Comparison of the distribution of the scalar sum of small-$R$ jet and lepton transverse momenta, $S_T$, between data and the background prediction in the signal region of the pair-production (PP) $\geq 3\ell$ channel. The background prediction is shown post-fit, i.e. after the fit to the data $S_T$ distributions under the background-only hypothesis. The last bin contains the overflow. An example distribution for a $B\bar B$ signal in the singlet model with $m_B$ = 900 GeV is overlaid.

Comparison of the distribution of the invariant mass of the $Z$ boson candidate and the highest-$p_T$ top-tagged large-$R$ jet, $m_{Zt}$, between data and the background prediction in the signal region of the single-production (SP) 2$\ell$ channel. The background prediction is shown post-fit, i.e. after the fit to the data $m_{Zt}$ distributions under the background-only hypothesis. The last bin contains the overflow. An example distribution for a single-$T$-quark signal with $m_T$ = 900 GeV and $\kappa_T = 0.5$ is overlaid.

Comparison of the distribution of the scalar sum of small-$R$ jet and lepton transverse momenta, $S_T$, between data and the background prediction in the signal region of the single-production (SP) $\geq 3\ell$ channel. The background prediction is shown post-fit, i.e. after the fit to the data $S_T$ distributions under the background-only hypothesis. The last bin contains the overflow. An example distribution for a single-$T$-quark signal with $m_T$ = 900 GeV and $\kappa_T$ = 0.5 is overlaid.

Upper limits at 95$\%$ CL on the cross section of vector-like quark pair production (PP) for $T\bar T$ in the singlet model. The expected limits are shown for the combination of the channels, as are the observed limits.

Upper limits at 95$\%$ CL on the cross section of vector-like quark pair production (PP) for $B\bar B$ in the singlet model. The expected limits are shown for the combination of the channels, as are the observed limits.

Upper limits at 95$\%$ CL on the cross section of vector-like quark pair production (PP) for $T\bar T$ in the doublet model. The expected limits are shown for the combination of the channels, as are the observed limits.

Upper limits at 95$\%$ CL on the cross section of vector-like quark pair production (PP) for $B\bar B$ in the doublet model. The expected limits are shown for the combination of the channels, as are the observed limits.

Upper limits at 95$\%$ CL on the cross section of vector-like quark pair production (PP) for $T\bar T$ with a BR of 100$\%$ to $Zt$. The expected limits are shown for the combination of the channels, as are the observed limits.

Upper limits at 95$\%$ CL on the cross section of vector-like quark pair production (PP) for $B\bar B$ with a BR of 100$\%$ to $Zb$. The expected limits are shown for the combination of the channels, as are the observed limits.

Expected 95$\%$ CL lower limits from the combination of the pair-production channels on the mass of vector-like quarks for all combinations of BRs for $T\rightarrow Zt$, $T\rightarrow Ht$, $T\rightarrow Wb$, adding up to unity.

Observed 95$\%$ CL lower limits from the combination of the pair-production channels on the mass of vector-like quarks for all combinations of BRs for $T\rightarrow Zt$, $T\rightarrow Ht$, $T\rightarrow Wb$, adding up to unity.

Expected 95$\%$ CL lower limits from the combination of the pair-production channels on the mass of vector-like quarks for all combinations of BRs for $B\rightarrow Zb$, $B\rightarrow Hb$, $B\rightarrow Wt$, adding up to unity.

Observed 95$\%$ CL lower limits from the combination of the pair-production channels on the mass of vector-like quarks for all combinations of BRs for $B\rightarrow Zb$, $B\rightarrow Hb$, $B\rightarrow Wt$, adding up to unity.

Upper limits at 95$\%$ CL on the cross section times BR to $Zt$ of single production (SP) of a $T$-quark. The expected limits are shown for the combination of the channels, as are the observed limits. The expected cross section times BR to $Zt$ for single-$T$-quark production is also shown for a coupling $\kappa_T = 0.5$, which corresponds to a coupling of $c_W = \sqrt{c^2_{W,L} + c^2_{W,R}} = 0.45$ from Ref. [14]. The BR assumed here corresponds to the singlet benchmark model, i.e. $\approx 25\%$.

