Normalized $\sigma_{\psi(2S)}/\sigma_{J/\psi}$ in $6.5<p_T<30.0\,GeV$ and $ 1 < y_{CM} < 1.935$ as functions of normalized $\text{N}^{{\text{corr.}}}_{\text{track}}$

Normalized $\sigma_{\psi(2S)}/\sigma_{J/\psi}$ in $6.5<p_T<30.0\,GeV$ and $ -2.865 < y_{CM} < 1.935$ as functions of normalized $\text{N}^{{\text{corr.}}}_{\text{track}}$

Normalized $\sigma_{\psi(2S)}/\sigma_{J/\psi}$ in $3.0<p_T<6.5\,GeV$ and $ -2.865 < y_{CM} < -2 $ as functions of normalized $\text{N}^{{\text{corr.}}}_{\text{track}}$

Normalized $\sigma_{\psi(2S)}/\sigma_{J/\psi}$ in $3.0<p_T<6.5\,GeV$ and $ 1 < y_{CM} < 1.935 $ as functions of normalized $\text{N}^{{\text{corr.}}}_{\text{track}}$

The model-independent 95\% \CL expected and observed upper limits set on ${\sigma(\PP\to 2\Pa+\PX)\mathcal{B}^2(\Pa\to 2\PGm)\alphaGen}$ over the range $0.21 < \MPa < 9\GeV$ for the combined 2016, 2017, and 2018 analyses. Mass ranges that overlap with \JPsi and \PgU resonances are excluded from the search

The 95\% \CL observed upper limits on the effective coupling $\CahLambda$ of the ALP to the SM Higgs assuming the branching fraction of the ALP to muons is 1 (blue) and 0.1 (orange), for both the expected (dashed) and observed (solid) limits

The 95\% \CL observed upper limits on the effective coupling $\cll/\Lambda$ of the ALP to the SM leptons. The orange shaded region represents the parameter space excluded by this search under three choices of $\CahLambda$ $1\TeV^{-2}$ (solid), $0.1\TeV^{-2}$ (dashed), and $0.01\TeV^{-2}$ (dotted)

The 95\% \CL observed upper limits on $\varepsilon^{2} \mathcal{B}(\ZDark \to \sDark \overline{\sDark}) \mathcal{B}^{2}(\sDark \rightarrow 2\PGm)$ for the vector portal model as a function of the dark scalar mass $\MsDark$ and dark vector boson mass $\MZDark$. The yellow and green bands indicate one and two standard deviation values of the limit, respectively. Because the model-independent limits are calculated only up to a dimuon mass of 60\GeV, the \sDark mass considered for these limits is below 60\GeV

The 95\% \CL observed upper limits for $\sigma(\PP\to\PhOneTwo\to 2\PaOne) \mathcal{B}^2(\PaOne\to 2\PGm)$ for the NMSSM as a function of $\MPaOne$ for $\MPhOneTwo$ = 90~GEV. The data presented here reflect the results of the 2017 and 2018 datasets combined with the previously published results of the 2016 dataset in \cite{CMS:2018jid}

The 95\% \CL observed upper limits for $\sigma(\PP\to\PhOneTwo\to 2\PaOne) \mathcal{B}^2(\PaOne\to 2\PGm)$ for the NMSSM as a function of $\MPaOne$ for $\MPhOneTwo$ = 125~GEV. The data presented here reflect the results of the 2017 and 2018 datasets combined with the previously published results of the 2016 dataset in \cite{CMS:2018jid}

The 95\% \CL observed upper limits for $\sigma(\PP\to\PhOneTwo\to 2\PaOne) \mathcal{B}^2(\PaOne\to 2\PGm)$ for the NMSSM as a function of $\MPaOne$ for $\MPhOneTwo$ = 150~GEV. The data presented here reflect the results of the 2017 and 2018 datasets combined with the previously published results of the 2016 dataset in \cite{CMS:2018jid}

The 95\% \CL observed upper limits (black solid curves) from this search as interpreted in the dark SUSY scenario for the process $\PP \to \Ph \to 2\nOne \to 2\gammaDark + 2\nDark \to 4\PGm + \PX$, with \mbox{$\MnOne = 60\GeV$} and $\MnDark = 1\GeV$. The limits are presented in the plane of $\varepsilon$ and $\MgammaDark$. The color gradient represents different branching fraction assumptions for \mbox{$\mathcal{B}(\Ph \to 2\nOne \to 2\gammaDark + 2\nDark)$}, ranging from dark orange (0.05\%) to light orange (10\%). The degradation of the limit around 1\GeV is attributed to the drop in the dimuon branching fraction $\mathcal{B}(\gammaDark \to 2\mu)$ due to the dimuon resonance of the $\phi$ meson~\cite{Batell:2009yf}

Electroweak corrections for the $R_{\Delta\phi}(p_\mathrm{T})$ distribution. The multiplicative combination is considered as the main electroweak correction factor and the additive combination as an uncertainty estimate.

Measured natural width

The measured inclusive ratio of production cross sections

Left panel.The vertical bars (boxes) represent the statistical (bin-to-bin systematic) uncertainties, while the horizontal bars give the bin widths. The global uncertainty (of 5.7%) is not graphically represented. The blue line represents the average of all the points. $ 12 < \mathrm{B} \, p_T < 70$ GeV and $ 0 < |y| < 2.4 $. Global uncertanties are not included in the table (5.7%)

Right panel.The vertical bars (boxes) represent the statistical (bin-to-bin systematic) uncertainties, while the horizontal bars give the bin widths. The global uncertainty (of 5.7%) is not graphically represented. The blue line represents the average of all the points. $ 12 < \mathrm{B} \, p_T < 70$ GeV and $ 0 < |y| < 2.4 $. Global uncertanties are not included in the table (5.7%)

Summary of the total uncertainty in the background prediction for each SR of the tt0L-low, tt0L-high, tt1L and tt2L analysis channels in the statistical combination. Their dominant contributions are indicated by individual lines. Individual uncertainties can be correlated, and do not necessarily add up in quadrature to the total background uncertainty.

Exclusion limits for colour-neutral scalar mediator dark matter models as a function of the mediator mass $m(\phi)$ for a DM mass $m_{\chi} = 1$ GeV. Associated production of DM with both single top quarks ($tW$ and $tj$ channels) and top quark pairs is considered. The limits are calculated at 95% CL and are expressed in terms of the ratio of the excluded cross section to the cross section for a coupling assumption of $g = g_q = g_{\chi} = 1$. The solid (dashed) lines show the observed (expected) exclusion limits for each individual channel and their statistical combination.

