Observed and expected 95% CL lower limits on the $T$-quark mass as a function of the $T$-quark width-to-mass ratio and the branching fraction of the $T \rightarrow Ht$ decay ($\Gamma_{T}$ is the $T$-quark width).

Cutflow table listing the number of events passing each criterion for a $T$-quark hypothesis with a mass of 1.6 TeV and $\kappa_{T} = 0.5$. The initial signal event yield is the predicted number of $T$-quark events inclusive in the Higgs-boson and top-quark decays for 139 fb$^{-1}$.

Observed 95% CL upper limits on the single $T$-quark production cross-section as a function of the $T$-quark coupling $\kappa_{T}$ and $m_{T}$.

Expected 95% CL upper limits on the single $T$-quark production cross-section as a function of the $T$-quark coupling $\kappa_{T}$ and $m_{T}$.

Observed and expected 95% CL lower limits on the $T$-quark mass as a function of the $T$-quark width-to-mass ratio and the branching fraction of the $T \rightarrow Wb$ decay ($\Gamma_{T}$ is the $T$-quark width).

Distributions of $s_{\text{T}}$ in the single-tau one-bin SR. The stacked histograms show the various SM background contributions. The hatched band indicates the total statistical and systematic uncertainty of the SM background. The $t\bar{t}$ (2 real $\tau$) and $t\bar{t}$ (1 real $\tau$) as well as the single-top background contributions are scaled with the normalization factors obtained from the background-only fit. Minor backgrounds are grouped together and denoted as 'Other'. This includes $t\bar{t}$-fake, single top, and other top (di-tau channel) or $t\bar{t}$-fake, $t\bar{t}+H$, multiboson, and other top (single-tau channel). The overlaid dotted lines show the additional contributions for signal scenarios close to the expected exclusion contour with the particle type and the mass and $\beta$ parameters for the simplified models indicated in the legend. For the leptoquark signal model the shapes of the distributions for $\text{LQ}_{3}^{\text{d}}$ and $\text{LQ}_{3}^{\text{v}}$ (not shown) are similar to that of $\text{LQ}_{3}^{\text{u}}$. The rightmost bin includes the overflow.

Distributions of $m_{\text{T}}(\tau)$ in the single-tau one-bin SR. The stacked histograms show the various SM background contributions. The hatched band indicates the total statistical and systematic uncertainty of the SM background. The $t\bar{t}$ (2 real $\tau$) and $t\bar{t}$ (1 real $\tau$) as well as the single-top background contributions are scaled with the normalization factors obtained from the background-only fit. Minor backgrounds are grouped together and denoted as 'Other'. This includes $t\bar{t}$-fake, single top, and other top (di-tau channel) or $t\bar{t}$-fake, $t\bar{t}+H$, multiboson, and other top (single-tau channel). The overlaid dotted lines show the additional contributions for signal scenarios close to the expected exclusion contour with the particle type and the mass and $\beta$ parameters for the simplified models indicated in the legend. For the leptoquark signal model the shapes of the distributions for $\text{LQ}_{3}^{\text{d}}$ and $\text{LQ}_{3}^{\text{v}}$ (not shown) are similar to that of $\text{LQ}_{3}^{\text{u}}$. The rightmost bin includes the overflow.

Distributions of $\Sigma m_{\text{T}}(b_{1,2})$ in the single-tau $p_{\text{T}}(\tau)$-binned SR. The stacked histograms show the various SM background contributions. The hatched band indicates the total statistical and systematic uncertainty of the SM background. The $t\bar{t}$ (2 real $\tau$) and $t\bar{t}$ (1 real $\tau$) as well as the single-top background contributions are scaled with the normalization factors obtained from the background-only fit. Minor backgrounds are grouped together and denoted as 'Other'. This includes $t\bar{t}$-fake, single top, and other top (di-tau channel) or $t\bar{t}$-fake, $t\bar{t}+H$, multiboson, and other top (single-tau channel). The overlaid dotted lines show the additional contributions for signal scenarios close to the expected exclusion contour with the particle type and the mass and $\beta$ parameters for the simplified models indicated in the legend. For the leptoquark signal model the shapes of the distributions for $\text{LQ}_{3}^{\text{d}}$ and $\text{LQ}_{3}^{\text{v}}$ (not shown) are similar to that of $\text{LQ}_{3}^{\text{u}}$. The rightmost bin includes the overflow.

Distributions of $p_{\text{T}}(\tau)$ in the single-tau $p_{\text{T}}(\tau)$-binned SR. The stacked histograms show the various SM background contributions. The hatched band indicates the total statistical and systematic uncertainty of the SM background. The $t\bar{t}$ (2 real $\tau$) and $t\bar{t}$ (1 real $\tau$) as well as the single-top background contributions are scaled with the normalization factors obtained from the background-only fit. Minor backgrounds are grouped together and denoted as 'Other'. This includes $t\bar{t}$-fake, single top, and other top (di-tau channel) or $t\bar{t}$-fake, $t\bar{t}+H$, multiboson, and other top (single-tau channel). The overlaid dotted lines show the additional contributions for signal scenarios close to the expected exclusion contour with the particle type and the mass and $\beta$ parameters for the simplified models indicated in the legend. For the leptoquark signal model the shapes of the distributions for $\text{LQ}_{3}^{\text{d}}$ and $\text{LQ}_{3}^{\text{v}}$ (not shown) are similar to that of $\text{LQ}_{3}^{\text{u}}$. The rightmost bin includes the overflow.

Observed event yields in data ('Observed') and expected event yields for SM background processes obtained from the background-only fit ('Total bkg.' and rows below) in the signal regions of the di-tau and single-tau channels. The quoted uncertainties include both the statistical and systematic uncertainties and are truncated at zero yield. By construction, no $t\bar{t}$ (2 real $\tau$) events can pass the selections in the single-tau channel. As the individual uncertainties are correlated, they do not add in quadrature to equal the total background uncertainty.

From left to right: upper limits at the 95% confidence level (CL) on the visible cross section ($\sigma_\text{vis}$) and on the number of signal events ($S_{\text{obs}}^{95}$). The third column ($S_{\text{exp}}^{95}$) shows the upper limit at the 95% CL on the number of signal events, given the expected number (and $\pm 1\,\sigma$ excursions on the expectation) of background events. The last two columns indicate the confidence level observed for the background-only hypothesis ($\text{CL}_{b}$), the discovery $p$-value ($p(s=0)$) and the significance ($Z$). In the di-tau SR, where fewer events are observed than predicted by the fitted background estimate, the $p$-value is capped at 0.5.

Expected and observed exclusion contours at the 95% confidence level for the vector third-generation leptoquark signal model, as a function of the mass $m(\text{LQ}_{3}^{\text{v}})$ and the branching fraction $B(\text{LQ}_{3}^{\text{v}} \rightarrow b\tau)$ into a quark and a charged lepton. The plot shows the exclusion contour for the minimal-coupling scenario. The limits are derived from the binned single-tau signal region.

Expected and observed exclusion contours at the 95% confidence level for the vector third-generation leptoquark signal model, as a function of the mass $m(\text{LQ}_{3}^{\text{v}})$ and the branching fraction $B(\text{LQ}_{3}^{\text{v}} \rightarrow b\tau)$ into a quark and a charged lepton. The plot shows the exclusion contour for the minimal-coupling scenario. The limits are derived from the binned single-tau signal region.

Expected and observed exclusion contours at the 95% confidence level for the vector third-generation leptoquark signal model, as a function of the mass $m(\text{LQ}_{3}^{\text{v}})$ and the branching fraction $B(\text{LQ}_{3}^{\text{v}} \rightarrow b\tau)$ into a quark and a charged lepton. The plot shows the exclusion contour for vector leptoquarks with additional gauge couplings. The limits are derived from the binned single-tau signal region.

Expected and observed exclusion contours at the 95% confidence level for the vector third-generation leptoquark signal model, as a function of the mass $m(\text{LQ}_{3}^{\text{v}})$ and the branching fraction $B(\text{LQ}_{3}^{\text{v}} \rightarrow b\tau)$ into a quark and a charged lepton. The plot shows the exclusion contour for vector leptoquarks with additional gauge couplings. The limits are derived from the binned single-tau signal region.

Exclusion contours at the 95% confidence level for the stop-stau signal model as a function of the masses of the top squark $m(\tilde{t}_{1})$ and of the tau slepton $m(\tilde{\tau}_{1})$. Expected and observed limits are shown for the present search in comparison to observed limits from previous ATLAS analyses based on data from Run-1 of the LHC at $\sqrt{s} = 8$ TeV [Eur. Phys. J. C 76 (2016)] and on a partial dataset from Run 2 at $\sqrt{s} = 13$ TeV [Phys. Rev. D 98 (2018) 032008]. The green band indicates the limit on the mass of the tau slepton (for a massless LSP) from the LEP experiments.

Exclusion contours at the 95% confidence level for the stop-stau signal model as a function of the masses of the top squark $m(\tilde{t}_{1})$ and of the tau slepton $m(\tilde{\tau}_{1})$. Expected and observed limits are shown for the present search in comparison to observed limits from previous ATLAS analyses based on data from Run-1 of the LHC at $\sqrt{s} = 8$ TeV [Eur. Phys. J. C 76 (2016)] and on a partial dataset from Run 2 at $\sqrt{s} = 13$ TeV [Phys. Rev. D 98 (2018) 032008]. The green band indicates the limit on the mass of the tau slepton (for a massless LSP) from the LEP experiments.

Expected and observed exclusion contours at the 95% confidence level for the scalar third-generation leptoquark signal model, as a function of the mass $m(\text{LQ}_{3}^{\text{u}})$ and the branching fraction $B(\text{LQ}_{3}^{\text{u}} \rightarrow q\ell)$ into a quark and a charged lepton. The plot shows the exclusion contour for up-type leptoquarks $\text{LQ}_{3}^{\text{u}})$ with charge $+2/3e$. The limits are derived from the binned single-tau signal region. Shown in gray for comparison are the observed exclusion-limit contours from the previous ATLAS publication that targets the same leptoquark models but is based on a subset of the Run-2 data [JHEP 06 (2019) 144]. In this previous publication five different analyses are considered that target not only the final state studied here but also the final states that correspond to a branching fraction $B(\text{LQ}_{3}^{\text{u}} \rightarrow q\ell)$ of 0 or 1, leading to the concave shapes of the gray exclusion contours.

Expected and observed exclusion contours at the 95% confidence level for the scalar third-generation leptoquark signal model, as a function of the mass $m(\text{LQ}_{3}^{\text{u}})$ and the branching fraction $B(\text{LQ}_{3}^{\text{u}} \rightarrow q\ell)$ into a quark and a charged lepton. The plot shows the exclusion contour for up-type leptoquarks $\text{LQ}_{3}^{\text{u}})$ with charge $+2/3e$. The limits are derived from the binned single-tau signal region. Shown in gray for comparison are the observed exclusion-limit contours from the previous ATLAS publication that targets the same leptoquark models but is based on a subset of the Run-2 data [JHEP 06 (2019) 144]. In this previous publication five different analyses are considered that target not only the final state studied here but also the final states that correspond to a branching fraction $B(\text{LQ}_{3}^{\text{u}} \rightarrow q\ell)$ of 0 or 1, leading to the concave shapes of the gray exclusion contours.

Expected and observed exclusion contours at the 95% confidence level for the scalar third-generation leptoquark signal model, as a function of the mass $m(\text{LQ}_{3}^{\text{d}})$ and the branching fraction $B(\text{LQ}_{3}^{\text{d}} \rightarrow q\ell)$ into a quark and a charged lepton. The plot shows the exclusion contour for down-type leptoquarks $\text{LQ}_{3}^{\text{d}})$ with charge $-1/3e$. The limits are derived from the binned single-tau signal region. Shown in gray for comparison are the observed exclusion-limit contours from the previous ATLAS publication that targets the same leptoquark models but is based on a subset of the Run-2 data [JHEP 06 (2019) 144]. In this previous publication five different analyses are considered that target not only the final state studied here but also the final states that correspond to a branching fraction $B(\text{LQ}_{3}^{\text{d}} \rightarrow q\ell)$ of 0 or 1, leading to the concave shapes of the gray exclusion contours.

Expected and observed exclusion contours at the 95% confidence level for the scalar third-generation leptoquark signal model, as a function of the mass $m(\text{LQ}_{3}^{\text{d}})$ and the branching fraction $B(\text{LQ}_{3}^{\text{d}} \rightarrow q\ell)$ into a quark and a charged lepton. The plot shows the exclusion contour for down-type leptoquarks $\text{LQ}_{3}^{\text{d}})$ with charge $-1/3e$. The limits are derived from the binned single-tau signal region. Shown in gray for comparison are the observed exclusion-limit contours from the previous ATLAS publication that targets the same leptoquark models but is based on a subset of the Run-2 data [JHEP 06 (2019) 144]. In this previous publication five different analyses are considered that target not only the final state studied here but also the final states that correspond to a branching fraction $B(\text{LQ}_{3}^{\text{d}} \rightarrow q\ell)$ of 0 or 1, leading to the concave shapes of the gray exclusion contours.

Upper limits on the signal cross section at the 95 % confidence level for the stop-stau signal model.

Upper limits on the signal cross section at the 95 % confidence level for the scalar third-generation leptoquark signal model with up-type leptoquarks.

Upper limits on the signal cross section at the 95 % confidence level for the scalar third-generation leptoquark signal model with down-type leptoquarks.

Upper limits on the signal cross section at the 95 % confidence level for the vector third-generation leptoquark signal model with minimal coupling (MC).

Upper limits on the signal cross section at the 95 % confidence level for the vector third-generation leptoquark signal model with additional gauge couplings (YM).

Acceptance of the one-bin signal region of the single-tau channel for pair production of up-type leptoquarks $\text{LQ}_{3}^{\text{u}}$.

Efficiency of the one-bin signal region of the single-tau channel for pair production of up-type leptoquarks $\text{LQ}_{3}^{\text{u}}$. The plot does not show efficiencies for a branching fraction $B(\text{LQ}_{3}^{\text{u}} \rightarrow b\tau)$ of 0 or 1 because here the acceptance at generator level becomes zero and the efficiency is thus undefined.

Acceptance of the first bin of the multi-bin signal region (50 GeV $< p_{\text{T}}(\tau) <$ 100 GeV) of the single-tau channel for pair production of up-type leptoquarks $\text{LQ}_{3}^{\text{u}}$.

Efficiency of the first bin of the multi-bin signal region (50 GeV $< p_{\text{T}}(\tau) <$ 100 GeV) of the single-tau channel for pair production of up-type leptoquarks $\text{LQ}_{3}^{\text{u}}$. The plot does not show efficiencies for a branching fraction $B(\text{LQ}_{3}^{\text{u}} \rightarrow b\tau)$ of 0 or 1 because here the acceptance at generator level becomes zero and the efficiency is thus undefined.

Acceptance of the middle bin of the multi-bin signal region (100 GeV $< p_{\text{T}}(\tau) <$ 200 GeV) of the single-tau channel for pair production of up-type leptoquarks $\text{LQ}_{3}^{\text{u}}$.

Efficiency of the middle bin of the multi-bin signal region (100 GeV $< p_{\text{T}}(\tau) <$ 200 GeV) of the single-tau channel for pair production of up-type leptoquarks $\text{LQ}_{3}^{\text{u}}$. The plot does not show efficiencies for a branching fraction $B(\text{LQ}_{3}^{\text{u}} \rightarrow b\tau)$ of 0 or 1 because here the acceptance at generator level becomes zero and the efficiency is thus undefined.

Acceptance of the last bin of the multi-bin signal region (200 GeV $< p_{\text{T}}(\tau)$) of the single-tau channel for pair production of up-type leptoquarks $\text{LQ}_{3}^{\text{u}}$.

Efficiency of the last bin of the multi-bin signal region (200 GeV $< p_{\text{T}}(\tau)$) of the single-tau channel for pair production of up-type leptoquarks $\text{LQ}_{3}^{\text{u}}$. The plot does not show efficiencies for a branching fraction $B(\text{LQ}_{3}^{\text{u}} \rightarrow b\tau)$ of 0 or 1 because here the acceptance at generator level becomes zero and the efficiency is thus undefined.

Acceptance of the signal region of the di-tau channel for pair production of up-type leptoquarks $\text{LQ}_{3}^{\text{u}}$.

Efficiency of the signal region of the di-tau channel for pair production of up-type leptoquarks $\text{LQ}_{3}^{\text{u}}$. The plot does not show efficiencies for a branching fraction $B(\text{LQ}_{3}^{\text{u}} \rightarrow b\tau)$ of 0 because here the acceptance at generator level becomes zero and the efficiency is thus undefined.

Acceptance of the one-bin signal region of the single-tau channel for pair production of down-type leptoquarks $\text{LQ}_{3}^{\text{d}}$.

Efficiency of the one-bin signal region of the single-tau channel for pair production of down-type leptoquarks $\text{LQ}_{3}^{\text{d}}$. The plot does not show efficiencies for a branching fraction $B(\text{LQ}_{3}^{\text{d}} \rightarrow t\tau)$ of 0 or 1 because here the acceptance at generator level becomes zero and the efficiency is thus undefined.

Acceptance of the first bin of the multi-bin signal region (50 GeV $< p_{\text{T}}(\tau) <$ 100 GeV) of the single-tau channel for pair production of down-type leptoquarks $\text{LQ}_{3}^{\text{d}}$.

Efficiency of the first bin of the multi-bin signal region (50 GeV $< p_{\text{T}}(\tau) <$ 100 GeV) of the single-tau channel for pair production of down-type leptoquarks $\text{LQ}_{3}^{\text{d}}$. The plot does not show efficiencies for a branching fraction $B(\text{LQ}_{3}^{\text{d}} \rightarrow t\tau)$ of 0 or 1 because here the acceptance at generator level becomes zero and the efficiency is thus undefined.

Acceptance of the middle bin of the multi-bin signal region (100 GeV $< p_{\text{T}}(\tau) <$ 200 GeV) of the single-tau channel for pair production of down-type leptoquarks $\text{LQ}_{3}^{\text{d}}$.

Efficiency of the middle bin of the multi-bin signal region (100 GeV $< p_{\text{T}}(\tau) <$ 200 GeV) of the single-tau channel for pair production of down-type leptoquarks $\text{LQ}_{3}^{\text{d}}$. The plot does not show efficiencies for a branching fraction $B(\text{LQ}_{3}^{\text{d}} \rightarrow t\tau)$ of 0 or 1 because here the acceptance at generator level becomes zero and the efficiency is thus undefined.

Acceptance of the last bin of the multi-bin signal region (200 GeV $< p_{\text{T}}(\tau)$) of the single-tau channel for pair production of down-type leptoquarks $\text{LQ}_{3}^{\text{d}}$.

Efficiency of the last bin of the multi-bin signal region (200 GeV $< p_{\text{T}}(\tau)$) of the single-tau channel for pair production of down-type leptoquarks $\text{LQ}_{3}^{\text{d}}$. The plot does not show efficiencies for a branching fraction $B(\text{LQ}_{3}^{\text{d}} \rightarrow t\tau)$ of 0 or 1 because here the acceptance at generator level becomes zero and the efficiency is thus undefined.

Acceptance of the signal region of the di-tau channel for pair production of down-type leptoquarks $\text{LQ}_{3}^{\text{d}}$.

Efficiency of the signal region of the di-tau channel for pair production of down-type leptoquarks $\text{LQ}_{3}^{\text{d}}$. The plot does not show efficiencies for a branching fraction $B(\text{LQ}_{3}^{\text{d}} \rightarrow t\tau)$ of 0 because here the acceptance at generator level becomes zero and the efficiency is thus undefined.

Acceptance of the one-bin signal region of the single-tau channel for pair production of vector leptoquarks $\text{LQ}_{3}^{\text{v}}$ in the minimal-coupling scenario.

Efficiency of the one-bin signal region of the single-tau channel for pair production of vector leptoquarks $\text{LQ}_{3}^{\text{v}}$ in the minimal-coupling scenario. The plot does not show efficiencies for a branching fraction $B(\text{LQ}_{3}^{\text{v}} \rightarrow b\tau)$ of 0 or 1 because here the acceptance at generator level becomes zero and the efficiency is thus undefined.

Acceptance of the first bin of the multi-bin signal region (50 GeV $< p_{\text{T}}(\tau) <$ 100 GeV) of the single-tau channel for pair production of vector leptoquarks $\text{LQ}_{3}^{\text{v}}$ in the minimal-coupling scenario.

Efficiency of the first bin of the multi-bin signal region (50 GeV $< p_{\text{T}}(\tau) <$ 100 GeV) of the single-tau channel for pair production of vector leptoquarks $\text{LQ}_{3}^{\text{v}}$ in the minimal-coupling scenario. The plot does not show efficiencies for a branching fraction $B(\text{LQ}_{3}^{\text{v}} \rightarrow b\tau)$ of 0 or 1 because here the acceptance at generator level becomes zero and the efficiency is thus undefined.

Acceptance of the middle bin of the multi-bin signal region (100 GeV $< p_{\text{T}}(\tau) <$ 200 GeV) of the single-tau channel for pair production of vector leptoquarks $\text{LQ}_{3}^{\text{v}}$ in the minimal-coupling scenario.

