CMS-EXO-21-002

CMS-EXO-21-002 ; CERN-EP-2022-008
Inclusive nonresonant multilepton probes of new phenomena at $\sqrt{s} = $ 13 TeV
CMS Collaboration
17 February 2022
Phys. Rev. D 105 (2022) 112007
Abstract: An inclusive search for nonresonant signatures of beyond the standard model (SM) phenomena in events with three or more charged leptons, including hadronically decaying $\tau$ leptons, is presented. The analysis is based on a data sample corresponding to an integrated luminosity of 138 fb$^{-1}$ of proton-proton collisions at $\sqrt{s} = $ 13 TeV, collected by the CMS experiment at the LHC in 2016-2018. Events are categorized based on the lepton and b-tagged jet multiplicities and various kinematic variables. Three scenarios of physics beyond the SM are probed, and signal-specific boosted decision trees are used for enhancing sensitivity. No significant deviations from the background expectations are observed. Lower limits are set at 95% confidence level on the mass of type-III seesaw heavy fermions in the range 845-1065 GeV for various decay branching fraction combinations to SM leptons. Doublet and singlet vector-like $\tau$ lepton extensions of the SM are excluded for masses below 1045 GeV and in the mass range 125-150 GeV, respectively. Scalar leptoquarks decaying exclusively to a top quark and a lepton are excluded below 1.12-1.42 TeV, depending on the lepton flavor. For the type-III seesaw as well as the vector-like doublet model, these constraints are the most stringent to date. For the vector-like singlet model, these are the first constraints from the LHC experiments. Detailed results are also presented to facilitate alternative theoretical interpretations.
Links: e-print arXiv:2202.08676 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ;

Figures & Tables	Summary	Additional Figures	References	CMS Publications

Figures
png pdf	Figure 1: Example processes illustrating production and decay of type-III seesaw heavy fermion pairs at the LHC that result in multilepton final states.
png pdf	Figure 1-a: Example processes illustrating production and decay of type-III seesaw heavy fermion pairs at the LHC that result in multilepton final states.
png pdf	Figure 1-b: Example processes illustrating production and decay of type-III seesaw heavy fermion pairs at the LHC that result in multilepton final states.
png pdf	Figure 2: Example processes illustrating production and decay of doublet vector-like $\tau$ lepton pairs at the LHC that result in multilepton final states. The right diagram also illustrates the singlet scenario.
png pdf	Figure 2-a: Example processes illustrating production and decay of doublet vector-like $\tau$ lepton pairs at the LHC that result in multilepton final states. The right diagram also illustrates the singlet scenario.
png pdf	Figure 2-b: Example processes illustrating production and decay of doublet vector-like $\tau$ lepton pairs at the LHC that result in multilepton final states. The right diagram also illustrates the singlet scenario.
png pdf	Figure 3: Example processes illustrating the production and decay of scalar leptoquark pairs in pp collisions at the LHC that result in multilepton final states.
png pdf	Figure 3-a: Example processes illustrating the production and decay of scalar leptoquark pairs in pp collisions at the LHC that result in multilepton final states.
png pdf	Figure 3-b: Example processes illustrating the production and decay of scalar leptoquark pairs in pp collisions at the LHC that result in multilepton final states.
png pdf	Figure 4: The distributions of ${M_{\mathrm {T}}}$ in 3L OnZ CR (upper left), visible diboson ${p_{\mathrm {T}}}$ in 4L ZZ CR (upper right), ${{p_{\mathrm {T}}} ^\text {miss}}$ in 2L1T MisID CR (lower left), and $ {H_{\mathrm {T}}} $ in 3L $ {{\mathrm{t} {}\mathrm{\bar{t}}} }$Z 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.