Expected and observed 95$\%$ CL limits from the combination of the single-production channels on the coupling of the $T$ quark to SM particles, $c_W = \sqrt c^2_L + c^2_R$, assuming the singlet-model BR of $\approx 25\%$, as a function of the mass of the $T$ quark, $m_T$. Values of $c_W$ larger than the observed limit are excluded.

Expected and observed 95$\%$ CL limits from the combination of the single-production channels on the mixing angle in the singlet model between the $T$ quark and the top quark, $|\sin\theta_L|$, as a function of the mass of the $T$ quark, $m_T$. Values of $|\sin\theta_L|$ enclosed by the observed limit are excluded, i.e. for $m_T$ larger than $\approx 1200$ GeV, no value of $|\sin\theta_L|$ is excluded.

Expected lower limit from the combination of the single-production channels on the mass of the $T$ quark as a function of the couplings of the $T$ quark to the $W$ boson, $\sqrt c^2_L + c^2_R$, and to the $Z$ boson, $\sqrt c^2_L + c^2_R$ with the assumption of equal BRs for $T\rightarrow Zt$ and $T\rightarrow Ht$ in the limit of large $T$-quark masses.

Observed lower limit from the combination of the single-production channels on the mass of the $T$ quark as a function of the couplings of the $T$ quark to the $W$ boson, $\sqrt c^2_L + c^2_R$, and to the $Z$ boson, $\sqrt c^2_L + c^2_R$ with the assumption of equal BRs for $T\rightarrow Zt$ and $T\rightarrow Ht$ in the limit of large $T$-quark masses.

Observed upper limits at 95$\%$ CL on $\sigma(pp\rightarrow T\bar T)$ for the combination of the pair-production channels for all combinations of BRs for $T\rightarrow Zt$, $T\rightarrow Ht$, $T\rightarrow Wb$ adding up to unity for a $T$-quark mass of 500 GeV.

Observed upper limits at 95$\%$ CL on $\sigma(pp\rightarrow T\bar T)$ for the combination of the pair-production channels for all combinations of BRs for $T\rightarrow Zt$, $T\rightarrow Ht$, $T\rightarrow Wb$ adding up to unity for a $T$-quark mass of 600 GeV.

Observed upper limits at 95$\%$ CL on $\sigma(pp\rightarrow T\bar T)$ for the combination of the pair-production channels for all combinations of BRs for $T\rightarrow Zt$, $T\rightarrow Ht$, $T\rightarrow Wb$ adding up to unity for a $T$-quark mass of 700 GeV.

Observed upper limits at 95$\%$ CL on $\sigma(pp\rightarrow T\bar T)$ for the combination of the pair-production channels for all combinations of BRs for $T\rightarrow Zt$, $T\rightarrow Ht$, $T\rightarrow Wb$ adding up to unity for a $T$-quark mass of 750 GeV.

Observed upper limits at 95$\%$ CL on $\sigma(pp\rightarrow T\bar T)$ for the combination of the pair-production channels for all combinations of BRs for $T\rightarrow Zt$, $T\rightarrow Ht$, $T\rightarrow Wb$ adding up to unity for a $T$-quark mass of 800 GeV.

Observed upper limits at 95$\%$ CL on $\sigma(pp\rightarrow T\bar T)$ for the combination of the pair-production channels for all combinations of BRs for $T\rightarrow Zt$, $T\rightarrow Ht$, $T\rightarrow Wb$ adding up to unity for a $T$-quark mass of 850 GeV.

Observed upper limits at 95$\%$ CL on $\sigma(pp\rightarrow T\bar T)$ for the combination of the pair-production channels for all combinations of BRs for $T\rightarrow Zt$, $T\rightarrow Ht$, $T\rightarrow Wb$ adding up to unity for a $T$-quark mass of 900 GeV.

Observed upper limits at 95$\%$ CL on $\sigma(pp\rightarrow T\bar T)$ for the combination of the pair-production channels for all combinations of BRs for $T\rightarrow Zt$, $T\rightarrow Ht$, $T\rightarrow Wb$ adding up to unity for a $T$-quark mass of 950 GeV.

Observed upper limits at 95$\%$ CL on $\sigma(pp\rightarrow T\bar T)$ for the combination of the pair-production channels for all combinations of BRs for $T\rightarrow Zt$, $T\rightarrow Ht$, $T\rightarrow Wb$ adding up to unity for a $T$-quark mass of 1000 GeV.

