Breakdown of relative systematic uncertainties in the measured ${t\bar{t}}$ cross-section. The quoted uncertainties are obtained by repeating the fit with a group of nuisance parameters fixed to their fitted values and subtracting in quadrature the resulting total uncertainty from the uncertainty of the complete fit. However, the total uncertainty is not the quadratic sum of the grouped impacts, as this approach neglects the correlation among the different groups.

The figure shows the measurement of the top quark pair production cross-section, $\sigma_{t\bar{t}}$, in lead-lead (Pb+Pb) collisions at a center-of-mass energy of $\sqrt{s_{\mathrm{NN}}} = 5.02$ TeV, based on 1.9 nb$^{-1}$ of data.

Product of acceptance and efficiency for pp->tbH(->Wh) as function of the charged Higgs boson mass for the resolved qqbb signal region.

Product of acceptance and efficiency for pp->tbH(->Wh) as function of the charged Higgs boson mass for the resolved lvbb signal region.

Product of acceptance and efficiency for pp->tbH(->Wh) as function of the charged Higgs boson mass for the merged lvbb signal region

Product of acceptance and efficiency for pp->tbH(->Wh) as function of the charged Higgs boson mass for the merged qqbb signal region

Distributions of the mWh observable in the low-purity signal regions of the resolved qqbb 5jex3bex event categories. The term ‘Others’ summarises events from tHjb, tWh, tttt, and SM Vh production. The distributions are presented after a background-only maximum-likelihood fit to data. The individual background uncertainty does not take into account the possible correlations between the nuisance parameter. The expected signal contribution assuming $m_{H^{\pm}}$ = 700 GeV, normalised to the expected limit of the cross-section times branching ratio ($\sigma_{sig}$ × B) of 0.064 pb, is shown as a dashed histogram.

Distributions of the mWh observable in the low-purity signal regions of the resolved qqbb 5jex4bin event categories. The term ‘Others’ summarises events from tHjb, tWh, tttt, and SM Vh production. The distributions are presented after a background-only maximum-likelihood fit to data. The individual background uncertainty does not take into account the possible correlations between the nuisance parameter. The expected signal contribution assuming $m_{H^{\pm}}$ = 700 GeV, normalised to the expected limit of the cross-section times branching ratio ($\sigma_{sig}$ × B) of 0.064 pb, is shown as a dashed histogram.

Distributions of the mWh observable in the low-purity signal regions of the resolved qqbb 6jin3bex event categories. The term ‘Others’ summarises events from tHjb, tWh, tttt, and SM Vh production. The distributions are presented after a background-only maximum-likelihood fit to data. The individual background uncertainty does not take into account the possible correlations between the nuisance parameter. The expected signal contribution assuming $m_{H^{\pm}}$ = 700 GeV, normalised to the expected limit of the cross-section times branching ratio ($\sigma_{sig}$ × B) of 0.064 pb, is shown as a dashed histogram.

Distributions of the mWh observable in the low-purity signal regions of the resolved qqbb 6jin4bin event categories. The term ‘Others’ summarises events from tHjb, tWh, tttt, and SM Vh production. The distributions are presented after a background-only maximum-likelihood fit to data. The individual background uncertainty does not take into account the possible correlations between the nuisance parameter. The expected signal contribution assuming $m_{H^{\pm}}$ = 700 GeV, normalised to the expected limit of the cross-section times branching ratio ($\sigma_{sig}$ × B) of 0.064 pb, is shown as a dashed histogram.

Distributions of the mWh observable in the high-purity signal regions of the resolved qqbb 5jex3bex event categories. The term ‘Others’ summarises events from tHjb, tWh, tttt, and SM Vh production. The distributions are presented after a background-only maximum-likelihood fit to data. The individual background uncertainty does not take into account the possible correlations between the nuisance parameter. The expected signal contribution assuming $m_{H^{\pm}}$ = 700 GeV, normalised to the expected limit of the cross-section times branching ratio ($\sigma_{sig}$ × B) of 0.064 pb, is shown as a dashed histogram.

Distributions of the mWh observable in the high-purity signal regions of the resolved qqbb 5jex4bin event categories. The term ‘Others’ summarises events from tHjb, tWh, tttt, and SM Vh production. The distributions are presented after a background-only maximum-likelihood fit to data. The individual background uncertainty does not take into account the possible correlations between the nuisance parameter. The expected signal contribution assuming $m_{H^{\pm}}$ = 700 GeV, normalised to the expected limit of the cross-section times branching ratio ($\sigma_{sig}$ × B) of 0.064 pb, is shown as a dashed histogram.

Distributions of the mWh observable in the high-purity signal regions of the resolved qqbb 6jin3bex event categories. The term ‘Others’ summarises events from tHjb, tWh, tttt, and SM Vh production. The distributions are presented after a background-only maximum-likelihood fit to data. The individual background uncertainty does not take into account the possible correlations between the nuisance parameter. The expected signal contribution assuming $m_{H^{\pm}}$ = 700 GeV, normalised to the expected limit of the cross-section times branching ratio ($\sigma_{sig}$ × B) of 0.064 pb, is shown as a dashed histogram.

Distributions of the mWh observable in the high-purity signal regions of the resolved qqbb 6jin4bin event categories. The term ‘Others’ summarises events from tHjb, tWh, tttt, and SM Vh production. The distributions are presented after a background-only maximum-likelihood fit to data. The individual background uncertainty does not take into account the possible correlations between the nuisance parameter. The expected signal contribution assuming $m_{H^{\pm}}$ = 700 GeV, normalised to the expected limit of the cross-section times branching ratio ($\sigma_{sig}$ × B) of 0.064 pb, is shown as a dashed histogram.

Distributions of the mWh observable in the signal regions of the resolved lvbb 5jex3bex event categories. The term ‘Others’ summarises events from tHjb, tWh, tttt, and SM Vh production. The distributions are presented after a background-only maximum-likelihood fit to data. The individual background uncertainty does not take into account the possible correlations between the nuisance parameter. The expected signal contribution assuming $m_{H^{\pm}}$ = 700 GeV, normalised to the expected limit of the cross-section times branching ratio ($\sigma_{sig}$ × B) of 0.064 pb, is shown as a dashed histogram.

Distributions of the mWh observable in the signal regions of the resolved lvbb 5jex4bin event categories. The term ‘Others’ summarises events from tHjb, tWh, tttt, and SM Vh production. The distributions are presented after a background-only maximum-likelihood fit to data. The individual background uncertainty does not take into account the possible correlations between the nuisance parameter. The expected signal contribution assuming $m_{H^{\pm}}$ = 700 GeV, normalised to the expected limit of the cross-section times branching ratio ($\sigma_{sig}$ × B) of 0.064 pb, is shown as a dashed histogram.

Distributions of the mWh observable in the signal regions of the resolved lvbb 6jin3bex event categories. The term ‘Others’ summarises events from tHjb, tWh, tttt, and SM Vh production. The distributions are presented after a background-only maximum-likelihood fit to data. The individual background uncertainty does not take into account the possible correlations between the nuisance parameter. The expected signal contribution assuming $m_{H^{\pm}}$ = 700 GeV, normalised to the expected limit of the cross-section times branching ratio ($\sigma_{sig}$ × B) of 0.064 pb, is shown as a dashed histogram.

Distributions of the mWh observable in the signal regions of the resolved lvbb 6jin4bin event categories. The term ‘Others’ summarises events from tHjb, tWh, tttt, and SM Vh production. The distributions are presented after a background-only maximum-likelihood fit to data. The individual background uncertainty does not take into account the possible correlations between the nuisance parameter. The expected signal contribution assuming $m_{H^{\pm}}$ = 700 GeV, normalised to the expected limit of the cross-section times branching ratio ($\sigma_{sig}$ × B) of 0.064 pb, is shown as a dashed histogram.

The mWh distributions in the Low-NN-score SRs of the merged qqbb 0b event categories. The term ‘Others’ summarises events from tHjb, tWh, tttt, and SM Vh production. The background prediction is shown after a background-only maximum-likelihood fit to data. The individual background uncertainty does not take into account the possible correlations between the nuisance parameter. The expected signal contributions assuming $m_{H^{\pm}}$ = 900 GeV and $m_{H^{\pm}}$ = 2000 GeV, normalised the expected limit of the cross-section times branching ratio ($\sigma_{sig}$ × B) values of 0.036 pb and 2.7 fb respectively, are shown as dashed histograms.

The mWh distributions in the Low-NN-score SRs of the merged qqbb 1b event categories. The term ‘Others’ summarises events from tHjb, tWh, tttt, and SM Vh production. The background prediction is shown after a background-only maximum-likelihood fit to data. The individual background uncertainty does not take into account the possible correlations between the nuisance parameter. The expected signal contributions assuming $m_{H^{\pm}}$ = 900 GeV and $m_{H^{\pm}}$ = 2000 GeV, normalised the expected limit of the cross-section times branching ratio ($\sigma_{sig}$ × B) values of 0.036 pb and 2.7 fb respectively, are shown as dashed histograms.

The mWh distributions in the High-NN-score SRs of the merged qqbb 0b event categories. The term ‘Others’ summarises events from tHjb, tWh, tttt, and SM Vh production. The background prediction is shown after a background-only maximum-likelihood fit to data. The individual background uncertainty does not take into account the possible correlations between the nuisance parameter. The expected signal contributions assuming $m_{H^{\pm}}$ = 900 GeV and $m_{H^{\pm}}$ = 2000 GeV, normalised the expected limit of the cross-section times branching ratio ($\sigma_{sig}$ × B) values of 0.036 pb and 2.7 fb respectively, are shown as dashed histograms.

The mWh distributions in the High-NN-score SRs of the merged qqbb 1b event categories. The term ‘Others’ summarises events from tHjb, tWh, tttt, and SM Vh production. The background prediction is shown after a background-only maximum-likelihood fit to data. The individual background uncertainty does not take into account the possible correlations between the nuisance parameter. The expected signal contributions assuming $m_{H^{\pm}}$ = 900 GeV and $m_{H^{\pm}}$ = 2000 GeV, normalised the expected limit of the cross-section times branching ratio ($\sigma_{sig}$ × B) values of 0.036 pb and 2.7 fb respectively, are shown as dashed histograms.

