Data selection efficiency as a function of nuclear recoil energy

Data points used in analysis in log_10(S2)-S1 space

The correlation matrix corresponding to the statistical uncertainties on the differential cross-section ($d\sigma/dp_T$) fit results for $W^-$. To combine with $W^+$ results (Fig8a), use the rows and columns ordered as $W^+$ and then $W^-$. Assume no correlation in the statistical uncertainties between $W^+$ and $W^-$ (zero entries in the off-diagonal blocks).

The correlation matrix corresponding to all of the systematic uncertainties on the differential cross-section ($d\sigma/dp_T$) fit results for $W^+$ and $W^-$ combined together, with rows and columns ordered as $W^+$ and then $W^-$.

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.

Single Event Sensitivity (SES) for the $K^{+}\rightarrow\pi^{+}X$ search as a function of X mass.

Model-independent constraints on the branching ratio of the $K^{+}\rightarrow\pi^{+}X$ decay

Model-independent constraints on the branching ratio of the $K^{+}\rightarrow\pi^{+}X$ decay

Observed model-independent upper limits at 90 % CL of $\mathcal{B}(K^{+}\rightarrow\pi^{+}X)$ as function of $X$ mass, for several $X$ lifetime hypotheses, assuming $X$ decays to visible SM particles.

Observed model-independent upper limits at 90 % CL of $\mathcal{B}(K^{+}\rightarrow\pi^{+}X)$ as function of $X$ mass, for several $X$ lifetime hypotheses, assuming $X$ decays to visible SM particles.

Di-muon mass spectrum of selected $K^{+}\rightarrow\pi^{+}\mu^{+}\mu^{-}$ events from 2017–2018 data.

Di-muon mass spectrum of selected $K^{+}\rightarrow\pi^{+}\mu^{+}\mu^{-}$ events from 2017–2018 data.

Expected and observed model-independent upper limits at 90 % CL for $\mathcal{B}(K^{+}\rightarrow\pi^{+}X)\times\mathcal{B}(X\rightarrow\mu^{+}\mu^{-})$ as a function of $m_{X}$ for $\tau_{X}=0$.

Expected and observed model-independent upper limits at 90 % CL for $\mathcal{B}(K^{+}\rightarrow\pi^{+}X)\times\mathcal{B}(X\rightarrow\mu^{+}\mu^{-})$ as a function of $m_{X}$ for $\tau_{X}=0$.

Observed model-independent upper limits at 90 % CL for $\mathcal{B}(K^{+}\rightarrow\pi^{+}X)\times\mathcal{B}(X\rightarrow\mu^{+}\mu^{-})$ for several $\tau_{X}$ values.

Observed model-independent upper limits at 90 % CL for $\mathcal{B}(K^{+}\rightarrow\pi^{+}X)\times\mathcal{B}(X\rightarrow\mu^{+}\mu^{-})$ for several $\tau_{X}$ values.

Branching ratio of the $K^{+}\rightarrow\pi^{+}A^{\prime}$ decay divided by the kinetic mixing coupling squared, $\varepsilon^{2}$, as a function of $m_{A^{\prime}}$ for the BC2 model with dark photon $A^{\prime}$.

Branching ratio of the $K^{+}\rightarrow\pi^{+}A^{\prime}$ decay divided by the kinetic mixing coupling squared, $\varepsilon^{2}$, as a function of $m_{A^{\prime}}$ for the BC2 model with dark photon $A^{\prime}$.

Excluded region, at 90 % CL, of the parameter space $(m_{A^{\prime}},\varepsilon)$ for a dark photon $A^{\prime}$, decaying invisibly, in the BC2 model for the NA62 $K^{+}\rightarrow\pi^{+}X_{\rm inv}$ search.

Excluded region, at 90 % CL, of the parameter space $(m_{A^{\prime}},\varepsilon)$ for a dark photon $A^{\prime}$, decaying invisibly, in the BC2 model for the NA62 $K^{+}\rightarrow\pi^{+}X_{\rm inv}$ search.

Excluded region, at 90 % CL, of the parameter space $(m_{A^{\prime}},\varepsilon)$ for a dark photon $A^{\prime}$, decaying invisibly, in the BC2 model for the NA62 $\pi^{0}\rightarrow{\rm inv}$ search.

Excluded region, at 90 % CL, of the parameter space $(m_{A^{\prime}},\varepsilon)$ for a dark photon $A^{\prime}$, decaying invisibly, in the BC2 model for the NA62 $\pi^{0}\rightarrow{\rm inv}$ search.

Branching ratio of the $K^{+}\rightarrow\pi^{+}S$ decay divided by $\text{sin}^{2}\theta$, as a function of $m_{S}$.

