Distributions of representative kinematic variables in the misidentified background-enriched same-sign region: (a) the Higgs boson transverse momentum ($p_\text{T}^H$) in the $WH(\tau_{\mathrm{had}}\tau_{\mathrm{had}})$ category, (b) the missing transverse momentum (${E_{\mathrm{T}}^{\mathrm{miss}}}$) in the $WH(\tau_{\mathrm{lep}}\tau_{\mathrm{had}})$ category, (c) the radial distance (dR$(\ell,\ell)$) between the two light leptons associated to the $Z\to\ell{}\ell$ decay process in the $ZH(\tau_{\mathrm{had}}\tau_{\mathrm{had}})$ category, and (d) the invariant mass ($m_{\ell\ell}$) of the two light leptons associated to the $Z\to\ell{}\ell$ decay in the $ZH(\tau_{\mathrm{lep}}\tau_{\mathrm{had}})$ category. The hatched band represents the pre-fit statistical, experimental and theoretical uncertainties. The signal contributions are considered as part of the predictions and are normalized as predicted by the Standard Model.

Post-fit distributions for NN-based analysis of the NN-scores in the $ZH(\tau_{\mathrm{had}}\tau_{\mathrm{had}})$ (a), $ZH(\tau_{\mathrm{lep}}\tau_{\mathrm{had}})$ (b), $WH(\tau_{\mathrm{had}}\tau_{\mathrm{had}})$ (c) and $WH(\tau_{\mathrm{lep}}\tau_{\mathrm{had}})$ (d) categories. The hatched band indicates the total post-fit uncertainty of the total predicted yields. The post-fit signal contributions are considered as part of the predictions.

Post-fit distributions for NN-based analysis of the NN-scores in the $ZH(\tau_{\mathrm{had}}\tau_{\mathrm{had}})$ (a), $ZH(\tau_{\mathrm{lep}}\tau_{\mathrm{had}})$ (b), $WH(\tau_{\mathrm{had}}\tau_{\mathrm{had}})$ (c) and $WH(\tau_{\mathrm{lep}}\tau_{\mathrm{had}})$ (d) categories. The hatched band indicates the total post-fit uncertainty of the total predicted yields. The post-fit signal contributions are considered as part of the predictions.

Post-fit distributions for NN-based analysis of the NN-scores in the $ZH(\tau_{\mathrm{had}}\tau_{\mathrm{had}})$ (a), $ZH(\tau_{\mathrm{lep}}\tau_{\mathrm{had}})$ (b), $WH(\tau_{\mathrm{had}}\tau_{\mathrm{had}})$ (c) and $WH(\tau_{\mathrm{lep}}\tau_{\mathrm{had}})$ (d) categories. The hatched band indicates the total post-fit uncertainty of the total predicted yields. The post-fit signal contributions are considered as part of the predictions.

Post-fit distributions for NN-based analysis of the NN-scores in the $ZH(\\tau_{\mathrm{had}}\tau_{\mathrm{had}})$ (a), $ZH(\tau_{\mathrm{lep}}\tau_{\mathrm{had}})$ (b), $WH(\tau_{\mathrm{had}}\tau_{\mathrm{had}})$ (c) and $WH(\tau_{\mathrm{lep}}\tau_{\mathrm{had}})$ (d) categories. The hatched band indicates the total post-fit uncertainty of the total predicted yields. The post-fit signal contributions are considered as part of the predictions.

Post-fit yields from the NN-based fit performed with $\mu_{VH}^{\tau\tau}=\mu_{ZH}^{\tau\tau}=\mu_{WH}^{\tau\tau}$. The symbol $-$ is used when no events or $<10^{-2}$ events are present.

Event yields as a function of $\log_{10}(S/B)$ for data, background, and a Higgs boson signal with $m_{H} = 125$ GeV. Final-discriminant bins in all regions are combined into bins of $\log_{10}(S/B)$, where $S$ is the fitted signal and $B$ is the fitted background from the NN-based fit. The Higgs boson signal contribution is shown after re-scaling the SM cross-section according to the value of the signal strength extracted from data ($\mu = 1.28$). In the lower panel, the pull of the data relative to the background-only expectation, evaluated as the difference between the data and the background-only expectation divided by the square-root sum of the data and background statistical uncertainty, is shown. The solid line shows the expected pull in each bin for the best-fit signal value.

The fitted values of the Higgs boson signal strength $\mu_{VH}^{\tau\tau}$ for $m_{H} = 125$ GeV for the $WH$ and $ZH$ processes and their combination from the NN-based fit. The individual $\mu_{VH}^{\tau\tau}$ values for the $(W/Z)H$ processes are obtained from a simultaneous fit with the signal strength for each of the $WH$ and $ZH$ processes floating independently. The probability of compatibility of the individual signal strengths is 56\%.

Post-fit distributions for mass-based analysis for $m_{\mathrm{MMC}}$ in the (a) $ZH(\tau_{\mathrm{had}}\tau_{\mathrm{had}})$, (b) $ZH(\tau_{\mathrm{lep}}\tau_{\mathrm{had}})$, and for $m_{\mathrm{2T}}$ in the (c) $WH(\tau_{\mathrm{had}}\tau_{\mathrm{had}})$ and (d) $WH(\tau_{\mathrm{lep}}\tau_{\mathrm{had}})$ categories. The hatched band indicates the total post-fit uncertainty of the total predicted yields. The post-fit signal contributions are considered as part of the predictions.

Post-fit distributions for mass-based analysis for $m_{\mathrm{MMC}}$ in the (a) $ZH(\tau_{\mathrm{had}}\tau_{\mathrm{had}})$, (b) $ZH(\tau_{\mathrm{lep}}\tau_{\mathrm{had}})$, and for $m_{\mathrm{2T}}$ in the (c) $WH(\tau_{\mathrm{had}}\tau_{\mathrm{had}})$ and (d) $WH(\tau_{\mathrm{lep}}\tau_{\mathrm{had}})$ categories. The hatched band indicates the total post-fit uncertainty of the total predicted yields. The post-fit signal contributions are considered as part of the predictions.

Post-fit distributions for mass-based analysis for $m_{\mathrm{MMC}}$ in the (a) $ZH(\tau_{\mathrm{had}}\tau_{\mathrm{had}})$, (b) $ZH(\tau_{\mathrm{lep}}\tau_{\mathrm{had}})$, and for $m_{\mathrm{2T}}$ in the (c) $WH(\tau_{\mathrm{had}}\tau_{\mathrm{had}})$ and (d) $WH(\tau_{\mathrm{lep}}\tau_{\mathrm{had}})$ categories. The hatched band indicates the total post-fit uncertainty of the total predicted yields. The post-fit signal contributions are considered as part of the predictions.

