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Example processes illustrating production and decay of type-III seesaw heavy fermion pairs at the LHC that result in multilepton final states.

Example processes illustrating production and decay of type-III seesaw heavy fermion pairs at the LHC that result in multilepton final states.

Example processes illustrating production and decay of doublet vector-like \PGt lepton pairs at the LHC that result in multilepton final states. The right diagram also illustrates the singlet scenario.

Example processes illustrating production and decay of doublet vector-like \PGt lepton pairs at the LHC that result in multilepton final states. The right diagram also illustrates the singlet scenario.

Example processes illustrating the production and decay of scalar leptoquark pairs in $\Pp\Pp$ collisions at the LHC that result in multilepton final states.

Example processes illustrating the production and decay of scalar leptoquark pairs in $\Pp\Pp$ collisions at the LHC that result in multilepton final states.

The distributions of \MT in 3L OnZ CR (upper left), visible diboson \pt in 4L $\ZZ$ CR (upper right), \ptmiss in 2L1T MisID CR (lower left), and $\HT$ in 3L $\ttZ$ CR (lower right) events. The rightmost bin contains the overflow events in each distribution. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the sum of statistical and systematic uncertainties in the SM background prediction.

The distributions of \MT in 3L OnZ CR (upper left), visible diboson \pt in 4L $\ZZ$ CR (upper right), \ptmiss in 2L1T MisID CR (lower left), and $\HT$ in 3L $\ttZ$ CR (lower right) events. The rightmost bin contains the overflow events in each distribution. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the sum of statistical and systematic uncertainties in the SM background prediction.

The distributions of \MT in 3L OnZ CR (upper left), visible diboson \pt in 4L $\ZZ$ CR (upper right), \ptmiss in 2L1T MisID CR (lower left), and $\HT$ in 3L $\ttZ$ CR (lower right) events. The rightmost bin contains the overflow events in each distribution. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the sum of statistical and systematic uncertainties in the SM background prediction.

The distributions of \MT in 3L OnZ CR (upper left), visible diboson \pt in 4L $\ZZ$ CR (upper right), \ptmiss in 2L1T MisID CR (lower left), and $\HT$ in 3L $\ttZ$ CR (lower right) events. The rightmost bin contains the overflow events in each distribution. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the sum of statistical and systematic uncertainties in the SM background prediction.

The distributions of \LT (upper left), \ptmiss (upper right), and $\HT$ (lower left) in all seven multilepton channels, and \mossf (lower right) in channels with at least one light lepton pair (4L, 3L1T, 3L, 2L2T, and 2L1T). The rightmost bin contains the overflow events in each distribution. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the sum of statistical and systematic uncertainties in the SM background prediction. As illustrative examples, a signal hypothesis for the production of the vector-like \PGt lepton in the doublet scenario of $m_{\vltau}=1\TeV$ and a scalar leptoquark coupled to a top quark and a \PGt lepton of $m_{\PS}=1\TeV$ are overlaid in the \LT and $\HT$ distributions respectively. Similarly, a signal hypothesis for the production of the type-III seesaw heavy fermions in the flavor-democratic scenario of $m_{\Sigma}=1\TeV$ is overlaid for the \ptmiss and \mossf distributions.

The distributions of \LT (upper left), \ptmiss (upper right), and $\HT$ (lower left) in all seven multilepton channels, and \mossf (lower right) in channels with at least one light lepton pair (4L, 3L1T, 3L, 2L2T, and 2L1T). The rightmost bin contains the overflow events in each distribution. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the sum of statistical and systematic uncertainties in the SM background prediction. As illustrative examples, a signal hypothesis for the production of the vector-like \PGt lepton in the doublet scenario of $m_{\vltau}=1\TeV$ and a scalar leptoquark coupled to a top quark and a \PGt lepton of $m_{\PS}=1\TeV$ are overlaid in the \LT and $\HT$ distributions respectively. Similarly, a signal hypothesis for the production of the type-III seesaw heavy fermions in the flavor-democratic scenario of $m_{\Sigma}=1\TeV$ is overlaid for the \ptmiss and \mossf distributions.

The distributions of \LT (upper left), \ptmiss (upper right), and $\HT$ (lower left) in all seven multilepton channels, and \mossf (lower right) in channels with at least one light lepton pair (4L, 3L1T, 3L, 2L2T, and 2L1T). The rightmost bin contains the overflow events in each distribution. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the sum of statistical and systematic uncertainties in the SM background prediction. As illustrative examples, a signal hypothesis for the production of the vector-like \PGt lepton in the doublet scenario of $m_{\vltau}=1\TeV$ and a scalar leptoquark coupled to a top quark and a \PGt lepton of $m_{\PS}=1\TeV$ are overlaid in the \LT and $\HT$ distributions respectively. Similarly, a signal hypothesis for the production of the type-III seesaw heavy fermions in the flavor-democratic scenario of $m_{\Sigma}=1\TeV$ is overlaid for the \ptmiss and \mossf distributions.

