. The values and uncertainties of the linear fit parameters $\widehat{A}$ and $\widehat{B}$ with the statistic and systematic uncertainties are shown in Fig. 9

The transverse-mass dependence of the $\widehat{R}$ parameter, shown in 40-50% centrality bin. The values and uncertainties of the linear fit parameters $\widehat{A}$ and $\widehat{B}$ with the statistic and systematic uncertainties are shown in Fig. 9

The transverse-mass dependence of the $\widehat{R}$ parameter, shown in 50-60% centrality bin. The values and uncertainties of the linear fit parameters $\widehat{A}$ and $\widehat{B}$ with the statistic and systematic uncertainties are shown in Fig. 9

The $H$ parameter that characterize the magnitude of the $\lambda/\lambda_{max}(m_T)$ and is defined in Eq. (15)., shown as functions of $N_{part}$.

The $\sigma$ parameter that characterize the width of the $\lambda/\lambda_{max}(m_T)$ and is defined in Eq. (15)., shown as functions of $N_{part}$.

The parameter $A$ of the affine linear fit to the inverse square of the Lévy-scale parameter that are defined in Eq.(12) as function of $N_{part}$

The parameter $B$ of the affine linear fit to the inverse square of the Lévy-scale parameter that are defined in Eq.(12) as function of $N_{part}$

The parameter $\widehat{A}$ of the affine linear fit to the inverse of the $\widehat{R}$ parameter that are defined in Eq.(14) as function of $N_{part}$.

The parameter $\widehat{B}$ of the affine linear fit to the inverse of the $\widehat{R}$ parameter that are defined in Eq.(14) as function of $N_{part}$.

The centrality dependence of $\alpha_0$, the $m_T$-averaged value of $\alpha$ as a function of $N_{part}$.

The Lévy scale parameter $R$ as a function of $N^{1/3}_{part}$ at $m_T=0.326$ GeV.

The Lévy scale parameter $R$ as a function of $N^{1/3}_{part}$ at $m_T=0.438$ GeV.

The Lévy scale parameter $R$ as a function of $N^{1/3}_{part}$ at $m_T=0.553$ GeV.

The Lévy scale parameter $R$ as a function of $N^{1/3}_{part}$ at $m_T=0.670$ GeV.

The Lévy scale parameter $R$ as a function of $N^{1/3}_{part}$ at $m_T=0.787$ GeV.

Monte Carlo calcuations with no mass drop assumed in 0-10%.

Monte Carlo calcuations with no mass drop assumed in 10-20%.

Monte Carlo calcuations with no mass drop assumed in 20-30%.

Monte Carlo calcuations with no mass drop assumed in 30-40%.

Monte Carlo calcuations with no mass drop assumed in 40-50%.

Monte Carlo calcuations with no mass drop assumed in 50-60%.

Monte Carlo calcuations with the best mass drop assumed in 0-10%.

Monte Carlo calcuations with the best mass drop assumed in 10-20%.

Monte Carlo calcuations with the best mass drop assumed in 20-30%.

Monte Carlo calcuations with the best mass drop assumed in 30-40%.

Monte Carlo calcuations with the best mass drop assumed in 40-50%.

Monte Carlo calcuations with the best mass drop assumed in 50-60%.

The best values of $B^{-1}_{\eta\prime}$ spectrum of the $\eta\prime$ condensate in the six centrality classes.

The centrality dependence of the best values of the in-medium mass of the $m^{*}_{\eta\prime}$.

The CL maps of the comparison of the MC to data in 0-10% (see Fig. 11).

The CL maps of the comparison of the MC to data in 10-20% (see Fig. 11).

The CL maps of the comparison of the MC to data in 20-30% (see Fig. 11).

The CL maps of the comparison of the MC to data in 30-40% (see Fig. 11).

The CL maps of the comparison of the MC to data in 40-50% (see Fig. 11).

The CL maps of the comparison of the MC to data in 50-60% (see Fig. 11).

Data from Figure 1, panel c, $k_{2}$ vs $N_{ch}$ for Pb+Pb collisions, 0.5 $ <p_{T}< $ 5 GeV/c, $|\eta|< $ 2.5

Data from Figure 1, panel c, $k_{2}$ vs $N_{ch}$ for Xe+Xe collisions, 0.5 $ <p_{T}< $ 5 GeV/c, $|\eta|< $ 2.5

Data from Figure 1, panel d, $k_{3}$ vs $N_{ch}$ for Pb+Pb collisions, 0.5 $ <p_{T}< $ 5 GeV/c, $|\eta|< $ 2.5

Data from Figure 1, panel d, $k_{3}$ vs $N_{ch}$ for Xe+Xe collisions, 0.5 $ <p_{T}< $ 5 GeV/c, $|\eta|< $ 2.5

Data from Figure 2, panel a, $N_{ch}k_{2}$ vs $N_{ch}$ for Pb+Pb collisions, 0.5 $ <p_{T}< $ 5 GeV/c, $|\eta|< $ 2.5

Data from Figure 2, panel a, $N_{ch}k_{2}$ vs $N_{ch}$ for Xe+Xe collisions, 0.5 $ <p_{T}< $ 5 GeV/c, $|\eta|< $ 2.5

Data from Figure 2, panel b, $N^{2}_{ch}k_{3}$ vs $N_{ch}$ for Pb+Pb collisions, 0.5 $ <p_{T}< $ 5 GeV/c, $|\eta|< $ 2.5

Data from Figure 2, panel b, $N^{2}_{ch}k_{3}$ vs $N_{ch}$ for Xe+Xe collisions, 0.5 $ <p_{T}< $ 5 GeV/c, $|\eta|< $ 2.5

Data from Figure 2, panel c, $\Gamma$ vs $N_{ch}$ for Pb+Pb collisions, 0.5 $ <p_{T}< $ 5 GeV/c, $|\eta|< $ 2.5

Data from Figure 2, panel c, $\Gamma$ vs $N_{ch}$ for Xe+Xe collisions, 0.5 $ <p_{T}< $ 5 GeV/c, $|\eta|< $ 2.5

Data from Figure 3, panel a, $\left\langle[p_{T}]\right\rangle / \left\langle[p_{T}]\right\rangle^{5\%}$ vs $N_{ch}/N^{5\%}_{ch}$ for Pb+Pb collisions, 0.5 $ <p_{T}< $ 5 GeV/c, $|\eta|< $ 2.5

Data from Figure 3, panel a, $\left\langle[p_{T}]\right\rangle / \left\langle[p_{T}]\right\rangle^{5\%}$ vs $N_{ch}/N^{5\%}_{ch}$ for Xe+Xe collisions, 0.5 $ <p_{T}< $ 5 GeV/c, $|\eta|< $ 2.5

Data from Figure 3, panel b, $k_{2}/k^{5\%}_{2} vs N_{ch}/N^{5\%}_{ch}$ for Pb+Pb collisions, 0.5 $ <p_{T}< $ 5 GeV/c, $|\eta|< $ 2.5

Data from Figure 3, panel b, $k_{2}/k^{5\%}_{2} vs N_{ch}/N^{5\%}_{ch}$ for Xe+Xe collisions, 0.5 $ <p_{T}< $ 5 GeV/c, $|\eta|< $ 2.5

Data from Figure 3, panel c, $k_{3}/k^{5\%}_{3} vs N_{ch}/N^{5\%}_{ch}$ for Pb+Pb collisions, 0.5 $ <p_{T}< $ 5 GeV/c, $|\eta|< $ 2.5

Data from Figure 3, panel c, $k_{3}/k^{5\%}_{3} vs N_{ch}/N^{5\%}_{ch}$ for Xe+Xe collisions, 0.5 $ <p_{T}< $ 5 GeV/c, $|\eta|< $ 2.5

