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.

The isolated-photon cross section ratio, 13 TeV to 7 TeV, from pQCD NLO calculations with JETPHOX. The calculations were obtained by choosing factorisation, normalisation, and fragmentation scales. The parton distribution function used in the calculations is NNPDF4.0 for the $\sqrt{s}=$13 TeV measurement and CT14 for the $\sqrt{s}=$7 TeV measurement. The fragmentation function is BFG II for both measurements.

Differential cross section of isolated photons as a function of $x_\mathrm{T}^{\gamma}$ measured in pp collisions at $\sqrt{s}=$13 TeV.

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.

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>

Normalized second-order cumulant of the Net-$\Xi$ number, ${\kappa}_{2}(\overline{\Xi}^{+} - \Xi^{-})/{\kappa}_{1}(\overline{\Xi}^{+} + \Xi^{-})$, in pp collisions at $\sqrt{s} = 5.02$ TeV

Normalized second-order cumulant of the Net-$\Xi$ number, ${\kappa}_{2}(\overline{\Xi}^{+} - \Xi^{-})/{\kappa}_{1}(\overline{\Xi}^{+} + \Xi^{-})$, in p-Pb collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02$ TeV

Normalized second-order cumulant of the Net-$\Xi$ number, ${\kappa}_{2}(\overline{\Xi}^{+} - \Xi^{-})/{\kappa}_{1}(\overline{\Xi}^{+} + \Xi^{-})$, in Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02$ TeV

$\chi^2$ profile obtained from the simultaneous comparison of the ${\kappa}_{2}(\overline{\Xi}^{+} - \Xi^{-})/{\kappa}_{1}(\overline{\Xi}^{+} + \Xi^{-})$ and $\rho_{\Delta\Xi\Delta\mathrm{K}}$ measured in Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02$ TeV with model calculations carried out with the Thermal-FIST code, for different values of the volume parameter $V_{\mathrm{c}}$

Covariance matrix of the Pearson correlation coefficient between the net-$\Xi$ number and net-K number, $\rho_{\Delta\Xi\Delta\mathrm{K}}$, in pp collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02$ TeV

Covariance matrix of the Pearson correlation coefficient between the net-$\Xi$ number and net-K number, $\rho_{\Delta\Xi\Delta\mathrm{K}}$, in p-Pb collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02$ TeV

Covariance matrix of the Pearson correlation coefficient between the net-$\Xi$ number and net-K number, $\rho_{\Delta\Xi\Delta\mathrm{K}}$, in Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02$ TeV

Covariance matrix of the normalized second-order cumulant of the Net-$\Xi$ number, ${\kappa}_{2}(\overline{\Xi}^{+} - \Xi^{-})/{\kappa}_{1}(\overline{\Xi}^{+} + \Xi^{-})$, in pp collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02$ TeV

Covariance matrix of the normalized second-order cumulant of the Net-$\Xi$ number, ${\kappa}_{2}(\overline{\Xi}^{+} - \Xi^{-})/{\kappa}_{1}(\overline{\Xi}^{+} + \Xi^{-})$, in p-Pb collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02$ TeV

Covariance matrix of the normalized second-order cumulant of the Net-$\Xi$ number, ${\kappa}_{2}(\overline{\Xi}^{+} - \Xi^{-})/{\kappa}_{1}(\overline{\Xi}^{+} + \Xi^{-})$, in Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02$ TeV

Distribution of the BDT output score in the the 3l channel signal region.

Distribution of the BDT output score in the 2lSC channel signal region.

Distribution of the BDT output score in the 2lSC+$\tau_{had}$ channel signal region.

Distribution of the BDT output score in the the 2l+2$\tau_{had}$ channel signal region.

Distribution of the BDT output score in the l+2$\tau_{had}$ channel signal region.

Invariant mass of the diphoton system in the $\gamma\gamma$+2(l,$\tau_{had}$) channel signal region.

Invariant mass of the diphoton system in the $\gamma\gamma$+$e/\mu$ channel in the loose BDT signal region.

Invariant mass of the diphoton system in the $\gamma\gamma$+$e/\mu$ channel in the medium BDT signal region.

Invariant mass of the diphoton system in the $\gamma\gamma$+$e/\mu$ channel in the tight BDT signal region.

Invariant mass of the diphoton system in the $\gamma\gamma$+$\tau$ channel in the loose BDT signal region.

Invariant mass of the diphoton system in the $\gamma\gamma$+$\tau$ channel in the medium BDT signal region.

Invariant mass of the diphoton system in the $\gamma\gamma$+$\tau$ channel in the tight BDT signal region.

Observed and expected 95% CL upper limits on the signal strength for the ML channels and the $\gamma\gamma$+ML channels.

Expected values of -2ln$\Lambda$ as a function of $\kappa_\lambda$ for the combination. All other coupling modifiers are fixed to their SM predictions and the expected limits are computed assuming the SM.

Observed values of -2ln$\Lambda$ as a function of $\kappa_\lambda$ for the combination. All other coupling modifiers are fixed to their SM predictions and the expected limits are computed assuming the SM.

Expected values of -2ln$\Lambda$ as a function of $\kappa_{2V}$ for the combination. All other coupling modifiers are fixed to their SM predictions and the expected limits are computed assuming the SM.

