95% CL upper limits as a function of (left) cτ_{π_d} and (right) M_φ. The upper plots show the expected and observed limits on σ(pp →φ^†φ) for m_{π_d} = 20 GeV: (a) using M_φ = 1.6 TeV and (b) using cτ_{π_d} = 20 mm. The lower plots show a comparison of the observed limits for all three dark pion masses: (c) using M_φ = 1.4 TeV, and (d) using cτ_{π_d} = 1 mm. The mediator mass-dependent theoretical cross-section is given with the band corresponding to the uncertainty from NNLL-Fast.

95% CL upper limits as a function of (left) cτ_{π_d} and (right) M_φ. The upper plots show the expected and observed limits on σ(pp →φ^†φ) for m_{π_d} = 20 GeV: (a) using M_φ = 1.6 TeV and (b) using cτ_{π_d} = 20 mm. The lower plots show a comparison of the observed limits for all three dark pion masses: (c) using M_φ = 1.4 TeV, and (d) using cτ_{π_d} = 1 mm. The mediator mass-dependent theoretical cross-section is given with the band corresponding to the uncertainty from NNLL-Fast.

95% CL exclusion contours as a function of M_φ and cτ_{π_d}. The expected and observed limits on σ(pp →φ^†φ) are shown for (a) m_{π_d} = 5 GeV, (b) m_{π_d} = 10 GeV, and (c) m_{π_d} = 20 GeV. A comparison of the observed limits is given in (d) for each of the three dark pion masses.

95% CL exclusion contours as a function of M_φ and cτ_{π_d}. The expected and observed limits on σ(pp →φ^†φ) are shown for (a) m_{π_d} = 5 GeV, (b) m_{π_d} = 10 GeV, and (c) m_{π_d} = 20 GeV. A comparison of the observed limits is given in (d) for each of the three dark pion masses.

95% CL exclusion contours as a function of M_φ and cτ_{π_d}. The expected and observed limits on σ(pp →φ^†φ) are shown for (a) m_{π_d} = 5 GeV, (b) m_{π_d} = 10 GeV, and (c) m_{π_d} = 20 GeV. A comparison of the observed limits is given in (d) for each of the three dark pion masses.

95% CL exclusion contours as a function of M_φ and cτ_{π_d}. The expected and observed limits on σ(pp →φ^†φ) are shown for (a) m_{π_d} = 5 GeV, (b) m_{π_d} = 10 GeV, and (c) m_{π_d} = 20 GeV. A comparison of the observed limits is given in (d) for each of the three dark pion masses.

Comparison of the 95% CL exclusion contours between ATLAS and CMS  for (a) models with m_{π_d} = 10 GeV and (b) models with m_{π_d} = 20 GeV. The expected and observed limits are shown for ATLAS, while only the observed limits in both the model agnostic and GNN cases are included for CMS. The expected limits from the CMS result are omitted, but are, in general, very close to the CMS observed limits.

Comparison of the 95% CL exclusion contours between ATLAS and CMS  for (a) models with m_{π_d} = 10 GeV and (b) models with m_{π_d} = 20 GeV. The expected and observed limits are shown for ATLAS, while only the observed limits in both the model agnostic and GNN cases are included for CMS. The expected limits from the CMS result are omitted, but are, in general, very close to the CMS observed limits.

Normalized minPTF distribution in data, with three selected signal samples for comparison

95% CL exclusion contours as a function of M_φ and cτ_{π_d} for the Cut-Based analysis. The expected and observed limits on σ(pp →φ^†φ) are shown for (a) m_{π_d} = 5 GeV, (b) m_{π_d} = 10 GeV, and (c) m_{π_d} = 20 GeV. A comparison of the observed limits is given in (d) for each of the three dark pion masses.

95% CL exclusion contours as a function of M_φ and cτ_{π_d} for the Cut-Based analysis. The expected and observed limits on σ(pp →φ^†φ) are shown for (a) m_{π_d} = 5 GeV, (b) m_{π_d} = 10 GeV, and (c) m_{π_d} = 20 GeV. A comparison of the observed limits is given in (d) for each of the three dark pion masses.

95% CL exclusion contours as a function of M_φ and cτ_{π_d} for the Cut-Based analysis. The expected and observed limits on σ(pp →φ^†φ) are shown for (a) m_{π_d} = 5 GeV, (b) m_{π_d} = 10 GeV, and (c) m_{π_d} = 20 GeV. A comparison of the observed limits is given in (d) for each of the three dark pion masses.

95% CL exclusion contours as a function of M_φ and cτ_{π_d} for the Cut-Based analysis. The expected and observed limits on σ(pp →φ^†φ) are shown for (a) m_{π_d} = 5 GeV, (b) m_{π_d} = 10 GeV, and (c) m_{π_d} = 20 GeV. A comparison of the observed limits is given in (d) for each of the three dark pion masses.

Comparison of observed and expected 95% CL limits of the Cut-Based analysis against the corresponding BDT-based analysis. Limits on σ(pp →φ^†φ) are shown as a function of M_φ and cτ_{π_d} for (a) m_{π_d} = 5 GeV, (b) m_{π_d} = 10 GeV, and (c) m_{π_d} = 20 GeV.

Comparison of observed and expected 95% CL limits of the Cut-Based analysis against the corresponding BDT-based analysis. Limits on σ(pp →φ^†φ) are shown as a function of M_φ and cτ_{π_d} for (a) m_{π_d} = 5 GeV, (b) m_{π_d} = 10 GeV, and (c) m_{π_d} = 20 GeV.

Comparison of observed and expected 95% CL limits of the Cut-Based analysis against the corresponding BDT-based analysis. Limits on σ(pp →φ^†φ) are shown as a function of M_φ and cτ_{π_d} for (a) m_{π_d} = 5 GeV, (b) m_{π_d} = 10 GeV, and (c) m_{π_d} = 20 GeV.

Normalized event-level BDT response distribution in data, with three selected signal samples for comparison.

Normalized jet-matched displaced vertex multiplicity (N_DV) distribution in data, with three selected signal samples for comparison.

Normalized event-level BDT response distribution in data, with three selected signal samples for comparison. All three signal models have M_φ = 1.8 TeV and cτ_{π_d} = 75 mm, but different m_{π_d}.

Normalized event-level BDT response distribution in data, with three selected signal samples for comparison. All three signal models have m_{π_d} = 10 GeV and cτ_{π_d} = 20 mm, but different M_φ.

Normalized event-level BDT response distribution in data, with three selected signal samples for comparison. All three signal models have m_{π_d} = 10 GeV and M_φ = 1.4 TeV, but different cτ_{π_d}.

Observed 95% CL limits for models with m_{π_d} = 5, 10, and 20 GeV and cτ_{π_d} = 1000 mm as a function of dark mediator mass. The mediator mass-dependent theoretical cross-section is given with the band corresponding to the uncertainty from NNLL-Fast.

Observed 95% CL limits for models with m_{π_d} = 5, 10, and 20 GeV and cτ_{π_d} = 500 mm as a function of dark mediator mass. The mediator mass-dependent theoretical cross-section is given with the band corresponding to the uncertainty from NNLL-Fast.

Observed 95% CL limits for models with m_{π_d} = 5, 10, and 20 GeV and cτ_{π_d} = 300 mm as a function of dark mediator mass. The mediator mass-dependent theoretical cross-section is given with the band corresponding to the uncertainty from NNLL-Fast.

Observed 95% CL limits for models with m_{π_d} = 5, 10, and 20 GeV and cτ_{π_d} = 150 mm as a function of dark mediator mass. The mediator mass-dependent theoretical cross-section is given with the band corresponding to the uncertainty from NNLL-Fast.

Observed 95% CL limits for models with m_{π_d} = 5, 10, and 20 GeV and cτ_{π_d} = 75 mm as a function of dark mediator mass. The mediator mass-dependent theoretical cross-section is given with the band corresponding to the uncertainty from NNLL-Fast.

Observed 95% CL limits for models with m_{π_d} = 5, 10, and 20 GeV and cτ_{π_d} = 20 mm as a function of dark mediator mass. The mediator mass-dependent theoretical cross-section is given with the band corresponding to the uncertainty from NNLL-Fast.

Observed 95% CL limits for models with m_{π_d} = 5, 10, and 20 GeV and cτ_{π_d} = 5 mm as a function of dark mediator mass. The mediator mass-dependent theoretical cross-section is given with the band corresponding to the uncertainty from NNLL-Fast.

Observed 95% CL limit for models with m_{π_d} = 5, 10, and 20 GeV and cτ_{π_d} = 2 mm as a function of dark mediator mass. The mediator mass-dependent theoretical cross-section is given with the band corresponding to the uncertainty from NNLL-Fast.

Observed 95% CL limits for models with m_{π_d} = 5, 10, and 20 GeV and cτ_{π_d} = 1 mm as a function of dark mediator mass. The mediator mass-dependent theoretical cross-section is given with the band corresponding to the uncertainty from NNLL-Fast.

Observed 95% CL limits for models with m_{π_d} = 5, 10, and 20 GeV and M_φ = 2.2 TeV as a function of dark pion lifetime. The mediator mass-dependent theoretical cross-section is given with the band corresponding to the uncertainty from NNLL-Fast.

Observed 95% CL limits for models with m_{π_d} = 5, 10, and 20 GeV and M_φ = 2 TeV as a function of dark pion lifetime. The mediator mass-dependent theoretical cross-section is given with the band corresponding to the uncertainty from NNLL-Fast.

Observed 95% CL limits for models with m_{π_d} = 5, 10, and 20 GeV and M_φ = 1.8 TeV as a function of dark pion lifetime. The mediator mass-dependent theoretical cross-section is given with the band corresponding to the uncertainty from NNLL-Fast.

Observed 95% CL limits for models with m_{π_d} = 5, 10, and 20 GeV and M_φ = 1.6 TeV as a function of dark pion lifetime. The mediator mass-dependent theoretical cross-section is given with the band corresponding to the uncertainty from NNLL-Fast.

Observed 95% CL limits for models with m_{π_d} = 5, 10, and 20 GeV and M_φ = 1.4 TeV as a function of dark pion lifetime. The mediator mass-dependent theoretical cross-section is given with the band corresponding to the uncertainty from NNLL-Fast.

Observed 95% CL limits for models with m_{π_d} = 5, 10, and 20 GeV and M_φ = 1 TeV as a function of dark pion lifetime. The mediator mass-dependent theoretical cross-section is given with the band corresponding to the uncertainty from NNLL-Fast.

Observed and expected 95% CL limits for models with m_{π_d} = 20 GeV as a function of M_φ and cτ_{π_d}.

Observed and expected 95% CL limits for models with m_{π_d} = 20 GeV as a function of M_φ and cτ_{π_d}.

Observed and expected 95% CL limits for models with m_{π_d} = 20 GeV as a function of M_φ and cτ_{π_d}.

Observed and expected 95% CL limits for models with m_{π_d} = 20 GeV as a function of M_φ and cτ_{π_d}.

Observed and expected 95% CL limits for models with m_{π_d} = 20 GeV as a function of M_φ and cτ_{π_d}.

Observed and expected 95% CL limits for models with m_{π_d} = 20 GeV as a function of M_φ and cτ_{π_d}.

Cut-Flow efficiencies for the m_{π_d} = 10 GeV, M_φ = 1600 GeV models for all cuts before entering the Search region (ABCD plane) and then for each of the ABCD regions separately.

Cut-Flow efficiencies for the m_{π_d} = 10 GeV, M_φ = 1400 GeV models for all cuts before entering the Search region (ABCD plane) and then for each of the ABCD regions separately.

Cut-Flow efficiencies for the m_{π_d} = 10 GeV, M_φ = 1000 GeV models for all cuts before entering the Search region (ABCD plane) and then for each of the ABCD regions separately.

Cut-Flow efficiencies for the m_{π_d} = 5 GeV, M_φ = 2200 GeV models for all cuts before entering the Search region (ABCD plane) and then for each of the ABCD regions separately.

Cut-Flow efficiencies for the m_{π_d} = 5 GeV, M_φ = 2000 GeV models for all cuts before entering the Search region (ABCD plane) and then for each of the ABCD regions separately.

Cut-Flow efficiencies for the m_{π_d} = 5 GeV, M_φ = 1800 GeV models for all cuts before entering the Search region (ABCD plane) and then for each of the ABCD regions separately.

Cut-Flow efficiencies for the m_{π_d} = 5 GeV, M_φ = 1600 GeV models for all cuts before entering the Search region (ABCD plane) and then for each of the ABCD regions separately.

Cut-Flow efficiencies for the m_{π_d} = 5 GeV, M_φ = 1400 GeV models for all cuts before entering the Search region (ABCD plane) and then for each of the ABCD regions separately.

Cut-Flow efficiencies for the m_{π_d} = 5 GeV, M_φ = 1000 GeV models for all cuts before entering the Search region (ABCD plane) and then for each of the ABCD regions separately.

Cut-Flow efficiencies for the m_{π_d} = 20 GeV, M_φ = 2200 GeV models for all cuts before entering the Search region (ABCD plane) and then for each of the ABCD regions separately.

Cut-Flow efficiencies for the m_{π_d} = 20 GeV, M_φ = 2000 GeV models for all cuts before entering the Search region (ABCD plane) and then for each of the ABCD regions separately.

Cut-Flow efficiencies for the m_{π_d} = 20 GeV, M_φ = 1800 GeV models for all cuts before entering the Search region (ABCD plane) and then for each of the ABCD regions separately.

Cut-Flow efficiencies for the m_{π_d} = 20 GeV, M_φ = 1600 GeV models for all cuts before entering the Search region (ABCD plane) and then for each of the ABCD regions separately.

Cut-Flow efficiencies for the m_{π_d} = 20 GeV, M_φ = 1400 GeV models for all cuts before entering the Search region (ABCD plane) and then for each of the ABCD regions separately.

Cut-Flow efficiencies for the m_{π_d} = 20 GeV, M_φ = 1000 GeV models for all cuts before entering the Search region (ABCD plane) and then for each of the ABCD regions separately.

Cut-Flow efficiencies for the m_{π_d} = 10 GeV, M_φ = 2200 GeV models for all cuts before entering the Search region (ABCD plane) and then for each of the ABCD regions separately.

Cut-Flow efficiencies for the m_{π_d} = 10 GeV, M_φ = 2000 GeV models for all cuts before entering the Search region (ABCD plane) and then for each of the ABCD regions separately.

Cut-Flow efficiencies for the m_{π_d} = 10 GeV, M_φ = 1800 GeV models for all cuts before entering the Search region (ABCD plane) and then for each of the ABCD regions separately.

Observed 95% $\text{CL}_\text{S}$ upper limits on the production cross-section times acceptance times branching ratio to jets, $\sigma \cdot A \cdot \text{BR}$, of Gaussian-shaped signals of 5%, 10%, and 15% width relative to their peak mass, $m_G$. Also included are the corresponding expected upper limits predicted for the case the $m_{jj}$ distribution is observed to be identical to the background prediction in each bin and the $1\sigma$ and $2\sigma$ envelopes of outcomes expected for Poisson fluctuations around the background expectation. Limits are derived from the J100 signal region.