Efficiency of the middle bin of the multi-bin signal region (100 GeV $< p_{\text{T}}(\tau) <$ 200 GeV) of the single-tau channel for pair production of vector leptoquarks $\text{LQ}_{3}^{\text{v}}$ in the minimal-coupling scenario. The plot does not show efficiencies for a branching fraction $B(\text{LQ}_{3}^{\text{v}} \rightarrow b\tau)$ of 0 or 1 because here the acceptance at generator level becomes zero and the efficiency is thus undefined.

Acceptance of the last bin of the multi-bin signal region (200 GeV $< p_{\text{T}}(\tau)$) of the single-tau channel for pair production of vector leptoquarks $\text{LQ}_{3}^{\text{v}}$ in the minimal-coupling scenario.

Efficiency of the last bin of the multi-bin signal region (200 GeV $< p_{\text{T}}(\tau)$) of the single-tau channel for pair production of vector leptoquarks $\text{LQ}_{3}^{\text{v}}$ in the minimal-coupling scenario. The plot does not show efficiencies for a branching fraction $B(\text{LQ}_{3}^{\text{v}} \rightarrow b\tau)$ of 0 or 1 because here the acceptance at generator level becomes zero and the efficiency is thus undefined.

Acceptance of the signal region of the di-tau channel for pair production of vector leptoquarks $\text{LQ}_{3}^{\text{v}}$ in the minimal-coupling scenario.

Efficiency of the signal region of the di-tau channel for pair production of vector leptoquarks $\text{LQ}_{3}^{\text{v}}$ in the minimal-coupling scenario. The plot does not show efficiencies for a branching fraction $B(\text{LQ}_{3}^{\text{v}} \rightarrow b\tau)$ of 0 because here the acceptance at generator level becomes zero and the efficiency is thus undefined.

Acceptance of the one-bin signal region of the single-tau channel for pair production of vector leptoquarks $\text{LQ}_{3}^{\text{v}}$ with additional gauge couplings.

Efficiency of the one-bin signal region of the single-tau channel for pair production of vector leptoquarks $\text{LQ}_{3}^{\text{v}}$ with additional gauge couplings. The plot does not show efficiencies for a branching fraction $B(\text{LQ}_{3}^{\text{v}} \rightarrow b\tau)$ of 0 or 1 because here the acceptance at generator level becomes zero and the efficiency is thus undefined.

Acceptance of the first bin of the multi-bin signal region (50 GeV $< p_{\text{T}}(\tau) <$ 100 GeV) of the single-tau channel for pair production of vector leptoquarks $\text{LQ}_{3}^{\text{v}}$ with additional gauge couplings.

Efficiency of the first bin of the multi-bin signal region (50 GeV $< p_{\text{T}}(\tau) <$ 100 GeV) of the single-tau channel for pair production of vector leptoquarks $\text{LQ}_{3}^{\text{v}}$ with additional gauge couplings. The plot does not show efficiencies for a branching fraction $B(\text{LQ}_{3}^{\text{v}} \rightarrow b\tau)$ of 0 or 1 because here the acceptance at generator level becomes zero and the efficiency is thus undefined.

Acceptance of the middle bin of the multi-bin signal region (100 GeV $< p_{\text{T}}(\tau) <$ 200 GeV) of the single-tau channel for pair production of vector leptoquarks $\text{LQ}_{3}^{\text{v}}$ with additional gauge couplings.

Efficiency of the middle bin of the multi-bin signal region (100 GeV $< p_{\text{T}}(\tau) <$ 200 GeV) of the single-tau channel for pair production of vector leptoquarks $\text{LQ}_{3}^{\text{v}}$ with additional gauge couplings. The plot does not show efficiencies for a branching fraction $B(\text{LQ}_{3}^{\text{v}} \rightarrow b\tau)$ of 0 or 1 because here the acceptance at generator level becomes zero and the efficiency is thus undefined.

Acceptance of the last bin of the multi-bin signal region (200 GeV $< p_{\text{T}}(\tau)$) of the single-tau channel for pair production of vector leptoquarks $\text{LQ}_{3}^{\text{v}}$ with additional gauge couplings.

Efficiency of the last bin of the multi-bin signal region (200 GeV $< p_{\text{T}}(\tau)$) of the single-tau channel for pair production of vector leptoquarks $\text{LQ}_{3}^{\text{v}}$ with additional gauge couplings. The plot does not show efficiencies for a branching fraction $B(\text{LQ}_{3}^{\text{v}} \rightarrow b\tau)$ of 0 or 1 because here the acceptance at generator level becomes zero and the efficiency is thus undefined.

Acceptance of the signal region of the di-tau channel for pair production of vector leptoquarks $\text{LQ}_{3}^{\text{v}}$ with additional gauge couplings.

Efficiency of the signal region of the di-tau channel for pair production of vector leptoquarks $\text{LQ}_{3}^{\text{v}}$ with additional gauge couplings. The plot does not show efficiencies for a branching fraction $B(\text{LQ}_{3}^{\text{v}} \rightarrow b\tau)$ of 0 because here the acceptance at generator level becomes zero and the efficiency is thus undefined.

Acceptance of the one-bin signal region of the single-tau channel for pair production of top squarks with decays via tau sleptons.

Efficiency of the one-bin signal region of the single-tau channel for pair production of top squarks with decays via tau sleptons.

Acceptance of the first bin of the multi-bin signal region (50 GeV $< p_{\text{T}}(\tau) <$ 100 GeV) of the single-tau channel for pair production of top squarks with decays via tau sleptons.

Efficiency of the first bin of the multi-bin signal region (50 GeV $< p_{\text{T}}(\tau) <$ 100 GeV) of the single-tau channel for pair production of top squarks with decays via tau sleptons.

Acceptance of the middle bin of the multi-bin signal region (100 GeV $< p_{\text{T}}(\tau) <$ 200 GeV) of the single-tau channel for pair production of top squarks with decays via tau sleptons.

Efficiency of the middle bin of the multi-bin signal region (100 GeV $< p_{\text{T}}(\tau) <$ 200 GeV) of the single-tau channel for pair production of top squarks with decays via tau sleptons.

Acceptance of the last bin of the multi-bin signal region (200 GeV $< p_{\text{T}}(\tau)$) of the single-tau channel for pair production of top squarks with decays via tau sleptons.

Efficiency of the last bin of the multi-bin signal region (200 GeV $< p_{\text{T}}(\tau)$) of the single-tau channel for pair production of top squarks with decays via tau sleptons.

Acceptance of the signal region of the di-tau channel for pair production of top squarks with decays via tau sleptons.

Efficiency of the signal region of the di-tau channel for pair production of top squarks with decays via tau sleptons.

Cutflow for the benchmark signal model $m(\tilde{t}_{1}) = 1350$ GeV, $m(\tilde{\tau}_{1}) = 1090$ GeV for the di-tau SR. The simulated sample contains 30,000 raw MC events. Weighted event yields are reported, normalized to an integrated luminosity of 139 fb$^{-1}$. 'Preselection' refers to the preselection for the di-tau channel.

Cutflow for the benchmark signal model $m(\tilde{t}_{1}) = 1350$ GeV, $m(\tilde{\tau}_{1}) = 1090$ GeV for the single-tau one-bin SR. The simulated sample contains 30,000 raw MC events. Weighted event yields are reported, normalized to an integrated luminosity of 139 fb$^{-1}$. 'Preselection' refers to the preselection for the single-tau channel.

Cutflow for the benchmark signal model $m(\tilde{t}_{1}) = 1350$ GeV, $m(\tilde{\tau}_{1}) = 1090$ GeV for the single-tau multi-bin SR. The simulated sample contains 30,000 raw MC events. Weighted event yields are reported, normalized to an integrated luminosity of 139 fb$^{-1}$. 'Preselection' refers to the preselection for the single-tau channel.

Cutflow for the benchmark signal model $m(\text{LQ}_{3}^{\text{u}}) = 1.2$ TeV, $\beta = 0.5$ for the di-tau SR. The simulated sample contains 210,000 raw MC events. Weighted event yields are reported, normalized to an integrated luminosity of 139 fb$^{-1}$. 'Preselection' refers to the preselection for the di-tau channel.

Cutflow for the benchmark signal model $m(\text{LQ}_{3}^{\text{u}}) = 1.2$ TeV, $\beta = 0.5$ for the single-tau one-bin SR. The simulated sample contains 210,000 raw MC events. Weighted event yields are reported, normalized to an integrated luminosity of 139 fb$^{-1}$. 'Preselection' refers to the preselection for the single-tau channel.

Cutflow for the benchmark signal model $m(\text{LQ}_{3}^{\text{u}}) = 1.2$ TeV, $\beta = 0.5$ for the single-tau multi-bin SR. The simulated sample contains 210,000 raw MC events. Weighted event yields are reported, normalized to an integrated luminosity of 139 fb$^{-1}$. 'Preselection' refers to the preselection for the single-tau channel.

Cutflow for the benchmark signal model $m(\text{LQ}_{3}^{\text{d}}) = 1.2$ TeV, $\beta = 0.5$ for the di-tau SR. The simulated sample contains 210,000 raw MC events. Weighted event yields are reported, normalized to an integrated luminosity of 139 fb$^{-1}$. 'Preselection' refers to the preselection for the di-tau channel.

Cutflow for the benchmark signal model $m(\text{LQ}_{3}^{\text{d}}) = 1.2$ TeV, $\beta = 0.5$ for the single-tau one-bin SR. The simulated sample contains 210,000 raw MC events. Weighted event yields are reported, normalized to an integrated luminosity of 139 fb$^{-1}$. 'Preselection' refers to the preselection for the single-tau channel.

Cutflow for the benchmark signal model $m(\text{LQ}_{3}^{\text{d}}) = 1.2$ TeV, $\beta = 0.5$ for the single-tau multi-bin SR. The simulated sample contains 210,000 raw MC events. Weighted event yields are reported, normalized to an integrated luminosity of 139 fb$^{-1}$. 'Preselection' refers to the preselection for the single-tau channel.

Cutflow for the benchmark signal model $m(\text{LQ}_{3}^{\text{v}}) = 1.4$ TeV, $\beta = 0.5$ in the minimal-coupling scenario for the di-tau SR. The simulated sample contains 50,000 raw MC events. Weighted event yields are reported, normalized to an integrated luminosity of 139 fb$^{-1}$. 'Preselection' refers to the preselection for the di-tau channel.

Cutflow for the benchmark signal model $m(\text{LQ}_{3}^{\text{v}}) = 1.4$ TeV, $\beta = 0.5$ in the minimal-coupling scenario for the single-tau one-bin SR. The simulated sample contains 50,000 raw MC events. Weighted event yields are reported, normalized to an integrated luminosity of 139 fb$^{-1}$. 'Preselection' refers to the preselection for the single-tau channel.

Cutflow for the benchmark signal model $m(\text{LQ}_{3}^{\text{v}}) = 1.4$ TeV, $\beta = 0.5$ in the minimal-coupling scenario for the single-tau multi-bin SR. The simulated sample contains 50,000 raw MC events. Weighted event yields are reported, normalized to an integrated luminosity of 139 fb$^{-1}$. 'Preselection' refers to the preselection for the single-tau channel.

Cutflow for the benchmark signal model $m(\text{LQ}_{3}^{\text{v}}) = 1.4$ TeV, $\beta = 0.5$ in the Yang--Mills scenario for the di-tau SR. The simulated sample contains 50,000 raw MC events. Weighted event yields are reported, normalized to an integrated luminosity of 139 fb$^{-1}$. 'Preselection' refers to the preselection for the di-tau channel.

Cutflow for the benchmark signal model $m(\text{LQ}_{3}^{\text{v}}) = 1.4$ TeV, $\beta = 0.5$ in the Yang--Mills scenario for the single-tau one-bin SR. The simulated sample contains 50,000 raw MC events. Weighted event yields are reported, normalized to an integrated luminosity of 139 fb$^{-1}$. 'Preselection' refers to the preselection for the single-tau channel.

Cutflow for the benchmark signal model $m(\text{LQ}_{3}^{\text{v}}) = 1.4$ TeV, $\beta = 0.5$ in the Yang--Mills scenario for the single-tau multi-bin SR. The simulated sample contains 50,000 raw MC events. Weighted event yields are reported, normalized to an integrated luminosity of 139 fb$^{-1}$. 'Preselection' refers to the preselection for the single-tau channel.

Leading tau Pt distributions obtained before the fit to data (Pre-Fit) showing the expected background and tuH signals after applying fake factors in the $t_{h}\tau_{lep}\tau_{had}$-2j region. Other MC includes single top, V+jets, and other small backgrounds. The tuH signals with nominal branching ratio of 0.1% are scaled using normalization factors of 2 to 50. Statistical and systematic uncertainties are included in the "Total background".

Leading tau Pt distributions obtained before the fit to data (Pre-Fit) showing the expected background and tuH signals after applying fake factors in the $t_{h}\tau_{lep}\tau_{had}$-3j region. Other MC includes single top, V+jets, and other small backgrounds. The tuH signals with nominal branching ratio of 0.1% are scaled using normalization factors of 2 to 50. Statistical and systematic uncertainties are included in the "Total background".

Leading tau Pt distributions obtained before the fit to data (Pre-Fit) showing the expected background and tuH signals after applying fake factors in the $t_{\ell}\tau_{had}\tau_{had}$SS region. Other MC includes single top, V+jets, and other small backgrounds. The tuH signals with nominal branching ratio of 0.1% are scaled using normalization factors of 2 to 50. Statistical and systematic uncertainties are included in the "Total background".

Leading tau Pt distributions obtained before the fit to data (Pre-Fit) showing the expected background and tuH signals after applying fake factors in the $t_{h}\tau_{had}\tau_{had}$-2j region. Rare includes single top, V+jets, and other small backgrounds. $\tau_{sub}$ real includes the contribution of fakes for which the sub-leading tau is real. The tuH signals with nominal branching ratio of 0.1% are scaled using normalization factors of 2 to 50. Statistical and systematic uncertainties are included in the "Total background".

Leading tau Pt distributions obtained before the fit to data (Pre-Fit) showing the expected background and tuH signals after applying fake factors in the $t_{h}\tau_{had}\tau_{had}$-3j region. Rare includes single top, V+jets, and other small backgrounds. $\tau_{sub}$ real includes the contribution of fakes for which the sub-leading tau is real. The tuH signals with nominal branching ratio of 0.1% are scaled using normalization factors of 2 to 50. Statistical and systematic uncertainties are included in the "Total background".

Leading tau Pt distributions obtained before the fit to data (Pre-Fit) showing the expected background and tuH signals after applying fake factors in the $t_{h}\tau_{had}\tau_{had}$-3jSS region. Rare includes single top, V+jets, and other small backgrounds. $\tau_{sub}$ real includes the contribution of fakes for which the sub-leading tau is real. The tuH signals with nominal branching ratio of 0.1% are scaled using normalization factors of 2 to 50. Statistical and systematic uncertainties are included in the "Total background".

Di-tau mass distributions obtained before the fit to data (Pre-Fit) showing the expected background and tuH signals after applying fake factors in the $t_{\ell}\tau_{had}\tau_{had}$ region. Other MC includes single top, V+jets, and other small backgrounds. The tuH signals with nominal branching ratio of 0.1% are scaled using normalization factors of 2 to 50. Statistical and systematic uncertainties are included in the "Total background".

Di-tau mass distributions obtained before the fit to data (Pre-Fit) showing the expected background and tuH signals after applying fake factors in the $t_{\ell}\tau_{had}$-1j region. Other MC includes single top, V+jets, and other small backgrounds. The tuH signals with nominal branching ratio of 0.1% are scaled using normalization factors of 2 to 50. Statistical and systematic uncertainties are included in the "Total background".

Di-tau mass distributions obtained before the fit to data (Pre-Fit) showing the expected background and tuH signals after applying fake factors in the $t_{\ell}\tau_{had}$-2j region. Other MC includes single top, V+jets, and other small backgrounds. The tuH signals with nominal branching ratio of 0.1% are scaled using normalization factors of 2 to 50. Statistical and systematic uncertainties are included in the "Total background".

Di-tau mass distributions obtained before the fit to data (Pre-Fit) showing the expected background and tuH signals after applying fake factors in the $t_{h}\tau_{lep}\tau_{had}$-2j region. Other MC includes single top, V+jets, and other small backgrounds. The tuH signals with nominal branching ratio of 0.1% are scaled using normalization factors of 2 to 50. Statistical and systematic uncertainties are included in the "Total background".

Di-tau mass distributions obtained before the fit to data (Pre-Fit) showing the expected background and tuH signals after applying fake factors in the $t_{h}\tau_{lep}\tau_{had}$-3j region. Other MC includes single top, V+jets, and other small backgrounds. The tuH signals with nominal branching ratio of 0.1% are scaled using normalization factors of 2 to 50. Statistical and systematic uncertainties are included in the "Total background".

Di-tau mass distributions obtained before the fit to data (Pre-Fit) showing the expected background and tuH signals after applying fake factors in the $t_{\ell}\tau_{had}\tau_{had}$SS region. Other MC includes single top, V+jets, and other small backgrounds. The tuH signals with nominal branching ratio of 0.1% are scaled using normalization factors of 2 to 50. Statistical and systematic uncertainties are included in the "Total background".

Di-tau mass distributions obtained before the fit to data (Pre-Fit) showing the expected background and tuH signals after applying fake factors in the $t_{h}\tau_{had}\tau_{had}$-2j region. Rare includes single top, V+jets, and other small backgrounds. $\tau_{sub}$ real includes the contribution of fakes for which the sub-leading tau is real. The tuH signals with nominal branching ratio of 0.1% are scaled using normalization factors of 2 to 50. Statistical and systematic uncertainties are included in the "Total background".

Di-tau mass distributions obtained before the fit to data (Pre-Fit) showing the expected background and tuH signals after applying fake factors in the $t_{h}\tau_{had}\tau_{had}$-3j region. Rare includes single top, V+jets, and other small backgrounds. $\tau_{sub}$ real includes the contribution of fakes for which the sub-leading tau is real. The tuH signals with nominal branching ratio of 0.1% are scaled using normalization factors of 2 to 50. Statistical and systematic uncertainties are included in the "Total background".

Di-tau mass distributions obtained before the fit to data (Pre-Fit) showing the expected background and tuH signals after applying fake factors in the $t_{h}\tau_{had}\tau_{had}$-3jSS region. Rare includes single top, V+jets, and other small backgrounds. $\tau_{sub}$ real includes the contribution of fakes for which the sub-leading tau is real. The tuH signals with nominal branching ratio of 0.1% are scaled using normalization factors of 2 to 50. Statistical and systematic uncertainties are included in the "Total background".

BDT output distributions obtained from a signal+background fit to the data for the tuH search in the $t_{\ell}\tau_{had}\tau_{had}$ region, Other MC includes single top, V+jets, and other small backgrounds. Statistical and systematic uncertainties are included in the "Total background". The signal shapes of tt(uH), tH, and their sum are also shown using a normalisation of 2 x $\mathcal{B}(\mathrm{t}\to\mathrm{uH})$ of 0.1%.

BDT output distributions obtained from a signal+background fit to the data for the tuH search in the $t_{\ell}\tau_{had}$-1j region, Other MC includes single top, V+jets, and other small backgrounds. Statistical and systematic uncertainties are included in the "Total background". The signal shapes of tt(uH), tH, and their sum are also shown using a normalisation of 2 x $\mathcal{B}(\mathrm{t}\to\mathrm{uH})$ of 0.1%.

BDT output distributions obtained from a signal+background fit to the data for the tuH search in the $t_{\ell}\tau_{had}$-2j region, Other MC includes single top, V+jets, and other small backgrounds. Statistical and systematic uncertainties are included in the "Total background". The signal shapes of tt(uH), tH, and their sum are also shown using a normalisation of 2 x $\mathcal{B}(\mathrm{t}\to\mathrm{uH})$ of 0.1%.

BDT output distributions obtained from a signal+background fit to the data for the tuH search in the $t_{h}\tau_{lep}\tau_{had}$-2j region, Other MC includes single top, V+jets, and other small backgrounds. Statistical and systematic uncertainties are included in the "Total background". The signal shapes of tt(uH), tH, and their sum are also shown using a normalisation of 2 x $\mathcal{B}(\mathrm{t}\to\mathrm{uH})$ of 0.1%.

BDT output distributions obtained from a signal+background fit to the data for the tuH search in the $t_{h}\tau_{lep}\tau_{had}$-3j region, Other MC includes single top, V+jets, and other small backgrounds. Statistical and systematic uncertainties are included in the "Total background". The signal shapes of tt(uH), tH, and their sum are also shown using a normalisation of 2 x $\mathcal{B}(\mathrm{t}\to\mathrm{uH})$ of 0.1%.

BDT output distributions obtained from a signal+background fit to the data for the tuH search in the $t_{\ell}\tau_{had}\tau_{had}$SS region, Other MC includes single top, V+jets, and other small backgrounds. Statistical and systematic uncertainties are included in the "Total background". The signal shapes of tt(uH), tH, and their sum are also shown using a normalisation of 2 x $\mathcal{B}(\mathrm{t}\to\mathrm{uH})$ of 0.1%.

