Comparison between data and background prediction before the fit (Pre-Fit) for the mass of the FCNC top-quark candidate in SR1. The uncertainty band includes both the statistical and systematic uncertainties in the background prediction. The four FCNC LH signals are also shown separately, normalized to five times the cross-section corresponding to the most stringent observed branching ratio limits. The first (last) bin in all distributions includes the underflow (overflow). The lower panels show the ratios of the data (Data) to the background prediction (Bkg.).

Comparison between data and background prediction before the fit (Pre-Fit) for the mass of the SM top-quark candidate in SR2. The uncertainty band includes both the statistical and systematic uncertainties in the background prediction. The four FCNC LH signals are also shown separately, normalized to five times the cross-section corresponding to the most stringent observed branching ratio limits. The first (last) bin in all distributions includes the underflow (overflow). The lower panels show the ratios of the data (Data) to the background prediction (Bkg.).

Comparison between data and background prediction before the fit (Pre-Fit) for the transverse momentum of the Z boson candidate in SR2. The uncertainty band includes both the statistical and systematic uncertainties in the background prediction. The four FCNC LH signals are also shown separately, normalized to five times the cross-section corresponding to the most stringent observed branching ratio limits. The first (last) bin in all distributions includes the underflow (overflow). The lower panels show the ratios of the data (Data) to the background prediction (Bkg.).

Comparison between data and background prediction after the fit to data (Post-Fit) for the FCNC tZu LH coupling extraction. The distribution is for the $D_{1}$ discriminant in the mass sideband CR1. The uncertainty band includes both the statistical and systematic uncertainties in the background prediction. The FCNC tZu LH signals are also separately shown, normalized to 500 times the best fit of the signal yield. The lower panels show the ratios of the data (Data) to the background prediction (Bkg.).

Comparison between data and background prediction after the fit to data (Post-Fit) for the FCNC tZu LH coupling extraction. The distribution is for the $D_{2}^{u}$ discriminant in the mass sideband CR2. The uncertainty band includes both the statistical and systematic uncertainties in the background prediction. The FCNC tZu LH signals are also separately shown, normalized to 500 times the best fit of the signal yield. The lower panels show the ratios of the data (Data) to the background prediction (Bkg.).

Comparison between data and background prediction after the fit to data (Post-Fit) for the FCNC tZu LH coupling extraction. The distribution is for the $D_{1}$ discriminant in SR1. The uncertainty band includes both the statistical and systematic uncertainties in the background prediction. The FCNC tZu LH signals are also separately shown, normalized to 50 times the best fit of the signal yield. The lower panels show the ratios of the data (Data) to the background prediction (Bkg.).

Comparison between data and background prediction after the fit to data (Post-Fit) for the FCNC tZu LH coupling extraction. The distribution is for the $D_{2}^{u}$ discriminant in SR2. The uncertainty band includes both the statistical and systematic uncertainties in the background prediction. The FCNC tZu LH signals are also separately shown, normalized to 50 times the best fit of the signal yield. The lower panels show the ratios of the data (Data) to the background prediction (Bkg.).

Comparison between data and background prediction after the fit to data (Post-Fit) for the FCNC tZc LH coupling extraction. The distribution is for the $D_{1}$ discriminant in the mass sideband CR1. The uncertainty band includes both the statistical and systematic uncertainties in the background prediction. The FCNC tZc LH signals are also separately shown, normalized to 500 times the best fit of the signal yield. The lower panels show the ratios of the data (Data) to the background prediction (Bkg.).

Comparison between data and background prediction after the fit to data (Post-Fit) for the FCNC tZc LH coupling extraction. The distribution is for the $D_{2}^{c}$ discriminant in the mass sideband CR2. The uncertainty band includes both the statistical and systematic uncertainties in the background prediction. The FCNC tZc LH signals are also separately shown, normalized to 500 times the best fit of the signal yield. The lower panels show the ratios of the data (Data) to the background prediction (Bkg.).

Comparison between data and background prediction after the fit to data (Post-Fit) for the FCNC tZc LH coupling extraction. The distribution is for the $D_{1}$ discriminant in SR1. The uncertainty band includes both the statistical and systematic uncertainties in the background prediction. The FCNC tZc LH signals are also separately shown, normalized to 50 times the best fit of the signal yield. The lower panels show the ratios of the data (Data) to the background prediction (Bkg.).

