Expected (dashed black line) and observed (solid red line) 95% CL exclusion limits on the compressed SUSY simplified model with a bino-like LSP and wino-like NLSPs being considered. These are shown with $\pm1\sigma_\text{exp}$ (yellow band) from experimental systematic and statistical uncertainties, and with $\pm1\sigma^{\text{SUSY}}_{\text{theory}}$ (red dotted lines) from signal cross-section uncertainties, respectively. The limits set by the ATLAS searches using the soft lepton signature is illustrated by the blue region while the limit imposed by the LEP experiments is shown in grey.

Expected (dashed black line) and observed (solid red line) 95% CL exclusion limits on the compressed SUSY simplified model with a bino-like LSP and wino-like NLSPs being considered. These are shown with $\pm1\sigma_ ext{exp}$ (yellow band) from experimental systematic and statistical uncertainties, and with $\pm1\sigma^{ ext{SUSY}}_{ ext{theory}}$ (red dotted lines) from signal cross-section uncertainties, respectively. The limits set by the ATLAS searches using the soft lepton signature is illustrated by the blue region while the limit imposed by the LEP experiments is shown in grey.

The expected upper limits on the cross-sections at 95% CL for the simplified SUSY model featuring the production of mass-degenerate pairs of wino-like $\widetilde{\chi}_{2}^{0}$ and $\widetilde{\chi}_{1}^{\pm}$ particles in association with at least two jets. The production modes considered are $\widetilde{\chi}_{2}^{0}\widetilde{\chi}_{1}^{\pm}$, $\widetilde{\chi}_{1}^{\pm}\widetilde{\chi}_{1}^{\mp}$, $\widetilde{\chi}_{2}^{0}\widetilde{\chi}_{2}^{0}$, and $\widetilde{\chi}_{1}^{\pm}\widetilde{\chi}_{1}^{\pm}$.

The observed upper limits on the cross-sections at 95% CL for the simplified SUSY model featuring the production of mass-degenerate pairs of wino-like $\widetilde{\chi}_{2}^{0}$ and $\widetilde{\chi}_{1}^{\pm}$ particles in association with at least two jets. The production modes considered are $\widetilde{\chi}_{2}^{0}\widetilde{\chi}_{1}^{\pm}$, $\widetilde{\chi}_{1}^{\pm}\widetilde{\chi}_{1}^{\mp}$, $\widetilde{\chi}_{2}^{0}\widetilde{\chi}_{2}^{0}$, and $\widetilde{\chi}_{1}^{\pm}\widetilde{\chi}_{1}^{\pm}$.

Truth-level signal acceptances in $\text{SR}_\text{2j}$ with BDT score $\in [0.88, 1.0]$. All of the considered production modes ($\widetilde{\chi}_{2}^{0}\widetilde{\chi}_{1}^{\pm}$, $\widetilde{\chi}_{1}^{\pm}\widetilde{\chi}_{1}^{\mp}$, $\widetilde{\chi}_{2}^{0}\widetilde{\chi}_{2}^{0}$, and $\widetilde{\chi}_{1}^{\pm}\widetilde{\chi}_{1}^{\pm}$) are included. The acceptance is defined as the fraction of accepted events divided by the total number of events in the generator-level signal Monte Carlo simulation. The generator-level selections are the same as the ones at reconstruction level.

Truth-level signal acceptances in $\text{SR}_{\geq\text{3j}}$ with BDT score $\in [0.88, 1.0]$. All of the considered production modes ($\widetilde{\chi}_{2}^{0}\widetilde{\chi}_{1}^{\pm}$, $\widetilde{\chi}_{1}^{\pm}\widetilde{\chi}_{1}^{\mp}$, $\widetilde{\chi}_{2}^{0}\widetilde{\chi}_{2}^{0}$, and $\widetilde{\chi}_{1}^{\pm}\widetilde{\chi}_{1}^{\pm}$) are included. The acceptance is defined as the fraction of accepted events divided by the total number of events in the generator-level signal Monte Carlo simulation. The generator-level selections are the same as the ones at reconstruction level.

Signal efficiencies in $\text{SR}_\text{2j}$ with BDT score $\in [0.88, 1.0]$. All of the considered production modes ($\widetilde{\chi}_{2}^{0}\widetilde{\chi}_{1}^{\pm}$, $\widetilde{\chi}_{1}^{\pm}\widetilde{\chi}_{1}^{\mp}$, $\widetilde{\chi}_{2}^{0}\widetilde{\chi}_{2}^{0}$, and $\widetilde{\chi}_{1}^{\pm}\widetilde{\chi}_{1}^{\pm}$) are included. The efficiency is defined by the number of events of reconstructed-level signal simulation divided by the number of events obtained at generator level. The generator-level selections are the same as the ones at reconstruction level.

Signal efficiencies in $\text{SR}_{\geq\text{3j}}$ with BDT score $\in [0.88, 1.0]$. All of the considered production modes ($\widetilde{\chi}_{2}^{0}\widetilde{\chi}_{1}^{\pm}$, $\widetilde{\chi}_{1}^{\pm}\widetilde{\chi}_{1}^{\mp}$, $\widetilde{\chi}_{2}^{0}\widetilde{\chi}_{2}^{0}$, and $\widetilde{\chi}_{1}^{\pm}\widetilde{\chi}_{1}^{\pm}$) are included. The efficiency is defined by the number of events of reconstructed-level signal simulation divided by the number of events obtained at generator level. The generator-level selections are the same as the ones at reconstruction level.

Event selection cutflows for signal samples with $m(\tilde\chi^0_2) =100~\text{GeV}$ and $\Delta m(\tilde\chi^0_2 / \tilde\chi^\pm_1,\tilde\chi^0_1) = 0.2~\text{GeV}, 1.0~\text{GeV},$ and $5.0~\text{GeV}$. The first number in the column for each mass point 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. All of the production modes are included. The total cross-section used to obtain the initial number of events ($\sigma$) includes the cuts applied at parton level as described in the main text.

Distributions of the $\mathrm{NN^{SvsB}}$ output for data and the expected background after the likelihood fit in the $SR_{cQu --}$ signal region. The post-fit background expectations are shown as filled histograms, the combined pre-fit background expectations are shown as dashed lines. The signal distribution using the Wilson coefficient values $c_{tu}^{(1)}=0.04$, $c_{Qu}^{(1)}=0.1$, $c_{Qu}^{(8)}=0.1$ is shown with a dotted line, normalized to the same number of events as the background.