Data from Figure 3, panel d, $\Gamma/\Gamma^{5\%}$ vs $N_{ch}/N^{5\%}_{ch}$ for Pb+Pb collisions, 0.5 $ <p_{T}< $ 5 GeV/c, $|\eta|< $ 2.5

Data from Figure 3, panel d, $\Gamma/\Gamma^{5\%}$ vs $N_{ch}/N^{5\%}_{ch}$ for Xe+Xe collisions, 0.5 $ <p_{T}< $ 5 GeV/c, $|\eta|< $ 2.5

Data from Figure 4, $\Delta p_{T}/\left\langle[p_{T}]\right\rangle_{0-1\%}$ vs $\Delta N_{ch}/\left\langle N_{ch}\right\rangle_{0-1\%}$ for Pb+Pb collisions, 0.5 $ <p_{T}< $ 5 GeV/c, $|\eta|< $ 2.5

Data from Figure 4, $\Delta p_{T}/\left\langle[p_{T}]\right\rangle_{0-1\%}$ vs $\Delta N_{ch}/\left\langle N_{ch}\right\rangle_{0-1\%}$ for Xe+Xe collisions, 0.5 $ <p_{T}< $ 5 GeV/c, $|\eta|< $ 2.5

Data from Figure 4, $\Delta p_{T}/\left\langle[p_{T}]\right\rangle_{0-1\%}$ vs $\Delta N_{ch}/\left\langle N_{ch}\right\rangle_{0-1\%}$ for Pb+Pb collisions, 0.5 $ <p_{T}< $ 2 GeV/c, $|\eta|< $ 2.5

Data from Figure 4, $\Delta p_{T}/\left\langle[p_{T}]\right\rangle_{0-1\%}$ vs $\Delta N_{ch}/\left\langle N_{ch}\right\rangle_{0-1\%}$ for Xe+Xe collisions, 0.5 $ <p_{T}< $ 2 GeV/c, $|\eta|< $ 2.5

Data from Second Supplementary Figure, Fig 6, panel a, Correlation between FCal $\Sigma E_{T}$ and $N_{ch}$ in Pb+Pb collisions

Data from Second Supplementary Figure, Fig 6, panel b, Correlation between $[p_{T}]$ - $\left\langle[p_{T}]\right\rangle_{0-1\%}$ vs $\Delta N_{ch}$/$\left\langle N_{ch}\right\rangle_{0-1\%}$ in Pb+Pb collisions

Data from Third Supplementary Figure, Fig 7, Normalized Event distribution of $N_{ch}$ /$N^{5\%}_{ch}$ for Pb+Pb collisions

Data from Third Supplementary Figure, Fig 7, Normalized Event distribution of $N_{ch}$ / $N^{5\%}_{ch}$ for Xe+Xe collisions

Data from Fourth Supplementary Figure, Fig 8, panel a, $\gamma$ vs $N_{ch}$ for Pb+Pb collisions, 0.5 $ <p_{T}< $ 5 GeV/c, $|\eta|< $ 2.5

Data from Fourth Supplementary Figure, Fig 8, panel a, $\gamma$ vs $N_{ch}$ for Xe+Xe collisions, 0.5 $ <p_{T}< $ 5 GeV/c, $|\eta|< $ 2.5

Data from Fourth Supplementary Figure, Fig 8, panel b, $\gamma/\gamma^{5\%}$ vs $N_{ch}/N^{5\%}_{ch}$ for Pb+Pb collisions, 0.5 $ <p_{T}< $ 5 GeV/c, $|\eta|< $ 2.5

Data from Fourth Supplementary Figure, Fig 8, panel b, $\gamma/\gamma^{5\%}$ vs $N_{ch}/N^{5\%}_{ch}$ for Xe+Xe collisions, 0.5 $ <p_{T}< $ 5 GeV/c, $|\eta|< $ 2.5

Data from Auxiliary Fig 1 panel a, Correlation between FCal $\Sigma E_{T}$ and $N_{ch}$ in Xe+Xe collisions

Data from Auxiliary Fig 1 panel b, Correlation between $[p_{T}]$ - $\left\langle[p_{T}]\right\rangle_{0-1\%}$ vs $\Delta N_{ch}$/$\left\langle N_{ch}\right\rangle_{0-1\%}$ in Xe+Xe collisions

Data from Auxiliary Fig 2 panel b, $N_{ch}$ /$N^{5\%}_{ch}$ vs Centrality [\%] for Pb+Pb collisions

Data from Auxiliary Fig 2 panel b, $N_{ch}$ /$N^{5\%}_{ch}$ vs Centrality [\%] for Xe+Xe collisions

Data from Auxiliary Fig 3 panel b, $[p_{T}]$ vs $N_{ch}$ for Xe+Xe collisions, 0.5 $ <p_{T}< $ 5 GeV/c, $|\eta|< $ 2.5

Data from Auxiliary Figure 4, $\Delta p_{T}/\left\langle[p_{T}]\right\rangle_{0-0.5\%}$ vs $\Delta N_{ch}/\left\langle N_{ch}\right\rangle_{0-0.5\%}$ for Pb+Pb collisions, 0.5 $ <p_{T}< $ 5 GeV/c, $|\eta|< $ 2.5

Data from Auxiliary Figure 4, $\Delta p_{T}/\left\langle[p_{T}]\right\rangle_{0-0.5\%}$ vs $\Delta N_{ch}/\left\langle N_{ch}\right\rangle_{0-0.5\%}$ for Xe+Xe collisions, 0.5 $ <p_{T}< $ 5 GeV/c, $|\eta|< $ 2.5

Data from Auxiliary Figure 4, $\Delta p_{T}/\left\langle[p_{T}]\right\rangle_{0-0.5\%}$ vs $\Delta N_{ch}/\left\langle N_{ch}\right\rangle_{0-0.5\%}$ for Pb+Pb collisions, 0.5 $ <p_{T}< $ 2 GeV/c, $|\eta|< $ 2.5

Data from Auxiliary Figure 4, $\Delta p_{T}/\left\langle[p_{T}]\right\rangle_{0-0.5\%}$ vs $\Delta N_{ch}/\left\langle N_{ch}\right\rangle_{0-0.5\%}$ for Xe+Xe collisions, 0.5 $ <p_{T}< $ 2 GeV/c, $|\eta|< $ 2.5

The pNN input variable visible transverse momentum $p_{\mathrm{T}}^{\mathrm{vis}}(\mu\tau_{\mathrm{had}})$ is shown in the SR with no cut on the pNN discriminant. The signal shape is normalized to the same integral as the total background prediction. Overflow events are included in the last bins.

The pNN input variable transverse mass $m_{\mathrm{T}}(\mu,E_{\mathrm{T}}^{\mathrm{miss}})$ is shown in the SR with no cut on the pNN discriminant. The signal shape is normalized to the same integral as the total background prediction. Overflow events are included in the last bins.

The pNN input variable MMC mass $m^{\mathrm{MMC}}(bb\tau\tau)$ is shown in the SR with no cut on the pNN discriminant. The signal shape is normalized to the same integral as the total background prediction. Overflow events are included in the last bins.

Mass distribution of the $\tau^+\tau^-$ system for each of the generated MC signal mass points for the $\mu\tau_{\mathrm{h}}$ category. All distributions are normalized assuming $\mathcal{B}(H\rightarrow aa\rightarrow b\bar{b}\tau^+\tau^-)=10\%$.

Mass distribution of the $\tau^+\tau^-$ system for each of the generated MC signal mass points for the $e\mu$ category. All distributions are normalized assuming $\mathcal{B}(H\rightarrow aa\rightarrow b\bar{b}\tau^+\tau^-)=10\%$.

The pNN spectrum in the three bins are shown separately for each mass hypothesis in the ($e\mu$, $1b$) category. The signal shape (normalized to $\mathcal{B}(H\rightarrow aa\rightarrow b\bar{b}\tau^+\tau^-)=1$) for each corresponding mass hypothesis is overlaid on top of the SM prediction. Bins used for different $m_a$ hypotheses are not statistically independent.