Observed values of -2ln$\Lambda$ as a function of $\kappa_{2V}$ for the combination. All other coupling modifiers are fixed to their SM predictions and the expected limits are computed assuming the SM.

Expected values of -2ln$\Lambda$ as a function of $\kappa_\lambda$ for the ML channels. All other coupling modifiers are fixed to their SM predictions and the expected limits are computed assuming the SM.

Observed values of -2ln$\Lambda$ as a function of $\kappa_\lambda$ for the ML channels. All other coupling modifiers are fixed to their SM predictions and the expected limits are computed assuming the SM.

Expected values of -2ln$\Lambda$ as a function of $\kappa_\lambda$ for the $\gamma\gamma$+ML channels. All other coupling modifiers are fixed to their SM predictions and the expected limits are computed assuming the SM.

Observed values of -2ln$\Lambda$ as a function of $\kappa_\lambda$ for the $\gamma\gamma$+ML channels. All other coupling modifiers are fixed to their SM predictions and the expected limits are computed assuming the SM.

Expected values of -2ln$\Lambda$ as a function of $\kappa_{2V}$ for the ML channels. All other coupling modifiers are fixed to their SM predictions and the expected limits are computed assuming the SM.

Observed values of -2ln$\Lambda$ as a function of $\kappa_{2V}$ for the ML channels. All other coupling modifiers are fixed to their SM predictions and the expected limits are computed assuming the SM.

Expected values of -2ln$\Lambda$ as a function of $\kappa_{2V}$ for the $\gamma\gamma$+ML channels. All other coupling modifiers are fixed to their SM predictions and the expected limits are computed assuming the SM.

Observed values of -2ln$\Lambda$ as a function of $\kappa_{2V}$ for the $\gamma\gamma$+ML channels. All other coupling modifiers are fixed to their SM predictions and the expected limits are computed assuming the SM.

Transverse momentum spectra of deuterons measured in Xe--Xe collisions at centre-of-mass per nucleon-nucleon energy of 5.44 TeV, as shown in Fig. 3 (left panel). Centrality class 20 to 40 percent.

Transverse momentum spectra of deuterons measured in Xe--Xe collisions at centre-of-mass per nucleon-nucleon energy of 5.44 TeV, as shown in Fig. 3 (left panel). Centrality class 40 to 60 percent.

Transverse momentum spectra of deuterons measured in Xe--Xe collisions at centre-of-mass per nucleon-nucleon energy of 5.44 TeV, as shown in Fig. 3 (left panel). Centrality class 60 to 90 percent.

Coalescence parameter B2 as a function of the transverse momentum per nucleon pT/A, in the centrality class 0 to 10 percent. The B2 is shown in Figure 7 (left panel).

Coalescence parameter B2 as a function of the transverse momentum per nucleon pT/A, in the centrality class 10 to 20 percent. The B2 is shown in Figure 7 (left panel).

Coalescence parameter B2 as a function of the transverse momentum per nucleon pT/A, in the centrality class 20 to 40 percent. The B2 is shown in Figure 7 (left panel).

Coalescence parameter B2 as a function of the transverse momentum per nucleon pT/A, in the centrality class 40 to 60 percent. The B2 is shown in Figure 7 (left panel).

Coalescence parameter B2 as a function of the transverse momentum per nucleon pT/A, in the centrality class 60 to 90 percent. The B2 is shown in Figure 7 (left panel).

Coalescence parameter B3 as a function of the transverse momentum per nucleon pT/A, in the centrality class 0 to 90 percent. The B3 is shown in Figure 7 (right panel).

Ratio of integrated yields of deuterons and of protons, as a function of the average charged particle multiplicity density. The d-to-p ratio is shown in Figure 5 (top panel).

Ratio of integrated yields of He3 and of protons, as a function of the average charged particle multiplicity density. The He3-to-p ratio is shown in Figure 5 (bottom panel).

Ratio of integrated yields of deuterons and of pions, as a function of the average charged particle multiplicity density. The d-to-pi ratio is shown in Figure 6 (top panel).

Ratio of integrated yields of He3 and of pions, as a function of the average charged particle multiplicity density. The He3-to-pi ratio is shown in Figure 6 (bottom panel).

B2 as a function of the average charged particle multiplicity density for pT-over-A equal to 0.75 GEV. The B2 vs. multiplicity is not shown in the paper.

(Anti)deuteron $v_2$ measured at midrapidity in the 0-20 centrality class, as shown in Fig. 8 (left panel).

(Anti)deuteron $v_2$ measured at midrapidity in the 20-40 centrality class, as shown in Fig. 8 (right panel).

Integrated (${}_{\Lambda}^{3}\mathrm{H} + {}^3_ {\overline{\Lambda}}\overline{\mathrm{H}}$)/2 yields in different V0M centrality classes

Hypertriton over He3 ratio as a function of multiplicity

Hypertriton over He3 ratio as a function of $p_{T}$ in 0-10% V0M centrality class

Hypertriton over He3 ratio as a function of $p_{T}$ in 10-30% V0M centrality class

Hypertriton over He3 ratio as a function of $p_{T}$ in 30-50% V0M centrality class