Summary of the observed and predicted number of events in the five 2$\ell$ control regions. The background prediction is shown after the combined likelihood fit to data under the signal-plus-background hypothesis across all control regions and signal regions. The uncertainties in the total yields are smaller than the sum in quadrature of the uncertainties in the individual contributions due to anti-correlations resulting from the likelihood fit. Int Conv refers to events with photon conversions in the inner detector, while Mat Conv refers to events with photon conversions in the detector material. QMisID refers to events with charge-misidentified lepton.

Summary of the observed and predicted number of events in the four 3$\ell$ control regions. The background prediction is shown after the combined likelihood fit to data under the signal-plus-background hypothesis across all control regions and signal regions. The uncertainties in the total yields are smaller than the sum in quadrature of the uncertainties in the individual contributions due to anti-correlations resulting from the likelihood fit. Int Conv refers to events with photon conversions in the inner detector, while Mat Conv refers to events with photon conversions in the detector material. QMisID refers to events with charge-misidentified lepton.

Comparison of the observed limits on the three WCs to the limit obtained by the ATLAS Run~1 analysis of events with $b$-tagged jets and a same-sign lepton pair [JHEP10(2015)150]. The cross-section limits from that analysis are converted to the limits on the WCs by using the fitted EFT parametrization. The bounds on the WCs are shown at the 68$\%$ CL (solid) and/or 95$\%$ CL (dashed) levels. For the ATLAS Run~1 analysis only the bounds at 95$\%$ CL are available. The vertical bar represents the SM prediction. The new-physics scale is set to $\Lambda = 1 \, \text{TeV}$.

Observed lower limits at 95$\%$ confidence level on the scale of new physics $\Lambda$ for Wilson coefficient values of 0.01, 1 and $4\pi^2$. The limits are compared with the limits obtained by the ATLAS Run~1 analysis of events with $b$-tagged jets and a same-sign lepton pair.

Observed and expected limits at 95$\%$ confidence level on the cross-section of $\sigma(pp \rightarrow tt)$.

2D likelihood scans of the Wilson coefficients $c_{tu}^{(1)}$ versus $c_{Qu}^{(1)}$. The new-physics scale is set to $\Lambda = 1 \, \text{TeV}$. In the table the $2\Delta$NLL values are shown which correspond to the minimized negative log likelihood for a given Wilson coefficient pair.

2D likelihood scans of the Wilson coefficients $c_{tu}^{(1)}$ versus $c_{Qu}^{(8)}$. The new-physics scale is set to $\Lambda = 1 \, \text{TeV}$. In the table the $2\Delta$NLL values are shown which correspond to the minimized negative log likelihood for a given Wilson coefficient pair.

2D likelihood scans of the Wilson coefficients $c_{Qu}^{(1)}$ versus $c_{Qu}^{(8)}$. The new-physics scale is set to $\Lambda = 1 \, \text{TeV}$. In the table the $2\Delta$NLL values are shown which correspond to the minimized negative log likelihood for a given Wilson coefficient pair.

1D-likelihood scan for $c_{tu}^{(1)}$. The observed and expected limits at 68\% and 95\% confidence level (CL) can be read off by finding the intersection of the likelihood scan curve with the 1$\sigma$ and 2$\sigma$ lines. The new-physics scale is set to $\Lambda = 1 \, \text{TeV}$. In the table the $2\Delta$NLL values are shown which correspond to the minimized negative log likelihood for a given Wilson coefficient value.

1D-likelihood scan for $c_{Qu}^{(1)}$. The observed and expected limits at 68\% and 95\% confidence level (CL) can be read off by finding the intersection of the likelihood scan curve with the 1$\sigma$ and 2$\sigma$ lines. The new-physics scale is set to $\Lambda = 1 \, \text{TeV}$. In the table the $2\Delta$NLL values are shown which correspond to the minimized negative log likelihood for a given Wilson coefficient value.

1D-likelihood scan for $c_{Qu}^{(8)}$. The observed and expected limits at 68\% and 95\% confidence level (CL) can be read off by finding the intersection of the likelihood scan curve with the 1$\sigma$ and 2$\sigma$ lines. The new-physics scale is set to $\Lambda = 1 \, \text{TeV}$. In the table the $2\Delta$NLL values are shown which correspond to the minimized negative log likelihood for a given Wilson coefficient value.

Self-normalised ZN energy as a function of the self-normalised charged-particle-multiplicity in pp collisions at $\sqrt{s}$ = 13 TeV in the high-ZN-energy classification (V0M+SPDClusters event classes).

Self-normalised ZN energy as a function of the self-normalised charged-particle-multiplicity in pp collisions at $\sqrt{s}$ = 13 TeV in the low-ZN-energy classification (V0M+SPDClusters event classes).

$K^{0}_{S}$ transverse momentum spectrum in pp collisions at $\sqrt{s}$ = 13 TeV in the high-ZN-energy classification (V0M+SPDClusters event classes).

$\Lambda+\overline{\Lambda}$ transverse momentum spectrum in pp collisions at $\sqrt{s}$ = 13 TeV in the high-ZN-energy classification (V0M+SPDClusters event classes).

$\Xi^{-}+\overline{\Xi}^{+}$ transverse momentum spectrum in pp collisions at $\sqrt{s}$ = 13 TeV in the high-ZN-energy classification (V0M+SPDClusters event classes).

$K^{0}_{S}$ transverse momentum yield ratios to class III in the high-ZN-energy classification (V0M+SPDClusters event classes) in pp collisions at $\sqrt{s}$ = 13 TeV.

$\Lambda+\overline{\Lambda}$ transverse momentum yield ratios to class III in the high-ZN-energy classification (V0M+SPDClusters event classes) in pp collisions at $\sqrt{s}$ = 13 TeV.

$\Xi^{-}+\overline{\Xi}^{+}$ transverse momentum yield ratios to class III in the high-ZN-energy classification (V0M+SPDClusters event classes) in pp collisions at $\sqrt{s}$ = 13 TeV.

$K^{0}_{S}$ transverse momentum spectrum in pp collisions at $\sqrt{s}$ = 13 TeV in the high-local-multiplicity classification (V0M+SPDClusters event classes).