Observed upper limits at 95$\%$ CL on $\sigma(pp\rightarrow T\bar T)$ for the combination of the pair-production channels for all combinations of BRs for $T\rightarrow Zt$, $T\rightarrow Ht$, $T\rightarrow Wb$ adding up to unity for a $T$-quark mass of 1050 GeV.

Observed upper limits at 95$\%$ CL on $\sigma(pp\rightarrow T\bar T)$ for the combination of the pair-production channels for all combinations of BRs for $T\rightarrow Zt$, $T\rightarrow Ht$, $T\rightarrow Wb$ adding up to unity for a $T$-quark mass of 1100 GeV.

Observed upper limits at 95$\%$ CL on $\sigma(pp\rightarrow T\bar T)$ for the combination of the pair-production channels for all combinations of BRs for $T\rightarrow Zt$, $T\rightarrow Ht$, $T\rightarrow Wb$ adding up to unity for a $T$-quark mass of 1150 GeV.

Observed upper limits at 95$\%$ CL on $\sigma(pp\rightarrow T\bar T)$ for the combination of the pair-production channels for all combinations of BRs for $T\rightarrow Zt$, $T\rightarrow Ht$, $T\rightarrow Wb$ adding up to unity for a $T$-quark mass of 1200 GeV.

Observed upper limits at 95$\%$ CL on $\sigma(pp\rightarrow T\bar T)$ for the combination of the pair-production channels for all combinations of BRs for $T\rightarrow Zt$, $T\rightarrow Ht$, $T\rightarrow Wb$ adding up to unity for a $T$-quark mass of 1300 GeV.

Observed upper limits at 95$\%$ CL on $\sigma(pp\rightarrow T\bar T)$ for the combination of the pair-production channels for all combinations of BRs for $T\rightarrow Zt$, $T\rightarrow Ht$, $T\rightarrow Wb$ adding up to unity for a $T$-quark mass of 1400 GeV.

Observed upper limits at 95$\%$ CL on $\sigma(pp\rightarrow B\bar B)$ for the combination of the pair-production channels for all combinations of BRs for $B\rightarrow Zb$, $B\rightarrow Hb$, $B\rightarrow Wt$ adding up to unity for a $B$-quark mass of 500 GeV.

Observed upper limits at 95$\%$ CL on $\sigma(pp\rightarrow B\bar B)$ for the combination of the pair-production channels for all combinations of BRs for $B\rightarrow Zb$, $B\rightarrow Hb$, $B\rightarrow Wt$ adding up to unity for a $B$-quark mass of 600 GeV.

Observed upper limits at 95$\%$ CL on $\sigma(pp\rightarrow B\bar B)$ for the combination of the pair-production channels for all combinations of BRs for $B\rightarrow Zb$, $B\rightarrow Hb$, $B\rightarrow Wt$ adding up to unity for a $B$-quark mass of 700 GeV.

Observed upper limits at 95$\%$ CL on $\sigma(pp\rightarrow B\bar B)$ for the combination of the pair-production channels for all combinations of BRs for $B\rightarrow Zb$, $B\rightarrow Hb$, $B\rightarrow Wt$ adding up to unity for a $B$-quark mass of 750 GeV.

Observed upper limits at 95$\%$ CL on $\sigma(pp\rightarrow B\bar B)$ for the combination of the pair-production channels for all combinations of BRs for $B\rightarrow Zb$, $B\rightarrow Hb$, $B\rightarrow Wt$ adding up to unity for a $B$-quark mass of 800 GeV.

Observed upper limits at 95$\%$ CL on $\sigma(pp\rightarrow B\bar B)$ for the combination of the pair-production channels for all combinations of BRs for $B\rightarrow Zb$, $B\rightarrow Hb$, $B\rightarrow Wt$ adding up to unity for a $B$-quark mass of 850 GeV.

Observed upper limits at 95$\%$ CL on $\sigma(pp\rightarrow B\bar B)$ for the combination of the pair-production channels for all combinations of BRs for $B\rightarrow Zb$, $B\rightarrow Hb$, $B\rightarrow Wt$ adding up to unity for a $B$-quark mass of 900 GeV.