Observed 95% $\text{CL}_\text{S}$ upper limits on the the value of the coupling to quarks, $g_q$, of the $Z^\prime$ model as a function of the resonance mass $m_{Z^\prime}$. Also included are the corresponding expected upper limits predicted for the case the $m_{jj}$ distribution is observed to be identical to the background prediction in each bin and the $1\sigma$ and $2\sigma$ envelopes of outcomes expected for Poisson fluctuations around the background expectation. Limits are derived from the J50 signal region.

Observed 95% $\text{CL}_\text{S}$ upper limits on the the value of the coupling to quarks, $g_q$, of the $Z^\prime$ model as a function of the resonance mass $m_{Z^\prime}$. Also included are the corresponding expected upper limits predicted for the case the $m_{jj}$ distribution is observed to be identical to the background prediction in each bin and the $1\sigma$ and $2\sigma$ envelopes of outcomes expected for Poisson fluctuations around the background expectation. Limits are derived from the J100 signal region.

Acceptance of simulated $Z^\prime$ signal events given the analysis event selection as a function of $m_{Z^\prime}$. The solid black line corresponds to the acceptance without a lower $m_{jj}$ requirement applied, the solid blue line includes the $m_{jj} > 344$ GeV requirement of the J50 signal region, and the solid red line includes the $m_{jj} > 481$ GeV requirement of the J100 signal region.

Numbers of events in each of the two considered datasets after consecutively applying the analysis selections.

Observed 95% confidence level (CL) exclusion limits for the (a) |U_e|² and (b) |U_μ|² mixing parameters versus the HNL mass. The expected (dashed line) exclusion limits are also shown. The 1σ and 2σ uncertainty bands around the expected exclusion limit reflect uncertainties in signal and background yields.

Data and estimated background comparison in the three lepton SRs defined for the e^±e^±μ^∓ decay mode. The hatched band represents the total uncertainty of the background. These signal regions are not orthogonal by construction, and data events can be found in more than one signal region.

Data and estimated background comparison in the three lepton SRs defined for the μ^±μ^±e^∓ decay mode. The hatched band represents the total uncertainty of the background. These signal regions are not orthogonal by construction, and data events can be found in more than one signal region.

Data and estimated background comparison in the two lepton SRs defined for the μ^±μ^±e^∓ decay mode. The hatched band represents the total uncertainty of the background. These signal regions are not orthogonal by construction, and data events can be found in more than one signal region.

Data and estimated background comparison in a region enriched in WZ SM processes, defined with N_lept^signal =3, m_T >80 GeV and SC leptons with p_T > 30 GeV, in addition to the preselection defined in Section 5. Events entering the SRs defined in Section 5 are vetoed. The last bin includes overflow. The uncertainties shown with hashed bands, include only the statistical uncertainties and the full uncertainties associated with the data-driven background estimates. The bottom panel shows the ratio of the observed data to the predicted yields.

Identification of the three lepton signal region chosen to set the limits for the e^±e^±μ^∓ decay mode. The observed (continuous line) and expected (dashed line) exclusion limits at 95% CL are also shown.

Identification of the three lepton signal region chosen to set the limits for the μ^±μ^±e^∓ decay mode. The observed (continuous line) and expected (dashed line) exclusion limits at 95% CL are also shown.

Identification of the two lepton signal region chosen to set the limits for the μ^±μ^±e^∓ decay mode. The observed (continuous line) and expected (dashed line) exclusion limits at 95% CL are also shown. The grey boxed area highlights the regions where the fit is not converging for the observed limit, given the low statistics. While they do not yield a result independently, they are further used in a combined fit with the three lepton regions. In these fits, the signal is floated simultaneously in the two lepton and 3ℓ regions, in which case there are enough statistics to converge on a limit. In this high mass region, the two lepton region gives a minor improvement to the limits in the combined fit when compared to the 3ℓ only result.

Observed 95% confidence-level exclusion in |U_μ|² versus the HNL mass, as obtained with the two lepton and three lepton signal regions, before the combination. The expected (dashed line) exclusion limits are also shown.

Observed 95% confidence-level exclusion in |U_μ|² versus the HNL mass, as obtained with the two lepton (blue) and three lepton (magenta) signal regions, before the combination. The expected (dashed line) exclusion limits are also shown. For complexness, also the combined two lepton and three lepton limits (black) are displayed, together with the 1σ and 2σ of the median expected limit.

Observed 95% confidence-level exclusion in |U_μ|² versus the HNL mass, as obtained with the three lepton only signal regions. The expected (dashed line) exclusion limits are also shown.

Observed 95% confidence-level exclusion in |U_μ|² versus the HNL mass, as obtained with the two lepton only signal regions. The expected (dashed line) exclusion limits are also shown. The grey boxed area highlights the regions where the fit is not converging for the observed limit, given the low statistics. While they do not yield a result independently, they are further used in a combined fit with the three lepton regions. In these fits, the signal is floated simultaneously in the two lepton and 3ℓ regions, in which case there are enough statistics to converge on a limit. In this high mass region, the two lepton region gives a minor improvement to the limits in the combined fit when compared to the 3ℓ only result.

Comparison between data and the background prediction for the (a) m_T(4ℓ, E_T^miss), (b) m^high(3ℓ), (c) m(Z), (d) E_T^miss, (e) p_T(Z), and (f) N_jets distribution in the (a, d) 2Z 0b, (b, e) 1Z 1b 2SFOS, and (c, f) 0Z 2SFOS region, after requiring the anomaly score to be below the 90% background rejection point. The background contributions after the likelihood fit to data ('post-fit') for the background-only hypothesis are shown as filled histograms. The 'tt+X' background component includes the tt̄Z, and tt̄H processes. The 'HF ℓ' ('LF ℓ') background component refers to processes containing one non-prompt light lepton from heavy-flavour (light-flavour) hadron decays. The ratio of the data to the background prediction ('Bkg.') is shown in the lower panel. The 'Other' contribution is dominated by the tWZ production. The size of the combined statistical and systematic uncertainty in the background prediction is indicated by the blue hatched band. The upward-pointing blue arrows indicate points for which the data-to-background ('Data/Bkg.’) ratio exceeds the vertical range of the figure. The last bin contains the overflow.

Comparison between data and the background prediction for the (a) m_T(4ℓ, E_T^miss), (b) m^high(3ℓ), (c) m(Z), (d) E_T^miss, (e) p_T(Z), and (f) N_jets distribution in the (a, d) 2Z 0b, (b, e) 1Z 1b 2SFOS, and (c, f) 0Z 2SFOS region, after requiring the anomaly score to be below the 90% background rejection point. The background contributions after the likelihood fit to data ('post-fit') for the background-only hypothesis are shown as filled histograms. The 'tt+X' background component includes the tt̄Z, and tt̄H processes. The 'HF ℓ' ('LF ℓ') background component refers to processes containing one non-prompt light lepton from heavy-flavour (light-flavour) hadron decays. The ratio of the data to the background prediction ('Bkg.') is shown in the lower panel. The 'Other' contribution is dominated by the tWZ production. The size of the combined statistical and systematic uncertainty in the background prediction is indicated by the blue hatched band. The upward-pointing blue arrows indicate points for which the data-to-background ('Data/Bkg.’) ratio exceeds the vertical range of the figure. The last bin contains the overflow.

Comparison between data and the background prediction for the (a) m_T(4ℓ, E_T^miss), (b) m^high(3ℓ), (c) m(Z), (d) E_T^miss, (e) p_T(Z), and (f) N_jets distribution in the (a, d) 2Z 0b, (b, e) 1Z 1b 2SFOS, and (c, f) 0Z 2SFOS region, after requiring the anomaly score to be below the 90% background rejection point. The background contributions after the likelihood fit to data ('post-fit') for the background-only hypothesis are shown as filled histograms. The 'tt+X' background component includes the tt̄Z, and tt̄H processes. The 'HF ℓ' ('LF ℓ') background component refers to processes containing one non-prompt light lepton from heavy-flavour (light-flavour) hadron decays. The ratio of the data to the background prediction ('Bkg.') is shown in the lower panel. The 'Other' contribution is dominated by the tWZ production. The size of the combined statistical and systematic uncertainty in the background prediction is indicated by the blue hatched band. The upward-pointing blue arrows indicate points for which the data-to-background ('Data/Bkg.’) ratio exceeds the vertical range of the figure. The last bin contains the overflow.

Comparison between data and the background prediction for the (a) N_jets, (b) E_T^miss, (c) m(3ℓ), and (d) H_T^lep distribution in the (a) HFe CR, (b) HFμ CR, (c) LFe CR, and (d) the Wγ^*/tt̄γ^* validation region. The background contributions after the likelihood fit to data ('post-fit') for the background-only hypothesis are shown as filled histograms. The ratio of the data to the background prediction ('Bkg.') is shown in the lower panel. The 'tt+X' background component includes the tt̄W, tt̄Z, and tt̄H processes. The 'Other' contribution in the 2ℓSS regions is dominated by the tt̄ and tt̄W production, and in the 3ℓ regions is dominated by the ZZ + LF production. The size of the combined statistical and systematic uncertainty in the background prediction is indicated by the blue hatched band. The upward-pointing blue arrows indicate points for which the data-to-background ('Data/Bkg.’) ratio exceeds the vertical range of the figure. The last bin contains the overflow.

Comparison between data and the background prediction for the (a) N_jets, (b) E_T^miss, (c) m(3ℓ), and (d) H_T^lep distribution in the (a) HFe CR, (b) HFμ CR, (c) LFe CR, and (d) the Wγ^*/tt̄γ^* validation region. The background contributions after the likelihood fit to data ('post-fit') for the background-only hypothesis are shown as filled histograms. The ratio of the data to the background prediction ('Bkg.') is shown in the lower panel. The 'tt+X' background component includes the tt̄W, tt̄Z, and tt̄H processes. The 'Other' contribution in the 2ℓSS regions is dominated by the tt̄ and tt̄W production, and in the 3ℓ regions is dominated by the ZZ + LF production. The size of the combined statistical and systematic uncertainty in the background prediction is indicated by the blue hatched band. The upward-pointing blue arrows indicate points for which the data-to-background ('Data/Bkg.’) ratio exceeds the vertical range of the figure. The last bin contains the overflow.

Comparison between data and the background prediction for the (a) N_jets, (b) E_T^miss, (c) m(3ℓ), and (d) H_T^lep distribution in the (a) HFe CR, (b) HFμ CR, (c) LFe CR, and (d) the Wγ^*/tt̄γ^* validation region. The background contributions after the likelihood fit to data ('post-fit') for the background-only hypothesis are shown as filled histograms. The ratio of the data to the background prediction ('Bkg.') is shown in the lower panel. The 'tt+X' background component includes the tt̄W, tt̄Z, and tt̄H processes. The 'Other' contribution in the 2ℓSS regions is dominated by the tt̄ and tt̄W production, and in the 3ℓ regions is dominated by the ZZ + LF production. The size of the combined statistical and systematic uncertainty in the background prediction is indicated by the blue hatched band. The upward-pointing blue arrows indicate points for which the data-to-background ('Data/Bkg.’) ratio exceeds the vertical range of the figure. The last bin contains the overflow.

Comparison between data and the background prediction for the (a) N_jets, (b) E_T^miss, (c) m(3ℓ), and (d) H_T^lep distribution in the (a) HFe CR, (b) HFμ CR, (c) LFe CR, and (d) the Wγ^*/tt̄γ^* validation region. The background contributions after the likelihood fit to data ('post-fit') for the background-only hypothesis are shown as filled histograms. The ratio of the data to the background prediction ('Bkg.') is shown in the lower panel. The 'tt+X' background component includes the tt̄W, tt̄Z, and tt̄H processes. The 'Other' contribution in the 2ℓSS regions is dominated by the tt̄ and tt̄W production, and in the 3ℓ regions is dominated by the ZZ + LF production. The size of the combined statistical and systematic uncertainty in the background prediction is indicated by the blue hatched band. The upward-pointing blue arrows indicate points for which the data-to-background ('Data/Bkg.’) ratio exceeds the vertical range of the figure. The last bin contains the overflow.

Comparison between data and the background prediction for the discovery regions included in the model-independent fit, after a background-only fit to data in the five cut-based control regions and ten low-anomaly score discovery regions ('post-fit'). All signal bins are shown ('SR') together with the low-anomaly score discovery regions ('CR'). The various requirements on the anomaly score corresponding to the specified background rejection cuts (99.9/99/90/50%) are shown for all the applicable SRs and CRs. The lower panels show the ratio of data to the background estimate ('Bkg'). The 'tt+X' background component includes the tt̄Z (4ℓ only) and tt̄H processes. The 'Other' contribution is dominated by the VH process. The size of the combined statistical and systematic uncertainty in the background prediction is indicated by the blue hatched band. The upward-pointing blue arrows indicate points for which the data-to-background ('Data/Bkg.’) ratio exceeds the vertical range of the figure.

Observed and expected excluded visible cross section limits, σ_vis for the model-independent regions. The various requirements on the anomaly score corresponding to the specified background rejection cuts (99.9/99/90/50%) are shown for all the applicable regions.

Comparison between data and the background estimate for the anomaly score distribution used in different benchmark regions, after a background-only fit to data ('post-fit'): (a) 4ℓ Q=0 0Z 0b 2SFOS e>μ, (b) 4ℓ Q=0 0Z ≥1b 2SFOS e>μ, (c) 4ℓ Q=0 1Z 0b 2SFOS μ>e, (d) 4ℓ Q=±2 0b e>μ, (e) 4ℓ Q=±2 ≥1b μ>e, and (f) the three ≥5ℓ regions: 0Z 0b μ>e, 0Z 0b e≥μ, and 0Z ≥1b, defined without AD. Distributions for one flavourful VLL_e signal point for a VLL mass of 1 TeV and scalar of 550 GeV, a wino-like chargino and neutralino signal point of mass 1.3 TeV, and a smuon signal point of mass 350 GeV and neutralino mass of 250 GeV are overlaid for comparison. The lower panels show the ratio of data to the background estimate ('Bkg.'). The 'tt+X' background component includes the tt̄Z (4ℓ only) and tt̄H processes. The 'Other' contribution is dominated by the VH process. The size of the combined statistical and systematic uncertainty in the signal-plus-background prediction is indicated by the blue hatched band. The upward-pointing blue arrow indicates a point for which the data-to-background ('Data/Bkg.’) ratio exceeds the vertical range of the figure.

Comparison between data and the background estimate for the anomaly score distribution used in different benchmark regions, after a background-only fit to data ('post-fit'): (a) 4ℓ Q=0 0Z 0b 2SFOS e>μ, (b) 4ℓ Q=0 0Z ≥1b 2SFOS e>μ, (c) 4ℓ Q=0 1Z 0b 2SFOS μ>e, (d) 4ℓ Q=±2 0b e>μ, (e) 4ℓ Q=±2 ≥1b μ>e, and (f) the three ≥5ℓ regions: 0Z 0b μ>e, 0Z 0b e≥μ, and 0Z ≥1b, defined without AD. Distributions for one flavourful VLL_e signal point for a VLL mass of 1 TeV and scalar of 550 GeV, a wino-like chargino and neutralino signal point of mass 1.3 TeV, and a smuon signal point of mass 350 GeV and neutralino mass of 250 GeV are overlaid for comparison. The lower panels show the ratio of data to the background estimate ('Bkg.'). The 'tt+X' background component includes the tt̄Z (4ℓ only) and tt̄H processes. The 'Other' contribution is dominated by the VH process. The size of the combined statistical and systematic uncertainty in the signal-plus-background prediction is indicated by the blue hatched band. The upward-pointing blue arrow indicates a point for which the data-to-background ('Data/Bkg.’) ratio exceeds the vertical range of the figure.