BDT output distributions obtained from a signal+background fit to the data for the tuH search in the $t_{h}\tau_{had}\tau_{had}$-2j region, Rare includes single top, V+jets, and other small backgrounds. $\tau_{sub}$ real includes the contribution of fakes for which the sub-leading tau is real. Statistical and systematic uncertainties are included in the "Total background". The signal shapes of tt(uH), tH, and their sum are also shown using a normalisation of 2 x $\mathcal{B}(\mathrm{t}\to\mathrm{uH})$ of 0.1%.

BDT output distributions obtained from a signal+background fit to the data for the tuH search in the $t_{h}\tau_{had}\tau_{had}$-3j region, Rare includes single top, V+jets, and other small backgrounds. $\tau_{sub}$ real includes the contribution of fakes for which the sub-leading tau is real. Statistical and systematic uncertainties are included in the "Total background". The signal shapes of tt(uH), tH, and their sum are also shown using a normalisation of 2 x $\mathcal{B}(\mathrm{t}\to\mathrm{uH})$ of 0.1%.

BDT output distributions obtained from a signal+background fit to the data for the tuH search in the $t_{h}\tau_{had}\tau_{had}$-3jSS region, Rare includes single top, V+jets, and other small backgrounds. $\tau_{sub}$ real includes the contribution of fakes for which the sub-leading tau is real. Statistical and systematic uncertainties are included in the "Total background". The signal shapes of tt(uH), tH, and their sum are also shown using a normalisation of 2 x $\mathcal{B}(\mathrm{t}\to\mathrm{uH})$ of 0.1%.

BDT output distributions obtained from a signal+background fit to the data for the tcH search in the $t_{\ell}\tau_{had}\tau_{had}$ region, Other MC includes single top, V+jets, and other small backgrounds. Statistical and systematic uncertainties are included in the "Total background". The signal shapes of tt(cH), tH, and their sum are also shown using a normalisation of 2 x $\mathcal{B}(\mathrm{t}\to\mathrm{cH})$ of 0.1%.

BDT output distributions obtained from a signal+background fit to the data for the tcH search in the $t_{\ell}\tau_{had}$-1j region, Other MC includes single top, V+jets, and other small backgrounds. Statistical and systematic uncertainties are included in the "Total background". The signal shapes of tt(cH), tH, and their sum are also shown using a normalisation of 2 x $\mathcal{B}(\mathrm{t}\to\mathrm{cH})$ of 0.1%.

BDT output distributions obtained from a signal+background fit to the data for the tcH search in the $t_{\ell}\tau_{had}$-2j region, Other MC includes single top, V+jets, and other small backgrounds. Statistical and systematic uncertainties are included in the "Total background". The signal shapes of tt(cH), tH, and their sum are also shown using a normalisation of 2 x $\mathcal{B}(\mathrm{t}\to\mathrm{cH})$ of 0.1%.

BDT output distributions obtained from a signal+background fit to the data for the tcH search in the $t_{h}\tau_{lep}\tau_{had}$-2j region, Other MC includes single top, V+jets, and other small backgrounds. Statistical and systematic uncertainties are included in the "Total background". The signal shapes of tt(cH), tH, and their sum are also shown using a normalisation of 2 x $\mathcal{B}(\mathrm{t}\to\mathrm{cH})$ of 0.1%.

BDT output distributions obtained from a signal+background fit to the data for the tcH search in the $t_{h}\tau_{lep}\tau_{had}$-3j region,Other MC includes single top, V+jets, and other small backgrounds. Statistical and systematic uncertainties are included in the "Total background". The signal shapes of tt(cH), tH, and their sum are also shown using a normalisation of 2 x $\mathcal{B}(\mathrm{t}\to\mathrm{cH})$ of 0.1%.

BDT output distributions obtained from a signal+background fit to the data for the tcH search in the $t_{\ell}\tau_{had}\tau_{had}$SS region, Other MC includes single top, V+jets, and other small backgrounds. Statistical and systematic uncertainties are included in the "Total background". The signal shapes of tt(cH), tH, and their sum are also shown using a normalisation of 2 x $\mathcal{B}(\mathrm{t}\to\mathrm{cH})$ of 0.1%.

BDT output distributions obtained from a signal+background fit to the data for the tcH search in the $t_{h}\tau_{had}\tau_{had}$-2j region, Rare includes single top, V+jets, and other small backgrounds. $\tau_{sub}$ real includes the contribution of fakes for which the sub-leading tau is real. Statistical and systematic uncertainties are included in the "Total background". The signal shapes of tt(cH), tH, and their sum are also shown using a normalisation of 2 x $\mathcal{B}(\mathrm{t}\to\mathrm{cH})$ of 0.1%.

BDT output distributions obtained from a signal+background fit to the data for the tcH search in the $t_{h}\tau_{had}\tau_{had}$-3j region, Rare includes single top, V+jets, and other small backgrounds. $\tau_{sub}$ real includes the contribution of fakes for which the sub-leading tau is real. Statistical and systematic uncertainties are included in the "Total background". The signal shapes of tt(cH), tH, and their sum are also shown using a normalisation of 2 x $\mathcal{B}(\mathrm{t}\to\mathrm{cH})$ of 0.1%.

BDT output distributions obtained from a signal+background fit to the data for the tcH search in the $t_{h}\tau_{had}\tau_{had}$-3jSS region, Rare includes single top, V+jets, and other small backgrounds. $\tau_{sub}$ real includes the contribution of fakes for which the sub-leading tau is real. Statistical and systematic uncertainties are included in the "Total background". The signal shapes of tt(cH), tH, and their sum are also shown using a normalisation of 2 x $\mathcal{B}(\mathrm{t}\to\mathrm{cH})$ of 0.1%.

95% CL upper limits on $\mathcal{B}(\mathrm{t}\to\mathrm{cH})$ for the individual searches as well as their combination, assuming $\mathcal{B}(\mathrm{t}\to\mathrm{uH}) = 0$. The observed limits are compared with the expected (median) limits under the background-only hypothesis. The surrounding shaded bands correspond to the 68% and 95% CL intervals around the expected limits, denoted by $\pm 1\sigma$ and $\pm 2\sigma$, respectively.

95% CL upper limits on $\mathcal{B}(\mathrm{t}\to\mathrm{uH})$ for the individual searches as well as their combination, assuming $\mathcal{B}(\mathrm{t}\to\mathrm{cH}) = 0$. The observed limits are compared with the expected (median) limits under the background-only hypothesis. The surrounding shaded bands correspond to the 68% and 95% CL intervals around the expected limits, denoted by $\pm 1\sigma$ and $\pm 2\sigma$, respectively.

Observed upper limits at 95% CL on the branching fractions in the plane of $\mathcal{B}(\mathrm{t}\to\mathrm{uH})$ and $\mathcal{B}(\mathrm{t}\to\mathrm{cH})$.

Expected upper limits at 95% CL on the branching fractions in the plane of $\mathcal{B}(\mathrm{t}\to\mathrm{uH})$ and $\mathcal{B}(\mathrm{t}\to\mathrm{cH})$.

Expected $+2\sigma$ upper limits at 95% CL on the branching fractions in the plane of $\mathcal{B}(\mathrm{t}\to\mathrm{uH})$ and $\mathcal{B}(\mathrm{t}\to\mathrm{cH})$.

Expected $+1\sigma$ upper limits at 95% CL on the branching fractions in the plane of $\mathcal{B}(\mathrm{t}\to\mathrm{uH})$ and $\mathcal{B}(\mathrm{t}\to\mathrm{cH})$.

Expected $-1\sigma$ upper limits at 95% CL on the branching fractions in the plane of $\mathcal{B}(\mathrm{t}\to\mathrm{uH})$ and $\mathcal{B}(\mathrm{t}\to\mathrm{cH})$.

Expected $-2\sigma$ upper limits at 95% CL on the branching fractions in the plane of $\mathcal{B}(\mathrm{t}\to\mathrm{uH})$ and $\mathcal{B}(\mathrm{t}\to\mathrm{cH})$.

Observed upper limits at 95% CL on the anomalous couplings in the plane of $C_{\mathrm{c\phi}}$ and $C_{\mathrm{u\phi}}$.

Expected upper limits at 95% CL on the anomalous couplings in the plane of $C_{\mathrm{c\phi}}$ and $C_{\mathrm{u\phi}}$.

Expected $+2\sigma$ upper limits at 95% CL on the anomalous couplings in the plane of $C_{\mathrm{c\phi}}$ and $C_{\mathrm{u\phi}}$.

Expected $+1\sigma$ upper limits at 95% CL on the anomalous couplings in the plane of $C_{\mathrm{c\phi}}$ and $C_{\mathrm{u\phi}}$.

Expected $-1\sigma$ upper limits at 95% CL on the anomalous couplings in the plane of $C_{\mathrm{c\phi}}$ and $C_{\mathrm{u\phi}}$.

Expected $-2\sigma$ upper limits at 95% CL on the anomalous couplings in the plane of $C_{\mathrm{c\phi}}$ and $C_{\mathrm{u\phi}}$.

Predicted and observed yields in each of the analysis regions considered in leptonic channel.

Predicted and observed yields in each of the analysis regions considered in hadronic channel.

Absolute uncertainties on $\mathcal{B}(\mathrm{t}\to\mathrm{qH})$ obtained from the combined fit to the data.

Summary of 95% CL upper limits on $\mathcal{B}(\mathrm{t}\to\mathrm{qH})$, significance and best-fit branching ratio in the signal regions. The values in the tables are in the form of observed(expected).

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.

The $m_{\mathrm{eff}}$ distribution in SR0$_{\mathrm{bveto}}^{\mathrm{loose}}$ and SR0$_{\mathrm{bveto}}^{\mathrm{tight}}$ for events passing the signal region requirements except the $m_{\mathrm{eff}}$ requirement. Distributions for data, the estimated SM backgrounds after the background-only fit, and an example SUSY scenario are shown. "Other" is the sum of the $tWZ$, $t\bar{t}WW$, $t\bar{t} ZZ$, $t\bar{t} WH$, $t\bar{t} HH$, $t\bar{t} tW$, and $t\bar{t}t\bar{t}$ backgrounds. The last bin captures the overflow events. The lower panel shows the ratio of the observed data to the expected SM background yield in each bin. Both the statistical and systematic uncertainties in the SM background are included in the shaded band. The red arrows indicate the $m_{\mathrm{eff}}$ selections in the signal regions.

The $m_{\mathrm{eff}}$ distribution in SR1$_{\mathrm{bveto}}^{\mathrm{loose}}$ and SR1$_{\mathrm{bveto}}^{\mathrm{tight}}$ for events passing the signal region requirements except the $m_{\mathrm{eff}}$ requirement. Distributions for data, the estimated SM backgrounds after the background-only fit, and an example SUSY scenario are shown. "Other" is the sum of the $tWZ$, $t\bar{t}WW$, $t\bar{t} ZZ$, $t\bar{t} WH$, $t\bar{t} HH$, $t\bar{t} tW$, and $t\bar{t}t\bar{t}$ backgrounds. The last bin captures the overflow events. The lower panel shows the ratio of the observed data to the expected SM background yield in each bin. Both the statistical and systematic uncertainties in the SM background are included in the shaded band. The red arrows indicate the $m_{\mathrm{eff}}$ selections in the signal regions.

The $m_{\mathrm{eff}}$ distribution in SR2$_{\mathrm{bveto}}^{\mathrm{loose}}$ and SR2$_{\mathrm{bveto}}^{\mathrm{tight}}$ for events passing the signal region requirements except the $m_{\mathrm{eff}}$ requirement. Distributions for data, the estimated SM backgrounds after the background-only fit, and an example SUSY scenario are shown. "Other" is the sum of the $tWZ$, $t\bar{t}WW$, $t\bar{t} ZZ$, $t\bar{t} WH$, $t\bar{t} HH$, $t\bar{t} tW$, and $t\bar{t}t\bar{t}$ backgrounds. The last bin captures the overflow events. The lower panel shows the ratio of the observed data to the expected SM background yield in each bin. Both the statistical and systematic uncertainties in the SM background are included in the shaded band. The red arrows indicate the $m_{\mathrm{eff}}$ selections in the signal regions.

The $m_{\mathrm{eff}}$ distribution in SR0$_{\mathrm{breq}}$ for events passing the signal region requirements except the $m_{\mathrm{eff}}$ requirement. Distributions for data, the estimated SM backgrounds after the background-only fit, and an example SUSY scenario are shown. "Other" is the sum of the $tWZ$, $t\bar{t}WW$, $t\bar{t} ZZ$, $t\bar{t} WH$, $t\bar{t} HH$, $t\bar{t} tW$, and $t\bar{t}t\bar{t}$ backgrounds. The last bin captures the overflow events. The lower panel shows the ratio of the observed data to the expected SM background yield in each bin. Both the statistical and systematic uncertainties in the SM background are included in the shaded band. The red arrows indicate the $m_{\mathrm{eff}}$ selections in the signal regions.

The $m_{\mathrm{eff}}$ distribution in SR1$_{\mathrm{breq}}$ for events passing the signal region requirements except the $m_{\mathrm{eff}}$ requirement. Distributions for data, the estimated SM backgrounds after the background-only fit, and an example SUSY scenario are shown. "Other" is the sum of the $tWZ$, $t\bar{t}WW$, $t\bar{t} ZZ$, $t\bar{t} WH$, $t\bar{t} HH$, $t\bar{t} tW$, and $t\bar{t}t\bar{t}$ backgrounds. The last bin captures the overflow events. The lower panel shows the ratio of the observed data to the expected SM background yield in each bin. Both the statistical and systematic uncertainties in the SM background are included in the shaded band. The red arrows indicate the $m_{\mathrm{eff}}$ selections in the signal regions.

The $m_{\mathrm{eff}}$ distribution in SR2$_{\mathrm{breq}}$ for events passing the signal region requirements except the $m_{\mathrm{eff}}$ requirement. Distributions for data, the estimated SM backgrounds after the background-only fit, and an example SUSY scenario are shown. "Other" is the sum of the $tWZ$, $t\bar{t}WW$, $t\bar{t} ZZ$, $t\bar{t} WH$, $t\bar{t} HH$, $t\bar{t} tW$, and $t\bar{t}t\bar{t}$ backgrounds. The last bin captures the overflow events. The lower panel shows the ratio of the observed data to the expected SM background yield in each bin. Both the statistical and systematic uncertainties in the SM background are included in the shaded band. The red arrows indicate the $m_{\mathrm{eff}}$ selections in the signal regions.

Expected 95% CL exclusion limits on the higgsino GGM models. The limits are set using the statistical combination of disjoint signal regions. Where two (or more) signal regions overlap, the signal region contributing its observed $\mathrm{CL}_{\mathrm{s}}$ value to the combination is the one with the better (best) expected $\mathrm{CL}_{\mathrm{s}}$ value.

$+1\sigma$ expected 95% CL exclusion limits on the higgsino GGM models. The limits are set using the statistical combination of disjoint signal regions. Where two (or more) signal regions overlap, the signal region contributing its observed $\mathrm{CL}_{\mathrm{s}}$ value to the combination is the one with the better (best) expected $\mathrm{CL}_{\mathrm{s}}$ value.

$-1\sigma$ expected 95% CL exclusion limits on the higgsino GGM models. The limits are set using the statistical combination of disjoint signal regions. Where two (or more) signal regions overlap, the signal region contributing its observed $\mathrm{CL}_{\mathrm{s}}$ value to the combination is the one with the better (best) expected $\mathrm{CL}_{\mathrm{s}}$ value.

Observed 95% CL exclusion limits on the higgsino GGM models. The limits are set using the statistical combination of disjoint signal regions. Where two (or more) signal regions overlap, the signal region contributing its observed $\mathrm{CL}_{\mathrm{s}}$ value to the combination is the one with the better (best) expected $\mathrm{CL}_{\mathrm{s}}$ value.

$+1\sigma$ observed 95% CL exclusion limits on the higgsino GGM models. The limits are set using the statistical combination of disjoint signal regions. Where two (or more) signal regions overlap, the signal region contributing its observed $\mathrm{CL}_{\mathrm{s}}$ value to the combination is the one with the better (best) expected $\mathrm{CL}_{\mathrm{s}}$ value.

$-1\sigma$ observed 95% CL exclusion limits on the higgsino GGM models. The limits are set using the statistical combination of disjoint signal regions. Where two (or more) signal regions overlap, the signal region contributing its observed $\mathrm{CL}_{\mathrm{s}}$ value to the combination is the one with the better (best) expected $\mathrm{CL}_{\mathrm{s}}$ value.

Expected 95% CL exclusion limits on wino NLSP pair production with RPV LSP decays via $\lambda_{12k}$, where $k \in{1,2}$. The limits are set using the statistical combination of disjoint signal regions. Where two (or more) signal regions overlap, the signal region contributing its observed $\mathrm{CL}_{\mathrm{s}}$ value to the combination is the one with the better (best) expected $\mathrm{CL}_{\mathrm{s}}$ value.

$+1\sigma$ expected 95% CL exclusion limits on wino NLSP pair production with RPV LSP decays via $\lambda_{12k}$, where $k \in{1,2}$. The limits are set using the statistical combination of disjoint signal regions. Where two (or more) signal regions overlap, the signal region contributing its observed $\mathrm{CL}_{\mathrm{s}}$ value to the combination is the one with the better (best) expected $\mathrm{CL}_{\mathrm{s}}$ value.

$-1\sigma$ expected 95% CL exclusion limits on wino NLSP pair production with RPV LSP decays via $\lambda_{12k}$, where $k \in{1,2}$. The limits are set using the statistical combination of disjoint signal regions. Where two (or more) signal regions overlap, the signal region contributing its observed $\mathrm{CL}_{\mathrm{s}}$ value to the combination is the one with the better (best) expected $\mathrm{CL}_{\mathrm{s}}$ value.

Observed 95% CL exclusion limits on wino NLSP pair production with RPV LSP decays via $\lambda_{12k}$, where $k \in{1,2}$. The limits are set using the statistical combination of disjoint signal regions. Where two (or more) signal regions overlap, the signal region contributing its observed $\mathrm{CL}_{\mathrm{s}}$ value to the combination is the one with the better (best) expected $\mathrm{CL}_{\mathrm{s}}$ value.

$+1\sigma$ bserved 95% CL exclusion limits on wino NLSP pair production with RPV LSP decays via $\lambda_{12k}$, where $k \in{1,2}$. The limits are set using the statistical combination of disjoint signal regions. Where two (or more) signal regions overlap, the signal region contributing its observed $\mathrm{CL}_{\mathrm{s}}$ value to the combination is the one with the better (best) expected $\mathrm{CL}_{\mathrm{s}}$ value.

$-1\sigma$ observed 95% CL exclusion limits on wino NLSP pair production with RPV LSP decays via $\lambda_{12k}$, where $k \in{1,2}$. The limits are set using the statistical combination of disjoint signal regions. Where two (or more) signal regions overlap, the signal region contributing its observed $\mathrm{CL}_{\mathrm{s}}$ value to the combination is the one with the better (best) expected $\mathrm{CL}_{\mathrm{s}}$ value.

Expected 95% CL exclusion limits on wino NLSP pair production with RPV LSP decays via $\lambda_{i33}$, where $i \in{1,2}$. The limits are set using the statistical combination of disjoint signal regions. Where two (or more) signal regions overlap, the signal region contributing its observed $\mathrm{CL}_{\mathrm{s}}$ value to the combination is the one with the better (best) expected $\mathrm{CL}_{\mathrm{s}}$ value.

$+1\sigma$ expected 95% CL exclusion limits on wino NLSP pair production with RPV LSP decays via $\lambda_{i33}$, where $i \in{1,2}$. The limits are set using the statistical combination of disjoint signal regions. Where two (or more) signal regions overlap, the signal region contributing its observed $\mathrm{CL}_{\mathrm{s}}$ value to the combination is the one with the better (best) expected $\mathrm{CL}_{\mathrm{s}}$ value.

$-1\sigma$ expected 95% CL exclusion limits on wino NLSP pair production with RPV LSP decays via $\lambda_{i33}$, where $i \in{1,2}$. The limits are set using the statistical combination of disjoint signal regions. Where two (or more) signal regions overlap, the signal region contributing its observed $\mathrm{CL}_{\mathrm{s}}$ value to the combination is the one with the better (best) expected $\mathrm{CL}_{\mathrm{s}}$ value.

Observed 95% CL exclusion limits on wino NLSP pair production with RPV LSP decays via $\lambda_{i33}$, where $i \in{1,2}$. The limits are set using the statistical combination of disjoint signal regions. Where two (or more) signal regions overlap, the signal region contributing its observed $\mathrm{CL}_{\mathrm{s}}$ value to the combination is the one with the better (best) expected $\mathrm{CL}_{\mathrm{s}}$ value.

$+1\sigma$ observed 95% CL exclusion limits on wino NLSP pair production with RPV LSP decays via $\lambda_{i33}$, where $i \in{1,2}$. The limits are set using the statistical combination of disjoint signal regions. Where two (or more) signal regions overlap, the signal region contributing its observed $\mathrm{CL}_{\mathrm{s}}$ value to the combination is the one with the better (best) expected $\mathrm{CL}_{\mathrm{s}}$ value.

