Upper limits on the production cross section times branching fraction of the b* RH hypothesis at a 95% CL. Dashed colored lines show the expected limits from the l+jets and all-hadronic channels, where the latter start at resonance masses of 1.4 TeV. The observed and expected limits from the combination are shown as solid and dashed black lines, respectively. The green and yellow bands show the 68 and 95% confidence intervals on the combined expected limits.

Upper limits on the production cross section times branching fraction of the b* VL hypothesis at a 95% CL. Dashed colored lines show the expected limits from the l+jets and all-hadronic channels, where the latter start at resonance masses of 1.4 TeV. The observed and expected limits from the combination are shown as solid and dashed black lines, respectively. The green and yellow bands show the 68 and 95% confidence intervals on the combined expected limits.

Upper limits on the production cross section times branching fraction of the B+b hypothesis at a 95% CL. Dashed colored lines show the expected limits from the l+jets and all-hadronic channels, where the latter start at resonance masses of 1.4 TeV. The observed and expected limits from the combination are shown as solid and dashed black lines, respectively. The green and yellow bands show the 68 and 95% confidence intervals on the combined expected limits.

Upper limits on the production cross section times branching fraction of the B+t hypothesis at a 95% CL. Dashed colored lines show the expected limits from the l+jets and all-hadronic channels, where the latter start at resonance masses of 1.4 TeV. The observed and expected limits from the combination are shown as solid and dashed black lines, respectively. The green and yellow bands show the 68 and 95% confidence intervals on the combined expected limits.

Correlation matrix between the fiducial cross sections for the four individual decay final states and the $ZZ^{*}$ normalisation factor.

Differential fiducial cross section for the transverse momentum $p_{T}^{4l}$ of the Higgs boson. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 . Measured value in the last bin is un upper limit at 95% CL.

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the transverse momentum $p_{T}^{4l}$ of the Higgs boson.

Differential fiducial cross section for the invariant mass $m_{12}$ of the leading Z boson. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the invariant mass $m_{12}$ of the leading Z boson.

Differential fiducial cross section for the invariant mass $m_{34}$ of the subleading Z boson. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the invariant mass $m_{34}$ of the subleading Z boson.

Differential fiducial cross section for the rapidity $|y_{4l}|$ of the Higgs boson. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the rapidity $|y_{4l}|$ of the Higgs boson.

Differential fiducial cross section for the production angle $|\cos\theta^{*}|$ of the leading Z boson. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the production angle $|\cos\theta^{*}|$ of the leading Z boson.

Differential fiducial cross section for the production angle $\cos\theta_{1}$ of the anti-lepton from the leading Z boson. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the production angle $\cos\theta_{1}$ of the anti-lepton from the leading Z boson.

Differential fiducial cross section for the production angle $\cos\theta_{2}$ of the anti-lepton from the subleading Z boson. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the production angle $\cos\theta_{2}$ of the anti-lepton from the subleading Z boson.

Differential fiducial cross section for the azimuthal angle $\phi$ of the decay planes of the two reconstructed Z bosons. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the azimuthal angle $\phi$ of the decay planes of the two reconstructed Z bosons.

Differential fiducial cross section for the azimuthal angle $\phi_{1}$ of the decay plane of the leading Z boson and the plane formed between its four-momentum and the z-axis. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the azimuthal angle $\phi_{1}$ of the decay plane of the leading Z boson and the plane formed between its four-momentum and the z-axis.

Differential fiducial cross section for the jet multiplicity $N_{jets}$. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the jet multiplicity $N_{jets}$.

Differential fiducial cross section for the inclusive jet multiplicity $N_{jets}$. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Differential fiducial cross section for the number of b-quark initiated jets $N_{b-jets}$. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the number of b-quark initiated jets $N_{b-jets}$.

Differential fiducial cross section for the transverse momentum of the leading jet $p_{T}^{lead.jet}$ in events with at least one jet. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the transverse momentum of the leading jet $p_{T}^{lead.jet}$ in events with at least one jet.

Differential fiducial cross section for the transverse momentum of the subleading jet $p_{T}^{sublead.jet}$ in events with at least two jets. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the transverse momentum of the subleading jet $p_{T}^{sublead.jet}$ in events with at least two jets.

Differential fiducial cross section for the invariant mass of the two highest-pT jets $m_{jj}$ in events with at least two jets. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the invariant mass of the two highest-pT jets $m_{jj}$ in events with at least two jets.

Differential fiducial cross section for the distance between the two highest-pT jets in pseudorapidity $\Delta\eta_{jj}$. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the distance between the two highest-pT jets in pseudorapidity $\Delta\eta_{jj}$.

Differential fiducial cross section for the distance between the two highest-pT jets in $\phi$ $\Delta\phi_{jj}$. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the distance between the two highest-pT jets in $\phi$ $\Delta\phi_{jj}$.

Differential fiducial cross section for the transverse momentum of the four lepton plus jet system, in events with at least one jet $p_{T}^{4lj}$. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the transverse momentum of the four lepton plus jet system, in events with at least one jet $p_{T}^{4lj}$.

Differential fiducial cross section for the transverse momentum of the four lepton plus di-jet system, in events with at least two jets $p_{T}^{4ljj}$. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 . Measured value in the last bin is un upper limit at 95% CL.

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the transverse momentum of the four lepton plus di-jet system, in events with at least two jets $p_{T}^{4ljj}$.

Differential fiducial cross section for the invariant mass of the four lepton plus jet system in events with at least one jet $m_{4lj}$. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the invariant mass of the four lepton plus jet system in events with at least one jet $m_{4lj}$.