$\Lambda+\overline{\Lambda}$ transverse momentum spectrum in pp collisions at $\sqrt{s}$ = 13 TeV in the high-local-multiplicity classification (V0M+SPDClusters event classes).

$\Xi^{-}+\overline{\Xi}^{+}$ transverse momentum spectrum in pp collisions at $\sqrt{s}$ = 13 TeV in the high-local-multiplicity classification (V0M+SPDClusters event classes).

$K^{0}_{S}$ transverse momentum yield ratios to class IV in the high-local-multiplicity classification (V0M+SPDClusters event classes) in pp collisions at $\sqrt{s}$ = 13 TeV.

$\Lambda+\overline{\Lambda}$ transverse momentum yield ratios to class IV in the high-local-multiplicity classification (V0M+SPDClusters event classes) in pp collisions at $\sqrt{s}$ = 13 TeV.

$\Xi^{-}+\overline{\Xi}^{+}$ transverse momentum yield ratios to class IV in the high-local-multiplicity classification (V0M+SPDClusters event classes) in pp collisions at $\sqrt{s}$ = 13 TeV.

Self-normalised yield ratios of $K^{0}_{S}$, $\Lambda+\overline{\Lambda}$, and $\Xi^{-}+\overline{\Xi}^{+}$ as a function of the self-normalised charged-particle multiplicity in pp collisions at $\sqrt{s}$ = 13 TeV in the standalone classification (V0M event classes).

Self-normalised yield ratios of $K^{0}_{S}$, $\Lambda+\overline{\Lambda}$, and $\Xi^{-}+\overline{\Xi}^{+}$ as a function of the self-normalised $ZN$ signal in pp collisions at $\sqrt{s}$ = 13 TeV in the standalone classification (V0M event classes).

Self-normalised yield ratios of $K^{0}_{S}$, $\Lambda+\overline{\Lambda}$, and $\Xi^{-}+\overline{\Xi}^{+}$ as a function of the self-normalised charged-particle multiplicity in pp collisions at $\sqrt{s}$ = 13 TeV in the high-local-multiplicity classification (V0M+SPDClusters event classes).

Self-normalised yield ratios of $K^{0}_{S}$, $\Lambda+\overline{\Lambda}$, and $\Xi^{-}+\overline{\Xi}^{+}$ as a function of the self-normalised charged-particle multiplicity in pp collisions at $\sqrt{s}$ = 13 TeV in the low-local-multiplicity classification (V0M+SPDClusters event classes).

Self-normalised yield ratios of $K^{0}_{S}$, $\Lambda+\overline{\Lambda}$, and $\Xi^{-}+\overline{\Xi}^{+}$ as a function of the self-normalised charged-particle multiplicity in pp collisions at $\sqrt{s}$ = 13 TeV in the high-ZN-energy classification (V0M+SPDClusters event classes).

Self-normalised yield ratios of $K^{0}_{S}$, $\Lambda+\overline{\Lambda}$, and $\Xi^{-}+\overline{\Xi}^{+}$ as a function of the self-normalised charged-particle multiplicity in pp collisions at $\sqrt{s}$ = 13 TeV in the low-ZN-energy classification (V0M+SPDClusters event classes).

Self-normalised yield ratios of $K^{0}_{S}$, $\Lambda+\overline{\Lambda}$, and $\Xi^{-}+\overline{\Xi}^{+}$ as a function of the self-normalised $ZN$ signal in pp collisions at $\sqrt{s}$ = 13 TeV in the high-local-multiplicity classification (V0M+SPDClusters event classes).

Self-normalised yield ratios of $K^{0}_{S}$, $\Lambda+\overline{\Lambda}$, and $\Xi^{-}+\overline{\Xi}^{+}$ as a function of the self-normalised $ZN$ signal in pp collisions at $\sqrt{s}$ = 13 TeV in the low-local-multiplicity classification (V0M+SPDClusters event classes).

Self-normalised yield ratios of $K^{0}_{S}$, $\Lambda+\overline{\Lambda}$, and $\Xi^{-}+\overline{\Xi}^{+}$ as a function of the self-normalised $ZN$ signal in pp collisions at $\sqrt{s}$ = 13 TeV in the high-ZN-energy classification (V0M+SPDClusters event classes).

Self-normalised yield ratios of $K^{0}_{S}$, $\Lambda+\overline{\Lambda}$, and $\Xi^{-}+\overline{\Xi}^{+}$ as a function of the self-normalised $ZN$ signal in pp collisions at $\sqrt{s}$ = 13 TeV in the low-ZN-energy classification (V0M+SPDClusters event classes).

Post-fit agreement between data and MC prediction for the $SR_{\mathrm{loose}}^{2\ell3j}$ signal region, which uses the invariant mass of the c-tagged jet and the geometrically closest b-tagged jet, $m_{\mathit{cb}}^{\mathrm{min}\Delta R}$, as an observable. The hatched uncertainty bands include all uncertainties and their correlations. The last bins contain overflow events. "Other Top" includes single-top-quark production and associated production of $t\bar{t}$ and single top quarks with bosons. "Non-Top" includes W+jets, Z+jets, and diboson processes.

Post-fit agreement between data and MC prediction for the $SR_{\mathrm{loose}}^{1\ell6ji}$ signal region, which uses the jet multiplicity, $N_{\mathrm{jets}}$, as an observable. The hatched uncertainty bands include all uncertainties and their correlations. The last bins contain overflow events. "Other Top" includes single-top-quark production and associated production of $t\bar{t}$ and single top quarks with bosons. "Non-Top" includes W+jets, Z+jets, and diboson processes.

Post-fit agreement between data and MC prediction for the $SR_{\mathrm{tight}}^{1\ell6ji}$ signal region, which uses the jet multiplicity, $N_{\mathrm{jets}}$, as an observable. The hatched uncertainty bands include all uncertainties and their correlations. The last bins contain overflow events. "Other Top" includes single-top-quark production and associated production of $t\bar{t}$ and single top quarks with bosons. "Non-Top" includes W+jets, Z+jets, and diboson processes.

Post-fit agreement between data and MC prediction for the $SR_{\mathrm{loose}}^{2\ell4ji}$ signal region, which uses the jet multiplicity, $N_{\mathrm{jets}}$, as an observable. The hatched uncertainty bands include all uncertainties and their correlations. The last bins contain overflow events. "Other Top" includes single-top-quark production and associated production of $t\bar{t}$ and single top quarks with bosons. "Non-Top" includes W+jets, Z+jets, and diboson processes.

