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% CL upper limits on the signal strength for the inclusive ggF HH production from the bb̄τ⁺τ^-, bb̄γγ, bb̄bb̄, multilepton and bb̄ℓℓ+E_T^miss decay channels, and their statistical combination. When deriving the limit on μ_ggF^HH (μ_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 ±1σ and ±2σ bands, is calculated under the assumption of no HH process and with all NPs profiled to the observed data.

Observed and expected 95% CL upper limits on the signal strength for the VBF HH production from the bb̄τ⁺τ^-, bb̄γγ, bb̄bb̄, multilepton and bb̄ℓℓ+E_T^miss decay channels, and their statistical combination. When deriving the limit on μ_ggF^HH (μ_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 ±1σ and ±2σ 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% CL on the inclusive ggF and VBF HH production cross-section from the bb̄τ⁺τ^-, bb̄γγ, bb̄bb̄, multilepton and bb̄ℓℓ+E_T^miss decay channels, and their statistical combination. The Higgs boson mass is set to 125 GeV when deriving the predicted SM cross-section (red band). The expected limits, along with the ±1σ and ±2σ 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% CL exclusion limits on the HH production cross-sections of (a) the inclusive ggF and VBF processes as a function of κ_λ, for the bb̄γγ (purple), bb̄τ⁺τ^- (green), multilepton (cyan), bb̄bb̄ (blue) and bb̄ℓℓ+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 κ_λ. 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% CL exclusion limits on the HH production cross-sections of the VBF process as a function of κ_2V, for the bb̄γγ (purple), bb̄τ⁺τ^- (green), multilepton (cyan), bb̄bb̄ (blue) and bb̄ℓℓ+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 κ_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% 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 bb̄τ⁺τ^-, bb̄γγ and bb̄bb̄ 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.

<b>Note: in the paper, uncertainties are given in relative terms. The HEPData table contains absolute numbers. The original data file, containing relative uncertainties as in the paper, is available via the 'Resources' button above.</b> Differential cross sections, $d\sigma/d\Delta\phi$, in the $p_{T,jet}^{lead}$ region of $2.5 \;\mathrm{GeV} < p_{T,jet}^{lead} < 7 \;\mathrm{GeV}$ for $N_{jet} \geq 3$, as obtained from the data, ARIADNE MC simulations, and perturbative calculations at $\mathcal{O}(\alpha_{s})$ and $\mathcal{O}(\alpha_{s}^{2})$ accuracy. Other details are as in the caption to Table 1.

<b>Note: in the paper, uncertainties are given in relative terms. The HEPData table contains absolute numbers. The original data file, containing relative uncertainties as in the paper, is available via the 'Resources' button above.</b> Differential cross sections, $d\sigma/d\Delta\phi$, in the $p_{T,jet}^{lead}$ region of $7 \;\mathrm{GeV} < p_{T,jet}^{lead} < 12 \;\mathrm{GeV}$ for $N_{jet} \geq 1$, as obtained from the data, ARIADNE MC simulations, and perturbative calculations at $\mathcal{O}(\alpha_{s})$ and $\mathcal{O}(\alpha_{s}^{2})$ accuracy. Other details are as in the caption to Table 1.

<b>Note: in the paper, uncertainties are given in relative terms. The HEPData table contains absolute numbers. The original data file, containing relative uncertainties as in the paper, is available via the 'Resources' button above.</b> Differential cross sections, $d\sigma/d\Delta\phi$, in the $p_{T,jet}^{lead}$ region of $7 \;\mathrm{GeV} < p_{T,jet}^{lead} < 12 \;\mathrm{GeV}$ for $N_{jet} \geq 2$, as obtained from the data, ARIADNE MC simulations, and perturbative calculations at $\mathcal{O}(\alpha_{s})$ and $\mathcal{O}(\alpha_{s}^{2})$ accuracy. Other details are as in the caption to Table 1.

<b>Note: in the paper, uncertainties are given in relative terms. The HEPData table contains absolute numbers. The original data file, containing relative uncertainties as in the paper, is available via the 'Resources' button above.</b> Differential cross sections, $d\sigma/d\Delta\phi$, in the $p_{T,jet}^{lead}$ region of $7 \;\mathrm{GeV} < p_{T,jet}^{lead} < 12 \;\mathrm{GeV}$ for $N_{jet} \geq 3$, as obtained from the data, ARIADNE MC simulations, and perturbative calculations at $\mathcal{O}(\alpha_{s})$ and $\mathcal{O}(\alpha_{s}^{2})$ accuracy. Other details are as in the caption to Table 1.