The pNN spectrum in the three bins are shown separately for each mass hypothesis in the ($\mu\tau_{\mathrm{had}}$,$2b$) category. The signal shape (normalized to $\mathcal{B}(H\rightarrow aa\rightarrow b\bar{b}\tau^+\tau^-)=1$) for each corresponding mass hypothesis is overlaid on top of the SM prediction. Bins used for different $m_a$ hypotheses are not statistically independent.

The pNN spectrum in the three bins are shown separately for each mass hypothesis in the ($e\mu$,$1B$) category. The signal shape (normalized to $\mathcal{B}(H\rightarrow aa\rightarrow b\bar{b}\tau^+\tau^-)=1$) for each corresponding mass hypothesis is overlaid on top of the SM prediction. Bins used for different $m_a$ hypotheses are not statistically independent.

The pNN spectrum in the three bins are shown separately for each mass hypothesis in the ($e\tau_{\mathrm{had}}$,$2b$) category. The signal shape (normalized to $\mathcal{B}(H\rightarrow aa\rightarrow b\bar{b}\tau^+\tau^-)=1$) for each corresponding mass hypothesis is overlaid on top of the SM prediction. Bins used for different $m_a$ hypotheses are not statistically independent.

The observed (solid) 95% C.L. upper limits on $(\sigma(H)/\sigma_{\mathrm{SM}}(H)) \mathcal{B}(H\rightarrow aa\rightarrow b\bar{b}\tau^+\tau^-)$ as a function of $m_a$ and the expected (dashed) limits under the background-only hypothesis when combining all categories. The inner green and outer yellow shaded bands show the $\pm 1\sigma$ and $\pm 2\sigma$ uncertainties of the expected limits.

The observed (solid) 95% C.L. upper limits on $(\sigma(H)/\sigma_{\mathrm{SM}}(H)) \mathcal{B}(H\rightarrow aa\rightarrow b\bar{b}\tau^+\tau^-)$ as a function of $m_a$ and the expected (dashed) limits under the background-only hypothesis when considering different categories based on the heavy-flavor objects separately. When the category is not used for a mass hypothesis, the limit is listed as zero.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_\lambda$ parameter for $b\bar{b}\gamma\gamma$.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_\lambda$ parameter for $b\bar{b}\ell\ell+E_\text{T}^{\text{miss}}$.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_\lambda$ parameter for Multilepton.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_\lambda$ parameter for combination.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_{2V}$ parameter for $b\bar{b}b\bar{b}$.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_{2V}$ parameter for $b\bar{b}\tau\tau$.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_{2V}$ parameter for $b\bar{b}\gamma\gamma$.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_{2V}$ parameter for $b\bar{b}\ell\ell+E_\text{T}^{\text{miss}}$.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_{2V}$ parameter for Multilepton.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_{2V}$ parameter for combination.

Observed and expected 95&percnt; CL upper limits on the signal strength for the inclusive ggF HH production from the bb&#772;&tau;⁺&tau;^-, bb&#772;&gamma;&gamma;, bb&#772;bb&#772;, multilepton and bb&#772;&#8467;&#8467;+E_T^miss decay channels, and their statistical combination. When deriving the limit on &mu;_ggF^HH (&mu;_VBF^HH), the VBF (ggF) HH production cross-section is fixed to the SM predicted value for m_H=125 GeV. The expected limit, along with the &plusmn;1&sigma; and &plusmn;2&sigma; bands, is calculated under the assumption of no HH process and with all NPs profiled to the observed data.

Observed and expected 95&percnt; CL upper limits on the signal strength for the VBF HH production from the bb&#772;&tau;⁺&tau;^-, bb&#772;&gamma;&gamma;, bb&#772;bb&#772;, multilepton and bb&#772;&#8467;&#8467;+E_T^miss decay channels, and their statistical combination. When deriving the limit on &mu;_ggF^HH (&mu;_VBF^HH), the VBF (ggF) HH production cross-section is fixed to the SM predicted value for m_H=125 GeV. The expected limit, along with the &plusmn;1&sigma; and &plusmn;2&sigma; bands, is calculated under the assumption of no HH process and with all NPs profiled to the observed data.

Observed and expected upper limits at 95&percnt; CL on the inclusive ggF and VBF HH production cross-section from the bb&#772;&tau;⁺&tau;^-, bb&#772;&gamma;&gamma;, bb&#772;bb&#772;, multilepton and bb&#772;&#8467;&#8467;+E_T^miss decay channels, and their statistical combination. The Higgs boson mass is set to 125&nbsp;GeV when deriving the predicted SM cross-section (red band). The expected limits, along with the &plusmn;1&sigma; and &plusmn;2&sigma; bands, are calculated under the assumption of no Higgs boson pair production and with all NPs profiled to the observed data.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_\lambda$ parameter for $b\bar{b}b\bar{b}$.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_\lambda$ parameter for $b\bar{b}\tau\tau$.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_\lambda$ parameter for $b\bar{b}\gamma\gamma$.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_\lambda$ parameter for $b\bar{b}\ell\ell+E_\text{T}^{\text{miss}}$.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_\lambda$ parameter for Multilepton.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_\lambda$ parameter for combination.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_{2V}$ parameter for $b\bar{b}b\bar{b}$.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_{2V}$ parameter for $b\bar{b}\tau\tau$.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_{2V}$ parameter for $b\bar{b}\gamma\gamma$.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_{2V}$ parameter for $b\bar{b}\ell\ell+E_\text{T}^{\text{miss}}$.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_{2V}$ parameter for Multilepton.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $\kappa_{2V}$ parameter for combination.

Observed (solid lines) and expected (dashed lines) 95&percnt; CL exclusion limits on the HH production cross-sections of (a) the inclusive ggF and VBF processes as a function of &kappa;_&lambda;, for the bb&#772;&gamma;&gamma; (purple), bb&#772;&tau;⁺&tau;^- (green), multilepton (cyan), bb&#772;bb&#772; (blue) and bb&#772;&#8467;&#8467;+E_T^miss (brown) decay channels and their combination (black). The expected limits assume no HH production. The red line shows the theory prediction for the ggF and VBF HH production cross-section as a function of &kappa;_&lambda;. The bands surrounding the red cross-section lines indicate the theoretical uncertainties on the predicted cross-section.

Observed (solid lines) and expected (dashed lines) 95&percnt; CL exclusion limits on the HH production cross-sections of the VBF process as a function of &kappa;_2V, for the bb&#772;&gamma;&gamma; (purple), bb&#772;&tau;⁺&tau;^- (green), multilepton (cyan), bb&#772;bb&#772; (blue) and bb&#772;&#8467;&#8467;+E_T^miss (brown) decay channels and their combination (black). The expected limits assume no VBF HH production. The ggF HH production cross-section is assumed to be as predicted by the SM. The ggF HH production cross-section is assumed to be as predicted by the SM. The red line shows the predicted VBF HH cross-section as a function of &kappa;_2V. The bands surrounding the red cross-section lines indicate the theoretical uncertainties on the predicted cross-section.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $c_{gghh}$ parameter for $b\bar{b}b\bar{b}$.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $c_{gghh}$ parameter for $b\bar{b}\tau\tau$.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $c_{gghh}$ parameter for $b\bar{b}\gamma\gamma$.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $c_{gghh}$ parameter for combination.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $c_{gghh}$ parameter for $b\bar{b}b\bar{b}$.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $c_{gghh}$ parameter for $b\bar{b}\tau\tau$.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $c_{gghh}$ parameter for $b\bar{b}\gamma\gamma$.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $c_{gghh}$ parameter for combination.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $c_{tthh}$ parameter for $b\bar{b}b\bar{b}$.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $c_{tthh}$ parameter for $b\bar{b}\tau\tau$.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $c_{tthh}$ parameter for $b\bar{b}\gamma\gamma$.