Post-fit distributions for mass-based analysis for $m_{\mathrm{MMC}}$ in the (a) $ZH(\tau_{\mathrm{had}}\tau_{\mathrm{had}})$, (b) $ZH(\tau_{\mathrm{lep}}\tau_{\mathrm{had}})$, and for $m_{\mathrm{2T}}$ in the (c) $WH(\tau_{\mathrm{had}}\tau_{\mathrm{had}})# and (d) $WH(\tau_{\mathrm{lep}}\tau_{\mathrm{had}})$ categories. The hatched band indicates the total post-fit uncertainty of the total predicted yields. The post-fit signal contributions are considered as part of the predictions.

The fitted values from the NN-based fit of the Higgs boson signal strength $\mu_{VH}^{\tau\tau}$ for $m_{H} = 125$ GeV are shown separately for the $WH(\tau_{\mathrm{lep}}\tau_{\mathrm{had}})$, $WH(\tau_{\mathrm{had}}\tau_{\mathrm{had}})$, $ZH(\tau_{\mathrm{lep}}\tau_{\mathrm{had}})$, $ZH(\tau_{\mathrm{had}}\tau_{\mathrm{had}})$ categories, the $WH$ and $ZH$ processes, and their full combination. The individual $\mu_{VH}^{\tau\tau}$ values for the $(W/Z)H$ processes are obtained from a simultaneous fit with the signal strength for each of the $WH$ and $ZH$ processes floating independently.

Summary table with the expected (exp) and observed (obs) values of the $\mu^{\tau\tau}_{\text{VH}}$ and the significance resulting from the mass-based fit.

Event yields as a function of $\log_{10}(S/B)$ for data, background, and a Higgs boson signal with $m_{H} = 125$ GeV. Final-discriminant bins in all regions are combined into bins of $\log_{10}(S/B)$, where $S$ is the fitted signal and $B$ is the fitted background from the NN-based fit. The Higgs boson signal contribution is shown after re-scaling the SM cross-section according to the value of the signal strength extracted from data ($\mu = 1.28$). In the lower panel, the pull of the data relative to the background-only expectation, evaluated as the difference between the data and the background-only expectation divided by the square-root sum of the data and background statistical uncertainty, is shown. The solid line shows the expected pull in each bin for the best-fit signal value.

Summary table with the expected (exp) and observed (obs) values of the $\mu^{\tau\tau}_{\text{VH}}$ and the significance resulting from the mass-based fit.

The fitted values from the mass-based fit of the Higgs boson signal strength $\mu_{VH}^{\tau\tau}$ for $m_{H} = 125$ GeV are shown for the $WH$ and $ZH$ processes and their combination. The individual $\mu_{VH}^{\tau\tau}$ values for the $(W/Z)H$ processes are obtained from a simultaneous fit with the signal strength for each of the $WH$ and $ZH$ processes floating independently. The probability of compatibility of the individual signal strengths is 85\%.

The fitted values from the mass-based fit of the Higgs boson signal strength $\mu_{VH}^{\tau\tau}$ for $m_{H} = 125$ GeV are shown separately for the $WH(\tau_{\mathrm{lep}}\tau_{\mathrm{had}})$, $WH(\tau_{\mathrm{had}}\tau_{\mathrm{had}})$, $ZH(\tau_{\mathrm{lep}}\tau_{\mathrm{had}})$, $ZH(\tau_{\mathrm{had}}\tau_{\mathrm{had}})$ categories, the $WH$ and $ZH$ processes, and their full combination. The individual $\mu_{VH}^{\tau\tau}$ values for the $(W/Z)H$ processes are obtained from a simultaneous fit with the signal strength for each of the $WH$ and $ZH$ processes floating independently.

Distributions of $d\phi({E_{\mathrm{T}}^{\mathrm{miss}}},\tau_{1})$ (left) and $\eta$ of the leading $p_\text{T}$ $\tau_{\mathrm{had}-\mathrm{vis}}$ (right) in the $WH(\tau_{\mathrm{had}}\tau_{\mathrm{had}})$ $Z\to\tau\tau$ validation region. The hatched band represents the pre-fit statistical, experimental and theoretical uncertainties. The signal contributions are considered as part of the predictions.

Distributions of $d\phi({E_{\mathrm{T}}^{\mathrm{miss}}},\tau_{1})$ (left) and $\eta$ of the leading $p_\text{T}$ $\tau_{\mathrm{had}-\mathrm{vis}}$ (right) in the $WH(\tau_{\mathrm{had}}\tau_{\mathrm{had}})$ $Z\to\tau\tau$ validation region. The hatched band represents the pre-fit statistical, experimental and theoretical uncertainties. The signal contributions are considered as part of the predictions.

Distributions of the radial distance $dR(\tau_{1},\tau_{2})$ between the two $\tau_{\mathrm{had}-\mathrm{vis}}$ (left) and of the ${E_{\mathrm{T}}^{\mathrm{miss}}}$ (right) in the $WH(\tau_{\mathrm{had}}\tau_{\mathrm{had}})$ $W\mathrm{ +jets}$ validation region. The hatched band represents the pre-fit statistical, experimental and theoretical uncertainties. The signal contributions are considered as part of the predictions.

Distributions of the radial distance $dR(\tau_{1},\tau_{2})$ between the two $\tau_{\mathrm{had}-\mathrm{vis}}$ (left) and of the ${E_{\mathrm{T}}^{\mathrm{miss}}}$ (right) in the $WH(\tau_{\mathrm{had}}\tau_{\mathrm{had}})$ $W\mathrm{ +jets}$ validation region. The hatched band represents the pre-fit statistical, experimental and theoretical uncertainties. The signal contributions are considered as part of the predictions.

Distributions of the ${m_{\mathrm{MMC}}}$ (left) and of the $p_\text{T}$ of the leading $p_\text{T}$ light lepton (right) in the $WH(\tau_{\mathrm{had}}\tau_{\mathrm{had}})$ $t\bar{t}$ validation region. The hatched band represents the pre-fit statistical, experimental and theoretical uncertainties. The signal contributions are considered as part of the predictions.

Distributions of the ${m_{\mathrm{MMC}}}$ (left) and of the $p_\text{T}$ of the leading $p_\text{T}$ light lepton (right) in the $WH(\tau_{\mathrm{had}}\tau_{\mathrm{had}})$ $t\bar{t}$ validation region. The hatched band represents the pre-fit statistical, experimental and theoretical uncertainties. The signal contributions are considered as part of the predictions.

Distributions of the $m_{\mathrm{2T}}$ (left) and of the $\eta$ of the leading $p_\text{T}$ $\tau_{\mathrm{had}-\mathrm{vis}}$ in the $WH(\tau_{\mathrm{lep}}\tau_{\mathrm{had}})$ $Z\to\tau\tau$ validation region. The hatched band represents the pre-fit statistical, experimental and theoretical uncertainties. The signal contributions are considered as part of the predictions.

Distributions of the $m_{\mathrm{2T}}$ (left) and of the $\eta$ of the leading $p_\text{T}$ $\tau_{\mathrm{had}-\mathrm{vis}}$ in the $WH(\tau_{\mathrm{lep}}\tau_{\mathrm{had}})$ $Z\to\tau\tau$ validation region. The hatched band represents the pre-fit statistical, experimental and theoretical uncertainties. The signal contributions are considered as part of the predictions.