<b>Note: in the paper, uncertainties are given in relative terms. The HEPData table contains absolute numbers. The original data file, containing relative uncertainties as in the paper, is available via the 'Resources' button above.</b> Differential cross sections, $d\sigma/d\Delta\phi$, in the $p_{T,jet}^{lead}$ region of $12 \;\mathrm{GeV} < p_{T,jet}^{lead} < 30 \;\mathrm{GeV}$ for $N_{jet} \geq 1$, as obtained from the data, ARIADNE MC simulations, and perturbative calculations at $\mathcal{O}(\alpha_{s})$ and $\mathcal{O}(\alpha_{s}^{2})$ accuracy. Other details are as in the caption to Table 1.

<b>Note: in the paper, uncertainties are given in relative terms. The HEPData table contains absolute numbers. The original data file, containing relative uncertainties as in the paper, is available via the 'Resources' button above.</b> Differential cross sections, $d\sigma/d\Delta\phi$, in the $p_{T,jet}^{lead}$ region of $12 \;\mathrm{GeV} < p_{T,jet}^{lead} < 30 \;\mathrm{GeV}$ for $N_{jet} \geq 2$, as obtained from the data, ARIADNE MC simulations, and perturbative calculations at $\mathcal{O}(\alpha_{s})$ and $\mathcal{O}(\alpha_{s}^{2})$ accuracy. Other details are as in the caption to Table 1.

<b>Note: in the paper, uncertainties are given in relative terms. The HEPData table contains absolute numbers. The original data file, containing relative uncertainties as in the paper, is available via the 'Resources' button above.</b> Differential cross sections, $d\sigma/d\Delta\phi$, in the $p_{T,jet}^{lead}$ region of $12 \;\mathrm{GeV} < p_{T,jet}^{lead} < 30 \;\mathrm{GeV}$ for $N_{jet} \geq 3$, as obtained from the data, ARIADNE MC simulations, and perturbative calculations at $\mathcal{O}(\alpha_{s})$ and $\mathcal{O}(\alpha_{s}^{2})$ accuracy. Other details are as in the caption to Table 1.

<b>Note: in the paper, uncertainties are given in relative terms. The HEPData table contains absolute numbers. The original data file, containing relative uncertainties as in the paper, is available via the 'Resources' button above.</b> Differential cross sections, $d\sigma/d\Delta\phi$, in the $Q^{2}$ region of $10 \;\mathrm{GeV}^{2} < Q^{2} < 50 \;\mathrm{GeV}^{2}$ for $N_{jet} \geq 1$, as obtained from the data, ARIADNE MC simulations, and perturbative calculations at $\mathcal{O}(\alpha_{s})$ and $\mathcal{O}(\alpha_{s}^{2})$ accuracy. Other details are as in the caption to Table 1.

<b>Note: in the paper, uncertainties are given in relative terms. The HEPData table contains absolute numbers. The original data file, containing relative uncertainties as in the paper, is available via the 'Resources' button above.</b> Differential cross sections, $d\sigma/d\Delta\phi$, in the $Q^{2}$ region of $10 \;\mathrm{GeV}^{2} < Q^{2} < 50 \;\mathrm{GeV}^{2}$ for $N_{jet} \geq 2$, as obtained from the data, ARIADNE MC simulations, and perturbative calculations at $\mathcal{O}(\alpha_{s})$ and $\mathcal{O}(\alpha_{s}^{2})$ accuracy. Other details are as in the caption to Table 1.

<b>Note: in the paper, uncertainties are given in relative terms. The HEPData table contains absolute numbers. The original data file, containing relative uncertainties as in the paper, is available via the 'Resources' button above.</b> Differential cross sections, $d\sigma/d\Delta\phi$, in the $Q^{2}$ region of $10 \;\mathrm{GeV}^{2} < Q^{2} < 50 \;\mathrm{GeV}^{2}$ for $N_{jet} \geq 3$, as obtained from the data, ARIADNE MC simulations, and perturbative calculations at $\mathcal{O}(\alpha_{s})$ and $\mathcal{O}(\alpha_{s}^{2})$ accuracy. Other details are as in the caption to Table 1.