The distributions of \LT (upper left), \ptmiss (upper right), and $\HT$ (lower left) in all seven multilepton channels, and \mossf (lower right) in channels with at least one light lepton pair (4L, 3L1T, 3L, 2L2T, and 2L1T). The rightmost bin contains the overflow events in each distribution. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the sum of statistical and systematic uncertainties in the SM background prediction. As illustrative examples, a signal hypothesis for the production of the vector-like \PGt lepton in the doublet scenario of $m_{\vltau}=1\TeV$ and a scalar leptoquark coupled to a top quark and a \PGt lepton of $m_{\PS}=1\TeV$ are overlaid in the \LT and $\HT$ distributions respectively. Similarly, a signal hypothesis for the production of the type-III seesaw heavy fermions in the flavor-democratic scenario of $m_{\Sigma}=1\TeV$ is overlaid for the \ptmiss and \mossf distributions.

Distributions of BDT score from the \textit{SS-M} $\mathcal{B}_{\Pe}=\mathcal{B}_{\PGm}=\mathcal{B}_{\PGt}$ BDT are shown for the 3L+2L1T CR (\cmsLeft), and the 4L $\ZZ$ CR (\cmsRight). The 3L+2L1T CR consists of the 3L OnZ, 3L \ZG, and 2L1T MisID CRs. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the sum of statistical and systematic uncertainties in the SM background prediction.

Distributions of BDT score from the \textit{SS-M} $\mathcal{B}_{\Pe}=\mathcal{B}_{\PGm}=\mathcal{B}_{\PGt}$ BDT are shown for the 3L+2L1T CR (\cmsLeft), and the 4L $\ZZ$ CR (\cmsRight). The 3L+2L1T CR consists of the 3L OnZ, 3L \ZG, and 2L1T MisID CRs. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the sum of statistical and systematic uncertainties in the SM background prediction.

Distributions of BDT score from the \textit{SS-M} $\mathcal{B}_{\Pe}=\mathcal{B}_{\PGm}=\mathcal{B}_{\PGt}$ BDT are shown for events lying outside the control regions in the three-lepton (3L, 2L1T, 1L2T) channels (\cmsLeft), and the four-lepton (4L, 3L1T, 2L2T, 1L3T) channels (\cmsRight). The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the sum of statistical and systematic uncertainties in the SM background prediction. For illustration, an example signal hypothesis for the production of the type-III seesaw heavy fermions in the flavor-democratic scenario for $m_{\Sigma}=550\GeV$ is also overlaid.

Distributions of BDT score from the \textit{SS-M} $\mathcal{B}_{\Pe}=\mathcal{B}_{\PGm}=\mathcal{B}_{\PGt}$ BDT are shown for events lying outside the control regions in the three-lepton (3L, 2L1T, 1L2T) channels (\cmsLeft), and the four-lepton (4L, 3L1T, 2L2T, 1L3T) channels (\cmsRight). The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the sum of statistical and systematic uncertainties in the SM background prediction. For illustration, an example signal hypothesis for the production of the type-III seesaw heavy fermions in the flavor-democratic scenario for $m_{\Sigma}=550\GeV$ is also overlaid.

The SR distributions of the fundamental $\LTmet$ table for the combined 2016--2018 data set. The detailed description of the bin numbers can be found in Tables~\ref{tab:binningtable3L}--\ref{tab:binningtableQuad}. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the sum of statistical and systematic uncertainties in the SM background prediction. The expected SM background distributions and the uncertainties are shown after fitting the data under the background-only hypothesis. For illustration, an example signal hypothesis for the production of the type-III seesaw heavy fermions in the flavor-democratic scenario for $m_{\Sigma}=1\TeV$, before the fit, is also overlaid.

The SR distributions of the fundamental $\LTmet$ table for the combined 2016--2018 data set. The detailed description of the bin numbers can be found in Tables~\ref{tab:binningtable3L}--\ref{tab:binningtableQuad}. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the sum of statistical and systematic uncertainties in the SM background prediction. The expected SM background distributions and the uncertainties are shown after fitting the data under the background-only hypothesis. For illustration, an example signal hypothesis for the production of the type-III seesaw heavy fermions in the flavor-democratic scenario for $m_{\Sigma}=1\TeV$, before the fit, is also overlaid.