Distributions of the $dR({\tau_{\mathrm{lep}}},{\tau_{\mathrm{had}}})$ between the two objects associated to the Higgs boson decay and of the invariant mass $m_{\ell,\ell}$ of the two light leptons in the $WH(\tau_{\mathrm{lep}}\tau_{\mathrm{had}})$ all-same-sign validation region. The hatched band represents the pre-fit statistical, experimental and theoretical uncertainties. The signal contributions are considered as part of the predictions.

Distributions of the $dR({\tau_{\mathrm{lep}}},{\tau_{\mathrm{had}}})$ between the two objects associated to the Higgs boson decay and of the invariant mass $m_{\ell,\ell}$ of the two light leptons in the $WH(\tau_{\mathrm{lep}}\tau_{\mathrm{had}})$ all-same-sign validation region. The hatched band represents the pre-fit statistical, experimental and theoretical uncertainties. The signal contributions are considered as part of the predictions.

Distributions of the NN-score in the signal regions sidebands of the $ZH(\tau_{\mathrm{lep}}\tau_{\mathrm{had}})$ (a), $ZH(\tau_{\mathrm{had}}\tau_{\mathrm{had}})$ (b), $WH(\tau_{\mathrm{lep}}\tau_{\mathrm{had}})$ (c), $WH(\tau_{\mathrm{had}}\tau_{\mathrm{had}})$ (d) categories.The hatched band represents the pre-fit statistical, experimental and theoretical uncertainties. The signal contributions are considered as part of the predictions and are normalized to the fit result performed with one parameter of interest.

Distributions of the NN-score in the signal regions sidebands of the $ZH(\tau_{\mathrm{lep}}\tau_{\mathrm{had}})$ (a), $ZH(\tau_{\mathrm{had}}\tau_{\mathrm{had}})$ (b), $WH(\tau_{\mathrm{lep}}\tau_{\mathrm{had}})$ (c), $WH(\tau_{\mathrm{had}}\tau_{\mathrm{had}})$ (d) categories.The hatched band represents the pre-fit statistical, experimental and theoretical uncertainties. The signal contributions are considered as part of the predictions and are normalized to the fit result performed with one parameter of interest.

Distributions of the NN-score in the signal regions sidebands of the $ZH(\tau_{\mathrm{lep}}\tau_{\mathrm{had}})$ (a), $ZH(\tau_{\mathrm{had}}\tau_{\mathrm{had}})$ (b), $WH(\tau_{\mathrm{lep}}\tau_{\mathrm{had}})$ (c), $WH(\tau_{\mathrm{had}}\tau_{\mathrm{had}})$ (d) categories.The hatched band represents the pre-fit statistical, experimental and theoretical uncertainties. The signal contributions are considered as part of the predictions and are normalized to the fit result performed with one parameter of interest.

Distributions of the NN-score in the signal regions sidebands of the $ZH(\tau_{\mathrm{lep}}\tau_{\mathrm{had}})$ (a), $ZH(\tau_{\mathrm{had}}\tau_{\mathrm{had}})$ (b), $WH(\tau_{\mathrm{lep}}\tau_{\mathrm{had}})$ (c), $WH(\tau_{\mathrm{had}}\tau_{\mathrm{had}})$ (d) categories.The hatched band represents the pre-fit statistical, experimental and theoretical uncertainties. The signal contributions are considered as part of the predictions and are normalized to the fit result performed with one parameter of interest.

Observed 95% CL upper limits on B(H&rarr;&nbsp;2&gamma;_d+X) for different &gamma;_d masses and a 125&nbsp;GeV Higgs boson, as a function of the dark-photon mean proper decay length c&tau;. The limits are shown for all search channels combined, assuming an FRVZ signal model. The hatched band denotes the region in which the branching ratio is larger than unity.

Observed 95% CL upper limits on B(H&rarr;&nbsp;2&gamma;_d+X) for a &gamma;_d mass of 100&nbsp;MeV, as a function of the dark-photon mean proper decay length c&tau;. The solid black curve shows the observed exclusion limit from their statistical combination. The hatched band denotes the region in which the branching ratio is larger than unity.

Observed 95% CL upper limits on B(H&rarr;&nbsp;2&gamma;_d+X) for a &gamma;_d mass of 10&nbsp;GeV, as a function of the dark-photon mean proper decay length c&tau;. The solid black curve shows the observed exclusion limit from their statistical combination. The hatched band denotes the region in which the branching ratio is larger than unity.

Acceptance times efficiency extrapolated as a function of c&tau;_&gamma;d for the &mu;DPJ channel (SR_&mu;), obtained for the different FRVZ MC signal mass points.

Acceptance times efficiency extrapolated as a function of c&tau;_&gamma;d for the low E_T^miss caloDPJ channel (SR_c^L), obtained for the different FRVZ MC signal mass points.

Acceptance times efficiency extrapolated as a function of c&tau;_&gamma;d for the high E_T^miss caloDPJ channel (SR_c^H), obtained for the different FRVZ MC signal mass points.

Observed (solid line) and expected (dashed line) 95% CL upper limits on B(H&rarr;&nbsp;2&gamma;_d+X) for FRVZ processes with a 125&nbsp;GeV Higgs boson as a function of dark photon mean proper decay length for the ggF, WH and VBF analyses. The full combination is shown as solid or dashed black lines for a dark photon mass of 17&nbsp;MeV.

Observed (solid line) and expected (dashed line) 95% CL upper limits on B(H&rarr;&nbsp;2&gamma;_d+X) for FRVZ processes with a 125&nbsp;GeV Higgs boson as a function of dark photon mean proper decay length for the ggF, WH and VBF analyses. The full combination is shown as solid or dashed black lines for a dark photon mass of 50&nbsp;MeV.

Observed (solid line) and expected (dashed line) 95% CL upper limits on B(H&rarr;&nbsp;2&gamma;_d+X) for FRVZ processes with a 125&nbsp;GeV Higgs boson as a function of dark photon mean proper decay length for the ggF, WH and VBF analyses. The full combination is shown as solid or dashed black lines for a dark photon mass of 400&nbsp;MeV.

Observed (solid line) and expected (dashed line) 95% CL upper limits on B(H&rarr;&nbsp;2&gamma;_d+X) for FRVZ processes with a 125&nbsp;GeV Higgs boson as a function of dark photon mean proper decay length for the ggF, WH and VBF analyses. The full combination is shown as solid or dashed black lines for a dark photon mass of 900&nbsp;MeV.

Observed (solid line) and expected (dashed line) 95% CL upper limits on B(H&rarr;&nbsp;2&gamma;_d+X) for FRVZ processes with a 125&nbsp;GeV Higgs boson as a function of dark photon mean proper decay length for the ggF, WH and VBF analyses. The full combination is shown as solid or dashed black lines for a dark photon mass of 2&nbsp;GeV.