png pdf	Figure 4-a: The distributions of ${M_{\mathrm {T}}}$ in 3L OnZ CR (upper left), visible diboson ${p_{\mathrm {T}}}$ in 4L ZZ CR (upper right), ${{p_{\mathrm {T}}} ^\text {miss}}$ in 2L1T MisID CR (lower left), and $ {H_{\mathrm {T}}} $ in 3L $ {{\mathrm{t} {}\mathrm{\bar{t}}} }$Z 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.
png pdf	Figure 4-b: The distributions of ${M_{\mathrm {T}}}$ in 3L OnZ CR (upper left), visible diboson ${p_{\mathrm {T}}}$ in 4L ZZ CR (upper right), ${{p_{\mathrm {T}}} ^\text {miss}}$ in 2L1T MisID CR (lower left), and $ {H_{\mathrm {T}}} $ in 3L $ {{\mathrm{t} {}\mathrm{\bar{t}}} }$Z 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.
png pdf	Figure 4-c: The distributions of ${M_{\mathrm {T}}}$ in 3L OnZ CR (upper left), visible diboson ${p_{\mathrm {T}}}$ in 4L ZZ CR (upper right), ${{p_{\mathrm {T}}} ^\text {miss}}$ in 2L1T MisID CR (lower left), and $ {H_{\mathrm {T}}} $ in 3L $ {{\mathrm{t} {}\mathrm{\bar{t}}} }$Z 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.
png pdf	Figure 4-d: The distributions of ${M_{\mathrm {T}}}$ in 3L OnZ CR (upper left), visible diboson ${p_{\mathrm {T}}}$ in 4L ZZ CR (upper right), ${{p_{\mathrm {T}}} ^\text {miss}}$ in 2L1T MisID CR (lower left), and $ {H_{\mathrm {T}}} $ in 3L $ {{\mathrm{t} {}\mathrm{\bar{t}}} }$Z 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.
png pdf	Figure 5: The distributions of ${L_{\mathrm {T}}}$ (upper left), ${{p_{\mathrm {T}}} ^\text {miss}}$ (upper right), and $ {H_{\mathrm {T}}} $ (lower left) in all seven multilepton channels, and ${M_{\text {OSSF}}}$ (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 $\tau$ lepton in the doublet scenario of $m_{{\tau ^{\prime}}} = $ 1 TeV and a scalar leptoquark coupled to a top quark and a $\tau$ lepton of $m_{\mathrm{S}} = $ 1 TeV are overlaid in the ${L_{\mathrm {T}}}$ and $ {H_{\mathrm {T}}} $ 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 ${{p_{\mathrm {T}}} ^\text {miss}}$ and ${M_{\text {OSSF}}}$ distributions.
png pdf	Figure 5-a: The distributions of ${L_{\mathrm {T}}}$ (upper left), ${{p_{\mathrm {T}}} ^\text {miss}}$ (upper right), and $ {H_{\mathrm {T}}} $ (lower left) in all seven multilepton channels, and ${M_{\text {OSSF}}}$ (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 $\tau$ lepton in the doublet scenario of $m_{{\tau ^{\prime}}} = $ 1 TeV and a scalar leptoquark coupled to a top quark and a $\tau$ lepton of $m_{\mathrm{S}} = $ 1 TeV are overlaid in the ${L_{\mathrm {T}}}$ and $ {H_{\mathrm {T}}} $ 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 ${{p_{\mathrm {T}}} ^\text {miss}}$ and ${M_{\text {OSSF}}}$ distributions.
png pdf	Figure 5-b: The distributions of ${L_{\mathrm {T}}}$ (upper left), ${{p_{\mathrm {T}}} ^\text {miss}}$ (upper right), and $ {H_{\mathrm {T}}} $ (lower left) in all seven multilepton channels, and ${M_{\text {OSSF}}}$ (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 $\tau$ lepton in the doublet scenario of $m_{{\tau ^{\prime}}} = $ 1 TeV and a scalar leptoquark coupled to a top quark and a $\tau$ lepton of $m_{\mathrm{S}} = $ 1 TeV are overlaid in the ${L_{\mathrm {T}}}$ and $ {H_{\mathrm {T}}} $ 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 ${{p_{\mathrm {T}}} ^\text {miss}}$ and ${M_{\text {OSSF}}}$ distributions.