Comparison between data and the background estimate for the anomaly score distribution used in different benchmark regions, after a background-only fit to data ('post-fit'): (a) 4ℓ Q=0 0Z 0b 2SFOS e>μ, (b) 4ℓ Q=0 0Z ≥1b 2SFOS e>μ, (c) 4ℓ Q=0 1Z 0b 2SFOS μ>e, (d) 4ℓ Q=±2 0b e>μ, (e) 4ℓ Q=±2 ≥1b μ>e, and (f) the three ≥5ℓ regions: 0Z 0b μ>e, 0Z 0b e≥μ, and 0Z ≥1b, defined without AD. Distributions for one flavourful VLL_e signal point for a VLL mass of 1 TeV and scalar of 550 GeV, a wino-like chargino and neutralino signal point of mass 1.3 TeV, and a smuon signal point of mass 350 GeV and neutralino mass of 250 GeV are overlaid for comparison. The lower panels show the ratio of data to the background estimate ('Bkg.'). The 'tt+X' background component includes the tt̄Z (4ℓ only) and tt̄H processes. The 'Other' contribution is dominated by the VH process. The size of the combined statistical and systematic uncertainty in the signal-plus-background prediction is indicated by the blue hatched band. The upward-pointing blue arrow indicates a point for which the data-to-background ('Data/Bkg.’) ratio exceeds the vertical range of the figure.

Comparison between data and the background estimate for the anomaly score distribution used in different benchmark regions, after a background-only fit to data ('post-fit'): (a) 4ℓ Q=0 0Z 0b 2SFOS e>μ, (b) 4ℓ Q=0 0Z ≥1b 2SFOS e>μ, (c) 4ℓ Q=0 1Z 0b 2SFOS μ>e, (d) 4ℓ Q=±2 0b e>μ, (e) 4ℓ Q=±2 ≥1b μ>e, and (f) the three ≥5ℓ regions: 0Z 0b μ>e, 0Z 0b e≥μ, and 0Z ≥1b, defined without AD. Distributions for one flavourful VLL_e signal point for a VLL mass of 1 TeV and scalar of 550 GeV, a wino-like chargino and neutralino signal point of mass 1.3 TeV, and a smuon signal point of mass 350 GeV and neutralino mass of 250 GeV are overlaid for comparison. The lower panels show the ratio of data to the background estimate ('Bkg.'). The 'tt+X' background component includes the tt̄Z (4ℓ only) and tt̄H processes. The 'Other' contribution is dominated by the VH process. The size of the combined statistical and systematic uncertainty in the signal-plus-background prediction is indicated by the blue hatched band. The upward-pointing blue arrow indicates a point for which the data-to-background ('Data/Bkg.’) ratio exceeds the vertical range of the figure.

Comparison between data and the background estimate for the anomaly score distribution used in different benchmark regions, after a background-only fit to data ('post-fit'): (a) 4ℓ Q=0 0Z 0b 2SFOS e>μ, (b) 4ℓ Q=0 0Z ≥1b 2SFOS e>μ, (c) 4ℓ Q=0 1Z 0b 2SFOS μ>e, (d) 4ℓ Q=±2 0b e>μ, (e) 4ℓ Q=±2 ≥1b μ>e, and (f) the three ≥5ℓ regions: 0Z 0b μ>e, 0Z 0b e≥μ, and 0Z ≥1b, defined without AD. Distributions for one flavourful VLL_e signal point for a VLL mass of 1 TeV and scalar of 550 GeV, a wino-like chargino and neutralino signal point of mass 1.3 TeV, and a smuon signal point of mass 350 GeV and neutralino mass of 250 GeV are overlaid for comparison. The lower panels show the ratio of data to the background estimate ('Bkg.'). The 'tt+X' background component includes the tt̄Z (4ℓ only) and tt̄H processes. The 'Other' contribution is dominated by the VH process. The size of the combined statistical and systematic uncertainty in the signal-plus-background prediction is indicated by the blue hatched band. The upward-pointing blue arrow indicates a point for which the data-to-background ('Data/Bkg.’) ratio exceeds the vertical range of the figure.

Comparison between data and the background estimate for the anomaly score distribution used in different benchmark regions, after a background-only fit to data ('post-fit'): (a) 4ℓ Q=0 0Z 0b 2SFOS e>μ, (b) 4ℓ Q=0 0Z ≥1b 2SFOS e>μ, (c) 4ℓ Q=0 1Z 0b 2SFOS μ>e, (d) 4ℓ Q=±2 0b e>μ, (e) 4ℓ Q=±2 ≥1b μ>e, and (f) the three ≥5ℓ regions: 0Z 0b μ>e, 0Z 0b e≥μ, and 0Z ≥1b, defined without AD. Distributions for one flavourful VLL_e signal point for a VLL mass of 1 TeV and scalar of 550 GeV, a wino-like chargino and neutralino signal point of mass 1.3 TeV, and a smuon signal point of mass 350 GeV and neutralino mass of 250 GeV are overlaid for comparison. The lower panels show the ratio of data to the background estimate ('Bkg.'). The 'tt+X' background component includes the tt̄Z (4ℓ only) and tt̄H processes. The 'Other' contribution is dominated by the VH process. The size of the combined statistical and systematic uncertainty in the signal-plus-background prediction is indicated by the blue hatched band. The upward-pointing blue arrow indicates a point for which the data-to-background ('Data/Bkg.’) ratio exceeds the vertical range of the figure.

Combined observed and expected limits at 95&percnt; CL on the cross-section (&sigma;) as a function of the VLL mass for the (a) VLL_e^D, (b) VLL_&mu;^D, (c) VLL_e^S, (d) VLL_&mu;^S models, and on the plane of the S_ji mass versus the VLL mass for the (e) flavourful VLL_e, and (f) flavourful VLL_&mu; models. The expected limits from the dedicated ATLAS search [<a href=" https://doi.org/10.1007/JHEP05%282025%29075">JHEP05(2025)075</a>], considering only the 4&#8467; channel, are overlaid in dashed grey lines in (a-d). The inner and outer bands around the expected limit are the &plusmn;1 &sigma; and &plusmn;2 &sigma; variations including all uncertainties, respectively.

Combined observed and expected limits at 95&percnt; CL on the cross-section (&sigma;) as a function of the VLL mass for the (a) VLL_e^D, (b) VLL_&mu;^D, (c) VLL_e^S, (d) VLL_&mu;^S models, and on the plane of the S_ji mass versus the VLL mass for the (e) flavourful VLL_e, and (f) flavourful VLL_&mu; models. The expected limits from the dedicated ATLAS search [<a href=" https://doi.org/10.1007/JHEP05%282025%29075">JHEP05(2025)075</a>], considering only the 4&#8467; channel, are overlaid in dashed grey lines in (a-d). The inner and outer bands around the expected limit are the &plusmn;1 &sigma; and &plusmn;2 &sigma; variations including all uncertainties, respectively.

Combined observed and expected limits at 95&percnt; CL on the cross-section (&sigma;) as a function of the VLL mass for the (a) VLL_e^D, (b) VLL_&mu;^D, (c) VLL_e^S, (d) VLL_&mu;^S models, and on the plane of the S_ji mass versus the VLL mass for the (e) flavourful VLL_e, and (f) flavourful VLL_&mu; models. The expected limits from the dedicated ATLAS search [<a href=" https://doi.org/10.1007/JHEP05%282025%29075">JHEP05(2025)075</a>], considering only the 4&#8467; channel, are overlaid in dashed grey lines in (a-d). The inner and outer bands around the expected limit are the &plusmn;1 &sigma; and &plusmn;2 &sigma; variations including all uncertainties, respectively.

Combined observed and expected limits at 95&percnt; CL on the cross-section (&sigma;) as a function of the VLL mass for the (a) VLL_e^D, (b) VLL_&mu;^D, (c) VLL_e^S, (d) VLL_&mu;^S models, and on the plane of the S_ji mass versus the VLL mass for the (e) flavourful VLL_e, and (f) flavourful VLL_&mu; models. The expected limits from the dedicated ATLAS search [<a href=" https://doi.org/10.1007/JHEP05%282025%29075">JHEP05(2025)075</a>], considering only the 4&#8467; channel, are overlaid in dashed grey lines in (a-d). The inner and outer bands around the expected limit are the &plusmn;1 &sigma; and &plusmn;2 &sigma; variations including all uncertainties, respectively.

Combined observed and expected limits at 95&percnt; CL on the cross-section (&sigma;) as a function of the VLL mass for the (a) VLL_e^D, (b) VLL_&mu;^D, (c) VLL_e^S, (d) VLL_&mu;^S models, and on the plane of the S_ji mass versus the VLL mass for the (e) flavourful VLL_e, and (f) flavourful VLL_&mu; models. The expected limits from the dedicated ATLAS search [<a href=" https://doi.org/10.1007/JHEP05%282025%29075">JHEP05(2025)075</a>], considering only the 4&#8467; channel, are overlaid in dashed grey lines in (a-d). The inner and outer bands around the expected limit are the &plusmn;1 &sigma; and &plusmn;2 &sigma; variations including all uncertainties, respectively.

Combined observed and expected limits at 95&percnt; CL on the cross-section (&sigma;) as a function of the VLL mass for the (a) VLL_e^D, (b) VLL_&mu;^D, (c) VLL_e^S, (d) VLL_&mu;^S models, and on the plane of the S_ji mass versus the VLL mass for the (e) flavourful VLL_e, and (f) flavourful VLL_&mu; models. The expected limits from the dedicated ATLAS search [<a href=" https://doi.org/10.1007/JHEP05%282025%29075">JHEP05(2025)075</a>], considering only the 4&#8467; channel, are overlaid in dashed grey lines in (a-d). The inner and outer bands around the expected limit are the &plusmn;1 &sigma; and &plusmn;2 &sigma; variations including all uncertainties, respectively.

Combined observed and expected limits at 95&percnt; CL on the cross-section (&sigma;) as a function of the VLL mass for the (a) VLL_e^D, (b) VLL_&mu;^D, (c) VLL_e^S, (d) VLL_&mu;^S models, and on the plane of the S_ji mass versus the VLL mass for the (e) flavourful VLL_e, and (f) flavourful VLL_&mu; models. The expected limits from the dedicated ATLAS search [<a href=" https://doi.org/10.1007/JHEP05%282025%29075">JHEP05(2025)075</a>], considering only the 4&#8467; channel, are overlaid in dashed grey lines in (a-d). The inner and outer bands around the expected limit are the &plusmn;1 &sigma; and &plusmn;2 &sigma; variations including all uncertainties, respectively.

Combined observed and expected limits at 95&percnt; CL on the cross-section (&sigma;) as a function of the VLL mass for the (a) VLL_e^D, (b) VLL_&mu;^D, (c) VLL_e^S, (d) VLL_&mu;^S models, and on the plane of the S_ji mass versus the VLL mass for the (e) flavourful VLL_e, and (f) flavourful VLL_&mu; models. The expected limits from the dedicated ATLAS search [<a href=" https://doi.org/10.1007/JHEP05%282025%29075">JHEP05(2025)075</a>], considering only the 4&#8467; channel, are overlaid in dashed grey lines in (a-d). The inner and outer bands around the expected limit are the &plusmn;1 &sigma; and &plusmn;2 &sigma; variations including all uncertainties, respectively.

Combined observed and expected limits at 95&percnt; CL on the cross-section (&sigma;) as a function of the VLL mass for the (a) VLL_e^D, (b) VLL_&mu;^D, (c) VLL_e^S, (d) VLL_&mu;^S models, and on the plane of the S_ji mass versus the VLL mass for the (e) flavourful VLL_e, and (f) flavourful VLL_&mu; models. The expected limits from the dedicated ATLAS search [<a href=" https://doi.org/10.1007/JHEP05%282025%29075">JHEP05(2025)075</a>], considering only the 4&#8467; channel, are overlaid in dashed grey lines in (a-d). The inner and outer bands around the expected limit are the &plusmn;1 &sigma; and &plusmn;2 &sigma; variations including all uncertainties, respectively.

Combined observed and expected limits at 95&percnt; CL on the cross-section (&sigma;) as a function of the VLL mass for the (a) VLL_e^D, (b) VLL_&mu;^D, (c) VLL_e^S, (d) VLL_&mu;^S models, and on the plane of the S_ji mass versus the VLL mass for the (e) flavourful VLL_e, and (f) flavourful VLL_&mu; models. The expected limits from the dedicated ATLAS search [<a href=" https://doi.org/10.1007/JHEP05%282025%29075">JHEP05(2025)075</a>], considering only the 4&#8467; channel, are overlaid in dashed grey lines in (a-d). The inner and outer bands around the expected limit are the &plusmn;1 &sigma; and &plusmn;2 &sigma; variations including all uncertainties, respectively.

Combined observed and expected limits at 95&percnt; CL on the cross-section (&sigma;) as a function of the VLL mass for the (a) VLL_e^D, (b) VLL_&mu;^D, (c) VLL_e^S, (d) VLL_&mu;^S models, and on the plane of the S_ji mass versus the VLL mass for the (e) flavourful VLL_e, and (f) flavourful VLL_&mu; models. The expected limits from the dedicated ATLAS search [<a href=" https://doi.org/10.1007/JHEP05%282025%29075">JHEP05(2025)075</a>], considering only the 4&#8467; channel, are overlaid in dashed grey lines in (a-d). The inner and outer bands around the expected limit are the &plusmn;1 &sigma; and &plusmn;2 &sigma; variations including all uncertainties, respectively.

Combined observed and expected limits at 95&percnt; CL on the cross-section (&sigma;) as a function of the VLL mass for the (a) VLL_e^D, (b) VLL_&mu;^D, (c) VLL_e^S, (d) VLL_&mu;^S models, and on the plane of the S_ji mass versus the VLL mass for the (e) flavourful VLL_e, and (f) flavourful VLL_&mu; models. The expected limits from the dedicated ATLAS search [<a href=" https://doi.org/10.1007/JHEP05%282025%29075">JHEP05(2025)075</a>], considering only the 4&#8467; channel, are overlaid in dashed grey lines in (a-d). The inner and outer bands around the expected limit are the &plusmn;1 &sigma; and &plusmn;2 &sigma; variations including all uncertainties, respectively.

Combined observed and expected limits at 95&percnt; CL for the (a) wino-like chargino and neutralino, and (b) smuon models, as a function of the masses of &chi;&#771;^&plusmn;₁ / &chi;&#771;⁰₂ and &chi;&#771;⁰₁, and &mu;_L,R and &Delta;m (&mu;_L,R, &chi;&#771;⁰₁), respectively. The expected limits from the dedicated ATLAS searches [<a href=" https://doi.org/10.1007/JHEP07%282021%29167">JHEP07(2021)167</a>, <a href=" https://doi.org/10.1007/JHEP12%282023%29081">JHEP12(2023)081</a>] are overlaid in dashed grey lines. The inner and outer bands around the expected limit are the &plusmn;1 &sigma; and &plusmn;2 &sigma; variations including all uncertainties, respectively.