Post-fit agreement between data and MC prediction for the $SR_{\mathrm{tight}}^{2\ell4ji}$ signal region, which uses the jet multiplicity, $N_{\mathrm{jets}}$, as an observable. The hatched uncertainty bands include all uncertainties and their correlations. The last bins contain overflow events. "Other Top" includes single-top-quark production and associated production of $t\bar{t}$ and single top quarks with bosons. "Non-Top" includes W+jets, Z+jets, and diboson processes.

Jet multiplicity and tagging criteria for the SRs and CRs in the single-lepton and dilepton channels. All single-lepton regions are defined in the 5-jet-exclusive and 6-jet-inclusive jet selections, all dilepton regions in the 3-jet-exclusive and 4-jet-inclusive jet selections. By construction, $\mathrm{SR}^{2\ell}_{\mathrm{tight}}$ only exists for the 4-jet-inclusive selection. Identical requirements on inclusive and exclusive working points, e.g., one c@22% and one c@11% in the $\mathrm{CR}_1^{1\ell}$, indicate a veto of additional tags at the inclusive working point.

Breakdown of the fiducial $t\bar{t}+{\geq}2c$ and $t\bar{t}+1c$ cross-section uncertainties. Systematic uncertainties are grouped into signal and background modeling, instrumental, and MC statistics categories. The table lists the fractional uncertainty in the measured cross-sections in percent and is estimated from the covariance matrix of the profile likelihood fit, following EPJC 84 (2024) 593. Individual groups of uncertainties can be added in quadrature to obtain the total uncertainty. JES and JER denote the jet energy scale and resolution uncertainties, respectively. The fractional uncertainties in the fitted $t\bar{t}+{\geq}1c$ and $t\bar{t}+\text{light}$ normalization factors are included in the data statistics category. For presentation purposes, all uncertainties are symmetrized.

Measured fiducial cross-section values in comparison with various NLO+PS predictions. The uncertainties in the predictions include independent and simultaneous variations of the $\mu_R$ and $\mu_F$ scales and uncertainties in the choice of the PDF set, but no uncertainties in the parton shower or hadronization. The uncertainties in the measured values include all statistical and systematic uncertainties. For presentation purposes, the quoted measurement and prediction uncertainties are symmetrized.

Measured and predicted values for the $t\bar{t}+{\geq}1b$, $t\bar{t}+{\geq}2c$, and $t\bar{t}+1c$ cross-sections and for the cross-section ratios of these processes to total $t\bar{t}+\text{jets}$ production. The quoted uncertainties in the measurements include statistical and systematic uncertainties. The predictions are taken from the nominal setup using inclusive $t\bar{t}$ Powheg+Pythia8 predictions for the $t\bar{t}+{\geq}2c$, $t\bar{t}+1c$, and $t\bar{t}+\text{light}$ processes, and $t\bar{t}+b\bar{b}$ Powheg+Pythia8 predictions for the $t\bar{t}+{\geq}1b$ process. The first use the 5FS, the latter the 4FS, where the $b$-quarks are treated as massive particles and are included in the matrix element calculation. The uncertainties in the predictions include independent and simultaneous variations of the $\mu_R$ and $\mu_F$ scales and uncertainties in the choice of the PDF set.

Nuisance parameters with a large impact on the fiducial measurement: ranking of the ten most impactful nuisance parameters for the $t\bar{t}+{\geq}2c$ cross-section measurement. The colored boxes indicate the impact of the nuisance parameters, $\Delta\mu$ (top axis), on the corresponding parameter of interest, $\mu$. They are calculated from the covariance matrix using the post-fit up (down) uncertainties of the parameter of interest and the nuisance parameter, $\sigma_{\mathrm{POI}}^{\mathrm{up}}$ and $\sigma_{\mathrm{NP}}^{\mathrm{up}}$ ($\sigma_{\mathrm{POI}}^{\mathrm{down}}$ and $\sigma_{\mathrm{NP}}^{\mathrm{down}}$), and their linear correlation coefficient, $\rho$, following EPJC 84 (2024) 593. The data points and error bars indicate the post-fit values and uncertainties of the nuisance parameters relative to their pre-fit values, $\theta_0$, in units of their pre-fit uncertainties, $\Delta \theta$ (bottom axis). A hollow circle indicates that the nuisance parameter has a Poisson constraint.

Nuisance parameters with a large impact on the fiducial measurement: ranking of the ten most impactful nuisance parameters for the $t\bar{t}+1c$ cross-section measurement. The colored boxes indicate the impact of the nuisance parameters, $\Delta\mu$ (top axis), on the corresponding parameter of interest, $\mu$. They are calculated from the covariance matrix using the post-fit up (down) uncertainties of the parameter of interest and the nuisance parameter, $\sigma_{\mathrm{POI}}^{\mathrm{up}}$ and $\sigma_{\mathrm{NP}}^{\mathrm{up}}$ ($\sigma_{\mathrm{POI}}^{\mathrm{down}}$ and $\sigma_{\mathrm{NP}}^{\mathrm{down}}$), and their linear correlation coefficient, $\rho$, following EPJC 84 (2024) 593. The data points and error bars indicate the post-fit values and uncertainties of the nuisance parameters relative to their pre-fit values, $\theta_0$, in units of their pre-fit uncertainties, $\Delta \theta$ (bottom axis). A hollow circle indicates that the nuisance parameter has a Poisson constraint.

Nuisance parameters with a large impact on the fiducial measurement: ranking of the ten most impactful nuisance parameters for the $t\bar{t}+{\geq}2c$ ratio to total $t\bar{t}+\text{jets}$ production. The colored boxes indicate the impact of the nuisance parameters, $\Delta\mu$ (top axis), on the corresponding parameter of interest, $\mu$. They are calculated from the covariance matrix using the post-fit up (down) uncertainties of the parameter of interest and the nuisance parameter, $\sigma_{\mathrm{POI}}^{\mathrm{up}}$ and $\sigma_{\mathrm{NP}}^{\mathrm{up}}$ ($\sigma_{\mathrm{POI}}^{\mathrm{down}}$ and $\sigma_{\mathrm{NP}}^{\mathrm{down}}$), and their linear correlation coefficient, $\rho$, following EPJC 84 (2024) 593. The data points and error bars indicate the post-fit values and uncertainties of the nuisance parameters relative to their pre-fit values, $\theta_0$, in units of their pre-fit uncertainties, $\Delta \theta$ (bottom axis). A hollow circle indicates that the nuisance parameter has a Poisson constraint.