png pdf	Figure 5-c: The distributions of ${L_{\mathrm {T}}}$ (upper left), ${{p_{\mathrm {T}}} ^\text {miss}}$ (upper right), and $ {H_{\mathrm {T}}} $ (lower left) in all seven multilepton channels, and ${M_{\text {OSSF}}}$ (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 $\tau$ lepton in the doublet scenario of $m_{{\tau ^{\prime}}} = $ 1 TeV and a scalar leptoquark coupled to a top quark and a $\tau$ lepton of $m_{\mathrm{S}} = $ 1 TeV are overlaid in the ${L_{\mathrm {T}}}$ and $ {H_{\mathrm {T}}} $ 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 ${{p_{\mathrm {T}}} ^\text {miss}}$ and ${M_{\text {OSSF}}}$ distributions.
png pdf	Figure 5-d: The distributions of ${L_{\mathrm {T}}}$ (upper left), ${{p_{\mathrm {T}}} ^\text {miss}}$ (upper right), and $ {H_{\mathrm {T}}} $ (lower left) in all seven multilepton channels, and ${M_{\text {OSSF}}}$ (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 $\tau$ lepton in the doublet scenario of $m_{{\tau ^{\prime}}} = $ 1 TeV and a scalar leptoquark coupled to a top quark and a $\tau$ lepton of $m_{\mathrm{S}} = $ 1 TeV are overlaid in the ${L_{\mathrm {T}}}$ and $ {H_{\mathrm {T}}} $ 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 ${{p_{\mathrm {T}}} ^\text {miss}}$ and ${M_{\text {OSSF}}}$ distributions.
png pdf	Figure 6: Distributions of BDT score from the SS-M $\mathcal {B}_{\mathrm{e}}=\mathcal {B}_{\mu}=\mathcal {B}_{\tau}$ BDT are shown for the 3L+2L1T CR (left), and the 4L ZZ CR (right). The 3L+2L1T CR consists of the 3L OnZ, 3L Z$\gamma$, 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.
png pdf	Figure 6-a: Distributions of BDT score from the SS-M $\mathcal {B}_{\mathrm{e}}=\mathcal {B}_{\mu}=\mathcal {B}_{\tau}$ BDT are shown for the 3L+2L1T CR (left), and the 4L ZZ CR (right). The 3L+2L1T CR consists of the 3L OnZ, 3L Z$\gamma$, 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.
png pdf	Figure 6-b: Distributions of BDT score from the SS-M $\mathcal {B}_{\mathrm{e}}=\mathcal {B}_{\mu}=\mathcal {B}_{\tau}$ BDT are shown for the 3L+2L1T CR (left), and the 4L ZZ CR (right). The 3L+2L1T CR consists of the 3L OnZ, 3L Z$\gamma$, 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.
png pdf	Figure 7: Distributions of BDT score from the SS-M $\mathcal {B}_{\mathrm{e}}=\mathcal {B}_{\mu}=\mathcal {B}_{\tau}$ BDT are shown for events lying outside the control regions in the three-lepton (3L, 2L1T, 1L2T) channels (left), and the four-lepton (4L, 3L1T, 2L2T, 1L3T) channels (right). 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.
png pdf	Figure 7-a: Distributions of BDT score from the SS-M $\mathcal {B}_{\mathrm{e}}=\mathcal {B}_{\mu}=\mathcal {B}_{\tau}$ BDT are shown for events lying outside the control regions in the three-lepton (3L, 2L1T, 1L2T) channels (left), and the four-lepton (4L, 3L1T, 2L2T, 1L3T) channels (right). 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.