$-1\sigma$ observed 95% CL exclusion limits on wino NLSP pair production with RPV LSP decays via $\lambda_{i33}$, where $i \in{1,2}$. The limits are set using the statistical combination of disjoint signal regions. Where two (or more) signal regions overlap, the signal region contributing its observed $\mathrm{CL}_{\mathrm{s}}$ value to the combination is the one with the better (best) expected $\mathrm{CL}_{\mathrm{s}}$ value.

Expected 95% CL exclusion limits on slepton/sneutrino NLSP pair production with RPV LSP decays via $\lambda_{12k}$, where $k \in{1,2}$. The limits are set using the statistical combination of disjoint signal regions. Where two (or more) signal regions overlap, the signal region contributing its observed $\mathrm{CL}_{\mathrm{s}}$ value to the combination is the one with the better (best) expected $\mathrm{CL}_{\mathrm{s}}$ value.

$+1\sigma$ expected 95% CL exclusion limits on slepton/sneutrino NLSP pair production with RPV LSP decays via $\lambda_{12k}$, where $k \in{1,2}$. The limits are set using the statistical combination of disjoint signal regions. Where two (or more) signal regions overlap, the signal region contributing its observed $\mathrm{CL}_{\mathrm{s}}$ value to the combination is the one with the better (best) expected $\mathrm{CL}_{\mathrm{s}}$ value.

$-1\sigma$ expected 95% CL exclusion limits on slepton/sneutrino NLSP pair production with RPV LSP decays via $\lambda_{12k}$, where $k \in{1,2}$. The limits are set using the statistical combination of disjoint signal regions. Where two (or more) signal regions overlap, the signal region contributing its observed $\mathrm{CL}_{\mathrm{s}}$ value to the combination is the one with the better (best) expected $\mathrm{CL}_{\mathrm{s}}$ value.

Observed 95% CL exclusion limits on slepton/sneutrino NLSP pair production with RPV LSP decays via $\lambda_{12k}$, where $k \in{1,2}$. The limits are set using the statistical combination of disjoint signal regions. Where two (or more) signal regions overlap, the signal region contributing its observed $\mathrm{CL}_{\mathrm{s}}$ value to the combination is the one with the better (best) expected $\mathrm{CL}_{\mathrm{s}}$ value.

$+1\sigma$ observed 95% CL exclusion limits on slepton/sneutrino NLSP pair production with RPV LSP decays via $\lambda_{12k}$, where $k \in{1,2}$. The limits are set using the statistical combination of disjoint signal regions. Where two (or more) signal regions overlap, the signal region contributing its observed $\mathrm{CL}_{\mathrm{s}}$ value to the combination is the one with the better (best) expected $\mathrm{CL}_{\mathrm{s}}$ value.

$-1\sigma$ observed 95% CL exclusion limits on slepton/sneutrino NLSP pair production with RPV LSP decays via $\lambda_{12k}$, where $k \in{1,2}$. The limits are set using the statistical combination of disjoint signal regions. Where two (or more) signal regions overlap, the signal region contributing its observed $\mathrm{CL}_{\mathrm{s}}$ value to the combination is the one with the better (best) expected $\mathrm{CL}_{\mathrm{s}}$ value.

Expected 95% CL exclusion limits on slepton/sneutrino NLSP pair production with RPV LSP decays via $\lambda_{i33}$, where $i \in{1,2}$. The limits are set using the statistical combination of disjoint signal regions. Where two (or more) signal regions overlap, the signal region contributing its observed $\mathrm{CL}_{\mathrm{s}}$ value to the combination is the one with the better (best) expected $\mathrm{CL}_{\mathrm{s}}$ value.

$+1\sigma$ expected 95% CL exclusion limits on slepton/sneutrino NLSP pair production with RPV LSP decays via $\lambda_{i33}$, where $i \in{1,2}$. The limits are set using the statistical combination of disjoint signal regions. Where two (or more) signal regions overlap, the signal region contributing its observed $\mathrm{CL}_{\mathrm{s}}$ value to the combination is the one with the better (best) expected $\mathrm{CL}_{\mathrm{s}}$ value.

$-1\sigma$ expected 95% CL exclusion limits on slepton/sneutrino NLSP pair production with RPV LSP decays via $\lambda_{i33}$, where $i \in{1,2}$. The limits are set using the statistical combination of disjoint signal regions. Where two (or more) signal regions overlap, the signal region contributing its observed $\mathrm{CL}_{\mathrm{s}}$ value to the combination is the one with the better (best) expected $\mathrm{CL}_{\mathrm{s}}$ value.

Observed 95% CL exclusion limits on slepton/sneutrino NLSP pair production with RPV LSP decays via $\lambda_{i33}$, where $i \in{1,2}$. The limits are set using the statistical combination of disjoint signal regions. Where two (or more) signal regions overlap, the signal region contributing its observed $\mathrm{CL}_{\mathrm{s}}$ value to the combination is the one with the better (best) expected $\mathrm{CL}_{\mathrm{s}}$ value.

$+1\sigma$ observed 95% CL exclusion limits on slepton/sneutrino NLSP pair production with RPV LSP decays via $\lambda_{i33}$, where $i \in{1,2}$. The limits are set using the statistical combination of disjoint signal regions. Where two (or more) signal regions overlap, the signal region contributing its observed $\mathrm{CL}_{\mathrm{s}}$ value to the combination is the one with the better (best) expected $\mathrm{CL}_{\mathrm{s}}$ value.

$-1\sigma$ observed 95% CL exclusion limits on slepton/sneutrino NLSP pair production with RPV LSP decays via $\lambda_{i33}$, where $i \in{1,2}$. The limits are set using the statistical combination of disjoint signal regions. Where two (or more) signal regions overlap, the signal region contributing its observed $\mathrm{CL}_{\mathrm{s}}$ value to the combination is the one with the better (best) expected $\mathrm{CL}_{\mathrm{s}}$ value.

Expected 95% CL exclusion limits on gluino NLSP pair production with RPV LSP decays via $\lambda_{12k}$, where $k \in{1,2}$. The limits are set using the statistical combination of disjoint signal regions. Where two (or more) signal regions overlap, the signal region contributing its observed $\mathrm{CL}_{\mathrm{s}}$ value to the combination is the one with the better (best) expected $\mathrm{CL}_{\mathrm{s}}$ value.

$+1\sigma$ expected 95% CL exclusion limits on gluino NLSP pair production with RPV LSP decays via $\lambda_{12k}$, where $k \in{1,2}$. The limits are set using the statistical combination of disjoint signal regions. Where two (or more) signal regions overlap, the signal region contributing its observed $\mathrm{CL}_{\mathrm{s}}$ value to the combination is the one with the better (best) expected $\mathrm{CL}_{\mathrm{s}}$ value.

$-1\sigma$ expected 95% CL exclusion limits on gluino NLSP pair production with RPV LSP decays via $\lambda_{12k}$, where $k \in{1,2}$. The limits are set using the statistical combination of disjoint signal regions. Where two (or more) signal regions overlap, the signal region contributing its observed $\mathrm{CL}_{\mathrm{s}}$ value to the combination is the one with the better (best) expected $\mathrm{CL}_{\mathrm{s}}$ value.

Observed 95% CL exclusion limits on gluino NLSP pair production with RPV LSP decays via $\lambda_{12k}$, where $k \in{1,2}$. The limits are set using the statistical combination of disjoint signal regions. Where two (or more) signal regions overlap, the signal region contributing its observed $\mathrm{CL}_{\mathrm{s}}$ value to the combination is the one with the better (best) expected $\mathrm{CL}_{\mathrm{s}}$ value.

$+1\sigma$ observed 95% CL exclusion limits on gluino NLSP pair production with RPV LSP decays via $\lambda_{12k}$, where $k \in{1,2}$. The limits are set using the statistical combination of disjoint signal regions. Where two (or more) signal regions overlap, the signal region contributing its observed $\mathrm{CL}_{\mathrm{s}}$ value to the combination is the one with the better (best) expected $\mathrm{CL}_{\mathrm{s}}$ value.

$-1\sigma$ observed 95% CL exclusion limits on gluino NLSP pair production with RPV LSP decays via $\lambda_{12k}$, where $k \in{1,2}$. The limits are set using the statistical combination of disjoint signal regions. Where two (or more) signal regions overlap, the signal region contributing its observed $\mathrm{CL}_{\mathrm{s}}$ value to the combination is the one with the better (best) expected $\mathrm{CL}_{\mathrm{s}}$ value.

Expected 95% CL exclusion limits on gluino NLSP pair production with RPV LSP decays via $\lambda_{i33}$, where $i \in{1,2}$. The limits are set using the statistical combination of disjoint signal regions. Where two (or more) signal regions overlap, the signal region contributing its observed $\mathrm{CL}_{\mathrm{s}}$ value to the combination is the one with the better (best) expected $\mathrm{CL}_{\mathrm{s}}$ value.

$+1\sigma$ expected 95% CL exclusion limits on gluino NLSP pair production with RPV LSP decays via $\lambda_{i33}$, where $i \in{1,2}$. The limits are set using the statistical combination of disjoint signal regions. Where two (or more) signal regions overlap, the signal region contributing its observed $\mathrm{CL}_{\mathrm{s}}$ value to the combination is the one with the better (best) expected $\mathrm{CL}_{\mathrm{s}}$ value.

$-1\sigma$ expected 95% CL exclusion limits on gluino NLSP pair production with RPV LSP decays via $\lambda_{i33}$, where $i \in{1,2}$. The limits are set using the statistical combination of disjoint signal regions. Where two (or more) signal regions overlap, the signal region contributing its observed $\mathrm{CL}_{\mathrm{s}}$ value to the combination is the one with the better (best) expected $\mathrm{CL}_{\mathrm{s}}$ value.

Observed 95% CL exclusion limits on gluino NLSP pair production with RPV LSP decays via $\lambda_{i33}$, where $i \in{1,2}$. The limits are set using the statistical combination of disjoint signal regions. Where two (or more) signal regions overlap, the signal region contributing its observed $\mathrm{CL}_{\mathrm{s}}$ value to the combination is the one with the better (best) expected $\mathrm{CL}_{\mathrm{s}}$ value.

$+1\sigma$ observed 95% CL exclusion limits on gluino NLSP pair production with RPV LSP decays via $\lambda_{i33}$, where $i \in{1,2}$. The limits are set using the statistical combination of disjoint signal regions. Where two (or more) signal regions overlap, the signal region contributing its observed $\mathrm{CL}_{\mathrm{s}}$ value to the combination is the one with the better (best) expected $\mathrm{CL}_{\mathrm{s}}$ value.

$-1\sigma$ observed 95% CL exclusion limits on gluino NLSP pair production with RPV LSP decays via $\lambda_{i33}$, where $i \in{1,2}$. The limits are set using the statistical combination of disjoint signal regions. Where two (or more) signal regions overlap, the signal region contributing its observed $\mathrm{CL}_{\mathrm{s}}$ value to the combination is the one with the better (best) expected $\mathrm{CL}_{\mathrm{s}}$ value.

Observed upper limit on the signal cross section in fb for the wino NLSP models with RPV LSP decays via $\lambda_{12k}$ where $k \in{1,2}$. The interpolation between signal scenarios studied is included for illustration purposes only and may be subject to interpolation effects in sparsely populated areas.

Observed upper limit on the signal cross section in fb for the wino NLSP models with RPV LSP decays via $\lambda_{i33}$ where $i \in{1,2}$. The interpolation between signal scenarios studied is included for illustration purposes only and may be subject to interpolation effects in sparsely populated areas.

Observed upper limit on the signal cross section in fb for the slepton/sneutrino NLSP models with RPV LSP decays via $\lambda_{12k}$ where $k \in{1,2}$. The interpolation between signal scenarios studied is included for illustration purposes only and may be subject to interpolation effects in sparsely populated areas.

Observed upper limit on the signal cross section in fb for the slepton/sneutrino NLSP models with RPV LSP decays via $\lambda_{i33}$ where $i \in{1,2}$. The interpolation between signal scenarios studied is included for illustration purposes only and may be subject to interpolation effects in sparsely populated areas.

Observed upper limit on the signal cross section in fb for the gluino NLSP models with RPV LSP decays via $\lambda_{12k}$ where $k \in{1,2}$. The interpolation between signal scenarios studied is included for illustration purposes only and may be subject to interpolation effects in sparsely populated areas.

Observed upper limit on the signal cross section in fb for the gluino NLSP models with RPV LSP decays via $\lambda_{i33}$ where $i \in{1,2}$. The interpolation between signal scenarios studied is included for illustration purposes only and may be subject to interpolation effects in sparsely populated areas.

Observed upper limit on the signal cross section in fb for the higgsino GGM models. The interpolation between signal scenarios studied is included for illustration purposes only and may be subject to interpolation effects in sparsely populated areas.

Best expected SR for the wino NLSP models with RPV LSP decays via $\lambda_{12k}$ where $k \in{1,2}$. A value of 1 corresponds to SR0$_{\mathrm{bveto}}^{\mathrm{loose}}$SR1$_{\mathrm{bveto}}^{\mathrm{loose}}$SR2$_{\mathrm{bveto}}^{\mathrm{loose}}$, 2 corresponds to SR0$_{\mathrm{bveto}}^{\mathrm{loose}}$SR1$_{\mathrm{bveto}}^{\mathrm{loose}}$SR2$_{\mathrm{bveto}}^{\mathrm{tight}}$, 3 corresponds to SR0$_{\mathrm{bveto}}^{\mathrm{loose}}$SR1$_{\mathrm{bveto}}^{\mathrm{tight}}$SR2$_{\mathrm{bveto}}^{\mathrm{loose}}$, 4 corresponds to SR0$_{\mathrm{bveto}}^{\mathrm{loose}}$SR1$_{\mathrm{bveto}}^{\mathrm{tight}}$SR2$_{\mathrm{bveto}}^{\mathrm{tight}}$, and 5 corresponds to SR0$_{\mathrm{bveto}}^{\mathrm{tight}}$SR1$_{\mathrm{bveto}}^{\mathrm{tight}}$SR2$_{\mathrm{bveto}}^{\mathrm{tight}}$.

Best expected SR for the wino NLSP models with RPV LSP decays via $\lambda_{i33}$ where $i \in{1,2}$. A value of 1 corresponds to SR0$_{\mathrm{bveto}}^{\mathrm{loose}}$SR1$_{\mathrm{bveto}}^{\mathrm{loose}}$SR2$_{\mathrm{bveto}}^{\mathrm{loose}}$, 2 corresponds to SR0$_{\mathrm{bveto}}^{\mathrm{loose}}$SR1$_{\mathrm{bveto}}^{\mathrm{loose}}$SR2$_{\mathrm{bveto}}^{\mathrm{tight}}$, 3 corresponds to SR0$_{\mathrm{bveto}}^{\mathrm{loose}}$SR1$_{\mathrm{bveto}}^{\mathrm{tight}}$SR2$_{\mathrm{bveto}}^{\mathrm{loose}}$, 4 corresponds to SR0$_{\mathrm{bveto}}^{\mathrm{loose}}$SR1$_{\mathrm{bveto}}^{\mathrm{tight}}$SR2$_{\mathrm{bveto}}^{\mathrm{tight}}$, and 5 corresponds to SR0$_{\mathrm{bveto}}^{\mathrm{tight}}$SR1$_{\mathrm{bveto}}^{\mathrm{tight}}$SR2$_{\mathrm{bveto}}^{\mathrm{tight}}$.

Best expected SR for the slepton/sneutrino NLSP models with RPV LSP decays via $\lambda_{12k}$ where $k \in{1,2}$. A value of 1 corresponds to SR0$_{\mathrm{bveto}}^{\mathrm{loose}}$SR1$_{\mathrm{bveto}}^{\mathrm{loose}}$SR2$_{\mathrm{bveto}}^{\mathrm{loose}}$, 2 corresponds to SR0$_{\mathrm{bveto}}^{\mathrm{loose}}$SR1$_{\mathrm{bveto}}^{\mathrm{loose}}$SR2$_{\mathrm{bveto}}^{\mathrm{tight}}$, 3 corresponds to SR0$_{\mathrm{bveto}}^{\mathrm{loose}}$SR1$_{\mathrm{bveto}}^{\mathrm{tight}}$SR2$_{\mathrm{bveto}}^{\mathrm{loose}}$, 4 corresponds to SR0$_{\mathrm{bveto}}^{\mathrm{loose}}$SR1$_{\mathrm{bveto}}^{\mathrm{tight}}$SR2$_{\mathrm{bveto}}^{\mathrm{tight}}$, and 5 corresponds to SR0$_{\mathrm{bveto}}^{\mathrm{tight}}$SR1$_{\mathrm{bveto}}^{\mathrm{tight}}$SR2$_{\mathrm{bveto}}^{\mathrm{tight}}$.

Best expected SR for the slepton/sneutrino NLSP models with RPV LSP decays via $\lambda_{i33}$ where $i \in{1,2}$. A value of 1 corresponds to SR0$_{\mathrm{bveto}}^{\mathrm{loose}}$SR1$_{\mathrm{bveto}}^{\mathrm{loose}}$SR2$_{\mathrm{bveto}}^{\mathrm{loose}}$, 2 corresponds to SR0$_{\mathrm{bveto}}^{\mathrm{loose}}$SR1$_{\mathrm{bveto}}^{\mathrm{loose}}$SR2$_{\mathrm{bveto}}^{\mathrm{tight}}$, 3 corresponds to SR0$_{\mathrm{bveto}}^{\mathrm{loose}}$SR1$_{\mathrm{bveto}}^{\mathrm{tight}}$SR2$_{\mathrm{bveto}}^{\mathrm{loose}}$, 4 corresponds to SR0$_{\mathrm{bveto}}^{\mathrm{loose}}$SR1$_{\mathrm{bveto}}^{\mathrm{tight}}$SR2$_{\mathrm{bveto}}^{\mathrm{tight}}$, and 5 corresponds to SR0$_{\mathrm{bveto}}^{\mathrm{tight}}$SR1$_{\mathrm{bveto}}^{\mathrm{tight}}$SR2$_{\mathrm{bveto}}^{\mathrm{tight}}$.

Best expected SR for the gluino NLSP models with RPV LSP decays via $\lambda_{12k}$ where $k \in{1,2}$. A value of 1 corresponds to SR0$_{\mathrm{bveto}}^{\mathrm{loose}}$SR1$_{\mathrm{bveto}}^{\mathrm{loose}}$SR2$_{\mathrm{bveto}}^{\mathrm{loose}}$, 2 corresponds to SR0$_{\mathrm{bveto}}^{\mathrm{loose}}$SR1$_{\mathrm{bveto}}^{\mathrm{loose}}$SR2$_{\mathrm{bveto}}^{\mathrm{tight}}$, 3 corresponds to SR0$_{\mathrm{bveto}}^{\mathrm{loose}}$SR1$_{\mathrm{bveto}}^{\mathrm{tight}}$SR2$_{\mathrm{bveto}}^{\mathrm{loose}}$, 4 corresponds to SR0$_{\mathrm{bveto}}^{\mathrm{loose}}$SR1$_{\mathrm{bveto}}^{\mathrm{tight}}$SR2$_{\mathrm{bveto}}^{\mathrm{tight}}$, and 5 corresponds to SR0$_{\mathrm{bveto}}^{\mathrm{tight}}$SR1$_{\mathrm{bveto}}^{\mathrm{tight}}$SR2$_{\mathrm{bveto}}^{\mathrm{tight}}$.

Best expected SR for the gluino NLSP models with RPV LSP decays via $\lambda_{i33}$ where $i \in{1,2}$. A value of 1 corresponds to SR0$_{\mathrm{bveto}}^{\mathrm{loose}}$SR1$_{\mathrm{bveto}}^{\mathrm{loose}}$SR2$_{\mathrm{bveto}}^{\mathrm{loose}}$, 2 corresponds to SR0$_{\mathrm{bveto}}^{\mathrm{loose}}$SR1$_{\mathrm{bveto}}^{\mathrm{loose}}$SR2$_{\mathrm{bveto}}^{\mathrm{tight}}$, 3 corresponds to SR0$_{\mathrm{bveto}}^{\mathrm{loose}}$SR1$_{\mathrm{bveto}}^{\mathrm{tight}}$SR2$_{\mathrm{bveto}}^{\mathrm{loose}}$, 4 corresponds to SR0$_{\mathrm{bveto}}^{\mathrm{loose}}$SR1$_{\mathrm{bveto}}^{\mathrm{tight}}$SR2$_{\mathrm{bveto}}^{\mathrm{tight}}$, and 5 corresponds to SR0$_{\mathrm{bveto}}^{\mathrm{tight}}$SR1$_{\mathrm{bveto}}^{\mathrm{tight}}$SR2$_{\mathrm{bveto}}^{\mathrm{tight}}$.

Best expected SR for the higgsino GGM models. A value of 6 corresponds to SR0-ZZ$^{\mathrm{loose}}$, 7 corresponds to SR0-ZZ$^{\mathrm{tight}}$, 8 corresponds to SR0-ZZ$^{\mathrm{loose}}_{\mathrm{bveto}}$, and 9 corresponds to SR0-ZZ$^{\mathrm{tight}}_{\mathrm{bveto}}$.

