The distribution of the BDT discriminants for the full 2016--2018 data set in the all-hadronic channel. The sample VR category shown is defined by $N_\textrm{RT} \geq 2$, $H_T > 1100$ GeV. The background from QCD multijet and $\textrm{t}\bar{\textrm{t}}$ production is derived from control regions in the data. Estimates for the $\textrm{t}\bar{\textrm{t}}\textrm{t}\bar{\textrm{t}}$ signal and other backgrounds are shown using simulated samples. The hatched bands correspond to the estimated total uncertainty.

The distribution of the BDT discriminants for the full 2016--2018 data set in the all-hadronic channel. The SR category shown in this figure is defined by $N_\textrm{RT}=1$, $N_\textrm{BT} \geq 1$, $H_T > 1400$ GeV. The background from QCD multijet and $\textrm{t}\bar{\textrm{t}}$ production is derived from control regions in the data. Estimates for the $\textrm{t}\bar{\textrm{t}}\textrm{t}\bar{\textrm{t}}$ signal and other backgrounds are shown using simulated samples. The hatched bands correspond to the estimated total uncertainty after the fit.

The distribution of the BDT discriminants for the full 2016--2018 data set in the all-hadronic channel. The SR category shown in this figure is defined by $N_\textrm{RT} = 2$, $H_T > 1100$ GeV. The background from QCD multijet and $\textrm{t}\bar{\textrm{t}}$ production is derived from control regions in the data. Estimates for the $\textrm{t}\bar{\textrm{t}}\textrm{t}\bar{\textrm{t}}$ signal and other backgrounds are shown using simulated samples. The hatched bands correspond to the estimated total uncertainty after the fit.

Expected and observed significance (in standard deviations) for $\textrm{t}\bar{\textrm{t}}\textrm{t}\bar{\textrm{t}}$ production from each final state and the combination with previous CMS results (EPJC 80 (2020) 75 and JHEP 11 (2019) 082). The same-sign dilepton and multilepton (SSDL\&ML) final state results are from EPJC 80 (2020) 75.

Measured signal strength ($\mu = \sigma_{\textrm{t}\bar{\textrm{t}}\textrm{t}\bar{\textrm{t}}}/ \sigma_{\textrm{t}\bar{\textrm{t}}\textrm{t}\bar{\textrm{t}}} ^{\textrm{SM}}$), corresponding cross section (in fb), and the expected and observed significance (in standard deviations) for $\textrm{t}\bar{\textrm{t}}\textrm{t}\bar{\textrm{t}}$ production from all analysis channels. This table shows production from each analysis channel in this Letter, the combination of those channels, the results from previously published results, and the full combination of all CMS 2016-2018 results.

Acceptances on TRUTH level of the DMt samples in the tW1L channel for all bins in the SR. The acceptance is defined as the number of weighted TRUTH events in the SR over the number of expected events without any selections. The maps include all samples in the $m_H - tan\beta$ plane with $m_a = 250~GeV$.

Efficiencies of the DMt samples in the tW2L SR. The efficiency is defined as the number of weighted reconstructed events over the number of weighted TRUTH events in the SR. The maps include all samples in the $m_a - m_H$ plane with $tan\beta = 1$.

Acceptances on TRUTH level of the DMt samples in the tW2L SR. The acceptance is defined as the number of weighted TRUTH events in the SR over the number of expected events without any selections. The maps include all samples in the $m_a - m_H$ plane with $tan\beta = 1$.

Efficiencies of the DMt samples in the tW2L SR. The efficiency is defined as the number of weighted reconstructed events over the number of weighted TRUTH events in the SR. The maps include all samples in the $m_H - tan\beta$ plane with $m_a = 250~GeV$.

Acceptances on TRUTH level of the DMt samples in the tW2L SR. The acceptance is defined as the number of weighted TRUTH events in the SR over the number of expected events without any selections. The maps include all samples in the $m_H - tan\beta$ plane with $m_a = 250~GeV$.