Exclusion limits for colour-neutral pseudoscalar mediator dark matter models as a function of the mediator mass $m(a)$ for a DM mass $m_{\chi} = 1$ GeV. Associated production of DM with both single top quarks ($tW$ and $tj$ channels) and top quark pairs is considered. The limits are calculated at 95% CL and are expressed in terms of the ratio of the excluded cross section to the cross section for a coupling assumption of $g = g_q = g_{\chi} = 1$. The solid (dashed) lines show the observed (expected) exclusion limits for each individual channel and their statistical combination.

$E_{\text{T}}^{\text{miss}}$ distribution in SR0X for the tt0L-low analysis. The contributions from all SM backgrounds are shown after the profile likelihood simultaneous fit to all tt0L-low CRs, with the hatched bands representing the total uncertainty. The category '$t\bar{t}$ (other)' represents $t\bar{t}$ events without extra jets or events with extra light-flavour jets. 'Other' includes contributions from $t\bar{t}W$, $tZ$ and $tWZ$ processes. The expected distributions for selected signal models are shown as dashed lines. The overflow events are included in the last bin. The bottom panels show the ratio of the observed data to the total SM background prediction, with the hatched area representing the total uncertainty in the background prediction and the red arrows marking data outside the vertical-axis range.

$E_{\text{T}}^{\text{miss}}$ distribution in SRWX for the tt0L-low analysis. The contributions from all SM backgrounds are shown after the profile likelihood simultaneous fit to all tt0L-low CRs, with the hatched bands representing the total uncertainty. The category '$t\bar{t}$ (other)' represents $t\bar{t}$ events without extra jets or events with extra light-flavour jets. 'Other' includes contributions from $t\bar{t}W$, $tZ$ and $tWZ$ processes. The expected distributions for selected signal models are shown as dashed lines. The overflow events are included in the last bin. The bottom panels show the ratio of the observed data to the total SM background prediction, with the hatched area representing the total uncertainty in the background prediction and the red arrows marking data outside the vertical-axis range.

$E_{\text{T}}^{\text{miss}}$ distribution in SRTX for the tt0L-low analysis. The contributions from all SM backgrounds are shown after the profile likelihood simultaneous fit to all tt0L-low CRs, with the hatched bands representing the total uncertainty. The category '$t\bar{t}$ (other)' represents $t\bar{t}$ events without extra jets or events with extra light-flavour jets. 'Other' includes contributions from $t\bar{t}W$, $tZ$ and $tWZ$ processes. The expected distributions for selected signal models are shown as dashed lines. The overflow events are included in the last bin. The bottom panels show the ratio of the observed data to the total SM background prediction, with the hatched area representing the total uncertainty in the background prediction and the red arrows marking data outside the vertical-axis range.

Exclusion limits for colour-neutral scalar mediator dark matter models as a function of the mediator mass $m(\phi)$ for a DM mass $m_{\chi} = 1$ GeV. Associated production of DM with both single top quarks ($tW$ and $tj$ channels) and top quark pairs is considered. The limits are calculated at 95% CL and are expressed in terms of the ratio of the excluded cross section to the nominal cross section for a coupling assumption of $g = g_q = g_{\chi} = 1$. The solid (dashed) lines show the observed (expected) exclusion limits for the tt0L-high and tt0L-low analyses and their statistical combination.

Exclusion limits for colour-neutral pseudoscalar mediator dark matter models as a function of the mediator mass $m(a)$ for a DM mass $m_{\chi} = 1$ GeV. Associated production of DM with both single top quarks ($tW$ and $tj$ channels) and top quark pairs is considered. The limits are calculated at 95% CL and are expressed in terms of the ratio of the excluded cross section to the nominal cross section for a coupling assumption of $g = g_q = g_{\chi} = 1$. The solid (dashed) lines show the observed (expected) exclusion limits for the tt0L-high and tt0L-low analyses and their statistical combination.

Exclusion limits for colour-neutral scalar mediator dark matter models as a function of the mediator mass $m(\phi)$ for a DM mass $m_{\chi} = 1$ GeV. Only associated production of DM with top quark pairs is considered for this interpretation. The limits are calculated at 95% CL and are expressed in terms of the ratio of the excluded cross section to the cross section for a coupling assumption of $g = g_q = g_{\chi} = 1$. The solid (dashed) lines show the observed (expected) exclusion limits for each individual channel and their statistical combination.

Exclusion limits for colour-neutral pseudoscalar mediator dark matter models as a function of the mediator mass $m(a)$ for a DM mass $m_{\chi} = 1$ GeV. Only associated production of DM with top quark pairs is considered for this interpretation. The limits are calculated at 95% CL and are expressed in terms of the ratio of the excluded cross section to the cross section for a coupling assumption of $g = g_q = g_{\chi} = 1$. The solid (dashed) lines show the observed (expected) exclusion limits for each individual channel and their statistical combination.

Exclusion limits for colour-neutral scalar mediator dark matter models as a function of the mediator mass $m(\phi)$ for a DM mass $m_{\chi} = 1$ GeV. Only associated production of DM with top quark pairs is considered for this interpretation. The limits are calculated at 95% CL and are expressed in terms of the ratio of the excluded cross section to the nominal cross section for a coupling assumption of $g = g_q = g_{\chi} = 1$. The solid (dashed) lines show the observed (expected) exclusion limits for the tt0L-high and tt0L-low analyses and their statistical combination.

Exclusion limits for colour-neutral pseudoscalar mediator dark matter models as a function of the mediator mass $m(a)$ for a DM mass $m_{\chi} = 1$ GeV. Only associated production of DM with top quark pairs is considered for this interpretation. The limits are calculated at 95% CL and are expressed in terms of the ratio of the excluded cross section to the nominal cross section for a coupling assumption of $g = g_q = g_{\chi} = 1$. The solid (dashed) lines show the observed (expected) exclusion limits for the tt0L-high and tt0L-low analyses and their statistical combination.