Comparison between data and background prediction after the fit to data (Post-Fit) for the FCNC tZc LH coupling extraction. The distribution is for the $D_{2}^{c}$ discriminant in SR2. The uncertainty band includes both the statistical and systematic uncertainties in the background prediction. The FCNC tZc LH signals are also separately shown, normalized to 50 times the best fit of the signal yield. The lower panels show the ratios of the data (Data) to the background prediction (Bkg.).

Comparison between data and background prediction after the fit to data (Post-Fit) for the FCNC tZu LH coupling extraction. The distribution is for the leading lepton $p_{T}$ in the $t\bar{t}$ CR. The uncertainty band includes both the statistical and systematic uncertainties in the background prediction. The FCNC tZu LH signals are also shown separately, normalized to $10^{3}$ times the best fit of the signal yield. The last bin includes the overflow. The lower panels show the ratios of the data (Data) to the background prediction (Bkg.).

Comparison between data and background prediction after the fit to data (Post-Fit) for the FCNC tZu LH coupling extraction. The distribution is for the third lepton $p_{T}$ in the $t\bar{t}$ CR. The uncertainty band includes both the statistical and systematic uncertainties in the background prediction. The FCNC tZu LH signals are also shown separately, normalized to $10^{3}$ times the best fit of the signal yield. The last bin includes the overflow. The lower panels show the ratios of the data (Data) to the background prediction (Bkg.).

Comparison between data and background prediction after the fit to data (Post-Fit) for the FCNC tZu LH coupling extraction. The distribution is for the leading lepton $p_{T}$ in the $t\bar{t}Z$ CR. The uncertainty band includes both the statistical and systematic uncertainties in the background prediction. The FCNC tZu LH signals are also shown separately, normalized to $10^{3}$ times the best fit of the signal yield. The last bin includes the overflow. The lower panels show the ratios of the data (Data) to the background prediction (Bkg.).

Comparison between data and background prediction after the fit to data (Post-Fit) for the FCNC tZu LH coupling extraction. The distribution is for the $D_{1}$ discriminant in the $t\bar{t}Z$ CR. The uncertainty band includes both the statistical and systematic uncertainties in the background prediction. The FCNC tZu LH signals are also shown separately, normalized to $10^{3}$ times the best fit of the signal yield. The lower panels show the ratios of the data (Data) to the background prediction (Bkg.).

Transverse profile for 70 GeV < pT < 100 GeV.

Longitudinal profile for pT > 100 GeV.

Transverse profile for pT > 100 GeV.

Average longitudinal profile

Transverse profile for pT > 100 GeV.

Fitted event-level b-tagging selection efficiency as a function of the dijet invariant mass. The uncertainties are evaluated by propagating the uncertainties on the fit parameters to the fitted efficiency.

Differential cross section as a function of $m_{\gamma\gamma}$. The table contains the values measured in data and theory predictions from SHERPA, DIPHOX and NNLOJET.

Differential cross section as a function of $p_{T,\gamma\gamma}$. The table contains the values measured in data and theory predictions from SHERPA, DIPHOX and NNLOJET.

Differential cross section as a function of $a_{T,\gamma\gamma}$. The table contains the values measured in data and theory predictions from SHERPA, DIPHOX and NNLOJET.

Differential cross section as a function of $\phi_{\eta}*$. The table contains the values measured in data and theory predictions from SHERPA, DIPHOX and NNLOJET.

Differential cross section as a function of $\pi-\Delta\phi_{\gamma\gamma}$. The table contains the values measured in data and theory predictions from SHERPA, DIPHOX and NNLOJET.

Differential cross section as a function of $|cos\theta*|^{(CS)}$. The table contains the values measured in data and theory predictions from SHERPA, DIPHOX and NNLOJET.

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.

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.

Upper limits on $\mathcal{B}(H\rightarrow aa\rightarrow bb\mu\mu)$ at 95% CL including the BDT cut as a function of the signal mass.

Upper limits on $\mathcal{B}(H\rightarrow aa\rightarrow bb\mu\mu)$ at 95% CL without the BDT cut as a function of the signal mass.

The number of events when applying each cut in the analysis for $m_a$ = 16 GeV. The first row shows the approximate total number of events scaled to the theoretical signal cross-section and luminosity of the full Run 2 dataset, assuming $ \mathcal{B}(H\rightarrow aa\rightarrow bb\mu\mu)$ = 0.16%.