The SR distributions of the fundamental $\LTmet$ table for the combined 2016--2018 data set. The detailed description of the bin numbers can be found in Tables~\ref{tab:binningtable3L}--\ref{tab:binningtableQuad}. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the sum of statistical and systematic uncertainties in the SM background prediction. The expected SM background distributions and the uncertainties are shown after fitting the data under the background-only hypothesis. For illustration, an example signal hypothesis for the production of the type-III seesaw heavy fermions in the flavor-democratic scenario for $m_{\Sigma}=1\TeV$, before the fit, is also overlaid.

The SR distributions of the fundamental $\LTmet$ table for the combined 2016--2018 data set. The detailed description of the bin numbers can be found in Tables~\ref{tab:binningtable3L}--\ref{tab:binningtableQuad}. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the sum of statistical and systematic uncertainties in the SM background prediction. The expected SM background distributions and the uncertainties are shown after fitting the data under the background-only hypothesis. For illustration, an example signal hypothesis for the production of the type-III seesaw heavy fermions in the flavor-democratic scenario for $m_{\Sigma}=1\TeV$, before the fit, is also overlaid.

The SR distributions of the fundamental \ST table for the combined 2016--2018 data set. The detailed description of the bin numbers can be found in Tables~\ref{tab:binningtable3L}--\ref{tab:binningtableQuad}. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the sum of statistical and systematic uncertainties in the SM background prediction. The expected SM background distributions and the uncertainties are shown after fitting the data under the background-only hypothesis. For illustration, an example signal hypothesis for the production of the vector-like \PGt lepton in the doublet scenario for $m_{\vltau}=1\TeV$, before the fit, is also overlaid.

The SR distributions of the fundamental \ST table for the combined 2016--2018 data set. The detailed description of the bin numbers can be found in Tables~\ref{tab:binningtable3L}--\ref{tab:binningtableQuad}. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the sum of statistical and systematic uncertainties in the SM background prediction. The expected SM background distributions and the uncertainties are shown after fitting the data under the background-only hypothesis. For illustration, an example signal hypothesis for the production of the vector-like \PGt lepton in the doublet scenario for $m_{\vltau}=1\TeV$, before the fit, is also overlaid.

The SR distributions of the fundamental \ST table for the combined 2016--2018 data set. The detailed description of the bin numbers can be found in Tables~\ref{tab:binningtable3L}--\ref{tab:binningtableQuad}. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the sum of statistical and systematic uncertainties in the SM background prediction. The expected SM background distributions and the uncertainties are shown after fitting the data under the background-only hypothesis. For illustration, an example signal hypothesis for the production of the vector-like \PGt lepton in the doublet scenario for $m_{\vltau}=1\TeV$, before the fit, is also overlaid.

The 3L SR distributions of the advanced \ST table for the combined 2016--2018 data set. The detailed description of the bin numbers can be found in Table~\ref{tab:binningtable3L}. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the sum of statistical and systematic uncertainties in the SM background prediction. The expected SM background distributions and the uncertainties are shown after fitting the data under the background-only hypothesis. For illustration, an example signal hypothesis for the production of the scalar leptoquark coupled to a top quark and a muon for $m_{\PS}=1.4\TeV$, before the fit, is also overlaid.

The 3L SR distributions of the advanced \ST table for the combined 2016--2018 data set. The detailed description of the bin numbers can be found in Table~\ref{tab:binningtable3L}. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the sum of statistical and systematic uncertainties in the SM background prediction. The expected SM background distributions and the uncertainties are shown after fitting the data under the background-only hypothesis. For illustration, an example signal hypothesis for the production of the scalar leptoquark coupled to a top quark and a muon for $m_{\PS}=1.4\TeV$, before the fit, is also overlaid.

The 3L SR distributions of the advanced \ST table for the combined 2016--2018 data set. The detailed description of the bin numbers can be found in Table~\ref{tab:binningtable3L}. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the sum of statistical and systematic uncertainties in the SM background prediction. The expected SM background distributions and the uncertainties are shown after fitting the data under the background-only hypothesis. For illustration, an example signal hypothesis for the production of the scalar leptoquark coupled to a top quark and a muon for $m_{\PS}=1.4\TeV$, before the fit, is also overlaid.

The 2L1T SR distributions of the advanced \ST table for the combined 2016--2018 data set. The detailed description of the bin numbers can be found in Table~\ref{tab:binningtable2L1T}. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the sum of statistical and systematic uncertainties in the SM background prediction. The expected SM background distributions and the uncertainties are shown after fitting the data under the background-only hypothesis. For illustration, an example signal hypothesis for the production of the scalar leptoquark coupled to a top quark and a muon for $m_{\PS}=1.4\TeV$, before the fit, is also overlaid.