Combined observed and expected limits at 95&percnt; CL for the (a) wino-like chargino and neutralino, and (b) smuon models, as a function of the masses of &chi;&#771;^&plusmn;₁ / &chi;&#771;⁰₂ and &chi;&#771;⁰₁, and &mu;_L,R and &Delta;m (&mu;_L,R, &chi;&#771;⁰₁), respectively. The expected limits from the dedicated ATLAS searches [<a href=" https://doi.org/10.1007/JHEP07%282021%29167">JHEP07(2021)167</a>, <a href=" https://doi.org/10.1007/JHEP12%282023%29081">JHEP12(2023)081</a>] are overlaid in dashed grey lines. The inner and outer bands around the expected limit are the &plusmn;1 &sigma; and &plusmn;2 &sigma; variations including all uncertainties, respectively.

Combined observed and expected limits at 95&percnt; CL for the (a) wino-like chargino and neutralino, and (b) smuon models, as a function of the masses of &chi;&#771;^&plusmn;₁ / &chi;&#771;⁰₂ and &chi;&#771;⁰₁, and &mu;_L,R and &Delta;m (&mu;_L,R, &chi;&#771;⁰₁), respectively. The expected limits from the dedicated ATLAS searches [<a href=" https://doi.org/10.1007/JHEP07%282021%29167">JHEP07(2021)167</a>, <a href=" https://doi.org/10.1007/JHEP12%282023%29081">JHEP12(2023)081</a>] are overlaid in dashed grey lines. The inner and outer bands around the expected limit are the &plusmn;1 &sigma; and &plusmn;2 &sigma; variations including all uncertainties, respectively.

Combined observed and expected limits at 95&percnt; CL for the (a) wino-like chargino and neutralino, and (b) smuon models, as a function of the masses of &chi;&#771;^&plusmn;₁ / &chi;&#771;⁰₂ and &chi;&#771;⁰₁, and &mu;_L,R and &Delta;m (&mu;_L,R, &chi;&#771;⁰₁), respectively. The expected limits from the dedicated ATLAS searches [<a href=" https://doi.org/10.1007/JHEP07%282021%29167">JHEP07(2021)167</a>, <a href=" https://doi.org/10.1007/JHEP12%282023%29081">JHEP12(2023)081</a>] are overlaid in dashed grey lines. The inner and outer bands around the expected limit are the &plusmn;1 &sigma; and &plusmn;2 &sigma; variations including all uncertainties, respectively.

Combined observed and expected limits at 95&percnt; CL for the (a) wino-like chargino and neutralino, and (b) smuon models, as a function of the masses of &chi;&#771;^&plusmn;₁ / &chi;&#771;⁰₂ and &chi;&#771;⁰₁, and &mu;_L,R and &Delta;m (&mu;_L,R, &chi;&#771;⁰₁), respectively. The expected limits from the dedicated ATLAS searches [<a href=" https://doi.org/10.1007/JHEP07%282021%29167">JHEP07(2021)167</a>, <a href=" https://doi.org/10.1007/JHEP12%282023%29081">JHEP12(2023)081</a>] are overlaid in dashed grey lines. The inner and outer bands around the expected limit are the &plusmn;1 &sigma; and &plusmn;2 &sigma; variations including all uncertainties, respectively.

Combined observed and expected limits at 95&percnt; CL for the (a) wino-like chargino and neutralino, and (b) smuon models, as a function of the masses of &chi;&#771;^&plusmn;₁ / &chi;&#771;⁰₂ and &chi;&#771;⁰₁, and &mu;_L,R and &Delta;m (&mu;_L,R, &chi;&#771;⁰₁), respectively. The expected limits from the dedicated ATLAS searches [<a href=" https://doi.org/10.1007/JHEP07%282021%29167">JHEP07(2021)167</a>, <a href=" https://doi.org/10.1007/JHEP12%282023%29081">JHEP12(2023)081</a>] are overlaid in dashed grey lines. The inner and outer bands around the expected limit are the &plusmn;1 &sigma; and &plusmn;2 &sigma; variations including all uncertainties, respectively.

Combined observed and expected limits at 95&percnt; CL for the (a) wino-like chargino and neutralino, and (b) smuon models, as a function of the masses of &chi;&#771;^&plusmn;₁ / &chi;&#771;⁰₂ and &chi;&#771;⁰₁, and &mu;_L,R and &Delta;m (&mu;_L,R, &chi;&#771;⁰₁), respectively. The expected limits from the dedicated ATLAS searches [<a href=" https://doi.org/10.1007/JHEP07%282021%29167">JHEP07(2021)167</a>, <a href=" https://doi.org/10.1007/JHEP12%282023%29081">JHEP12(2023)081</a>] are overlaid in dashed grey lines. The inner and outer bands around the expected limit are the &plusmn;1 &sigma; and &plusmn;2 &sigma; variations including all uncertainties, respectively.

Combined observed and expected limits at 95&percnt; CL for the (a) wino-like chargino and neutralino, and (b) smuon models, as a function of the masses of &chi;&#771;^&plusmn;₁ / &chi;&#771;⁰₂ and &chi;&#771;⁰₁, and &mu;_L,R and &Delta;m (&mu;_L,R, &chi;&#771;⁰₁), respectively. The expected limits from the dedicated ATLAS searches [<a href=" https://doi.org/10.1007/JHEP07%282021%29167">JHEP07(2021)167</a>, <a href=" https://doi.org/10.1007/JHEP12%282023%29081">JHEP12(2023)081</a>] are overlaid in dashed grey lines. The inner and outer bands around the expected limit are the &plusmn;1 &sigma; and &plusmn;2 &sigma; variations including all uncertainties, respectively.

Comparison between data and the background prediction for the distribution of the b-jet multiplicity in the WZ/ttZ CR after the VV jet multiplicity correction. The background contributions after the likelihood fit to data (&apos;post-fit&apos;) for the background-only hypothesis are shown as filled histograms. The lower panel shows the ratio of data to the background estimate (&apos;Bkg.&apos;). The &apos;tt+X&apos; background component includes the tt&#772;W, tt&#772;Z, and tt&#772;H processes. The &apos;Other&apos; contribution is dominated by the tZq production. The size of the combined statistical and systematic uncertainty in the background prediction is indicated by the blue hatched band. The last bin contains the overflow.

Comparison between data and the background prediction for the event yields in the HF_e CR, HF_&mu;, Conversions, and LF_e CRs, after a background-only fit to data (&apos;Post-fit&apos;). The lower panel shows the ratio of data to the background estimate (&apos;Bkg.&apos;). The &apos;tt+X&apos; background component includes the tt&#772;W, tt&#772;Z, and tt&#772;H processes. The &apos;Other&apos; contribution is dominated by the ZZ+LF process. The size of the combined statistical and systematic uncertainty in the background prediction is indicated by the blue hatched band.

Comparison between data and the background prediction for the discovery regions included in the model-independent fit, before any fit to data (&apos;pre-fit&apos;). All signal bins are shown (&apos;SR&apos;) together with the low-anomaly score discovery regions (&apos;CR&apos;). The various requirements on the anomaly score corresponding to the specified background rejection cuts (99.9/99/90/50&percnt;) are shown for all the applicable SRs and CRs. The lower panels show the ratio of data to the background estimate (&apos;Bkg&apos;). The &apos;tt+X&apos; background component includes the tt&#772;Z (4&#8467; only) and tt&#772;H processes. The &apos;Other&apos; contribution is dominated by the VH process. The size of the combined statistical and systematic uncertainty in the background prediction is indicated by the blue hatched band. The upward-pointing blue arrows indicate points for which the data-to-background (&apos;Data/Bkg.’) ratio exceeds the vertical range of the figure.

Comparison between data and the background estimate for the anomaly score distribution used in different benchmark regions before any fit to data (&apos;pre-fit&apos;): (a) 4&#8467; Q=0 0Z 0b 2SFOS e&gt;&mu;, (b) 4&#8467; Q=0 0Z &ge;1b 2SFOS e&gt;&mu;, (c) 4&#8467; Q=0 1Z 0b 2SFOS &mu;&gt;e, (d) 4&#8467; Q=&plusmn;2 0b e&gt;&mu;, (e) 4&#8467; Q=&plusmn;2 &ge;1b &mu;&gt;e, and (f) the three &ge;5&#8467; regions: 0Z 0b &mu;&gt;e, 0Z 0b e&ge;&mu;, and 0Z &ge;1b, defined without AD. Distributions for one flavourful VLL_e signal point for a VLL mass of 1 TeV and scalar of 550 GeV, a wino-like chargino and neutralino signal point of mass 1.3 TeV, and a smuon signal point of mass 350 GeV and neutralino mass of 250 GeV are overlaid for comparison. The lower panels show the ratio of data to the background estimate (&apos;Bkg.&apos;). The &apos;tt+X&apos; background component includes the tt&#772;Z (4&#8467; only) and tt&#772;H processes. The &apos;Other&apos; contribution is dominated by the VH process. The size of the combined statistical and systematic uncertainty in the signal-plus-background prediction is indicated by the blue hatched band. The upward-pointing blue arrow indicates a point for which the data-to-background (&apos;Data/Bkg.’) ratio exceeds the vertical range of the figure.

Comparison between data and the background estimate for the anomaly score distribution used in different benchmark regions before any fit to data (&apos;pre-fit&apos;): (a) 4&#8467; Q=0 0Z 0b 2SFOS e&gt;&mu;, (b) 4&#8467; Q=0 0Z &ge;1b 2SFOS e&gt;&mu;, (c) 4&#8467; Q=0 1Z 0b 2SFOS &mu;&gt;e, (d) 4&#8467; Q=&plusmn;2 0b e&gt;&mu;, (e) 4&#8467; Q=&plusmn;2 &ge;1b &mu;&gt;e, and (f) the three &ge;5&#8467; regions: 0Z 0b &mu;&gt;e, 0Z 0b e&ge;&mu;, and 0Z &ge;1b, defined without AD. Distributions for one flavourful VLL_e signal point for a VLL mass of 1 TeV and scalar of 550 GeV, a wino-like chargino and neutralino signal point of mass 1.3 TeV, and a smuon signal point of mass 350 GeV and neutralino mass of 250 GeV are overlaid for comparison. The lower panels show the ratio of data to the background estimate (&apos;Bkg.&apos;). The &apos;tt+X&apos; background component includes the tt&#772;Z (4&#8467; only) and tt&#772;H processes. The &apos;Other&apos; contribution is dominated by the VH process. The size of the combined statistical and systematic uncertainty in the signal-plus-background prediction is indicated by the blue hatched band. The upward-pointing blue arrow indicates a point for which the data-to-background (&apos;Data/Bkg.’) ratio exceeds the vertical range of the figure.

Comparison between data and the background estimate for the anomaly score distribution used in different benchmark regions before any fit to data (&apos;pre-fit&apos;): (a) 4&#8467; Q=0 0Z 0b 2SFOS e&gt;&mu;, (b) 4&#8467; Q=0 0Z &ge;1b 2SFOS e&gt;&mu;, (c) 4&#8467; Q=0 1Z 0b 2SFOS &mu;&gt;e, (d) 4&#8467; Q=&plusmn;2 0b e&gt;&mu;, (e) 4&#8467; Q=&plusmn;2 &ge;1b &mu;&gt;e, and (f) the three &ge;5&#8467; regions: 0Z 0b &mu;&gt;e, 0Z 0b e&ge;&mu;, and 0Z &ge;1b, defined without AD. Distributions for one flavourful VLL_e signal point for a VLL mass of 1 TeV and scalar of 550 GeV, a wino-like chargino and neutralino signal point of mass 1.3 TeV, and a smuon signal point of mass 350 GeV and neutralino mass of 250 GeV are overlaid for comparison. The lower panels show the ratio of data to the background estimate (&apos;Bkg.&apos;). The &apos;tt+X&apos; background component includes the tt&#772;Z (4&#8467; only) and tt&#772;H processes. The &apos;Other&apos; contribution is dominated by the VH process. The size of the combined statistical and systematic uncertainty in the signal-plus-background prediction is indicated by the blue hatched band. The upward-pointing blue arrow indicates a point for which the data-to-background (&apos;Data/Bkg.’) ratio exceeds the vertical range of the figure.

Comparison between data and the background estimate for the anomaly score distribution used in different benchmark regions before any fit to data (&apos;pre-fit&apos;): (a) 4&#8467; Q=0 0Z 0b 2SFOS e&gt;&mu;, (b) 4&#8467; Q=0 0Z &ge;1b 2SFOS e&gt;&mu;, (c) 4&#8467; Q=0 1Z 0b 2SFOS &mu;&gt;e, (d) 4&#8467; Q=&plusmn;2 0b e&gt;&mu;, (e) 4&#8467; Q=&plusmn;2 &ge;1b &mu;&gt;e, and (f) the three &ge;5&#8467; regions: 0Z 0b &mu;&gt;e, 0Z 0b e&ge;&mu;, and 0Z &ge;1b, defined without AD. Distributions for one flavourful VLL_e signal point for a VLL mass of 1 TeV and scalar of 550 GeV, a wino-like chargino and neutralino signal point of mass 1.3 TeV, and a smuon signal point of mass 350 GeV and neutralino mass of 250 GeV are overlaid for comparison. The lower panels show the ratio of data to the background estimate (&apos;Bkg.&apos;). The &apos;tt+X&apos; background component includes the tt&#772;Z (4&#8467; only) and tt&#772;H processes. The &apos;Other&apos; contribution is dominated by the VH process. The size of the combined statistical and systematic uncertainty in the signal-plus-background prediction is indicated by the blue hatched band. The upward-pointing blue arrow indicates a point for which the data-to-background (&apos;Data/Bkg.’) ratio exceeds the vertical range of the figure.

Comparison between data and the background estimate for the anomaly score distribution used in different benchmark regions before any fit to data (&apos;pre-fit&apos;): (a) 4&#8467; Q=0 0Z 0b 2SFOS e&gt;&mu;, (b) 4&#8467; Q=0 0Z &ge;1b 2SFOS e&gt;&mu;, (c) 4&#8467; Q=0 1Z 0b 2SFOS &mu;&gt;e, (d) 4&#8467; Q=&plusmn;2 0b e&gt;&mu;, (e) 4&#8467; Q=&plusmn;2 &ge;1b &mu;&gt;e, and (f) the three &ge;5&#8467; regions: 0Z 0b &mu;&gt;e, 0Z 0b e&ge;&mu;, and 0Z &ge;1b, defined without AD. Distributions for one flavourful VLL_e signal point for a VLL mass of 1 TeV and scalar of 550 GeV, a wino-like chargino and neutralino signal point of mass 1.3 TeV, and a smuon signal point of mass 350 GeV and neutralino mass of 250 GeV are overlaid for comparison. The lower panels show the ratio of data to the background estimate (&apos;Bkg.&apos;). The &apos;tt+X&apos; background component includes the tt&#772;Z (4&#8467; only) and tt&#772;H processes. The &apos;Other&apos; contribution is dominated by the VH process. The size of the combined statistical and systematic uncertainty in the signal-plus-background prediction is indicated by the blue hatched band. The upward-pointing blue arrow indicates a point for which the data-to-background (&apos;Data/Bkg.’) ratio exceeds the vertical range of the figure.