Differential fiducial cross section for the invariant mass of the four lepton plus di-jet system in events with at least two jets $m_{4ljj}$. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the invariant mass of the four lepton plus di-jet system in events with at least two jets $m_{4ljj}$.

Differential fiducial cross section for the leading vs. subleading Z boson mass $m_{12}$vs.$m_{34}$. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the leading vs. subleading Z boson mass $m_{12}$vs.$m_{34}$.

Differential fiducial cross section for the leading vs. subleading Z boson mass $m_{12}$vs.$m_{34}$ in $ll\mu\mu$ final states. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Differential fiducial cross section for the leading vs. subleading Z boson mass $m_{12}$vs.$m_{34}$ in $llee$ final states. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the leading vs. subleading Z boson mass m12 vs. m34 in $ll\mu\mu$ and $llee$ final states.

Differential fiducial cross section of the $p_{T}^{4l}$ distribution in $|y_{4l}|$ bins. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section of the $p_{T}^{4l}$ distribution in $|y_{4l}|$ bins.

Differential fiducial cross section of the $p_{T}^{4l}$ distribution in $N_{jets}$ bins. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section of the $p_{T}^{4l}$ distribution in $N_{jets}$ bins.

Differential fiducial cross section for transverse momentum of the four lepton system vs. the transverse momentum of the four lepton plus jet system $p_{T}^{4l}$vs.$p_{T}^{4lj}$. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for transverse momentum of the four lepton system vs. the transverse momentum of the four lepton plus jet system $p_{T}^{4l}$vs.$p_{T}^{4lj}$.

Differential fiducial cross section for the transverse momentum of the four lepton plus jet system vs the invariant mass of the four lepton plus jet system $p_{T}^{4l}$vs.$m_{4lj}$. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the transverse momentum of the four lepton plus jet system vs the invariant mass of the four lepton plus jet system $p_{T}^{4l}$vs.$m_{4lj}$.

Differential fiducial cross section for the transverse momentum of the four lepton vs the transverse momentum of the leading jet $p_{T}^{4l}$vs.$p_{T}^{l.jet}$. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the transverse momentum of the four lepton vs the transverse momentum of the leading jet $p_{T}^{4l}$vs.$p_{T}^{lead.jet}$.

Differential fiducial cross section for the transverse momentum of the leading jet vs the rapidity of the leading jet $p_{T}^{lead.jet}$vs.$|y^{lead.jet}|$. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the transverse momentum of the leading jet vs the rapidity of the leading jet $p_{T}^{lead.jet}$vs.$|y^{lead.jet}|$.

Differential fiducial cross section for the transverse momentum of the leading jet vs the transverse momentum of the subleading jet $p_{T}^{lead.jet}$vs.$p_{T}^{sublead.jet}$. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the transverse momentum of the leading jet vs the transverse momentum of the subleading jet $p_{T}^{lead.jet}$vs.$p_{T}^{sublead.jet}$.

Differential fiducial cross section for the leading Z boson mass $m_{12}$ in $4\mu$ and $4e$ final states. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Differential fiducial cross section for the leading Z boson mass $m_{12}$ in $2e2\mu$ and $2\mu2e$ final states. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the leading Z boson mass $m_{12}$ in $4l$ and $2l2l$ final states.

Differential fiducial cross section for the subleading Z boson mass $m_{34}$ in $4\mu$ and $4e$ final states. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Differential fiducial cross section for the subleading Z boson mass $m_{34}$ in $2e2\mu$ and $2\mu2e$ final states. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the subleading Z boson mass $m_{34}$ in $4l$ and $2l2l$ final states.

Differential fiducial cross section for the azimuthal angle $\phi$ of the decay planes of the two reconstructed Z bosons in $4\mu$ and $4e$ final states. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Differential fiducial cross section for the azimuthal angle $\phi$ of the decay planes of the two reconstructed Z bosons in $2e2\mu$ and $2\mu2e$ final states. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the azimuthal angle $\phi$ of the decay planes of the two reconstructed Z bosons in $4l$ and $2l2l$ final states.

Differential fiducial cross section for the leading vs. subleading Z boson mass $m_{12}$vs.$m_{34}$ in $4\mu$ and $4e$ final states. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Differential fiducial cross section for the leading vs. subleading Z boson mass $m_{12}$vs.$m_{34}$ in $2\mu2e$ and $2e2\mu$ final states. The measured cross sections are compared to predictions provided by NNLOPS + XH. NNLOPS is normalised to the N3LO total cross section with a K-factor = 1.1 .

Correlation matrix between the measured cross sections and the $ZZ^{*}$ background normalization corresponding to the differential fiducial cross section for the leading vs. subleading Z boson mass $m_{12}$vs.$m_{34}$ in $4l$ and $2l2l$ final states.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Parametrization of the $A_{X}$ factor, defined as the fraction of diphoton resonances satisfying the fiducial acceptance at the particle level, as function of $m_{X}$ obtained from the narrow width simulated signal samples produced in gluon fusion.

The correction factor, $C_{X}$, defined as the ratio between the number of reconstructed signal events passing the analysis cuts and the number of signal events at the particle level generated within the fiducial volume, and acceptance correction factor, $A_{X}$, defined as the fraction of diphoton resonances satisfying the fiducial acceptance at the particle level. Both are computed for NWA spin-0 models as a function of $m_{X}$.