Nuisance parameters with a large impact on the fiducial measurement: ranking of the ten most impactful nuisance parameters for the $t\bar{t}+1c$ ratio to total $t\bar{t}+\text{jets}$ production. The colored boxes indicate the impact of the nuisance parameters, $\Delta\mu$ (top axis), on the corresponding parameter of interest, $\mu$. They are calculated from the covariance matrix using the post-fit up (down) uncertainties of the parameter of interest and the nuisance parameter, $\sigma_{\mathrm{POI}}^{\mathrm{up}}$ and $\sigma_{\mathrm{NP}}^{\mathrm{up}}$ ($\sigma_{\mathrm{POI}}^{\mathrm{down}}$ and $\sigma_{\mathrm{NP}}^{\mathrm{down}}$), and their linear correlation coefficient, $\rho$, following EPJC 84 (2024) 593. The data points and error bars indicate the post-fit values and uncertainties of the nuisance parameters relative to their pre-fit values, $\theta_0$, in units of their pre-fit uncertainties, $\Delta \theta$ (bottom axis). A hollow circle indicates that the nuisance parameter has a Poisson constraint.

Efficiencies and rejection rates for the $b$- and $c$-jet tagging working points of the $b/c$-tagger, as well as the selection cuts on the discriminants, $\mathcal{D}_b'$ and $\mathcal{D}_c'$ that define the tagging bins. The primes indicate that a standard logistic function is applied to the discriminants. The b@70% and c@22% working points are inclusive of their respective tighter working points. The values were estimated from single-lepton and dilepton $t\bar{t}$ events simulated with Powheg + Pythia 8.

Efficiencies and rejection rates for the $b$- and $c$-jet tagging working points of the $b/c$-tagger, as well as the selection cuts on the discriminants, $\mathcal{D}_b'$ and $\mathcal{D}_c'$ that define the tagging bins. The primes indicate that a standard logistic function is applied to the discriminants. The b@70% and c@22% working points are inclusive of their respective tighter working points. The values were estimated from single-lepton and dilepton $t\bar{t}$ events simulated with Powheg + Pythia 8.

Pre-fit event yields in the twelve single-lepton and dilepton control regions (CRs) of the analysis. The quoted uncertainties include both statistical and systematic components, but all normalization factors are fixed to their pre-fit values with no uncertainties. All uncertainties are assumed to be uncorrelated. "Other Top" includes single-top-quark production and associated production of $t\bar{t}$ and single top quarks with bosons. "Non-Top" includes W+jets, Z+jets, and diboson processes. The "Fakes" category includes events from misidentified leptons and non-prompt leptons, estimated through the data-driven matrix method in the single-lepton channel and through MC predictions in the dilepton channel.

Pre-fit event yields in the seven signal regions (SRs) of the analysis. The quoted uncertainties include both statistical and systematic components, but all normalization factors are fixed to their pre-fit values with no uncertainties. All uncertainties are assumed to be uncorrelated. "Other Top" includes single-top-quark production and associated production of $t\bar{t}$ and single top quarks with bosons. "Non-Top" includes W+jets, Z+jets, and diboson processes. The "Fakes" category includes events from misidentified leptons and non-prompt leptons, estimated through the data-driven matrix method in the single-lepton channel and through MC predictions in the dilepton channel.

Post-fit event yields in the twelve single-lepton and dilepton control regions (CRs) of the analysis. The quoted uncertainties include both statistical and systematic components, and post-fit correlations between uncertainties are taken into account. "Other Top" includes single-top-quark production and associated production of $t\bar{t}$ and single top quarks with bosons. "Non-Top" includes W+jets, Z+jets, and diboson processes. The "Fakes" category includes events from misidentified leptons and non-prompt leptons, estimated through the data-driven matrix method in the single-lepton channel and through MC predictions in the dilepton channel.

Post-fit event yields in the seven signal regions (SRs) of the analysis. The quoted uncertainties include both statistical and systematic components, and post-fit correlations between uncertainties are taken into account. "Other Top" includes single-top-quark production and associated production of $t\bar{t}$ and single top quarks with bosons. "Non-Top" includes W+jets, Z+jets, and diboson processes. The "Fakes" category includes events from misidentified leptons and non-prompt leptons, estimated through the data-driven matrix method in the single-lepton channel and through MC predictions in the dilepton channel.

Multiplicity dependence of the near-side width $\sigma$ in pp collisions at $\sqrt{s_{\rm NN}} = 13$ TeV. Obtained in transverse momentum intervals $3.0 < p_\mathrm{T, trig} < 4.0$ GeV/$c$ and $1.0 < p_\mathrm{T, assoc} < 2.0$ GeV/$c$. The mulitplicity is estimated with midrapidity multiplicity estimator ($|\eta|<1.0,\,p_\mathrm{T}>0.2$ GeV/$c$).

Multiplicity dependence of the near-side width $\sigma$ in pp collisions at $\sqrt{s_{\rm NN}} = 13$ TeV. Obtained in transverse momentum intervals $3.0 < p_\mathrm{T, trig} < 4.0$ GeV/$c$ and $2.0 < p_\mathrm{T, assoc} < 3.0$ GeV/$c$. The mulitplicity is estimated with midrapidity multiplicity estimator ($|\eta|<1.0,\,p_\mathrm{T}>0.2$ GeV/$c$).

Multiplicity dependence of the near-side width $\sigma$ in pp collisions at $\sqrt{s_{\rm NN}} = 13$ TeV. Obtained in transverse momentum intervals $3.0 < p_\mathrm{T, assoc} < p_\mathrm{T, trig} < 4.0$ GeV/$c$. The multiplicity is estimated with midrapidity multiplicity estimator ($|\eta|<1.0,\,p_\mathrm{T}>0.2$ GeV/$c$).

Multiplicity dependence of the near-side width $\sigma$ in pp collisions at $\sqrt{s_{\rm NN}} = 13$ TeV. Obtained in transverse momentum intervals $4.0 < p_\mathrm{T, trig} < 8.0$ GeV/$c$ and $1.0 < p_\mathrm{T, assoc} < 2.0$ GeV/$c$. The mulitplicity is estimated with midrapidity multiplicity estimator ($|\eta|<1.0,\,p_\mathrm{T}>0.2$ GeV/$c$).