The mWh distributions in the Low-NN-score SRs of the merged lvbb 0b event categories. The term ‘Others’ summarises events from tHjb, tWh, tttt, and SM Vh production. The background prediction is shown after a background-only maximum-likelihood fit to data. The individual background uncertainty does not take into account the possible correlations between the nuisance parameter. The expected signal contributions assuming $m_{H^{\pm}}$ = 900 GeV and $m_{H^{\pm}}$ = 2000 GeV, normalised the expected limit of the cross-section times branching ratio ($\sigma_{sig}$ × B) values of 0.036 pb and 2.7 fb respectively, are shown as dashed histograms.

The mWh distributions in the Low-NN-score SRs of the merged lvbb 1b event categories. The term ‘Others’ summarises events from tHjb, tWh, tttt, and SM Vh production. The background prediction is shown after a background-only maximum-likelihood fit to data. The individual background uncertainty does not take into account the possible correlations between the nuisance parameter. The expected signal contributions assuming $m_{H^{\pm}}$ = 900 GeV and $m_{H^{\pm}}$ = 2000 GeV, normalised the expected limit of the cross-section times branching ratio ($\sigma_{sig}$ × B) values of 0.036 pb and 2.7 fb respectively, are shown as dashed histograms.

The mWh distributions in the Medium-NN-score SRs of the merged lvbb 0b event categories. The term ‘Others’ summarises events from tHjb, tWh, tttt, and SM Vh production. The background prediction is shown after a background-only maximum-likelihood fit to data. The individual background uncertainty does not take into account the possible correlations between the nuisance parameter. The expected signal contributions assuming $m_{H^{\pm}}$ = 900 GeV and $m_{H^{\pm}}$ = 2000 GeV, normalised the expected limit of the cross-section times branching ratio ($\sigma_{sig}$ × B) values of 0.036 pb and 2.7 fb respectively, are shown as dashed histograms.

The mWh distributions in the Medium-NN-score SRs of the merged lvbb 1b event categories. The term ‘Others’ summarises events from tHjb, tWh, tttt, and SM Vh production. The background prediction is shown after a background-only maximum-likelihood fit to data. The individual background uncertainty does not take into account the possible correlations between the nuisance parameter. The expected signal contributions assuming $m_{H^{\pm}}$ = 900 GeV and $m_{H^{\pm}}$ = 2000 GeV, normalised the expected limit of the cross-section times branching ratio ($\sigma_{sig}$ × B) values of 0.036 pb and 2.7 fb respectively, are shown as dashed histograms.

The mWh distributions in the High-NN-score SRs of the merged lvbb 0b event categories. The term ‘Others’ summarises events from tHjb, tWh, tttt, and SM Vh production. The background prediction is shown after a background-only maximum-likelihood fit to data. The individual background uncertainty does not take into account the possible correlations between the nuisance parameter. The expected signal contributions assuming $m_{H^{\pm}}$ = 900 GeV and $m_{H^{\pm}}$ = 2000 GeV, normalised the expected limit of the cross-section times branching ratio ($\sigma_{sig}$ × B) values of 0.036 pb and 2.7 fb respectively, are shown as dashed histograms.

The mWh distributions in the High-NN-score SRs of the merged lvbb 1b event categories. The term ‘Others’ summarises events from tHjb, tWh, tttt, and SM Vh production. The background prediction is shown after a background-only maximum-likelihood fit to data. The individual background uncertainty does not take into account the possible correlations between the nuisance parameter. The expected signal contributions assuming $m_{H^{\pm}}$ = 900 GeV and $m_{H^{\pm}}$ = 2000 GeV, normalised the expected limit of the cross-section times branching ratio ($\sigma_{sig}$ × B) values of 0.036 pb and 2.7 fb respectively, are shown as dashed histograms.

Cutflow table for a few selected signal samples after applying the selection requirements of the resolved analysis. At the initial cut stage, all events from the tbH ± → W ± h(→ b b) production process (including those from the fully hadronic decay channel) are considered.

Cutflow table for a few selected signal samples after applying the selection requirements of the merged analysis. At the initial cut stage, all events from the tbH ± → W ± h(→ bb) production process (including those from the fully hadronic decay channel) are considered.

Expected exclusion limit $(+1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos.

Observed exclusion limit at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos.

Observed exclusion limit $(+1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos.

Observed exclusion limit $(-1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos.

Expected exclusion limit at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos.

Expected exclusion limit $(-1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos.

Expected exclusion limit $(+1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos.

Observed exclusion limit at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos.

Observed exclusion limit $(+1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos.

Observed exclusion limit $(-1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos.

Expected exclusion limit $(-1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-HM1.

Expected exclusion limit $(+1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-HM1.

Expected exclusion limit at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-HM1.

Observed exclusion limit $(+1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-HM1.

Observed exclusion limit $(-1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-HM1.

Observed exclusion limit at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-HM1.

Expected exclusion limit $(-1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-HM2.

Expected exclusion limit $(+1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-HM2.

Expected exclusion limit at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-HM2.

Observed exclusion limit $(+1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-HM2.

Observed exclusion limit $(-1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-HM2.

Observed exclusion limit at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-HM2.

Expected exclusion limit $(-1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-HM3.

Expected exclusion limit $(+1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-HM3.

Expected exclusion limit at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-HM3.

Observed exclusion limit $(+1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-HM3.

Observed exclusion limit $(-1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-HM3.

Observed exclusion limit at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-HM3.

Expected exclusion limit $(-1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-Comp1.

Expected exclusion limit $(+1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-Comp1.

Expected exclusion limit at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-Comp1.

Observed exclusion limit $(+1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-Comp1.

Observed exclusion limit $(-1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-Comp1.

Observed exclusion limit at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-Comp1.

Expected exclusion limit $(-1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-Comp2.

Expected exclusion limit $(+1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-Comp2.

Expected exclusion limit at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-Comp2.

Observed exclusion limit $(+1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-Comp2.

Observed exclusion limit $(-1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-Comp2.

Observed exclusion limit at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-Comp2.

Expected exclusion limit $(-1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-Comp3.

Expected exclusion limit $(+1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-Comp3.

Expected exclusion limit at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-Comp3.

Observed exclusion limit $(+1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-Comp3.

Observed exclusion limit $(-1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-Comp3.

Observed exclusion limit at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-Comp3.

Expected exclusion limit $(-1\sigma)$ at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-Comp-1c.

Expected exclusion limit at 95% CL for pair production of top squarks decaying to charm quarks and neutralinos when only considering SR-Comp-1c.

Expected exclusion limit at 95% CL for pair production of top squarks decaying to top or charm quarks and 1 GeV neutralinos for different branching fraction assumptions.

Expected exclusion limit $(-1\sigma)$ at 95% CL for pair production of top squarks decaying to top or charm quarks and 1 GeV neutralinos for different branching fraction assumptions.

Expected exclusion limit $(+1\sigma)$ at 95% CL for pair production of top squarks decaying to top or charm quarks and 1 GeV neutralinos for different branching fraction assumptions.

Observed exclusion limit at 95% CL for pair production of top squarks decaying to top or charm quarks and 1 GeV neutralinos for different branching fraction assumptions.

Observed exclusion limit $(+1\sigma)$ at 95% CL for pair production of top squarks decaying to top or charm quarks and 1 GeV neutralinos for different branching fraction assumptions.

Observed exclusion limit $(-1\sigma)$ at 95% CL for pair production of top squarks decaying to top or charm quarks and 1 GeV neutralinos for different branching fraction assumptions.

Expected exclusion limit at 95% CL for pair production of top squarks decaying to top or charm quarks and 200 GeV neutralinos for different branching fraction assumptions.

Expected exclusion limit $(-1\sigma)$ at 95% CL for pair production of top squarks decaying to top or charm quarks and 200 GeV neutralinos for different branching fraction assumptions.

Expected exclusion limit $(+1\sigma)$ at 95% CL for pair production of top squarks decaying to top or charm quarks and 200 GeV neutralinos for different branching fraction assumptions.

Observed exclusion limit at 95% CL for pair production of top squarks decaying to top or charm quarks and 200 GeV neutralinos for different branching fraction assumptions.

Observed exclusion limit $(+1\sigma)$ at 95% CL for pair production of top squarks decaying to top or charm quarks and 200 GeV neutralinos for different branching fraction assumptions.

Observed exclusion limit $(-1\sigma)$ at 95% CL for pair production of top squarks decaying to top or charm quarks and 200 GeV neutralinos for different branching fraction assumptions.

Expected exclusion limit $(-1\sigma)$ at 95% CL for pair production of up-type scalar LQs coupled to first generation leptons and second generation quarks.

Expected exclusion limit $(+1\sigma)$ at 95% CL for pair production of up-type scalar LQs coupled to first generation leptons and second generation quarks.

Expected exclusion limit at 95% CL for pair production of up-type scalar LQs coupled to first generation leptons and second generation quarks.

Observed exclusion limit $(+1\sigma)$ at 95% CL for pair production of up-type scalar LQs coupled to first generation leptons and second generation quarks.

Observed exclusion limit $(-1\sigma)$ at 95% CL for pair production of up-type scalar LQs coupled to first generation leptons and second generation quarks.

Observed exclusion limit at 95% CL for pair production of up-type scalar LQs coupled to first generation leptons and second generation quarks.

Expected exclusion limit $(-1\sigma)$ at 95% CL for pair production of up-type scalar LQs coupled to second generation leptons and quarks.

Expected exclusion limit $(+1\sigma)$ at 95% CL for pair production of up-type scalar LQs coupled to second generation leptons and quarks.

Expected exclusion limit at 95% CL for pair production of up-type scalar LQs coupled to second generation leptons and quarks.

Observed exclusion limit $(+1\sigma)$ at 95% CL for pair production of up-type scalar LQs coupled to second generation leptons and quarks.

Observed exclusion limit $(-1\sigma)$ at 95% CL for pair production of up-type scalar LQs coupled to second generation leptons and quarks.