Comparison between data and the background estimate for the anomaly score distribution used in different benchmark regions before any fit to data (&apos;pre-fit&apos;): (a) 4&#8467; Q=0 0Z 0b 2SFOS e&gt;&mu;, (b) 4&#8467; Q=0 0Z &ge;1b 2SFOS e&gt;&mu;, (c) 4&#8467; Q=0 1Z 0b 2SFOS &mu;&gt;e, (d) 4&#8467; Q=&plusmn;2 0b e&gt;&mu;, (e) 4&#8467; Q=&plusmn;2 &ge;1b &mu;&gt;e, and (f) the three &ge;5&#8467; regions: 0Z 0b &mu;&gt;e, 0Z 0b e&ge;&mu;, and 0Z &ge;1b, defined without AD. Distributions for one flavourful VLL_e signal point for a VLL mass of 1 TeV and scalar of 550 GeV, a wino-like chargino and neutralino signal point of mass 1.3 TeV, and a smuon signal point of mass 350 GeV and neutralino mass of 250 GeV are overlaid for comparison. The lower panels show the ratio of data to the background estimate (&apos;Bkg.&apos;). The &apos;tt+X&apos; background component includes the tt&#772;Z (4&#8467; only) and tt&#772;H processes. The &apos;Other&apos; contribution is dominated by the VH process. The size of the combined statistical and systematic uncertainty in the signal-plus-background prediction is indicated by the blue hatched band. The upward-pointing blue arrow indicates a point for which the data-to-background (&apos;Data/Bkg.’) ratio exceeds the vertical range of the figure.

Observed profile likelihood scans of $\kappa_\lambda$. The scans are performed by varying only the coupling modifier of interest, while all other relevant coupling modifiers are fixed to unity.

Expected profile likelihood scans of $\kappa_\lambda$. The scans are performed by varying only the coupling modifier of interest, while all other relevant coupling modifiers are fixed to unity.

Observed profile likelihood scans of $\kappa_{2V}$. The scans are performed by varying only the coupling modifier of interest, while all other relevant coupling modifiers are fixed to unity.

Expected profile likelihood scans of $\kappa_{2V}$. The scans are performed by varying only the coupling modifier of interest, while all other relevant coupling modifiers are fixed to unity.

Confidence level contours at 68% (solid line) and 95% (dashed line) in the $(\kappa_\lambda, \kappa_{2V})$ parameter space, when all other coupling modifiers are fixed to their SM predictions. The corresponding expected contours are shown by the inner and outer shaded regions The SM prediction is indicated by the star, while the best-fit value is denoted by the cross.

Confidence level contours at 68% (solid line) and 95% (dashed line) in the $(\kappa_\lambda, \kappa_{2V})$ parameter space, when all other coupling modifiers are fixed to their SM predictions. The corresponding expected contours are shown by the inner and outer shaded regions The SM prediction is indicated by the star, while the best-fit value is denoted by the cross.

Observed $m_{\gamma\gamma}$ distributions for the high-mass categories in Run 2. The lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed $m_{\gamma\gamma}$ distributions for the high-mass categories in Run 3. The lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed $m_{\gamma\gamma}$ distributions for the high-mass categories in Run 2. The lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed $m_{\gamma\gamma}$ distributions for the high-mass categories in Run 3. The lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed $m_{\gamma\gamma}$ distributions for the high-mass categories in Run 2. 3he lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed $m_{\gamma\gamma}$ distributions for the high-mass categories in Run 3. The lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed $m_{\gamma\gamma}$ distributions for the low-mass categories in Run 2. The lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed $m_{\gamma\gamma}$ distributions for the low-mass categories in Run 3. The lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed $m_{\gamma\gamma}$ distributions for the low-mass categories in Run 2. The lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed $m_{\gamma\gamma}$ distributions for the low-mass categories in Run 3. The lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed $m_{\gamma\gamma}$ distributions for the low-mass categories in Run 2. The lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed $m_{\gamma\gamma}$ distributions for the low-mass categories in Run 3. The lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed $m_{\gamma\gamma}$ distributions for the low-mass categories in Run 2. The lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed $m_{\gamma\gamma}$ distributions for the low-mass categories in Run 3. The lines show the fit results for the continuum background only (light dotted), adding the single Higgs boson background (black dotted) and the full fit (solid).

Observed and expected profiled likelihood scans on $\kappa_\lambda$ for the low-mass (LM) and high-mass (HM) regions separately and for their combination. The scan is performed by floating the indicated parameter of interest while fixing all the others to their SM value.

Observed and expected profiled likelihood scans on $\kappa_\lambda$ for the low-mass (LM) and high-mass (HM) regions separately and for their combination. The scan is performed by floating the indicated parameter of interest while fixing all the others to their SM value.

Observed and expected profiled likelihood scans on $\kappa_\lambda$ for the low-mass (LM) and high-mass (HM) regions separately and for their combination. The scan is performed by floating the indicated parameter of interest while fixing all the others to their SM value.

Observed and expected profiled likelihood scans on $\kappa_\lambda$ for the low-mass (LM) and high-mass (HM) regions separately and for their combination. The scan is performed by floating the indicated parameter of interest while fixing all the others to their SM value.

Observed and expected profiled likelihood scans on $\kappa_\lambda$ for the low-mass (LM) and high-mass (HM) regions separately and for their combination. The scan is performed by floating the indicated parameter of interest while fixing all the others to their SM value.

Observed and expected profiled likelihood scans on $\kappa_\lambda$ for the low-mass (LM) and high-mass (HM) regions separately and for their combination. The scan is performed by floating the indicated parameter of interest while fixing all the others to their SM value.

The expected number of events (estimated by using simulation) from the SM HH signals and single Higgs boson production, and the expected number of events from the continuum background, evaluated in the 120 GeV < $m_{\gamma\gamma}$ < 130 GeV window in Run 3 for the different low-mass (LM) and high-mass (HM) categories. For comparison, the number of data events is also shown. The uncertainties in the HH signals and single Higgs boson backgrounds include the systematic uncertainties discussed in Section 6. Asymmetric uncertainties arise primarily from the theory calculation of the SM ggF HH cross section and the large uncertainty in the yield of single Higgs bosons produced in ggF events in association with heavy-flavour jets. The uncertainty in the continuum background is given by the sum in quadrature of the statistical uncertainty from the fit to the data and the spurious signal uncertainty.

Data (dots) and post-fit SM distribution (histograms) of m_&#8467;j in (a, b) SR-1L-ej and (c, d) SR-2L-ej of the e+light-jet channel obtained by a CR+SR background-only fit for Run&nbsp;2 and Run&nbsp;3, respectively. The lower panel shows the ratio of observed data to the total post- and pre-fit SM prediction. The last bin includes the overflow. Uncertainties in the background estimates include both the statistical and systematic uncertainties, with correlations between uncertainties taken into account. The dashed lines show the predicted yields for two benchmark signal models corresponding to S&#771;₁ (m, y_de) = (2.0&nbsp;TeV, 1.0) and S&#771;₁ (m, y_de) = (3.0&nbsp;TeV, 1.0), respectively. Note: the values in the table are normalized by the width of corresponding bin

Data (dots) and post-fit SM distribution (histograms) of m_&#8467;j in (a, b) SR-1L-&mu;j and (c, d) SR-2L-&mu;j of the &mu;+light-jet channel obtained by a CR+SR background-only fit for Run&nbsp;2 and Run&nbsp;3, respectively. The lower panel shows the ratio of observed data to the total post- and pre-fit SM prediction. The last bin includes the overflow. Uncertainties in the background estimates include both the statistical and systematic uncertainties, with correlations between uncertainties taken into account. The dashed lines show the predicted yields for two benchmark signal models corresponding to S&#771;₁ (m, y_s&mu;) = (2.0&nbsp;TeV, 1.5) and S&#771;₁ (m, y_s&mu;) = (3.0&nbsp;TeV, 1.5), respectively. Note: the values in the table are normalized by the width of corresponding bin

Data (dots) and post-fit SM distribution (histograms) of m_&#8467;j in (a, b) SR-1L-&mu;j and (c, d) SR-2L-&mu;j of the &mu;+light-jet channel obtained by a CR+SR background-only fit for Run&nbsp;2 and Run&nbsp;3, respectively. The lower panel shows the ratio of observed data to the total post- and pre-fit SM prediction. The last bin includes the overflow. Uncertainties in the background estimates include both the statistical and systematic uncertainties, with correlations between uncertainties taken into account. The dashed lines show the predicted yields for two benchmark signal models corresponding to S&#771;₁ (m, y_s&mu;) = (2.0&nbsp;TeV, 1.5) and S&#771;₁ (m, y_s&mu;) = (3.0&nbsp;TeV, 1.5), respectively. Note: the values in the table are normalized by the width of corresponding bin

Data (dots) and post-fit SM distribution (histograms) of m_&#8467;j in (a, b) SR-1L-&mu;j and (c, d) SR-2L-&mu;j of the &mu;+light-jet channel obtained by a CR+SR background-only fit for Run&nbsp;2 and Run&nbsp;3, respectively. The lower panel shows the ratio of observed data to the total post- and pre-fit SM prediction. The last bin includes the overflow. Uncertainties in the background estimates include both the statistical and systematic uncertainties, with correlations between uncertainties taken into account. The dashed lines show the predicted yields for two benchmark signal models corresponding to S&#771;₁ (m, y_s&mu;) = (2.0&nbsp;TeV, 1.5) and S&#771;₁ (m, y_s&mu;) = (3.0&nbsp;TeV, 1.5), respectively. Note: the values in the table are normalized by the width of corresponding bin

Data (dots) and post-fit SM distribution (histograms) of m_&#8467;j in (a, b) SR-1L-&mu;j and (c, d) SR-2L-&mu;j of the &mu;+light-jet channel obtained by a CR+SR background-only fit for Run&nbsp;2 and Run&nbsp;3, respectively. The lower panel shows the ratio of observed data to the total post- and pre-fit SM prediction. The last bin includes the overflow. Uncertainties in the background estimates include both the statistical and systematic uncertainties, with correlations between uncertainties taken into account. The dashed lines show the predicted yields for two benchmark signal models corresponding to S&#771;₁ (m, y_s&mu;) = (2.0&nbsp;TeV, 1.5) and S&#771;₁ (m, y_s&mu;) = (3.0&nbsp;TeV, 1.5), respectively. Note: the values in the table are normalized by the width of corresponding bin

Data (dots) and post-fit SM distribution (histograms) of m_&#8467;j in (a, b) SR-1L-eb and (c, d) SR-2L-eb of the e+b-jet channel obtained by a CR+SR background-only fit for Run&nbsp;2 and Run&nbsp;3, respectively. The lower panel shows the ratio of observed data to the total post- and pre-fit SM prediction. The last bin includes the overflow. Uncertainties in the background estimates include both the statistical and systematic uncertainties, with correlations between uncertainties taken into account. The dashed lines show the predicted yields for two benchmark signal models corresponding to S&#771;₁ (m, y_be) = (1.5&nbsp;TeV, 2.5) and S&#771;₁ (m, y_be) = (2.0&nbsp;TeV, 2.5), respectively. Note: the values in the table are normalized by the width of corresponding bin

Data (dots) and post-fit SM distribution (histograms) of m_&#8467;j in (a, b) SR-1L-eb and (c, d) SR-2L-eb of the e+b-jet channel obtained by a CR+SR background-only fit for Run&nbsp;2 and Run&nbsp;3, respectively. The lower panel shows the ratio of observed data to the total post- and pre-fit SM prediction. The last bin includes the overflow. Uncertainties in the background estimates include both the statistical and systematic uncertainties, with correlations between uncertainties taken into account. The dashed lines show the predicted yields for two benchmark signal models corresponding to S&#771;₁ (m, y_be) = (1.5&nbsp;TeV, 2.5) and S&#771;₁ (m, y_be) = (2.0&nbsp;TeV, 2.5), respectively. Note: the values in the table are normalized by the width of corresponding bin

Data (dots) and post-fit SM distribution (histograms) of m_&#8467;j in (a, b) SR-1L-eb and (c, d) SR-2L-eb of the e+b-jet channel obtained by a CR+SR background-only fit for Run&nbsp;2 and Run&nbsp;3, respectively. The lower panel shows the ratio of observed data to the total post- and pre-fit SM prediction. The last bin includes the overflow. Uncertainties in the background estimates include both the statistical and systematic uncertainties, with correlations between uncertainties taken into account. The dashed lines show the predicted yields for two benchmark signal models corresponding to S&#771;₁ (m, y_be) = (1.5&nbsp;TeV, 2.5) and S&#771;₁ (m, y_be) = (2.0&nbsp;TeV, 2.5), respectively. Note: the values in the table are normalized by the width of corresponding bin

Data (dots) and post-fit SM distribution (histograms) of m_&#8467;j in (a, b) SR-1L-eb and (c, d) SR-2L-eb of the e+b-jet channel obtained by a CR+SR background-only fit for Run&nbsp;2 and Run&nbsp;3, respectively. The lower panel shows the ratio of observed data to the total post- and pre-fit SM prediction. The last bin includes the overflow. Uncertainties in the background estimates include both the statistical and systematic uncertainties, with correlations between uncertainties taken into account. The dashed lines show the predicted yields for two benchmark signal models corresponding to S&#771;₁ (m, y_be) = (1.5&nbsp;TeV, 2.5) and S&#771;₁ (m, y_be) = (2.0&nbsp;TeV, 2.5), respectively. Note: the values in the table are normalized by the width of corresponding bin

Data (dots) and post-fit SM distribution (histograms) of m_&#8467;j in (a, b) SR-1L-&mu;b and (c, d) SR-2L-&mu;b of the &mu;+b-jet channel obtained by a CR+SR background-only fit for Run&nbsp;2 and Run&nbsp;3, respectively. The lower panel shows the ratio of observed data to the total post- and pre-fit SM prediction. The last bin includes the overflow. Uncertainties in the background estimates include both the statistical and systematic uncertainties, with correlations between uncertainties taken into account. The dashed lines show the predicted yields for two benchmark signal models corresponding to S&#771;₁ (m, y_b&mu;) = (1.5&nbsp;TeV, 1.5) and S&#771;₁ (m, y_b&mu;) = (2.0&nbsp;TeV, 1.5), respectively. Note: the values in the table are normalized by the width of corresponding bin

Data (dots) and post-fit SM distribution (histograms) of m_&#8467;j in (a, b) SR-1L-&mu;b and (c, d) SR-2L-&mu;b of the &mu;+b-jet channel obtained by a CR+SR background-only fit for Run&nbsp;2 and Run&nbsp;3, respectively. The lower panel shows the ratio of observed data to the total post- and pre-fit SM prediction. The last bin includes the overflow. Uncertainties in the background estimates include both the statistical and systematic uncertainties, with correlations between uncertainties taken into account. The dashed lines show the predicted yields for two benchmark signal models corresponding to S&#771;₁ (m, y_b&mu;) = (1.5&nbsp;TeV, 1.5) and S&#771;₁ (m, y_b&mu;) = (2.0&nbsp;TeV, 1.5), respectively. Note: the values in the table are normalized by the width of corresponding bin

Data (dots) and post-fit SM distribution (histograms) of m_&#8467;j in (a, b) SR-1L-&mu;b and (c, d) SR-2L-&mu;b of the &mu;+b-jet channel obtained by a CR+SR background-only fit for Run&nbsp;2 and Run&nbsp;3, respectively. The lower panel shows the ratio of observed data to the total post- and pre-fit SM prediction. The last bin includes the overflow. Uncertainties in the background estimates include both the statistical and systematic uncertainties, with correlations between uncertainties taken into account. The dashed lines show the predicted yields for two benchmark signal models corresponding to S&#771;₁ (m, y_b&mu;) = (1.5&nbsp;TeV, 1.5) and S&#771;₁ (m, y_b&mu;) = (2.0&nbsp;TeV, 1.5), respectively. Note: the values in the table are normalized by the width of corresponding bin

Data (dots) and post-fit SM distribution (histograms) of m_&#8467;j in (a, b) SR-1L-&mu;b and (c, d) SR-2L-&mu;b of the &mu;+b-jet channel obtained by a CR+SR background-only fit for Run&nbsp;2 and Run&nbsp;3, respectively. The lower panel shows the ratio of observed data to the total post- and pre-fit SM prediction. The last bin includes the overflow. Uncertainties in the background estimates include both the statistical and systematic uncertainties, with correlations between uncertainties taken into account. The dashed lines show the predicted yields for two benchmark signal models corresponding to S&#771;₁ (m, y_b&mu;) = (1.5&nbsp;TeV, 1.5) and S&#771;₁ (m, y_b&mu;) = (2.0&nbsp;TeV, 1.5), respectively. Note: the values in the table are normalized by the width of corresponding bin

Exclusion limits for minimal models of S&#771;₁ production with only y_de being non-zero obtained from a simultaneous fit to SR-1L and SR-2L of the e+light-jet channel combining Run-2 and Run-3 data. All limits are computed at 95&percnt; CL and the observed (red solid lines) and expected (black dashed lines) exclusion limits are shown in the m(S&#771;₁) &ndash; y_de plane. The observed exclusion should be interpreted as the region above the red line. The yellow inner (green outer) shaded band around the expected limits corresponds to the &plusmn;1 &sigma; (&plusmn;2 &sigma;) variations of the expected limit, accounting for all uncertainties. The observed limit obtained from ATLAS searches for LQ pair production is also shown as dark blue line [13]. Constraints from weak charge measurements of protons and nuclei on y_de couplings derived by Ref. [10] are shown as light magenta line.