Observed value of the test statistic (-2ln$\Lambda$), as a function of the $c_{tthh}$ parameter for combination.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $c_{tthh}$ parameter for $b\bar{b}b\bar{b}$.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $c_{tthh}$ parameter for $b\bar{b}\tau\tau$.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $c_{tthh}$ parameter for $b\bar{b}\gamma\gamma$.

Expected value of the test statistic (-2ln$\Lambda$), as a function of the $c_{tthh}$ parameter for combination.

Observed and expected 95&percnt; CL combined upper limits on the cross-section for the SM and seven BSM HEFT benchmarks (arXiv:2304.01968 [hep-ph]) in the ggF process, describing representative signal kinematics and m_HH shape features obtained by varying multiple HEFT coefficients. The expected limits from the bb&#772;&tau;⁺&tau;^-, bb&#772;&gamma;&gamma; and bb&#772;bb&#772; decay channels are presented as well. Theoretical predictions, estimated using specific sets of coefficient values defined in the benchmarks, are shown as red cross dots.

Differential away-side a function of Deltaphi 0%-20% collisions. Systematic uncertainties for background subtraction and global scale uncertainties are given.

Differential away-side a function of Deltaphi 0%-20% collisions. Systematic uncertainties for background subtraction and global scale uncertainties are given.

Differential away-side a function of Deltaphi 0%-20% collisions. Systematic uncertainties for background subtraction and global scale uncertainties are given.

Differential away-side a function of Deltaphi 0%-20% collisions. Systematic uncertainties for background subtraction and global scale uncertainties are given.

Differential away-side a function of Deltaphi 0%-20% collisions. Systematic uncertainties for background subtraction and global scale uncertainties are given.

Differential away-side a function of Deltaphi 0%-20% collisions. Systematic uncertainties for background subtraction and global scale uncertainties are given.

Differential away-side a function of Deltaphi 0%-20% collisions. Systematic uncertainties for background subtraction and global scale uncertainties are given.

Differential away-side a function of Deltaphi 0%-20% collisions. Systematic uncertainties for background subtraction and global scale uncertainties are given.

Differential away-side a function of Deltaphi 0%-20% collisions. Systematic uncertainties for background subtraction and global scale uncertainties are given.

Differential away-side a function of Deltaphi 0%-20% collisions. Systematic uncertainties for background subtraction and global scale uncertainties are given.

Differential away-side a function of Deltaphi 0%-20% collisions. Systematic uncertainties for background subtraction and global scale uncertainties are given.

Differential away-side a function of Deltaphi 20%-40% collisions. Systematic uncertainties for background subtraction and global scale uncertainties are given.

Differential away-side a function of Deltaphi 20%-40% collisions. Systematic uncertainties for background subtraction and global scale uncertainties are given.

Differential away-side a function of Deltaphi 20%-40% collisions. Systematic uncertainties for background subtraction and global scale uncertainties are given.

Differential away-side a function of Deltaphi 20%-40% collisions. Systematic uncertainties for background subtraction and global scale uncertainties are given.

Differential away-side a function of Deltaphi 20%-40% collisions. Systematic uncertainties for background subtraction and global scale uncertainties are given.

Differential away-side a function of Deltaphi 20%-40% collisions. Systematic uncertainties for background subtraction and global scale uncertainties are given.

Differential away-side a function of Deltaphi 20%-40% collisions. Systematic uncertainties for background subtraction and global scale uncertainties are given.

Differential away-side a function of Deltaphi 20%-40% collisions. Systematic uncertainties for background subtraction and global scale uncertainties are given.

Differential away-side a function of Deltaphi 20%-40% collisions. Systematic uncertainties for background subtraction and global scale uncertainties are given.

Differential away-side a function of Deltaphi 20%-40% collisions. Systematic uncertainties for background subtraction and global scale uncertainties are given.

Differential away-side a function of Deltaphi 20%-40% collisions. Systematic uncertainties for background subtraction and global scale uncertainties are given.

Differential away-side a function of Deltaphi 20%-40% collisions. Systematic uncertainties for background subtraction and global scale uncertainties are given.