The 1L2T SR distribution of the advanced \ST table for the combined 2016--2018 data set. The detailed description of the bin numbers can be found in Table~\ref{tab:binningtable1L2T}. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the sum of statistical and systematic uncertainties in the SM background prediction. The expected SM background distributions and the uncertainties are shown after fitting the data under the background-only hypothesis. An example signal hypothesis for the production of the scalar leptoquark coupled to a top quark and a muon for $m_{\PS}=1.4\TeV$, before the fit, is also overlaid. For this category, the signal yield is negligible and is not visible in the figure.

The 2L1T SR distributions of the advanced \ST table for the combined 2016--2018 data set. The detailed description of the bin numbers can be found in Table~\ref{tab:binningtable2L1T}. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the sum of statistical and systematic uncertainties in the SM background prediction. The expected SM background distributions and the uncertainties are shown after fitting the data under the background-only hypothesis. For illustration, an example signal hypothesis for the production of the scalar leptoquark coupled to a top quark and a muon for $m_{\PS}=1.4\TeV$, before the fit, is also overlaid.

The 4L, 3L1T, 2L2T and 1L3T SR distributions of the advanced \ST table for the combined 2016--2018 data set. The detailed description of the bin numbers can be found in Table~\ref{tab:binningtableQuad}. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the sum of statistical and systematic uncertainties in the SM background prediction. The expected SM background distributions and the uncertainties are shown after fitting the data under the background-only hypothesis. For illustration, an example signal hypothesis for the production of the scalar leptoquark coupled to a top quark and a muon for $m_{\PS}=1.4\TeV$, before the fit, is also overlaid.

The 2L1T SR distributions of the advanced \ST table for the combined 2016--2018 data set. The detailed description of the bin numbers can be found in Table~\ref{tab:binningtable2L1T}. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the sum of statistical and systematic uncertainties in the SM background prediction. The expected SM background distributions and the uncertainties are shown after fitting the data under the background-only hypothesis. For illustration, an example signal hypothesis for the production of the scalar leptoquark coupled to a top quark and a muon for $m_{\PS}=1.4\TeV$, before the fit, is also overlaid.

The 4L, 3L1T, 2L2T and 1L3T SR distributions of the advanced \ST table for the combined 2016--2018 data set. The detailed description of the bin numbers can be found in Table~\ref{tab:binningtableQuad}. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the sum of statistical and systematic uncertainties in the SM background prediction. The expected SM background distributions and the uncertainties are shown after fitting the data under the background-only hypothesis. For illustration, an example signal hypothesis for the production of the scalar leptoquark coupled to a top quark and a muon for $m_{\PS}=1.4\TeV$, before the fit, is also overlaid.

The 1L2T SR distribution of the advanced \ST table for the combined 2016--2018 data set. The detailed description of the bin numbers can be found in Table~\ref{tab:binningtable1L2T}. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the sum of statistical and systematic uncertainties in the SM background prediction. The expected SM background distributions and the uncertainties are shown after fitting the data under the background-only hypothesis. An example signal hypothesis for the production of the scalar leptoquark coupled to a top quark and a muon for $m_{\PS}=1.4\TeV$, before the fit, is also overlaid. For this category, the signal yield is negligible and is not visible in the figure.

The 4L, 3L1T, 2L2T and 1L3T SR distributions of the advanced \ST table for the combined 2016--2018 data set. The detailed description of the bin numbers can be found in Table~\ref{tab:binningtableQuad}. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the sum of statistical and systematic uncertainties in the SM background prediction. The expected SM background distributions and the uncertainties are shown after fitting the data under the background-only hypothesis. For illustration, an example signal hypothesis for the production of the scalar leptoquark coupled to a top quark and a muon for $m_{\PS}=1.4\TeV$, before the fit, is also overlaid.

The 4L, 3L1T, 2L2T and 1L3T SR distributions of the advanced \ST table for the combined 2016--2018 data set. The detailed description of the bin numbers can be found in Table~\ref{tab:binningtableQuad}. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the sum of statistical and systematic uncertainties in the SM background prediction. The expected SM background distributions and the uncertainties are shown after fitting the data under the background-only hypothesis. For illustration, an example signal hypothesis for the production of the scalar leptoquark coupled to a top quark and a muon for $m_{\PS}=1.4\TeV$, before the fit, is also overlaid.