Multiplicity dependence of the near-side width $\sigma$ in pp collisions at $\sqrt{s_{\rm NN}} = 13$ TeV. Obtained in transverse momentum intervals $4.0 < p_\mathrm{T, trig} < 8.0$ GeV/$c$ and $2.0 < p_\mathrm{T, assoc} < 3.0$ GeV/$c$. The mulitplicity is estimated with midrapidity multiplicity estimator ($|\eta|<1.0,\,p_\mathrm{T}>0.2$ GeV/$c$).

Multiplicity dependence of the near-side width $\sigma$ in pp collisions at $\sqrt{s_{\rm NN}} = 13$ TeV. Obtained in transverse momentum intervals $4.0 < p_\mathrm{T, trig} < 8.0$ GeV/$c$ and $3.0 < p_\mathrm{T, assoc} < 4.0$ GeV/$c$. The mulitplicity is estimated with midrapidity multiplicity estimator ($|\eta|<1.0,\,p_\mathrm{T}>0.2$ GeV/$c$).

Multiplicity dependence of the near-side width $\sigma$ in pp collisions at $\sqrt{s_{\rm NN}} = 13$ TeV. Obtained in transverse momentum intervals $4.0 < p_\mathrm{T, assoc} < p_\mathrm{T, trig} < 8.0$ GeV/$c$. The multiplicity is estimated with midrapidity multiplicity estimator ($|\eta|<1.0,\,p_\mathrm{T}>0.2$ GeV/$c$).

Multiplicity dependence of the near-side width $\sigma$ in pp collisions at $\sqrt{s_{\rm NN}} = 13$ TeV. Obtained in transverse momentum intervals $1.0 < p_\mathrm{T, assoc} < p_\mathrm{T, trig} < 2.0$ GeV/$c$. The multiplicity is estimated with forward multiplicity estimator.

Multiplicity dependence of the near-side width $\sigma$ in pp collisions at $\sqrt{s_{\rm NN}} = 13$ TeV. Obtained in transverse momentum intervals $2.0 < p_\mathrm{T, trig} < 3.0$ GeV/$c$ and $1.0 < p_\mathrm{T, assoc} < 2.0$ GeV/$c$. The mulitplicity is estimated with forward multiplicity estimator.

Multiplicity dependence of the near-side width $\sigma$ in pp collisions at $\sqrt{s_{\rm NN}} = 13$ TeV. Obtained in transverse momentum intervals $2.0 < p_\mathrm{T, assoc} < p_\mathrm{T, trig} < 3.0$ GeV/$c$. The multiplicity is estimated with forward multiplicity estimator.

Multiplicity dependence of the near-side width $\sigma$ in pp collisions at $\sqrt{s_{\rm NN}} = 13$ TeV. Obtained in transverse momentum intervals $3.0 < p_\mathrm{T, trig} < 4.0$ GeV/$c$ and $1.0 < p_\mathrm{T, assoc} < 2.0$ GeV/$c$. The mulitplicity is estimated with forward multiplicity estimator.

Multiplicity dependence of the near-side width $\sigma$ in pp collisions at $\sqrt{s_{\rm NN}} = 13$ TeV. Obtained in transverse momentum intervals $3.0 < p_\mathrm{T, trig} < 4.0$ GeV/$c$ and $2.0 < p_\mathrm{T, assoc} < 3.0$ GeV/$c$. The mulitplicity is estimated with forward multiplicity estimator.

Multiplicity dependence of the near-side width $\sigma$ in pp collisions at $\sqrt{s_{\rm NN}} = 13$ TeV. Obtained in transverse momentum intervals $3.0 < p_\mathrm{T, assoc} < p_\mathrm{T, trig} < 4.0$ GeV/$c$. The multiplicity is estimated with forward multiplicity estimator.

Multiplicity dependence of the near-side width $\sigma$ in pp collisions at $\sqrt{s_{\rm NN}} = 13$ TeV. Obtained in transverse momentum intervals $4.0 < p_\mathrm{T, trig} < 8.0$ GeV/$c$ and $1.0 < p_\mathrm{T, assoc} < 2.0$ GeV/$c$. The mulitplicity is estimated with forward multiplicity estimator.

Multiplicity dependence of the near-side width $\sigma$ in pp collisions at $\sqrt{s_{\rm NN}} = 13$ TeV. Obtained in transverse momentum intervals $4.0 < p_\mathrm{T, trig} < 8.0$ GeV/$c$ and $2.0 < p_\mathrm{T, assoc} < 3.0$ GeV/$c$. The mulitplicity is estimated with forward multiplicity estimator.

Multiplicity dependence of the near-side width $\sigma$ in pp collisions at $\sqrt{s_{\rm NN}} = 13$ TeV. Obtained in transverse momentum intervals $4.0 < p_\mathrm{T, trig} < 8.0$ GeV/$c$ and $3.0 < p_\mathrm{T, assoc} < 4.0$ GeV/$c$. The mulitplicity is estimated with forward multiplicity estimator.

Multiplicity dependence of the near-side width $\sigma$ in pp collisions at $\sqrt{s_{\rm NN}} = 13$ TeV. Obtained in transverse momentum intervals $4.0 < p_\mathrm{T, assoc} < p_\mathrm{T, trig} < 8.0$ GeV/$c$. The multiplicity is estimated with forward multiplicity estimator.

Multiplicity dependence of the fragmentation yield $Y^{frag}$ in pp collisions at $\sqrt{s_{\rm NN}} = 13$ TeV. Obtained in transverse momentum intervals $1.0 < p_\mathrm{T, assoc} < p_\mathrm{T, trig} < 2.0$ GeV/$c$. The mulitplicity is estimated with midrapidity multiplicity estimator ($|\eta|<1.0,\,p_\mathrm{T}>0.2$ GeV/$c$).

Multiplicity dependence of the fragmentation yield $Y^{frag}$ in pp collisions at $\sqrt{s_{\rm NN}} = 13$ TeV. Obtained in transverse momentum intervals $2.0 < p_\mathrm{T, trig} < 3.0$ GeV/$c$ and $1.0 < p_\mathrm{T, assoc} < 2.0$ GeV/$c$. The mulitplicity is estimated with midrapidity multiplicity estimator ($|\eta|<1.0,\,p_\mathrm{T}>0.2$ GeV/$c$).