Efficiencies of the DMt samples in the tj1L channel for all bins in the SR. The efficiency is defined as the number of weighted reconstructed events over the number of weighted TRUTH events in the SR. The map includes all used samples in the $m_H - tan\beta$ plane with $m_a = 250~GeV$.

Acceptances on TRUTH level of the DMt samples in the tj1L channel for all bins in the SR. The acceptance is defined as the number of weighted TRUTH events in the SR over the number of expected events without any selections. The map includes all used samples in the $m_H - tan\beta$ plane with $m_a = 250~GeV$.

Upper limits on signal strength (excluded cross section over theoretical cross section) of the tW1L analysis considering only DMt signal.

Upper limits on excluded cross sections of the tW1L analysis considering only the DMt signal.

The expected exclusion contours as a function of $(m_a, m_{H^{\pm}})$, assuming only $tW$+DM contributions, for the tW1L analysis channel.

The observed exclusion contours as a function of $(m_a, m_{H^{\pm}})$, assuming only $tW$+DM contributions, for the tW1L analysis channel.

Upper limits on signal strength (excluded cross section over theoretical cross section) of the tW1L analysis considering only DMt signal.

Upper limits on excluded cross sections of the tW1L analysis considering only the DMt signal.

The expected exclusion contours as a function of $(m_{H^{\pm}}, \tan\beta)$, assuming only $tW$+DM contributions, for the tW1L analysis channel.

The observed exclusion contours as a function of $(m_{H^{\pm}}, \tan\beta)$, assuming only $tW$+DM contributions, for the tW1L analysis channel.

Upper limits on signal strength (excluded cross section over theoretical cross section) of the tW2L analysis considering only DMt signal.

Upper limits on excluded cross sections of the tW2L analysis considering only the DMt signal.

The expected exclusion contours as a function of $(m_a, m_{H^{\pm}})$, assuming only $tW$+DM contributions, for the tW2L analysis channel.

The observed exclusion contours as a function of $(m_a, m_{H^{\pm}})$, assuming only $tW$+DM contributions, for the tW2L analysis channel.

Upper limits on signal strength (excluded cross section over theoretical cross section) of the tW2L analysis considering only DMt signal.

Upper limits on excluded cross sections of the tW2L analysis considering only the DMt signal.

The expected exclusion contours as a function of $(m_{H^{\pm}}, \tan\beta)$, assuming only $tW$+DM contributions, for the tW2L analysis channel.

The observed exclusion contours as a function of $(m_{H^{\pm}}, \tan\beta)$, assuming only $tW$+DM contributions, for the tW2L analysis channel.

Upper limits on signal strength (excluded cross section over theoretical cross section) of the combined tW1L and tW2L analyses considering only the DMt signal.

Upper limits on excluded cross sections of the combined tW1L and tW2L analyses considering only the DMt signal.

The expected exclusion contours as a function of $(m_a, m_{H^{\pm}})$, assuming only $tW$+DM contributions, for the statistical combination of the tW1L and tW2L analysis channel.

The observed exclusion contours as a function of $(m_a, m_{H^{\pm}})$, assuming only $tW$+DM contributions, for the statistical combination of the tW1L and tW2L analysis channel.

Upper limits on signal strength (excluded cross section over theoretical cross section) of the combined tW1L and tW2L analyses considering only the DMt signal.

Upper limits on excluded cross sections of the combined tW1L and tW2L analyses considering only the DMt signal.

The expected exclusion contours as a function of $(m_{H^{\pm}}, \tan\beta)$, assuming only $tW$+DM contributions, for the statistical combination of the tW1L and tW2L analysis channel.

The observed exclusion contours as a function of $(m_{H^{\pm}}, \tan\beta)$, assuming only $tW$+DM contributions, for the statistical combination of the tW1L and tW2L analysis channel.