Effect of event selections on a scalar MC signal sample generated for $m_{X}$ = 15 GeV and on the data. For the MC sample, the efficiencies are shown after applying event weights and a truth level filter that requires two photons with $p^{\gamma\gamma}_{T}>40$ GeV; for the data, the absolute yields are shown. The initial yields for data include a trigger preselection that is the OR of a list of single photon and diphoton triggers. The "2 $loose$ photons" step includes the kinematic acceptance cuts.

Parameterization of the Double Sided Crystal Ball function parameters describing the scalar mass resolution model as a function of $m_{X}$ [GeV].

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Measured fiducial differential cross sections for the jet multiplicity in the high-p$_{\mathrm{T}}$ region in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events. The statistical, systematic, and luminosity uncertainties are given.

Measured fiducial differential cross sections for the $\Delta R_{Z,j}^{min}$ in the high-p$_{\mathrm{T}}$ region in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events. The statistical, systematic, and luminosity uncertainties are given.

Measured fiducial differential cross sections for the $r_{Z,j}$ in the high-p$_{\mathrm{T}}$ region in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events. The statistical, systematic, and luminosity uncertainties are given.

Measured fiducial differential cross sections for the $r_{Z,j}$ in the collinear region in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events. The statistical, systematic, and luminosity uncertainties are given.

Measured fiducial differential cross sections for the $r_{Z,j}$ in the back-to-back region in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events. The statistical, systematic, and luminosity uncertainties are given.

Measured fiducial differential cross sections for the jet multiplicity in the collinear region in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events. The statistical, systematic, and luminosity uncertainties are given.

Measured fiducial differential cross sections for the jet multiplicity in the back-to-back region in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events. The statistical, systematic, and luminosity uncertainties are given.

Measured fiducial differential cross sections for the H$_{\mathrm{T}}$ in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events. The statistical, systematic, and luminosity uncertainties are given.

Measured fiducial differential cross sections for the $\Delta R_{Z,j}^{min}$ in the high-S$_{\mathrm{T}}$ region in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events. The statistical, systematic, and luminosity uncertainties are given.

Measured fiducial differential cross sections for the jet multiplicity in the high-S$_{\mathrm{T}}$ region in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events. The statistical, systematic, and luminosity uncertainties are given.

Systematic uncertainties for the Z boson p$_{\mathrm{T}}$ in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events. The uncertainties are presented as a percentage of the measured cross-section for the upward variation of each source of uncertainty in each bin.

Systematic uncertainties for the leading jet p$_{\mathrm{T}}$ in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events. The uncertainties are presented as a percentage of the measured cross-section for the upward variation of each source of uncertainty in each bin.

Systematic uncertainties for the jet multiplicity in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events. The uncertainties are presented as a percentage of the measured cross-section for the upward variation of each source of uncertainty in each bin.

Systematic uncertainties for the jet multiplicity in the high-p$_{\mathrm{T}}$ region in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events. The uncertainties are presented as a percentage of the measured cross-section for the upward variation of each source of uncertainty in each bin.

Systematic uncertainties for the $\Delta R_{Z,j}^{min}$ in the high-p$_{\mathrm{T}}$ region in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events. The uncertainties are presented as a percentage of the measured cross-section for the upward variation of each source of uncertainty in each bin.

Systematic uncertainties for the $r_{Z,j}$ in the high-p$_{\mathrm{T}}$ region in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events. The uncertainties are presented as a percentage of the measured cross-section for the upward variation of each source of uncertainty in each bin.

Systematic uncertainties for the $r_{Z,j}$ in the collinear region in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events. The uncertainties are presented as a percentage of the measured cross-section for the upward variation of each source of uncertainty in each bin.

Systematic uncertainties for the $r_{Z,j}$ in the back-to-back region in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events. The uncertainties are presented as a percentage of the measured cross-section for the upward variation of each source of uncertainty in each bin.

Systematic uncertainties for the jet multiplicity in the collinear region in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events. The uncertainties are presented as a percentage of the measured cross-section for the upward variation of each source of uncertainty in each bin.

Systematic uncertainties for the jet multiplicity in the back-to-back region in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events. The uncertainties are presented as a percentage of the measured cross-section for the upward variation of each source of uncertainty in each bin.

Systematic uncertainties for the H$_{\mathrm{T}}$ in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events. The uncertainties are presented as a percentage of the measured cross-section for the upward variation of each source of uncertainty in each bin.

Systematic uncertainties for the $\Delta R_{Z,j}^{min}$ in the high-S$_{\mathrm{T}}$ region in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events. The uncertainties are presented as a percentage of the measured cross-section for the upward variation of each source of uncertainty in each bin.

Systematic uncertainties for the jet multiplicity in the high-S$_{\mathrm{T}}$ region in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events. The uncertainties are presented as a percentage of the measured cross-section for the upward variation of each source of uncertainty in each bin.

Correction scale factor from the cross section calculated with leptons at the Born-level to the cross section calculated with dressed leptons as a function of the Z boson p$_{\mathrm{T}}$ in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events, averaging the electron and muon channels, derived with Sherpa2.2.11. The systematic uncertainty is obtained with an enveloppe around scale factors computed from Sherpa2.2.1 and MG5_aMC+Py8 CKKWL.

Correction scale factor from the cross section calculated with leptons at the Born-level to the cross section calculated with dressed leptons as a function of the leading jet p$_{\mathrm{T}}$ in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events, averaging the electron and muon channels, derived with Sherpa2.2.11. The systematic uncertainty is obtained with an enveloppe around scale factors computed from Sherpa2.2.1 and MG5_aMC+Py8 CKKWL.