The 4L, 3L1T, 2L2T and 1L3T SR distributions of the advanced \ST table for the combined 2016--2018 data set. The detailed description of the bin numbers can be found in Table~\ref{tab:binningtableQuad}. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the sum of statistical and systematic uncertainties in the SM background prediction. The expected SM background distributions and the uncertainties are shown after fitting the data under the background-only hypothesis. For illustration, an example signal hypothesis for the production of the scalar leptoquark coupled to a top quark and a muon for $m_{\PS}=1.4\TeV$, before the fit, is also overlaid.

The 4L, 3L1T, 2L2T and 1L3T SR distributions of the advanced \ST table for the combined 2016--2018 data set. The detailed description of the bin numbers can be found in Table~\ref{tab:binningtableQuad}. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the sum of statistical and systematic uncertainties in the SM background prediction. The expected SM background distributions and the uncertainties are shown after fitting the data under the background-only hypothesis. For illustration, an example signal hypothesis for the production of the scalar leptoquark coupled to a top quark and a muon for $m_{\PS}=1.4\TeV$, before the fit, is also overlaid.

The \textit{SS-M} $\mathcal{B}_{\Pe}=\mathcal{B}_{\PGm}=\mathcal{B}_{\PGt}$ BDT regions for the 3-lepton (upper) and 4-lepton (lower) channels for the 2016--2018 data sets. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the sum of statistical and systematic uncertainties in the SM background prediction. The expected SM background distributions and the uncertainties are shown after fitting the data under the background-only hypothesis. For illustration, an example signal hypothesis for the production of the type-III seesaw heavy fermions in the flavor-democratic scenario for $m_{\Sigma}=550\GeV$, before the fit, is also overlaid.

The \textit{SS-M} $\mathcal{B}_{\Pe}=\mathcal{B}_{\PGm}=\mathcal{B}_{\PGt}$ BDT regions for the 3-lepton (upper) and 4-lepton (lower) channels for the 2016--2018 data sets. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the sum of statistical and systematic uncertainties in the SM background prediction. The expected SM background distributions and the uncertainties are shown after fitting the data under the background-only hypothesis. For illustration, an example signal hypothesis for the production of the type-III seesaw heavy fermions in the flavor-democratic scenario for $m_{\Sigma}=550\GeV$, before the fit, is also overlaid.

The \textit{SS-H} $\mathcal{B}_{\Pe}=\mathcal{B}_{\PGm}=\mathcal{B}_{\PGt}$ BDT regions for the 3-lepton (upper) and 4-lepton (lower) channels for the 2016--2018 data sets. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the sum of statistical and systematic uncertainties in the SM background prediction. The expected SM background distributions and the uncertainties are shown after fitting the data under the background-only hypothesis. For illustration, an example signal hypothesis for the production of the type-III seesaw heavy fermions in the flavor-democratic scenario for $m_{\Sigma}=1\TeV$, before the fit, is also overlaid.

The \textit{SS-H} $\mathcal{B}_{\Pe}=\mathcal{B}_{\PGm}=\mathcal{B}_{\PGt}$ BDT regions for the 3-lepton (upper) and 4-lepton (lower) channels for the 2016--2018 data sets. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the sum of statistical and systematic uncertainties in the SM background prediction. The expected SM background distributions and the uncertainties are shown after fitting the data under the background-only hypothesis. For illustration, an example signal hypothesis for the production of the type-III seesaw heavy fermions in the flavor-democratic scenario for $m_{\Sigma}=1\TeV$, before the fit, is also overlaid.

The \textit{SS-M} $\mathcal{B}_{\PGt}=1$ BDT regions for the 3-lepton (upper) and 4-lepton (lower) channels for the 2016--2018 data sets. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the sum of statistical and systematic uncertainties in the SM background prediction. The expected SM background distributions and the uncertainties are shown after fitting the data under the background-only hypothesis. For illustration, an example signal hypothesis for the production of the type-III seesaw heavy fermions in the scenario with mixing exclusively to \PGt lepton for $m_{\Sigma}=550\GeV$, before the fit, is also overlaid.

The \textit{SS-M} $\mathcal{B}_{\PGt}=1$ BDT regions for the 3-lepton (upper) and 4-lepton (lower) channels for the 2016--2018 data sets. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the sum of statistical and systematic uncertainties in the SM background prediction. The expected SM background distributions and the uncertainties are shown after fitting the data under the background-only hypothesis. For illustration, an example signal hypothesis for the production of the type-III seesaw heavy fermions in the scenario with mixing exclusively to \PGt lepton for $m_{\Sigma}=550\GeV$, before the fit, is also overlaid.