Exclusion limits for minimal models of S&#771;₁ production with only y_s&mu; being non-zero obtained from a simultaneous fit to SR-1L and SR-2L of the &mu;+light-jet channel combining Run-2 and Run-3 data. All limits are computed at 95&percnt; CL and the observed (red solid lines) and expected (black dashed lines) exclusion limits are shown in the m(S&#771;₁) &ndash; y_s&mu; plane. The observed exclusion should be interpreted as the region above the red line. The yellow inner (green outer) shaded band around the expected limits corresponds to the &plusmn;1 &sigma; (&plusmn;2 &sigma;) variations of the expected limit, accounting for all uncertainties. The observed limit obtained from ATLAS searches for LQ pair production is also shown as dark blue line [13].

Exclusion limits for minimal models of S&#771;₁ production with only y_be being non-zero obtained from a simultaneous fit to SR-1L and SR-2L of the e+b-jet channel combining Run-2 and Run-3 data. All limits are computed at 95&percnt; CL and the observed (red solid lines) and expected (black dashed lines) exclusion limits are shown in the m(S&#771;₁) &ndash; y_be plane. The observed exclusion should be interpreted as the region above the red line. The yellow inner (green outer) shaded band around the expected limits corresponds to the &plusmn;1 &sigma; (&plusmn;2 &sigma;) variations of the expected limit, accounting for all uncertainties. The observed limit obtained from ATLAS searches for LQ pair production is also shown as dark blue line [13].

Exclusion limits for minimal models of S&#771;₁ production with only y_b&mu; being non-zero obtained from a simultaneous fit to SR-1L and SR-2L of the &mu;+b-jet channel combining Run-2 and Run-3 data. All limits are computed at 95&percnt; CL and the observed (red solid lines) and expected (black dashed lines) exclusion limits are shown in the m(S&#771;₁) &ndash; y_b&mu; plane. The observed exclusion should be interpreted as the region above the red line. The yellow inner (green outer) shaded band around the expected limits corresponds to the &plusmn;1 &sigma; (&plusmn;2 &sigma;) variations of the expected limit, accounting for all uncertainties. The observed limit obtained from ATLAS searches for LQ pair production is also shown as dark blue line [13].

Exclusion limits for minimal models of S&#771;₁ production obtained from a fit to SR-1L, SR-2L and their combination of (a) the e+light-jet, (b) the &mu;+light-jet, (c) the e+b-jet and (d) the &mu;+b-jet channel using Run-2 and Run-3 data. All limits are computed at 95&percnt; CL and the observed (solid lines) and expected (dashed lines) exclusion limits are shown in the m(S&#771;₁) &ndash; y plane. The observed exclusion regions should be interpreted as the region above the solid lines. Constraints from weak charge measurements of protons and nuclei&nbsp; and ATLAS searches for LQ pair production&nbsp; are shown as light magenta and dark blue areas, respectively.

Exclusion limits for minimal models of S&#771;₁ production obtained from a fit to SR-1L, SR-2L and their combination of (a) the e+light-jet, (b) the &mu;+light-jet, (c) the e+b-jet and (d) the &mu;+b-jet channel using Run-2 and Run-3 data. All limits are computed at 95&percnt; CL and the observed (solid lines) and expected (dashed lines) exclusion limits are shown in the m(S&#771;₁) &ndash; y plane. The observed exclusion regions should be interpreted as the region above the solid lines. Constraints from weak charge measurements of protons and nuclei&nbsp; and ATLAS searches for LQ pair production&nbsp; are shown as light magenta and dark blue areas, respectively.

Exclusion limits for minimal models of S&#771;₁ production obtained from a fit to SR-1L, SR-2L and their combination of (a) the e+light-jet, (b) the &mu;+light-jet, (c) the e+b-jet and (d) the &mu;+b-jet channel using Run-2 and Run-3 data. All limits are computed at 95&percnt; CL and the observed (solid lines) and expected (dashed lines) exclusion limits are shown in the m(S&#771;₁) &ndash; y plane. The observed exclusion regions should be interpreted as the region above the solid lines. Constraints from weak charge measurements of protons and nuclei&nbsp; and ATLAS searches for LQ pair production&nbsp; are shown as light magenta and dark blue areas, respectively.

Exclusion limits for minimal models of S&#771;₁ production obtained from a fit to SR-1L, SR-2L and their combination of (a) the e+light-jet, (b) the &mu;+light-jet, (c) the e+b-jet and (d) the &mu;+b-jet channel using Run-2 and Run-3 data. All limits are computed at 95&percnt; CL and the observed (solid lines) and expected (dashed lines) exclusion limits are shown in the m(S&#771;₁) &ndash; y plane. The observed exclusion regions should be interpreted as the region above the solid lines. Constraints from weak charge measurements of protons and nuclei&nbsp; and ATLAS searches for LQ pair production&nbsp; are shown as light magenta and dark blue areas, respectively.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for resonant production of $\tilde{S}$ in (a) Run 2 SR-1L-$ej$ and (b) Run 2 SR-2L-$ej$ and (c) Run 3 SR-1-$ej$ and (d) Run 3 SR-2-$ej$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for resonant production of $\tilde{S}$ in (a) Run 2 SR-1L-$ej$ and (b) Run 2 SR-2L-$ej$ and (c) Run 3 SR-1-$ej$ and (d) Run 3 SR-2-$ej$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for resonant production of $\tilde{S}$ in (a) Run 2 SR-1L-$ej$ and (b) Run 2 SR-2L-$ej$ and (c) Run 3 SR-1-$ej$ and (d) Run 3 SR-2-$ej$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for resonant production of $\tilde{S}$ in (a) Run 2 SR-1L-$ej$ and (b) Run 2 SR-2L-$ej$ and (c) Run 3 SR-1-$ej$ and (d) Run 3 SR-2-$ej$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for DY+SP production of $\tilde{S}$ in (a) Run 2 SR-1L-$ej$ and (b) Run 2 SR-2L-$ej$ and (c) Run 3 SR-1-$ej$ and (d) Run 3 SR-2-$ej$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for DY+SP production of $\tilde{S}$ in (a) Run 2 SR-1L-$ej$ and (b) Run 2 SR-2L-$ej$ and (c) Run 3 SR-1-$ej$ and (d) Run 3 SR-2-$ej$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for DY+SP production of $\tilde{S}$ in (a) Run 2 SR-1L-$ej$ and (b) Run 2 SR-2L-$ej$ and (c) Run 3 SR-1-$ej$ and (d) Run 3 SR-2-$ej$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for DY+SP production of $\tilde{S}$ in (a) Run 2 SR-1L-$ej$ and (b) Run 2 SR-2L-$ej$ and (c) Run 3 SR-1-$ej$ and (d) Run 3 SR-2-$ej$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for resonant production of $\tilde{S}$ in (a) Run 2 SR-1L-$\mu j$ and (b) Run 2 SR-2L-$\mu j$ and (c) Run 3 SR-1L-$\mu j$ and (d) Run 3 SR-2L-$\mu j$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for resonant production of $\tilde{S}$ in (a) Run 2 SR-1L-$\mu j$ and (b) Run 2 SR-2L-$\mu j$ and (c) Run 3 SR-1L-$\mu j$ and (d) Run 3 SR-2L-$\mu j$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for resonant production of $\tilde{S}$ in (a) Run 2 SR-1L-$\mu j$ and (b) Run 2 SR-2L-$\mu j$ and (c) Run 3 SR-1L-$\mu j$ and (d) Run 3 SR-2L-$\mu j$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for resonant production of $\tilde{S}$ in (a) Run 2 SR-1L-$\mu j$ and (b) Run 2 SR-2L-$\mu j$ and (c) Run 3 SR-1L-$\mu j$ and (d) Run 3 SR-2L-$\mu j$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for DY+SP production of $\tilde{S}$ in (a) Run 2 SR-1L-$\mu j$ and (b) Run 2 SR-2L-$\mu j$ and (c) Run 3 SR-1L-$\mu j$ and (d) Run 3 SR-2L-$\mu j$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for DY+SP production of $\tilde{S}$ in (a) Run 2 SR-1L-$\mu j$ and (b) Run 2 SR-2L-$\mu j$ and (c) Run 3 SR-1L-$\mu j$ and (d) Run 3 SR-2L-$\mu j$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for DY+SP production of $\tilde{S}$ in (a) Run 2 SR-1L-$\mu j$ and (b) Run 2 SR-2L-$\mu j$ and (c) Run 3 SR-1L-$\mu j$ and (d) Run 3 SR-2L-$\mu j$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for DY+SP production of $\tilde{S}$ in (a) Run 2 SR-1L-$\mu j$ and (b) Run 2 SR-2L-$\mu j$ and (c) Run 3 SR-1L-$\mu j$ and (d) Run 3 SR-2L-$\mu j$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for resonant production of $\tilde{S}$ in (a) Run 2 SR-1L-$eb$ and (b) Run 2 SR-2L-$eb$ and (c) Run 3 SR-1L-$eb$ and (d) Run 3 SR-2L-$eb$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for resonant production of $\tilde{S}$ in (a) Run 2 SR-1L-$eb$ and (b) Run 2 SR-2L-$eb$ and (c) Run 3 SR-1L-$eb$ and (d) Run 3 SR-2L-$eb$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for resonant production of $\tilde{S}$ in (a) Run 2 SR-1L-$eb$ and (b) Run 2 SR-2L-$eb$ and (c) Run 3 SR-1L-$eb$ and (d) Run 3 SR-2L-$eb$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for resonant production of $\tilde{S}$ in (a) Run 2 SR-1L-$eb$ and (b) Run 2 SR-2L-$eb$ and (c) Run 3 SR-1L-$eb$ and (d) Run 3 SR-2L-$eb$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for DY+SP of $\tilde{S}$ in (a) Run 2 SR-1L-$eb$ and (b) Run 2 SR-2L-$eb$ and (c) Run 3 SR-1L-$eb$ and (d) Run 3 SR-2L-$eb$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for DY+SP of $\tilde{S}$ in (a) Run 2 SR-1L-$eb$ and (b) Run 2 SR-2L-$eb$ and (c) Run 3 SR-1L-$eb$ and (d) Run 3 SR-2L-$eb$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for DY+SP of $\tilde{S}$ in (a) Run 2 SR-1L-$eb$ and (b) Run 2 SR-2L-$eb$ and (c) Run 3 SR-1L-$eb$ and (d) Run 3 SR-2L-$eb$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for DY+SP of $\tilde{S}$ in (a) Run 2 SR-1L-$eb$ and (b) Run 2 SR-2L-$eb$ and (c) Run 3 SR-1L-$eb$ and (d) Run 3 SR-2L-$eb$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for resonant production of $\tilde{S}$ in (a) Run 2 SR-1L-$\mu b$ and (b) Run 2 SR-2L-$\mu b$ and (c) Run 3 SR-1L-$\mu b$ and (d) Run 3 SR-2L-$\mu b$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for resonant production of $\tilde{S}$ in (a) Run 2 SR-1L-$\mu b$ and (b) Run 2 SR-2L-$\mu b$ and (c) Run 3 SR-1L-$\mu b$ and (d) Run 3 SR-2L-$\mu b$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for resonant production of $\tilde{S}$ in (a) Run 2 SR-1L-$\mu b$ and (b) Run 2 SR-2L-$\mu b$ and (c) Run 3 SR-1L-$\mu b$ and (d) Run 3 SR-2L-$\mu b$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for resonant production of $\tilde{S}$ in (a) Run 2 SR-1L-$\mu b$ and (b) Run 2 SR-2L-$\mu b$ and (c) Run 3 SR-1L-$\mu b$ and (d) Run 3 SR-2L-$\mu b$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for DY+SP production of $\tilde{S}$ in (a) Run 2 SR-1L-$\mu b$ and (b) Run 2 SR-2L-$\mu b$ and (c) Run 3 SR-1L-$\mu b$ and (d) Run 3 SR-2L-$\mu b$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for DY+SP production of $\tilde{S}$ in (a) Run 2 SR-1L-$\mu b$ and (b) Run 2 SR-2L-$\mu b$ and (c) Run 3 SR-1L-$\mu b$ and (d) Run 3 SR-2L-$\mu b$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for DY+SP production of $\tilde{S}$ in (a) Run 2 SR-1L-$\mu b$ and (b) Run 2 SR-2L-$\mu b$ and (c) Run 3 SR-1L-$\mu b$ and (d) Run 3 SR-2L-$\mu b$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Values of the signal acceptance multiplied by the selection efficiency ($A\times\epsilon$) for DY+SP production of $\tilde{S}$ in (a) Run 2 SR-1L-$\mu b$ and (b) Run 2 SR-2L-$\mu b$ and (c) Run 3 SR-1L-$\mu b$ and (d) Run 3 SR-2L-$\mu b$. The $A \times \epsilon$ values are calculated as the number of events of reconstructed-level signal simulation divided by the total cross-section of the signal process times the integrated luminosity.

Event selection cutflows of SR-1L-$eb$ for the signal sample with $m(\tilde{S}) = 2$ TeV and $y_{be} = 1.0$ individually for resonant production (RP) and combined Drell-Yan plus single production (DY+SP). The first number in the column for each mass points corresponds to the signal event yield after applying the associated cut while the second number in parentheses represents the efficiency with respect to the previous cut.