Representative fit distribution in the different flavour leptons signal region for the tt2L analysis: each bin of such distribution, starting from the red arrow, corresponds to a single SR included in the fit. 'FNP' includes the contribution from fake/non-prompt lepton background arising from jets (mainly $\pi/K$, heavy-flavour hadron decays and photon conversion) misidentified as leptons, estimated in a purely data-driven way. 'Other' includes contributions from $t\bar{t}W$, $tZ$ and $tWZ$ processes. The total uncertainty in the SM expectation is represented with hatched bands and the expected distributions for selected signal models are shown as dashed lines.

Signal acceptance in SR0X, SRWX and SRTX for simplified DM+$t\bar{t}$ model, defined as the number of accepted events at generator level in signal Monte Carlo simulation divided by the total number of events in the sample.

Signal acceptance in SR0X, SRWX and SRTX for simplified DM+$tW$ model, defined as the number of accepted events at generator level in signal Monte Carlo simulation divided by the total number of events in the sample.

Signal acceptance in SR0X, SRWX and SRTX for simplified DM+$tj$ model, defined as the number of accepted events at generator level in signal Monte Carlo simulation divided by the total number of events in the sample.

Signal efficiency in SR0X, SRWX and SRTX for simplified DM+$t\bar{t}$ model, defined as the number of selected reconstructed events divided by the acceptance.

Signal efficiency in SR0X, SRWX and SRTX for simplified DM+$tW$ model, defined as the number of selected reconstructed events divided by the acceptance.

Signal efficiency in SR0X, SRWX and SRTX for simplified DM+$tj$ model, defined as the number of selected reconstructed events divided by the acceptance.

Cutflow for the reference point DM+$t\bar{t}$ $m(\phi, \chi) = (10, 1)$ GeV in signal region SR0X. The column labelled 'weighted' shows the event yield including all correction factors applied to simulation, and is normalised to 139 fb$^{-1}$. A notable exception concerns the 'weighted' numbers in the first and the second row, labelled 'Total' and 'Filtered', which correspond to $\mathcal{L}\cdot\sigma$ and $\mathcal{L}\cdot\sigma\cdot\epsilon$ expected, respectively. The 'Skim' selection requires the $p_{\text{T}}$ of the leading four jets to be above (80, 60, 40, 40) GeV, the missing transverse momentum $E_{\text{T}}^{\text{miss}} > 140$ GeV, the missing momentum significance $\mathcal{S} > 8$, $\Delta\phi_{\min}(\vec{p}_{\text{T,1-4}},\vec{p}_{\text{T}}^{\text{miss}}) > 0.4$ and a lepton veto. The 'Orthogonalisation' selection is defined in the main body. In total 2045000 raw MC events were generated prior to the specified cuts, with the column 'Unweighted yield' collecting the numbers after each cut.

Cutflow for the reference point DM+$t\bar{t}$ $m(\phi, \chi) = (10, 1)$ GeV in signal region SRWX. The column labelled 'weighted' shows the event yield including all correction factors applied to simulation, and is normalised to 139 fb$^{-1}$. A notable exception concerns the 'weighted' numbers in the first and the second row, labelled 'Total' and 'Filtered', which correspond to $\mathcal{L}\cdot\sigma$ and $\mathcal{L}\cdot\sigma\cdot\epsilon$ expected, respectively. The 'Skim' selection requires the $p_{\text{T}}$ of the leading four jets to be above (80, 60, 40, 40) GeV, the missing transverse momentum $E_{\text{T}}^{\text{miss}} > 140$ GeV, the missing momentum significance $\mathcal{S} > 8$, $\Delta\phi_{\min}(\vec{p}_{\text{T,1-4}},\vec{p}_{\text{T}}^{\text{miss}}) > 0.4$ and a lepton veto. The 'Orthogonalisation' selection is defined in the main body. In total 2045000 raw MC events were generated prior to the specified cuts, with the column 'Unweighted yield' collecting the numbers after each cut.

Cutflow for the reference point DM+$t\bar{t}$ $m(\phi, \chi) = (10, 1)$ GeV in signal region SRTX. The column labelled 'weighted' shows the event yield including all correction factors applied to simulation, and is normalised to 139 fb$^{-1}$. A notable exception concerns the 'weighted' numbers in the first and the second row, labelled 'Total' and 'Filtered', which correspond to $\mathcal{L}\cdot\sigma$ and $\mathcal{L}\cdot\sigma\cdot\epsilon$ expected, respectively. The 'Skim' selection requires the $p_{\text{T}}$ of the leading four jets to be above (80, 60, 40, 40) GeV, the missing transverse momentum $E_{\text{T}}^{\text{miss}} > 140$ GeV, the missing momentum significance $\mathcal{S} > 8$, $\Delta\phi_{\min}(\vec{p}_{\text{T,1-4}},\vec{p}_{\text{T}}^{\text{miss}}) > 0.4$ and a lepton veto. The 'Orthogonalisation' selection is defined in the main body. In total 2045000 raw MC events were generated prior to the specified cuts, with the column 'Unweighted yield' collecting the numbers after each cut.

Cutflow for the reference point DM+$t\bar{t}$ $m(a, \chi) = (10, 1)$ GeV in signal region SR0X. The column labelled 'weighted' shows the event yield including all correction factors applied to simulation, and is normalised to 139 fb$^{-1}$. A notable exception concerns the 'weighted' numbers in the first and the second row, labelled 'Total' and 'Filtered', which correspond to $\mathcal{L}\cdot\sigma$ and $\mathcal{L}\cdot\sigma\cdot\epsilon$ expected, respectively. The 'Skim' selection requires the $p_{\text{T}}$ of the leading four jets to be above (80, 60, 40, 40) GeV, the missing transverse momentum $E_{\text{T}}^{\text{miss}} > 140$ GeV, the missing momentum significance $\mathcal{S} > 8$, $\Delta\phi_{\min}(\vec{p}_{\text{T,1-4}},\vec{p}_{\text{T}}^{\text{miss}}) > 0.4$ and a lepton veto. The 'Orthogonalisation' selection is defined in the main body. In total 400000 raw MC events were generated prior to the specified cuts, with the column 'Unweighted yield' collecting the numbers after each cut.