Correction scale factor from the cross section calculated with leptons at the Born-level to the cross section calculated with dressed leptons as a function of the jet multiplicity in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events, averaging the electron and muon channels, derived with Sherpa2.2.11. The systematic uncertainty is obtained with an enveloppe around scale factors computed from Sherpa2.2.1 and MG5_aMC+Py8 CKKWL.

Correction scale factor from the cross section calculated with leptons at the Born-level to the cross section calculated with dressed leptons as a function of the jet multiplicity in the high-p$_{\mathrm{T}}$ region in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events, averaging the electron and muon channels, derived with Sherpa2.2.11. The systematic uncertainty is obtained with an enveloppe around scale factors computed from Sherpa2.2.1 and MG5_aMC+Py8 CKKWL.

Correction scale factor from the cross section calculated with leptons at the Born-level to the cross section calculated with dressed leptons as a function of the $\Delta R_{Z,j}^{min}$ in the high-p$_{\mathrm{T}}$ region in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events, averaging the electron and muon channels, derived with Sherpa2.2.11. The systematic uncertainty is obtained with an enveloppe around scale factors computed from Sherpa2.2.1 and MG5_aMC+Py8 CKKWL.

Correction scale factor from the cross section calculated with leptons at the Born-level to the cross section calculated with dressed leptons as a function of the $r_{Z,j}$ in the high-p$_{\mathrm{T}}$ region in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events, averaging the electron and muon channels, derived with Sherpa2.2.11. The systematic uncertainty is obtained with an enveloppe around scale factors computed from Sherpa2.2.1 and MG5_aMC+Py8 CKKWL.

Correction scale factor from the cross section calculated with leptons at the Born-level to the cross section calculated with dressed leptons as a function of the $r_{Z,j}$ in the collinear region in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events, averaging the electron and muon channels, derived with Sherpa2.2.11. The systematic uncertainty is obtained with an enveloppe around scale factors computed from Sherpa2.2.1 and MG5_aMC+Py8 CKKWL.

Correction scale factor from the cross section calculated with leptons at the Born-level to the cross section calculated with dressed leptons as a function of the $r_{Z,j}$ in the back-to-back region in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events, averaging the electron and muon channels, derived with Sherpa2.2.11. The systematic uncertainty is obtained with an enveloppe around scale factors computed from Sherpa2.2.1 and MG5_aMC+Py8 CKKWL.

Correction scale factor from the cross section calculated with leptons at the Born-level to the cross section calculated with dressed leptons as a function of the jet multiplicity in the collinear region in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events, averaging the electron and muon channels, derived with Sherpa2.2.11. The systematic uncertainty is obtained with an enveloppe around scale factors computed from Sherpa2.2.1 and MG5_aMC+Py8 CKKWL.

Correction scale factor from the cross section calculated with leptons at the Born-level to the cross section calculated with dressed leptons as a function of the jet multiplicity in the back-to-back region in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events, averaging the electron and muon channels, derived with Sherpa2.2.11. The systematic uncertainty is obtained with an enveloppe around scale factors computed from Sherpa2.2.1 and MG5_aMC+Py8 CKKWL.

Correction scale factor from the cross section calculated with leptons at the Born-level to the cross section calculated with dressed leptons as a function of the H$_{\mathrm{T}}$ in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events, averaging the electron and muon channels, derived with Sherpa2.2.11. The systematic uncertainty is obtained with an enveloppe around scale factors computed from Sherpa2.2.1 and MG5_aMC+Py8 CKKWL.

Correction scale factor from the cross section calculated with leptons at the Born-level to the cross section calculated with dressed leptons as a function of the $\Delta R_{Z,j}^{min}$ in the high-S$_{\mathrm{T}}$ region in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events, averaging the electron and muon channels, derived with Sherpa2.2.11. The systematic uncertainty is obtained with an enveloppe around scale factors computed from Sherpa2.2.1 and MG5_aMC+Py8 CKKWL.

Correction scale factor from the cross section calculated with leptons at the Born-level to the cross section calculated with dressed leptons as a function of the jet multiplicity in the high-S$_{\mathrm{T}}$ region in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events, averaging the electron and muon channels, derived with Sherpa2.2.11. The systematic uncertainty is obtained with an enveloppe around scale factors computed from Sherpa2.2.1 and MG5_aMC+Py8 CKKWL.

Correction scale factor from the cross section calculated with an overlap removal with jets of pT greater than 100 GeV to the cross section calculated with an overlap removal with jets of pT greater than 30 GeV as a function of the Z boson p$_{\mathrm{T}}$ in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events, averaging the electron and muon channels, derived with Sherpa2.2.11. The systematic uncertainty is obtained with an enveloppe around scale factors computed from Sherpa2.2.1 and MG5_aMC+Py8 CKKWL.

Correction scale factor from the cross section calculated with an overlap removal with jets of pT greater than 100 GeV to the cross section calculated with an overlap removal with jets of pT greater than 30 GeV as a function of the leading jet p$_{\mathrm{T}}$ in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events, averaging the electron and muon channels, derived with Sherpa2.2.11. The systematic uncertainty is obtained with an enveloppe around scale factors computed from Sherpa2.2.1 and MG5_aMC+Py8 CKKWL.

Correction scale factor from the cross section calculated with an overlap removal with jets of pT greater than 100 GeV to the cross section calculated with an overlap removal with jets of pT greater than 30 GeV as a function of the jet multiplicity in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events, averaging the electron and muon channels, derived with Sherpa2.2.11. The systematic uncertainty is obtained with an enveloppe around scale factors computed from Sherpa2.2.1 and MG5_aMC+Py8 CKKWL.