Differential away-side $\Delta_{AA}$ for ${\pi/2<\Delta\phi<\pi}$

Differential away-side $\Delta_{AA}$ for ${\pi/2<\Delta\phi<\pi}$

Differential away-side $\Delta_{AA}$ for ${\pi/2<\Delta\phi<\pi}$

R32 for $H_{T2}$, 0.2 x $H_{T2} < $p_{T,3}$

R32 for $H_{T2}$, 0.3 x $H_{T2} < $p_{T,3}$

R32 for $H_{T2}$, pT,jet

R32 for delta y

R32 for delta y max

R32 for $m_{jj}$

R32 for $m_{jj, max}$

R43 for $H_{T2}$, 60 GeV < $p_{T,3}$

R43 for $H_{T2}$, 0.1 x $H_{T2} < $p_{T,3}$

R43 for $H_{T2}$, 0.3 x $H_{T2} < $p_{T,3}$

R43 for $H_{T2}$, pT,jet

R43 for $Delta y_{jj}$

R43 for $Delta y_{jj, max}$

R43 for $m_{jj}$

R43 for $m_{jj, max}$

R54 for $H_{T2}$, 60 GeV < $p_{T,3}$

R54 for $H_{T2}$, 0.1 x $H_{T2} < $p_{T,3}$

R54 for $H_{T2}$, 0.3 x $H_{T2} < $p_{T,3}$

R54 for $Delta y_{jj}$

R54 for $Delta y_{jj, max}$

R54 for $m_{jj}$

R54 for $m_{jj, max}$

R42 for $H_{T2}$, 60 GeV < $p_{T,3}$

R42 for $H_{T2}$, 0.1 x $H_{T2} < $p_{T,3}$

R42 for $H_{T2}$, 0.3 x $H_{T2} < $p_{T,3}$

R42, pT,jet

R42 for $Delta y_{jj}$

R42 for $Delta y_{jj, max}$

R42 for $m_{jj}$

R42 for $m_{jj}$

HT2, $p_{T,3}$ > 60 GeV, $N_{jet}$ >= 2

HT2, $p_{T,3}$ > 60 GeV, $N_{jet}$ >=3

HT2, $p_{T,3}$ > 60 GeV, $N_{jet}$ >=4

HT2, $p_{T,3}$ > 60 GeV, $N_{jet}$ >= 5

HT2, $p_{T,3}$/HT2 > 0.05, $N_{jet}$ >= 2

HT2, $p_{T,3}$/HT2 > 0.05, $N_{jet}$ >=3

HT2, $p_{T,3}$/HT2 > 0.05, $N_{jet}$ >=4

HT2, $p_{T,3}$/HT2 > 0.05, $N_{jet}$ >= 5

HT2, $p_{T,3}$/HT2 > 0.10, $N_{jet}$ >= 2

HT2, $p_{T,3}$/HT2 > 0.10, $N_{jet}$ >=3

HT2, $p_{T,3}$/HT2 > 0.10, $N_{jet}$ >=4

HT2, $p_{T,3}$/HT2 > 0.10, $N_{jet}$ >= 5

HT2, $p_{T,3}$/HT2 > 0.20, $N_{jet}$ >= 2

HT2, $p_{T,3}$/HT2 > 0.20, $N_{jet}$ >=3

HT2, $p_{T,3}$/HT2 > 0.20, $N_{jet}$ >=4

HT2, $p_{T,3}$/HT2 > 0.20, $N_{jet}$ >= 5

HT2, $p_{T,3}$/HT2 > 0.30, $N_{jet}$ >= 2

HT2, $p_{T,3}$/HT2 > 0.30, $N_{jet}$ >=3

HT2, $p_{T,3}$/HT2 > 0.30, $N_{jet}$ >=4

HT2, $p_{T,3}$/HT2 > 0.30, $N_{jet}$ >= 5

pTnincl

pTnincl

pTnincl

mjj max, $N_{jet}$ >= 2

mjj max, $N_{jet}$ >= 3

mjj max, $N_{jet}$ >= 4

mjj max, $N_{jet}$ >= 5

$m_{jj}$ $N_{jet}$ >= 2

$m_{jj}$ $N_{jet}$ >= 3

$m_{jj}$ $N_{jet}$ >= 4

$m_{jj}$ $N_{jet}$ >= 5

$Delta y_{jj}$ $N_{jet}$ >= 2

$Delta y_{jj}$ $N_{jet}$ >= 3

$Delta y_{jj}$ $N_{jet}$ >= 4

$Delta y_{jj}$ $N_{jet}$ >= 5

$Delta y_{jj, max}$, $N_{jet}$ >= 2

$Delta y_{jj, max}$, $N_{jet}$ >= 3

$Delta y_{jj, max}$, $N_{jet}$ >= 4

$Delta y_{jj, max}$, $N_{jet}$ >= 5

R32 for $H_{T2}$, 60 GeV < $p_{T,3}$

R32 for $H_{T2}$, 0.05 x $H_{T2} < $p_{T,3}$

R32 for $H_{T2}$, 0.1 x $H_{T2} < $p_{T,3}$

R32 for $H_{T2}$, 0.2 x $H_{T2} < $p_{T,3}$

R32 for $H_{T2}$, 0.3 x $H_{T2} < $p_{T,3}$

Differential cross-section in bins of subleading muon $p_\mathrm{T]$. The actual measurement is unbinned and available with examples at <a href="https://gitlab.cern.ch/atlas-physics/public/sm-z-jets-omnifold-2024">gitlab.cern.ch/atlas-physics/public/sm-z-jets-omnifold-2024</a>

Differential cross-section in bins of leading muon $\eta$. The actual measurement is unbinned and available with examples at <a href="https://gitlab.cern.ch/atlas-physics/public/sm-z-jets-omnifold-2024">gitlab.cern.ch/atlas-physics/public/sm-z-jets-omnifold-2024</a>

Differential cross-section in bins of subleading muon $\eta$. The actual measurement is unbinned and available with examples at <a href="https://gitlab.cern.ch/atlas-physics/public/sm-z-jets-omnifold-2024">gitlab.cern.ch/atlas-physics/public/sm-z-jets-omnifold-2024</a>

Differential cross-section in bins of leading muon $\phi$. The actual measurement is unbinned and available with examples at <a href="https://gitlab.cern.ch/atlas-physics/public/sm-z-jets-omnifold-2024">gitlab.cern.ch/atlas-physics/public/sm-z-jets-omnifold-2024</a>

Differential cross-section in bins of subleading muon $\phi$. The actual measurement is unbinned and available with examples at <a href="https://gitlab.cern.ch/atlas-physics/public/sm-z-jets-omnifold-2024">gitlab.cern.ch/atlas-physics/public/sm-z-jets-omnifold-2024</a>

Differential cross-section in bins of leading charged particle jet $p_\mathrm{T]$. The actual measurement is unbinned and available with examples at <a href="https://gitlab.cern.ch/atlas-physics/public/sm-z-jets-omnifold-2024">gitlab.cern.ch/atlas-physics/public/sm-z-jets-omnifold-2024</a>

Differential cross-section in bins of subleading charged particle jet $p_\mathrm{T]$. The actual measurement is unbinned and available with examples at <a href="https://gitlab.cern.ch/atlas-physics/public/sm-z-jets-omnifold-2024">gitlab.cern.ch/atlas-physics/public/sm-z-jets-omnifold-2024</a>

Differential cross-section in bins of leading charged particle jet rapidity. The actual measurement is unbinned and available with examples at <a href="https://gitlab.cern.ch/atlas-physics/public/sm-z-jets-omnifold-2024">gitlab.cern.ch/atlas-physics/public/sm-z-jets-omnifold-2024</a>

Differential cross-section in bins of subleading charged particle jet rapidity. The actual measurement is unbinned and available with examples at <a href="https://gitlab.cern.ch/atlas-physics/public/sm-z-jets-omnifold-2024">gitlab.cern.ch/atlas-physics/public/sm-z-jets-omnifold-2024</a>

Differential cross-section in bins of leading charged particle jet azimuth. The actual measurement is unbinned and available with examples at <a href="https://gitlab.cern.ch/atlas-physics/public/sm-z-jets-omnifold-2024">gitlab.cern.ch/atlas-physics/public/sm-z-jets-omnifold-2024</a>

Differential cross-section in bins of subleading charged particle jet azimuth. The actual measurement is unbinned and available with examples at <a href="https://gitlab.cern.ch/atlas-physics/public/sm-z-jets-omnifold-2024">gitlab.cern.ch/atlas-physics/public/sm-z-jets-omnifold-2024</a>

Differential cross-section in bins of leading charged particle jet mass. The actual measurement is unbinned and available with examples at <a href="https://gitlab.cern.ch/atlas-physics/public/sm-z-jets-omnifold-2024">gitlab.cern.ch/atlas-physics/public/sm-z-jets-omnifold-2024</a>

Differential cross-section in bins of subleading charged particle jet mass. The actual measurement is unbinned and available with examples at <a href="https://gitlab.cern.ch/atlas-physics/public/sm-z-jets-omnifold-2024">gitlab.cern.ch/atlas-physics/public/sm-z-jets-omnifold-2024</a>

Differential cross-section in bins of leading charged particle jet constituent multiplicity. The actual measurement is unbinned and available with examples at <a href="https://gitlab.cern.ch/atlas-physics/public/sm-z-jets-omnifold-2024">gitlab.cern.ch/atlas-physics/public/sm-z-jets-omnifold-2024</a>

Differential cross-section in bins of subleading charged particle jet constituent multiplicity. The actual measurement is unbinned and available with examples at <a href="https://gitlab.cern.ch/atlas-physics/public/sm-z-jets-omnifold-2024">gitlab.cern.ch/atlas-physics/public/sm-z-jets-omnifold-2024</a>

Differential cross-section in bins of leading charged particle jet $\tau_1$. The actual measurement is unbinned and available with examples at <a href="https://gitlab.cern.ch/atlas-physics/public/sm-z-jets-omnifold-2024">gitlab.cern.ch/atlas-physics/public/sm-z-jets-omnifold-2024</a>

Differential cross-section in bins of subleading charged particle jet $\tau_1$. The actual measurement is unbinned and available with examples at <a href="https://gitlab.cern.ch/atlas-physics/public/sm-z-jets-omnifold-2024">gitlab.cern.ch/atlas-physics/public/sm-z-jets-omnifold-2024</a>

Differential cross-section in bins of leading charged particle jet $\tau_2$. The actual measurement is unbinned and available with examples at <a href="https://gitlab.cern.ch/atlas-physics/public/sm-z-jets-omnifold-2024">gitlab.cern.ch/atlas-physics/public/sm-z-jets-omnifold-2024</a>

Differential cross-section in bins of subleading charged particle jet $\tau_2$. The actual measurement is unbinned and available with examples at <a href="https://gitlab.cern.ch/atlas-physics/public/sm-z-jets-omnifold-2024">gitlab.cern.ch/atlas-physics/public/sm-z-jets-omnifold-2024</a>

Differential cross-section in bins of leading charged particle jet $\tau_3$. The actual measurement is unbinned and available with examples at <a href="https://gitlab.cern.ch/atlas-physics/public/sm-z-jets-omnifold-2024">gitlab.cern.ch/atlas-physics/public/sm-z-jets-omnifold-2024</a>