Cutflow for the reference point DM+$t\bar{t}$ $m(a, \chi) = (10, 1)$ GeV in signal region SRWX. The column labelled 'weighted' shows the event yield including all correction factors applied to simulation, and is normalised to 139 fb$^{-1}$. A notable exception concerns the 'weighted' numbers in the first and the second row, labelled 'Total' and 'Filtered', which correspond to $\mathcal{L}\cdot\sigma$ and $\mathcal{L}\cdot\sigma\cdot\epsilon$ expected, respectively. The 'Skim' selection requires the $p_{\text{T}}$ of the leading four jets to be above (80, 60, 40, 40) GeV, the missing transverse momentum $E_{\text{T}}^{\text{miss}} > 140$ GeV, the missing momentum significance $\mathcal{S} > 8$, $\Delta\phi_{\min}(\vec{p}_{\text{T,1-4}},\vec{p}_{\text{T}}^{\text{miss}}) > 0.4$ and a lepton veto. The 'Orthogonalisation' selection is defined in the main body. In total 400000 raw MC events were generated prior to the specified cuts, with the column 'Unweighted yield' collecting the numbers after each cut.

Cutflow for the reference point DM+$t\bar{t}$ $m(a, \chi) = (10, 1)$ GeV in signal region SRTX. The column labelled 'weighted' shows the event yield including all correction factors applied to simulation, and is normalised to 139 fb$^{-1}$. A notable exception concerns the 'weighted' numbers in the first and the second row, labelled 'Total' and 'Filtered', which correspond to $\mathcal{L}\cdot\sigma$ and $\mathcal{L}\cdot\sigma\cdot\epsilon$ expected, respectively. The 'Skim' selection requires the $p_{\text{T}}$ of the leading four jets to be above (80, 60, 40, 40) GeV, the missing transverse momentum $E_{\text{T}}^{\text{miss}} > 140$ GeV, the missing momentum significance $\mathcal{S} > 8$, $\Delta\phi_{\min}(\vec{p}_{\text{T,1-4}},\vec{p}_{\text{T}}^{\text{miss}}) > 0.4$ and a lepton veto. The 'Orthogonalisation' selection is defined in the main body. In total 400000 raw MC events were generated prior to the specified cuts, with the column 'Unweighted yield' collecting the numbers after each cut.

Cutflow for the reference point DM+$tW$ $m(\phi, \chi) = (10, 1)$ GeV in signal region SR0X. The column labelled 'weighted' shows the event yield including all correction factors applied to simulation, and is normalised to 139 fb$^{-1}$. A notable exception concerns the 'weighted' numbers in the first and the second row, labelled 'Total' and 'Filtered', which correspond to $\mathcal{L}\cdot\sigma$ and $\mathcal{L}\cdot\sigma\cdot\epsilon$ expected, respectively. The 'Skim' selection requires the $p_{\text{T}}$ of the leading four jets to be above (80, 60, 40, 40) GeV, the missing transverse momentum $E_{\text{T}}^{\text{miss}} > 140$ GeV, the missing momentum significance $\mathcal{S} > 8$, $\Delta\phi_{\min}(\vec{p}_{\text{T,1-4}},\vec{p}_{\text{T}}^{\text{miss}}) > 0.4$ and a lepton veto. The 'Orthogonalisation' selection is defined in the main body. In total 120000 raw MC events were generated prior to the specified cuts, with the column 'Unweighted yield' collecting the numbers after each cut.

Cutflow for the reference point DM+$tW$ $m(\phi, \chi) = (10, 1)$ GeV in signal region SRWX. The column labelled 'weighted' shows the event yield including all correction factors applied to simulation, and is normalised to 139 fb$^{-1}$. A notable exception concerns the 'weighted' numbers in the first and the second row, labelled 'Total' and 'Filtered', which correspond to $\mathcal{L}\cdot\sigma$ and $\mathcal{L}\cdot\sigma\cdot\epsilon$ expected, respectively. The 'Skim' selection requires the $p_{\text{T}}$ of the leading four jets to be above (80, 60, 40, 40) GeV, the missing transverse momentum $E_{\text{T}}^{\text{miss}} > 140$ GeV, the missing momentum significance $\mathcal{S} > 8$, $\Delta\phi_{\min}(\vec{p}_{\text{T,1-4}},\vec{p}_{\text{T}}^{\text{miss}}) > 0.4$ and a lepton veto. The 'Orthogonalisation' selection is defined in the main body. In total 120000 raw MC events were generated prior to the specified cuts, with the column 'Unweighted yield' collecting the numbers after each cut.

Cutflow for the reference point DM+$tW$ $m(\phi, \chi) = (10, 1)$ GeV in signal region SRTX. The column labelled 'weighted' shows the event yield including all correction factors applied to simulation, and is normalised to 139 fb$^{-1}$. A notable exception concerns the 'weighted' numbers in the first and the second row, labelled 'Total' and 'Filtered', which correspond to $\mathcal{L}\cdot\sigma$ and $\mathcal{L}\cdot\sigma\cdot\epsilon$ expected, respectively. The 'Skim' selection requires the $p_{\text{T}}$ of the leading four jets to be above (80, 60, 40, 40) GeV, the missing transverse momentum $E_{\text{T}}^{\text{miss}} > 140$ GeV, the missing momentum significance $\mathcal{S} > 8$, $\Delta\phi_{\min}(\vec{p}_{\text{T,1-4}},\vec{p}_{\text{T}}^{\text{miss}}) > 0.4$ and a lepton veto. The 'Orthogonalisation' selection is defined in the main body. In total 120000 raw MC events were generated prior to the specified cuts, with the column 'Unweighted yield' collecting the numbers after each cut.

Cutflow for the reference point DM+$tW$ $m(a, \chi) = (10, 1)$ GeV in signal region SR0X. The column labelled 'weighted' shows the event yield including all correction factors applied to simulation, and is normalised to 139 fb$^{-1}$. A notable exception concerns the 'weighted' numbers in the first and the second row, labelled 'Total' and 'Filtered', which correspond to $\mathcal{L}\cdot\sigma$ and $\mathcal{L}\cdot\sigma\cdot\epsilon$ expected, respectively. The 'Skim' selection requires the $p_{\text{T}}$ of the leading four jets to be above (80, 60, 40, 40) GeV, the missing transverse momentum $E_{\text{T}}^{\text{miss}} > 140$ GeV, the missing momentum significance $\mathcal{S} > 8$, $\Delta\phi_{\min}(\vec{p}_{\text{T,1-4}},\vec{p}_{\text{T}}^{\text{miss}}) > 0.4$ and a lepton veto. The 'Orthogonalisation' selection is defined in the main body. In total 100000 raw MC events were generated prior to the specified cuts, with the column 'Unweighted yield' collecting the numbers after each cut.