Observed exclusion limit at 95% CL for pair production of up-type scalar LQs coupled to second generation leptons and quarks.

Observed upper limit on the cross-section at 95% CL for pair production of top squarks decaying into charm quarks and neutralinos for the fit with the best expected CL$_\mathrm{S}$.

Observed upper limit on the cross-section for pair production of up-type scalar LQs coupled to first generation leptons and second generation quarks.

Observed upper limit on the cross-section for pair production of up-type scalar LQs coupled to second generation leptons and quarks.

Expected upper limit on the cross-section $(-1\sigma)$ for $U(1)$ vector LQ models in the minimal coupling scenario with $\beta_{23}=1$, corresponding to a branching fraction $\mathcal{B}(\mathrm{vLQ}^\mathrm{u,min}_{23}\rightarrow c\nu) = 0.5$.

Expected upper limit on the cross-section $(+1\sigma)$ for $U(1)$ vector LQ models in the minimal coupling scenario with $\beta_{23}=1$, corresponding to a branching fraction $\mathcal{B}(\mathrm{vLQ}^\mathrm{u,min}_{23}\rightarrow c\nu) = 0.5$.

Expected upper limit on the cross-section for $U(1)$ vector LQ models in the minimal coupling scenario with $\beta_{23}=1$, corresponding to a branching fraction $\mathcal{B}(\mathrm{vLQ}^\mathrm{u,min}_{23}\rightarrow c\nu) = 0.5$.

Observed upper limit on the cross-section for $U(1)$ vector LQ models in the minimal coupling scenario with $\beta_{23}=1$, corresponding to a branching fraction $\mathcal{B}(\mathrm{vLQ}^\mathrm{u,min}_{23}\rightarrow c\nu) = 0.5$.

Expected upper limit on the cross-section $(-1\sigma)$ for $U(1)$ vector LQ models in the Yang-Mills coupling scenario with $\beta_{23}=1$, corresponding to a branching fraction $\mathcal{B}(\mathrm{vLQ}^\mathrm{u,YM}_{23}\rightarrow c\nu) = 0.5$.

Expected upper limit on the cross-section $(+1\sigma)$ for $U(1)$ vector LQ models in the Yang-Mills coupling scenario with $\beta_{23}=1$, corresponding to a branching fraction $\mathcal{B}(\mathrm{vLQ}^\mathrm{u,YM}_{23}\rightarrow c\nu) = 0.5$.

Expected upper limit on the cross-section for $U(1)$ vector LQ models in the Yang-Mills coupling scenario with $\beta_{23}=1$, corresponding to a branching fraction $\mathcal{B}(\mathrm{vLQ}^\mathrm{u,YM}_{23}\rightarrow c\nu) = 0.5$.

Observed upper limit on the cross-section for $U(1)$ vector LQ models in the Yang-Mills coupling scenario with $\beta_{23}=1$, corresponding to a branching fraction $\mathcal{B}(\mathrm{vLQ}^\mathrm{u,YM}_{23}\rightarrow c\nu) = 0.5$.

Distribution of $R_{\mathrm{ISR}}$ in SR-Comp-1c showing the data and the expected backgrounds, after simultaneously fitting all the control regions. The pre-fit yields for a representative $m(\tilde{t}_1,\tilde{\chi}_1^0)=(450,430)$ GeV signal is included. Processes with top quarks and multiple vector bosons are included in "Other". The right-most bin does not include the overflow entry but the $x$-axis range is chosen to include all observed data.

Distribution of $E_\mathrm{T}^\mathrm{miss}\mathrm{ Sig.}$ in SR-HM1 showing the data and the expected backgrounds, after simultaneously fitting all the control regions. The pre-fit yields for a representative $m(\tilde{t}_1,\tilde{\chi}_1^0)=(1000,1)$ GeV signal is included. Processes with top quarks and multiple vector bosons are included in "Other". The right-most bin does not include the overflow entry but the $x$-axis range is chosen to include all observed data.

Distribution of $m_{\mathrm{T}}^{\mathrm{min}}(c)$ in SR-HM2 showing the data and the expected backgrounds, after simultaneously fitting all the control regions. The pre-fit yields for a representative $m(\tilde{t}_1,\tilde{\chi}_1^0)=(750,450)$ GeV signal is included. Processes with top quarks and multiple vector bosons are included in "Other". The right-most bin does not include the overflow entry but the $x$-axis range is chosen to include all observed data.

Distribution of $R_{\mathrm{ISR}}$ in SR-Comp1 showing the data and the expected backgrounds, after simultaneously fitting all the control regions. The pre-fit yields for a representative $m(\tilde{t}_1,\tilde{\chi}_1^0)=(600,550)$ GeV signal is included. Processes with top quarks and multiple vector bosons are included in "Other". The right-most bin does not include the overflow entry but the $x$-axis range is chosen to include all observed data.

Distribution of $R_{\mathrm{ISR}}$ in SR-Comp2 showing the data and the expected backgrounds, after simultaneously fitting all the control regions. The pre-fit yields for a representative $m(\tilde{t}_1,\tilde{\chi}_1^0)=(550,470)$ GeV signal is included. Processes with top quarks and multiple vector bosons are included in "Other". The right-most bin does not include the overflow entry but the $x$-axis range is chosen to include all observed data.

Distribution of $R_{\mathrm{ISR}}$ in SR-Comp3 showing the data and the expected backgrounds, after simultaneously fitting all the control regions. The pre-fit yields for a representative $m(\tilde{t}_1,\tilde{\chi}_1^0)=(550,375)$ GeV signal is included. Processes with top quarks and multiple vector bosons are included in "Other". The right-most bin does not include the overflow entry but the $x$-axis range is chosen to include all observed data.

Acceptance across the SUSY signal grid for SR-Comp-1c.

Acceptance across the SUSY signal grid for SR-HM1.

Acceptance across the SUSY signal grid for SR-HM2.

Acceptance across the SUSY signal grid for SR-HM3.

Acceptance across the SUSY signal grid for SR-HM-Disc.

Acceptance across the SUSY signal grid for SR-Comp1.

Acceptance across the SUSY signal grid for SR-Comp2.

Acceptance across the SUSY signal grid for SR-Comp3.

Acceptance across the $\mathrm{LQ}^\mathrm{u}_{21}$ signal grid for SR-HM1.

Acceptance across the $\mathrm{LQ}^\mathrm{u}_{21}$ signal grid for SR-HM2.

Acceptance across the $\mathrm{LQ}^\mathrm{u}_{21}$ signal grid for SR-HM3.

Acceptance across the $\mathrm{LQ}^\mathrm{u}_{21}$ signal grid for SR-HM-Disc.

Acceptance across the $\mathrm{LQ}^\mathrm{u}_{22}$ signal grid for SR-HM1.

Acceptance across the $\mathrm{LQ}^\mathrm{u}_{22}$ signal grid for SR-HM2.

Acceptance across the $\mathrm{LQ}^\mathrm{u}_{22}$ signal grid for SR-HM3.

Acceptance across the $\mathrm{LQ}^\mathrm{u}_{22}$ signal grid for SR-HM-Disc.

Acceptance for the $\mathrm{vLQ}^\mathrm{u,min}_{23}$ signal model in SR-HM1.

Acceptance for the $\mathrm{vLQ}^\mathrm{u,min}_{23}$ signal model in SR-HM2.

Acceptance for the $\mathrm{vLQ}^\mathrm{u,min}_{23}$ signal model in SR-HM3.

Acceptance for the $\mathrm{vLQ}^\mathrm{u,min}_{23}$ signal model in SR-HM-Disc.

Acceptance for the $\mathrm{vLQ}^\mathrm{u,YM}_{23}$ signal model in SR-HM1.

Acceptance for the $\mathrm{vLQ}^\mathrm{u,YM}_{23}$ signal model in SR-HM2.

Acceptance for the $\mathrm{vLQ}^\mathrm{u,YM}_{23}$ signal model in SR-HM3.

Acceptance for the $\mathrm{vLQ}^\mathrm{u,YM}_{23}$ signal model in SR-HM-Disc.

Efficiency for the $\mathrm{vLQ}^\mathrm{u,min}_{23}$ signal model in SR-HM1. Due to the limited statistical power of the signal samples, efficiencies can fluctuate and can drop to zero.

Efficiency for the $\mathrm{vLQ}^\mathrm{u,min}_{23}$ signal model in SR-HM2. Due to the limited statistical power of the signal samples, efficiencies can fluctuate and can drop to zero.

Efficiency for the $\mathrm{vLQ}^\mathrm{u,min}_{23}$ signal model in SR-HM3. Due to the limited statistical power of the signal samples, efficiencies can fluctuate and can drop to zero.

Efficiency for the $\mathrm{vLQ}^\mathrm{u,min}_{23}$ signal model in SR-HM-Disc. Due to the limited statistical power of the signal samples, efficiencies can fluctuate and can drop to zero.

Efficiency for the $\mathrm{vLQ}^\mathrm{u,YM}_{23}$ signal model in SR-HM1. Due to the limited statistical power of the signal samples, efficiencies can fluctuate and can drop to zero.

Efficiency for the $\mathrm{vLQ}^\mathrm{u,YM}_{23}$ signal model in SR-HM2. Due to the limited statistical power of the signal samples, efficiencies can fluctuate and can drop to zero.

Efficiency for the $\mathrm{vLQ}^\mathrm{u,YM}_{23}$ signal model in SR-HM3. Due to the limited statistical power of the signal samples, efficiencies can fluctuate and can drop to zero.

Efficiency for the $\mathrm{vLQ}^\mathrm{u,YM}_{23}$ signal model in SR-HM-Disc. Due to the limited statistical power of the signal samples, efficiencies can fluctuate and can drop to zero.

Acceptance times efficiency across the SUSY signal grid for SR-Comp-1c.

Acceptance times efficiency across the SUSY signal grid for SR-HM1.

Acceptance times efficiency across the SUSY signal grid for SR-HM2.

Acceptance times efficiency across the SUSY signal grid for SR-HM3.

Acceptance times efficiency across the SUSY signal grid for SR-HM-Disc.

Acceptance times efficiency across the SUSY signal grid for SR-Comp1.