Acceptance across the wino NLSP $\lambda_{12k}\neq 0$ models for SR0$_{\mathrm{bveto}}^{\mathrm{loose}}$. The interpolation between signal scenarios studied is included for illustration purposes only and may be subject to interpolation effects in sparsely populated areas.

Efficiency across the wino NLSP $\lambda_{12k}\neq 0$ models for SR0$_{\mathrm{bveto}}^{\mathrm{loose}}$. The interpolation between signal scenarios studied is included for illustration purposes only and may be subject to interpolation effects in sparsely populated areas.

Acceptance across the wino NLSP $\lambda_{12k}\neq 0$ models for SR0$_{\mathrm{bveto}}^{\mathrm{tight}}$. The interpolation between signal scenarios studied is included for illustration purposes only and may be subject to interpolation effects in sparsely populated areas.

Efficiency across the wino NLSP $\lambda_{12k}\neq 0$ models for SR0$_{\mathrm{bveto}}^{\mathrm{tight}}$. The interpolation between signal scenarios studied is included for illustration purposes only and may be subject to interpolation effects in sparsely populated areas.

Acceptance across the wino NLSP $\lambda_{12k}\neq 0$ models for SR0$_{\mathrm{breq}}$. The interpolation between signal scenarios studied is included for illustration purposes only and may be subject to interpolation effects in sparsely populated areas.

Efficiency across the wino NLSP $\lambda_{12k}\neq 0$ models for SR0$_{\mathrm{breq}}$. The interpolation between signal scenarios studied is included for illustration purposes only and may be subject to interpolation effects in sparsely populated areas.

Acceptance across the wino NLSP $\lambda_{i33}\neq 0$ models for SR1$_{\mathrm{bveto}}^{\mathrm{loose}}$. The interpolation between signal scenarios studied is included for illustration purposes only and may be subject to interpolation effects in sparsely populated areas.

Efficiency across the wino NLSP $\lambda_{i33}\neq 0$ models for SR1$_{\mathrm{bveto}}^{\mathrm{loose}}$. The interpolation between signal scenarios studied is included for illustration purposes only and may be subject to interpolation effects in sparsely populated areas.

Acceptance across the wino NLSP $\lambda_{i33}\neq 0$ models for SR1$_{\mathrm{bveto}}^{\mathrm{tight}}$. The interpolation between signal scenarios studied is included for illustration purposes only and may be subject to interpolation effects in sparsely populated areas.

Efficiency across the wino NLSP $\lambda_{i33}\neq 0$ models for SR1$_{\mathrm{bveto}}^{\mathrm{tight}}$. The interpolation between signal scenarios studied is included for illustration purposes only and may be subject to interpolation effects in sparsely populated areas.

Acceptance across the wino NLSP $\lambda_{i33}\neq 0$ models for SR1$_{\mathrm{breq}}$. The interpolation between signal scenarios studied is included for illustration purposes only and may be subject to interpolation effects in sparsely populated areas.

Efficiency across the wino NLSP $\lambda_{i33}\neq 0$ models for SR1$_{\mathrm{breq}}$. The interpolation between signal scenarios studied is included for illustration purposes only and may be subject to interpolation effects in sparsely populated areas.

Acceptance across the wino NLSP $\lambda_{i33}\neq 0$ models for SR2$_{\mathrm{bveto}}^{\mathrm{loose}}$. The interpolation between signal scenarios studied is included for illustration purposes only and may be subject to interpolation effects in sparsely populated areas.

Efficiency across the wino NLSP $\lambda_{i33}\neq 0$ models for SR2$_{\mathrm{bveto}}^{\mathrm{loose}}$. The interpolation between signal scenarios studied is included for illustration purposes only and may be subject to interpolation effects in sparsely populated areas.

Acceptance across the wino NLSP $\lambda_{i33}\neq 0$ models for SR2$_{\mathrm{bveto}}^{\mathrm{tight}}$. The interpolation between signal scenarios studied is included for illustration purposes only and may be subject to interpolation effects in sparsely populated areas.

Efficiency across the wino NLSP $\lambda_{i33}\neq 0$ models for SR2$_{\mathrm{bveto}}^{\mathrm{tight}}$. The interpolation between signal scenarios studied is included for illustration purposes only and may be subject to interpolation effects in sparsely populated areas.

Acceptance across the wino NLSP $\lambda_{i33}\neq 0$ models for SR2$_{\mathrm{breq}}$. The interpolation between signal scenarios studied is included for illustration purposes only and may be subject to interpolation effects in sparsely populated areas.

Efficiency across the wino NLSP $\lambda_{i33}\neq 0$ models for SR2$_{\mathrm{breq}}$. The interpolation between signal scenarios studied is included for illustration purposes only and may be subject to interpolation effects in sparsely populated areas.

Acceptance across the GGM Higgsino grid for SR0-ZZ$^{\mathrm{loose}}$. The interpolation between signal scenarios studied is included for illustration purposes only and may be subject to interpolation effects in sparsely populated areas.

Efficiency across the GGM Higgsino grid for SR0-ZZ$^{\mathrm{loose}}$. The interpolation between signal scenarios studied is included for illustration purposes only and may be subject to interpolation effects in sparsely populated areas.

Acceptance across the GGM Higgsino grid for SR0-ZZ$^{\mathrm{tight}}$. The interpolation between signal scenarios studied is included for illustration purposes only and may be subject to interpolation effects in sparsely populated areas.

Efficiency across the GGM Higgsino grid for SR0-ZZ$^{\mathrm{tight}}$. The interpolation between signal scenarios studied is included for illustration purposes only and may be subject to interpolation effects in sparsely populated areas.

Acceptance across the GGM Higgsino grid for SR0-ZZ$_{\mathrm{bveto}}^{\mathrm{loose}}$. The interpolation between signal scenarios studied is included for illustration purposes only and may be subject to interpolation effects in sparsely populated areas.

Efficiency across the GGM Higgsino grid for SR0-ZZ$_{\mathrm{bveto}}^{\mathrm{loose}}$. The interpolation between signal scenarios studied is included for illustration purposes only and may be subject to interpolation effects in sparsely populated areas.

Acceptance across the GGM Higgsino grid for SR0-ZZ$_{\mathrm{bveto}}^{\mathrm{tight}}$. The interpolation between signal scenarios studied is included for illustration purposes only and may be subject to interpolation effects in sparsely populated areas.

Efficiency across the GGM Higgsino grid for SR0-ZZ$_{\mathrm{bveto}}^{\mathrm{tight}}$. The interpolation between signal scenarios studied is included for illustration purposes only and may be subject to interpolation effects in sparsely populated areas.

The $p_{\mathrm{T}}$ of the light leptons in distribution in SR0$_{\mathrm{bveto}}^{\mathrm{loose}}$. Distributions for data, the estimated SM backgrounds after the background-only fit, and an example SUSY scenario are shown. "Other" is the sum of the $tWZ$, $t\bar{t}WW$, $t\bar{t} ZZ$, $t\bar{t} WH$, $t\bar{t} HH$, $t\bar{t} tW$, and $t\bar{t}t\bar{t}$ backgrounds. The last bin captures the overflow events. The lower panel shows the ratio of the observed data to the expected SM background yield in each bin. Both the statistical and systematic uncertainties in the SM background are included in the shaded band.

The $p_{\mathrm{T}}$ of the light leptons in distribution in SR0-ZZ$^{\mathrm{loose}}$. Distributions for data, the estimated SM backgrounds after the background-only fit, and an example SUSY scenario are shown. "Other" is the sum of the $tWZ$, $t\bar{t}WW$, $t\bar{t} ZZ$, $t\bar{t} WH$, $t\bar{t} HH$, $t\bar{t} tW$, and $t\bar{t}t\bar{t}$ backgrounds. The last bin captures the overflow events. The lower panel shows the ratio of the observed data to the expected SM background yield in each bin. Both the statistical and systematic uncertainties in the SM background are included in the shaded band.

The $p_{\mathrm{T}}$ of the light leptons in distribution in SR0-ZZ$^{\mathrm{tight}}$. Distributions for data, the estimated SM backgrounds after the background-only fit, and an example SUSY scenario are shown. "Other" is the sum of the $tWZ$, $t\bar{t}WW$, $t\bar{t} ZZ$, $t\bar{t} WH$, $t\bar{t} HH$, $t\bar{t} tW$, and $t\bar{t}t\bar{t}$ backgrounds. The last bin captures the overflow events. The lower panel shows the ratio of the observed data to the expected SM background yield in each bin. Both the statistical and systematic uncertainties in the SM background are included in the shaded band.

The $p_{\mathrm{T}}$ of the light leptons in distribution in SR0-ZZ$_{\mathrm{bveto}}^{\mathrm{loose}}$. Distributions for data, the estimated SM backgrounds after the background-only fit, and an example SUSY scenario are shown. "Other" is the sum of the $tWZ$, $t\bar{t}WW$, $t\bar{t} ZZ$, $t\bar{t} WH$, $t\bar{t} HH$, $t\bar{t} tW$, and $t\bar{t}t\bar{t}$ backgrounds. The last bin captures the overflow events. The lower panel shows the ratio of the observed data to the expected SM background yield in each bin. Both the statistical and systematic uncertainties in the SM background are included in the shaded band.

The $p_{\mathrm{T}}$ of the light leptons in distribution in SR5L. Distributions for data, the estimated SM backgrounds after the background-only fit, and an example SUSY scenario are shown. "Other" is the sum of the $tWZ$, $t\bar{t}WW$, $t\bar{t} ZZ$, $t\bar{t} WH$, $t\bar{t} HH$, $t\bar{t} tW$, and $t\bar{t}t\bar{t}$ backgrounds. The last bin captures the overflow events. The lower panel shows the ratio of the observed data to the expected SM background yield in each bin. Both the statistical and systematic uncertainties in the SM background are included in the shaded band.

The $p_{\mathrm{T}}$ of the light leptons in distribution in SR1$_{\mathrm{bveto}}^{\mathrm{loose}}$. Distributions for data, the estimated SM backgrounds after the background-only fit, and an example SUSY scenario are shown. "Other" is the sum of the $tWZ$, $t\bar{t}WW$, $t\bar{t} ZZ$, $t\bar{t} WH$, $t\bar{t} HH$, $t\bar{t} tW$, and $t\bar{t}t\bar{t}$ backgrounds. The last bin captures the overflow events. The lower panel shows the ratio of the observed data to the expected SM background yield in each bin. Both the statistical and systematic uncertainties in the SM background are included in the shaded band.

The $p_{\mathrm{T}}$ of the taus leptons in distribution in SR1$_{\mathrm{bveto}}^{\mathrm{loose}}$. Distributions for data, the estimated SM backgrounds after the background-only fit, and an example SUSY scenario are shown. "Other" is the sum of the $tWZ$, $t\bar{t}WW$, $t\bar{t} ZZ$, $t\bar{t} WH$, $t\bar{t} HH$, $t\bar{t} tW$, and $t\bar{t}t\bar{t}$ backgrounds. The last bin captures the overflow events. The lower panel shows the ratio of the observed data to the expected SM background yield in each bin. Both the statistical and systematic uncertainties in the SM background are included in the shaded band.

The $p_{\mathrm{T}}$ of the light taus in distribution in SR2$_{\mathrm{bveto}}^{\mathrm{loose}}$. Distributions for data, the estimated SM backgrounds after the background-only fit, and an example SUSY scenario are shown. "Other" is the sum of the $tWZ$, $t\bar{t}WW$, $t\bar{t} ZZ$, $t\bar{t} WH$, $t\bar{t} HH$, $t\bar{t} tW$, and $t\bar{t}t\bar{t}$ backgrounds. The last bin captures the overflow events. The lower panel shows the ratio of the observed data to the expected SM background yield in each bin. Both the statistical and systematic uncertainties in the SM background are included in the shaded band.

The lepton flavour and multiplicities in events with four light leptons and a Z veto. Distributions for data, the estimated SM backgrounds after the background-only fit, and an example SUSY scenario are shown. "Other" is the sum of the $tWZ$, $t\bar{t}WW$, $t\bar{t} ZZ$, $t\bar{t} WH$, $t\bar{t} HH$, $t\bar{t} tW$, and $t\bar{t}t\bar{t}$ backgrounds. The last bin captures the overflow events. The lower panel shows the ratio of the observed data to the expected SM background yield in each bin. Both the statistical and systematic uncertainties in the SM background are included in the shaded band.

The lepton flavour and multiplicities in events with four light leptons and one Z candidate. Distributions for data, the estimated SM backgrounds after the background-only fit, and an example SUSY scenario are shown. "Other" is the sum of the $tWZ$, $t\bar{t}WW$, $t\bar{t} ZZ$, $t\bar{t} WH$, $t\bar{t} HH$, $t\bar{t} tW$, and $t\bar{t}t\bar{t}$ backgrounds. The last bin captures the overflow events. The lower panel shows the ratio of the observed data to the expected SM background yield in each bin. Both the statistical and systematic uncertainties in the SM background are included in the shaded band.

The lepton flavour and multiplicities in events with four light leptons and two Z candidates. Distributions for data, the estimated SM backgrounds after the background-only fit, and an example SUSY scenario are shown. "Other" is the sum of the $tWZ$, $t\bar{t}WW$, $t\bar{t} ZZ$, $t\bar{t} WH$, $t\bar{t} HH$, $t\bar{t} tW$, and $t\bar{t}t\bar{t}$ backgrounds. The last bin captures the overflow events. The lower panel shows the ratio of the observed data to the expected SM background yield in each bin. Both the statistical and systematic uncertainties in the SM background are included in the shaded band.

The lepton flavour and multiplicities in events with exactly five light leptons. Distributions for data, the estimated SM backgrounds after the background-only fit, and an example SUSY scenario are shown. "Other" is the sum of the $tWZ$, $t\bar{t}WW$, $t\bar{t} ZZ$, $t\bar{t} WH$, $t\bar{t} HH$, $t\bar{t} tW$, and $t\bar{t}t\bar{t}$ backgrounds. The last bin captures the overflow events. The lower panel shows the ratio of the observed data to the expected SM background yield in each bin. Both the statistical and systematic uncertainties in the SM background are included in the shaded band.

The lepton flavour and multiplicities in events with three light leptons and one tau and a Z veto. Distributions for data, the estimated SM backgrounds after the background-only fit, and an example SUSY scenario are shown. "Other" is the sum of the $tWZ$, $t\bar{t}WW$, $t\bar{t} ZZ$, $t\bar{t} WH$, $t\bar{t} HH$, $t\bar{t} tW$, and $t\bar{t}t\bar{t}$ backgrounds. The last bin captures the overflow events. The lower panel shows the ratio of the observed data to the expected SM background yield in each bin. Both the statistical and systematic uncertainties in the SM background are included in the shaded band.

The lepton flavour and multiplicities in events with three light leptons and one tau and one Z candidate. Distributions for data, the estimated SM backgrounds after the background-only fit, and an example SUSY scenario are shown. "Other" is the sum of the $tWZ$, $t\bar{t}WW$, $t\bar{t} ZZ$, $t\bar{t} WH$, $t\bar{t} HH$, $t\bar{t} tW$, and $t\bar{t}t\bar{t}$ backgrounds. The last bin captures the overflow events. The lower panel shows the ratio of the observed data to the expected SM background yield in each bin. Both the statistical and systematic uncertainties in the SM background are included in the shaded band.

The lepton flavour and multiplicities in events with two light leptons and two taus and a Z veto. Distributions for data, the estimated SM backgrounds after the background-only fit, and an example SUSY scenario are shown. "Other" is the sum of the $tWZ$, $t\bar{t}WW$, $t\bar{t} ZZ$, $t\bar{t} WH$, $t\bar{t} HH$, $t\bar{t} tW$, and $t\bar{t}t\bar{t}$ backgrounds. The last bin captures the overflow events. The lower panel shows the ratio of the observed data to the expected SM background yield in each bin. Both the statistical and systematic uncertainties in the SM background are included in the shaded band.

The lepton flavour and multiplicities in events with two light leptons and two taus and one Z candidate. Distributions for data, the estimated SM backgrounds after the background-only fit, and an example SUSY scenario are shown. "Other" is the sum of the $tWZ$, $t\bar{t}WW$, $t\bar{t} ZZ$, $t\bar{t} WH$, $t\bar{t} HH$, $t\bar{t} tW$, and $t\bar{t}t\bar{t}$ backgrounds. The last bin captures the overflow events. The lower panel shows the ratio of the observed data to the expected SM background yield in each bin. Both the statistical and systematic uncertainties in the SM background are included in the shaded band.

Cutflow event yields in regions SR0$_{\mathrm{bveto}}^{\mathrm{loose}}$, SR0$_{\mathrm{bveto}}^{\mathrm{tight}}$, SR0$_{\mathrm{breq}}$, and SR5L for RPV models with the $\lambda_{12k}\neq 0$ coupling. All yields correspond to weighted events, so that effects from lepton reconstruction efficiencies, trigger corrections, pileup reweighting, etc., are included. They are normalized to the integrated luminosity of the data sample, $\int L dt = 139\,\mbox{fb\(^{-1}\)}$. The preliminary event reduction is a centralized stage where at least two electrons/muons with uncalibrated $p_{\mathrm{T}} >$ 9 GeV are required.

Cutflow event yields in regions SR1$_{\mathrm{bveto}}^{\mathrm{loose}}$, SR1$_{\mathrm{bveto}}^{\mathrm{tight}}$, and SR1$_{\mathrm{breq}}$ for RPV models with the $\lambda_{i33}\neq 0$ coupling. All yields correspond to weighted events, so that effects from lepton reconstruction efficiencies, trigger corrections, pileup reweighting, etc., are included. They are normalized to the integrated luminosity of the data sample, $\int L dt = 139\,\mbox{fb\(^{-1}\)}$. The preliminary event reduction is a centralized stage where at least two electrons/muons with uncalibrated $p_{\mathrm{T}} >$ 9 GeV are required.

Cutflow event yields in regions SR2$_{\mathrm{bveto}}^{\mathrm{loose}}$, SR2$_{\mathrm{bveto}}^{\mathrm{tight}}$, and SR2$_{\mathrm{breq}}$ for RPV models with the $\lambda_{i33}\neq 0$ coupling. All yields correspond to weighted events, so that effects from lepton reconstruction efficiencies, trigger corrections, pileup reweighting, etc., are included. They are normalized to the integrated luminosity of the data sample, $\int L dt = 139\,\mbox{fb\(^{-1}\)}$. The preliminary event reduction is a centralized stage where at least two electrons/muons with uncalibrated $p_{\mathrm{T}} >$ 9 GeV are required.

Cutflow event yields in regions SR0-ZZ$^{\mathrm{loose}}$, SR0-ZZ$^{\mathrm{tight}}$, SR0-ZZ$_{\mathrm{bveto}}^{\mathrm{loose}}$, SR0-ZZ$_{\mathrm{bveto}}^{\mathrm{tight}}$, and SR5L the higgsino GGM RPC model with BR($\tilde{\chi}^{0}_1 \rightarrow Z \tilde{G}$) = 50% and higgsino masses of 200 GeV, or BR($\tilde{\chi}^{0}_1 \rightarrow Z \tilde{G}$) = 100% and higgsino masses of 300 GeV. All yields correspond to weighted events, so that effects from lepton reconstruction efficiencies, trigger corrections, pileup reweighting, etc., are included. They are normalized to the integrated luminosity of the data sample, $\int L dt = 139\,\mbox{fb\(^{-1}\)}$. The generator filter is a selection of $\geq$4e/$\mu$/$\tau_{\mathrm{had-vis}}$ leptons with $p_{\mathrm{T}}(e,\mu)>4$GeV, $p_{\mathrm{T}}(\tau_{\mathrm{had-vis}})>15$GeV and $|\eta|<2.8$ and is applied during the MC generation of the simulated events. The preliminary event reduction is a centralized stage where at least two electrons/muons with uncalibrated $p_{\mathrm{T}} > 9$ GeV are required.

Summary of the total efficiencies. Quoted uncertainties correspond to statistical uncertainties of the simulated samples used. For the $B_c^+\to J/\psi \pi^+$ channel, the efficiency $\epsilon_{B_c^+\to J/\psi \pi^+}$ entering the equations for $R_{D_s^{(*)+}/\pi^+}$ is shown, while the efficiency for the full dataset is not defined.

The BDT distribution of the di-Higgs ggF signal for two different values of $\kappa_{\lambda}$ and the main backgrounds in the low mass region ($m^{*}_{b\bar{b}\gamma\gamma} < 350$ GeV). Distributions are normalized to unit area. The dotted lines denote the category boundaries. Events with a BDT score below 0.881 in the low mass region are discarded.

The BDT distribution (with x-axis zoomed in) of the di-Higgs ggF signal for two different values of $\kappa_{\lambda}$ and the main backgrounds in the low mass region ($m^{*}_{b\bar{b}\gamma\gamma} < 350$ GeV). Distributions are normalized to unit area. The dotted lines denote the category boundaries. Events with a BDT score below 0.881 in the low mass region are discarded. The range of BDT scores is from 0.8 to 1.

The BDT distribution (with x-axis zoomed in) of the di-Higgs ggF signal for two different values of $\kappa_{\lambda}$ and the main backgrounds in the low mass region ($m^{*}_{b\bar{b}\gamma\gamma} < 350$ GeV). Distributions are normalized to unit area. The dotted lines denote the category boundaries. Events with a BDT score below 0.881 in the low mass region are discarded. The range of BDT scores is from 0.8 to 1.