Upper limits on signal strength (excluded cross section over theoretical cross section) of the tW1L analysis considering the DMt$\bar{t}$+DMt signal.

The expected exclusion contours as a function of $(m_a, m_{H^{\pm}})$, assuming DM$t\bar{t}$ and DM$t$ contributions, for the tW1L analysis channel.

The observed exclusion contours as a function of $(m_a, m_{H^{\pm}})$, assuming DM$t\bar{t}$ and DM$t$ contributions, for the tW1L analysis channel.

Upper limits on signal strength (excluded cross section over theoretical cross section) of the tW1L analysis considering the DMt$\bar{t}$+DMt signal.

The expected exclusion contours as a function of $(m_{H^{\pm}}, \tan\beta)$, assuming DM$t\bar{t}$ and DM$t$ contributions, for the tW1L analysis channel.

The observed exclusion contours as a function of $(m_{H^{\pm}}, \tan\beta)$, assuming DM$t\bar{t}$ and DM$t$ contributions, for the tW1L analysis channel.

Upper limits on signal strength (excluded cross section over theoretical cross section) of the tW2L analysis considering the DMt$\bar{t}$+DMt signal.

The expected exclusion contours as a function of $(m_a, m_{H^{\pm}})$, assuming DM$t\bar{t}$ and DM$t$ contributions, for the tW2L analysis channel.

The observed exclusion contours as a function of $(m_a, m_{H^{\pm}})$, assuming DM$t\bar{t}$ and DM$t$ contributions, for the tW2L analysis channel.

Upper limits on signal strength (excluded cross section over theoretical cross section) of the tW2L analysis considering the DMt$\bar{t}$+DMt signal.

The expected exclusion contours as a function of $(m_{H^{\pm}}, \tan\beta)$, assuming DM$t\bar{t}$ and DM$t$ contributions, for the tW2L analysis channel.

The observed exclusion contours as a function of $(m_{H^{\pm}}, \tan\beta)$, assuming DM$t\bar{t}$ and DM$t$ contributions, for the tW2L analysis channel.

Upper limits on signal strength (excluded cross section over theoretical cross section) of the combined tW1L and tW2L analyses considering the DMt$\bar{t}$+DMt signal.

The expected exclusion contours as a function of $(m_a, m_{H^{\pm}})$, assuming DM$t\bar{t}$ and DM$t$ contributions, for the statistical combination of the tW1L and tW2L analysis channel.

The observed exclusion contours as a function of $(m_a, m_{H^{\pm}})$, assuming DM$t\bar{t}$ and DM$t$ contributions, for the statistical combination of the tW1L and tW2L analysis channel.

Upper limits on signal strength (excluded cross section over theoretical cross section) of the combined tW1L and tW2L analyses considering the DMt$\bar{t}$+DMt signal.

The expected exclusion contours as a function of $(m_{H^{\pm}}, \tan\beta)$, assuming DM$t\bar{t}$ and DM$t$ contributions, for the statistical combination of the tW1L and tW2L analysis channel.

The observed exclusion contours as a function of $(m_{H^{\pm}}, \tan\beta)$, assuming DM$t\bar{t}$ and DM$t$ contributions, for the statistical combination of the tW1L and tW2L analysis channel.

Upper limits on signal strength (excluded cross section over theoretical cross section) of the tj1L analysis considering only the DMt signal.

Upper limits on upper limits on excluded cross sections of the tj1L analysis considering only the DMt signal.

The expected and observed cross section exclusion limits as a function of $m_{H^{\pm}}$ in the tj1L analysis channel for signal models with $m_a = 250~GeV$, and $\tan\beta=0.3$. The $\sigma^{}_\mathrm{BSM}$ is the cross section of the $t$-channel DM production process.

The expected and observed cross section exclusion limits as a function of $m_{H^{\pm}}$ in the tj1L analysis channel for signal models with $m_a = 250~GeV$, and $\tan\beta=0.5$. The $\sigma^{}_\mathrm{BSM}$ is the cross section of the $t$-channel DM production process.