Observed (solid line) and expected (dashed line) 95% CL upper limits on B(H&rarr;&nbsp;2&gamma;_d+X) for FRVZ processes with a 125&nbsp;GeV Higgs boson as a function of dark photon mean proper decay length for the ggF, WH and VBF analyses. The full combination is shown as solid or dashed black lines for a dark photon mass of 6&nbsp;GeV.

Observed (solid line) and expected (dashed line) 95% CL upper limits on B(H&rarr;&nbsp;2&gamma;_d+X) for FRVZ processes with a 125&nbsp;GeV Higgs boson as a function of dark photon mean proper decay length for the ggF, WH and VBF analyses. The full combination is shown as solid or dashed black lines for a dark photon mass of 15&nbsp;GeV.

Observed 95% CL upper limits on B(H&rarr;&nbsp;2&gamma;_d+X) for different &gamma;_d masses and a 125&nbsp;GeV Higgs boson, as a function of the dark-photon mean proper decay length c&tau;. The limits are shown for the SR_&mu; search channel, assuming an FRVZ signal model. The hatched band denotes the region in which the branching ratio is larger than unity.

Observed 95% CL upper limits on B(H&rarr;&nbsp;2&gamma;_d+X) for different &gamma;_d masses and a 125&nbsp;GeV Higgs boson, as a function of the dark-photon mean proper decay length c&tau;. The limits are shown for the SR_c^L search channel, assuming an FRVZ signal model. The hatched band denotes the region in which the branching ratio is larger than unity.

Observed 95% CL upper limits on B(H&rarr;&nbsp;2&gamma;_d+X) for different &gamma;_d masses and a 125&nbsp;GeV Higgs boson, as a function of the dark-photon mean proper decay length c&tau;. The limits are shown for the SR_c^H search channel, assuming an FRVZ signal model. The hatched band denotes the region in which the branching ratio is larger than unity.

Observed 95% CL upper limits on B(H&rarr;&nbsp;2&gamma;_d+X) for different &gamma;_d masses and a 125&nbsp;GeV Higgs boson, as a function of the dark-photon mean proper decay length c&tau;. The limits are shown for all search channels combined, assuming an FRVZ signal model. The hatched band denotes the region in which the branching ratio is larger than unity.

Distribution of $m_{\mathrm{JJ}}$ in the SR (black points) compared to the background-only expectation, where the shape is derived from the CR and the normalisation is fitted in the SR.

Observed and expected limits at 95% CL on the cross-section times branching ratio for the production of dark quarks through a $Z^\prime$ as a function of the $Z^\prime$ mass for model A (see the text for details). The darker and lighter shaded bands around the expected limits represent the $\pm 1 \sigma$ and $\pm 2 \sigma$ uncertainty range, respectively.

The predicted theory cross-section times branching ratio for the production of dark quarks through a $Z^\prime$ as a function of the $Z^\prime$ mass for model A (see the text for details). In the theory model, a universal coupling of the $Z^\prime$ to each SM quark $g_q$ is assumed and the dark quarks are all represented by one species with an effective coupling $g_{q_d}$ to the $Z^\prime$. For model A, the predicted cross-section is shown for $g_q=0.05$ and $g_{q_d} = 0.2$.

Observed and expected limits at 95% CL on the cross-section times branching ratio for the production of dark quarks through a $Z^\prime$ as a function of the $Z^\prime$ mass for model B (see the text for details). The darker and lighter shaded bands around the expected limits represent the $\pm 1 \sigma$ and $\pm 2 \sigma$ uncertainty range, respectively.

The predicted theory cross-section times branching ratio for the production of dark quarks through a $Z^\prime$ as a function of the $Z^\prime$ mass for model B (see the text for details). In the theory model, a universal coupling of the $Z^\prime$ to each SM quark $g_q$ is assumed and the dark quarks are all represented by one species with an effective coupling $g_{q_d}$ to the $Z^\prime$. For model B, the predicted cross-section is shown for $g_q=0.15$ and $g_{q_d} = 0.5$.

Observed and expected limits at 95% CL on the cross-section times branching ratio for the production of dark quarks through a $Z^\prime$ as a function of the $Z^\prime$ mass for model C (see the text for details). The darker and lighter shaded bands around the expected limits represent the $\pm 1 \sigma$ and $\pm 2 \sigma$ uncertainty range, respectively.

The predicted theory cross-section times branching ratio for the production of dark quarks through a $Z^\prime$ as a function of the $Z^\prime$ mass for model C (see the text for details). In the theory model, a universal coupling of the $Z^\prime$ to each SM quark $g_q$ is assumed and the dark quarks are all represented by one species with an effective coupling $g_{q_d}$ to the $Z^\prime$. For model C, the predicted cross-section is shown for $g_q=0.15$ and $g_{q_d}= 0.5$.

Observed and expected limits at 95% CL on the cross-section times branching ratio for the production of dark quarks through a $Z^\prime$ as a function of the $Z^\prime$ mass for model D (see the text for details). The darker and lighter shaded bands around the expected limits represent the $\pm 1 \sigma$ and $\pm 2 \sigma$ uncertainty range, respectively.

The predicted theory cross-section times branching ratio for the production of dark quarks through a $Z^\prime$ as a function of the $Z^\prime$ mass for model D (see the text for details). In the theory model, a universal coupling of the $Z^\prime$ to each SM quark $g_q$ is assumed and the dark quarks are all represented by one species with an effective coupling $g_{q_d}$ to the $Z^\prime$. For model D, the predicted cross-section is shown for $g_q=0.05$ and $g_{q_d} = 0.2$.

Relative efficiency (in %) of each stage of the analysis selection with respect to the previous one for models A through D and $m_{Z^\prime}=2.5$ TeV. Approximately 90000 events were generated per signal mass hypothesis.

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

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

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

Likelihood observed contours at 68% CL (solid line) and 95% CL (dashed line) in the $c_{gghh}$ versus $c_{hhh}$ HEFT parameter space, with the remaining coefficient fixed to its SM value. The best-fit value, denoted by a cross in the plot, corresponds to the very first entry in the table.

Likelihood expected contours at 68% CL (teal shaded region) 95% CL (yellow shaded region) in the $c_{gghh}$ versus $c_{hhh}$ HEFT parameter space, with the remaining coefficient fixed to its SM value. In the plot, the SM prediction is indicated by the star.

Likelihood observed contours at 68% CL (solid line) and 95% CL (dashed line) in the $c_{tthh}$ versus $c_{hhh}$ HEFT parameter space, with the remaining coefficient fixed to its SM value. The best-fit value, denoted by a cross in the plot, corresponds to the very first entry in the table.

Likelihood exptected contours at 68% CL (teal shaded region) and 95% CL (yellow shaded region) in the $c_{tthh}$ versus $c_{hhh}$ HEFT parameter space, with the remaining coefficient fixed to its SM value. In the plot, the SM prediction is indicated by the star.