Observed upper limits at 95$\%$ CL on $\sigma(pp\rightarrow B\bar B)$ for the combination of the pair-production channels for all combinations of BRs for $B\rightarrow Zb$, $B\rightarrow Hb$, $B\rightarrow Wt$ adding up to unity for a $B$-quark mass of 950 GeV.

Observed upper limits at 95$\%$ CL on $\sigma(pp\rightarrow B\bar B)$ for the combination of the pair-production channels for all combinations of BRs for $B\rightarrow Zb$, $B\rightarrow Hb$, $B\rightarrow Wt$ adding up to unity for a $B$-quark mass of 1000 GeV.

Observed upper limits at 95$\%$ CL on $\sigma(pp\rightarrow B\bar B)$ for the combination of the pair-production channels for all combinations of BRs for $B\rightarrow Zb$, $B\rightarrow Hb$, $B\rightarrow Wt$ adding up to unity for a $B$-quark mass of 1050 GeV.

Observed upper limits at 95$\%$ CL on $\sigma(pp\rightarrow B\bar B)$ for the combination of the pair-production channels for all combinations of BRs for $B\rightarrow Zb$, $B\rightarrow Hb$, $B\rightarrow Wt$ adding up to unity for a $B$-quark mass of 1100 GeV.

Observed upper limits at 95$\%$ CL on $\sigma(pp\rightarrow B\bar B)$ for the combination of the pair-production channels for all combinations of BRs for $B\rightarrow Zb$, $B\rightarrow Hb$, $B\rightarrow Wt$ adding up to unity for a $B$-quark mass of 1150 GeV.

Observed upper limits at 95$\%$ CL on $\sigma(pp\rightarrow B\bar B)$ for the combination of the pair-production channels for all combinations of BRs for $B\rightarrow Zb$, $B\rightarrow Hb$, $B\rightarrow Wt$ adding up to unity for a $B$-quark mass of 1200 GeV.

Observed upper limits at 95$\%$ CL on $\sigma(pp\rightarrow B\bar B)$ for the combination of the pair-production channels for all combinations of BRs for $B\rightarrow Zb$, $B\rightarrow Hb$, $B\rightarrow Wt$ adding up to unity for a $B$-quark mass of 1300 GeV.

Observed upper limits at 95$\%$ CL on $\sigma(pp\rightarrow B\bar B)$ for the combination of the pair-production channels for all combinations of BRs for $B\rightarrow Zb$, $B\rightarrow Hb$, $B\rightarrow Wt$ adding up to unity for a $B$-quark mass of 1400 GeV.

Observed upper limits at 95$\%$ CL on the cross section times BR to $Zt$ as a function of the vector-like $T$-quark mass and coupling $\kappa_T$ for the combination of the SP $2\ell$ and SP $\geq 3\ell$ channels.

Signal cutflows for the $B\bar B$ process in the singlet model in the PP $2\ell$ $0-1$J channel in the 0-large-$R$ jet SR. Only statistical uncertainties are shown.

Signal cutflows for the $B\bar B$ process in the singlet model in the PP $2\ell$ $0-1$J channel in the 1-large-$R$ jet SR. Only statistical uncertainties are shown.

Signal cutflows for the $B\bar B$ process in the doublet model in the PP $2\ell$ $0-1$J channel in the 0-large-$R$ jet SR. Only statistical uncertainties are shown.

Signal cutflows for the $B\bar B$ process in the doublet model in the PP $2\ell$ $0-1$J channel in the 1-large-$R$ jet SR. Only statistical uncertainties are shown.

Signal cutflows for the $B\bar B$ process in the case of 100$\%$ BR for $B \rightarrow Zb$ in the PP $2\ell$ $0-1$J channel in the 0-large-$R$ jet SR. Only statistical uncertainties are shown.

Signal cutflows for the $B\bar B$ process in the case of 100$\%$ BR for $B \rightarrow Zb$ in the PP $2\ell$ $0-1$J channel in the 1-large-$R$ jet SR. Only statistical uncertainties are shown.

Signal cutflows for the $T\bar T$ process in the singlet model in the PP $2\ell$ $0-1$J channel in the 0-large-$R$ jet SR. Only statistical uncertainties are shown.