The BDT distribution (with x-axis zoomed in) of the di-Higgs ggF signal for two different values of $\kappa_{\lambda}$ and the main backgrounds in the low mass region ($m^{*}_{b\bar{b}\gamma\gamma} < 350$ GeV). Distributions are normalized to unit area. The dotted lines denote the category boundaries. Events with a BDT score below 0.881 in the low mass region are discarded. The range of BDT scores is from 0.8 to 1.

The BDT distribution (with x-axis zoomed in) of the di-Higgs ggF signal for two different values of $\kappa_{\lambda}$ and the main backgrounds in the low mass region ($m^{*}_{b\bar{b}\gamma\gamma} < 350$ GeV). Distributions are normalized to unit area. The dotted lines denote the category boundaries. Events with a BDT score below 0.881 in the low mass region are discarded. The range of BDT scores is from 0.8 to 1.

The BDT distribution of the di-Higgs ggF signal for two different values of $\kappa_{\lambda}$ and the main backgrounds in the high mass region ($m^{*}_{b\bar{b}\gamma\gamma} > 350$ GeV). Distributions are normalized to unit area. The dotted lines denote the category boundaries. Events with a BDT score below 0.857 in the high mass region are discarded.

The BDT distribution of the di-Higgs ggF signal for two different values of $\kappa_{\lambda}$ and the main backgrounds in the high mass region ($m^{*}_{b\bar{b}\gamma\gamma} > 350$ GeV). Distributions are normalized to unit area. The dotted lines denote the category boundaries. Events with a BDT score below 0.857 in the high mass region are discarded.

The BDT distribution of the di-Higgs ggF signal for two different values of $\kappa_{\lambda}$ and the main backgrounds in the high mass region ($m^{*}_{b\bar{b}\gamma\gamma} > 350$ GeV). Distributions are normalized to unit area. The dotted lines denote the category boundaries. Events with a BDT score below 0.857 in the high mass region are discarded.

The BDT distribution of the di-Higgs ggF signal for two different values of $\kappa_{\lambda}$ and the main backgrounds in the high mass region ($m^{*}_{b\bar{b}\gamma\gamma} > 350$ GeV). Distributions are normalized to unit area. The dotted lines denote the category boundaries. Events with a BDT score below 0.857 in the high mass region are discarded.

The BDT distribution (with x-axis zoomed in) of the di-Higgs ggF signal for two different values of $\kappa_{\lambda}$ and the main backgrounds in the high mass region ($m^{*}_{b\bar{b}\gamma\gamma} > 350$ GeV). Distributions are normalized to unit area. The dotted lines denote the category boundaries. Events with a BDT score below 0.857 in the high mass region are discarded. The range of BDT scores is from 0.8 to 1.

The BDT distribution (with x-axis zoomed in) of the di-Higgs ggF signal for two different values of $\kappa_{\lambda}$ and the main backgrounds in the high mass region ($m^{*}_{b\bar{b}\gamma\gamma} > 350$ GeV). Distributions are normalized to unit area. The dotted lines denote the category boundaries. Events with a BDT score below 0.857 in the high mass region are discarded. The range of BDT scores is from 0.8 to 1.

The BDT distribution (with x-axis zoomed in) of the di-Higgs ggF signal for two different values of $\kappa_{\lambda}$ and the main backgrounds in the high mass region ($m^{*}_{b\bar{b}\gamma\gamma} > 350$ GeV). Distributions are normalized to unit area. The dotted lines denote the category boundaries. Events with a BDT score below 0.857 in the high mass region are discarded. The range of BDT scores is from 0.8 to 1.

The BDT distribution (with x-axis zoomed in) of the di-Higgs ggF signal for two different values of $\kappa_{\lambda}$ and the main backgrounds in the high mass region ($m^{*}_{b\bar{b}\gamma\gamma} > 350$ GeV). Distributions are normalized to unit area. The dotted lines denote the category boundaries. Events with a BDT score below 0.857 in the high mass region are discarded. The range of BDT scores is from 0.8 to 1.

The $BDT_{tot}$ score for the benchmark signal $m_{X}$ = 300 GeV and for the main backgrounds. Distributions are normalized to unit area. The dotted line denotes the event selection threshold. Events with a $BDT_{tot}$ score below 0.85 for $m_{X}$ = 300 GeV are discarded.

The $BDT_{tot}$ score for the benchmark signal $m_{X}$ = 300 GeV and for the main backgrounds. Distributions are normalized to unit area. The dotted line denotes the event selection threshold. Events with a $BDT_{tot}$ score below 0.85 for $m_{X}$ = 300 GeV are discarded.

The $BDT_{tot}$ score for the benchmark signal $m_{X}$ = 300 GeV and for the main backgrounds. Distributions are normalized to unit area. The dotted line denotes the event selection threshold. Events with a $BDT_{tot}$ score below 0.85 for $m_{X}$ = 300 GeV are discarded.

The $BDT_{tot}$ score for the benchmark signal $m_{X}$ = 300 GeV and for the main backgrounds. Distributions are normalized to unit area. The dotted line denotes the event selection threshold. Events with a $BDT_{tot}$ score below 0.85 for $m_{X}$ = 300 GeV are discarded.

The $BDT_{tot}$ score for the benchmark signal $m_{X}$ = 500 GeV and for the main backgrounds. Distributions are normalized to unit area. The dotted line denotes the event selection threshold. Events with a $BDT_{tot}$ score below 0.75 for $m_{X}$ = 500 GeV are discarded.

The $BDT_{tot}$ score for the benchmark signal $m_{X}$ = 500 GeV and for the main backgrounds. Distributions are normalized to unit area. The dotted line denotes the event selection threshold. Events with a $BDT_{tot}$ score below 0.75 for $m_{X}$ = 500 GeV are discarded.

The $BDT_{tot}$ score for the benchmark signal $m_{X}$ = 500 GeV and for the main backgrounds. Distributions are normalized to unit area. The dotted line denotes the event selection threshold. Events with a $BDT_{tot}$ score below 0.75 for $m_{X}$ = 500 GeV are discarded.

The $BDT_{tot}$ score for the benchmark signal $m_{X}$ = 500 GeV and for the main backgrounds. Distributions are normalized to unit area. The dotted line denotes the event selection threshold. Events with a $BDT_{tot}$ score below 0.75 for $m_{X}$ = 500 GeV are discarded.

Distributions of $m_{\gamma\gamma}$ in high mass BDT tight category for the nonresonant $HH$ search. The data-derived fractions of nonresonant $\gamma\gamma$, $\gamma$-jet or jet-$\gamma$, and dijet background are applied and the total background is normalized to the data sideband.

Distributions of $m_{\gamma\gamma}$ in high mass BDT tight category for the nonresonant $HH$ search. The data-derived fractions of nonresonant $\gamma\gamma$, $\gamma$-jet or jet-$\gamma$, and dijet background are applied and the total background is normalized to the data sideband.

Distributions of $m_{\gamma\gamma}$ in high mass BDT tight category for the nonresonant $HH$ search. The data-derived fractions of nonresonant $\gamma\gamma$, $\gamma$-jet or jet-$\gamma$, and dijet background are applied and the total background is normalized to the data sideband.

Distributions of $m_{\gamma\gamma}$ in high mass BDT tight category for the nonresonant $HH$ search. The data-derived fractions of nonresonant $\gamma\gamma$, $\gamma$-jet or jet-$\gamma$, and dijet background are applied and the total background is normalized to the data sideband.

Distributions of $m_{\gamma\gamma}$ in high mass BDT loose category for the nonresonant $HH$ search. The data-derived fractions of nonresonant $\gamma\gamma$, $\gamma$-jet or jet-$\gamma$, and dijet background are applied and the total background is normalized to the data sideband.

Distributions of $m_{\gamma\gamma}$ in high mass BDT loose category for the nonresonant $HH$ search. The data-derived fractions of nonresonant $\gamma\gamma$, $\gamma$-jet or jet-$\gamma$, and dijet background are applied and the total background is normalized to the data sideband.

Distributions of $m_{\gamma\gamma}$ in high mass BDT loose category for the nonresonant $HH$ search. The data-derived fractions of nonresonant $\gamma\gamma$, $\gamma$-jet or jet-$\gamma$, and dijet background are applied and the total background is normalized to the data sideband.

Distributions of $m_{\gamma\gamma}$ in high mass BDT loose category for the nonresonant $HH$ search. The data-derived fractions of nonresonant $\gamma\gamma$, $\gamma$-jet or jet-$\gamma$, and dijet background are applied and the total background is normalized to the data sideband.

Distributions of $m_{\gamma\gamma}$ in low mass BDT tight category for the nonresonant $HH$ search. The data-derived fractions of nonresonant $\gamma\gamma$, $\gamma$-jet or jet-$\gamma$, and dijet background are applied and the total background is normalized to the data sideband.

Distributions of $m_{\gamma\gamma}$ in low mass BDT tight category for the nonresonant $HH$ search. The data-derived fractions of nonresonant $\gamma\gamma$, $\gamma$-jet or jet-$\gamma$, and dijet background are applied and the total background is normalized to the data sideband.

Distributions of $m_{\gamma\gamma}$ in low mass BDT tight category for the nonresonant $HH$ search. The data-derived fractions of nonresonant $\gamma\gamma$, $\gamma$-jet or jet-$\gamma$, and dijet background are applied and the total background is normalized to the data sideband.

Distributions of $m_{\gamma\gamma}$ in low mass BDT tight category for the nonresonant $HH$ search. The data-derived fractions of nonresonant $\gamma\gamma$, $\gamma$-jet or jet-$\gamma$, and dijet background are applied and the total background is normalized to the data sideband.

Distributions of $m_{\gamma\gamma}$ in low mass BDT loose category for the nonresonant $HH$ search. The data-derived fractions of nonresonant $\gamma\gamma$, $\gamma$-jet or jet-$\gamma$, and dijet background are applied and the total background is normalized to the data sideband.

Distributions of $m_{\gamma\gamma}$ in low mass BDT loose category for the nonresonant $HH$ search. The data-derived fractions of nonresonant $\gamma\gamma$, $\gamma$-jet or jet-$\gamma$, and dijet background are applied and the total background is normalized to the data sideband.

Distributions of $m_{\gamma\gamma}$ in low mass BDT loose category for the nonresonant $HH$ search. The data-derived fractions of nonresonant $\gamma\gamma$, $\gamma$-jet or jet-$\gamma$, and dijet background are applied and the total background is normalized to the data sideband.

Distributions of $m_{\gamma\gamma}$ in low mass BDT loose category for the nonresonant $HH$ search. The data-derived fractions of nonresonant $\gamma\gamma$, $\gamma$-jet or jet-$\gamma$, and dijet background are applied and the total background is normalized to the data sideband.

Distributions of $m_{\gamma\gamma}$ for the selections used for the resonance mass point $m_{X}$ = 300 GeV for the resonant search. The data-derived fractions of nonresonant $\gamma\gamma$, $\gamma$-jet or jet-$\gamma$, and dijet background are applied and the total background is normalized to the data sideband. The scalar resonance signal is scaled to a total production cross section $\sigma(pp \rightarrow X \rightarrow HH)$ = 370 fb.

Distributions of $m_{\gamma\gamma}$ for the selections used for the resonance mass point $m_{X}$ = 300 GeV for the resonant search. The data-derived fractions of nonresonant $\gamma\gamma$, $\gamma$-jet or jet-$\gamma$, and dijet background are applied and the total background is normalized to the data sideband. The scalar resonance signal is scaled to a total production cross section $\sigma(pp \rightarrow X \rightarrow HH)$ = 370 fb.

Distributions of $m_{\gamma\gamma}$ for the selections used for the resonance mass point $m_{X}$ = 300 GeV for the resonant search. The data-derived fractions of nonresonant $\gamma\gamma$, $\gamma$-jet or jet-$\gamma$, and dijet background are applied and the total background is normalized to the data sideband. The scalar resonance signal is scaled to a total production cross section $\sigma(pp \rightarrow X \rightarrow HH)$ = 370 fb.

Distributions of $m_{\gamma\gamma}$ for the selections used for the resonance mass point $m_{X}$ = 300 GeV for the resonant search. The data-derived fractions of nonresonant $\gamma\gamma$, $\gamma$-jet or jet-$\gamma$, and dijet background are applied and the total background is normalized to the data sideband. The scalar resonance signal is scaled to a total production cross section $\sigma(pp \rightarrow X \rightarrow HH)$ = 370 fb.

Distributions of $m_{\gamma\gamma}$ for the selections used for the resonance mass point $m_{X}$ = 500 GeV for the resonant search. The data-derived fractions of nonresonant $\gamma\gamma$, $\gamma$-jet or jet-$\gamma$, and dijet background are applied and the total background is normalized to the data sideband. The scalar resonance signal is scaled to a total production cross section $\sigma(pp \rightarrow X \rightarrow HH)$ = 67 fb.

Distributions of $m_{\gamma\gamma}$ for the selections used for the resonance mass point $m_{X}$ = 500 GeV for the resonant search. The data-derived fractions of nonresonant $\gamma\gamma$, $\gamma$-jet or jet-$\gamma$, and dijet background are applied and the total background is normalized to the data sideband. The scalar resonance signal is scaled to a total production cross section $\sigma(pp \rightarrow X \rightarrow HH)$ = 67 fb.

Distributions of $m_{\gamma\gamma}$ for the selections used for the resonance mass point $m_{X}$ = 500 GeV for the resonant search. The data-derived fractions of nonresonant $\gamma\gamma$, $\gamma$-jet or jet-$\gamma$, and dijet background are applied and the total background is normalized to the data sideband. The scalar resonance signal is scaled to a total production cross section $\sigma(pp \rightarrow X \rightarrow HH)$ = 67 fb.

Distributions of $m_{\gamma\gamma}$ for the selections used for the resonance mass point $m_{X}$ = 500 GeV for the resonant search. The data-derived fractions of nonresonant $\gamma\gamma$, $\gamma$-jet or jet-$\gamma$, and dijet background are applied and the total background is normalized to the data sideband. The scalar resonance signal is scaled to a total production cross section $\sigma(pp \rightarrow X \rightarrow HH)$ = 67 fb.

The number of data events observed in the 120 GeV < $m_{\gamma\gamma}$ < 130 GeV window, the number of $HH$ signal events expected for $\kappa_{\lambda}$ = 1 and for $\kappa_{\lambda}$ = 10, and events expected for single Higgs boson production (estimated using MC simulation), as well as for continuum background. For the single Higgs boson, Rest includes VBF, $WH$, $tHqb$, and $tHW$. The values are obtained from a fit of the Asimov data set generated under the SM signal-plus-background hypothesis, $\kappa_{\lambda}$ = 1. The continuum background component of the Asimov data set is obtained from the fit of the data sideband. The uncertainties in $HH$ signals and single Higgs boson background include the systematic uncertainties discussed in Section 6. The uncertainty in the continuum background is given by the sum in quadrature of the statistical uncertainty from the fit to the data and the spurious-signal uncertainty.

The number of data events observed in the 120 GeV < $m_{\gamma\gamma}$ < 130 GeV window, the number of $HH$ signal events expected for $\kappa_{\lambda}$ = 1 and for $\kappa_{\lambda}$ = 10, and events expected for single Higgs boson production (estimated using MC simulation), as well as for continuum background. For the single Higgs boson, Rest includes VBF, $WH$, $tHqb$, and $tHW$. The values are obtained from a fit of the Asimov data set generated under the SM signal-plus-background hypothesis, $\kappa_{\lambda}$ = 1. The continuum background component of the Asimov data set is obtained from the fit of the data sideband. The uncertainties in $HH$ signals and single Higgs boson background include the systematic uncertainties discussed in Section 6. The uncertainty in the continuum background is given by the sum in quadrature of the statistical uncertainty from the fit to the data and the spurious-signal uncertainty.

The number of data events observed in the 120 GeV < $m_{\gamma\gamma}$ < 130 GeV window, the number of $HH$ signal events expected for $\kappa_{\lambda}$ = 1 and for $\kappa_{\lambda}$ = 10, and events expected for single Higgs boson production (estimated using MC simulation), as well as for continuum background. For the single Higgs boson, Rest includes VBF, $WH$, $tHqb$, and $tHW$. The values are obtained from a fit of the Asimov data set generated under the SM signal-plus-background hypothesis, $\kappa_{\lambda}$ = 1. The continuum background component of the Asimov data set is obtained from the fit of the data sideband. The uncertainties in $HH$ signals and single Higgs boson background include the systematic uncertainties discussed in Section 6. The uncertainty in the continuum background is given by the sum in quadrature of the statistical uncertainty from the fit to the data and the spurious-signal uncertainty.

The number of data events observed in the 120 GeV < $m_{\gamma\gamma}$ < 130 GeV window, the number of $HH$ signal events expected for $\kappa_{\lambda}$ = 1 and for $\kappa_{\lambda}$ = 10, and events expected for single Higgs boson production (estimated using MC simulation), as well as for continuum background. For the single Higgs boson, Rest includes VBF, $WH$, $tHqb$, and $tHW$. The values are obtained from a fit of the Asimov data set generated under the SM signal-plus-background hypothesis, $\kappa_{\lambda}$ = 1. The continuum background component of the Asimov data set is obtained from the fit of the data sideband. The uncertainties in $HH$ signals and single Higgs boson background include the systematic uncertainties discussed in Section 6. The uncertainty in the continuum background is given by the sum in quadrature of the statistical uncertainty from the fit to the data and the spurious-signal uncertainty.

Observed and expected limits at 95% CL on the cross section of nonresonant Higgs boson pair production as a function of the Higgs boson self-coupling modifier $\kappa_{\lambda}= \lambda_{HHH}/\lambda^{\textrm{SM}}_{HHH}$. The expected constraints on $\kappa_{\lambda}$ are obtained with a background hypothesis excluding $pp \rightarrow HH$ production. The $\pm 1\sigma$ and $\pm 2\sigma$ variations about the expected limit due to statistical and systematic uncertainties are also shown. The theory prediction curve represents the scenario where all parameters and couplings are set to their SM values except for $\kappa_{\lambda}$. The uncertainty band of the theory prediction curve shows the cross-section uncertainty.

Observed and expected limits at 95% CL on the cross section of nonresonant Higgs boson pair production as a function of the Higgs boson self-coupling modifier $\kappa_{\lambda}= \lambda_{HHH}/\lambda^{\textrm{SM}}_{HHH}$. The expected constraints on $\kappa_{\lambda}$ are obtained with a background hypothesis excluding $pp \rightarrow HH$ production. The $\pm 1\sigma$ and $\pm 2\sigma$ variations about the expected limit due to statistical and systematic uncertainties are also shown. The theory prediction curve represents the scenario where all parameters and couplings are set to their SM values except for $\kappa_{\lambda}$. The uncertainty band of the theory prediction curve shows the cross-section uncertainty.

Observed and expected limits at 95% CL on the cross section of nonresonant Higgs boson pair production as a function of the Higgs boson self-coupling modifier $\kappa_{\lambda}= \lambda_{HHH}/\lambda^{\textrm{SM}}_{HHH}$. The expected constraints on $\kappa_{\lambda}$ are obtained with a background hypothesis excluding $pp \rightarrow HH$ production. The $\pm 1\sigma$ and $\pm 2\sigma$ variations about the expected limit due to statistical and systematic uncertainties are also shown. The theory prediction curve represents the scenario where all parameters and couplings are set to their SM values except for $\kappa_{\lambda}$. The uncertainty band of the theory prediction curve shows the cross-section uncertainty.

Observed and expected limits at 95% CL on the cross section of nonresonant Higgs boson pair production as a function of the Higgs boson self-coupling modifier $\kappa_{\lambda}= \lambda_{HHH}/\lambda^{\textrm{SM}}_{HHH}$. The expected constraints on $\kappa_{\lambda}$ are obtained with a background hypothesis excluding $pp \rightarrow HH$ production. The $\pm 1\sigma$ and $\pm 2\sigma$ variations about the expected limit due to statistical and systematic uncertainties are also shown. The theory prediction curve represents the scenario where all parameters and couplings are set to their SM values except for $\kappa_{\lambda}$. The uncertainty band of the theory prediction curve shows the cross-section uncertainty.

Values of the negative log-profile-likelihood ratio ($-2ln\Lambda$) as a function of $\kappa_{\lambda}$ evaluated for the combination of all the categories of the nonresonant search. The coupling of the Higgs boson to fermions and gauge bosons is set to SM values in the profile likelihood calculation. The Asimov data set is generated under the SM signal-plus-background hypothesis, $\kappa_{\lambda}$= 1. All systematic uncertainties, including the theoretical uncertainties in the di-Higgs boson production cross section, are included. The intersections of the solid curves and the horizontal dashed lines indicate the 1$\sigma$ and 2$\sigma$ confidence-level intervals.

Values of the negative log-profile-likelihood ratio ($-2ln\Lambda$) as a function of $\kappa_{\lambda}$ evaluated for the combination of all the categories of the nonresonant search. The coupling of the Higgs boson to fermions and gauge bosons is set to SM values in the profile likelihood calculation. The Asimov data set is generated under the SM signal-plus-background hypothesis, $\kappa_{\lambda}$= 1. All systematic uncertainties, including the theoretical uncertainties in the di-Higgs boson production cross section, are included. The intersections of the solid curves and the horizontal dashed lines indicate the 1$\sigma$ and 2$\sigma$ confidence-level intervals.