<b>Note: in the paper, uncertainties are given in relative terms. The HEPData table contains absolute numbers. The original data file, containing relative uncertainties as in the paper, is available via the 'Resources' button above.</b> Differential cross sections, $d\sigma/d\Delta\phi$, in the $Q^{2}$ region of $50 \;\mathrm{GeV}^{2} < Q^{2} < 100 \;\mathrm{GeV}^{2}$ for $N_{jet} \geq 1$, as obtained from the data, ARIADNE MC simulations, and perturbative calculations at $\mathcal{O}(\alpha_{s})$ and $\mathcal{O}(\alpha_{s}^{2})$ accuracy. Other details are as in the caption to Table 1.

<b>Note: in the paper, uncertainties are given in relative terms. The HEPData table contains absolute numbers. The original data file, containing relative uncertainties as in the paper, is available via the 'Resources' button above.</b> Differential cross sections, $d\sigma/d\Delta\phi$, in the $Q^{2}$ region of $50 \;\mathrm{GeV}^{2} < Q^{2} < 100 \;\mathrm{GeV}^{2}$ for $N_{jet} \geq 2$, as obtained from the data, ARIADNE MC simulations, and perturbative calculations at $\mathcal{O}(\alpha_{s})$ and $\mathcal{O}(\alpha_{s}^{2})$ accuracy. Other details are as in the caption to Table 1.

<b>Note: in the paper, uncertainties are given in relative terms. The HEPData table contains absolute numbers. The original data file, containing relative uncertainties as in the paper, is available via the 'Resources' button above.</b> Differential cross sections, $d\sigma/d\Delta\phi$, in the $Q^{2}$ region of $50 \;\mathrm{GeV}^{2} < Q^{2} < 100 \;\mathrm{GeV}^{2}$ for $N_{jet} \geq 3$, as obtained from the data, ARIADNE MC simulations, and perturbative calculations at $\mathcal{O}(\alpha_{s})$ and $\mathcal{O}(\alpha_{s}^{2})$ accuracy. Other details are as in the caption to Table 1.

<b>Note: in the paper, uncertainties are given in relative terms. The HEPData table contains absolute numbers. The original data file, containing relative uncertainties as in the paper, is available via the 'Resources' button above.</b> Differential cross sections, $d\sigma/d\Delta\phi$, in the $Q^{2}$ region of $100 \;\mathrm{GeV}^{2} < Q^{2} < 350 \;\mathrm{GeV}^{2}$ for $N_{jet} \geq 1$, as obtained from the data, ARIADNE MC simulations, and perturbative calculations at $\mathcal{O}(\alpha_{s})$ and $\mathcal{O}(\alpha_{s}^{2})$ accuracy. Other details are as in the caption to Table 1.

<b>Note: in the paper, uncertainties are given in relative terms. The HEPData table contains absolute numbers. The original data file, containing relative uncertainties as in the paper, is available via the 'Resources' button above.</b> Differential cross sections, $d\sigma/d\Delta\phi$, in the $Q^{2}$ region of $100 \;\mathrm{GeV}^{2} < Q^{2} < 350 \;\mathrm{GeV}^{2}$ for $N_{jet} \geq 2$, as obtained from the data, ARIADNE MC simulations, and perturbative calculations at $\mathcal{O}(\alpha_{s})$ and $\mathcal{O}(\alpha_{s}^{2})$ accuracy. Other details are as in the caption to Table 1.

<b>Note: in the paper, uncertainties are given in relative terms. The HEPData table contains absolute numbers. The original data file, containing relative uncertainties as in the paper, is available via the 'Resources' button above.</b> Differential cross sections, $d\sigma/d\Delta\phi$, in the $Q^{2}$ region of $100 \;\mathrm{GeV}^{2} < Q^{2} < 350 \;\mathrm{GeV}^{2}$ for $N_{jet} \geq 3$, as obtained from the data, ARIADNE MC simulations, and perturbative calculations at $\mathcal{O}(\alpha_{s})$ and $\mathcal{O}(\alpha_{s}^{2})$ accuracy. Other details are as in the caption to Table 1.

QED correction factors for inclusive measurement, as estimated with RAPGAP.

QED correction factors for $2.5 \;\mathrm{GeV} < p_{T,jet}^{lead} < 7 \;\mathrm{GeV}$ and $N_{jet} \geq 1$, as estimated with RAPGAP.