Branching ratio of the $K^{+}\rightarrow\pi^{+}S$ decay divided by $\text{sin}^{2}\theta$, as a function of $m_{S}$.

Excluded regions, at 90 % CL, of the parameter space $(m_{S},\rm{sin}^{2}\theta)$ for a dark scalar $S$, in the BC4-inv model for the NA62 $K^{+}\rightarrow\pi^{+}X_{\rm inv}$ search.

Excluded regions, at 90 % CL, of the parameter space $(m_{S},\rm{sin}^{2}\theta)$ for a dark scalar $S$, in the BC4-inv model for the NA62 $K^{+}\rightarrow\pi^{+}X_{\rm inv}$ search.

Excluded regions, at 90 % CL, of the parameter space $(m_{S},\rm{sin}^{2}\theta)$ for a dark scalar $S$, in the BC4-inv model for the NA62 $\pi^{0}\rightarrow{\rm inv}$ search.

Excluded regions, at 90 % CL, of the parameter space $(m_{S},\rm{sin}^{2}\theta)$ for a dark scalar $S$, in the BC4-inv model for the NA62 $\pi^{0}\rightarrow{\rm inv}$ search.

Excluded regions, at 90 % CL, of the parameter space $(m_{S},\rm{sin}^{2}\theta$) for a dar scalar S, in the BC4 model, from the NA62 $K^{+}\rightarrow\pi^{+}X_{\rm inv}$ search.

Excluded regions, at 90 % CL, of the parameter space $(m_{S},\rm{sin}^{2}\theta$) for a dar scalar S, in the BC4 model, from the NA62 $K^{+}\rightarrow\pi^{+}X_{\rm inv}$ search.

Excluded regions, at 90 % CL, of the parameter space $(m_{S},\rm{sin}^{2}\theta$) for a dar scalar S, in the BC4 model, from the NA62 $K^{+}\rightarrow\pi^{+}\mu^{+}\mu^{-}$ study.

Excluded regions, at 90 % CL, of the parameter space $(m_{S},\rm{sin}^{2}\theta$) for a dar scalar S, in the BC4 model, from the NA62 $K^{+}\rightarrow\pi^{+}\mu^{+}\mu^{-}$ study.

Branching ratio of the $K^{+}\rightarrow\pi^{+}a$ decay divided by $(C_{ff}/\Lambda)^{2}$, as a function of $m_{a}$, assuming Λ = 1 TeV.

Branching ratio of the $K^{+}\rightarrow\pi^{+}a$ decay divided by $(C_{ff}/\Lambda)^{2}$, as a function of $m_{a}$, assuming Λ = 1 TeV.

Excluded regions, at 90 % CL, of the parameter space $(m_{a}, C_{ff}/\Lambda)$ for an ALP $a$, in the BC10-inv model, evaluated assuming $\Lambda = 1$ TeV, for the NA62 $K^{+}\rightarrow\pi^{+}X_{\rm inv}$ search.

Excluded regions, at 90 % CL, of the parameter space $(m_{a}, C_{ff}/\Lambda)$ for an ALP $a$, in the BC10-inv model, evaluated assuming $\Lambda = 1$ TeV, for the NA62 $K^{+}\rightarrow\pi^{+}X_{\rm inv}$ search.

Excluded regions, at 90 % CL, of the parameter space $(m_{a}, C_{ff}/\Lambda)$ for an ALP $a$, in the BC10-inv model, evaluated assuming $\Lambda = 1$ TeV, for the NA62 $\pi^{0}\rightarrow\rm{inv}$ search.

Excluded regions, at 90 % CL, of the parameter space $(m_{a}, C_{ff}/\Lambda)$ for an ALP $a$, in the BC10-inv model, evaluated assuming $\Lambda = 1$ TeV, for the NA62 $\pi^{0}\rightarrow\rm{inv}$ search.

Excluded regions, at 90 % CL, of the parameter space $(m_{a}, C_{ff}/\lambda)$ for an ALP $a$, in the BC10 model, evaluated assuming $\Lambda = 1$ TeV for the NA62 $K^{+}\rightarrow\pi^{+}X_{\rm inv}$ search.

Excluded regions, at 90 % CL, of the parameter space $(m_{a}, C_{ff}/\lambda)$ for an ALP $a$, in the BC10 model, evaluated assuming $\Lambda = 1$ TeV for the NA62 $K^{+}\rightarrow\pi^{+}X_{\rm inv}$ search.

Excluded regions, at 90 % CL, of the parameter space $(m_{a}, C_{ff}/\lambda)$ for an ALP $a$, in the BC10 model, evaluated assuming $\Lambda = 1$ TeV for the NA62 $\pi^{0}\rightarrow\rm{inv}$ search.