Cutflow for the reference point DM+$tW$ $m(a, \chi) = (10, 1)$ GeV in signal region SRWX. The column labelled 'weighted' shows the event yield including all correction factors applied to simulation, and is normalised to 139 fb$^{-1}$. A notable exception concerns the 'weighted' numbers in the first and the second row, labelled 'Total' and 'Filtered', which correspond to $\mathcal{L}\cdot\sigma$ and $\mathcal{L}\cdot\sigma\cdot\epsilon$ expected, respectively. The 'Skim' selection requires the $p_{\text{T}}$ of the leading four jets to be above (80, 60, 40, 40) GeV, the missing transverse momentum $E_{\text{T}}^{\text{miss}} > 140$ GeV, the missing momentum significance $\mathcal{S} > 8$, $\Delta\phi_{\min}(\vec{p}_{\text{T,1-4}},\vec{p}_{\text{T}}^{\text{miss}}) > 0.4$ and a lepton veto. The 'Orthogonalisation' selection is defined in the main body. In total 100000 raw MC events were generated prior to the specified cuts, with the column 'Unweighted yield' collecting the numbers after each cut.

Cutflow for the reference point DM+$tW$ $m(a, \chi) = (10, 1)$ GeV in signal region SRTX. The column labelled 'weighted' shows the event yield including all correction factors applied to simulation, and is normalised to 139 fb$^{-1}$. A notable exception concerns the 'weighted' numbers in the first and the second row, labelled 'Total' and 'Filtered', which correspond to $\mathcal{L}\cdot\sigma$ and $\mathcal{L}\cdot\sigma\cdot\epsilon$ expected, respectively. The 'Skim' selection requires the $p_{\text{T}}$ of the leading four jets to be above (80, 60, 40, 40) GeV, the missing transverse momentum $E_{\text{T}}^{\text{miss}} > 140$ GeV, the missing momentum significance $\mathcal{S} > 8$, $\Delta\phi_{\min}(\vec{p}_{\text{T,1-4}},\vec{p}_{\text{T}}^{\text{miss}}) > 0.4$ and a lepton veto. The 'Orthogonalisation' selection is defined in the main body. In total 100000 raw MC events were generated prior to the specified cuts, with the column 'Unweighted yield' collecting the numbers after each cut.

Cutflow for the reference point DM+$tj$ $m(\phi, \chi) = (10, 1)$ GeV in signal region SR0X. The column labelled 'weighted' shows the event yield including all correction factors applied to simulation, and is normalised to 139 fb$^{-1}$. A notable exception concerns the 'weighted' numbers in the first and the second row, labelled 'Total' and 'Filtered', which correspond to $\mathcal{L}\cdot\sigma$ and $\mathcal{L}\cdot\sigma\cdot\epsilon$ expected, respectively. The 'Skim' selection requires the $p_{\text{T}}$ of the leading four jets to be above (80, 60, 40, 40) GeV, the missing transverse momentum $E_{\text{T}}^{\text{miss}} > 140$ GeV, the missing momentum significance $\mathcal{S} > 8$, $\Delta\phi_{\min}(\vec{p}_{\text{T,1-4}},\vec{p}_{\text{T}}^{\text{miss}}) > 0.4$ and a lepton veto. The 'Orthogonalisation' selection is defined in the main body. In total 169000 raw MC events were generated prior to the specified cuts, with the column 'Unweighted yield' collecting the numbers after each cut.

Cutflow for the reference point DM+$tj$ $m(\phi, \chi) = (10, 1)$ GeV in signal region SRWX. The column labelled 'weighted' shows the event yield including all correction factors applied to simulation, and is normalised to 139 fb$^{-1}$. A notable exception concerns the 'weighted' numbers in the first and the second row, labelled 'Total' and 'Filtered', which correspond to $\mathcal{L}\cdot\sigma$ and $\mathcal{L}\cdot\sigma\cdot\epsilon$ expected, respectively. The 'Skim' selection requires the $p_{\text{T}}$ of the leading four jets to be above (80, 60, 40, 40) GeV, the missing transverse momentum $E_{\text{T}}^{\text{miss}} > 140$ GeV, the missing momentum significance $\mathcal{S} > 8$, $\Delta\phi_{\min}(\vec{p}_{\text{T,1-4}},\vec{p}_{\text{T}}^{\text{miss}}) > 0.4$ and a lepton veto. The 'Orthogonalisation' selection is defined in the main body. In total 169000 raw MC events were generated prior to the specified cuts, with the column 'Unweighted yield' collecting the numbers after each cut.

Cutflow for the reference point DM+$tj$ $m(\phi, \chi) = (10, 1)$ GeV in signal region SRTX. The column labelled 'weighted' shows the event yield including all correction factors applied to simulation, and is normalised to 139 fb$^{-1}$. A notable exception concerns the 'weighted' numbers in the first and the second row, labelled 'Total' and 'Filtered', which correspond to $\mathcal{L}\cdot\sigma$ and $\mathcal{L}\cdot\sigma\cdot\epsilon$ expected, respectively. The 'Skim' selection requires the $p_{\text{T}}$ of the leading four jets to be above (80, 60, 40, 40) GeV, the missing transverse momentum $E_{\text{T}}^{\text{miss}} > 140$ GeV, the missing momentum significance $\mathcal{S} > 8$, $\Delta\phi_{\min}(\vec{p}_{\text{T,1-4}},\vec{p}_{\text{T}}^{\text{miss}}) > 0.4$ and a lepton veto. The 'Orthogonalisation' selection is defined in the main body. In total 169000 raw MC events were generated prior to the specified cuts, with the column 'Unweighted yield' collecting the numbers after each cut.