The \textit{SS-H} $\mathcal{B}_{\PGt}=1$ BDT regions for the 3-lepton (upper) and 4-lepton (lower) channels for the 2016--2018 data sets. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the sum of statistical and systematic uncertainties in the SM background prediction. The expected SM background distributions and the uncertainties are shown after fitting the data under the background-only hypothesis. For illustration, an example signal hypothesis for the production of the type-III seesaw heavy fermions in the scenario with mixing exclusively to \PGt lepton for $m_{\Sigma}=850\GeV$, before the fit, is also overlaid.

The \textit{SS-H} $\mathcal{B}_{\PGt}=1$ BDT regions for the 3-lepton (upper) and 4-lepton (lower) channels for the 2016--2018 data sets. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the sum of statistical and systematic uncertainties in the SM background prediction. The expected SM background distributions and the uncertainties are shown after fitting the data under the background-only hypothesis. For illustration, an example signal hypothesis for the production of the type-III seesaw heavy fermions in the scenario with mixing exclusively to \PGt lepton for $m_{\Sigma}=850\GeV$, before the fit, is also overlaid.

The \textit{VLL-M} BDT regions for the 3-lepton (upper) and 4-lepton (lower) channels for the 2016--2018 data sets. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the sum of statistical and systematic uncertainties in the SM background prediction. The expected SM background distributions and the uncertainties are shown after fitting the data under the background-only hypothesis. For illustration, an example signal hypothesis for the production of the vector-like \PGt lepton in the doublet scenario for $m_{\vltau}=400\GeV$, before the fit, is also overlaid.

The \textit{VLL-M} BDT regions for the 3-lepton (upper) and 4-lepton (lower) channels for the 2016--2018 data sets. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the sum of statistical and systematic uncertainties in the SM background prediction. The expected SM background distributions and the uncertainties are shown after fitting the data under the background-only hypothesis. For illustration, an example signal hypothesis for the production of the vector-like \PGt lepton in the doublet scenario for $m_{\vltau}=400\GeV$, before the fit, is also overlaid.

The \textit{VLL-H} BDT regions for the 3-lepton (upper) and 4-lepton (lower) channels for the 2016--2018 data sets. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the sum of statistical and systematic uncertainties in the SM background prediction. The expected SM background distributions and the uncertainties are shown after fitting the data under the background-only hypothesis. For illustration, an example signal hypothesis for the production of the vector-like \PGt lepton in the doublet scenario for $m_{\vltau}=900\GeV$, before the fit, is also overlaid.

The \textit{VLL-H} BDT regions for the 3-lepton (upper) and 4-lepton (lower) channels for the 2016--2018 data sets. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the sum of statistical and systematic uncertainties in the SM background prediction. The expected SM background distributions and the uncertainties are shown after fitting the data under the background-only hypothesis. For illustration, an example signal hypothesis for the production of the vector-like \PGt lepton in the doublet scenario for $m_{\vltau}=900\GeV$, before the fit, is also overlaid.

The \textit{LQ-M} $\mathcal{B}_{\PGt}=1$ BDT regions for the 3-lepton (upper) and 4-lepton (lower) channels for the 2016--2018 data sets. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the sum of statistical and systematic uncertainties in the SM background prediction. The expected SM background distributions and the uncertainties are shown after fitting the data under the background-only hypothesis. For illustration, an example signal hypothesis for the production of the scalar leptoquark coupled to a top quark and a \PGt lepton for $m_{\PS}=700\GeV$, before the fit, is also overlaid.

The \textit{LQ-M} $\mathcal{B}_{\PGt}=1$ BDT regions for the 3-lepton (upper) and 4-lepton (lower) channels for the 2016--2018 data sets. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the sum of statistical and systematic uncertainties in the SM background prediction. The expected SM background distributions and the uncertainties are shown after fitting the data under the background-only hypothesis. For illustration, an example signal hypothesis for the production of the scalar leptoquark coupled to a top quark and a \PGt lepton for $m_{\PS}=700\GeV$, before the fit, is also overlaid.

The \textit{LQ-H} $\mathcal{B}_{\PGt}=1$ BDT regions for the 3-lepton (upper) and 4-lepton (lower) channels for the 2016--2018 data sets. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the sum of statistical and systematic uncertainties in the SM background prediction. The expected SM background distributions and the uncertainties are shown after fitting the data under the background-only hypothesis. For illustration, an example signal hypothesis for the production of the scalar leptoquark coupled to a top quark and a \PGt lepton for $m_{\PS}=1.2\TeV$, before the fit, is also overlaid.