Excluded regions, at 90 % CL, of the parameter space $(m_{a}, C_{ff}/\lambda)$ for an ALP $a$, in the BC10 model, evaluated assuming $\Lambda = 1$ TeV for the NA62 $\pi^{0}\rightarrow\rm{inv}$ search.

Excluded regions, at 90 % CL, of the parameter space $(m_{a}, C_{ff}/\lambda)$ for an ALP $a$, in the BC10 model, evaluated assuming $\Lambda = 1$ TeV for the NA62 $K^{+}\rightarrow\pi^{+}\mu^{+}\mu^{-}$ study.

Excluded regions, at 90 % CL, of the parameter space $(m_{a}, C_{ff}/\lambda)$ for an ALP $a$, in the BC10 model, evaluated assuming $\Lambda = 1$ TeV for the NA62 $K^{+}\rightarrow\pi^{+}\mu^{+}\mu^{-}$ study.

Branching ratio of the $K^{+}\rightarrow\pi^{+}a$ decay divided by $(C_{GG}/\Lambda)^{2}$, as a function of $m_{a}$, assuming $\Lambda = 1$ TeV.

Branching ratio of the $K^{+}\rightarrow\pi^{+}a$ decay divided by $(C_{GG}/\Lambda)^{2}$, as a function of $m_{a}$, assuming $\Lambda = 1$ TeV.

Excluded regions, at 90 % CL, of the parameter space $(m_{a}, C_{GG}/\Lambda)$ for an ALP $a$, of the BC11 model, evaluated assuming $\Lambda = 1$ TeV, from the NA62 search for $K^{+}\rightarrow\pi^{+}X_{\rm inv}$.

Excluded regions, at 90 % CL, of the parameter space $(m_{a}, C_{GG}/\Lambda)$ for an ALP $a$, of the BC11 model, evaluated assuming $\Lambda = 1$ TeV, from the NA62 search for $K^{+}\rightarrow\pi^{+}X_{\rm inv}$.

Excluded regions, at 90 % CL, of the parameter space $(m_{a}, C_{GG}/\Lambda)$ for an ALP $a$, of the BC11 model, evaluated assuming $\Lambda = 1$ TeV, from the NA62 search for $\pi^{0}\rightarrow\rm{inv}$.

Excluded regions, at 90 % CL, of the parameter space $(m_{a}, C_{GG}/\Lambda)$ for an ALP $a$, of the BC11 model, evaluated assuming $\Lambda = 1$ TeV, from the NA62 search for $\pi^{0}\rightarrow\rm{inv}$.

Excluded regions, at 90 % CL, of the parameter space $(m_{a}, C_{GG}/\Lambda)$ for an ALP $a$, of the BC11 model, evaluated assuming $\Lambda = 1$ TeV, from the NA62 $K^{+}\rightarrow\pi^{+}\gamma\gamma$ study.

Excluded regions, at 90 % CL, of the parameter space $(m_{a}, C_{GG}/\Lambda)$ for an ALP $a$, of the BC11 model, evaluated assuming $\Lambda = 1$ TeV, from the NA62 $K^{+}\rightarrow\pi^{+}\gamma\gamma$ study.

Data (dots) and post-fit SM distribution (histograms) of m_ℓj 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 2 and Run 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 S̃₁ (m, y_de) = (2.0 TeV, 1.0) and S̃₁ (m, y_de) = (3.0 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_ℓj in (a, b) SR-1L-μj and (c, d) SR-2L-μj of the μ+light-jet channel obtained by a CR+SR background-only fit for Run 2 and Run 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 S̃₁ (m, y_sμ) = (2.0 TeV, 1.5) and S̃₁ (m, y_sμ) = (3.0 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_ℓj in (a, b) SR-1L-μj and (c, d) SR-2L-μj of the μ+light-jet channel obtained by a CR+SR background-only fit for Run 2 and Run 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 S̃₁ (m, y_sμ) = (2.0 TeV, 1.5) and S̃₁ (m, y_sμ) = (3.0 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_ℓj in (a, b) SR-1L-μj and (c, d) SR-2L-μj of the μ+light-jet channel obtained by a CR+SR background-only fit for Run 2 and Run 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 S̃₁ (m, y_sμ) = (2.0 TeV, 1.5) and S̃₁ (m, y_sμ) = (3.0 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_ℓj in (a, b) SR-1L-μj and (c, d) SR-2L-μj of the μ+light-jet channel obtained by a CR+SR background-only fit for Run 2 and Run 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 S̃₁ (m, y_sμ) = (2.0 TeV, 1.5) and S̃₁ (m, y_sμ) = (3.0 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_ℓj 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 2 and Run 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 S̃₁ (m, y_be) = (1.5 TeV, 2.5) and S̃₁ (m, y_be) = (2.0 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_ℓj 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 2 and Run 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 S̃₁ (m, y_be) = (1.5 TeV, 2.5) and S̃₁ (m, y_be) = (2.0 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_ℓj 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 2 and Run 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 S̃₁ (m, y_be) = (1.5 TeV, 2.5) and S̃₁ (m, y_be) = (2.0 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_ℓj 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 2 and Run 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 S̃₁ (m, y_be) = (1.5 TeV, 2.5) and S̃₁ (m, y_be) = (2.0 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_ℓj in (a, b) SR-1L-μb and (c, d) SR-2L-μb of the μ+b-jet channel obtained by a CR+SR background-only fit for Run 2 and Run 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 S̃₁ (m, y_bμ) = (1.5 TeV, 1.5) and S̃₁ (m, y_bμ) = (2.0 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_ℓj in (a, b) SR-1L-μb and (c, d) SR-2L-μb of the μ+b-jet channel obtained by a CR+SR background-only fit for Run 2 and Run 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 S̃₁ (m, y_bμ) = (1.5 TeV, 1.5) and S̃₁ (m, y_bμ) = (2.0 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_ℓj in (a, b) SR-1L-μb and (c, d) SR-2L-μb of the μ+b-jet channel obtained by a CR+SR background-only fit for Run 2 and Run 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 S̃₁ (m, y_bμ) = (1.5 TeV, 1.5) and S̃₁ (m, y_bμ) = (2.0 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_ℓj in (a, b) SR-1L-μb and (c, d) SR-2L-μb of the μ+b-jet channel obtained by a CR+SR background-only fit for Run 2 and Run 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 S̃₁ (m, y_bμ) = (1.5 TeV, 1.5) and S̃₁ (m, y_bμ) = (2.0 TeV, 1.5), respectively. Note: the values in the table are normalized by the width of corresponding bin