Event selection cutflows of SR-2L-$eb$ for the signal sample with $m(\tilde{S}) = 2$ TeV and $y_{be} = 1.0$ individually for resonant production (RP) and combined Drell-Yan plus single production (DY+SP). The first number in the column for each mass points corresponds to the signal event yield after applying the associated cut while the second number in parentheses represents the efficiency with respect to the previous cut.

Event selection cutflows of SR-1L-$ej$ for the signal sample with $m(\tilde{S}) = 2$ TeV and $y_{de} = 1.0$ individually for resonant production (RP) and combined Drell-Yan plus single production (DY+SP). The first number in the column for each mass points corresponds to the signal event yield after applying the associated cut while the second number in parentheses represents the efficiency with respect to the previous cut.

Event selection cutflows of SR-2L-$ej$ for the signal sample with $m(\tilde{S}) = 2$ TeV and $y_{de} = 1.0$ individually for resonant production (RP) and combined Drell-Yan plus single production (DY+SP). The first number in the column for each mass points corresponds to the signal event yield after applying the associated cut while the second number in parentheses represents the efficiency with respect to the previous cut.

Event selection cutflows of SR-1L-$\mu b$ for the signal sample with $m(\tilde{S}) = 2$ TeV and $y_{b\mu} = 1.0$ individually for resonant production (RP) and combined Drell-Yan plus single production (DY+SP). The first number in the column for each mass points corresponds to the signal event yield after applying the associated cut while the second number in parentheses represents the efficiency with respect to the previous cut.

Event selection cutflows of SR-2L-$\mu b$ for the signal sample with $m(\tilde{S}) = 2$ TeV and $y_{b\mu} = 1.0$ individually for resonant production (RP) and combined Drell-Yan plus single production (DY+SP). The first number in the column for each mass points corresponds to the signal event yield after applying the associated cut while the second number in parentheses represents the efficiency with respect to the previous cut.

Event selection cutflows of SR-1L-$\mu j$ for the signal sample with $m(\tilde{S}) = 2$ TeV and $y_{s\mu} = 1.0$ individually for resonant production (RP) and combined Drell-Yan plus single production (DY+SP). The first number in the column for each mass points corresponds to the signal event yield after applying the associated cut while the second number in parentheses represents the efficiency with respect to the previous cut.

Event selection cutflows of SR-2L-$\mu j$ for the signal sample with $m(\tilde{S}) = 2$ TeV and $y_{s\mu} = 1.0$ individually for resonant production (RP) and combined Drell-Yan plus single production (DY+SP). The first number in the column for each mass points corresponds to the signal event yield after applying the associated cut while the second number in parentheses represents the efficiency with respect to the previous cut.

Unfolded $R(\rho_{s})$ observable in the 2-to-3 measurement (normalized and divided by bin width). The parton level is defined with two stable top-quarks and a jet with $p_{T}>50$ GeV and $|\eta|<2.5$.

Covariance matrix for statistical effects of the measured $R(\rho_{s})$ observable after unfolding, for the 2-to-3 measurement (normalized)

Covariance matrix for statistical and systematic effects of the measured $R(\rho_{s})$ observable after unfolding, for the 2-to-3 measurement (normalized)

Impact of systematic uncertainties on the 2-to-3 unfolded observable. Values are given in percentage of bin content.

Central value and breakdown of the uncertainties affecting the top-quark pole mass extraction from the 2-to-3 unfolded observable.

Unfolded number of events in the 2-to-7measurement (not normalized). The parton level is defined with two neutrinos, one electron and one muon of opposite electric charges, two $b$-jets and an additional jet (extrajet). The four-momentum of the sum of neutrinos has transverse component larger than 30 GeV. The $p_{T}$-leading lepton has $p_{T}>28$ GeV, while the sub-leading has $p_{T}>20$ GeV. The two $b$-jets with have $p_{T}>30$ GeV and the extrajet has $p^\text{extrajet}_{T}>60$ GeV. All the leptons and jets are separated by $\Delta R >0.4$ and have $|\eta|<2.5$.

Covariance matrix for statistical effects of the measured number of events after unfolding, for the 2-to-7 measurement (not normalized)

Covariance matrix for statistical and systematic effects of the measured number of events after unfolding, for the 2-to-7 measurement (not normalized)

Unfolded $R(\rho_{s})$ observable in the 2-to-7 measurement (normalized and divided by bin width). The parton level is defined with two neutrinos, one electron and one muon of opposite electric charges, two $b$-jets and an additional jet (extrajet). The four-momentum of the sum of neutrinos has transverse component larger than 30 GeV. The $p_{T}$-leading lepton has $p_{T}>28$ GeV, while the sub-leading has $p_{T}>20$ GeV. The two $b$-jets with have $p_{T}>30$ GeV and the extrajet has $p^\text{extrajet}_{T}>60$ GeV. All the leptons and jets are separated by $\Delta R >0.4$ and have $|\eta|<2.5$.

Covariance matrix for statistical effects of the measured $R(\rho_{s})$ observable after unfolding, for the 2-to-7 measurement (normalized)

Covariance matrix for statistical and systematic effects of the measured $R(\rho_{s})$ observable after unfolding, for the 2-to-7 measurement (normalized)

Impact of systematic uncertainties on the 2-to-7 unfolded observable. Values are given in percentage of bin content.

Central value and breakdown of the uncertainties affecting the top-quark pole mass extraction from the 2-to-7 unfolded observable.

Distributions of the VLQ-candidate mass, m_VLQ, in the (a&ndash;c) SRs, (d&ndash;f) W+jets CRs and (g&ndash;i) tt&#772; CRs after the fit to the background-only hypothesis. The columns correspond from left to right to the low-, middle-, and high-p_T^W bins in each region. Other includes remaining backgrounds from top quarks or that contain two W/Z bosons. The last bin includes overflow. Note: the 'Data' values in the table are normalized by the width of the bin to correspond to the number of events per 100 GeV

Distributions of the VLQ-candidate mass, m_VLQ, in the (a&ndash;c) SRs, (d&ndash;f) W+jets CRs and (g&ndash;i) tt&#772; CRs after the fit to the background-only hypothesis. The columns correspond from left to right to the low-, middle-, and high-p_T^W bins in each region. Other includes remaining backgrounds from top quarks or that contain two W/Z bosons. The last bin includes overflow. Note: the 'Data' values in the table are normalized by the width of the bin to correspond to the number of events per 100 GeV

Distributions of the VLQ-candidate mass, m_VLQ, in the (a&ndash;c) SRs, (d&ndash;f) W+jets CRs and (g&ndash;i) tt&#772; CRs after the fit to the background-only hypothesis. The columns correspond from left to right to the low-, middle-, and high-p_T^W bins in each region. Other includes remaining backgrounds from top quarks or that contain two W/Z bosons. The last bin includes overflow. Note: the 'Data' values in the table are normalized by the width of the bin to correspond to the number of events per 100 GeV

Distributions of the VLQ-candidate mass, m_VLQ, in the (a&ndash;c) SRs, (d&ndash;f) W+jets CRs and (g&ndash;i) tt&#772; CRs after the fit to the background-only hypothesis. The columns correspond from left to right to the low-, middle-, and high-p_T^W bins in each region. Other includes remaining backgrounds from top quarks or that contain two W/Z bosons. The last bin includes overflow. Note: the 'Data' values in the table are normalized by the width of the bin to correspond to the number of events per 100 GeV

Distributions of the VLQ-candidate mass, m_VLQ, in the (a&ndash;c) SRs, (d&ndash;f) W+jets CRs and (g&ndash;i) tt&#772; CRs after the fit to the background-only hypothesis. The columns correspond from left to right to the low-, middle-, and high-p_T^W bins in each region. Other includes remaining backgrounds from top quarks or that contain two W/Z bosons. The last bin includes overflow. Note: the 'Data' values in the table are normalized by the width of the bin to correspond to the number of events per 100 GeV

Distributions of the VLQ-candidate mass, m_VLQ, in the (a&ndash;c) SRs, (d&ndash;f) W+jets CRs and (g&ndash;i) tt&#772; CRs after the fit to the background-only hypothesis. The columns correspond from left to right to the low-, middle-, and high-p_T^W bins in each region. Other includes remaining backgrounds from top quarks or that contain two W/Z bosons. The last bin includes overflow. Note: the 'Data' values in the table are normalized by the width of the bin to correspond to the number of events per 100 GeV

Distributions of the VLQ-candidate mass, m_VLQ, in the W+jets VRs (a-f) and tt&#772; VRs (g-i) after the fit to the background-only hypothesis. The columns correspond from left to right to the low-, middle-, and high-p_T^W bins in each region. Other includes remaining backgrounds from top quarks or containing combinations having two W/Z bosons. Last bin includes overflow. Note: the 'Data' values in the table are normalized by the width of the bin to correspond to the number of events per 100 GeV

Distributions of the VLQ-candidate mass, m_VLQ, in the W+jets VRs (a-f) and tt&#772; VRs (g-i) after the fit to the background-only hypothesis. The columns correspond from left to right to the low-, middle-, and high-p_T^W bins in each region. Other includes remaining backgrounds from top quarks or containing combinations having two W/Z bosons. Last bin includes overflow. Note: the 'Data' values in the table are normalized by the width of the bin to correspond to the number of events per 100 GeV

Distributions of the VLQ-candidate mass, m_VLQ, in the W+jets VRs (a-f) and tt&#772; VRs (g-i) after the fit to the background-only hypothesis. The columns correspond from left to right to the low-, middle-, and high-p_T^W bins in each region. Other includes remaining backgrounds from top quarks or containing combinations having two W/Z bosons. Last bin includes overflow. Note: the 'Data' values in the table are normalized by the width of the bin to correspond to the number of events per 100 GeV

Distributions of the VLQ-candidate mass, m_VLQ, in the W+jets VRs (a-f) and tt&#772; VRs (g-i) after the fit to the background-only hypothesis. The columns correspond from left to right to the low-, middle-, and high-p_T^W bins in each region. Other includes remaining backgrounds from top quarks or containing combinations having two W/Z bosons. Last bin includes overflow. Note: the 'Data' values in the table are normalized by the width of the bin to correspond to the number of events per 100 GeV

Distributions of the VLQ-candidate mass, m_VLQ, in the W+jets VRs (a-f) and tt&#772; VRs (g-i) after the fit to the background-only hypothesis. The columns correspond from left to right to the low-, middle-, and high-p_T^W bins in each region. Other includes remaining backgrounds from top quarks or containing combinations having two W/Z bosons. Last bin includes overflow. Note: the 'Data' values in the table are normalized by the width of the bin to correspond to the number of events per 100 GeV

Distributions of the VLQ-candidate mass, m_VLQ, in the W+jets VRs (a-f) and tt&#772; VRs (g-i) after the fit to the background-only hypothesis. The columns correspond from left to right to the low-, middle-, and high-p_T^W bins in each region. Other includes remaining backgrounds from top quarks or containing combinations having two W/Z bosons. Last bin includes overflow. Note: the 'Data' values in the table are normalized by the width of the bin to correspond to the number of events per 100 GeV

Expected (background-only) and observed 95&percnt;&nbsp;CL upper limits on the VLQ coupling &kappa; as functions of the VLQ mass m_Q, for T-singlet (a) and Y-triplet (b) vector-like quarks. The green and yellow bands indicate the systematic uncertainties which are profiled in the fit for the observed upper limits. For the T-singlet model, the result of the latest ATLAS combination of searches for single vector-like top-quarks&nbsp; is overlaid; this includes the decay modes T&rarr;H t and T&rarr;Z t. These interpretations are limited to parameter combinations for which the model corrections are valid, by restricting the VLQ relative width to &Gamma;_Q/m_Q &lt; 0.5, as indicated by the grey dashed line.

Expected (background-only) and observed 95&percnt;&nbsp;CL upper limits on the VLQ coupling &kappa; as functions of the VLQ mass m_Q, for T-singlet (a) and Y-triplet (b) vector-like quarks. The green and yellow bands indicate the systematic uncertainties which are profiled in the fit for the observed upper limits. For the T-singlet model, the result of the latest ATLAS combination of searches for single vector-like top-quarks&nbsp; is overlaid; this includes the decay modes T&rarr;H t and T&rarr;Z t. These interpretations are limited to parameter combinations for which the model corrections are valid, by restricting the VLQ relative width to &Gamma;_Q/m_Q &lt; 0.5, as indicated by the grey dashed line.

Exclusion limit (at 95&percnt; CL) for (a) T-singlet and (b) Y-triplet, expressed in terms of an upper limit on the VLQ relative width &Gamma;_Q/m_Q, within its validity range for the modelling used, as a function of the VLQ mass m_Q. This is an alternative presentation of the upper limit set in terms of the coupling &kappa; in Figure&nbsp;6. As can be seen by the fact the interference-included and signal-only exclusion curves overlap almost entirely, the effect of neglecting the interference is negligible for the vector-like Y-quark.

Exclusion limit (at 95&percnt; CL) for (a) T-singlet and (b) Y-triplet, expressed in terms of an upper limit on the VLQ relative width &Gamma;_Q/m_Q, within its validity range for the modelling used, as a function of the VLQ mass m_Q. This is an alternative presentation of the upper limit set in terms of the coupling &kappa; in Figure&nbsp;6. As can be seen by the fact the interference-included and signal-only exclusion curves overlap almost entirely, the effect of neglecting the interference is negligible for the vector-like Y-quark.

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $p_{\mathrm{T}}^{\mathrm{lead.\,lep.}}$.

Fiducial differential cross-sections as a function of $p_{\mathrm{T}}^{\mathrm{sub-lead.\,lep.}}$. The measured cross-section values are shown as points with error bars giving the statistical uncertainty and solid bands indicating the size of the total uncertainty. The right-hand-side axis indicates the integrated cross-section of the rightmost bin. The results are compared to fixed-order nNNLO QCD + NLO EW predictions of Matrix 2.1, with the NNLO + PS predictions from Powheg MiNNLO + Pythia8 and Geneva + Pythia8, as well as Sherpa2.2.12 NLO + PS predictions. The last three predictions are combined with Sherpa 2.2.2 for the $gg$ initial state and Sherpa 2.2.12 for electroweak $WWjj$ production. These contributions are modelled at LO but a NLO QCD $k$-factor of 1.7 is applied for gluon induced production. Theoretical predictions are indicated as markers with vertical lines denoting PDF, scale and parton shower uncertainties. Markers are staggered for better visibility.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable $p_{\mathrm{T}}^{\mathrm{sub-lead.\,lep.}}$.

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $p_{\mathrm{T}}^{\mathrm{sub-lead.\,lep.}}$.

Fiducial differential cross-sections as a function of $p_{\mathrm{T},e\mu}$. The measured cross-section values are shown as points with error bars giving the statistical uncertainty and solid bands indicating the size of the total uncertainty. The right-hand-side axis indicates the integrated cross-section of the rightmost bin. The results are compared to fixed-order nNNLO QCD + NLO EW predictions of Matrix 2.1, with the NNLO + PS predictions from Powheg MiNNLO + Pythia8 and Geneva + Pythia8, as well as Sherpa2.2.12 NLO + PS predictions. The last three predictions are combined with Sherpa 2.2.2 for the $gg$ initial state and Sherpa 2.2.12 for electroweak $WWjj$ production. These contributions are modelled at LO but a NLO QCD $k$-factor of 1.7 is applied for gluon induced production. Theoretical predictions are indicated as markers with vertical lines denoting PDF, scale and parton shower uncertainties. Markers are staggered for better visibility.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable $p_{\mathrm{T},e\mu}$.