Multiplicity dependence of the fragmentation yield $Y^{frag}$ in pp collisions at $\sqrt{s_{\rm NN}} = 13$ TeV. Obtained in transverse momentum intervals $2.0 < p_\mathrm{T, assoc} < p_\mathrm{T, trig} < 3.0$ GeV/$c$. The mulitplicity is estimated with midrapidity multiplicity estimator ($|\eta|<1.0,\,p_\mathrm{T}>0.2$ GeV/$c$).

Multiplicity dependence of the fragmentation yield $Y^{frag}$ in pp collisions at $\sqrt{s_{\rm NN}} = 13$ TeV. Obtained in transverse momentum intervals $3.0 < p_\mathrm{T, trig} < 4.0$ GeV/$c$ and $1.0 < p_\mathrm{T, assoc} < 2.0$ GeV/$c$. The mulitplicity is estimated with midrapidity multiplicity estimator ($|\eta|<1.0,\,p_\mathrm{T}>0.2$ GeV/$c$).

Multiplicity dependence of the fragmentation yield $Y^{frag}$ in pp collisions at $\sqrt{s_{\rm NN}} = 13$ TeV. Obtained in transverse momentum intervals $3.0 < p_\mathrm{T, trig} < 4.0$ GeV/$c$ and $2.0 < p_\mathrm{T, assoc} < 3.0$ GeV/$c$. The mulitplicity is estimated with midrapidity multiplicity estimator ($|\eta|<1.0,\,p_\mathrm{T}>0.2$ GeV/$c$).

Multiplicity dependence of the fragmentation yield $Y^{frag}$ in pp collisions at $\sqrt{s_{\rm NN}} = 13$ TeV. Obtained in transverse momentum intervals $3.0 < p_\mathrm{T, assoc} < p_\mathrm{T, trig} < 4.0$ GeV/$c$. The mulitplicity is estimated with midrapidity multiplicity estimator ($|\eta|<1.0,\,p_\mathrm{T}>0.2$ GeV/$c$).

Multiplicity dependence of the fragmentation yield $Y^{frag}$ in pp collisions at $\sqrt{s_{\rm NN}} = 13$ TeV. Obtained in transverse momentum intervals $4.0 < p_\mathrm{T, trig} < 8.0$ GeV/$c$ and $1.0 < p_\mathrm{T, assoc} < 2.0$ GeV/$c$. The mulitplicity is estimated with midrapidity multiplicity estimator ($|\eta|<1.0,\,p_\mathrm{T}>0.2$ GeV/$c$).

Multiplicity dependence of the fragmentation yield $Y^{frag}$ in pp collisions at $\sqrt{s_{\rm NN}} = 13$ TeV. Obtained in transverse momentum intervals $4.0 < p_\mathrm{T, trig} < 8.0$ GeV/$c$ and $2.0 < p_\mathrm{T, assoc} < 3.0$ GeV/$c$. The mulitplicity is estimated with midrapidity multiplicity estimator ($|\eta|<1.0,\,p_\mathrm{T}>0.2$ GeV/$c$).

Multiplicity dependence of the fragmentation yield $Y^{frag}$ in pp collisions at $\sqrt{s_{\rm NN}} = 13$ TeV. Obtained in transverse momentum intervals $4.0 < p_\mathrm{T, trig} < 8.0$ GeV/$c$ and $3.0 < p_\mathrm{T, assoc} < 4.0$ GeV/$c$. The mulitplicity is estimated with midrapidity multiplicity estimator ($|\eta|<1.0,\,p_\mathrm{T}>0.2$ GeV/$c$).

Multiplicity dependence of the fragmentation yield $Y^{frag}$ in pp collisions at $\sqrt{s_{\rm NN}} = 13$ TeV. Obtained in transverse momentum intervals $4.0 < p_\mathrm{T, assoc} < p_\mathrm{T, trig} < 8.0$ GeV/$c$. The mulitplicity is estimated with midrapidity multiplicity estimator ($|\eta|<1.0,\,p_\mathrm{T}>0.2$ GeV/$c$).

Multiplicity dependence of the fragmentation yield $Y^{frag}$ in pp collisions at $\sqrt{s_{\rm NN}} = 13$ TeV. Obtained in transverse momentum intervals $1.0 < p_\mathrm{T, assoc} < p_\mathrm{T, trig} < 2.0$ GeV/$c$. The mulitplicity is estimated with forward multiplicity estimator.

Multiplicity dependence of the fragmentation yield $Y^{frag}$ in pp collisions at $\sqrt{s_{\rm NN}} = 13$ TeV. Obtained in transverse momentum intervals $2.0 < p_\mathrm{T, trig} < 3.0$ GeV/$c$ and $1.0 < p_\mathrm{T, assoc} < 2.0$ GeV/$c$. The mulitplicity is estimated with forward multiplicity estimator.

Multiplicity dependence of the fragmentation yield $Y^{frag}$ in pp collisions at $\sqrt{s_{\rm NN}} = 13$ TeV. Obtained in transverse momentum intervals $2.0 < p_\mathrm{T, assoc} < p_\mathrm{T, trig} < 3.0$ GeV/$c$. The mulitplicity is estimated with forward multiplicity estimator.

Multiplicity dependence of the fragmentation yield $Y^{frag}$ in pp collisions at $\sqrt{s_{\rm NN}} = 13$ TeV. Obtained in transverse momentum intervals $3.0 < p_\mathrm{T, trig} < 4.0$ GeV/$c$ and $1.0 < p_\mathrm{T, assoc} < 2.0$ GeV/$c$. The mulitplicity is estimated with forward multiplicity estimator.

Multiplicity dependence of the fragmentation yield $Y^{frag}$ in pp collisions at $\sqrt{s_{\rm NN}} = 13$ TeV. Obtained in transverse momentum intervals $3.0 < p_\mathrm{T, trig} < 4.0$ GeV/$c$ and $2.0 < p_\mathrm{T, assoc} < 3.0$ GeV/$c$. The mulitplicity is estimated with forward multiplicity estimator.

Multiplicity dependence of the fragmentation yield $Y^{frag}$ in pp collisions at $\sqrt{s_{\rm NN}} = 13$ TeV. Obtained in transverse momentum intervals $3.0 < p_\mathrm{T, assoc} < p_\mathrm{T, trig} < 4.0$ GeV/$c$. The mulitplicity is estimated with forward multiplicity estimator.