The observed (filled circles) and expected (hollow circles) 95% CL upper limits on the $HH$ ggF production cross-section in the Standard Model and for seven HEFT benchmark points. The teal and yellow colored bands indicate the $\pm 1\sigma$ and $\pm 2\sigma$ variations on the expected limit due to statistical and systematic uncertainties. The predicted cross-sections of each of the models under consideration are shown by the red crosses. The contribution from VBF production to the total $HH$ production cross-section is neglected.

Likelihood observed contours at 68% CL (solid line) and 95% CL (dashed line) in the $c_{{H}\boxed{}}$ versus $c_{H}$ SMEFT parameter space, with the remaining coefficient fixed to its SM value. The best-fit value, denoted by a cross in the plot, corresponds to the very first entry in the table.

Likelihood expected contours at 68% CL (teal shaded region) 95% CL (yellow shaded region) in the $c_{{H}\boxed{}}$ versus $c_{H}$ SMEFT parameter space, with the remaining coefficient fixed to its SM value. In the plot, the SM prediction is indicated by the star.

The acceptance times efficiency for the signal ggF $HH$ process as a function of the coupling modifier $\kappa_{\lambda}$ in each analysis category. The other coupling modifiers affecting ggF $HH$ production are fixed to their SM predictions. The bands indicate the simulation statistical uncertainty.

The acceptance times efficiency for the signal VBF $HH$ process as a function of the coupling modifier $\kappa_{\lambda}$ in each analysis category. When varying $\kappa_{\lambda}$, the other coupling modifiers affecting the VBF $HH$ production mode are set to their SM predictions. The bands indicate the simulation statistical uncertainty.

The acceptance times efficiency for the signal VBF $HH$ process as a function of the coupling modifier $\kappa_{2V}$ in each analysis category. When varying $\kappa_{2V}$, the other coupling modifiers affecting the VBF $HH$ production mode are set to their SM predictions. The bands indicate the simulation statistical uncertainty.

Expected yields of the signal $HH$ process as a function of the coupling modifier $\kappa_{\lambda}$ after applying the analysis preselection and in each analysis category after the final selection. The $HH$ yield is obtained considering both the $ggF$ and $VBF$ contributions. The other coupling modifiers affecting $HH$ production are fixed to their SM predictions. The bands indicate the simulation statistical uncertainty.

The acceptance times efficiency for the signal ggF $HH$ process in each analysis category as a function of the $c_{hhh}$ HEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

The acceptance times efficiency for the signal ggF $HH$ process in each analysis category as a function of the $c_{tthh}$ HEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

The acceptance times efficiency for the signal ggF $HH$ process in each analysis category as a function of the $c_{gghh}$ HEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

The acceptance times efficiency for the signal ggF $HH$ process in each analysis category as a function of the $c_{H}$ SMEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

The acceptance times efficiency for the signal ggF $HH$ process in each analysis category as a function of the $c_{{H}\boxed{}}$ SMEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

The yield of the signal ggF $HH$ process in each analysis category as a function of the $c_{hhh}$ HEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

The yield of the signal ggF $HH$ process in each analysis category as a function of the $c_{tthh}$ HEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

The yield of the signal ggF $HH$ process in each analysis category as a function of the $c_{gghh}$ HEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

The yield of the signal ggF $HH$ process in each analysis category as a function of the $c_{H}$ SMEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

The yield of the signal ggF $HH$ process in each analysis category as a function of the $c_{{H}\boxed{}}$ SMEFT coefficients. The dashed lines denote values that are excluded at 95% CL. The bottom panels show the efficiency of the sum of all analysis categories.

Distributions of the diphoton invariant mass for events in data (black dots with error bars) compared to the sum of the expected signal and backgrounds (histograms) in the low mass 1 region.

Distributions of the diphoton invariant mass for events in data (black dots with error bars) compared to the sum of the expected signal and backgrounds (histograms) in the low mass 2 region.

Distributions of the diphoton invariant mass for events in data (black dots with error bars) compared to the sum of the expected signal and backgrounds (histograms) in the low mass 3 region.

Distributions of the diphoton invariant mass for events in data (black dots with error bars) compared to the sum of the expected signal and backgrounds (histograms) in the low mass 4 region.

Distributions of the diphoton invariant mass for events in data (black dots with error bars) compared to the sum of the expected signal and backgrounds (histograms) in the high mass 1 region.

Distributions of the diphoton invariant mass for events in data (black dots with error bars) compared to the sum of the expected signal and backgrounds (histograms) in the high mass 2 region.

Distributions of the diphoton invariant mass for events in data (black dots with error bars) compared to the sum of the expected signal and backgrounds (histograms) in the high mass 3 region.

Observed (solid line) value of $-2\ln\Lambda$ as a function of the $c_{hhh}$ HEFT coefficients when all other coupling modifiers are fixed to the SM value

Expected (dashed line) value of $-2\ln\Lambda$ as a function of the $c_{hhh}$ HEFT coefficients when all other coupling modifiers are fixed to the SM value

Observed (solid line) value of $-2\ln\Lambda$ as a function of the $c_{gghh}$ HEFT coefficients when all other coupling modifiers are fixed to the SM value

Expected (dashed line) value of $-2\ln\Lambda$ as a function of the $c_{gghh}$ HEFT coefficients when all other coupling modifiers are fixed to the SM value

Observed (solid line) value of $-2\ln\Lambda$ as a function of the $c_{tthh}$ HEFT coefficients when all other coupling modifiers are fixed to the SM value

Expected (dashed line) value of $-2\ln\Lambda$ as a function of the $c_{tthh}$ HEFT coefficients when all other coupling modifiers are fixed to the SM value

Observed (solid line) value of $-2\ln\Lambda$ as a function of the $c_{H}$ SMEFT coefficients when all other coupling modifiers are fixed to the SM value.

Expected (dashed line) value of $-2\ln\Lambda$ as a function of the $c_{H}$ SMEFT coefficients when all other coupling modifiers are fixed to the SM value.

Observed (solid line) value of $-2\ln\Lambda$ as a function of the $c_{{H}\boxed{}}$ SMEFT coefficients when all other coupling modifiers are fixed to the SM value.

Expected (dashed line) value of $-2\ln\Lambda$ as a function of the $c_{{H}\boxed{}}$ SMEFT coefficients when all other coupling modifiers are fixed to the SM value.

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

Likelihood profiles of the $\kappa_\lambda$ parameter.

Likelihood profiles of the $\kappa_{2V}$ parameter.

The 95% CL upper limits on the $HH$ cross-section for different values of $\kappa_\lambda$. The expected limits assume no $HH$ production. The red line shows the theory prediction for the combined ggF $HH$ and VBF $HH$ cross-section as a function of $\kappa_\lambda$ where all parameters and couplings are set to their SM values except $\kappa_\lambda$. The bands surrounding the red cross-section line indicate the theoretical uncertainty on the predicted cross-section. The $\kappa_\lambda$ values in the interval $[-6.7, 15.3]$ cannot be excluded by this analysis.