The number of events when applying each cut in the analysis for $m_a$ = 20 GeV. The first row shows the approximate total number of events scaled to the theoretical signal cross-section and luminosity of the full Run 2 dataset, assuming $ \mathcal{B}(H\rightarrow aa\rightarrow bb\mu\mu)$ = 0.16%.

The number of events when applying each cut in the analysis for $m_a$ = 30 GeV. The first row shows the approximate total number of events scaled to the theoretical signal cross-section and luminosity of the full Run 2 dataset, assuming $ \mathcal{B}(H\rightarrow aa\rightarrow bb\mu\mu)$ = 0.16%.

The number of events when applying each cut in the analysis for $m_a$ = 40 GeV. The first row shows the approximate total number of events scaled to the theoretical signal cross-section and luminosity of the full Run 2 dataset, assuming $ \mathcal{B}(H\rightarrow aa\rightarrow bb\mu\mu)$ = 0.16%.

The number of events when applying each cut in the analysis for $m_a$ = 50 GeV. The first row shows the approximate total number of events scaled to the theoretical signal cross-section and luminosity of the full Run 2 dataset, assuming $ \mathcal{B}(H\rightarrow aa\rightarrow bb\mu\mu)$ = 0.16%.

The number of events when applying each cut in the analysis for $m_a$ = 60 GeV. The first row shows the approximate total number of events scaled to the theoretical signal cross-section and luminosity of the full Run 2 dataset, assuming $ \mathcal{B}(H\rightarrow aa\rightarrow bb\mu\mu)$ = 0.16%.

Post-fit $m_\text{T}(\gamma, E_\text{T}^\text{miss})$ distribution in the inclusive signal region for the dark-photon search with the 125 GeV mass $\mathcal{B}(H \to \gamma \gamma_\text{d})$ signal normalization set to zero. A $H \to \gamma \gamma_\text{d}$ decay signal is shown for two different mass hypotheses, 125 GeV and 500 GeV, and scaled to a $\mathcal{B}(H \to \gamma \gamma_\text{d})$ of 2% and 1%, respectively. Events with $m_\text{T}(\gamma, E_\text{T}^\text{miss})$ larger than the rightmost bin boundary are added to that bin.

The 95% CL upper limit on the Higgs boson production cross-section times branching ratio to $\gamma \gamma_\text{d}$ is shown for different VBF-produced scalar-mediator-mass hypotheses in the NWA. The theoretically predicted cross-section of a Higgs boson produced via VBF and with the $\mathcal{B}(H \to \gamma \gamma_\text{d}) =$ 5% is superimposed on the $\pm 1\sigma$ and $\pm 2\sigma$ NNLO QCD + NLO EW uncertainty band of the expected production cross-section limit.

Post-fit $m_\text{jj}$ distribution in the inclusive signal region. The Higgs boson invisible decay signal is scaled to a $\mathcal{B}_\text{inv}$ of 37%. Events with $m_\text{jj}$ larger than the rightmost bin boundary are added to that bin.

Post-fit $m_\text{jj}$ distribution in the one-lepton control region $W_{\ell \nu}^\gamma$ CR. Events with $m_\text{jj}$ larger than the rightmost bin boundary are added to that bin.

Post-fit $m_\text{T}$ distribution in the one lepton control region. Events with $m_\text{T}$ larger than the rightmost bin boundary are added to that bin.

Post-fit photon centrality distribution in the zero lepton signal plus control region with the $\mathcal{B}_\text{inv}$ signal normalization set to zero in the fit.

Post-fit photon $E_\text{T}$ distribution in the zero lepton signal region with the $\mathcal{B}_\text{inv}$ signal normalization set to zero in the fit.

Post-fit photon centrality distribution in the zero lepton signal plus control region resulting from the fit to the $m_\text{jj}$ distribution for EW $Z \gamma + \text{jets}$. The post-fit uncertainties include statistical, experimental, and theory contributions.

Post-fit photon $E_\text{T}$ distribution in the zero lepton signal region resulting from the fit to the $m_\text{jj}$ distribution for EW $Z \gamma + \text{jets}$. The post-fit uncertainties include statistical, experimental, and theory contributions.

Post-fit DNN output score distribution in the one lepton control region.