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $p_{\mathrm{T},e\mu}$.

Fiducial differential cross-sections as a function of $|y_{e\mu}|$. The measured cross-section values are shown as points with error bars giving the statistical uncertainty and solid bands indicating the size of the total uncertainty. The results are compared to fixed-order nNNLO QCD + NLO EW predictions of Matrix 2.1, with the NNLO + PS predictions from Powheg MiNNLO + Pythia8 and Geneva + Pythia8, as well as Sherpa2.2.12 NLO + PS predictions. The last three predictions are combined with Sherpa 2.2.2 for the $gg$ initial state and Sherpa 2.2.12 for electroweak $WWjj$ production. These contributions are modelled at LO but a NLO QCD $k$-factor of 1.7 is applied for gluon induced production. Theoretical predictions are indicated as markers with vertical lines denoting PDF, scale and parton shower uncertainties. Markers are staggered for better visibility.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable $|y_{e\mu}|$.

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $|y_{e\mu}|$.

Fiducial differential cross-sections as a function of $m_{e\mu}$. The measured cross-section values are shown as points with error bars giving the statistical uncertainty and solid bands indicating the size of the total uncertainty. The right-hand-side axis indicates the integrated cross-section of the rightmost bin. The results are compared to fixed-order nNNLO QCD + NLO EW predictions of Matrix 2.1, with the NNLO + PS predictions from Powheg MiNNLO + Pythia8 and Geneva + Pythia8, as well as Sherpa2.2.12 NLO + PS predictions. The last three predictions are combined with Sherpa 2.2.2 for the $gg$ initial state and Sherpa 2.2.12 for electroweak $WWjj$ production. These contributions are modelled at LO but a NLO QCD $k$-factor of 1.7 is applied for gluon induced production. Theoretical predictions are indicated as markers with vertical lines denoting PDF, scale and parton shower uncertainties. Markers are staggered for better visibility.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable $m_{e\mu}$.

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $m_{e\mu}$.

Fiducial differential cross-sections as a function of $|\Delta\phi_{e\mu}|$. The measured cross-section values are shown as points with error bars giving the statistical uncertainty and solid bands indicating the size of the total uncertainty. The results are compared to fixed-order nNNLO QCD + NLO EW predictions of Matrix 2.1, with the NNLO + PS predictions from Powheg MiNNLO + Pythia8 and Geneva + Pythia8, as well as Sherpa2.2.12 NLO + PS predictions. The last three predictions are combined with Sherpa 2.2.2 for the $gg$ initial state and Sherpa 2.2.12 for electroweak $WWjj$ production. These contributions are modelled at LO but a NLO QCD $k$-factor of 1.7 is applied for gluon induced production. Theoretical predictions are indicated as markers with vertical lines denoting PDF, scale and parton shower uncertainties. Markers are staggered for better visibility.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable $|\Delta\phi_{e\mu}|$.

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $|\Delta\phi_{e\mu}|$.

Fiducial differential cross-sections as a function of $\cos(\theta^{*})$. The measured cross-section values are shown as points with error bars giving the statistical uncertainty and solid bands indicating the size of the total uncertainty. The results are compared to fixed-order nNNLO QCD + NLO EW predictions of Matrix 2.1, with the NNLO + PS predictions from Powheg MiNNLO + Pythia8 and Geneva + Pythia8, as well as Sherpa2.2.12 NLO + PS predictions. The last three predictions are combined with Sherpa 2.2.2 for the $gg$ initial state and Sherpa 2.2.12 for electroweak $WWjj$ production. These contributions are modelled at LO but a NLO QCD $k$-factor of 1.7 is applied for gluon induced production. Theoretical predictions are indicated as markers with vertical lines denoting PDF, scale and parton shower uncertainties. Markers are staggered for better visibility.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable $\cos(\theta^{*})$.

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $\cos(\theta^{*})$.

Fiducial differential cross-sections as a function of $E_{\mathrm{T}}^{\mathrm{miss}}$. The measured cross-section values are shown as points with error bars giving the statistical uncertainty and solid bands indicating the size of the total uncertainty. The right-hand-side axis indicates the integrated cross-section of the rightmost bin. The results are compared to fixed-order nNNLO QCD + NLO EW predictions of Matrix 2.1, with the NNLO + PS predictions from Powheg MiNNLO + Pythia8 and Geneva + Pythia8, as well as Sherpa2.2.12 NLO + PS predictions. The last three predictions are combined with Sherpa 2.2.2 for the $gg$ initial state and Sherpa 2.2.12 for electroweak $WWjj$ production. These contributions are modelled at LO but a NLO QCD $k$-factor of 1.7 is applied for gluon induced production. Theoretical predictions are indicated as markers with vertical lines denoting PDF, scale and parton shower uncertainties. Markers are staggered for better visibility.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable $E_{\mathrm{T}}^{\mathrm{miss}}$.

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $E_{\mathrm{T}}^{\mathrm{miss}}$.

Fiducial differential cross-sections as a function of $H_{\mathrm{T}}^{\mathrm{lep}+\mathrm{MET}}$. The measured cross-section values are shown as points with error bars giving the statistical uncertainty and solid bands indicating the size of the total uncertainty. The right-hand-side axis indicates the integrated cross-section of the rightmost bin. The results are compared to fixed-order nNNLO QCD + NLO EW predictions of Matrix 2.1, with the NNLO + PS predictions from Powheg MiNNLO + Pythia8 and Geneva + Pythia8, as well as Sherpa2.2.12 NLO + PS predictions. The last three predictions are combined with Sherpa 2.2.2 for the $gg$ initial state and Sherpa 2.2.12 for electroweak $WWjj$ production. These contributions are modelled at LO but a NLO QCD $k$-factor of 1.7 is applied for gluon induced production. Theoretical predictions are indicated as markers with vertical lines denoting PDF, scale and parton shower uncertainties. Markers are staggered for better visibility.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable $H_{\mathrm{T}}^{\mathrm{lep}+\mathrm{MET}}$.

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $H_{\mathrm{T}}^{\mathrm{lep}+\mathrm{MET}}$.

Fiducial differential cross-sections as a function of $m_{\mathrm{T},e\mu}$. The measured cross-section values are shown as points with error bars giving the statistical uncertainty and solid bands indicating the size of the total uncertainty. The right-hand-side axis indicates the integrated cross-section of the rightmost bin. The results are compared to fixed-order nNNLO QCD + NLO EW predictions of Matrix 2.1, with the NNLO + PS predictions from Powheg MiNNLO + Pythia8 and Geneva + Pythia8, as well as Sherpa2.2.12 NLO + PS predictions. The last three predictions are combined with Sherpa 2.2.2 for the $gg$ initial state and Sherpa 2.2.12 for electroweak $WWjj$ production. These contributions are modelled at LO but a NLO QCD $k$-factor of 1.7 is applied for gluon induced production. Theoretical predictions are indicated as markers with vertical lines denoting PDF, scale and parton shower uncertainties. Markers are staggered for better visibility.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable $m_{\mathrm{T},e\mu}$.

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $m_{\mathrm{T},e\mu}$.

Fiducial differential cross-sections as a function of the number of jets. The measured cross-section values are shown as points with error bars giving the statistical uncertainty and solid bands indicating the size of the total uncertainty. The results are compared to fixed-order nNNLO QCD + NLO EW predictions of Matrix 2.1, with the NNLO + PS predictions from Powheg MiNNLO + Pythia8 and Geneva + Pythia8, as well as Sherpa2.2.12 NLO + PS predictions. The last three predictions are combined with Sherpa 2.2.2 for the $gg$ initial state and Sherpa 2.2.12 for electroweak $WWjj$ production. These contributions are modelled at LO but a NLO QCD $k$-factor of 1.7 is applied for gluon induced production. Theoretical predictions are indicated as markers with vertical lines denoting PDF, scale and parton shower uncertainties. Markers are staggered for better visibility.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable Number of jets ($p_{\mathrm{T}} > $ 30 GeV).

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable Number of jets ($p_{\mathrm{T}} > $ 30 GeV).

Fiducial differential cross-sections as a function of $S_{\mathrm{T}}$. The measured cross-section values are shown as points with error bars giving the statistical uncertainty and solid bands indicating the size of the total uncertainty. The right-hand-side axis indicates the integrated cross-section of the rightmost bin. The results are compared to fixed-order nNNLO QCD + NLO EW predictions of Matrix 2.1, with the NNLO + PS predictions from Powheg MiNNLO + Pythia8 and Geneva + Pythia8, as well as Sherpa2.2.12 NLO + PS predictions. The last three predictions are combined with Sherpa 2.2.2 for the $gg$ initial state and Sherpa 2.2.12 for electroweak $WWjj$ production. These contributions are modelled at LO but a NLO QCD $k$-factor of 1.7 is applied for gluon induced production. Theoretical predictions are indicated as markers with vertical lines denoting PDF, scale and parton shower uncertainties. Markers are staggered for better visibility.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable $S_{\mathrm{T}}$.

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $S_{\mathrm{T}}$.

Fiducial differential cross-sections for $p_{\mathrm{T},e\mu}$ in the region with 85 $<m_{e\mu}<$ 150, for the nNNLO MATRIX prediction and various four flavour PDF sets. The measured cross-section values are shown as points with error bars giving the statistical uncertainty and solid bands indicating the size of the total uncertainty. The right-hand-side axis indicates the integrated cross-section of the rightmost bin. The measurement is compared to fixed-order nNNLO QCD + NLO EW predictions of Matrix 2.1 using four different four-flavour NNLO PDF sets: NNPDF3.0, NNPDF3.1, CT18, and MSHT20.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable $p_{\mathrm{T},e\mu}$ (85 $<m_{e\mu}<$ 150).

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $p_{\mathrm{T},e\mu}$ (85 $<m_{e\mu}<$ 150).

Fiducial differential cross-sections for $|y_{e\mu}|$ in the region with 85 $<m_{e\mu}<$ 150, for the nNNLO MATRIX prediction and various four flavour PDF sets. The measured cross-section values are shown as points with error bars giving the statistical uncertainty and solid bands indicating the size of the total uncertainty. The measurement is compared to fixed-order nNNLO QCD + NLO EW predictions of Matrix 2.1 using four different four-flavour NNLO PDF sets: NNPDF3.0, NNPDF3.1, CT18, and MSHT20.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable $|y_{e\mu}|$ (85 $<m_{e\mu}<$ 150).

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $|y_{e\mu}|$ (85 $<m_{e\mu}<$ 150).

Fiducial differential cross-sections for $p_{\mathrm{T},e\mu}$ in the region with 150 $<m_{e\mu}<$ 250, for the nNNLO MATRIX prediction and various four flavour PDF sets. The measured cross-section values are shown as points with error bars giving the statistical uncertainty and solid bands indicating the size of the total uncertainty. The right-hand-side axis indicates the integrated cross-section of the rightmost bin. The measurement is compared to fixed-order nNNLO QCD + NLO EW predictions of Matrix 2.1 using four different four-flavour NNLO PDF sets: NNPDF3.0, NNPDF3.1, CT18, and MSHT20.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable $p_{\mathrm{T},e\mu}$ (150 $<m_{e\mu}<$ 250).

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $p_{\mathrm{T},e\mu}$ (150 $<m_{e\mu}<$ 250).

Fiducial differential cross-sections for $|y_{e\mu}|$ in the region with 150 $<m_{e\mu}<$ 250, for the nNNLO MATRIX prediction and various four flavour PDF sets. The measured cross-section values are shown as points with error bars giving the statistical uncertainty and solid bands indicating the size of the total uncertainty. The measurement is compared to fixed-order nNNLO QCD + NLO EW predictions of Matrix 2.1 using four different four-flavour NNLO PDF sets: NNPDF3.0, NNPDF3.1, CT18, and MSHT20.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable $|y_{e\mu}|$ (150 $<m_{e\mu}<$ 250).

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $|y_{e\mu}|$ (150 $<m_{e\mu}<$ 250).

Fiducial differential cross-sections for $p_{\mathrm{T},e\mu}$ in the region with $m_{e\mu}>$ 250, for the nNNLO MATRIX prediction and various four flavour PDF sets. The measured cross-section values are shown as points with error bars giving the statistical uncertainty and solid bands indicating the size of the total uncertainty. The right-hand-side axis indicates the integrated cross-section of the rightmost bin. The measurement is compared to fixed-order nNNLO QCD + NLO EW predictions of Matrix 2.1 using four different four-flavour NNLO PDF sets: NNPDF3.0, NNPDF3.1, CT18, and MSHT20.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable $p_{\mathrm{T},e\mu}$ ($m_{e\mu}>$ 250).

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $p_{\mathrm{T},e\mu}$ ($m_{e\mu}>$ 250).

Fiducial differential cross-sections for $|y_{e\mu}|$ in the region with $m_{e\mu}>$ 250, for the nNNLO MATRIX prediction and various four flavour PDF sets. The measured cross-section values are shown as points with error bars giving the statistical uncertainty and solid bands indicating the size of the total uncertainty. The measurement is compared to fixed-order nNNLO QCD + NLO EW predictions of Matrix 2.1 using four different four-flavour NNLO PDF sets: NNPDF3.0, NNPDF3.1, CT18, and MSHT20.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable $|y_{e\mu}|$ ($m_{e\mu}>$ 250).

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $|y_{e\mu}|$ ($m_{e\mu}>$ 250).

Measured value of the charge asymmetry, $A_{C}$.

Charge asymmetry $A_C$ measured as a function of the absolute difference of the absolute lepton rapidities $||\eta_{l+}|-|\eta_{l-}||$. The measured values are shown as points, whose error bars represent the statistical uncertainty, while the solid bands indicate the size of the total uncertainty. In the bottom panel, the central value of the charge asymmetry divided by the total uncertainty of the $A_C$ measurement is shown. The measurement is compared with the NNLO+PS predictions from Powheg MiNNLO+Pythia8 with vertical lines denoting PDF uncertainties.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable $A_{C}$ vs. $||\eta_{l+}|-|\eta_{l-}||$.

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $A_{C}$ vs. $||\eta_{l+}|-|\eta_{l-}||$.

Charge asymmetry $A_C$ measured as a function of the invariant mass of the dilepton system $m_{e\mu}$. The measured values are shown as points, whose error bars represent the statistical uncertainty, while the solid bands indicate the size of the total uncertainty. In the bottom panel, the central value of the charge asymmetry divided by the total uncertainty of the $A_C$ measurement is shown. The measurement is compared with the NNLO+PS predictions from Powheg MiNNLO+Pythia8 with vertical lines denoting PDF uncertainties.

Correlation matrix of the statistical uncertainties in the measured fiducial cross section for the observable $A_{C}$ vs. $m_{e\mu}$.

Correlation matrix of the total uncertainties in the measured fiducial cross section for the observable $A_{C}$ vs. $m_{e\mu}$.

Measured value of the asymmetry in the CP-odd observable $O_{z}$, $A_{CP}$.