Multiplicity dependence of the fragmentation yield $Y^{frag}$ in pp collisions at $\sqrt{s_{\rm NN}} = 13$ TeV. Obtained in transverse momentum intervals $4.0 < p_\mathrm{T, trig} < 8.0$ GeV/$c$ and $1.0 < p_\mathrm{T, assoc} < 2.0$ GeV/$c$. The mulitplicity is estimated with forward multiplicity estimator.

Multiplicity dependence of the fragmentation yield $Y^{frag}$ in pp collisions at $\sqrt{s_{\rm NN}} = 13$ TeV. Obtained in transverse momentum intervals $4.0 < p_\mathrm{T, trig} < 8.0$ GeV/$c$ and $2.0 < p_\mathrm{T, assoc} < 3.0$ GeV/$c$. The mulitplicity is estimated with forward multiplicity estimator.

Multiplicity dependence of the fragmentation yield $Y^{frag}$ in pp collisions at $\sqrt{s_{\rm NN}} = 13$ TeV. Obtained in transverse momentum intervals $4.0 < p_\mathrm{T, trig} < 8.0$ GeV/$c$ and $3.0 < p_\mathrm{T, assoc} < 4.0$ GeV/$c$. The mulitplicity is estimated with forward multiplicity estimator.

Multiplicity dependence of the fragmentation yield $Y^{frag}$ in pp collisions at $\sqrt{s_{\rm NN}} = 13$ TeV. Obtained in transverse momentum intervals $4.0 < p_\mathrm{T, assoc} < p_\mathrm{T, trig} < 8.0$ GeV/$c$. The mulitplicity is estimated with forward multiplicity estimator.

Self-Normalized $J/\psi$ yields in the same arms before and after dimuon subtraction and the comparison with PYTHIA 8 simulations

Self-normalized $\psi(2S)$ to $J/\psi$ yields ratio as a function of Self-normalized $N_{ch}$ in the same arms

Self-normalized $\psi(2S)$ to $J/\psi$ yields ratio as a function of Self-normalized $N_{ch}$ in opposite arms

Two graphs show the results of the scan over the horizontal and vertical displacements of the antiproton beam (see Table 3, before) and the horizontal and vertical angles (on the right). The color represents the intensity of the signal obtained on the MCP from the annihilations of the trapped antiprotons. The parameter space has been organized in this way, assuming that displacements and angles have independent effects, not for physics reasons, but because scanning over the full parameter space would have been impossible time-wise (10 steps per dimension 4 dimensions x 5 min of duration of the script ~35 days!).

Results of the beam steering optimization. Convergence plot of the highest observed number of annihilation events.

Results of the beam steering optimization. Density plots of the evaluations in the four-parameter space dimensions.

Results of the beam steering optimization. Density plots of the evaluations in the four-parameter space dimensions.

Results of the beam steering optimization. Density plots of the evaluations in the four-parameter space dimensions.

Results of the beam steering optimization. Density plots of the evaluations in the four-parameter space dimensions.

Results of the trap closing time optimization. Convergence plot of the highest observed number of annihilation events.

Results of the trap closing time optimization. Number of observed annihilation events as a function of the trap closing time. The result is different from the one in 2022 (Figure 6) because the capture electrode voltage was raised from 10 to 15 kV.

Synchronization results in the asynchronous parallel operation mode, showing the time difference between the start of different parallel scripts, in a schedule of 50 scripts. Both plots are accompanied by a single point plot adjacent on the right, representing the average δT over all 50 runs. In the same-duration script case (a), the high average can be explained by intrinsic delays included in Tamer and Monkey to avoid race conditions. In the different-duration script case (b), a linear trend is visible that comes from the increase in the duration time between different Kaslis. The bottom plot shows δT corrected for the linear trend, showing the average jitter value of -5 to 5 s.

Synchronization results in the asynchronous parallel operation mode, showing the time difference between the start of different parallel scripts, in a schedule of 50 scripts. Both plots are accompanied by a single point plot adjacent on the right, representing the average δT over all 50 runs. In the same-duration script case (a), the high average can be explained by intrinsic delays included in Tamer and Monkey to avoid race conditions. In the different-duration script case (b), a linear trend is visible that comes from the increase in the duration time between different Kaslis. The bottom plot shows δT corrected for the linear trend, showing the average jitter value of -5 to 5 s.

Synchronization results in the asynchronous parallel operation mode, showing the time difference between the start of different parallel scripts, in a schedule of 50 scripts. Both plots are accompanied by a single point plot adjacent on the right, representing the average δT over all 50 runs. In the same-duration script case (a), the high average can be explained by intrinsic delays included in Tamer and Monkey to avoid race conditions. In the different-duration script case (b), a linear trend is visible that comes from the increase in the duration time between different Kaslis. The bottom plot shows δT corrected for the linear trend, showing the average jitter value of -5 to 5 s.

Synchronization results in the synchronous parallel operation mode, showing the time difference between the start of different parallel scripts, in a schedule of 50 scripts. Both in the same-duration case (a) and in the different-duration case (b), the time difference between the start of different parallel scripts is stable around 5 ms, independently of the duration of the scripts. Both plots are accompanied by a single point plot adjacent on the right, representing the average δT over all 50 runs.

Synchronization results in the synchronous parallel operation mode, showing the time difference between the start of different parallel scripts, in a schedule of 50 scripts. Both in the same-duration case (a) and in the different-duration case (b), the time difference between the start of different parallel scripts is stable around 5 ms, independently of the duration of the scripts. Both plots are accompanied by a single point plot adjacent on the right, representing the average δT over all 50 runs.

The cutflow table for $N1$ and $N2$ signal samples for different mass points. The samples consist of both $ee$ and $\mu\mu$ final states in equal ratio. Each sample is normalized to a total cross-section of 0.1 pb. The abbreviations used in the table are, SC = Same Charge, SF = Same Flavor.

The cutflow table for $N3$ signal samples for different mass points. The samples consist of both $ee$ and $\mu\mu$ final states in equal ratio. Each sample is normalized to a total cross-section of 10 pb. The abbreviations used in the table are, SS = Same Charge, SF = Same Flavor.

Expected and observed upper limits on the strength of HNL mixing with electron neutrinos

Expected and observed upper limits on the strength of HNL mixing with muon neutrinos

Expected and observed upper limits on the strength of HNL mixing with tau neutrinos