Acceptance times efficiency across the SUSY signal grid for SR-Comp2.

Acceptance times efficiency across the SUSY signal grid for SR-Comp3.

Acceptance times efficiency across the $\mathrm{LQ}^\mathrm{u}_{21}$ signal grid for SR-HM1.

Acceptance times efficiency across the $\mathrm{LQ}^\mathrm{u}_{21}$ signal grid for SR-HM2.

Acceptance times efficiency across the $\mathrm{LQ}^\mathrm{u}_{21}$ signal grid for SR-HM3.

Acceptance times efficiency across the $\mathrm{LQ}^\mathrm{u}_{21}$ signal grid for SR-HM-Disc.

Acceptance times efficiency across the $\mathrm{LQ}^\mathrm{u}_{22}$ signal grid for SR-HM1.

Acceptance times efficiency across the $\mathrm{LQ}^\mathrm{u}_{22}$ signal grid for SR-HM2.

Acceptance times efficiency across the $\mathrm{LQ}^\mathrm{u}_{22}$ signal grid for SR-HM3.

Acceptance times efficiency across the $\mathrm{LQ}^\mathrm{u}_{22}$ signal grid for SR-HM-Disc.

Acceptance times efficiency for the $\mathrm{vLQ}^\mathrm{u,min}_{23}$ signal model in SR-HM1.

Acceptance times efficiency for the $\mathrm{vLQ}^\mathrm{u,min}_{23}$ signal model in SR-HM2.

Acceptance times efficiency for the $\mathrm{vLQ}^\mathrm{u,min}_{23}$ signal model in SR-HM3.

Acceptance times efficiency for the $\mathrm{vLQ}^\mathrm{u,min}_{23}$ signal model in SR-HM-Disc.

Acceptance times efficiency for the $\mathrm{vLQ}^\mathrm{u,YM}_{23}$ signal model in SR-HM1.

Acceptance times efficiency for the $\mathrm{vLQ}^\mathrm{u,YM}_{23}$ signal model in SR-HM2.

Acceptance times efficiency for the $\mathrm{vLQ}^\mathrm{u,YM}_{23}$ signal model in SR-HM3.

Acceptance times efficiency for the $\mathrm{vLQ}^\mathrm{u,YM}_{23}$ signal model in SR-HM-Disc.

Cutflow table for SR-Comp-1c using the $m(\tilde{t}_{1},\tilde{\chi}_{1}^{0}) = (450,430)$ GeV signal point as the benchmark. All jet-related variables use jets with $p_\mathrm{T}>20$ GeV. The "Preselection" requirement includes: $E_\mathrm{T}^\mathrm{miss}>250$ GeV; events containing electrons or muons are vetoed; at least two jets must be present of which at least one must be identified as a $c$-tagged jet; events with jets that have been identified as $b$-tagged are discarded; the minimum azimuthal angular ($\phi$) distance between the (up to) four leading jets and the $\vec{p}_\mathrm{T}^\mathrm{miss}$ is required to be greater than 0.4.

Cutflow table for SR-Comp1 using the $m(\tilde{t}_{1},\tilde{\chi}_{1}^{0}) = (600,550)$ GeV signal point as the benchmark. All jet-related variables use jets with $p_\mathrm{T}>20$ GeV. The "Preselection" requirement includes: $E_\mathrm{T}^\mathrm{miss}>250$ GeV; events containing electrons or muons are vetoed; at least two jets must be present of which at least one must be identified as a $c$-tagged jet; events with jets that have been identified as $b$-tagged are discarded; the minimum azimuthal angular ($\phi$) distance between the (up to) four leading jets and the $\vec{p}_\mathrm{T}^\mathrm{miss}$ is required to be greater than 0.4.

Cutflow table for SR-Comp2 using the $m(\tilde{t}_{1},\tilde{\chi}_{1}^{0}) = (550,470)$ GeV signal point as the benchmark. All jet-related variables use jets with $p_\mathrm{T}>20$ GeV. The "Preselection" requirement includes: $E_\mathrm{T}^\mathrm{miss}>250$ GeV; events containing electrons or muons are vetoed; at least two jets must be present of which at least one must be identified as a $c$-tagged jet; events with jets that have been identified as $b$-tagged are discarded; the minimum azimuthal angular ($\phi$) distance between the (up to) four leading jets and the $\vec{p}_\mathrm{T}^\mathrm{miss}$ is required to be greater than 0.4.

Cutflow table for SR-Comp3 using the $m(\tilde{t}_{1},\tilde{\chi}_{1}^{0}) = (550,375)$ GeV signal point as the benchmark. All jet-related variables use jets with $p_\mathrm{T}>20$ GeV. The "Preselection" requirement includes: $E_\mathrm{T}^\mathrm{miss}>250$ GeV; events containing electrons or muons are vetoed; at least two jets must be present of which at least one must be identified as a $c$-tagged jet; events with jets that have been identified as $b$-tagged are discarded; the minimum azimuthal angular ($\phi$) distance between the (up to) four leading jets and the $\vec{p}_\mathrm{T}^\mathrm{miss}$ is required to be greater than 0.4.

Cutflow table for SR-HM1 using the $m(\tilde{t}_{1},\tilde{\chi}_{1}^{0}) = (1000,1)$ GeV signal point as the benchmark. All jet-related variables use jets with $p_\mathrm{T}>40$ GeV, however, the $E_\mathrm{T}^\mathrm{miss}$ is calculated with jets with $p_\mathrm{T}>20$ GeV. The "Preselection" requirement includes: $E_\mathrm{T}^\mathrm{miss}>250$ GeV; events containing electrons or muons are vetoed; at least two jets must be present of which at least one must be identified as a $c$-tagged jet; events with jets that have been identified as $b$-tagged are discarded; the minimum azimuthal angular ($\phi$) distance between the (up to) four leading jets and the $\vec{p}_\mathrm{T}^\mathrm{miss}$ is required to be greater than 0.4.

Cutflow table for SR-HM2 using the $m(\tilde{t}_{1},\tilde{\chi}_{1}^{0}) = (750,450)$ GeV signal point as the benchmark. All jet-related variables use jets with $p_\mathrm{T}>40$ GeV, however, the $E_\mathrm{T}^\mathrm{miss}$ is calculated with jets with $p_\mathrm{T}>20$ GeV. The "Preselection" requirement includes: $E_\mathrm{T}^\mathrm{miss}>250$ GeV; events containing electrons or muons are vetoed; at least two jets must be present of which at least one must be identified as a $c$-tagged jet; events with jets that have been identified as $b$-tagged are discarded; the minimum azimuthal angular ($\phi$) distance between the (up to) four leading jets and the $\vec{p}_\mathrm{T}^\mathrm{miss}$ is required to be greater than 0.4.

Cutflow table for SR-HM3 using the $m(\tilde{t}_{1},\tilde{\chi}_{1}^{0}) = (750,450)$ GeV signal point as the benchmark. All jet-related variables use jets with $p_\mathrm{T}>40$ GeV, however, the $E_\mathrm{T}^\mathrm{miss}$ is calculated with jets with $p_\mathrm{T}>20$ GeV. The "Preselection" requirement includes: $E_\mathrm{T}^\mathrm{miss}>250$ GeV; events containing electrons or muons are vetoed; at least two jets must be present of which at least one must be identified as a $c$-tagged jet; events with jets that have been identified as $b$-tagged are discarded; the minimum azimuthal angular ($\phi$) distance between the (up to) four leading jets and the $\vec{p}_\mathrm{T}^\mathrm{miss}$ is required to be greater than 0.4.

Cutflow table for SR-HM-Disc using the $m(\tilde{t}_{1},\tilde{\chi}_{1}^{0}) = (750,450)$ GeV signal point as the benchmark. All jet-related variables use jets with $p_\mathrm{T}>40$ GeV, however, the $E_\mathrm{T}^\mathrm{miss}$ is calculated with jets with $p_\mathrm{T}>20$ GeV. The "Preselection" requirement includes: $E_\mathrm{T}^\mathrm{miss}>250$ GeV; events containing electrons or muons are vetoed; at least two jets must be present of which at least one must be identified as a $c$-tagged jet; events with jets that have been identified as $b$-tagged are discarded; the minimum azimuthal angular ($\phi$) distance between the (up to) four leading jets and the $\vec{p}_\mathrm{T}^\mathrm{miss}$ is required to be greater than 0.4.

Cutflow table for SR-HM1 using the $m(\mathrm{LQ}_{21}^\mathrm{u}) = 600$ GeV signal point, with a 50% branching fraction to $c\nu$, as the benchmark. All jet-related variables use jets with $p_\mathrm{T}>40$ GeV, however, the $E_\mathrm{T}^\mathrm{miss}$ is calculated with jets with $p_\mathrm{T}>20$ GeV. The "Preselection" requirement includes: $E_\mathrm{T}^\mathrm{miss}>250$ GeV; events containing electrons or muons are vetoed; at least two jets must be present of which at least one must be identified as a $c$-tagged jet; events with jets that have been identified as $b$-tagged are discarded; the minimum azimuthal angular ($\phi$) distance between the (up to) four leading jets and the $\vec{p}_\mathrm{T}^\mathrm{miss}$ is required to be greater than 0.4.

Cutflow table for SR-HM2 using the $m(\mathrm{LQ}_{21}^\mathrm{u}) = 600$ GeV signal point, with a 50% branching fraction to $c\nu$, as the benchmark. All jet-related variables use jets with $p_\mathrm{T}>40$ GeV, however, the $E_\mathrm{T}^\mathrm{miss}$ is calculated with jets with $p_\mathrm{T}>20$ GeV. The "Preselection" requirement includes: $E_\mathrm{T}^\mathrm{miss}>250$ GeV; events containing electrons or muons are vetoed; at least two jets must be present of which at least one must be identified as a $c$-tagged jet; events with jets that have been identified as $b$-tagged are discarded; the minimum azimuthal angular ($\phi$) distance between the (up to) four leading jets and the $\vec{p}_\mathrm{T}^\mathrm{miss}$ is required to be greater than 0.4.