Signal cutflows for the $T\bar T$ process in the singlet model in the PP $2\ell$ $0-1$J channel in the 1-large-$R$ jet SR. Only statistical uncertainties are shown.

Signal cutflows for the $T\bar T$ process in the doublet model in the PP $2\ell$ $0-1$J channel in the 0-large-$R$ jet SR. Only statistical uncertainties are shown.

Signal cutflows for the $T\bar T$ process in the doublet model in the PP $2\ell$ $0-1$J channel in the 1-large-$R$ jet SR. Only statistical uncertainties are shown.

Signal cutflows for the $T\bar T$ process in the case of 100$\%$ BR for $T \rightarrow Zt$ in the PP $2\ell$ $0-1$J channel in the 0-large-$R$ jet SR. Only statistical uncertainties are shown.

Signal cutflows for the $T\bar T$ process in the case of 100$\%$ BR for $T \rightarrow Zt$ in the PP $2\ell$ $0-1$J channel in the 1-large-$R$ jet SR. Only statistical uncertainties are shown.

Signal cutflows for the $T\bar T$ process in the singlet model in the PP $2\ell$ $\geq 2$J channel. Only statistical uncertainties are shown.

Signal cutflows for the $B\bar B$ process in the singlet model in the PP $2\ell$ $\geq 2$J channel. Only statistical uncertainties are shown.

Signal cutflows for the $T\bar T$ process in the doublet model in the PP $2\ell$ $\geq 2$J channel. Only statistical uncertainties are shown.

Signal cutflows for the $B\bar B$ process in the doublet model in the PP $2\ell$ $\geq 2$J channel. Only statistical uncertainties are shown.

Signal cutflows for the $T\bar T$ process in the case of 100$\%$ BR for $T \rightarrow Zt$ in the PP $2\ell$ $\geq 2$J channel. Only statistical uncertainties are shown.

Signal cutflows for the $B\bar B$ process in the case of 100$\%$ BR for $B \rightarrow Zb$ in the PP $2\ell$ $\geq 2$J channel. Only statistical uncertainties are shown.

Signal cutflows for the $T\bar T$ process in the singlet model in the PP $\geq 3\ell$ channel. Only statistical uncertainties are shown.

Signal cutflows for the $B\bar B$ process in the singlet model in the PP $\geq 3\ell$ channel. Only statistical uncertainties are shown.

Signal cutflows for the $T\bar T$ process in the doublet model in the PP $\geq 3\ell$ channel. Only statistical uncertainties are shown.

Signal cutflows for the $B\bar B$ process in the doublet model in the PP $\geq 3\ell$ channel. Only statistical uncertainties are shown.

Signal cutflows for the $T\bar T$ process in the case of 100$\%$ BR for $T \rightarrow Zt$ in the PP $\geq 3\ell$ channel. Only statistical uncertainties are shown.

Signal cutflows for the $B\bar B$ process in the case of 100$\%$ BR for $B \rightarrow Zb$ in the PP $\geq 3\ell$ channel. Only statistical uncertainties are shown.

Signal cutflows for single-$T$-quark production with $\kappa_T = 0.5$ in the SP $2\ell$ channel. Only statistical uncertainties are shown.

Signal cutflows for single-$T$-quark production with $\kappa_T = 0.5$ in the SP $\geq 3\ell$ channel. Only statistical uncertainties are shown.

Signal efficiencies in $\%$ in the PP $2\ell$ $0-1$J channel in the 0-large-$R$ jet SR. Uncertainties are statistical only.

Signal efficiencies in $\%$ in the PP $2\ell$ $0-1$J channel in the 1-large-$R$ jet SR. Uncertainties are statistical only.

Signal efficiencies in $\%$ in the PP $2\ell$ $\geq 2$J channel. Uncertainties are statistical only.

Signal efficiencies in $\%$ in the PP $\geq 3\ell$ channel. Uncertainties are statistical only.

Signal efficiencies in $\%$ in the SP $2\ell$ channel for $\kappa_T = 0.5$. Uncertainties are statistical only.

Signal efficiencies in $\%$ in the SP $\geq 3\ell$ channel for $\kappa_T = 0.5$. Uncertainties are statistical only.