Differential cross-section in bins of subleading charged particle jet $\tau_3$. The actual measurement is unbinned and available with examples at <a href="https://gitlab.cern.ch/atlas-physics/public/sm-z-jets-omnifold-2024">gitlab.cern.ch/atlas-physics/public/sm-z-jets-omnifold-2024</a>

Differential cross-section in bins of leading charged particle jet $\tau_{21}$. The actual measurement is unbinned and available with examples at <a href="https://gitlab.cern.ch/atlas-physics/public/sm-z-jets-omnifold-2024">gitlab.cern.ch/atlas-physics/public/sm-z-jets-omnifold-2024</a>

Differential cross-section in bins of $\Delta R$ between the leading charged particle jet and the dilepton system. The actual measurement is unbinned and available with examples at <a href="https://gitlab.cern.ch/atlas-physics/public/sm-z-jets-omnifold-2024">gitlab.cern.ch/atlas-physics/public/sm-z-jets-omnifold-2024</a>

Statistical covariance between bins of Table 2

Mean multiplicity of $K^{0}_{S}$ per unit $(\eta, \phi)$ in the transverse region vs. leading-jet $p_{T}$

Statistical covariance between bins of Table 3

Mean scalar sum-$p_{T}$ of $K^{0}_{S}$ per unit $(\eta, \phi)$ in the away region vs. leading-jet $p_{T}$

Statistical covariance between bins of Table 4

Mean scalar sum-$p_{T}$ of $K^{0}_{S}$ per unit $(\eta, \phi)$ in the towards region vs. leading-jet $p_{T}$

Statistical covariance between bins of Table 5

Mean scalar sum-$p_{T}$ of $K^{0}_{S}$ per unit $(\eta, \phi)$ in the transverse region vs. leading-jet $p_{T}$

Statistical covariance between bins of Table 6

Ratio of the multiplicity of $K^{0}_{S}$ to prompt charged particles in the away region vs. leading-jet $p_{T}$

Statistical covariance between bins of Table 7

Ratio of the multiplicity of $K^{0}_{S}$ to prompt charged particles in the towards region vs. leading-jet $p_{T}$

Statistical covariance between bins of Table 8

Ratio of the multiplicity of $K^{0}_{S}$ to prompt charged particles in the transverse region vs. leading-jet $p_{T}$

Statistical covariance between bins of Table 9

Ratio of the scalar sum-pt of $K^{0}_{S}$ to prompt charged particles in the away region vs. leading-jet $p_{T}$

Statistical covariance between bins of Table 10

Ratio of the scalar sum-pt of $K^{0}_{S}$ to prompt charged particles in the towards region vs. leading-jet $p_{T}$

Statistical covariance between bins of Table 11

Ratio of the scalar sum-pt of $K^{0}_{S}$ to prompt charged particles in the transverse region vs. leading-jet $p_{T}$

Statistical covariance between bins of Table 12

Mean-$p_{T}$ of $K^{0}_{S}$ in the away region vs. leading-jet $p_{T}$

Statistical covariance between bins of Table 13

Mean-$p_{T}$ of $K^{0}_{S}$ in the towards region vs. leading-jet $p_{T}$

Statistical covariance between bins of Table 14

Mean-$p_{T}$ of $K^{0}_{S}$ in the transverse region vs. leading-jet $p_{T}$

Statistical covariance between bins of Table 15

Mean multiplicity of $\Lambda$ and $\bar{\Lambda}$ per unit $(\eta, \phi)$ in the away region vs. leading-jet $p_{T}$

Statistical covariance between bins of Table 16

Mean multiplicity of $\Lambda$ and $\bar{\Lambda}$ per unit $(\eta, \phi)$ in the towards region vs. leading-jet $p_{T}$

Statistical covariance between bins of Table 17

Mean multiplicity of $\Lambda$ and $\bar{\Lambda}$ per unit $(\eta, \phi)$ in the transverse region vs. leading-jet $p_{T}$

Statistical covariance between bins of Table 18

Mean scalar sum-$p_{T}$ of $\Lambda$ and $\bar{\Lambda}$ per unit $(\eta, \phi)$ in the away region vs. leading-jet $p_{T}$

Statistical covariance between bins of Table 19

Mean scalar sum-$p_{T}$ of $\Lambda$ and $\bar{\Lambda}$ per unit $(\eta, \phi)$ in the towards region vs. leading-jet $p_{T}$

Statistical covariance between bins of Table 20

Mean scalar sum-$p_{T}$ of $\Lambda$ and $\bar{\Lambda}$ per unit $(\eta, \phi)$ in the transverse region vs. leading-jet $p_{T}$

Statistical covariance between bins of Table 21

Ratio of the multiplicity of $\Lambda$ and $\bar{\Lambda}$ to prompt charged particles in the away region vs. leading-jet $p_{T}$

Statistical covariance between bins of Table 22

Ratio of the multiplicity of $\Lambda$ and $\bar{\Lambda}$ to prompt charged particles in the towards region vs. leading-jet $p_{T}$

Statistical covariance between bins of Table 23

Ratio of the multiplicity of $\Lambda$ and $\bar{\Lambda}$ to prompt charged particles in the transverse region vs. leading-jet $p_{T}$

Statistical covariance between bins of Table 24

Ratio of the scalar sum-pt of $\Lambda$ and $\bar{\Lambda}$ to prompt charged particles in the away region vs. leading-jet $p_{T}$

Statistical covariance between bins of Table 25

Ratio of the scalar sum-pt of $\Lambda$ and $\bar{\Lambda}$ to prompt charged particles in the towards region vs. leading-jet $p_{T}$

Statistical covariance between bins of Table 26

Ratio of the scalar sum-pt of $\Lambda$ and $\bar{\Lambda}$ to prompt charged particles in the transverse region vs. leading-jet $p_{T}$

Statistical covariance between bins of Table 27

Ratio of the multiplicity of $\Lambda$ and $\bar{\Lambda}$ to $K^{0}_{S}$ in the away region vs. leading-jet $p_{T}$

Statistical covariance between bins of Table 28

Ratio of the multiplicity of $\Lambda$ and $\bar{\Lambda}$ to $K^{0}_{S}$ in the towards region vs. leading-jet $p_{T}$

Statistical covariance between bins of Table 29

Ratio of the multiplicity of $\Lambda$ and $\bar{\Lambda}$ to $K^{0}_{S}$ in the transverse region vs. leading-jet $p_{T}$

Statistical covariance between bins of Table 30

Ratio of the scalar sum-pt of $\Lambda$ and $\bar{\Lambda}$ to $K^{0}_{S}$ in the away region vs. leading-jet $p_{T}$

Statistical covariance between bins of Table 31

Ratio of the scalar sum-pt of $\Lambda$ and $\bar{\Lambda}$ to $K^{0}_{S}$ in the towards region vs. leading-jet $p_{T}$

Statistical covariance between bins of Table 32

Ratio of the scalar sum-pt of $\Lambda$ and $\bar{\Lambda}$ to $K^{0}_{S}$ in the transverse region vs. leading-jet $p_{T}$

Statistical covariance between bins of Table 33

Mean-$p_{T}$ of $\Lambda$ and $\bar{\Lambda}$ in the away region vs. leading-jet $p_{T}$

Statistical covariance between bins of Table 34

Mean-$p_{T}$ of $\Lambda$ and $\bar{\Lambda}$ in the towards region vs. leading-jet $p_{T}$

Statistical covariance between bins of Table 35

Mean-$p_{T}$ of $\Lambda$ and $\bar{\Lambda}$ in the transverse region vs. leading-jet $p_{T}$

Statistical covariance between bins of Table 36

Mean multiplicity of $K^{0}_{S}$ per unit $(\eta, \phi)$ in the away region vs. $N_\textrm{ch,trans}$

Statistical covariance between bins of Table 37

Mean multiplicity of $K^{0}_{S}$ per unit $(\eta, \phi)$ in the towards region vs. $N_\textrm{ch,trans}$