Cutflow table for SR-HM3 using the $m(\mathrm{LQ}_{21}^\mathrm{u}) = 600$ GeV signal point, with a 50% branching fraction to $c\nu$, as the benchmark. All jet-related variables use jets with $p_\mathrm{T}>40$ GeV, however, the $E_\mathrm{T}^\mathrm{miss}$ is calculated with jets with $p_\mathrm{T}>20$ GeV. The "Preselection" requirement includes: $E_\mathrm{T}^\mathrm{miss}>250$ GeV; events containing electrons or muons are vetoed; at least two jets must be present of which at least one must be identified as a $c$-tagged jet; events with jets that have been identified as $b$-tagged are discarded; the minimum azimuthal angular ($\phi$) distance between the (up to) four leading jets and the $\vec{p}_\mathrm{T}^\mathrm{miss}$ is required to be greater than 0.4.

Cutflow table for SR-HM-Disc using the $m(\mathrm{LQ}_{21}^\mathrm{u}) = 600$ GeV signal point, with a 50% branching fraction to $c\nu$, as the benchmark. All jet-related variables use jets with $p_\mathrm{T}>40$ GeV, however, the $E_\mathrm{T}^\mathrm{miss}$ is calculated with jets with $p_\mathrm{T}>20$ GeV. The "Preselection" requirement includes: $E_\mathrm{T}^\mathrm{miss}>250$ GeV; events containing electrons or muons are vetoed; at least two jets must be present of which at least one must be identified as a $c$-tagged jet; events with jets that have been identified as $b$-tagged are discarded; the minimum azimuthal angular ($\phi$) distance between the (up to) four leading jets and the $\vec{p}_\mathrm{T}^\mathrm{miss}$ is required to be greater than 0.4.

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.

The figure shows the post-fit distribution of events as a function of $H_{\mathrm{T}}^{\ell,j} = \sum_{\ell,j} p_{T}^{\ell,j}$, scalar sum of $p_T$ for all jets and leptons in the $\ell+$jets channel, in proton-lead (p+Pb) collisions at a center-of-mass energy of $\sqrt{s_{\mathrm{NN}}} = 8.16$ TeV, with an integrated luminosity of 165 nb$^{-1}$. The data correspond to the $1\ell 1b$ $\mu$+jets channel in a pre-fit configuration. The stacked histograms represent different processes contributing to the event yield, including top quark pair production ($t\bar{t}$), single top, $W$ boson production with $b$, $c$, and light quarks, $Z$ boson production with $b$, $c$, and light quarks, diboson, and fake lepton backgrounds.

The figure shows the pre-fit distribution of events as a function of $H_{\mathrm{T}}^{\ell,j} = \sum_{\ell,j} p_{T}^{\ell,j}$, scalar sum of $p_T$ for all jets and leptons in the $\ell+$jets channel, in proton-lead (p+Pb) collisions at a center-of-mass energy of $\sqrt{s_{\mathrm{NN}}} = 8.16$ TeV, with an integrated luminosity of 165 nb$^{-1}$. The data correspond to the $1\ell 2bincl$ $e$+jets channel in a pre-fit configuration. The stacked histograms represent different processes contributing to the event yield, including top quark pair production ($t\bar{t}$), single top, $W$ boson production with $b$, $c$, and light quarks, $Z$ boson production with $b$, $c$, and light quarks, diboson, and fake lepton backgrounds.

The figure shows the post-fit distribution of events as a function of $H_{\mathrm{T}}^{\ell,j} = \sum_{\ell,j} p_{T}^{\ell,j}$, scalar sum of $p_T$ for all jets and leptons in the $\ell+$jets channel, in proton-lead (p+Pb) collisions at a center-of-mass energy of $\sqrt{s_{\mathrm{NN}}} = 8.16$ TeV, with an integrated luminosity of 165 nb$^{-1}$. The data correspond to the $1\ell 2bincl$ $e$+jets channel in a pre-fit configuration. The stacked histograms represent different processes contributing to the event yield, including top quark pair production ($t\bar{t}$), single top, $W$ boson production with $b$, $c$, and light quarks, $Z$ boson production with $b$, $c$, and light quarks, diboson, and fake lepton backgrounds.

The figure shows the pre-fit distribution of events as a function of $H_{\mathrm{T}}^{\ell,j} = \sum_{\ell,j} p_{T}^{\ell,j}$, scalar sum of $p_T$ for all jets and leptons in the $\ell+$jets channel, in proton-lead (p+Pb) collisions at a center-of-mass energy of $\sqrt{s_{\mathrm{NN}}} = 8.16$ TeV, with an integrated luminosity of 165 nb$^{-1}$. The data correspond to the $1\ell 2bincl$ $\mu$+jets channel in a pre-fit configuration. The stacked histograms represent different processes contributing to the event yield, including top quark pair production ($t\bar{t}$), single top, $W$ boson production with $b$, $c$, and light quarks, $Z$ boson production with $b$, $c$, and light quarks, diboson, and fake lepton backgrounds.

The figure shows the post-fit distribution of events as a function of $H_{\mathrm{T}}^{\ell,j} = \sum_{\ell,j} p_{T}^{\ell,j}$, scalar sum of $p_T$ for all jets and leptons in the $\ell+$jets channel, in proton-lead (p+Pb) collisions at a center-of-mass energy of $\sqrt{s_{\mathrm{NN}}} = 8.16$ TeV, with an integrated luminosity of 165 nb$^{-1}$. The data correspond to the $1\ell 2bincl$ $\mu$+jets channel in a pre-fit configuration. The stacked histograms represent different processes contributing to the event yield, including top quark pair production ($t\bar{t}$), single top, $W$ boson production with $b$, $c$, and light quarks, $Z$ boson production with $b$, $c$, and light quarks, diboson, and fake lepton backgrounds.

The figure shows the pre-fit distribution of events as a function of $H_{\mathrm{T}}^{\ell,j} = \sum_{\ell,j} p_{T}^{\ell,j}$, scalar sum of $p_T$ for all jets and leptons in the $\ell+$jets channel, in proton-lead (p+Pb) collisions at a center-of-mass energy of $\sqrt{s_{\mathrm{NN}}} = 8.16$ TeV, with an integrated luminosity of 165 nb\(^{-1}\) in the 2\(\ell\)1b signal region. The histogram represents the number of events per GeV, with the data points shown as black dots and their associated uncertainties. The stacked colored histograms indicate different processes: \(t\bar{t}\) (red), single top (orange), \(Z+b\) (dark blue), \(Z+c\) (medium blue), \(Z+\)light (light blue), diboson (gray), and fake lepton (purple). The hatched area represents the uncertainty in the predictions.

The figure shows the post-fit distribution of events as a function of $H_{\mathrm{T}}^{\ell,j} = \sum_{\ell,j} p_{T}^{\ell,j}$, scalar sum of $p_T$ for all jets and leptons in the $\ell+$jets channel, in proton-lead (p+Pb) collisions at a center-of-mass energy of $\sqrt{s_{\mathrm{NN}}} = 8.16$ TeV, with an integrated luminosity of 165 nb\(^{-1}\) in the 2\(\ell\)1b signal region. The histogram represents the number of events per GeV, with the data points shown as black dots and their associated uncertainties. The stacked colored histograms indicate different processes: \(t\bar{t}\) (red), single top (orange), \(Z+b\) (dark blue), \(Z+c\) (medium blue), \(Z+\)light (light blue), diboson (gray), and fake lepton (purple). The hatched area represents the uncertainty in the predictions.

The figure shows the pre-fit distribution of events as a function of $H_{\mathrm{T}}^{\ell,j} = \sum_{\ell,j} p_{T}^{\ell,j}$, scalar sum of $p_T$ for all jets and leptons in the $\ell+$jets channel, in proton-lead (p+Pb) collisions at a center-of-mass energy of $\sqrt{s_{\mathrm{NN}}} = 8.16$ TeV, with an integrated luminosity of 165 nb\(^{-1}\) in the 2\(\ell\)2bincl signal region. The histogram represents the number of events per GeV, with the data points shown as black dots and their associated uncertainties. The stacked colored histograms indicate different processes: \(t\bar{t}\) (red), single top (orange), \(Z+b\) (dark blue), \(Z+c\) (medium blue), \(Z+\)light (light blue), diboson (gray), and fake lepton (purple). The hatched area represents the uncertainty in the predictions.

The figure shows the post-fit distribution of events as a function of $H_{\mathrm{T}}^{\ell,j} = \sum_{\ell,j} p_{T}^{\ell,j}$, scalar sum of $p_T$ for all jets and leptons in the $\ell+$jets channel, in proton-lead (p+Pb) collisions at a center-of-mass energy of $\sqrt{s_{\mathrm{NN}}} = 8.16$ TeV, with an integrated luminosity of 165 nb\(^{-1}\) in the 2\(\ell\)2bincl signal region. The histogram represents the number of events per GeV, with the data points shown as black dots and their associated uncertainties. The stacked colored histograms indicate different processes: \(t\bar{t}\) (red), single top (orange), \(Z+b\) (dark blue), \(Z+c\) (medium blue), \(Z+\)light (light blue), diboson (gray), and fake lepton (purple). The hatched area represents the uncertainty in the predictions.

The correlation matrix of the fit parameters for the six combined regions, including the signal regions (electron+jets: 1-lepton 1-bjet and 1-lepton 2-bjet inclusive, muon+jets: 1-lepton 1-bjet and 1-lepton 2-bjet inclusive, dilepton: 2-lepton 1-bjet and 2-lepton 2-bjet inclusive) is shown.