Values of the negative log-profile-likelihood ratio ($-2ln\Lambda$) as a function of $\kappa_{\lambda}$ evaluated for the combination of all the categories of the nonresonant search. The coupling of the Higgs boson to fermions and gauge bosons is set to SM values in the profile likelihood calculation. The Asimov data set is generated under the SM signal-plus-background hypothesis, $\kappa_{\lambda}$= 1. All systematic uncertainties, including the theoretical uncertainties in the di-Higgs boson production cross section, are included. The intersections of the solid curves and the horizontal dashed lines indicate the 1$\sigma$ and 2$\sigma$ confidence-level intervals.

Values of the negative log-profile-likelihood ratio ($-2ln\Lambda$) as a function of $\kappa_{\lambda}$ evaluated for the combination of all the categories of the nonresonant search. The coupling of the Higgs boson to fermions and gauge bosons is set to SM values in the profile likelihood calculation. The Asimov data set is generated under the SM signal-plus-background hypothesis, $\kappa_{\lambda}$= 1. All systematic uncertainties, including the theoretical uncertainties in the di-Higgs boson production cross section, are included. The intersections of the solid curves and the horizontal dashed lines indicate the 1$\sigma$ and 2$\sigma$ confidence-level intervals.

The number of events observed in the 120 < $m_{\gamma\gamma}$ < 130 GeV window in data, the number of events expected for scalar resonance signals of masses $m_{X}$ = 300 GeV and $m_{X}$ = 500 GeV assuming a total production cross section $\sigma(pp \rightarrow X \rightarrow HH)$ equal to the observed exclusion limits of Figure 15, and events expected for SM $HH$ and single Higgs boson production (estimated using MC simulation), as well as for continuum background. The values are obtained from a fit of the Asimov data set generated under the signal-plus-background hypothesis. The continuum background component of the Asimov data set is obtained from the fit of the data sideband. The uncertainties in the resonant signals and the SM $HH$ and single-Higgs-boson backgrounds include the systematic uncertainties discussed in Section 6. The uncertainty in the continuum background is given by the sum in quadrature of the statistical uncertainty from the fit to the data and the spurious-signal uncertainty.

The number of events observed in the 120 < $m_{\gamma\gamma}$ < 130 GeV window in data, the number of events expected for scalar resonance signals of masses $m_{X}$ = 300 GeV and $m_{X}$ = 500 GeV assuming a total production cross section $\sigma(pp \rightarrow X \rightarrow HH)$ equal to the observed exclusion limits of Figure 15, and events expected for SM $HH$ and single Higgs boson production (estimated using MC simulation), as well as for continuum background. The values are obtained from a fit of the Asimov data set generated under the signal-plus-background hypothesis. The continuum background component of the Asimov data set is obtained from the fit of the data sideband. The uncertainties in the resonant signals and the SM $HH$ and single-Higgs-boson backgrounds include the systematic uncertainties discussed in Section 6. The uncertainty in the continuum background is given by the sum in quadrature of the statistical uncertainty from the fit to the data and the spurious-signal uncertainty.

The number of events observed in the 120 < $m_{\gamma\gamma}$ < 130 GeV window in data, the number of events expected for scalar resonance signals of masses $m_{X}$ = 300 GeV and $m_{X}$ = 500 GeV assuming a total production cross section $\sigma(pp \rightarrow X \rightarrow HH)$ equal to the observed exclusion limits of Figure 15, and events expected for SM $HH$ and single Higgs boson production (estimated using MC simulation), as well as for continuum background. The values are obtained from a fit of the Asimov data set generated under the signal-plus-background hypothesis. The continuum background component of the Asimov data set is obtained from the fit of the data sideband. The uncertainties in the resonant signals and the SM $HH$ and single-Higgs-boson backgrounds include the systematic uncertainties discussed in Section 6. The uncertainty in the continuum background is given by the sum in quadrature of the statistical uncertainty from the fit to the data and the spurious-signal uncertainty.

The number of events observed in the 120 < $m_{\gamma\gamma}$ < 130 GeV window in data, the number of events expected for scalar resonance signals of masses $m_{X}$ = 300 GeV and $m_{X}$ = 500 GeV assuming a total production cross section $\sigma(pp \rightarrow X \rightarrow HH)$ equal to the observed exclusion limits of Figure 15, and events expected for SM $HH$ and single Higgs boson production (estimated using MC simulation), as well as for continuum background. The values are obtained from a fit of the Asimov data set generated under the signal-plus-background hypothesis. The continuum background component of the Asimov data set is obtained from the fit of the data sideband. The uncertainties in the resonant signals and the SM $HH$ and single-Higgs-boson backgrounds include the systematic uncertainties discussed in Section 6. The uncertainty in the continuum background is given by the sum in quadrature of the statistical uncertainty from the fit to the data and the spurious-signal uncertainty.

Observed and expected limits at 95% CL on the production cross section of a narrow-width scalar resonance $X$ as a function of the mass $m_{X}$ of the hypothetical scalar particle. The black solid line represents the observed upper limits. The dashed line represents the expected upper limits. The $\pm 1\sigma$ and $\pm 2\sigma$ variations about the expected limit due to statistical and systematic uncertainties are also shown.

Observed and expected limits at 95% CL on the production cross section of a narrow-width scalar resonance $X$ as a function of the mass $m_{X}$ of the hypothetical scalar particle. The black solid line represents the observed upper limits. The dashed line represents the expected upper limits. The $\pm 1\sigma$ and $\pm 2\sigma$ variations about the expected limit due to statistical and systematic uncertainties are also shown.

Observed and expected limits at 95% CL on the production cross section of a narrow-width scalar resonance $X$ as a function of the mass $m_{X}$ of the hypothetical scalar particle. The black solid line represents the observed upper limits. The dashed line represents the expected upper limits. The $\pm 1\sigma$ and $\pm 2\sigma$ variations about the expected limit due to statistical and systematic uncertainties are also shown.

Observed and expected limits at 95% CL on the production cross section of a narrow-width scalar resonance $X$ as a function of the mass $m_{X}$ of the hypothetical scalar particle. The black solid line represents the observed upper limits. The dashed line represents the expected upper limits. The $\pm 1\sigma$ and $\pm 2\sigma$ variations about the expected limit due to statistical and systematic uncertainties are also shown.

Breakdown of the dominant systematic uncertainties. The impact of the uncertainties is defined according to the statistical analysis described in Section 7. It corresponds to the relative variation of the expected upper limit on the cross section when re-evaluating the profile likelihood ratio after fixing the nuisance parameter in question to its best-fit value, while all remaining nuisance parameters remain free to float. The impact is shown in %. Only systematic uncertainties with an impact of at least 0.2% are shown. Uncertainties of the "Norm. + Shape" type affect both the normalization and the parameters of the functional form. The rest of the uncertainties affect only the yields.

Breakdown of the dominant systematic uncertainties. The impact of the uncertainties is defined according to the statistical analysis described in Section 7. It corresponds to the relative variation of the expected upper limit on the cross section when re-evaluating the profile likelihood ratio after fixing the nuisance parameter in question to its best-fit value, while all remaining nuisance parameters remain free to float. The impact is shown in %. Only systematic uncertainties with an impact of at least 0.2% are shown. Uncertainties of the "Norm. + Shape" type affect both the normalization and the parameters of the functional form. The rest of the uncertainties affect only the yields.

Breakdown of the dominant systematic uncertainties. The impact of the uncertainties is defined according to the statistical analysis described in Section 7. It corresponds to the relative variation of the expected upper limit on the cross section when re-evaluating the profile likelihood ratio after fixing the nuisance parameter in question to its best-fit value, while all remaining nuisance parameters remain free to float. The impact is shown in %. Only systematic uncertainties with an impact of at least 0.2% are shown. Uncertainties of the "Norm. + Shape" type affect both the normalization and the parameters of the functional form. The rest of the uncertainties affect only the yields.

Breakdown of the dominant systematic uncertainties. The impact of the uncertainties is defined according to the statistical analysis described in Section 7. It corresponds to the relative variation of the expected upper limit on the cross section when re-evaluating the profile likelihood ratio after fixing the nuisance parameter in question to its best-fit value, while all remaining nuisance parameters remain free to float. The impact is shown in %. Only systematic uncertainties with an impact of at least 0.2% are shown. Uncertainties of the "Norm. + Shape" type affect both the normalization and the parameters of the functional form. The rest of the uncertainties affect only the yields.

Cutflow for nonresonant di-Higgs ggF signal sample, yields are normalized to 139 $fb^{-1}$.

Cutflow for nonresonant di-Higgs ggF signal sample, yields are normalized to 139 $fb^{-1}$.

Cutflow for nonresonant di-Higgs ggF signal sample, yields are normalized to 139 $fb^{-1}$.

Cutflow for nonresonant di-Higgs ggF signal sample, yields are normalized to 139 $fb^{-1}$.

Cutflow for resonant signal sample, with $m_{X}$ = 300 GeV, yields are normalized to 139 $fb^{-1}$.

Cutflow for resonant signal sample, with $m_{X}$ = 300 GeV, yields are normalized to 139 $fb^{-1}$.

Cutflow for resonant signal sample, with $m_{X}$ = 300 GeV, yields are normalized to 139 $fb^{-1}$.

Cutflow for resonant signal sample, with $m_{X}$ = 300 GeV, yields are normalized to 139 $fb^{-1}$.

Cutflow for resonant signal sample, with $m_{X}$ = 500 GeV, yields are normalized to 139 $fb^{-1}$.

Cutflow for resonant signal sample, with $m_{X}$ = 500 GeV, yields are normalized to 139 $fb^{-1}$.

Cutflow for resonant signal sample, with $m_{X}$ = 500 GeV, yields are normalized to 139 $fb^{-1}$.

Cutflow for resonant signal sample, with $m_{X}$ = 500 GeV, yields are normalized to 139 $fb^{-1}$.

Comparison of $m_{b\bar{b}}$ distributions when applying the specific b-jet energy calibration and the nominal jet energy calibration. The distributions are fitted using a Bukin function, and the values of the peak position, resolution and the relative improvement are reported in the legend.

Comparison of $m_{b\bar{b}}$ distributions when applying the specific b-jet energy calibration and the nominal jet energy calibration. The distributions are fitted using a Bukin function, and the values of the peak position, resolution and the relative improvement are reported in the legend.

Comparison of $m_{b\bar{b}}$ distributions when applying the specific b-jet energy calibration and the nominal jet energy calibration. The distributions are fitted using a Bukin function, and the values of the peak position, resolution and the relative improvement are reported in the legend.

Comparison of $m_{b\bar{b}}$ distributions when applying the specific b-jet energy calibration and the nominal jet energy calibration. The distributions are fitted using a Bukin function, and the values of the peak position, resolution and the relative improvement are reported in the legend.

Fit results of $m_{b\bar{b}}$ distributions when applying the specific b-jet energy calibration and the nominal jet energy calibration. The distributions are fitted using a Bukin function, and the values of the peak position, resolution and the relative improvement are reported in the legend.

Fit results of $m_{b\bar{b}}$ distributions when applying the specific b-jet energy calibration and the nominal jet energy calibration. The distributions are fitted using a Bukin function, and the values of the peak position, resolution and the relative improvement are reported in the legend.

Fit results of $m_{b\bar{b}}$ distributions when applying the specific b-jet energy calibration and the nominal jet energy calibration. The distributions are fitted using a Bukin function, and the values of the peak position, resolution and the relative improvement are reported in the legend.

Fit results of $m_{b\bar{b}}$ distributions when applying the specific b-jet energy calibration and the nominal jet energy calibration. The distributions are fitted using a Bukin function, and the values of the peak position, resolution and the relative improvement are reported in the legend.

The relative amount (purity) of expected events from SM $HH$ and single Higgs boson production processes for each of the four categories of the nonresonant search. The Higgs boson pair production with $k_{\lambda} = 1$ is considered as signal in (a), while the case with $k_{\lambda} = 10$ is considered as signal in (b).

The relative amount (purity) of expected events from SM $HH$ and single Higgs boson production processes for each of the four categories of the nonresonant search. The Higgs boson pair production with $k_{\lambda} = 1$ is considered as signal in (a), while the case with $k_{\lambda} = 10$ is considered as signal in (b).

The relative amount (purity) of expected events from SM $HH$ and single Higgs boson production processes for each of the four categories of the nonresonant search. The Higgs boson pair production with $k_{\lambda} = 1$ is considered as signal in (a), while the case with $k_{\lambda} = 10$ is considered as signal in (b).

The relative amount (purity) of expected events from SM $HH$ and single Higgs boson production processes for each of the four categories of the nonresonant search. The Higgs boson pair production with $k_{\lambda} = 1$ is considered as signal in (a), while the case with $k_{\lambda} = 10$ is considered as signal in (b).

The expected significance in each of the four categories of the nonresonant search. The Higgs boson pair production with $k_{\lambda} = 1$ is considered as signal in (a), while the case with $k_{\lambda} = 10$ is considered as signal in (b). The single Higgs boson processes and the di-photon continuum spectrum are considered as background.

The expected significance in each of the four categories of the nonresonant search. The Higgs boson pair production with $k_{\lambda} = 1$ is considered as signal in (a), while the case with $k_{\lambda} = 10$ is considered as signal in (b). The single Higgs boson processes and the di-photon continuum spectrum are considered as background.

The expected significance in each of the four categories of the nonresonant search. The Higgs boson pair production with $k_{\lambda} = 1$ is considered as signal in (a), while the case with $k_{\lambda} = 10$ is considered as signal in (b). The single Higgs boson processes and the di-photon continuum spectrum are considered as background.

The expected significance in each of the four categories of the nonresonant search. The Higgs boson pair production with $k_{\lambda} = 1$ is considered as signal in (a), while the case with $k_{\lambda} = 10$ is considered as signal in (b). The single Higgs boson processes and the di-photon continuum spectrum are considered as background.

Spurious signal result for the exponential pdf for the various ggF nonresonant di-Higgs categories. In each category, the spurious signal value ($n_{sp}$) and its ratio to the expected statistical error ($Z_{spur}$) from data are shown.

Spurious signal result for the exponential pdf for the various ggF nonresonant di-Higgs categories. In each category, the spurious signal value ($n_{sp}$) and its ratio to the expected statistical error ($Z_{spur}$) from data are shown.

Spurious signal result for the exponential pdf for the various ggF nonresonant di-Higgs categories. In each category, the spurious signal value ($n_{sp}$) and its ratio to the expected statistical error ($Z_{spur}$) from data are shown.

Spurious signal result for the exponential pdf for the various ggF nonresonant di-Higgs categories. In each category, the spurious signal value ($n_{sp}$) and its ratio to the expected statistical error ($Z_{spur}$) from data are shown.

Spurious signal result for the exponential pdf as function of the resonant di-Higgs signal mass. The spurious signal value and its ratio to the expected statistical error from data are shown.

Spurious signal result for the exponential pdf as function of the resonant di-Higgs signal mass. The spurious signal value and its ratio to the expected statistical error from data are shown.

Spurious signal result for the exponential pdf as function of the resonant di-Higgs signal mass. The spurious signal value and its ratio to the expected statistical error from data are shown.

Spurious signal result for the exponential pdf as function of the resonant di-Higgs signal mass. The spurious signal value and its ratio to the expected statistical error from data are shown.

Distributions of the signal efficiency as a function of $\kappa_{\lambda}$, for the di-Higgs boson ggF nonresonant production mode. The range of $\kappa_{\lambda}$ in the table is from -10 to 10.

Distributions of the signal efficiency as a function of $\kappa_{\lambda}$, for the di-Higgs boson ggF nonresonant production mode. The range of $\kappa_{\lambda}$ in the table is from -10 to 10.

Distributions of the signal efficiency as a function of $\kappa_{\lambda}$, for the di-Higgs boson ggF nonresonant production mode. The range of $\kappa_{\lambda}$ in the table is from -10 to 10.

Distributions of the signal efficiency as a function of $\kappa_{\lambda}$, for the di-Higgs boson ggF nonresonant production mode. The range of $\kappa_{\lambda}$ in the table is from -10 to 10.

Distributions of the signal efficiency as a function of $\kappa_{\lambda}$, for the di-Higgs boson VBF nonresonant production mode. The range of $\kappa_{\lambda}$ in the table is from -10 to 10.

Distributions of the signal efficiency as a function of $\kappa_{\lambda}$, for the di-Higgs boson VBF nonresonant production mode. The range of $\kappa_{\lambda}$ in the table is from -10 to 10.

Distributions of the signal efficiency as a function of $\kappa_{\lambda}$, for the di-Higgs boson VBF nonresonant production mode. The range of $\kappa_{\lambda}$ in the table is from -10 to 10.

Distributions of the signal efficiency as a function of $\kappa_{\lambda}$, for the di-Higgs boson VBF nonresonant production mode. The range of $\kappa_{\lambda}$ in the table is from -10 to 10.

Values of the negative log-profile-likelihood ($-2ln\Lambda$) as a function of $\kappa_{\lambda}$ evaluated for the combination of all the categories of the nonresonant search. The coupling of the Higgs boson to fermions and gauge bosons is set to SM values in the profile likelihood calculation. The Asimov data set is generated under the SM signal-plus-background hypothesis, $\kappa_{\lambda}$= 1. All systematic uncertainties, including the theoretical uncertainties on the di-Higgs boson production cross section, are included. The intersections of the solid curves and the horizontal dashed lines indicate the 1$\sigma$ and 2$\sigma$ confidence level intervals. The best fit value corresponds to $\kappa_{\lambda}$ = $2.8^{+2.0}_{-2.2}(^{+3.8}_{-4.3})$ for the 1$\sigma$(2$\sigma$) confidence interval. The expected value corresponds to $\kappa_{\lambda}$ = $1.0^{+5.5}_{-2.4}(^{+7.3}_{-4.2})$ for the 1$\sigma$(2$\sigma$) confidence interval. The dashed curves represent values of the negative log-profile-likelihood where the Higgs boson branching fractions and the cross section of the production modes are varied as a function of $\kappa_{\lambda}$. In this case,the best fit value corresponds to $\kappa_{\lambda}$ = $2.7^{+2.0}_{-2.2}(^{+3.8}_{-4.3})$ and the expected value corresponds to $\kappa_{\lambda}$ = $1.0^{+5.4}_{-2.5}(^{+7.3}_{-4.3})$ for the 1$\sigma$(2$\sigma$) confidence interval.

Values of the negative log-profile-likelihood ($-2ln\Lambda$) as a function of $\kappa_{\lambda}$ evaluated for the combination of all the categories of the nonresonant search. The coupling of the Higgs boson to fermions and gauge bosons is set to SM values in the profile likelihood calculation. The Asimov data set is generated under the SM signal-plus-background hypothesis, $\kappa_{\lambda}$= 1. All systematic uncertainties, including the theoretical uncertainties on the di-Higgs boson production cross section, are included. The intersections of the solid curves and the horizontal dashed lines indicate the 1$\sigma$ and 2$\sigma$ confidence level intervals. The best fit value corresponds to $\kappa_{\lambda}$ = $2.8^{+2.0}_{-2.2}(^{+3.8}_{-4.3})$ for the 1$\sigma$(2$\sigma$) confidence interval. The expected value corresponds to $\kappa_{\lambda}$ = $1.0^{+5.5}_{-2.4}(^{+7.3}_{-4.2})$ for the 1$\sigma$(2$\sigma$) confidence interval. The dashed curves represent values of the negative log-profile-likelihood where the Higgs boson branching fractions and the cross section of the production modes are varied as a function of $\kappa_{\lambda}$. In this case,the best fit value corresponds to $\kappa_{\lambda}$ = $2.7^{+2.0}_{-2.2}(^{+3.8}_{-4.3})$ and the expected value corresponds to $\kappa_{\lambda}$ = $1.0^{+5.4}_{-2.5}(^{+7.3}_{-4.3})$ for the 1$\sigma$(2$\sigma$) confidence interval.

Values of the negative log-profile-likelihood ($-2ln\Lambda$) as a function of $\kappa_{\lambda}$ evaluated for the combination of all the categories of the nonresonant search. The coupling of the Higgs boson to fermions and gauge bosons is set to SM values in the profile likelihood calculation. The Asimov data set is generated under the SM signal-plus-background hypothesis, $\kappa_{\lambda}$= 1. All systematic uncertainties, including the theoretical uncertainties on the di-Higgs boson production cross section, are included. The intersections of the solid curves and the horizontal dashed lines indicate the 1$\sigma$ and 2$\sigma$ confidence level intervals. The best fit value corresponds to $\kappa_{\lambda}$ = $2.8^{+2.0}_{-2.2}(^{+3.8}_{-4.3})$ for the 1$\sigma$(2$\sigma$) confidence interval. The expected value corresponds to $\kappa_{\lambda}$ = $1.0^{+5.5}_{-2.4}(^{+7.3}_{-4.2})$ for the 1$\sigma$(2$\sigma$) confidence interval. The dashed curves represent values of the negative log-profile-likelihood where the Higgs boson branching fractions and the cross section of the production modes are varied as a function of $\kappa_{\lambda}$. In this case,the best fit value corresponds to $\kappa_{\lambda}$ = $2.7^{+2.0}_{-2.2}(^{+3.8}_{-4.3})$ and the expected value corresponds to $\kappa_{\lambda}$ = $1.0^{+5.4}_{-2.5}(^{+7.3}_{-4.3})$ for the 1$\sigma$(2$\sigma$) confidence interval.