QED correction factors for $2.5 \;\mathrm{GeV} < p_{T,jet}^{lead} < 7 \;\mathrm{GeV}$ and $N_{jet} \geq 2$, as estimated with RAPGAP.

QED correction factors for $2.5 \;\mathrm{GeV} < p_{T,jet}^{lead} < 7 \;\mathrm{GeV}$ and $N_{jet} \geq 3$, as estimated with RAPGAP.

QED correction factors for $7 \;\mathrm{GeV} < p_{T,jet}^{lead} < 12 \;\mathrm{GeV}$ and $N_{jet} \geq 1$, as estimated with RAPGAP.

QED correction factors for $7 \;\mathrm{GeV} < p_{T,jet}^{lead} < 12 \;\mathrm{GeV}$ and $N_{jet} \geq 2$, as estimated with RAPGAP.

QED correction factors for $7 \;\mathrm{GeV} < p_{T,jet}^{lead} < 12 \;\mathrm{GeV}$ and $N_{jet} \geq 3$, as estimated with RAPGAP.

QED correction factors for $12 \;\mathrm{GeV} < p_{T,jet}^{lead} < 30 \;\mathrm{GeV}$ and $N_{jet} \geq 1$, as estimated with RAPGAP.

QED correction factors for $12 \;\mathrm{GeV} < p_{T,jet}^{lead} < 30 \;\mathrm{GeV}$ and $N_{jet} \geq 2$, as estimated with RAPGAP.

QED correction factors for $12 \;\mathrm{GeV} < p_{T,jet}^{lead} < 30 \;\mathrm{GeV}$ and $N_{jet} \geq 3$, as estimated with RAPGAP.

QED correction factors for $10 \;\mathrm{GeV}^{2} < Q^{2} < 50 \;\mathrm{GeV}^{2}$ and $N_{jet} \geq 1$, as estimated with RAPGAP.

QED correction factors for $10 \;\mathrm{GeV}^{2} < Q^{2} < 50 \;\mathrm{GeV}^{2}$ and $N_{jet} \geq 2$, as estimated with RAPGAP.

QED correction factors for $10 \;\mathrm{GeV}^{2} < Q^{2} < 50 \;\mathrm{GeV}^{2}$ and $N_{jet} \geq 3$, as estimated with RAPGAP.

QED correction factors for $50 \;\mathrm{GeV}^{2} < Q^{2} < 100 \;\mathrm{GeV}^{2}$ and $N_{jet} \geq 1$, as estimated with RAPGAP.

QED correction factors for $50 \;\mathrm{GeV}^{2} < Q^{2} < 100 \;\mathrm{GeV}^{2}$ and $N_{jet} \geq 2$, as estimated with RAPGAP.

QED correction factors for $50 \;\mathrm{GeV}^{2} < Q^{2} < 100 \;\mathrm{GeV}^{2}$ and $N_{jet} \geq 3$, as estimated with RAPGAP.

QED correction factors for $100 \;\mathrm{GeV}^{2} < Q^{2} < 350 \;\mathrm{GeV}^{2}$ and $N_{jet} \geq 1$, as estimated with RAPGAP.

QED correction factors for $100 \;\mathrm{GeV}^{2} < Q^{2} < 350 \;\mathrm{GeV}^{2}$ and $N_{jet} \geq 2$, as estimated with RAPGAP.

QED correction factors for $100 \;\mathrm{GeV}^{2} < Q^{2} < 350 \;\mathrm{GeV}^{2}$ and $N_{jet} \geq 3$, as estimated with RAPGAP.

The correlation matrix for the inclusive measurement. The azimuthal correlation angle $\Delta\phi$ of each lepton--leading-jet pair was assigned a bin ID between 0 to 59 segmented uniformly from 0 to $\pi$. This bin ID was offset by multiples of 60 based on the jet multiplicity so that the pair from a single jet event, as suggested by the MC simulation, was assigned a value between 0 to 59, dijet events were given 60 to 119, trijet 120 to 179, and four or more jets 180 to 239.

The correlation matrix for $2.5 \;\mathrm{GeV} < p_{T,jet}^{lead} < 7 \;\mathrm{GeV}$. Other details are as in the caption to Fig. 13.