The impact of systematic uncertainties on the fitted signal-strength parameter $\hat{\mu}$ for the combined (six signal regions ($e+$jets: $1\ell1b$ and $1\ell2b\mathrm{incl}$, $\mu+$jets: $1\ell1b$ and $1\ell2b\mathrm{incl}$, dilepton: $2\ell1b$ and $2\ell2b\mathrm{incl}$) fit of all channels. Only the 15 most significant systematic uncertainties are shown and listed in decreasing order of their impact on $\mu$ on the $y$-axis. The empty (filled) blue/cyan boxes correspond to the pre-fit (post-fit) impact on $\mu$, referring to the upper $x$-axis. The impact of each systematic uncertainty, $\Delta \mu$, is calculated by comparing the nominal best-fit value of $\mu$ with the result of the fit when fixing the corresponding nuisance parameter $\theta$ to its best-fit value $\hat{\theta}$ shifted by its pre-fit (post-fit) uncertainties $\hat{\theta} \pm \Delta \theta(\hat{\theta} \pm \Delta \hat{\theta})$. The black points, which refer to the lower $x$-axis, show the pulls of the fitted nuisance parameters, i.e., the deviations of the fitted parameters $\hat{\theta}$ from their nominal values $\theta_0$, normalized to their nominal uncertainties $\Delta \theta$. The black lines show the post-fit uncertainties of the nuisance parameters, relative to their nominal uncertainties, which are indicated by the dashed lines.

Breakdown of relative systematic uncertainties in the measured ${t\bar{t}}$ cross-section. The quoted uncertainties are obtained by repeating the fit with a group of nuisance parameters fixed to their fitted values and subtracting in quadrature the resulting total uncertainty from the uncertainty of the complete fit. However, the total uncertainty is not the quadratic sum of the grouped impacts, as this approach neglects the correlation among the different groups.

The signal strength $\mu_{t\bar{t}}$, defined as the ratio of the observed signal for the combined six signal regions ($e+$jets: $1\ell1b$ and $1\ell2b\mathrm{incl}$, $\mu+$jets: $1\ell1b$ and $1\ell2b\mathrm{incl}$, dilepton: $2\ell1b$ and $2\ell2b\mathrm{incl}$.) to the SM expectation with no nPDF effects included, is measured using a binned profile-likelihood method. The parameter $\mu_{t\bar{t}}$ is determined by the fit to the $H_{T}^{\ell,j}$ data distributions in the six signal regions, where the $H_{T}^{\ell,j}$ variable is defined as the scalar sum of the transverse momenta of the leptons and HI jets. Over all 9% uncertainties is observed

The figure shows the measurement of the top quark pair production cross-section, $\sigma_{t\bar{t}}$, in proton-lead (p+Pb) collisions at a center-of-mass energy of $\sqrt{s_{\mathrm{NN}}} = 8.16$ TeV, based on 165 nb$^{-1}$ of data. The central measured value is shown alongside theoretical predictions using various parton distribution functions (PDFs): MCFM TUJU21, MCFM nNNPDF30, MCFM nCTEQ15HQ, and MCFM EPPS21. The green and yellow bands represent the total and statistical uncertainties of the data, respectively. Additional measurements for comparison include the CMS result at 8.16 TeV for p+Pb collisions and an extrapolated ATLAS+CMS result for pp collisions at 8 TeV. Relevant references are indicated: PRL 119 (2017) 242001 and JHEP 07 (2023) 213.

The ATLAS measurement of \( R_{p\text{Pb}} \) as a function of the nuclear modification factor in proton-lead (\( p\) + Pb) collisions at a center-of-mass energy per nucleon pair \( \sqrt{s_{NN}} = 8.16 \) TeV, with an integrated luminosity of 165 nb\(^{-1}\). The black points represent theoretical predictions from various MCFM parton distribution functions (PDFs): TUJU21, nNNPDF30, nCTEQ15HQ, and EPPS21. The green band indicates the total uncertainty of the data, while the yellow band represents the statistical uncertainty. The dashed line at \( R_{p\text{Pb}} = 1 \) shows the expected value in the absence of nuclear modifications.

Local observed significance for signal discovery at different (mX, mS). The points show where the significance was evaluated. The band at mS = 125 GeV is not shown as those points are equivalent to those already probed in Phys. Rev. D 106 (2022) 052001.

Signal region yield for each of the simulated signal samples and interpolated signal points that were analyzed in the 1 b-jet Signal Region, normalized to a cross section of 1 fb. The signal region yields for one of the signals is found in Table 2 of the paper.

Signal region yield for each of the simulated signal samples and interpolated signal points that were analyzed in the 2 b-jet Signal Region, normalized to a cross section of 1 fb. The signal region yields for one of the signals is found in Table 2 of the paper.

Figure 8(left) of the article. Differential fiducial cross-section of the Z boson $p_T$ in events with $Z (\rightarrow ll) \ge 1 $ b-jets. The thin inner band corresponds to the statistical uncertainty of the data, and the outer band to statistical and systematic uncertainties of the data, added in quadrature.

Figure 8(right) of the article. Differential fiducial cross-section of the leading $b$-jet $p_T$ in events with $Z (\rightarrow ll) \ge 1 $ b-jets. The thin inner band corresponds to the statistical uncertainty of the data, and the outer band to statistical and systematic uncertainties of the data, added in quadrature.

Figure 9 of the article. Differential fiducial cross-section of the $\Delta R$ between the $Z$ boson and the leading $b$-jet in events with $Z (\rightarrow ll) \ge 1 $ b-jets. The thin inner band corresponds to the statistical uncertainty of the data, and the outer band to statistical and systematic uncertainties of the data, added in quadrature.

Figure 10(left) of the article. Differential fiducial cross-section of the $\Delta \phi$ between the leading and sub-leading $b$-jets in events with $Z (\rightarrow ll) \ge 2 $ b-jets. The thin inner band corresponds to the statistical uncertainty of the data, and the outer band to statistical and systematic uncertainties of the data, added in quadrature.

Figure 10(right) of the article. Differential fiducial cross-section of the invariant mass of the leading and sub-leading $b$-jets in events with $Z (\rightarrow ll) \ge 2 $ b-jets. The thin inner band corresponds to the statistical uncertainty of the data, and the outer band to statistical and systematic uncertainties of the data, added in quadrature.

Figure 11(left) of the article. Differential fiducial cross-section of the Z boson $p_T$ in events with $Z (\rightarrow ll) \ge 1 $ c-jets. The thin inner band corresponds to the statistical uncertainty of the data, and the outer band to statistical and systematic uncertainties of the data, added in quadrature.

Figure 11(right) of the article. Differential fiducial cross-section of the leading $c$-jet $p_T$ in events with $Z (\rightarrow ll) \ge 1 $ c-jets. The thin inner band corresponds to the statistical uncertainty of the data, and the outer band to statistical and systematic uncertainties of the data, added in quadrature.

Figure 12 of the article. Differential fiducial cross-section of the leading $c$-jet $x_F$ in events with $Z (\rightarrow ll) \ge 1 $ c-jets. The thin inner band corresponds to the statistical uncertainty of the data, and the outer band to statistical and systematic uncertainties of the data, added in quadrature.

Correction factors from parton level done with flavour dressing algorithms as seen in Ref. [2] of the paper to hadron level with R 0.3 cone labelling (see Tables 18 & 24) for the differential cross-section of the Z boson $p_T$ in events with $Z (\rightarrow ll) \ge 1 $ b-jets. Systematic errors include Sherpa 2.2.11 and MGaMC+Py8 FxFx uncertainties for what concerns the passage from hadron level flavour dressing to hadron level cone labelling, plus statistical uncertainty of Pythia8 simulations used for parton to hadron corrections. See Table 4.

Correction factors from parton level done with flavour dressing algorithms as seen in Ref. [2] of the paper to hadron level with R 0.3 cone labelling (see Tables 19 & 25) for the differential cross-section of the Z boson $p_T$ in events with $Z (\rightarrow ll) \ge 1 $ c-jets. Systematic errors include Sherpa 2.2.11 and MGaMC+Py8 FxFx uncertainties for what concerns the passage from hadron level flavour dressing to hadron level cone labelling, plus statistical uncertainty of Pythia8 simulations used for parton to hadron corrections. See Table 9.

Correction factors from parton level done with flavour dressing algorithms as seen in Ref. [2] of the paper to hadron level with R 0.3 cone labelling (see Tables 20 & 26) for the differential cross-section of the leading $b$-jet $p_T$ in events with $Z (\rightarrow ll) \ge 1 $ b-jets. Systematic errors include Sherpa 2.2.11 and MGaMC+Py8 FxFx uncertainties for what concerns the passage from hadron level flavour dressing to hadron level cone labelling, plus statistical uncertainty of Pythia8 simulations used for parton to hadron corrections. See Table 5.

Correction factors from parton level done with flavour dressing algorithms as seen in Ref. [2] of the paper to hadron level with R 0.3 cone labelling (see Tables 21 & 27) for the differential cross-section of the leading $c$-jet $p_T$ in events with $Z (\rightarrow ll) \ge 1 $ c-jets. Systematic errors include Sherpa 2.2.11 and MGaMC+Py8 FxFx uncertainties for what concerns the passage from hadron level flavour dressing to hadron level cone labelling, plus statistical uncertainty of Pythia8 simulations used for parton to hadron corrections. See Table 10.

Correction factors from parton level done with flavour dressing algorithms as seen in Ref. [2] of the paper to hadron level with R 0.3 cone labelling (see Tables 22 & 28) for the differential cross-section of the leading $c$-jet $x_F$ in events with $Z (\rightarrow ll) \ge 1 $ c-jets. Systematic errors include Sherpa 2.2.11 and MGaMC+Py8 FxFx uncertainties for what concerns the passage from hadron level flavour dressing to hadron level cone labelling, plus statistical uncertainty of Pythia8 simulations used for parton to hadron corrections. See Table 11.

Correction factors from parton level done with flavour dressing algorithms as seen in Ref. [2] of the paper of the paper to hadron level with R 0.3 cone labelling (see Tables 23 & 29) for the differential cross-section of $\Delta R$ between the $Z$ boson and the leading $b$-jet in events with $Z (\rightarrow ll) \ge 1 $ b-jets. Systematic errors include Sherpa 2.2.11 and MGaMC+Py8 FxFx uncertainties for what concerns the passage from hadron level flavour dressing to hadron level cone labelling, plus statistical uncertainty of Pythia8 simulations used for parton to hadron corrections. See Table 6.

Correction factors from hadron level done with flavour dressing algorithms as seen in Ref. [2] of the paper to hadron level R 0.3 cone labelling for the differential cross-section of the Z boson $p_T$ in events with $Z (\rightarrow ll) \ge 1 $ b-jets. Systematic errors include Sherpa 2.2.11 and MGaMC+Py8 FxFx uncertainties. See Table 12.