Statistical covariance between bins of Table 38

Mean multiplicity of $K^{0}_{S}$ per unit $(\eta, \phi)$ in the transverse region vs. $N_\textrm{ch,trans}$

Statistical covariance between bins of Table 39

Mean scalar sum-$p_{T}$ of $K^{0}_{S}$ per unit $(\eta, \phi)$ in the away region vs. $N_\textrm{ch,trans}$

Statistical covariance between bins of Table 40

Mean scalar sum-$p_{T}$ of $K^{0}_{S}$ per unit $(\eta, \phi)$ in the towards region vs. $N_\textrm{ch,trans}$

Statistical covariance between bins of Table 41

Mean scalar sum-$p_{T}$ of $K^{0}_{S}$ per unit $(\eta, \phi)$ in the transverse region vs. $N_\textrm{ch,trans}$

Statistical covariance between bins of Table 42

Ratio of the multiplicity of $K^{0}_{S}$ to prompt charged particles in the away region vs. $N_\textrm{ch,trans}$

Statistical covariance between bins of Table 43

Ratio of the multiplicity of $K^{0}_{S}$ to prompt charged particles in the towards region vs. $N_\textrm{ch,trans}$

Statistical covariance between bins of Table 44

Ratio of the multiplicity of $K^{0}_{S}$ to prompt charged particles in the transverse region vs. $N_\textrm{ch,trans}$

Statistical covariance between bins of Table 45

Ratio of the scalar sum-pt of $K^{0}_{S}$ to prompt charged particles in the away region vs. $N_\textrm{ch,trans}$

Statistical covariance between bins of Table 46

Ratio of the scalar sum-pt of $K^{0}_{S}$ to prompt charged particles in the towards region vs. $N_\textrm{ch,trans}$

Statistical covariance between bins of Table 47

Ratio of the scalar sum-pt of $K^{0}_{S}$ to prompt charged particles in the transverse region vs. $N_\textrm{ch,trans}$

Statistical covariance between bins of Table 48

Mean-$p_{T}$ of $K^{0}_{S}$ in the away region vs. $N_\textrm{ch,trans}$

Statistical covariance between bins of Table 49

Mean-$p_{T}$ of $K^{0}_{S}$ in the towards region vs. $N_\textrm{ch,trans}$

Statistical covariance between bins of Table 50

Mean-$p_{T}$ of $K^{0}_{S}$ in the transverse region vs. $N_\textrm{ch,trans}$

Statistical covariance between bins of Table 51

Mean multiplicity of $\Lambda$ and $\bar{\Lambda}$ per unit $(\eta, \phi)$ in the away region vs. $N_\textrm{ch,trans}$

Statistical covariance between bins of Table 52

Mean multiplicity of $\Lambda$ and $\bar{\Lambda}$ per unit $(\eta, \phi)$ in the towards region vs. $N_\textrm{ch,trans}$

Statistical covariance between bins of Table 53

Mean multiplicity of $\Lambda$ and $\bar{\Lambda}$ per unit $(\eta, \phi)$ in the transverse region vs. $N_\textrm{ch,trans}$

Statistical covariance between bins of Table 54

Mean scalar sum-$p_{T}$ of $\Lambda$ and $\bar{\Lambda}$ per unit $(\eta, \phi)$ in the away region vs. $N_\textrm{ch,trans}$

Statistical covariance between bins of Table 55

Mean scalar sum-$p_{T}$ of $\Lambda$ and $\bar{\Lambda}$ per unit $(\eta, \phi)$ in the towards region vs. $N_\textrm{ch,trans}$

Statistical covariance between bins of Table 56

Mean scalar sum-$p_{T}$ of $\Lambda$ and $\bar{\Lambda}$ per unit $(\eta, \phi)$ in the transverse region vs. $N_\textrm{ch,trans}$

Statistical covariance between bins of Table 57

Ratio of the multiplicity of $\Lambda$ and $\bar{\Lambda}$ to prompt charged particles in the away region vs. $N_\textrm{ch,trans}$

Statistical covariance between bins of Table 58

Ratio of the multiplicity of $\Lambda$ and $\bar{\Lambda}$ to prompt charged particles in the towards region vs. $N_\textrm{ch,trans}$

Statistical covariance between bins of Table 59

Ratio of the multiplicity of $\Lambda$ and $\bar{\Lambda}$ to prompt charged particles in the transverse region vs. $N_\textrm{ch,trans}$

Statistical covariance between bins of Table 60

Ratio of the scalar sum-pt of $\Lambda$ and $\bar{\Lambda}$ to prompt charged particles in the away region vs. $N_\textrm{ch,trans}$

Statistical covariance between bins of Table 61

Ratio of the scalar sum-pt of $\Lambda$ and $\bar{\Lambda}$ to prompt charged particles in the towards region vs. $N_\textrm{ch,trans}$

Statistical covariance between bins of Table 62

Ratio of the scalar sum-pt of $\Lambda$ and $\bar{\Lambda}$ to prompt charged particles in the transverse region vs. $N_\textrm{ch,trans}$

Statistical covariance between bins of Table 63

Ratio of the multiplicity of $\Lambda$ and $\bar{\Lambda}$ to $K^{0}_{S}$ in the away region vs. $N_\textrm{ch,trans}$

Statistical covariance between bins of Table 64

Ratio of the multiplicity of $\Lambda$ and $\bar{\Lambda}$ to $K^{0}_{S}$ in the towards region vs. $N_\textrm{ch,trans}$

Statistical covariance between bins of Table 65

Ratio of the multiplicity of $\Lambda$ and $\bar{\Lambda}$ to $K^{0}_{S}$ in the transverse region vs. $N_\textrm{ch,trans}$

Statistical covariance between bins of Table 66

Ratio of the scalar sum-pt of $\Lambda$ and $\bar{\Lambda}$ to $K^{0}_{S}$ in the away region vs. $N_\textrm{ch,trans}$

Statistical covariance between bins of Table 67

Ratio of the scalar sum-pt of $\Lambda$ and $\bar{\Lambda}$ to $K^{0}_{S}$ in the towards region vs. $N_\textrm{ch,trans}$

Statistical covariance between bins of Table 68

Ratio of the scalar sum-pt of $\Lambda$ and $\bar{\Lambda}$ to $K^{0}_{S}$ in the transverse region vs. $N_\textrm{ch,trans}$

Statistical covariance between bins of Table 69

Mean-$p_{T}$ of $\Lambda$ and $\bar{\Lambda}$ in the away region vs. $N_\textrm{ch,trans}$

Statistical covariance between bins of Table 70

Mean-$p_{T}$ of $\Lambda$ and $\bar{\Lambda}$ in the towards region vs. $N_\textrm{ch,trans}$

Statistical covariance between bins of Table 71

Mean-$p_{T}$ of $\Lambda$ and $\bar{\Lambda}$ in the transverse region vs. $N_\textrm{ch,trans}$

Statistical covariance between bins of Table 72

Expected (dashed line) value of $-2\ln\Lambda$ as a function of $\kappa_{\lambda}$ for the combined fit, when all other coupling modifiers are fixed to their SM predictions.

Observed (solid line) value of $-2\ln\Lambda$ as a function of $\kappa_{2V}$ for the combined fit, when all other coupling modifiers are fixed to their SM predictions.

Expected (dashed line) value of $-2\ln\Lambda$ as a function of $\kappa_{2V}$ for the combined fit, when all other coupling modifiers are fixed to their SM predictions.

Likelihood observed contours at 68% CL (solid line) and 95% CL (dashed line) in the ($\kappa_{\lambda}$, $\kappa_{2V}$) parameter space, when all other coupling modifiers are fixed to their SM predictions. The best-fit value, denoted by a cross in the plot, corresponds to the very first entry in the table.