Cutflow for the reference point DM+$tj$ $m(a, \chi) = (10, 1)$ GeV in signal region SR0X. The column labelled 'weighted' shows the event yield including all correction factors applied to simulation, and is normalised to 139 fb$^{-1}$. A notable exception concerns the 'weighted' numbers in the first and the second row, labelled 'Total' and 'Filtered', which correspond to $\mathcal{L}\cdot\sigma$ and $\mathcal{L}\cdot\sigma\cdot\epsilon$ expected, respectively. The 'Skim' selection requires the $p_{\text{T}}$ of the leading four jets to be above (80, 60, 40, 40) GeV, the missing transverse momentum $E_{\text{T}}^{\text{miss}} > 140$ GeV, the missing momentum significance $\mathcal{S} > 8$, $\Delta\phi_{\min}(\vec{p}_{\text{T,1-4}},\vec{p}_{\text{T}}^{\text{miss}}) > 0.4$ and a lepton veto. The 'Orthogonalisation' selection is defined in the main body. In total 140000 raw MC events were generated prior to the specified cuts, with the column 'Unweighted yield' collecting the numbers after each cut.

Cutflow for the reference point DM+$tj$ $m(a, \chi) = (10, 1)$ GeV in signal region SRWX. The column labelled 'weighted' shows the event yield including all correction factors applied to simulation, and is normalised to 139 fb$^{-1}$. A notable exception concerns the 'weighted' numbers in the first and the second row, labelled 'Total' and 'Filtered', which correspond to $\mathcal{L}\cdot\sigma$ and $\mathcal{L}\cdot\sigma\cdot\epsilon$ expected, respectively. The 'Skim' selection requires the $p_{\text{T}}$ of the leading four jets to be above (80, 60, 40, 40) GeV, the missing transverse momentum $E_{\text{T}}^{\text{miss}} > 140$ GeV, the missing momentum significance $\mathcal{S} > 8$, $\Delta\phi_{\min}(\vec{p}_{\text{T,1-4}},\vec{p}_{\text{T}}^{\text{miss}}) > 0.4$ and a lepton veto. The 'Orthogonalisation' selection is defined in the main body. In total 140000 raw MC events were generated prior to the specified cuts, with the column 'Unweighted yield' collecting the numbers after each cut.

Cutflow for the reference point DM+$tj$ $m(a, \chi) = (10, 1)$ GeV in signal region SRTX. The column labelled 'weighted' shows the event yield including all correction factors applied to simulation, and is normalised to 139 fb$^{-1}$. A notable exception concerns the 'weighted' numbers in the first and the second row, labelled 'Total' and 'Filtered', which correspond to $\mathcal{L}\cdot\sigma$ and $\mathcal{L}\cdot\sigma\cdot\epsilon$ expected, respectively. The 'Skim' selection requires the $p_{\text{T}}$ of the leading four jets to be above (80, 60, 40, 40) GeV, the missing transverse momentum $E_{\text{T}}^{\text{miss}} > 140$ GeV, the missing momentum significance $\mathcal{S} > 8$, $\Delta\phi_{\min}(\vec{p}_{\text{T,1-4}},\vec{p}_{\text{T}}^{\text{miss}}) > 0.4$ and a lepton veto. The 'Orthogonalisation' selection is defined in the main body. In total 140000 raw MC events were generated prior to the specified cuts, with the column 'Unweighted yield' collecting the numbers after each cut.

Distribution of ${E}_{T}^{miss}$ after the fit of the multijet backgrounds, in the electron channel, in the $t\bar{t}$ 3-jets VR, without applying the cut on ${E}_{T}^{miss}$. Simulated events are normalised to the expected number of events given the integrated luminosity, after applying the normalisation factors obtained in the multijet fit. The last bin includes the overflow. The uncertainty band indicates the simulation's statistical uncertainty, the normalisation uncertainties for different processes ($40$ % for $W$+jets production, $30$ % for multijet background and $6$ % for top-quark processes) and the multijet background shape uncertainty in each bin, summed in quadrature. The lower panel of the figure shows the ratio of the data to the prediction.

Distribution of ${E}_{T}^{miss}$ after the fit of the multijet backgrounds, in the electron channel, in the $t\bar{t}$ 4-jets VR, without applying the cut on ${E}_{T}^{miss}$. Simulated events are normalised to the expected number of events given the integrated luminosity, after applying the normalisation factors obtained in the multijet fit. The last bin includes the overflow. The uncertainty band indicates the simulation's statistical uncertainty, the normalisation uncertainties for different processes ($40$ % for $W$+jets production, $30$ % for multijet background and $6$ % for top-quark processes) and the multijet background shape uncertainty in each bin, summed in quadrature. The lower panel of the figure shows the ratio of the data to the prediction.

Distribution of $m_{T}^{W}$ after the fit of the multijet backgrounds, in the muon channel, in the signal region, without applying the cut on $m_{T}^{W}$. Simulated events are normalised to the expected number of events given the integrated luminosity, after applying the normalisation factors obtained in the multijet fit. The last bin includes the overflow. The uncertainty band indicates the simulation's statistical uncertainty, the normalisation uncertainties for different processes ($40$ % for $W$+jets production, $30$ % for multijet background and $6$ % for top-quark processes) and the multijet background shape uncertainty in each bin, summed in quadrature. The lower panel of the figure shows the ratio of the data to the prediction.

Distribution of $m_{T}^{W}$ after the fit of the multijet backgrounds, in the muon channel, in the $W$+jets VR, without applying the cut on $m_{T}^{W}$. Simulated events are normalised to the expected number of events given the integrated luminosity, after applying the normalisation factors obtained in the multijet fit. The last bin includes the overflow. The uncertainty band indicates the simulation's statistical uncertainty, the normalisation uncertainties for different processes ($40$ % for $W$+jets production, $30$ % for multijet background and $6$ % for top-quark processes) and the multijet background shape uncertainty in each bin, summed in quadrature. The lower panel of the figure shows the ratio of the data to the prediction.

Distribution of $m_{T}^{W}$ after the fit of the multijet backgrounds, in the muon channel, in the $t\bar{t}$ 3-jets VR, without applying the cut on $m_{T}^{W}$. Simulated events are normalised to the expected number of events given the integrated luminosity, after applying the normalisation factors obtained in the multijet fit. The last bin includes the overflow. The uncertainty band indicates the simulation's statistical uncertainty, the normalisation uncertainties for different processes ($40$ % for $W$+jets production, $30$ % for multijet background and $6$ % for top-quark processes) and the multijet background shape uncertainty in each bin, summed in quadrature. The lower panel of the figure shows the ratio of the data to the prediction.