Correction factors from hadron level done with flavour dressing algorithms as seen in Ref. [2] of the paper to hadron level with R 0.3 cone labelling for the differential cross-section of the Z boson $p_T$ in events with $Z (\rightarrow ll) \ge 1 $ c-jets. Systematic errors include Sherpa 2.2.11 and MGaMC+Py8 FxFx uncertainties. See Table 13.

Correction factors from hadron level done with flavour dressing algorithms as seen in Ref. [2] of the paper to hadron level with R 0.3 cone labelling for the differential cross-section of the leading $b$-jet $p_T$ in events with $Z (\rightarrow ll) \ge 1 $ b-jets. Systematic errors include Sherpa 2.2.11 and MGaMC+Py8 FxFx uncertainties. See Table 14.

Correction factors from hadron level done with flavour dressing algorithms as seen in Ref. [2] of the paper to hadron level with R 0.3 cone labelling for the differential cross-section of the leading $c$-jet $p_T$ in events with $Z (\rightarrow ll) \ge 1 $ c-jets. Systematic errors include Sherpa 2.2.11 and MGaMC+Py8 FxFx uncertainties. See Table 15.

Correction factors from hadron level done with flavour dressing algorithms as seen in Ref. [2] of the paper to hadron level with R 0.3 cone labelling for the differential cross-section of the leading $c$-jet $x_F$ in events with $Z (\rightarrow ll) \ge 1 $ c-jets. Systematic errors include Sherpa 2.2.11 and MGaMC+Py8 FxFx uncertainties. See Table 16.

Correction factors from hadron level done with flavour dressing algorithms as seen in Ref. [2] of the paper of the paper to hadron level with R 0.3 cone labelling for the differential cross-section of $\Delta R$ between the $Z$ boson and the leading $b$-jet in events with $Z (\rightarrow ll) \ge 1 $ b-jets. Systematic errors include Sherpa 2.2.11 and MGaMC+Py8 FxFx uncertainties. See Table 17.

Correction factors from parton level to hadron level for the differential cross-section of the Z boson $p_T$ in events with $Z (\rightarrow ll) \ge 1 $ b-jets. Systematic errors statistical uncertainty of Pythia8 simulations. See Table 12.

Correction factors from parton level to hadron level for the differential cross-section of the Z boson $p_T$ in events with $Z (\rightarrow ll) \ge 1 $ c-jets. Systematic errors include statistical uncertainty of Pythia8 simulations. See Table 13.

Correction factors from parton level to hadron level for the differential cross-section of the leading $b$-jet $p_T$ in events with $Z (\rightarrow ll) \ge 1 $ b-jets. Systematic errors include statistical uncertainty of Pythia8 simulations. See Table 14.

Correction factors from parton level to hadron level for the differential cross-section of the leading $c$-jet $p_T$ in events with $Z (\rightarrow ll) \ge 1 $ c-jets. Systematic errors include statistical uncertainty of Pythia8 simulations. See Table 15.

Correction factors from parton level to hadron level for the differential cross-section of the leading $c$-jet $x_F$ in events with $Z (\rightarrow ll) \ge 1 $ c-jets. Systematic errors include statistical uncertainty of Pythia8 simulations. See Table 16.

Correction factors from parton level to hadron level for the differential cross-section of $\Delta R$ between the $Z$ boson and the leading $b$-jet in events with $Z (\rightarrow ll) \ge 1 $ b-jets. Systematic errors include statistical uncertainty of Pythia8 simulations. See Table 17.

Observed event yields in $\textrm{SR}$ compared with post-fit expectations from Monte Carlo simulations, as a function of the scalar sum of lepton and jet transverse momenta, $H_{\mathrm{T}}$. The last bin includes overflow events. `Signal (prod.)' and `Signal (dec.)' refer to the single-top-quark production and top-quark pair decay signal contributions, respectively.

Expected and observed 95$\%$ CL upper limits on the branching ratio corresponding to the decay of a top quark to a muon and a tau lepton through a cLFV process for scalar, vector and tensor couplings. In the vector case, all vector operators are assumed to contribute simultaneously with the same effective coupling strength. The table shows the endpoint values of $\mathcal{B}(\mathrm{t}\to\mu\tau\mathrm{u})$ and $\mathcal{B}(\mathrm{t}\to\mu\tau\mathrm{c})$, which are interpolated linearly for each limit.

Expected and observed 95$\%$ CL upper limits on the Wilson coefficients for scalar, vector and tensor couplings of a top quark to a muon and a tau lepton through a cLFV process. In the vector case, all vector operators are assumed to contribute simultaneously with the same effective coupling strength. The table shows the endpoint values of the $|c^{\mu\tau\mathrm{ut}}|$ and $|c^{\mu\tau\mathrm{ct}}|$ Wilson coefficients, which are interpolated assuming a linear relationship between $\mathcal{B}(\mathrm{t}\to\mu\tau\mathrm{u})$ and $\mathcal{B}(\mathrm{t}\to\mu\tau\mathrm{c})$.

Observed event yields in $\textrm{SR}$ compared with pre-fit expectations from Monte Carlo simulations, as a function of the scalar sum of lepton and jet transverse momenta, $H_{\mathrm{T}}$. The last bin includes overflow events. The signal yields represent a leptoquark mass of $m_{S_{1}} = 1$ TeV and a coupling strength of $\lambda^{\textrm{LQ}} = 2.0$.

Observed event yields in $\textrm{SR}$ compared with post-fit expectations from Monte Carlo simulations, as a function of the scalar sum of lepton and jet transverse momenta, $H_{\mathrm{T}}$. The last bin includes overflow events. The signal yields represent a leptoquark mass of $m_{S_{1}} = 1$ TeV and a coupling strength of $\lambda^{\textrm{LQ}} = 2.0$.

Observed and expected exclusion 95$\%$ CL upper limits on the $S_{1}$ leptoquark coupling strength $\lambda^{\textrm{LQ}}$ as a function of LQ mass, $m_{S_{1}}$.

Theoretical cross-sections for single-top-quark production and top-quark decays through cLFV interactions involving vector, scalar and tensor EFT Wilson coefficients. The column titled as $c^{(ijk3)}_{\textrm{vector}}$ represents the individual cross-section contributions from each of $c_{\mathsf{lq}}^{-(ijk3)}$, $c_{\mathsf{eq}}^{(ijk3)}$, $c_{\mathsf{lu}}^{(ijk3)}$ and $c_{\mathsf{eu}}^{(ijk3)}$. The coefficient indices represent the lepton flavour generations ($i,j = 1,2,3$ where $i \neq j$) and light quark flavour generations ($k = 1,2$). The single-top-quark production cross-sections are quoted for $u$- and $c$-quark couplings separately, while they are combined for the $t\bar{t}$ decay process ($q_k = u,c$). The scale and PDF uncertainties are given. The value of each Wilson coefficient is set to 1.0 for the calculation of the cross-section.

Requirements for each analysis region. The symbol $\ell_{3}$ denotes the lowest $p_{\mathrm{T}}$ lepton. In $\mathrm{CR}t\bar{t}\mu$ an additional requirement is placed on the leading muon $p_{\mathrm{T}}$ ($p^{\mu_1}_\mathrm{T}$) and dilepton invariant masses in order to reject signal events.

Post-fit event yields for each analysis region entering the fit, with correlations on the full systematic uncertainties taken into account as determined in the fit under a signal+background hypothesis. The 'fake electron' category in the CR$t\bar{t}\mu$ control region collects small contributions primarily from $t\bar{t}\gamma$ and $Z\gamma$ which enter the event selection due to photon conversions.

Expected and observed 95$\%$ CL upper limits on Wilson coefficients corresponding to 2Q2L EFT operators which could introduce a cLFV top decay in the $\mu\tau$ channel, and existing limits from JHEP04 (2019) 014 (previous). The previous limits shown for $c^{1(ijk3)}_{\mathsf{lequ}}$ and $c^{3(ijk3)}_{\mathsf{lequ}}$ are tightened by a factor of $\sqrt{2}$, as JHEP04 (2019) 014 does not assume that these operators are Hermitian. Results are shown separately for the $\mu\tau ut$ and $\mu\tau ct$ interactions. The lepton generations are denoted by $i,j=2,3$ for $\mu$ and $\tau$ (where $i \neq j$) and the quark generations are denoted by $k=1,2$ for $u$ and $c$, respectively.

Expected and observed 95$\%$ CL upper limits on the branching ratio ($\mathcal{B}$) corresponding to the decay of a top quark to a muon and a $\tau$ lepton through a cLFV process using specific Wilson coefficients corresponding to 2Q2L EFT operators. Results are shown separately for $\mu\tau ut$ and $\mu\tau ct$ interactions. The lepton generations are denoted by $i,j=2,3$ for $\mu$ and $\tau$ (where $i \neq j$) and the quark generations are denoted by $k=1,2$ for $u$ and $c$, respectively.

Expected and observed 95% CL upper limits on the inclusive branching ratio ($\mathcal{B}$) corresponding to the decay of a top quark to a muon and a $\tau$-lepton through a cLFV process. Limits are shown for the statistical uncertainty only and for the full set of statistical and systematic uncertainties.

Expected and observed 95$\%$ CL upper limits on the Wilson coefficients corresponding to EFT operators inducing the decay of a top quark to a muon, a tau lepton and an up quark through a cLFV process ($\mu\tau ut$ interaction).

Expected and observed 95$\%$ CL upper limits on the Wilson coefficients corresponding to EFT operators inducing the decay of a top quark to a muon, a tau lepton and a charm quark through a cLFV process ($\mu\tau ct$ interaction).

Ranking of nuisance parameters by post-fit impact on cLFV signal strength $\mu$ (the parameter of interest, POI). The pre-fit (post-fit) impact of each nuisance parameter is calculated as the difference to the fitted value of cLFV signal strength between the nominal fit and a 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. The pulls of the nuisance parameters are calculated relative to zero. These pulls and their post-fit errors, $\Delta\hat{\theta} / \Delta\theta$, are given in the second column of the table.