Likelihood expected contours at 68% CL (teal shaded region) and 95% CL (yellow shaded region) in the ($\kappa_{\lambda}$, $\kappa_{2V}$) parameter space, when all other coupling modifiers are fixed to their SM predictions. In the plot, the SM prediction is indicated by the star.

Likelihood contours at 68% (solid line) and 95% (dashed line) CL in the ($c_{hhh}$, $c_{gghh}$) parameter space, when all other Wilson coefficients are fixed to their SM values. The corresponding expected contours are shown by the inner and outer shaded regions. The SM prediction is indicated by the star, while the observed best-fit value is denoted by the black cross. The best-fit value corresponds to the very first entry in the table.

Likelihood contours at 68% (solid line) and 95% (dashed line) CL in the ($c_{hhh}$, $c_{gghh}$) parameter space, when all other Wilson coefficients are fixed to their SM values. The corresponding expected contours are shown by the inner and outer shaded regions. The SM prediction is indicated by the star, while the observed best-fit value is denoted by the black cross.

Likelihood contours at 68% (solid line) and 95% (dashed line) CL in the ($c_{hhh}$, $c_{tthh}$) parameter space, when all other Wilson coefficients are fixed to their SM values. The corresponding expected contours are shown by the inner and outer shaded regions. The SM prediction is indicated by the star, while the observed best-fit value is denoted by the black cross. The best-fit value corresponds to the very first entry in the table.

Likelihood contours at 68% (solid line) and 95% (dashed line) CL in the ($c_{hhh}$, $c_{tthh}$) parameter space, when all other Wilson coefficients are fixed to their SM values. The corresponding expected contours are shown by the inner and outer shaded regions. The SM prediction is indicated by the star, while the observed best-fit value is denoted by the black cross.

Likelihood contours at 68% (solid line) and 95% (dashed line) CL in the ($c_{H}$, $c_{H◻}$) parameter space, when all other Wilson coefficients are fixed to their SM values. The corresponding expected contours are shown by the inner and outer shaded regions. The SM prediction is indicated by the star, while the observed best-fit value is denoted by the black cross. The best-fit value corresponds to the very first entry in the table.

Likelihood contours at 68% (solid line) and 95% (dashed line) CL in the ($c_{H}$, $c_{H◻}$) parameter space, when all other Wilson coefficients are fixed to their SM values. The corresponding expected contours are shown by the inner and outer shaded regions. The SM prediction is indicated by the star, while the observed best-fit value is denoted by the black cross.

The acceptance times efficiency [in %] for the signal ggF $HH$ process as a function of the coupling modifier $\kappa_{\lambda}$ in each analysis category for the $\tau_{\mathrm{had}}\tau_{\mathrm{had}}$ channel. The other coupling modifiers affecting ggF $HH$ production are fixed to their SM predictions.

The acceptance times efficiency [in %] for the signal ggF $HH$ process as a function of the coupling modifier $\kappa_{\lambda}$ in each analysis category for the $\tau_{\mathrm{lep}}\tau_{\mathrm{had}}$ SLT channel. The other coupling modifiers affecting ggF $HH$ production are fixed to their SM predictions.

The acceptance times efficiency [in %] for the signal ggF $HH$ process as a function of the coupling modifier $\kappa_{\lambda}$ in each analysis category for the $\tau_{\mathrm{lep}}\tau_{\mathrm{had}}$ LTT channel. The other coupling modifiers affecting ggF $HH$ production are fixed to their SM predictions.

The acceptance times efficiency [in %] for the signal VBF $HH$ process as a function of the coupling modifier $\kappa_{\lambda}$ in each analysis category for the $\tau_{\mathrm{had}}\tau_{\mathrm{had}}$ channel. The other coupling modifiers affecting VBF $HH$ production are fixed to their SM predictions.

The acceptance times efficiency [in %] for the signal VBF $HH$ process as a function of the coupling modifier $\kappa_{\lambda}$ in each analysis category for the $\tau_{\mathrm{lep}}\tau_{\mathrm{had}}$ SLT channel. The other coupling modifiers affecting VBF $HH$ production are fixed to their SM predictions.

The acceptance times efficiency [in %] for the signal VBF $HH$ process as a function of the coupling modifier $\kappa_{\lambda}$ in each analysis category for the $\tau_{\mathrm{lep}}\tau_{\mathrm{had}}$ LTT channel. The other coupling modifiers affecting VBF $HH$ production are fixed to their SM predictions.

The acceptance times efficiency [in %] for the signal VBF $HH$ process as a function of the coupling modifier $\kappa_{2V}$ in each analysis category for the $\tau_{\mathrm{had}}\tau_{\mathrm{had}}$ channel. The other coupling modifiers affecting VBF $HH$ production are fixed to their SM predictions.

The acceptance times efficiency [in %] for the signal VBF $HH$ process as a function of the coupling modifier $\kappa_{2V}$ in each analysis category for the $\tau_{\mathrm{lep}}\tau_{\mathrm{had}}$ SLT channel. The other coupling modifiers affecting VBF $HH$ production are fixed to their SM predictions.

The acceptance times efficiency [in %] for the signal VBF $HH$ process as a function of the coupling modifier $\kappa_{2V}$ in each analysis category for the $\tau_{\mathrm{lep}}\tau_{\mathrm{had}}$ LTT channel. The other coupling modifiers affecting VBF $HH$ production are fixed to their SM predictions.

Expected (dashed line) value of $-2\ln\Lambda$ as a function of $\kappa_{\lambda}$ for the fit to the $\tau_{\mathrm{had}}\tau_{\mathrm{had}}$ channel, when all other coupling modifiers are fixed to their SM predictions.

Expected (dashed line) value of $-2\ln\Lambda$ as a function of $\kappa_{\lambda}$ for the fit to the $\tau_{\mathrm{lep}}\tau_{\mathrm{had}}$ channel, when all other coupling modifiers are fixed to their SM predictions.

Observed (solid line) value of $-2\ln\Lambda$ as a function of $\kappa_{\lambda}$ for the fit to the $\tau_{\mathrm{had}}\tau_{\mathrm{had}}$ channel, when all other coupling modifiers are fixed to their SM predictions.

Observed (solid line) value of $-2\ln\Lambda$ as a function of $\kappa_{\lambda}$ for the fit to the $\tau_{\mathrm{lep}}\tau_{\mathrm{had}}$ channel, when all other coupling modifiers are fixed to their SM predictions.

Expected (dashed line) value of $-2\ln\Lambda$ as a function of $\kappa_{2V}$ for the fit to the $\tau_{\mathrm{had}}\tau_{\mathrm{had}}$ channel, when all other coupling modifiers are fixed to their SM predictions.

Expected (dashed line) value of $-2\ln\Lambda$ as a function of $\kappa_{2V}$ for the fit to the $\tau_{\mathrm{lep}}\tau_{\mathrm{had}}$ channel, when all other coupling modifiers are fixed to their SM predictions.

Observed (solid line) value of $-2\ln\Lambda$ as a function of $\kappa_{2V}$ for the fit to the $\tau_{\mathrm{had}}\tau_{\mathrm{had}}$ channel, when all other coupling modifiers are fixed to their SM predictions.

Observed (solid line) value of $-2\ln\Lambda$ as a function of $\kappa_{2V}$ for the fit to the $\tau_{\mathrm{lep}}\tau_{\mathrm{had}}$ channel, when all other coupling modifiers are fixed to their SM predictions.

Summary of the expected (blue) and observed (orange) one-dimensional constraints at 68% (solid error bars) and 95% (dashed error bars) CL on the coefficients of selected HEFT (top) and SMEFT (bottom) operators describing Higgs boson interactions affecting $HH$ production through gluon-gluon fusion. The results are obtained from one dimensional scans of the profile log-likelihood assuming that all other Wilson coefficients are fixed to their SM values. The contribution from VBF $HH$ production is neglected.