The 95% CL upper limits on the VBF $HH$ cross section for different values of $\kappa_{2V}$. The expected limits assume no VBF $HH$ production. SM ggF $HH$ production is considered as background. The red line shows the theory prediction for the VBF $HH$ cross-section as a function of $\kappa_{2V}$ where all parameters and couplings are set to their SM values except $\kappa_{2V}$. The uncertainty band is smaller than the width of the plotted line. The $\kappa_{2V}$ values in the interval $[-0.3, 2.4]$ cannot be excluded by this analysis.

$R_\text{CP}$ plotted as a function of approximated $x_p$ for $-1.0 < y_b < 0.0$ and $0.0 < y^* < 1.0$, constructed using $\langle y_{\text{b}} \rangle$ and $\langle y^{*} \rangle$. The proton-going direction is defined by $y_{\text{b}} > 0$.

$R_\text{CP}$ plotted as a function of approximated $x_p$ for $-1.0 < y_b < 0.0$ and $1.0 < y^* < 2.0$, constructed using $\langle y_{\text{b}} \rangle$ and $\langle y^{*} \rangle$. The proton-going direction is defined by $y_{\text{b}} > 0$.

$R_\text{CP}$ plotted as a function of approximated $x_p$ for $-1.0 < y_b < 0.0$ and $2.0 < y^* < 3.0$, constructed using $\langle y_{\text{b}} \rangle$ and $\langle y^{*} \rangle$. The proton-going direction is defined by $y_{\text{b}} > 0$.

$R_\text{CP}$ plotted as a function of approximated $x_p$ for $0.0 < y_b < 1.0$ and $0.0 < y^* < 1.0$, constructed using $\langle y_{\text{b}} \rangle$ and $\langle y^{*} \rangle$. The proton-going direction is defined by $y_{\text{b}} > 0$.

$R_\text{CP}$ plotted as a function of approximated $x_p$ for $0.0 < y_b < 1.0$ and $1.0 < y^* < 2.0$, constructed using $\langle y_{\text{b}} \rangle$ and $\langle y^{*} \rangle$. The proton-going direction is defined by $y_{\text{b}} > 0$.

$R_\text{CP}$ plotted as a function of approximated $x_p$ for $0.0 < y_b < 1.0$ and $2.0 < y^* < 4.0$, constructed using $\langle y_{\text{b}} \rangle$ and $\langle y^{*} \rangle$. The proton-going direction is defined by $y_{\text{b}} > 0$.

$R_\text{CP}$ plotted as a function of approximated $x_p$ for $1.0 < y_b < 2.0$ and $0.0 < y^* < 1.0$, constructed using $\langle y_{\text{b}} \rangle$ and $\langle y^{*} \rangle$. The proton-going direction is defined by $y_{\text{b}} > 0$.

$R_\text{CP}$ plotted as a function of approximated $x_p$ for $1.0 < y_b < 2.0$ and $1.0 < y^* < 2.0$, constructed using $\langle y_{\text{b}} \rangle$ and $\langle y^{*} \rangle$. The proton-going direction is defined by $y_{\text{b}} > 0$.

$R_\text{CP}$ plotted as a function of approximated $x_p$ for $1.0 < y_b < 2.0$ and $2.0 < y^* < 3.0$, constructed using $\langle y_{\text{b}} \rangle$ and $\langle y^{*} \rangle$. The proton-going direction is defined by $y_{\text{b}} > 0$.

$R_\text{CP}$ plotted as a function of approximated $x_p$ for $2.0 < y_b < 3.0$ and $0.0 < y^* < 1.0$, constructed using $\langle y_{\text{b}} \rangle$ and $\langle y^{*} \rangle$. The proton-going direction is defined by $y_{\text{b}} > 0$.

$R_\text{CP}$ plotted as a function of approximated $x_p$ for $2.0 < y_b < 3.0$ and $1.0 < y^* < 2.0$, constructed using $\langle y_{\text{b}} \rangle$ and $\langle y^{*} \rangle$. The proton-going direction is defined by $y_{\text{b}} > 0$.

$R_\text{CP}$ plotted as a function of approximated $x_p$ for $3.0 < y_b < 4.0$ and $0.0 < y^* < 1.0$, constructed using $\langle y_{\text{b}} \rangle$ and $\langle y^{*} \rangle$. The proton-going direction is defined by $y_{\text{b}} > 0$.

$R_\text{CP}$ plotted as a function of approximated $x_{Pb}$ for $-3.0 < y_b < -2.0$ and $0.0 < y^* < 1.0$, constructed using $\langle y_{\text{b}} \rangle$ and $\langle y^{*} \rangle$. The proton-going direction is defined by $y_{\text{b}} > 0$.

$R_\text{CP}$ plotted as a function of approximated $x_{Pb}$ for $-2.0 < y_b < -1.0$ and $0.0 < y^* < 1.0$, constructed using $\langle y_{\text{b}} \rangle$ and $\langle y^{*} \rangle$. The proton-going direction is defined by $y_{\text{b}} > 0$.

$R_\text{CP}$ plotted as a function of approximated $x_{Pb}$ for $-2.0 < y_b < -1.0$ and $1.0 < y^* < 2.0$, constructed using $\langle y_{\text{b}} \rangle$ and $\langle y^{*} \rangle$. The proton-going direction is defined by $y_{\text{b}} > 0$.

$R_\text{CP}$ plotted as a function of approximated $x_{Pb}$ for $-1.0 < y_b < 0.0$ and $0.0 < y^* < 1.0$, constructed using $\langle y_{\text{b}} \rangle$ and $\langle y^{*} \rangle$. The proton-going direction is defined by $y_{\text{b}} > 0$.

$R_\text{CP}$ plotted as a function of approximated $x_{Pb}$ for $-1.0 < y_b < 0.0$ and $1.0 < y^* < 2.0$, constructed using $\langle y_{\text{b}} \rangle$ and $\langle y^{*} \rangle$. The proton-going direction is defined by $y_{\text{b}} > 0$.

$R_\text{CP}$ plotted as a function of approximated $x_{Pb}$ for $-1.0 < y_b < 0.0$ and $2.0 < y^* < 3.0$, constructed using $\langle y_{\text{b}} \rangle$ and $\langle y^{*} \rangle$. The proton-going direction is defined by $y_{\text{b}} > 0$.

$R_\text{CP}$ plotted as a function of approximated $x_{Pb}$ for $0.0 < y_b < 1.0$ and $0.0 < y^* < 1.0$, constructed using $\langle y_{\text{b}} \rangle$ and $\langle y^{*} \rangle$. The proton-going direction is defined by $y_{\text{b}} > 0$.

$R_\text{CP}$ plotted as a function of approximated $x_{Pb}$ for $0.0 < y_b < 1.0$ and $1.0 < y^* < 2.0$, constructed using $\langle y_{\text{b}} \rangle$ and $\langle y^{*} \rangle$. The proton-going direction is defined by $y_{\text{b}} > 0$.

$R_\text{CP}$ plotted as a function of approximated $x_{Pb}$ for $0.0 < y_b < 1.0$ and $2.0 < y^* < 4.0$, constructed using $\langle y_{\text{b}} \rangle$ and $\langle y^{*} \rangle$. The proton-going direction is defined by $y_{\text{b}} > 0$.