Correction scale factor from the cross section calculated with an overlap removal with jets of pT greater than 100 GeV to the cross section calculated with an overlap removal with jets of pT greater than 30 GeV as a function of the jet multiplicity in the high-p$_{\mathrm{T}}$ region in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events, averaging the electron and muon channels, derived with Sherpa2.2.11. The systematic uncertainty is obtained with an enveloppe around scale factors computed from Sherpa2.2.1 and MG5_aMC+Py8 CKKWL.

Correction scale factor from the cross section calculated with an overlap removal with jets of pT greater than 100 GeV to the cross section calculated with an overlap removal with jets of pT greater than 30 GeV as a function of the $\Delta R_{Z,j}^{min}$ in the high-p$_{\mathrm{T}}$ region in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events, averaging the electron and muon channels, derived with Sherpa2.2.11. The systematic uncertainty is obtained with an enveloppe around scale factors computed from Sherpa2.2.1 and MG5_aMC+Py8 CKKWL.

Correction scale factor from the cross section calculated with an overlap removal with jets of pT greater than 100 GeV to the cross section calculated with an overlap removal with jets of pT greater than 30 GeV as a function of the $r_{Z,j}$ in the high-p$_{\mathrm{T}}$ region in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events, averaging the electron and muon channels, derived with Sherpa2.2.11. The systematic uncertainty is obtained with an enveloppe around scale factors computed from Sherpa2.2.1 and MG5_aMC+Py8 CKKWL.

Correction scale factor from the cross section calculated with an overlap removal with jets of pT greater than 100 GeV to the cross section calculated with an overlap removal with jets of pT greater than 30 GeV as a function of the $r_{Z,j}$ in the collinear region in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events, averaging the electron and muon channels, derived with Sherpa2.2.11. The systematic uncertainty is obtained with an enveloppe around scale factors computed from Sherpa2.2.1 and MG5_aMC+Py8 CKKWL.

Correction scale factor from the cross section calculated with an overlap removal with jets of pT greater than 100 GeV to the cross section calculated with an overlap removal with jets of pT greater than 30 GeV as a function of the $r_{Z,j}$ in the back-to-back region in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events, averaging the electron and muon channels, derived with Sherpa2.2.11. The systematic uncertainty is obtained with an enveloppe around scale factors computed from Sherpa2.2.1 and MG5_aMC+Py8 CKKWL.

Correction scale factor from the cross section calculated with an overlap removal with jets of pT greater than 100 GeV to the cross section calculated with an overlap removal with jets of pT greater than 30 GeV as a function of the jet multiplicity in the collinear region in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events, averaging the electron and muon channels, derived with Sherpa2.2.11. The systematic uncertainty is obtained with an enveloppe around scale factors computed from Sherpa2.2.1 and MG5_aMC+Py8 CKKWL.

Correction scale factor from the cross section calculated with an overlap removal with jets of pT greater than 100 GeV to the cross section calculated with an overlap removal with jets of pT greater than 30 GeV as a function of the jet multiplicity in the back-to-back region in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events, averaging the electron and muon channels, derived with Sherpa2.2.11. The systematic uncertainty is obtained with an enveloppe around scale factors computed from Sherpa2.2.1 and MG5_aMC+Py8 CKKWL.

Correction scale factor from the cross section calculated with an overlap removal with jets of pT greater than 100 GeV to the cross section calculated with an overlap removal with jets of pT greater than 30 GeV as a function of the H$_{\mathrm{T}}$ in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events, averaging the electron and muon channels, derived with Sherpa2.2.11. The systematic uncertainty is obtained with an enveloppe around scale factors computed from Sherpa2.2.1 and MG5_aMC+Py8 CKKWL.

Correction scale factor from the cross section calculated with an overlap removal with jets of pT greater than 100 GeV to the cross section calculated with an overlap removal with jets of pT greater than 30 GeV as a function of the $\Delta R_{Z,j}^{min}$ in the high-S$_{\mathrm{T}}$ region in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events, averaging the electron and muon channels, derived with Sherpa2.2.11. The systematic uncertainty is obtained with an enveloppe around scale factors computed from Sherpa2.2.1 and MG5_aMC+Py8 CKKWL.

Correction scale factor from the cross section calculated with an overlap removal with jets of pT greater than 100 GeV to the cross section calculated with an overlap removal with jets of pT greater than 30 GeV as a function of the jet multiplicity in the high-S$_{\mathrm{T}}$ region in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events, averaging the electron and muon channels, derived with Sherpa2.2.11. The systematic uncertainty is obtained with an enveloppe around scale factors computed from Sherpa2.2.1 and MG5_aMC+Py8 CKKWL.

Measured fiducial differential cross sections for the Z boson p$_{\mathrm{T}}$ in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events, where the EW Zjj contribution is treated as signal and not subtracted as background. The statistical, systematic, and luminosity uncertainties are given.

Measured fiducial differential cross sections for the leading jet p$_{\mathrm{T}}$ in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events, where the EW Zjj contribution is treated as signal and not subtracted as background. The statistical, systematic, and luminosity uncertainties are given.

Measured fiducial differential cross sections for the jet multiplicity in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events, where the EW Zjj contribution is treated as signal and not subtracted as background. The statistical, systematic, and luminosity uncertainties are given.