The correlation matrix for $7 \;\mathrm{GeV} < p_{T,jet}^{lead} < 12 \;\mathrm{GeV}$. Other details are as in the caption to Fig. 13.

The correlation matrix for $12 \;\mathrm{GeV} < p_{T,jet}^{lead} < 30 \;\mathrm{GeV}$. Other details are as in the caption to Fig. 13.

The correlation matrix for $10 \;\mathrm{GeV}^{2} < Q^{2} < 50 \;\mathrm{GeV}^{2}$. Other details are as in the caption to Fig. 13.

The correlation matrix for $50 \;\mathrm{GeV}^{2} < Q^{2} < 100 \;\mathrm{GeV}^{2}$. Other details are as in the caption to Fig. 13.

The correlation matrix for $100 \;\mathrm{GeV}^{2} < Q^{2} < 350 \;\mathrm{GeV}^{2}$. Other details are as in the caption to Fig. 13.

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} < $p_{T,3}$

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.

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

The figure shows the post-fit distribution of events as a function of $H_{\mathrm{T}}^{\ell,j} = \sum_{\ell,j} p_{T}^{\ell,j}$, scalar sum of $p_T$ for all jets and leptons in the $\ell+$jets channel, in proton-lead (p+Pb) collisions at a center-of-mass energy of $\sqrt{s_{\mathrm{NN}}} = 8.16$ TeV, with an integrated luminosity of 165 nb$^{-1}$. The data correspond to the $1\ell 1b$ $\mu$+jets channel in a pre-fit configuration. The stacked histograms represent different processes contributing to the event yield, including top quark pair production ($t\bar{t}$), single top, $W$ boson production with $b$, $c$, and light quarks, $Z$ boson production with $b$, $c$, and light quarks, diboson, and fake lepton backgrounds.

The figure shows the pre-fit distribution of events as a function of $H_{\mathrm{T}}^{\ell,j} = \sum_{\ell,j} p_{T}^{\ell,j}$, scalar sum of $p_T$ for all jets and leptons in the $\ell+$jets channel, in proton-lead (p+Pb) collisions at a center-of-mass energy of $\sqrt{s_{\mathrm{NN}}} = 8.16$ TeV, with an integrated luminosity of 165 nb$^{-1}$. The data correspond to the $1\ell 2bincl$ $e$+jets channel in a pre-fit configuration. The stacked histograms represent different processes contributing to the event yield, including top quark pair production ($t\bar{t}$), single top, $W$ boson production with $b$, $c$, and light quarks, $Z$ boson production with $b$, $c$, and light quarks, diboson, and fake lepton backgrounds.

The figure shows the post-fit distribution of events as a function of $H_{\mathrm{T}}^{\ell,j} = \sum_{\ell,j} p_{T}^{\ell,j}$, scalar sum of $p_T$ for all jets and leptons in the $\ell+$jets channel, in proton-lead (p+Pb) collisions at a center-of-mass energy of $\sqrt{s_{\mathrm{NN}}} = 8.16$ TeV, with an integrated luminosity of 165 nb$^{-1}$. The data correspond to the $1\ell 2bincl$ $e$+jets channel in a pre-fit configuration. The stacked histograms represent different processes contributing to the event yield, including top quark pair production ($t\bar{t}$), single top, $W$ boson production with $b$, $c$, and light quarks, $Z$ boson production with $b$, $c$, and light quarks, diboson, and fake lepton backgrounds.

The figure shows the pre-fit distribution of events as a function of $H_{\mathrm{T}}^{\ell,j} = \sum_{\ell,j} p_{T}^{\ell,j}$, scalar sum of $p_T$ for all jets and leptons in the $\ell+$jets channel, in proton-lead (p+Pb) collisions at a center-of-mass energy of $\sqrt{s_{\mathrm{NN}}} = 8.16$ TeV, with an integrated luminosity of 165 nb$^{-1}$. The data correspond to the $1\ell 2bincl$ $\mu$+jets channel in a pre-fit configuration. The stacked histograms represent different processes contributing to the event yield, including top quark pair production ($t\bar{t}$), single top, $W$ boson production with $b$, $c$, and light quarks, $Z$ boson production with $b$, $c$, and light quarks, diboson, and fake lepton backgrounds.