Values of the negative log-profile-likelihood ($-2ln\Lambda$) as a function of $\kappa_{\lambda}$ evaluated for the combination of all the categories of the nonresonant search. The coupling of the Higgs boson to fermions and gauge bosons is set to SM values in the profile likelihood calculation. The Asimov data set is generated under the SM signal-plus-background hypothesis, $\kappa_{\lambda}$= 1. All systematic uncertainties, including the theoretical uncertainties on the di-Higgs boson production cross section, are included. The intersections of the solid curves and the horizontal dashed lines indicate the 1$\sigma$ and 2$\sigma$ confidence level intervals. The best fit value corresponds to $\kappa_{\lambda}$ = $2.8^{+2.0}_{-2.2}(^{+3.8}_{-4.3})$ for the 1$\sigma$(2$\sigma$) confidence interval. The expected value corresponds to $\kappa_{\lambda}$ = $1.0^{+5.5}_{-2.4}(^{+7.3}_{-4.2})$ for the 1$\sigma$(2$\sigma$) confidence interval. The dashed curves represent values of the negative log-profile-likelihood where the Higgs boson branching fractions and the cross section of the production modes are varied as a function of $\kappa_{\lambda}$. In this case,the best fit value corresponds to $\kappa_{\lambda}$ = $2.7^{+2.0}_{-2.2}(^{+3.8}_{-4.3})$ and the expected value corresponds to $\kappa_{\lambda}$ = $1.0^{+5.4}_{-2.5}(^{+7.3}_{-4.3})$ for the 1$\sigma$(2$\sigma$) confidence interval.

Minimum BDT value of the events passing the selection criteria of the resonant search. The combined BDT score is formed using as coefficients $C_{1}$ = 0.65 and $C_{2}$ = 1 − $C_{1}$. The selection efficiency for the resonant $X \rightarrow HH$ signal is also shown.

Minimum BDT value of the events passing the selection criteria of the resonant search. The combined BDT score is formed using as coefficients $C_{1}$ = 0.65 and $C_{2}$ = 1 − $C_{1}$. The selection efficiency for the resonant $X \rightarrow HH$ signal is also shown.

Minimum BDT value of the events passing the selection criteria of the resonant search. The combined BDT score is formed using as coefficients $C_{1}$ = 0.65 and $C_{2}$ = 1 − $C_{1}$. The selection efficiency for the resonant $X \rightarrow HH$ signal is also shown.

Minimum BDT value of the events passing the selection criteria of the resonant search. The combined BDT score is formed using as coefficients $C_{1}$ = 0.65 and $C_{2}$ = 1 − $C_{1}$. The selection efficiency for the resonant $X \rightarrow HH$ signal is also shown.

The number of data and fitted simulated events in each bin of the $|d_{0}^{\mu}|$ distribution in the $10<p_{\textrm{T}}^{\mu}<20$ GeV selection in the $\mu-\mu$ channel.

The number of data and fitted simulated events in each bin of the $|d_{0}^{\mu}|$ distribution in the $20<p_{\textrm{T}}^{\mu}<250$ GeV selection in the $e-\mu$ channel.

The number of data and fitted simulated events in each bin of the $|d_{0}^{\mu}|$ distribution in the $20<p_{\textrm{T}}^{\mu}<250$ GeV selection in the $\mu-\mu$ channel.

The measurement of the ratio of the rate of decay of W bosons to τ-leptons and muons, $R(\tau/\mu)=B(W\rightarrow\tau\nu_\tau)/B(W\rightarrow \mu\nu_\mu)$.

Distribution of the NN output in the $\geq$1fj$\,$SR in data and the expected contribution of the signal and background processes after the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions considering the correlations of the uncertainties as obtained by the fit.

Distribution of the NN output in the $t\bar{t}\gamma\,$CR in data and the expected contribution of the signal and background processes after the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions considering the correlations of the uncertainties as obtained by the fit.

Total event yield in the $W\gamma\,$CR in data and the expected contribution of the signal and background processes after the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions considering the correlations of the uncertainties as obtained by the fit.

Distribution of the scalar sum of the jet transverse momenta in the 0fj$\,$SR in data and for the sum of all processes expectations before the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions. The first and last bins include the underflow and overflow, respectively.

Distribution of the $\eta$ of the $b$-tagged jet in the 0fj$\,$SR in data and for the sum of all processes expectations before the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions.

Distribution of the reconstructed top-quark mass in the 0fj$\,$SR in data and for the sum of all processes expectations before the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions. The first and last bins include the underflow and overflow, respectively.

Distribution of the $p_{\mathrm{T}}$ of the top-quark+photon system in the 0fj$\,$SR in data and for the sum of all processes expectations before the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions and the last bin includes the overflow.

Distribution of the photon $p_{\mathrm{T}}$ in the 0fj$\,$SR in data and for the sum of all processes expectations before the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions and the last bin includes the overflow.

Distribution of the photon $\eta$ in the 0fj$\,$SR in data and for the sum of all processes expectations before the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions.

Distribution of the scalar sum of the jet transverse momenta in the $\geq$1fj$\,$SR in data and for the sum of all processes expectations before the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions and the last bin includes the overflow.

Distribution of the invariant mass of the $b$-tagged jet and the highest-$p_{\mathrm{T}}$ forward jet in the $\geq$1fj$\,$SR in data and for the sum of all processes expectations before the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions and the last bin includes the overflow.

Distribution of $p_{\mathrm{T}}$ of the highest-$p_{\mathrm{T}}$ forward jet in the $\geq$1fj$\,$SR in data and for the sum of all processes expectations before the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions and the last bin includes the overflow.

Distribution of the difference in $\eta$ between the highest-$p_{\mathrm{T}}$ forward jet and the photon in the $\geq$1fj$\,$SR in data and for the sum of all processes expectations before the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions and the last bin includes the overflow.

Distribution of the energy of the system formed by the highest-$p_{\mathrm{T}}$ forward jet and the photon in the $\geq$1fj$\,$SR in data and for the sum of all processes expectations before the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions. The first and last bins include the underflow and overflow, respectively.

Distribution of the $\eta$ of the $b$-tagged jet in the $\geq$1fj$\,$SR in data and for the sum of all processes expectations before the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions.

Distribution of the reconstructed top-quark mass in the $\geq$1fj$\,$SR in data and for the sum of all processes expectations before the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions. The first and last bins include the underflow and overflow, respectively.

Distribution of the $p_{\mathrm{T}}$ of the top-quark and photon system in the $\geq$1fj$\,$SR in data and for the sum of all processes expectations before the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions and the last bin includes the overflow.

Distribution of the photon $p_{\mathrm{T}}$ in the $\geq$1fj$\,$SR in data and for the sum of all processes expectations before the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions and the last bin includes the overflow.

Distribution of the photon $\eta$ in the $\geq$1fj$\,$SR in data and for the sum of all processes expectations before the profile-likelihood fit. The "Total" column corresponds to the sum of the expected contributions from the signal and background processes. The uncertainty represents the sum of statistical and systematic uncertainties in the signal and background predictions.

Ordered list of the 30 systematic uncertainties with the largest impact on the measured signal normalisation in the fit to data in the parton-level measurement considered as nuisance parameters (NPs) in the profile-likelihood fit. The column "NP value, error" corresponds to the nominal best-fit values and the corresponding uncertainties. The impact of each NP, $\Delta\sigma$/$\sigma_{\mathrm{pred}}$, is computed by comparing the nominal best-fit value of the POI ($\sigma$/$\sigma_{\mathrm{pred}}$) with the result of the fits when fixing the considered NP to its best-fit value shifted by its pre-fit and post-fit uncertainties. The corresponding impacts are listed in the "POI impact prefit high/low" and "POI impact high/low" columns, respectively. The "MC stat." NPs represent the MC statistical uncertainty and they enter the likelihood with a Poisson term, while all the other NPs enter the likelihood via a Gaussian term.

Ordered list of the 30 systematic uncertainties with the largest impact on the measured signal normalisation in the fit to data in the particle-level measurement considered as nuisance parameters (NPs) in the profile-likelihood fit. The column "NP value, error" corresponds to the nominal best-fit values and the corresponding uncertainties. The impact of each NP, $\Delta\sigma$/$\sigma_{\mathrm{pred}}$, is computed by comparing the nominal best-fit value of the POI ($\sigma$/$\sigma_{\mathrm{pred}}$) with the result of the fits when fixing the considered NP to its best-fit value shifted by its pre-fit and post-fit uncertainties. The corresponding impacts are listed in the "POI impact prefit high/low" and "POI impact high/low" columns, respectively. The "MC stat." NPs represent the MC statistical uncertainty and they enter the likelihood with a Poisson term, while all the other NPs enter the likelihood via a Gaussian term.

This table lists the kinematic requirements on parton-level objects used to define of the fiducial phase space for the parton-level measurement. Frixione isolation ($\href{https://arxiv.org/abs/hep-ph/9801442}{\text{hep-ph/9801442}}$) with a chosen radius of $\Delta R = 0.2$ is applied to photons ($\gamma$). The measured fiducial parton-level cross section is $\sigma_{tq\gamma}\times\mathcal{B}(t\rightarrow l\nu b) = 688\pm 23(\text{stat.})^{+75}_{-71}(\text{syst.})\,$fb.

This table lists the kinematic requirements on particle-level objects used to define of the fiducial phase space for the particle-level measurement. The particle level objects are photons ($\gamma$) not from a hadron decay, neutrinos not from a hadron decay ($\nu$), prompt electrons and muons ($\ell$) "dressed" by adding close-by ($\Delta R < 0.1$) photons, and anti-$k_t$ $R = 0.4$ jets built from stable particles ($\tau > 30\,$ps) and tau leptons excluding neutrinos and prompt dressed muons. Jets are $b$-tagged ($b$-jet) using ghost-matched $b$-hadrons with $p_{\text{T}} > 5\,$GeV. Apart from the kinematic requirements, isolation and overlap removal criteria are applied. Jets within $\Delta R = 0.4$ of a photon are removed if the $p_{\text{T}}$ of charged particles within $\Delta R = 0.3$ of the photon is smaller than $10\,\%$ of its $p_{\text{T}}$. Jets within $\Delta R = 0.4$ of a lepton are removed. Events are removed where a photon is close ($\Delta R < 0.4$) to a lepton or a surviving jet. The measured fiducial particle-level cross section is $\sigma_{tq\gamma}\times\mathcal{B}(t\rightarrow l\nu b)+\sigma_{t(\rightarrow l\nu b\gamma)q} = 303\pm 9(\text{stat.})^{+33}_{-32}(\text{syst.})\,$fb.

The unfolded differential charge asymmetry as a function of the longitudinal boost of the top pair system. The measured values are given with statistical and systematic uncertainties. The SM theory predictions calculated at NNLO in QCD and NLO in EW theory are listed. The scale uncertainty is obtained by varying renormalisation and factorisation scales independently by a factor of 2 or 0.5 around $\mu_0$ to calculate the maximum and minimum value of the asymmetry, respectively. The nominal value $\mu_0$ is chosen as $H_T/4$. The variations in which one scale is multiplied by 2 while the other scale is divided by 2 are excluded. Finally, the scale and MC integration uncertainties are added in quadrature.

The unfolded inclusive leptonic asymmetry. The unfolded $A_C^{\ell\bar{\ell}}$ is obtained in the reduced phase-space defined by the requirement $|\Delta |\eta_{\ell\bar{\ell}}||<2.5$. The measured values are given with statistical and systematic uncertainties. The SM theory predictions calculated at NLO in QCD and NLO in EW theory are listed. The theory uncertainty is obtained by varying both scales by a factor of 0.5 or 2.0 to calculate the minimum and maximum value of the asymmetry, respectively.

The unfolded differential leptonic asymmetry as a function of the invariant mass of the di-lepton pair. The unfolded $A_C^{\ell\bar{\ell}}$ is obtained in the reduced phase-space defined by the requirement $|\Delta |\eta_{\ell\bar{\ell}}||<2.5$. The measured values are given with statistical and systematic uncertainties. The SM theory predictions calculated at NLO in QCD and NLO in EW theory are listed. The theory uncertainty is obtained by varying both scales by a factor of 0.5 or 2.0 to calculate the minimum and maximum value of the asymmetry, respectively.

The unfolded differential leptonic asymmetry as a function of the transverse momentum of the di-lepton pair. The unfolded $A_C^{\ell\bar{\ell}}$ is obtained in the reduced phase-space defined by the requirement $|\Delta |\eta_{\ell\bar{\ell}}||<2.5$. The measured values are given with statistical and systematic uncertainties. The SM theory predictions calculated at NLO in QCD and NLO in EW theory are listed. The theory uncertainty is obtained by varying both scales by a factor of 0.5 or 2.0 to calculate the minimum and maximum value of the asymmetry, respectively.

The unfolded differential leptonic asymmetry as a function of the longitudinal boost of the di-lepton pair. The unfolded $A_C^{\ell\bar{\ell}}$ is obtained in the reduced phase-space defined by the requirement $|\Delta |\eta_{\ell\bar{\ell}}||<2.5$. The measured values are given with statistical and systematic uncertainties. The SM theory predictions calculated at NLO in QCD and NLO in EW theory are listed. The theory uncertainty is obtained by varying both scales by a factor of 0.5 or 2.0 to calculate the minimum and maximum value of the asymmetry, respectively.

Individual 68% and 95% CL bounds on the relevant Wilson coefficients of the SM Effective Field Theory in units of $\text{TeV}^{-2}$. The bounds are derived from the $A_C^{t\bar{t}}$ inclusive measurement. The experimental uncertainties are accounted for, in the form of the complete covariance matrix that keeps track of correlations between bins for the differential measurement. The theory uncertainty from the NNLO QCD + NLO EW calculation is included by explicitly varying the renormalization and factorization scales, or the parton density functions, in the calculation and registering the variations in the intervals.

Individual 68% and 95% CL bounds on the relevant Wilson coefficients of the SM Effective Field Theory in units of $\text{TeV}^{-2}$. The bounds are derived from the $A_C^{t\bar{t}}$ vs $m_{t\bar{t}}$ measurement. The experimental uncertainties are accounted for, in the form of the complete covariance matrix that keeps track of correlations between bins for the differential measurement. The theory uncertainty from the NNLO QCD + NLO EW calculation is included by explicitly varying the renormalization and factorization scales, or the parton density functions, in the calculation and registering the variations in the intervals.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{t\bar{t}}$ inclusive measurement. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{t\bar{t}}$ vs $\beta_{z,t\bar{t}}$ measurement for $\beta_{z,t\bar{t}}$ $\in$ [0,0.3]. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{t\bar{t}}$ vs $\beta_{z,t\bar{t}}$ measurement for $\beta_{z,t\bar{t}}$ $\in$ [0.3,0.6]. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{t\bar{t}}$ vs $\beta_{z,t\bar{t}}$ measurement for $\beta_{z,t\bar{t}}$ $\in$ [0.6,0.8]. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{t\bar{t}}$ vs $\beta_{z,t\bar{t}}$ measurement for $\beta_{z,t\bar{t}}$ $\in$ [0.8,1]. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{t\bar{t}}$ vs $m_{t\bar{t}}$ measurement for $m_{t\bar{t}}$ < 500 GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{t\bar{t}}$ vs $m_{t\bar{t}}$ measurement for $m_{t\bar{t}}$ $\in$ [500,750] GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{t\bar{t}}$ vs $m_{t\bar{t}}$ measurement for $m_{t\bar{t}}$ $\in$ [750,1000] GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{t\bar{t}}$ vs $m_{t\bar{t}}$ measurement for $m_{t\bar{t}}$ $\in$ [1000,1500] GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{t\bar{t}}$ vs $m_{t\bar{t}}$ measurement for $m_{t\bar{t}}$ > 1500 GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{t\bar{t}}$ vs $p_{T,t\bar{t}}$ measurement for $p_{T,t\bar{t}}$ < 30 GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{t\bar{t}}$ vs $p_{T,t\bar{t}}$ measurement for $p_{T,t\bar{t}}$ $\in$ [30,120] GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{t\bar{t}}$ vs $p_{T,t\bar{t}}$ measurement for $p_{T,t\bar{t}}$ > 120 GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{\ell\ell}$ inclusive measurement. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{\ell\ell}$ vs $\beta_{z,\ell\bar{\ell}}$ measurement for $\beta_{z,\ell\bar{\ell}}$ $\in$[0,0.3]. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{\ell\ell}$ vs $\beta_{z,\ell\bar{\ell}}$ measurement for $\beta_{z,\ell\bar{\ell}}$ $\in$[0.3,0.6]. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{\ell\ell}$ vs $\beta_{z,\ell\bar{\ell}}$ measurement for $\beta_{z,\ell\bar{\ell}}$ $\in$[0.6,0.8]. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{\ell\ell}$ vs $\beta_{z,\ell\bar{\ell}}$ measurement for $\beta_{z,\ell\bar{\ell}}$ $\in$[0.8,1]. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{\ell\ell}$ vs $m_{\ell\bar{\ell}}$ measurement for $m_{\ell\bar{\ell}}$ < 200 GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{\ell\ell}$ vs $m_{\ell\bar{\ell}}$ measurement for $m_{\ell\bar{\ell}}$ $\in$ [200,300] GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{\ell\ell}$ vs $m_{\ell\bar{\ell}}$ measurement for $m_{\ell\bar{\ell}}$ $\in$ [300,400] GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{\ell\ell}$ vs $m_{\ell\bar{\ell}}$ measurement for $m_{\ell\bar{\ell}}$ > 400 GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{\ell\ell}$ vs $p_{T,\ell\bar{\ell}}$ measurement for $p_{T,\ell\bar{\ell}}$ < 20 GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{\ell\ell}$ vs $p_{T,\ell\bar{\ell}}$ measurement for $p_{T,\ell\bar{\ell}}$ $\in$ [20, 70] GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Ranking of the systematic uncertainties with marginalisation for the $A_C^{\ell\ell}$ vs $p_{T,\ell\bar{\ell}}$ measurement for $p_{T,\ell\bar{\ell}}$ > 70 GeV. The effect on unfolded $A_C$ for down and up variation of the systematic uncertainty is shown, respectively. The pulls and constraints of the ranked NPs are obtained from data.

Post-marginalisation correlation coefficients $\rho_{ij}$ of nuisance parameters for the $A_C^{t\bar{t}}$ inclusive measurement. Only $|\rho_{ij}| > 0.05$ values are included.

Post-marginalisation correlation coefficients $\rho_{ij}$ of nuisance parameters for the $A_C^{t\bar{t}}$ vs $m_{t\bar{t}}$ measurement. Only $|\rho_{ij}| > 0.05$ values are included.

Post-marginalisation correlation coefficients $\rho_{ij}$ of nuisance parameters for the $A_C^{t\bar{t}}$ vs $p_{T,t\bar{t}}$ measurement. Only $|\rho_{ij}| > 0.05$ values are included.

Post-marginalisation correlation coefficients $\rho_{ij}$ of nuisance parameters for the $A_C^{t\bar{t}}$ vs $\beta_{z,t\bar{t}}$ measurement. Only $|\rho_{ij}| > 0.05$ values are included.

Post-marginalisation correlation coefficients $\rho_{ij}$ of nuisance parameters for the $A_C^{\ell\ell}$ inclusive measurement. Only $|\rho_{ij}| > 0.05$ values are included.

Post-marginalisation correlation coefficients $\rho_{ij}$ of nuisance parameters for the $A_C^{\ell\ell}$ vs $m_{\ell\bar{\ell}}$ measurement. Only $|\rho_{ij}| > 0.05$ values are included.

Post-marginalisation correlation coefficients $\rho_{ij}$ of nuisance parameters for the $A_C^{\ell\ell}$ vs $p_{T,\ell\bar{\ell}}$ measurement. Only $|\rho_{ij}| > 0.05$ values are included.

Post-marginalisation correlation coefficients $\rho_{ij}$ of nuisance parameters for the $A_C^{\ell\ell}$ vs $\beta_{z,\ell\bar{\ell}}$ measurement. Only $|\rho_{ij}| > 0.05$ values are included.

Covariance matrix for the $A_C^{t\bar{t}}$ vs $m_{t\bar{t}}$ measurement.

Covariance matrix for the $A_C^{t\bar{t}}$ vs $p_{T,t\bar{t}}$ measurement.

Covariance matrix for the $A_C^{t\bar{t}}$ vs $\beta_{z,t\bar{t}}$ measurement.

Covariance matrix for the $A_C^{\ell\ell}$ vs $m_{\ell\bar{\ell}}$ measurement.

Covariance matrix for the $A_C^{\ell\ell}$ vs $p_{T,\ell\bar{\ell}}$ measurement.

Covariance matrix for the $A_C^{\ell\ell}$ vs $\beta_{z,\ell\bar{\ell}}$ measurement.