Measured fiducial differential cross sections for the jet multiplicity in the high-p$_{\mathrm{T}}$ region in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events, where the EW Zjj contribution is treated as signal and not subtracted as background. The statistical, systematic, and luminosity uncertainties are given.

Measured fiducial differential cross sections for the $\Delta R_{Z,j}^{min}$ in the high-p$_{\mathrm{T}}$ region in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events, where the EW Zjj contribution is treated as signal and not subtracted as background. The statistical, systematic, and luminosity uncertainties are given.

Measured fiducial differential cross sections for the $r_{Z,j}$ in the high-p$_{\mathrm{T}}$ region in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events, where the EW Zjj contribution is treated as signal and not subtracted as background. The statistical, systematic, and luminosity uncertainties are given.

Measured fiducial differential cross sections for the $r_{Z,j}$ in the collinear region in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events, where the EW Zjj contribution is treated as signal and not subtracted as background. The statistical, systematic, and luminosity uncertainties are given.

Measured fiducial differential cross sections for the $r_{Z,j}$ in the back-to-back region in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events, where the EW Zjj contribution is treated as signal and not subtracted as background. The statistical, systematic, and luminosity uncertainties are given.

Measured fiducial differential cross sections for the jet multiplicity in the collinear region in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events, where the EW Zjj contribution is treated as signal and not subtracted as background. The statistical, systematic, and luminosity uncertainties are given.

Measured fiducial differential cross sections for the jet multiplicity in the back-to-back region in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events, where the EW Zjj contribution is treated as signal and not subtracted as background. The statistical, systematic, and luminosity uncertainties are given.

Measured fiducial differential cross sections for the H$_{\mathrm{T}}$ in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events, where the EW Zjj contribution is treated as signal and not subtracted as background. The statistical, systematic, and luminosity uncertainties are given.

Measured fiducial differential cross sections for the $\Delta R_{Z,j}^{min}$ in the high-S$_{\mathrm{T}}$ region in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events, where the EW Zjj contribution is treated as signal and not subtracted as background. The statistical, systematic, and luminosity uncertainties are given.

Measured fiducial differential cross sections for the jet multiplicity in the high-S$_{\mathrm{T}}$ region in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events, where the EW Zjj contribution is treated as signal and not subtracted as background. The statistical, systematic, and luminosity uncertainties are given.

Systematic uncertainties for the Z boson p$_{\mathrm{T}}$ in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events, where the EW Zjj contribution is treated as signal and not subtracted as background. The uncertainties are presented as a percentage of the measured cross-section for the upward variation of each source of uncertainty in each bin.

Systematic uncertainties for the leading jet p$_{\mathrm{T}}$ in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events, where the EW Zjj contribution is treated as signal and not subtracted as background. The uncertainties are presented as a percentage of the measured cross-section for the upward variation of each source of uncertainty in each bin.

Systematic uncertainties for the jet multiplicity in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events, where the EW Zjj contribution is treated as signal and not subtracted as background. The uncertainties are presented as a percentage of the measured cross-section for the upward variation of each source of uncertainty in each bin.

Systematic uncertainties for the jet multiplicity in the high-p$_{\mathrm{T}}$ region in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events, where the EW Zjj contribution is treated as signal and not subtracted as background. The uncertainties are presented as a percentage of the measured cross-section for the upward variation of each source of uncertainty in each bin.

Systematic uncertainties for the $\Delta R_{Z,j}^{min}$ in the high-p$_{\mathrm{T}}$ region in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events, where the EW Zjj contribution is treated as signal and not subtracted as background. The uncertainties are presented as a percentage of the measured cross-section for the upward variation of each source of uncertainty in each bin.

Systematic uncertainties for the $r_{Z,j}$ in the high-p$_{\mathrm{T}}$ region in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events, where the EW Zjj contribution is treated as signal and not subtracted as background. The uncertainties are presented as a percentage of the measured cross-section for the upward variation of each source of uncertainty in each bin.

Systematic uncertainties for the $r_{Z,j}$ in the collinear region in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events, where the EW Zjj contribution is treated as signal and not subtracted as background. The uncertainties are presented as a percentage of the measured cross-section for the upward variation of each source of uncertainty in each bin.

Systematic uncertainties for the $r_{Z,j}$ in the back-to-back region in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events, where the EW Zjj contribution is treated as signal and not subtracted as background. The uncertainties are presented as a percentage of the measured cross-section for the upward variation of each source of uncertainty in each bin.

Systematic uncertainties for the jet multiplicity in the collinear region in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events, where the EW Zjj contribution is treated as signal and not subtracted as background. The uncertainties are presented as a percentage of the measured cross-section for the upward variation of each source of uncertainty in each bin.

Systematic uncertainties for the jet multiplicity in the back-to-back region in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events, where the EW Zjj contribution is treated as signal and not subtracted as background. The uncertainties are presented as a percentage of the measured cross-section for the upward variation of each source of uncertainty in each bin.

Systematic uncertainties for the H$_{\mathrm{T}}$ in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events, where the EW Zjj contribution is treated as signal and not subtracted as background. The uncertainties are presented as a percentage of the measured cross-section for the upward variation of each source of uncertainty in each bin.

Systematic uncertainties for the $\Delta R_{Z,j}^{min}$ in the high-S$_{\mathrm{T}}$ region in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events, where the EW Zjj contribution is treated as signal and not subtracted as background. The uncertainties are presented as a percentage of the measured cross-section for the upward variation of each source of uncertainty in each bin.