Yields for the EW $Z \gamma + \text{jets}$ process are shown after each selection along with relative and absolute signal acceptance efficiencies.

Yields for the 125 GeV Higgs boson with $\mathcal{B}_\text{inv.} =$ 1 signal produced by the vector boson fusion process in association with a final state photon are shown after each selection along with relative and absolute signal acceptance efficiencies.

Yields for the 125 GeV Higgs boson with $\mathcal{B}(H \to \gamma \gamma_\text{d}) =$ 1 signal produced by the vector boson fusion process are shown after each selection along with relative and absolute signal acceptance efficiencies.

Distribution of $m_{\mathrm{T},3l}$ in the JNLow SR after the background-only fit. The uncertainty on the expected number of background events includes all statistical and systematic post-fit uncertainties with the correlations between various background sources taken into account.

Distribution of $H_\text{T} + E_\text{T}^\text{miss}$ in the Q0 SR after the background-only fit. The uncertainty on the expected number of background events includes all statistical and systematic post-fit uncertainties with the correlations between various background sources taken into account.

Distribution of $H_\text{T} + E_\text{T}^\text{miss}$ in the Q2 SR after the background-only fit. The uncertainty on the expected number of background events includes all statistical and systematic post-fit uncertainties with the correlations between various background sources taken into account.

Distribution of $m_{\mathrm{T},3l}$ in the ZL-CR after the background-only fit.

Distribution of $m_{\mathrm{T},3l}$ in the Fake-CR after the background-only fit.

Distribution of $H_\text{T} + E_\text{T}^\text{miss}$ in the Q0 DB-CR after the background-only fit.

Distribution of $H_\text{T} + E_\text{T}^\text{miss}$ in the Q0 RT-CR after the background-only fit.

Expected and observed exclusion limit for the combination of the two- (from Ref. EXOT-2018-33), three- and four-lepton channels, for the type-III seesaw process with the corresponding one- and two-standard-deviation uncertainty bands, showing the 95% CL upper limit on the cross-section.

Expected and observed 95% ( $CL_s$ ) exclusion limits in the three lepton channel for the type-III seesaw process with the corresponding one- and two-standard-deviation bands, showing the 95% CL upper limit on the cross-section.

Expected and observed 95% ( $CL_s$ ) exclusion limits in the four lepton channel for the type-III seesaw process with the corresponding one- and two-standard-deviation bands, showing the 95% CL upper limit on the cross-section.

Cross-sections of signal Monte Carlo samples for each mass point considered in this analysis. Leading order cross-sections ( $\sigma_{LO}$ ) are computed by the generator and then rescaled to next-to-leading cross-sections ( $\sigma_{NLO+NLL}$ ), with their corresponding uncertainties, using information taken from Refs. C1C1 and N2C1.

Expected signal and background yields after each of the analysis selection cuts for the 800 GeV mass hypothesis in the ZL SR. Preselection represents events with at least three leptons.

Expected signal and background yields after each of the analysis selection cuts for the 800 GeV mass hypothesis in the ZLVeto SR. Preselection represents events with at least three leptons.

Expected signal and background yields after each of the analysis selection cuts for the 800 GeV mass hypothesis in the JNLow SR. Preselection represents events with at least three leptons.

Expected signal and background yields after each of the analysis selection cuts for the 800 GeV mass hypothesis in the Q0 SR. Preselection represents events with at least three leptons.

Expected signal and background yields after each of the analysis selection cuts for the 800 GeV mass hypothesis in the Q2 SR. Preselection represents events with at least three leptons.

Expected signal and background yields after each of the analysis selection cuts for the 800 GeV mass hypothesis in the ZL CR. Preselection represents events with at least three leptons.

Expected signal and background yields after each of the analysis selection cuts for the 800 GeV mass hypothesis in the Q0-DB CR. Preselection represents events with at least three leptons.

Expected signal and background yields after each of the analysis selection cuts for the 800 GeV mass hypothesis in the Q0-RT CR. Preselection represents events with at least three leptons.

Expected background yields and observed data after the background-only fit, in the three-lepton CRs and VRs.

Expected background yields and observed data after the background-only fit, in the four-lepton CRs and VRs.

Expected and observed 95% ( $CL_s$ ) exclusion limits in the three and four lepton channels for the type-III seesaw process with the corresponding one- and two-standard-deviation bands, showing the 95% CL upper limit on the cross-section.

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.