The impact of the eight most important systematic uncertainties on \(R_t\), in %.

The post-fit yields in the two SRs. All uncertainties applied in the analysis are included.

Limits on EFT parameters and Vtb extracted from the analysis. The upper and lower limits correspond to 95% CL.

Results of the main analysis.

Pre-fit distribution of the NN discriminant \(D_{\text{nn}}\) in SR plus.

Post-fit distribution of the NN discriminant \(D_{\text{nn}}\) in SR plus.

Post-fit distribution of the \(\Delta\phi(\vec{p}_{T}^{miss},\mu)\) variable in the muon-plus CR.

Pre-fit distribution of the NN discriminant \(D_{\text{nn}}\) in SR minus.

Post-fit distribution of the NN discriminant \(D_{\text{nn}}\) in SR minus.

Post-fit distribution of the \(\Delta\phi(\vec{p}_{T}^{miss},\mu)\) variable in the muon-minus CR.

Pre-fit distribution of the invariant mass of the untagged jet and the b-tagged jet, \(m(jb)\), in SR plus.

Pre-fit distribution of the absolute value of the pseudorapidity of the untagged jet, \(|\eta(j)|\), in SR plus.

Pre-fit distribution of the absolute value of the difference in \(p_{\text{T}}\) between the reconstructed W boson and the jet pair, \(|\Delta p_{\text{T}}(W, jb)|\), in SR plus.

Pre-fit distribution of the difference in azimuth angle between the reconstructed W boson and the jet pair, \(|\Delta\phi(W, jb)|\), in SR plus.

Pre-fit distribution of the invariant mass of the reconstructed top quark, \(m(t)\), in SR plus.

Pre-fit distribution of the absolute value of the difference in pseudorapidity between the charged lepton and the untagged jet, \(|\Delta\eta(\ell ,j)|\), SR plus.

Pre-fit distribution of the angular distance of the charged lepton and the untagged jet, \(\Delta R(\ell ,j)\), in SR plus.

Pre-fit distribution of the absolute value of the difference in pseudorapidity between the b-tagged jet and the charged lepton, \(|\Delta\eta(b,\ell )|\), in SR plus.

Fraction of events where both bosons are longitudinally polarized in the region with $p_T^Z>200$ GeV using two unconstrained parameters.

Numbers of observed and expected events in the 00-enhanced signal regions, before the fit. The total uncertainties are quoted.

Summary of the relative uncertainties in the measured longitudinal-longitudinal fractions $f_{00}$. The uncertainties are reported as percentages.

Numbers of observed and expected events in the 00-enhanced signal regions, after the fit. The total uncertainties are quoted.

$|\Delta Y(l_{W}Z)|$ Migration matrix RAZ Region $p_{T}^{WZ}< 20$ GeV of the TT state.

$|\Delta Y(l_{W}Z)|$ Migration matrix RAZ Region $p_{T}^{WZ}< 40$ GeV of the TT state.

$|\Delta Y(l_{W}Z)|$ Migration matrix RAZ Region $p_{T}^{WZ}< 70$ GeV of the TT state.

$|\Delta Y(l_{W}Z)|$ Migration matrix RAZ Region $p_{T}^{WZ}< 20$ GeV of of the sum of all polarization.

$|\Delta Y(l_{W}Z)|$ Migration matrix RAZ Region $p_{T}^{WZ}< 40$ GeV of of the sum of all polarization.

$|\Delta Y(l_{W}Z)|$ Migration matrix RAZ Region $p_{T}^{WZ}< 70$ GeV of of the sum of all polarization.

$|\Delta Y(WZ)|$ Migration matrix RAZ Region $p_{T}^{WZ}< 20$ GeV of the TT state.

$|\Delta Y(WZ)|$ Migration matrix RAZ Region $p_{T}^{WZ}< 40$ GeV of the TT state.

$|\Delta Y(WZ)|$ Migration matrix RAZ Region $p_{T}^{WZ}< 70$ GeV of the TT state.

$|\Delta Y(WZ)|$ Migration matrix RAZ Region $p_{T}^{WZ}< 20$ GeV of of the sum of all polarization.

$|\Delta Y(WZ)|$ Migration matrix RAZ Region $p_{T}^{WZ}< 40$ GeV of of the sum of all polarization.

$|\Delta Y(WZ)|$ Migration matrix RAZ Region $p_{T}^{WZ}< 70$ GeV of of the sum of all polarization.

The $\mathcal{D}$ value for the unfolded $|\Delta Y(l_{W}Z)|$ distributions of the TT polarization state as a function of the $p_T^{WZ}$ cut value.

The $\mathcal{D}$ value for the unfolded $|\Delta Y(WZ)|$ distributions of the TT polarization state as a function of the $p_T^{WZ}$ cut value.

Measured normalized differential $|\Delta Y(l_{W}Z)|$ cross-section of the TT state in the RAZ Region $p_{T}^{WZ}< 20$ GeV. The total uncertainties are quoted. The last bin covers all events above the lower end of the bin.

Measured normalized differential $|\Delta Y(l_{W}Z)|$ cross-section of the TT state in the RAZ Region $p_{T}^{WZ}< 40$ GeV. The total uncertainties are quoted. The last bin covers all events above the lower end of the bin.

Measured normalized differential $|\Delta Y(l_{W}Z)|$ cross-section of the TT state in the RAZ Region $p_{T}^{WZ}< 70$ GeV. The total uncertainties are quoted. The last bin covers all events above the lower end of the bin.

Measured normalized differential $|\Delta Y(WZ)|$ cross-section of the TT state in the RAZ Region $p_{T}^{WZ}< 20$ GeV. The total uncertainties are quoted. The last bin covers all events above the lower end of the bin.

Measured normalized differential $|\Delta Y(WZ)|$ cross-section of the TT state in the RAZ Region $p_{T}^{WZ}< 40$ GeV. The total uncertainties are quoted. The last bin covers all events above the lower end of the bin.

Measured normalized differential $|\Delta Y(WZ)|$ cross-section of the TT state in the RAZ Region $p_{T}^{WZ}< 70$ GeV. The total uncertainties are quoted. The last bin covers all events above the lower end of the bin.

Measured normalized differential $|\Delta Y(l_{W}Z)|$ cross-section of the sum of polarization states in the RAZ Region $p_{T}^{WZ}< 20$ GeV. The total uncertainties are quoted. The last bin covers all events above the lower end of the bin.

Measured normalized differential $|\Delta Y(l_{W}Z)|$ cross-section of the sum of polarization states in the RAZ Region $p_{T}^{WZ}< 40$ GeV. The total uncertainties are quoted. The last bin covers all events above the lower end of the bin.

Measured normalized differential $|\Delta Y(l_{W}Z)|$ cross-section of the sum of polarization states in the RAZ Region $p_{T}^{WZ}< 70$ GeV. The total uncertainties are quoted. The last bin covers all events above the lower end of the bin.

Measured normalized differential $|\Delta Y(WZ)|$ cross-section of the sum of polarization states in the RAZ Region $p_{T}^{WZ}< 20$ GeV. The total uncertainties are quoted. The last bin covers all events above the lower end of the bin.

Measured normalized differential $|\Delta Y(WZ)|$ cross-section of the sum of polarization states in the RAZ Region $p_{T}^{WZ}< 40$ GeV. The total uncertainties are quoted. The last bin covers all events above the lower end of the bin.

Measured normalized differential $|\Delta Y(WZ)|$ cross-section of the sum of polarization states in the RAZ Region $p_{T}^{WZ}< 70$ GeV. The total uncertainties are quoted. The last bin covers all events above the lower end of the bin.

Summary of the relative uncertainties in the measured depth of the TT state in the RAZ Region $p_{T}^{WZ}<20$ GeV using $|\Delta Y(l_{W}Z)|$. The uncertainties are reported as percentages.

Summary of the relative uncertainties in the measured depth of the TT state in the RAZ Region $p_{T}^{WZ}<40$ GeV using $|\Delta Y(l_{W}Z)|$. The uncertainties are reported as percentages.

Summary of the relative uncertainties in the measured depth of the TT state in the RAZ Region $p_{T}^{WZ}<70$ GeV using $|\Delta Y(l_{W}Z)|$. The uncertainties are reported as percentages.

Summary of the relative uncertainties in the measured depth of the TT state in the RAZ Region $p_{T}^{WZ}<20$ GeV using $|\Delta Y(WZ)|$. The uncertainties are reported as percentages.

Summary of the relative uncertainties in the measured depth of the TT state in the RAZ Region $p_{T}^{WZ}<40$ GeV using $|\Delta Y(WZ)|$. The uncertainties are reported as percentages.

Summary of the relative uncertainties in the measured depth of the TT state in the RAZ Region $p_{T}^{WZ}<70$ GeV using $|\Delta Y(WZ)|$. The uncertainties are reported as percentages.

Summary of the relative uncertainties in the measured depth of the sum of polarization states in the RAZ Region $p_{T}^{WZ}<20$ GeV using $|\Delta Y(l_{W}Z)|$. The uncertainties are reported as percentages.

Summary of the relative uncertainties in the measured depth of the sum of polarization states in the RAZ Region $p_{T}^{WZ}<40$ GeV using $|\Delta Y(l_{W}Z)|$. The uncertainties are reported as percentages.

Summary of the relative uncertainties in the measured depth of the sum of polarization states in the RAZ Region $p_{T}^{WZ}<70$ GeV using $|\Delta Y(l_{W}Z)|$. The uncertainties are reported as percentages.

Summary of the relative uncertainties in the measured depth of the sum of polarization states in the RAZ Region $p_{T}^{WZ}<20$ GeV using $|\Delta Y(WZ)|$. The uncertainties are reported as percentages.

Summary of the relative uncertainties in the measured depth of the sum of polarization states in the RAZ Region $p_{T}^{WZ}<40$ GeV using $|\Delta Y(WZ)|$. The uncertainties are reported as percentages.

Summary of the relative uncertainties in the measured depth of the sum of polarization states in the RAZ Region $p_{T}^{WZ}<70$ GeV using $|\Delta Y(WZ)|$. The uncertainties are reported as percentages.