The figure shows the post-fit distribution of events as a function of $H_{\mathrm{T}}^{\ell,j} = \sum_{\ell,j} p_{T}^{\ell,j}$, scalar sum of $p_T$ for all jets and leptons in the $\ell+$jets channel, in proton-lead (p+Pb) collisions at a center-of-mass energy of $\sqrt{s_{\mathrm{NN}}} = 8.16$ TeV, with an integrated luminosity of 165 nb$^{-1}$. The data correspond to the $1\ell 2bincl$ $\mu$+jets channel in a pre-fit configuration. The stacked histograms represent different processes contributing to the event yield, including top quark pair production ($t\bar{t}$), single top, $W$ boson production with $b$, $c$, and light quarks, $Z$ boson production with $b$, $c$, and light quarks, diboson, and fake lepton backgrounds.

The figure shows the pre-fit distribution of events as a function of $H_{\mathrm{T}}^{\ell,j} = \sum_{\ell,j} p_{T}^{\ell,j}$, scalar sum of $p_T$ for all jets and leptons in the $\ell+$jets channel, in proton-lead (p+Pb) collisions at a center-of-mass energy of $\sqrt{s_{\mathrm{NN}}} = 8.16$ TeV, with an integrated luminosity of 165 nb\(^{-1}\) in the 2\(\ell\)1b signal region. The histogram represents the number of events per GeV, with the data points shown as black dots and their associated uncertainties. The stacked colored histograms indicate different processes: \(t\bar{t}\) (red), single top (orange), \(Z+b\) (dark blue), \(Z+c\) (medium blue), \(Z+\)light (light blue), diboson (gray), and fake lepton (purple). The hatched area represents the uncertainty in the predictions.

The figure shows the post-fit distribution of events as a function of $H_{\mathrm{T}}^{\ell,j} = \sum_{\ell,j} p_{T}^{\ell,j}$, scalar sum of $p_T$ for all jets and leptons in the $\ell+$jets channel, in proton-lead (p+Pb) collisions at a center-of-mass energy of $\sqrt{s_{\mathrm{NN}}} = 8.16$ TeV, with an integrated luminosity of 165 nb\(^{-1}\) in the 2\(\ell\)1b signal region. The histogram represents the number of events per GeV, with the data points shown as black dots and their associated uncertainties. The stacked colored histograms indicate different processes: \(t\bar{t}\) (red), single top (orange), \(Z+b\) (dark blue), \(Z+c\) (medium blue), \(Z+\)light (light blue), diboson (gray), and fake lepton (purple). The hatched area represents the uncertainty in the predictions.

The figure shows the pre-fit distribution of events as a function of $H_{\mathrm{T}}^{\ell,j} = \sum_{\ell,j} p_{T}^{\ell,j}$, scalar sum of $p_T$ for all jets and leptons in the $\ell+$jets channel, in proton-lead (p+Pb) collisions at a center-of-mass energy of $\sqrt{s_{\mathrm{NN}}} = 8.16$ TeV, with an integrated luminosity of 165 nb\(^{-1}\) in the 2\(\ell\)2bincl signal region. The histogram represents the number of events per GeV, with the data points shown as black dots and their associated uncertainties. The stacked colored histograms indicate different processes: \(t\bar{t}\) (red), single top (orange), \(Z+b\) (dark blue), \(Z+c\) (medium blue), \(Z+\)light (light blue), diboson (gray), and fake lepton (purple). The hatched area represents the uncertainty in the predictions.

The figure shows the post-fit distribution of events as a function of $H_{\mathrm{T}}^{\ell,j} = \sum_{\ell,j} p_{T}^{\ell,j}$, scalar sum of $p_T$ for all jets and leptons in the $\ell+$jets channel, in proton-lead (p+Pb) collisions at a center-of-mass energy of $\sqrt{s_{\mathrm{NN}}} = 8.16$ TeV, with an integrated luminosity of 165 nb\(^{-1}\) in the 2\(\ell\)2bincl signal region. The histogram represents the number of events per GeV, with the data points shown as black dots and their associated uncertainties. The stacked colored histograms indicate different processes: \(t\bar{t}\) (red), single top (orange), \(Z+b\) (dark blue), \(Z+c\) (medium blue), \(Z+\)light (light blue), diboson (gray), and fake lepton (purple). The hatched area represents the uncertainty in the predictions.