The \textit{LQ-H} $\mathcal{B}_{\PGt}=1$ BDT regions for the 3-lepton (upper) and 4-lepton (lower) channels for the 2016--2018 data sets. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the sum of statistical and systematic uncertainties in the SM background prediction. The expected SM background distributions and the uncertainties are shown after fitting the data under the background-only hypothesis. For illustration, an example signal hypothesis for the production of the scalar leptoquark coupled to a top quark and a \PGt lepton for $m_{\PS}=1.2\TeV$, before the fit, is also overlaid.

The \textit{LQ-M} $\mathcal{B}_{\Pe}+\mathcal{B}_{\PGm}=1$ BDT regions for the 3-lepton (upper) and 4-lepton (lower) channels for the 2016--2018 data sets. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the sum of statistical and systematic uncertainties in the SM background prediction. The expected SM background distributions and the uncertainties are shown after fitting the data under the background-only hypothesis. For illustration, an example signal hypothesis for the production of the scalar leptoquark coupled to a top quark and a muon for $m_{\PS}=700\GeV$, before the fit, is also overlaid.

The \textit{LQ-M} $\mathcal{B}_{\Pe}+\mathcal{B}_{\PGm}=1$ BDT regions for the 3-lepton (upper) and 4-lepton (lower) channels for the 2016--2018 data sets. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the sum of statistical and systematic uncertainties in the SM background prediction. The expected SM background distributions and the uncertainties are shown after fitting the data under the background-only hypothesis. For illustration, an example signal hypothesis for the production of the scalar leptoquark coupled to a top quark and a muon for $m_{\PS}=700\GeV$, before the fit, is also overlaid.

Observed and expected upper limits at 95\% \CL on the production cross section for the type-III seesaw fermions in the flavor-democratic scenario using the table schemes and the BDT regions of the \textit{SS-M} and the \textit{SS-H} $\mathcal{B}_{\Pe}=\mathcal{B}_{\PGm}=\mathcal{B}_{\PGt}$ BDTs. To the left of the vertical dashed gray line, the limits are shown from the advanced \ST table, and to the right the limits are shown from the BDT regions.

The \textit{LQ-H} $\mathcal{B}_{\Pe}+\mathcal{B}_{\PGm}=1$ BDT regions for the 3-lepton (upper) and 4-lepton (lower) channels for the 2016--2018 data sets. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the sum of statistical and systematic uncertainties in the SM background prediction. The expected SM background distributions and the uncertainties are shown after fitting the data under the background-only hypothesis. For illustration, an example signal hypothesis for the production of the scalar leptoquark coupled to a top quark and an electron for $m_{\PS}=1.4\TeV$, before the fit, is also overlaid.

Observed (\cmsLeft) and expected (\cmsRight) lower limits at 95\% \CL on the mass of the type-III seesaw fermions in the plane defined by $\mathcal{B}_{\Pe}$ and $\mathcal{B}_{\PGt}$, with the constraint that \mbox{$\mathcal{B}_{\Pe} + \mathcal{B}_{\Pgm} + \mathcal{B}_{\Pgt}=1$}. These limits arise from the \textit{SS-H} $\mathcal{B}_{\PGt}=1$ BDT when $\mathcal{B}_{\PGt} \ge 0.9$, and by the \textit{SS-H} $\mathcal{B}_{\Pe}=\mathcal{B}_{\PGm}=\mathcal{B}_{\PGt}$ BDT for the other decay branching fraction combinations.

The \textit{LQ-H} $\mathcal{B}_{\Pe}+\mathcal{B}_{\PGm}=1$ BDT regions for the 3-lepton (upper) and 4-lepton (lower) channels for the 2016--2018 data sets. The lower panel shows the ratio of observed events to the total expected background prediction. The gray band on the ratio represents the sum of statistical and systematic uncertainties in the SM background prediction. The expected SM background distributions and the uncertainties are shown after fitting the data under the background-only hypothesis. For illustration, an example signal hypothesis for the production of the scalar leptoquark coupled to a top quark and an electron for $m_{\PS}=1.4\TeV$, before the fit, is also overlaid.

Observed (\cmsLeft) and expected (\cmsRight) lower limits at 95\% \CL on the mass of the type-III seesaw fermions in the plane defined by $\mathcal{B}_{\Pe}$ and $\mathcal{B}_{\PGt}$, with the constraint that \mbox{$\mathcal{B}_{\Pe} + \mathcal{B}_{\Pgm} + \mathcal{B}_{\Pgt}=1$}. These limits arise from the \textit{SS-H} $\mathcal{B}_{\PGt}=1$ BDT when $\mathcal{B}_{\PGt} \ge 0.9$, and by the \textit{SS-H} $\mathcal{B}_{\Pe}=\mathcal{B}_{\PGm}=\mathcal{B}_{\PGt}$ BDT for the other decay branching fraction combinations.