Cross sections of the DMt samples in the tW1L channel. The maps include all samples in the $m_a - m_H$ plane with $tan\beta = 1$.

Cross sections of the DMt samples in the tW1L channel. The maps include all samples in the $m_H - tan\beta$ plane with $m_a = 250~GeV$.

Cross sections times branching ratio of the DMt samples in the tW2L channel. The maps include all samples in the $m_a - m_H$ plane with $tan\beta = 1$.

Cross sections times branching ratio of the DMt samples in the tW2L channel. The maps include all samples in the $m_H - tan\beta$ plane with $m_a = 250~GeV$.

Cross sections of the DMt samples in the tj1L channel. The map includes all samples in the $m_H - tan\beta$ plane with $m_a = 250~GeV$.

MC generator filter efficiencies of the DMt samples in the tW1L channel. The maps include all samples in the $m_a - m_H$ plane with $tan\beta = 1$.

MC generator filter efficiencies of the DMt samples in the tW1L channel. The maps include all samples in the $m_H - tan\beta$ plane with $m_a = 250~GeV$.

MC generator filter efficiencies of the DMt samples in the tW2L channel. The maps include all samples in the $m_a - m_H$ plane with $tan\beta = 1$.

MC generator filter efficiencies of the DMt samples in the tW2L channel. The maps include all samples in the $m_H - tan\beta$ plane with $m_a = 250~GeV$.

MC generator filter efficiencies of the DMt samples in the tj1L channel. The map includes all samples in the $m_H - tan\beta$ plane with $m_a = 250~GeV$.

Background-only fit results for the tW1L and tW2L signal regions. The backgrounds which contribute only a small amount (rare processes such as triboson, Higgs boson production processes, $t\bar{t}t\bar{t}$, $t\bar{t}WW$ and non-prompt or misidentified leptons background) are grouped and labelled as ``Others´´. The quoted uncertainties on the fitted SM background include both the statistical and systematic uncertainties.

Background-only fit results for the tj1L signal regions. The backgrounds which contribute only a small amount ($Z$+jets, rare processes such as $tWZ$, triboson, Higgs boson production processes, ,$t\bar{t}t\bar{t}$, $t\bar{t}WW$) are grouped and labelled as ``Others´´. The quoted uncertainties on the fitted SM background include both the statistical and systematic uncertainties.

Cutflow of the weighted events with statistical uncertainties for two DMt samples in all bins of the tW1L channel. The PreSelection includes at least 1 lepton in the event, at least 1 $b$-jet with $p_{\mathrm{T}} > 50~GeV$, $m\mathrm{_{T}^{lep}} > 30~GeV$, $\Delta\phi\mathrm{_{4jets, MET}^{min}} > 0.5$ and $E\mathrm{_{T}^{miss}} > 200~GeV$.

Cutflow of the weighted events with statistical uncertainties for two DMt samples in the tW2L channel. The PreSelection includes at least 2 leptons in the event, at least 1 $b$-jet with $p_{\mathrm{T}} > 40~GeV$, $m_{ll} > 40~GeV$, $m\mathrm{_{T2}} > 40~GeV$, $\Delta\phi\mathrm{_{4jets, MET}^{min}} > 0.5$ and $E\mathrm{_{T}^{miss}} > 200~GeV$.

Cutflow of the weighted events with the statistical uncertainties (except for the first cuts) for two DMt samples in all bins off the tj1L channel. The PreSelection includes at least 1 lepton in the event, at least 1 $b$-jet with $p_{\mathrm{T}} > 50~GeV$, $m\mathrm{_{T}^{lep}} > 30~GeV$, $\Delta\phi\mathrm{_{4jets, MET}^{min}} > 0.5$ and $E\mathrm{_{T}^{miss}} > 200~GeV$.