Distribution of $m_{T}^{W}$ after the fit of the multijet backgrounds, in the muon channel, in the $t\bar{t}$ 4-jets VR, without applying the cut on $m_{T}^{W}$. Simulated events are normalised to the expected number of events given the integrated luminosity, after applying the normalisation factors obtained in the multijet fit. The last bin includes the overflow. The uncertainty band indicates the simulation's statistical uncertainty, the normalisation uncertainties for different processes ($40$ % for $W$+jets production, $30$ % for multijet background and $6$ % for top-quark processes) and the multijet background shape uncertainty in each bin, summed in quadrature. The lower panel of the figure shows the ratio of the data to the prediction.

Expected distributions of the MEM discriminant $P(S|X)$ in the SR, for the s-channel single-top signal, and for the $t\bar{t}$ and $W$+jets backgrounds, for MEM discriminant values larger than $2.0\times10^{-4}$. Each distribution is normalised to unity. The binning is the same as the optimised binning used in the signal extraction fit, resulting in a non-linear horizontal scale.

Distribution of the MEM discriminant $P(S|X)$ in the $W$+jets VR. Simulated events are normalised to the expected number of events given the integrated luminosity, after applying the normalisation factors obtained in the multijet fit presented in Section 5 in the paper. The uncertainty band indicates the simulation's statistical uncertainty and the normalisation uncertainties for the various processes in each bin, summed in quadrature. The ratio of the observed number to the predicted number of events in each bin is shown in the lower panel of the figure, with different vertical axis ranges. The binning is the same as the optimised binning used in the signal extraction fit described in Section 8 in the paper, resulting in a non-linear horizontal scale.

Distribution of the MEM discriminant $P(S|X)$ in the $t\bar{t}$ 3-jets VR. Simulated events are normalised to the expected number of events given the integrated luminosity, after applying the normalisation factors obtained in the multijet fit presented in Section 5 in the paper. The uncertainty band indicates the simulation's statistical uncertainty and the normalisation uncertainties for the various processes in each bin, summed in quadrature. The ratio of the observed number to the predicted number of events in each bin is shown in the lower panel of the figure, with different vertical axis ranges. The binning is the same as the optimised binning used in the signal extraction fit described in Section 8 in the paper, resulting in a non-linear horizontal scale.

Distribution of the MEM discriminant $P(S|X)$ in the $t\bar{t}$ 4-jets VR. Simulated events are normalised to the expected number of events given the integrated luminosity, after applying the normalisation factors obtained in the multijet fit presented in Section 5 in the paper. The uncertainty bands indicate the simulation's statistical uncertainty and the normalisation uncertainties for the various processes in each bin, summed in quadrature. The ratio of the observed number to the predicted number of events in each bin is shown in the lower panel of the figure, with different vertical axis ranges. The binning is the same as the optimised binning used in the signal extraction fit described in Section 8 in the paper, resulting in a non-linear horizontal scale.

Distribution of the MEM discriminant $P(S|X)$ in the SR before the fit to data, for MEM discriminant values larger than $2.0\times10^{-4}$. The lower panel of the figure shows the ratio of the data to the prediction, with different vertical axis ranges. The uncertainty band indicates the total uncertainties and their correlations in each bin. The uncertainties in the $t\bar{t}$ and $W$+jets normalisation factors, as well as in the s-channel signal cross-section, are not defined pre-fit and therefore not included. The binning is the same as the optimised binning used in the fit, resulting in a non-linear horizontal scale.

Distribution of the MEM discriminant $P(S|X)$ in the SR after the fit to data, for MEM discriminant values larger than $2.0\times10^{-4}$. The lower panel of the figure shows the ratio of the data to the prediction, with different vertical axis ranges. The uncertainty band indicates the total uncertainties and their correlations in each bin. The binning is the same as the optimised binning used in the fit, resulting in a non-linear horizontal scale.

Distribution of the MEM discriminant $P(S|X)$ in the SR after the fit to data, for MEM discriminant values larger than $2.0\times10^{-4}$, after subtraction of all backgrounds. The fitted distribution for the simulation of the signal is shown together with the post-fit uncertainty in the backgrounds. The binning is the same as the optimised binning used in the fit, resulting in a non-linear horizontal scale.

Pre-fit and post-fit event yields in the SR, for MEM discriminant values larger than $2.0\times10^{-4}$. The central value of the event yield for each process is calculated by summing the values of the discriminant bin contents, using the nominal expected yield for the pre-fit value, and the best-fit estimate for the post-fit value. The error includes statistical and systematic uncertainties summed in quadrature. All sources of systematic uncertainties are included, taking into account correlations and anti-correlations in the post-fit case. The uncertainties in the $t\bar{t}$ and $W$+jets normalisation factors, as well as in the s-channel signal cross-section, are not defined pre-fit and therefore only included in the post-fit uncertainties.

Observed impact of the different sources of uncertainty on the measured s-channel signal cross-section, grouped by categories. The impact of each category is obtained by repeating the fit after having fixed the set of nuisance parameters corresponding to that category, subtracting the square of the resulting uncertainty from the square of the uncertainty found in the full fit, and calculating the square root. The 'Systematic uncertainties' category combines all sources of systematic uncertainties. The statistical uncertainty is obtained by repeating the fit after having fixed all nuisance parameters, including the $t\bar{t}$ and $W$+jets normalisation factors. 'Total' gives the total uncertainty on the measurement.

Observed impact of the different sources of $t\bar{t}$ modelling uncertainty on the measured s-channel signal cross-section. The impact of each category is obtained by repeating the fit after having fixed the set of nuisance parameters corresponding to that category, subtracting the square of the resulting uncertainty from the square of the uncertainty found in the full fit, and calculating the square root. 'PS & had.' refers to the parton shower and hadronisation model, and 'ME/PS matching' to the matching of the ME to the parton shower.

Observed impact of the different sources of s-channel modelling uncertainty on the measured s-channel signal cross-section. The impact of each category is obtained by repeating the fit after having fixed the set of nuisance parameters corresponding to that category, subtracting the square of the resulting uncertainty from the square of the uncertainty found in the full fit, and calculating the square root. 'PS & had.' refers to the parton shower and hadronisation model, as described in Section 7 in the paper.

Observed impact of the different sources of t-channel modelling uncertainty on the measured s-channel signal cross-section. The impact of each category is obtained by repeating the fit after having fixed the set of nuisance parameters corresponding to that category, subtracting the square of the resulting uncertainty from the square of the uncertainty found in the full fit, and calculating the square root. 'PS & had.' refers to the parton shower and hadronisation model, as described in Section 7 in the paper.