Systematic uncertainties for the jet multiplicity in the high-S$_{\mathrm{T}}$ region in Z($\to \ell^{+} \ell^{-}$) + high p$_{\mathrm{T}}$ jets events, where the EW Zjj contribution is treated as signal and not subtracted as background. The uncertainties are presented as a percentage of the measured cross-section for the upward variation of each source of uncertainty in each bin.

Dijet signal efficiencies as a function of the signal mass and lifetime for events satisfying all event and vertex requirements, with corrections based on systematic differences in the vertex reconstruction efficiency between data and simulation.

The distribution of $d_{\mathrm{BV}}$ for $\geq$5-track one-vertex events in data and three simulated multijet signal samples each with a mass of 1600 GeV. The production cross section for each signal model is assumed to be the lower limit excluded by CMS-EXO-17-018, corresponding to values of 0.8, 0.25, and 0.15 fb for the samples with $c\tau =$ 0.3, 1.0, and 10 mm, respectively. The last bin includes the overflow events. This bin includes one event in data with a vertex with large $d_{\mathrm{BV}}$ that appears to arise from tracks originating from separate pp interaction vertices, consistent with background.

Distribution of the $x$-$y$ distances between vertices, $d_{\mathrm{VV}}$, for 2017 and 2018 data. The background distribution $d_{\mathrm{VV}}^{\kern 0.15em\mathrm{C}}$ (blue continuous line) is constructed from one-vertex events in data, and is normalized to the number of two-vertex events in data with two 3-track vertices. The two vertical red dashed lines separate the regions used in the fit.

Distribution of the $x$-$y$ distances between vertices, $d_{\mathrm{VV}}$, for 2017 and 2018 data. The background distribution $d_{\mathrm{VV}}^{\kern 0.15em\mathrm{C}}$ (blue continuous line) is constructed from one-vertex events in data, and is normalized to the number of two-vertex events in data which have exactly one 4-track vertex and one 3-track vertex. The two vertical red dashed lines separate the regions used in the fit.

Distribution of the $x$-$y$ distances between vertices, $d_{\mathrm{VV}}$, for 2017 and 2018 data. The background distribution $d_{\mathrm{VV}}^{\kern 0.15em\mathrm{C}}$ (blue continuous line) is constructed from one-vertex events in data, and is normalized to the number of two-vertex events in data with two 4-track vertices. The two vertical red dashed lines separate the regions used in the fit.

Distribution of the $x$-$y$ distances between vertices, $d_{\mathrm{VV}}$, for 2017 and 2018 data. The background distribution $d_{\mathrm{VV}}^{\kern 0.15em\mathrm{C}}$ (blue continuous line) is constructed from one-vertex events in data, and is normalized using $\geq$5-track one-vertex event information. The two vertical red dashed lines separate the regions used in the fit.

Predicted yields for the background-only normalized template, predicted yields for three simulated multijet signals each with a mass of 1600 GeV, and the observed yield in each $d_{\mathrm{VV}}$ bin. The production cross section for each signal model is assumed to be the lower limit excluded by CMS-EXO-17-018, corresponding to values of 0.8, 0.25, and 0.15 fb for samples with $c\tau =$ 0.3, 1.0, and 10 mm, respectively. The uncertainties in the signal yields and the systematic uncertainties in the background prediction reflect the systematic uncertainties given in the text.

Observed 95% CL upper limits on the product of cross section and branching fraction squared for the multijet signals, as a function of mass and $c\tau$. The overlaid mass-lifetime exclusion curves assume pair-production cross sections for the neutralino (red) and gluino (purple) with 100% branching fraction to each model's respective decay mode specified. The solid black (dashed colored) lines represent the observed (median expected) limits at 95% CL. The thin black lines represent the variation of the observed limit within theoretical uncertainties of the signal cross section. The thin dashed colored lines represent the region containing 68% of the expected limit distribution under the background-only hypothesis. The observed limits from the CMS displaced jets search (CMS-EXO-19-021) are also shown in teal for comparison.

Observed 95% CL upper limits on the product of cross section and branching fraction squared for the multijet signals, as a function of mass and $c\tau$. The overlaid mass-lifetime exclusion curves assume pair-production cross sections for the neutralino (red) and gluino (purple) with 100% branching fraction to each model's respective decay mode specified. The solid black (dashed colored) lines represent the observed (median expected) limits at 95% CL. The thin black lines represent the variation of the observed limit within theoretical uncertainties of the signal cross section. The thin dashed colored lines represent the region containing 68% of the expected limit distribution under the background-only hypothesis. The observed limits from the CMS displaced jets search (CMS-EXO-19-021) are also shown in teal for comparison.

Observed 95% CL upper limits on the product of cross section and branching fraction squared for the multijet signals, as a function of mass and $c\tau$. The overlaid mass-lifetime exclusion curves assume pair-production cross sections for the neutralino (red) and gluino (purple) with 100% branching fraction to each model's respective decay mode specified. The solid black (dashed colored) lines represent the observed (median expected) limits at 95% CL. The thin black lines represent the variation of the observed limit within theoretical uncertainties of the signal cross section. The thin dashed colored lines represent the region containing 68% of the expected limit distribution under the background-only hypothesis. The observed limits from the CMS displaced jets search (CMS-EXO-19-021) are also shown in teal for comparison.