Observed and expected upper limits at 95\% \CL on the production cross section for the type-III seesaw fermions in the flavor-democratic scenario using the table schemes and the BDT regions of the \textit{SS-M} and the \textit{SS-H} $\mathcal{B}_{\Pe}=\mathcal{B}_{\PGm}=\mathcal{B}_{\PGt}$ BDTs. To the left of the vertical dashed gray line, the limits are shown from the advanced \ST table, and to the right the limits are shown from the BDT regions.

Observed (\cmsLeft) and expected (\cmsRight) lower limits at 95\% \CL on the mass of the type-III seesaw fermions in the plane defined by $\mathcal{B}_{\Pe}$ and $\mathcal{B}_{\PGt}$, with the constraint that \mbox{$\mathcal{B}_{\Pe} + \mathcal{B}_{\Pgm} + \mathcal{B}_{\Pgt}=1$}. These limits arise from the \textit{SS-H} $\mathcal{B}_{\PGt}=1$ BDT when $\mathcal{B}_{\PGt} \ge 0.9$, and by the \textit{SS-H} $\mathcal{B}_{\Pe}=\mathcal{B}_{\PGm}=\mathcal{B}_{\PGt}$ BDT for the other decay branching fraction combinations.

Observed (\cmsLeft) and expected (\cmsRight) lower limits at 95\% \CL on the mass of the type-III seesaw fermions in the plane defined by $\mathcal{B}_{\Pe}$ and $\mathcal{B}_{\PGt}$, with the constraint that \mbox{$\mathcal{B}_{\Pe} + \mathcal{B}_{\Pgm} + \mathcal{B}_{\Pgt}=1$}. These limits arise from the \textit{SS-H} $\mathcal{B}_{\PGt}=1$ BDT when $\mathcal{B}_{\PGt} \ge 0.9$, and by the \textit{SS-H} $\mathcal{B}_{\Pe}=\mathcal{B}_{\PGm}=\mathcal{B}_{\PGt}$ BDT for the other decay branching fraction combinations.

Observed and expected upper limits at 95\% \CL on the production cross section for the vector-like \PGt leptons: doublet model (\cmsLeft), and singlet model (\cmsRight). For the doublet vector-like lepton model, to the left of the vertical dashed gray line, the limits are shown from the advanced \ST table, while to the right the limits are shown from the BDT regions. For the singlet vector-like lepton model, the limit is shown from the advanced \ST table for all masses.

Observed and expected upper limits at 95\% \CL on the production cross section for the vector-like \PGt leptons: doublet model (\cmsLeft), and singlet model (\cmsRight). For the doublet vector-like lepton model, to the left of the vertical dashed gray line, the limits are shown from the advanced \ST table, while to the right the limits are shown from the BDT regions. For the singlet vector-like lepton model, the limit is shown from the advanced \ST table for all masses.

Observed and expected upper limits at 95\% \CL on the production cross section for the scalar leptoquarks: $\mathcal{B}_{\Pe}=1$ (upper left), $\mathcal{B}_{\PGm}=1$ (upper right), and $\mathcal{B}_{\PGt}=1$ (lower). In each figure, the limits to the left of the vertical dashed gray line are shown from the advanced \ST table, and to the right are shown from the BDT regions.

Observed and expected upper limits at 95\% \CL on the production cross section for the scalar leptoquarks: $\mathcal{B}_{\Pe}=1$ (upper left), $\mathcal{B}_{\PGm}=1$ (upper right), and $\mathcal{B}_{\PGt}=1$ (lower). In each figure, the limits to the left of the vertical dashed gray line are shown from the advanced \ST table, and to the right are shown from the BDT regions.

Observed and expected upper limits at 95\% \CL on the production cross section for the scalar leptoquarks: $\mathcal{B}_{\Pe}=1$ (upper left), $\mathcal{B}_{\PGm}=1$ (upper right), and $\mathcal{B}_{\PGt}=1$ (lower). In each figure, the limits to the left of the vertical dashed gray line are shown from the advanced \ST table, and to the right are shown from the BDT regions.

Observed and expected upper limits at 95\% \CL on the production cross section for the scalar leptoquarks: $\mathcal{B}_{\Pe}=1$ (upper left), $\mathcal{B}_{\PGm}=1$ (upper right), and $\mathcal{B}_{\PGt}=1$ (lower). In each figure, the limits to the left of the vertical dashed gray line are shown from the advanced \ST table, and to the right are shown from the BDT regions.