The correlation matrix of the fit parameters for the six combined regions, including the signal regions (electron+jets: 1-lepton 1-bjet and 1-lepton 2-bjet inclusive, muon+jets: 1-lepton 1-bjet and 1-lepton 2-bjet inclusive, dilepton: 2-lepton 1-bjet and 2-lepton 2-bjet inclusive) is shown.

The impact of systematic uncertainties on the fitted signal-strength parameter $\hat{\mu}$ for the combined (six signal regions ($e+$jets: $1\ell1b$ and $1\ell2b\mathrm{incl}$, $\mu+$jets: $1\ell1b$ and $1\ell2b\mathrm{incl}$, dilepton: $2\ell1b$ and $2\ell2b\mathrm{incl}$) fit of all channels. Only the 15 most significant systematic uncertainties are shown and listed in decreasing order of their impact on $\mu$ on the $y$-axis. The empty (filled) blue/cyan boxes correspond to the pre-fit (post-fit) impact on $\mu$, referring to the upper $x$-axis. The impact of each systematic uncertainty, $\Delta \mu$, is calculated by comparing the nominal best-fit value of $\mu$ with the result of the fit when fixing the corresponding nuisance parameter $\theta$ to its best-fit value $\hat{\theta}$ shifted by its pre-fit (post-fit) uncertainties $\hat{\theta} \pm \Delta \theta(\hat{\theta} \pm \Delta \hat{\theta})$. The black points, which refer to the lower $x$-axis, show the pulls of the fitted nuisance parameters, i.e., the deviations of the fitted parameters $\hat{\theta}$ from their nominal values $\theta_0$, normalized to their nominal uncertainties $\Delta \theta$. The black lines show the post-fit uncertainties of the nuisance parameters, relative to their nominal uncertainties, which are indicated by the dashed lines.

Breakdown of relative systematic uncertainties in the measured ${t\bar{t}}$ cross-section. The quoted uncertainties are obtained by repeating the fit with a group of nuisance parameters fixed to their fitted values and subtracting in quadrature the resulting total uncertainty from the uncertainty of the complete fit. However, the total uncertainty is not the quadratic sum of the grouped impacts, as this approach neglects the correlation among the different groups.

The signal strength $\mu_{t\bar{t}}$, defined as the ratio of the observed signal for the combined six signal regions ($e+$jets: $1\ell1b$ and $1\ell2b\mathrm{incl}$, $\mu+$jets: $1\ell1b$ and $1\ell2b\mathrm{incl}$, dilepton: $2\ell1b$ and $2\ell2b\mathrm{incl}$.) to the SM expectation with no nPDF effects included, is measured using a binned profile-likelihood method. The parameter $\mu_{t\bar{t}}$ is determined by the fit to the $H_{T}^{\ell,j}$ data distributions in the six signal regions, where the $H_{T}^{\ell,j}$ variable is defined as the scalar sum of the transverse momenta of the leptons and HI jets. Over all 9% uncertainties is observed

The figure shows the measurement of the top quark pair production cross-section, $\sigma_{t\bar{t}}$, in proton-lead (p+Pb) collisions at a center-of-mass energy of $\sqrt{s_{\mathrm{NN}}} = 8.16$ TeV, based on 165 nb$^{-1}$ of data. The central measured value is shown alongside theoretical predictions using various parton distribution functions (PDFs): MCFM TUJU21, MCFM nNNPDF30, MCFM nCTEQ15HQ, and MCFM EPPS21. The green and yellow bands represent the total and statistical uncertainties of the data, respectively. Additional measurements for comparison include the CMS result at 8.16 TeV for p+Pb collisions and an extrapolated ATLAS+CMS result for pp collisions at 8 TeV. Relevant references are indicated: PRL 119 (2017) 242001 and JHEP 07 (2023) 213.

The ATLAS measurement of \( R_{p\text{Pb}} \) as a function of the nuclear modification factor in proton-lead (\( p\) + Pb) collisions at a center-of-mass energy per nucleon pair \( \sqrt{s_{NN}} = 8.16 \) TeV, with an integrated luminosity of 165 nb\(^{-1}\). The black points represent theoretical predictions from various MCFM parton distribution functions (PDFs): TUJU21, nNNPDF30, nCTEQ15HQ, and EPPS21. The green band indicates the total uncertainty of the data, while the yellow band represents the statistical uncertainty. The dashed line at \( R_{p\text{Pb}} = 1 \) shows the expected value in the absence of nuclear modifications.