Exclusion limits for minimal models of S̃₁ 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% CL and the observed (red solid lines) and expected (black dashed lines) exclusion limits are shown in the m(S̃₁) – 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 ±1 σ (±2 σ) 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 S̃₁ production with only y_sμ being non-zero obtained from a simultaneous fit to SR-1L and SR-2L of the μ+light-jet channel combining Run-2 and Run-3 data. All limits are computed at 95% CL and the observed (red solid lines) and expected (black dashed lines) exclusion limits are shown in the m(S̃₁) – y_sμ 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 ±1 σ (±2 σ) 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 S̃₁ 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% CL and the observed (red solid lines) and expected (black dashed lines) exclusion limits are shown in the m(S̃₁) – 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 ±1 σ (±2 σ) 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 S̃₁ production with only y_bμ being non-zero obtained from a simultaneous fit to SR-1L and SR-2L of the μ+b-jet channel combining Run-2 and Run-3 data. All limits are computed at 95% CL and the observed (red solid lines) and expected (black dashed lines) exclusion limits are shown in the m(S̃₁) – y_bμ 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 ±1 σ (±2 σ) 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 S̃₁ production obtained from a fit to SR-1L, SR-2L and their combination of (a) the e+light-jet, (b) the μ+light-jet, (c) the e+b-jet and (d) the μ+b-jet channel using Run-2 and Run-3 data. All limits are computed at 95% CL and the observed (solid lines) and expected (dashed lines) exclusion limits are shown in the m(S̃₁) – 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  and ATLAS searches for LQ pair production  are shown as light magenta and dark blue areas, respectively.

Exclusion limits for minimal models of S̃₁ production obtained from a fit to SR-1L, SR-2L and their combination of (a) the e+light-jet, (b) the μ+light-jet, (c) the e+b-jet and (d) the μ+b-jet channel using Run-2 and Run-3 data. All limits are computed at 95% CL and the observed (solid lines) and expected (dashed lines) exclusion limits are shown in the m(S̃₁) – 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  and ATLAS searches for LQ pair production  are shown as light magenta and dark blue areas, respectively.

Exclusion limits for minimal models of S̃₁ production obtained from a fit to SR-1L, SR-2L and their combination of (a) the e+light-jet, (b) the μ+light-jet, (c) the e+b-jet and (d) the μ+b-jet channel using Run-2 and Run-3 data. All limits are computed at 95% CL and the observed (solid lines) and expected (dashed lines) exclusion limits are shown in the m(S̃₁) – 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  and ATLAS searches for LQ pair production  are shown as light magenta and dark blue areas, respectively.

Exclusion limits for minimal models of S̃₁ production obtained from a fit to SR-1L, SR-2L and their combination of (a) the e+light-jet, (b) the μ+light-jet, (c) the e+b-jet and (d) the μ+b-jet channel using Run-2 and Run-3 data. All limits are computed at 95% CL and the observed (solid lines) and expected (dashed lines) exclusion limits are shown in the m(S̃₁) – 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  and ATLAS searches for LQ pair production  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.