Observed 95% CL upper limits on the product of cross section and branching fraction squared for the dijet signals, as a function of mass and $c\tau$. The overlaid mass-lifetime exclusion curves assume pair-production cross sections for the top squark with 100% branching fraction to each model's respective decay mode specified. The solid black (dashed colored) lines represent the observed (median expected) limits at 95% CL. The thin black lines represent the variation of the observed limit within theoretical uncertainties of the signal cross section. The thin dashed colored lines represent the region containing 68% of the expected limit distribution under the background-only hypothesis. The observed limits from the CMS displaced jets search (CMS-EXO-19-021) are also shown in teal for comparison.

Observed 95% CL upper limits on the product of cross section and branching fraction squared for the dijet signals, as a function of mass and $c\tau$. The overlaid mass-lifetime exclusion curves assume pair-production cross sections for the top squark with 100% branching fraction to each model's respective decay mode specified. The solid black (dashed colored) lines represent the observed (median expected) limits at 95% CL. The thin black lines represent the variation of the observed limit within theoretical uncertainties of the signal cross section. The thin dashed colored lines represent the region containing 68% of the expected limit distribution under the background-only hypothesis. The observed limits from the CMS displaced jets search (CMS-EXO-19-021) are also shown in teal for comparison.

Observed and expected 95% CL upper limits on the product of cross section and branching fraction squared, as a function of mass for multijet signals, for a fixed $c\tau$ of 300um in the full Run-2 data set. The neutralino and gluino pair production cross sections are shown for the multijet signals.

Observed and expected 95% CL upper limits on the product of cross section and branching fraction squared, as a function of mass for dijet signals, for a fixed $c\tau$ of 300um in the full Run-2 data set. The top squark pair-production cross section is shown for the dijet signals.

Observed and expected 95% CL upper limits on the product of cross section and branching fraction squared, as a function of mass for multijet signals, for a fixed $c\tau$ of 1 mm in the full Run-2 data set. The neutralino and gluino pair production cross sections are shown for the multijet signals.

Observed and expected 95% CL upper limits on the product of cross section and branching fraction squared, as a function of mass for dijet signals, for a fixed $c\tau$ of 1 mm in the full Run-2 data set. The top squark pair-production cross section is shown for the dijet signals.

Observed and expected 95% CL upper limits on the product of cross section and branching fraction squared, as a function of mass for multijet signals, for a fixed $c\tau$ of 10 mm in the full Run-2 data set. The neutralino and gluino pair production cross sections are shown for the multijet signals.

Observed and expected 95% CL upper limits on the product of cross section and branching fraction squared, as a function of mass for dijet signals, for a fixed $c\tau$ of 10 mm in the full Run-2 data set. The top squark pair-production cross section is shown for the dijet signals.

Observed and expected 95% CL upper limits on the product of cross section and branching fraction squared, as a function of $c\tau$ for multijet signals, for a fixed mass of 800 GeV in the full Run-2 data set. The neutralino and gluino pair production cross sections are shown for the multijet signals.

Observed and expected 95% CL upper limits on the product of cross section and branching fraction squared, as a function of $c\tau$ for dijet signals, for a fixed mass of 800 GeV in the full Run-2 data set. The top squark pair-production cross section is shown for the dijet signals.

Observed and expected 95% CL upper limits on the product of cross section and branching fraction squared, as a function of $c\tau$ for multijet signals, for a fixed mass of 1600 GeV in the full Run-2 data set. The neutralino and gluino pair production cross sections are shown for the multijet signals.

Observed and expected 95% CL upper limits on the product of cross section and branching fraction squared, as a function of $c\tau$ for dijet signals, for a fixed mass of 1600 GeV in the full Run-2 data set. The top squark pair-production cross section is shown for the dijet signals.

Observed and expected 95% CL upper limits on the product of cross section and branching fraction squared, as a function of $c\tau$ for multijet signals, for a fixed mass of 2400 GeV in the full Run-2 data set. The neutralino and gluino pair production cross sections are shown for the multijet signals. For $m$ = 2400 GeV, the expected neutralino cross section is $\approx 8\times 10^{-5}$ fb and is not shown.

Observed and expected 95% CL upper limits on the product of cross section and branching fraction squared, as a function of $c\tau$ for dijet signals, for a fixed mass of 2400 GeV in the full Run-2 data set. The top squark pair-production cross section is shown for the dijet signals.

Data-to-simulation efficiency correction factors, shown for multijet and dijet signal topologies in several ranges of $c\tau$. Note that these correction factors account for the two long-lived particles in the simulated events, and are therefore the total correction factors used to scale event yields rather than the correction factors one would apply to individual vertices.

Distribution of the azimuthal angle between vertices, $\Delta\phi_{\mathrm{VV}}$, for 2017 and 2018 data. The background distribution (blue continuous line) is constructed from 3-track one-vertex events in data, and is normalized to the number of 3-track two-vertex events in data.

Distribution of the azimuthal angle between vertices, $\Delta\phi_{\mathrm{VV}}$, for 2017 and 2018 data. The background distribution (blue continuous line) is constructed from 4-track and 3-track one-vertex events in data, and is normalized to the number of two-vertex events in data which have exactly one 4-track vertex and one 3-track vertex.

Distribution of the azimuthal angle between vertices, $\Delta\phi_{\mathrm{VV}}$, for 2017 and 2018 data. The background distribution (blue continuous line) is constructed from 4-track one-vertex events in data, and is normalized to the number of 4-track two-vertex events in data.

Distribution of the azimuthal angle between vertices, $\Delta\phi_{\mathrm{VV}}$, for 2017 and 2018 data. The background distribution (blue continuous line) is constructed from $\geq$5-track one-vertex events in data, and is normalized using one-vertex event information. No $\geq$5-track two-vertex data events pass the selection.