$R_\text{CP}$ plotted as a function of approximated $x_{Pb}$ for $1.0 < y_b < 2.0$ and $0.0 < y^* < 1.0$, constructed using $\langle y_{\text{b}} \rangle$ and $\langle y^{*} \rangle$. The proton-going direction is defined by $y_{\text{b}} > 0$.

$R_\text{CP}$ plotted as a function of approximated $x_{Pb}$ for $1.0 < y_b < 2.0$ and $1.0 < y^* < 2.0$, constructed using $\langle y_{\text{b}} \rangle$ and $\langle y^{*} \rangle$. The proton-going direction is defined by $y_{\text{b}} > 0$.

$R_\text{CP}$ plotted as a function of approximated $x_{Pb}$ for $1.0 < y_b < 2.0$ and $2.0 < y^* < 3.0$, constructed using $\langle y_{\text{b}} \rangle$ and $\langle y^{*} \rangle$. The proton-going direction is defined by $y_{\text{b}} > 0$.

$R_\text{CP}$ plotted as a function of approximated $x_{Pb}$ for $2.0 < y_b < 3.0$ and $0.0 < y^* < 1.0$, constructed using $\langle y_{\text{b}} \rangle$ and $\langle y^{*} \rangle$. The proton-going direction is defined by $y_{\text{b}} > 0$.

$R_\text{CP}$ plotted as a function of approximated $x_{Pb}$ for $2.0 < y_b < 3.0$ and $1.0 < y^* < 2.0$, constructed using $\langle y_{\text{b}} \rangle$ and $\langle y^{*} \rangle$. The proton-going direction is defined by $y_{\text{b}} > 0$.

$R_\text{CP}$ plotted as a function of approximated $x_{Pb}$ for $3.0 < y_b < 4.0$ and $0.0 < y^* < 1.0$, constructed using $\langle y_{\text{b}} \rangle$ and $\langle y^{*} \rangle$. The proton-going direction is defined by $y_{\text{b}} > 0$.

$R_\text{CP}$ plotted as a function of approximated $x_\mathrm{F}$ for $-3.0 < y_b < -2.0$ and $0.0 < y^* < 1.0$, constructed using $\langle y_{\text{b}} \rangle$ and $\langle y^{*} \rangle$. The proton-going direction is defined by $y_{\text{b}} > 0$.

$R_\text{CP}$ plotted as a function of approximated $x_\mathrm{F}$ for $-2.0 < y_b < -1.0$ and $0.0 < y^* < 1.0$, constructed using $\langle y_{\text{b}} \rangle$ and $\langle y^{*} \rangle$. The proton-going direction is defined by $y_{\text{b}} > 0$.

$R_\text{CP}$ plotted as a function of approximated $x_\mathrm{F}$ for $-2.0 < y_b < -1.0$ and $1.0 < y^* < 2.0$, constructed using $\langle y_{\text{b}} \rangle$ and $\langle y^{*} \rangle$. The proton-going direction is defined by $y_{\text{b}} > 0$.

$R_\text{CP}$ plotted as a function of approximated $x_\mathrm{F}$ for $-1.0 < y_b < 0.0$ and $0.0 < y^* < 1.0$, constructed using $\langle y_{\text{b}} \rangle$ and $\langle y^{*} \rangle$. The proton-going direction is defined by $y_{\text{b}} > 0$.

$R_\text{CP}$ plotted as a function of approximated $x_\mathrm{F}$ for $-1.0 < y_b < 0.0$ and $1.0 < y^* < 2.0$, constructed using $\langle y_{\text{b}} \rangle$ and $\langle y^{*} \rangle$. The proton-going direction is defined by $y_{\text{b}} > 0$.

$R_\text{CP}$ plotted as a function of approximated $x_\mathrm{F}$ for $-1.0 < y_b < 0.0$ and $2.0 < y^* < 3.0$, constructed using $\langle y_{\text{b}} \rangle$ and $\langle y^{*} \rangle$. The proton-going direction is defined by $y_{\text{b}} > 0$.

$R_\text{CP}$ plotted as a function of approximated $x_\mathrm{F}$ for $0.0 < y_b < 1.0$ and $0.0 < y^* < 1.0$, constructed using $\langle y_{\text{b}} \rangle$ and $\langle y^{*} \rangle$. The proton-going direction is defined by $y_{\text{b}} > 0$.

$R_\text{CP}$ plotted as a function of approximated $x_\mathrm{F}$ for $0.0 < y_b < 1.0$ and $1.0 < y^* < 2.0$, constructed using $\langle y_{\text{b}} \rangle$ and $\langle y^{*} \rangle$. The proton-going direction is defined by $y_{\text{b}} > 0$.

$R_\text{CP}$ plotted as a function of approximated $x_\mathrm{F}$ for $0.0 < y_b < 1.0$ and $2.0 < y^* < 4.0$, constructed using $\langle y_{\text{b}} \rangle$ and $\langle y^{*} \rangle$. The proton-going direction is defined by $y_{\text{b}} > 0$.

$R_\text{CP}$ plotted as a function of approximated $x_\mathrm{F}$ for $1.0 < y_b < 2.0$ and $0.0 < y^* < 1.0$, constructed using $\langle y_{\text{b}} \rangle$ and $\langle y^{*} \rangle$. The proton-going direction is defined by $y_{\text{b}} > 0$.

$R_\text{CP}$ plotted as a function of approximated $x_\mathrm{F}$ for $1.0 < y_b < 2.0$ and $1.0 < y^* < 2.0$, constructed using $\langle y_{\text{b}} \rangle$ and $\langle y^{*} \rangle$. The proton-going direction is defined by $y_{\text{b}} > 0$.

$R_\text{CP}$ plotted as a function of approximated $x_\mathrm{F}$ for $1.0 < y_b < 2.0$ and $2.0 < y^* < 3.0$, constructed using $\langle y_{\text{b}} \rangle$ and $\langle y^{*} \rangle$. The proton-going direction is defined by $y_{\text{b}} > 0$.

$R_\text{CP}$ plotted as a function of approximated $x_\mathrm{F}$ for $2.0 < y_b < 3.0$ and $0.0 < y^* < 1.0$, constructed using $\langle y_{\text{b}} \rangle$ and $\langle y^{*} \rangle$. The proton-going direction is defined by $y_{\text{b}} > 0$.

$R_\text{CP}$ plotted as a function of approximated $x_\mathrm{F}$ for $2.0 < y_b < 3.0$ and $1.0 < y^* < 2.0$, constructed using $\langle y_{\text{b}} \rangle$ and $\langle y^{*} \rangle$. The proton-going direction is defined by $y_{\text{b}} > 0$.

$R_\text{CP}$ plotted as a function of approximated $x_\mathrm{F}$ for $3.0 < y_b < 4.0$ and $0.0 < y^* < 1.0$, constructed using $\langle y_{\text{b}} \rangle$ and $\langle y^{*} \rangle$. The proton-going direction is defined by $y_{\text{b}} > 0$.