Observed impact of the different sources of $tW$ modelling uncertainty on the measured s-channel signal cross-section, grouped by categories. The impact of each category is obtained by repeating the fit after having fixed the set of nuisance parameters corresponding to that category, subtracting the square of the resulting uncertainty from the square of the uncertainty found in the full fit, and calculating the square root. 'PS & had.' refers to the parton shower and hadronisation model, and '$t\bar{t}$ overlap' to the algorithm removing the overlap between $tW$ and $t\bar{t}$ production at NLO, as described in Section 7 in the paper.

Observed impact of the different sources of PDF uncertainties on the measured s-channel signal cross-section, grouped by categories. The impact of each category is obtained by repeating the fit after having fixed the set of nuisance parameters corresponding to that category, subtracting the square of the resulting uncertainty from the square of the uncertainty found in the full fit, and calculating the square root.

Comparison between data and prediction after the fit to data in the signal region for the leading-jet $p_{T}$. The last bin includes the overflow. The uncertainty band includes all uncertainties and their correlations. The lower panel of the figure shows the ratio of the data to the prediction.

Comparison between data and prediction after the fit to data in the signal region for the leading-jet $\eta$. The uncertainty band includes all uncertainties and their correlations. The lower panel of the figure shows the ratio of the data to the prediction.

Comparison between data and prediction after the fit to data in the signal region for the subleading-jet $p_{T}$. The last bin includes the overflow. The uncertainty band includes all uncertainties and their correlations. The lower panel of the figure shows the ratio of the data to the prediction.

Comparison between data and prediction after the fit to data in the signal region for the subleading-jet $\eta$. The uncertainty band includes all uncertainties and their correlations. The lower panel of the figure shows the ratio of the data to the prediction.

Comparison between data and prediction after the fit to data in the signal region for the lepton $p_{T}$. The last bin includes the overflow. The uncertainty band includes all uncertainties and their correlations. The lower panel of the figure shows the ratio of the data to the prediction.

Comparison between data and prediction after the fit to data in the signal region for the lepton $\eta$. The uncertainty band includes all uncertainties and their correlations. The lower panel of the figure shows the ratio of the data to the prediction.

Comparison between data and prediction after the fit to data in the signal region for the ${E}_{T}^{miss}$. The last bin includes the overflow. The uncertainty band includes all uncertainties and their correlations. The lower panel of the figure shows the ratio of the data to the prediction.

Comparison between data and prediction after the fit to data in the signal region for the $m_{T}^{W}$. The last bin includes the overflow. The uncertainty band includes all uncertainties and their correlations. The lower panel of the figure shows the ratio of the data to the prediction.

Nuisance parameters ranked according to their post-fit impacts on the best-fit value of the ratio $\mu$ of the measured cross-section to the predicted cross-section. In the figure, only the 20 nuisance parameters with the largest post-fit impacts are shown. The empty (solid) blue rectangles illustrate the pre-fit (post-fit) impact on $\mu$, corresponding to the upper axis. The pre-fit (post-fit) impact of each nuisance parameter, $\Delta\mu$, is calculated as the difference in the fitted value of $\mu$ between the nominal fit and the fit when fixing the corresponding nuisance parameter to $\hat{\theta}\pm\Delta\theta$ ($\hat{\theta}\pm\Delta\hat{\theta}$), where $\hat{\theta}$ is the best-fit value of the nuisance parameter and $\Delta\theta$ ($\Delta\hat{\theta}$) is its pre-fit (post-fit) uncertainty. Several systematic uncertainties are split into different nuisance parameters, which are indicated by NP. JES (JER) indicates jet energy scale (resolution), and $\gamma$ indicates a nuisance parameter associated to the MC statistics in one of the 18 bins numbered from 0 to 17. The black points show the best-fit values of the nuisance parameters, with the error bars representing the post-fit uncertainties. Each nuisance parameter is shown wrt. its nominal value, $\theta_0$, and in units of its pre-fit uncertainty, except the free-floating normalisation factors of the $t\bar{t}$ and $W$+jets backgrounds, and the parameters associated to the MC statistics in each bin, for which the post-fit values and uncertainties are shown.

Correlation matrix of the nuisance parameters and of the ratio $\mu$ of the measured cross-section to the predicted cross-section. The correlations are given after the fit to data. In the figure, only the parameters which have a correlation of at least 0.2 with any other parameter are shown.

Distribution of the MEM discriminant $P(S|X)$ in the SR for MEM discriminant values larger than $2.0\times10^{-4}$, for the collision data used for the measurement, and for 1000 pseudo-data replicas, generated using a bootstrapping technique, in order to assess the statistical correlations between this measurement and others, for the purpose of combinations. The replicas are obtained by reweighting each observed data event by a random integer generated according to Poisson statistics, using the <a href="https://zenodo.org/record/5361038">BootstrapGenerator</a> software package , which implements a technique described in <a href="https://cds.cern.ch/record/2759945/">ATL-PHYS-PUB-2021-011</a>. The ATLAS event number and run number of each event are used as seed to uniquely but reproducibly initialise the random number generator for each event. Each pseudo-data replica is assigned an index, ranging from 0 to 999, corresponding to the random number index used consistently for each observed data event.

Measured values of the signal cross-section and of the $t\bar{t}$ and $W$+jets normalisation factors, obtained by statistical-only fits to the collision data used for the measurement, and to 1000 pseudo-data replicas, generated using a bootstrapping technique, in order to assess the statistical correlations between this measurement and others, for the purpose of combinations. The central values and their statistical uncertainties are obtained by repeating the fit after having fixed all nuisance parameters, except the $t\bar{t}$ and $W$+jets normalisation factors, which are let free-floating (unlike for the statistical uncertainty on the cross-section quoted in the paper). The replicas are obtained by reweighting each observed data event by a random integer generated according to Poisson statistics, using the <a href="https://zenodo.org/record/5361038">BootstrapGenerator</a> software package , which implements a technique described in <a href="https://cds.cern.ch/record/2759945/">ATL-PHYS-PUB-2021-011</a>. The ATLAS event number and run number of each event are used as seed to uniquely but reproducibly initialise the random number generator for each event. Each pseudo-data replica is assigned an index, ranging from 0 to 999, corresponding to the random number index used consistently for each observed data event.