$\langle T_{\text{AB}} \rangle$ normalized per-event dijet yields in $0-10$% collisions as a function of $\langle y_{\text{b}} \rangle$ for $40.0 < p_{\text{T,Avg}} \text{ [GeV]} < 49.6$ and $0.0 < y^{*} < 1.0$.

$\langle T_{\text{AB}} \rangle$ normalized per-event dijet yields in $60-90$% collisions as a function of $\langle y_{\text{b}} \rangle$ for $40.0 < p_{\text{T,Avg}} \text{ [GeV]} < 49.6$ and $0.0 < y^{*} < 1.0$.

$\langle T_{\text{AB}} \rangle$ normalized per-event dijet yields in $0-10$% collisions as a function of $\langle y_{\text{b}} \rangle$ for $49.6 < p_{\text{T,Avg}} \text{ [GeV]} < 61.4$ and $0.0 < y^{*} < 1.0$.

$\langle T_{\text{AB}} \rangle$ normalized per-event dijet yields in $60-90$% collisions as a function of $\langle y_{\text{b}} \rangle$ for $49.6 < p_{\text{T,Avg}} \text{ [GeV]} < 61.4$ and $0.0 < y^{*} < 1.0$.

$\langle T_{\text{AB}} \rangle$ normalized per-event dijet yields in $0-10$% collisions as a function of $\langle y_{\text{b}} \rangle$ for $61.4 < p_{\text{T,Avg}} \text{ [GeV]} < 76.1$ and $0.0 < y^{*} < 1.0$.

$\langle T_{\text{AB}} \rangle$ normalized per-event dijet yields in $60-90$% collisions as a function of $\langle y_{\text{b}} \rangle$ for $61.4 < p_{\text{T,Avg}} \text{ [GeV]} < 76.1$ and $0.0 < y^{*} < 1.0$.

$\langle T_{\text{AB}} \rangle$ normalized per-event dijet yields in $0-10$% collisions as a function of $\langle y_{\text{b}} \rangle$ for $40.0 < p_{\text{T,Avg}} \text{ [GeV]} < 49.6$ and $1.0 < y^{*} < 2.0$.

$\langle T_{\text{AB}} \rangle$ normalized per-event dijet yields in $60-90$% collisions as a function of $\langle y_{\text{b}} \rangle$ for $40.0 < p_{\text{T,Avg}} \text{ [GeV]} < 49.6$ and $1.0 < y^{*} < 2.0$.

$\langle T_{\text{AB}} \rangle$ normalized per-event dijet yields in $0-10$% collisions as a function of $\langle y_{\text{b}} \rangle$ for $49.6 < p_{\text{T,Avg}} \text{ [GeV]} < 61.4$ and $1.0 < y^{*} < 2.0$.

$\langle T_{\text{AB}} \rangle$ normalized per-event dijet yields in $60-90$% collisions as a function of $\langle y_{\text{b}} \rangle$ for $49.6 < p_{\text{T,Avg}} \text{ [GeV]} < 61.4$ and $1.0 < y^{*} < 2.0$.

$\langle T_{\text{AB}} \rangle$ normalized per-event dijet yields in $0-10$% collisions as a function of $\langle y_{\text{b}} \rangle$ for $61.4 < p_{\text{T,Avg}} \text{ [GeV]} < 76.1$ and $1.0 < y^{*} < 2.0$.

$\langle T_{\text{AB}} \rangle$ normalized per-event dijet yields in $60-90$% collisions as a function of $\langle y_{\text{b}} \rangle$ for $61.4 < p_{\text{T,Avg}} \text{ [GeV]} < 76.1$ and $1.0 < y^{*} < 2.0$.

$\langle T_{\text{AB}} \rangle$ normalized per-event dijet yields in $0-10$% collisions as a function of $\langle y_{\text{b}} \rangle$ for $40.0 < p_{\text{T,Avg}} \text{ [GeV]} < 49.6$ and $2.0 < y^{*} < 4.0$.

$\langle T_{\text{AB}} \rangle$ normalized per-event dijet yields in $60-90$% collisions as a function of $\langle y_{\text{b}} \rangle$ for $40.0 < p_{\text{T,Avg}} \text{ [GeV]} < 49.6$ and $2.0 < y^{*} < 4.0$.

$\langle T_{\text{AB}} \rangle$ normalized per-event dijet yields in $0-10$% collisions as a function of $\langle y_{\text{b}} \rangle$ for $49.6 < p_{\text{T,Avg}} \text{ [GeV]} < 61.4$ and $2.0 < y^{*} < 4.0$.

$\langle T_{\text{AB}} \rangle$ normalized per-event dijet yields in $60-90$% collisions as a function of $\langle y_{\text{b}} \rangle$ for $49.6 < p_{\text{T,Avg}} \text{ [GeV]} < 61.4$ and $2.0 < y^{*} < 4.0$.

$\langle T_{\text{AB}} \rangle$ normalized per-event dijet yields in $0-10$% collisions as a function of $\langle y_{\text{b}} \rangle$ for $61.4 < p_{\text{T,Avg}} \text{ [GeV]} < 76.1$ and $2.0 < y^{*} < 4.0$.

$\langle T_{\text{AB}} \rangle$ normalized per-event dijet yields in $60-90$% collisions as a function of $\langle y_{\text{b}} \rangle$ for $61.4 < p_{\text{T,Avg}} \text{ [GeV]} < 76.1$ and $2.0 < y^{*} < 4.0$.

Table with post-fit yields in the four regions used in the measurement. The correlations of the nuisance parameters, as obtained by the fit, are considered for the calculation of the uncertainties.

Ratio of the $t\bar{t}$ to the $Z$-boson cross section compared to the predictions for several sets of parton distribution functions. The total cross section for $t\bar{t}$ production and the fiducial cross section for $Z$-boson production are used. The uncertainty on the prediction represents the PDF+$\alpha_{s}$ variations.

Nuisance parameter ranking plot for the $t\bar{t}$ signal-strength. Only the 10 most important nuisance parameters are shown. The impact of each nuisance parameter on the measured cross section, is defined as the shift induced in measured cross-section as the nuisance parameter is shifted by its pre-fit and post-fit uncertainties from its nominal best-fit value and then fixed while all other nuisance parameters profiled.

Nuisance parameter ranking plot for the ratio of the $t\bar{t}$ and $Z$-boson signal-strengths. Only the 10 most important nuisance parameters are shown. The impact of each nuisance parameter on the measured ratio, is defined as the shift induced in measured ratio as the nuisance parameter is shifted by its pre-fit and post-fit uncertainties from its nominal best-fit value and then fixed while all other nuisance parameters profiled.

Nuisance parameter ranking plot for the $Z$-boson signal-strength. Only the 10 most important nuisance parameters are shown. The impact of each nuisance parameter on the measured cross section, is defined as the shift induced in measured cross-section as the nuisance parameter is shifted by its pre-fit and post-fit uncertainties from its nominal best-fit value and then fixed while all other nuisance parameters profiled.