png pdf	Figure 7-b: Distributions of BDT score from the SS-M $\mathcal {B}_{\mathrm{e}}=\mathcal {B}_{\mu}=\mathcal {B}_{\tau}$ BDT are shown for events lying outside the control regions in the three-lepton (3L, 2L1T, 1L2T) channels (left), and the four-lepton (4L, 3L1T, 2L2T, 1L3T) channels (right). 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.
png pdf	Figure 8: The SR distributions of the fundamental $ {L_{\mathrm {T}}} $+${{p_{\mathrm {T}}} ^\text {miss}}$ table for the combined 2016-2018 data set. The detailed description of the bin numbers can be found in Tables 3-6. 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.
png pdf	Figure 8-a: The SR distributions of the fundamental $ {L_{\mathrm {T}}} $+${{p_{\mathrm {T}}} ^\text {miss}}$ table for the combined 2016-2018 data set. The detailed description of the bin numbers can be found in Tables 3-6. 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.
png pdf	Figure 8-b: The SR distributions of the fundamental $ {L_{\mathrm {T}}} $+${{p_{\mathrm {T}}} ^\text {miss}}$ table for the combined 2016-2018 data set. The detailed description of the bin numbers can be found in Tables 3-6. 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.
png pdf	Figure 8-c: The SR distributions of the fundamental $ {L_{\mathrm {T}}} $+${{p_{\mathrm {T}}} ^\text {miss}}$ table for the combined 2016-2018 data set. The detailed description of the bin numbers can be found in Tables 3-6. 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.
png pdf	Figure 9: The SR distributions of the fundamental ${S_{\mathrm {T}}}$ table for the combined 2016-2018 data set. The detailed description of the bin numbers can be found in Tables 3-6. 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 $\tau$ lepton in the doublet scenario for $m_{{\tau ^{\prime}}} = $ 1 TeV, before the fit, is also overlaid.
png pdf	Figure 9-a: The SR distributions of the fundamental ${S_{\mathrm {T}}}$ table for the combined 2016-2018 data set. The detailed description of the bin numbers can be found in Tables 3-6. 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 $\tau$ lepton in the doublet scenario for $m_{{\tau ^{\prime}}} = $ 1 TeV, before the fit, is also overlaid.
png pdf	Figure 9-b: The SR distributions of the fundamental ${S_{\mathrm {T}}}$ table for the combined 2016-2018 data set. The detailed description of the bin numbers can be found in Tables 3-6. 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 $\tau$ lepton in the doublet scenario for $m_{{\tau ^{\prime}}} = $ 1 TeV, before the fit, is also overlaid.
png pdf	Figure 9-c: The SR distributions of the fundamental ${S_{\mathrm {T}}}$ table for the combined 2016-2018 data set. The detailed description of the bin numbers can be found in Tables 3-6. 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 $\tau$ lepton in the doublet scenario for $m_{{\tau ^{\prime}}} = $ 1 TeV, before the fit, is also overlaid.
png pdf	Figure 10: The 3L SR distributions of the advanced ${S_{\mathrm {T}}}$ table for the combined 2016-2018 data set. The detailed description of the bin numbers can be found in Table 3. 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_{\mathrm{S}} = $ 1.4 TeV, before the fit, is also overlaid.
png pdf	Figure 10-a: The 3L SR distributions of the advanced ${S_{\mathrm {T}}}$ table for the combined 2016-2018 data set. The detailed description of the bin numbers can be found in Table 3. 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_{\mathrm{S}} = $ 1.4 TeV, before the fit, is also overlaid.
png pdf	Figure 10-b: The 3L SR distributions of the advanced ${S_{\mathrm {T}}}$ table for the combined 2016-2018 data set. The detailed description of the bin numbers can be found in Table 3. 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_{\mathrm{S}} = $ 1.4 TeV, before the fit, is also overlaid.
png pdf	Figure 10-c: The 3L SR distributions of the advanced ${S_{\mathrm {T}}}$ table for the combined 2016-2018 data set. The detailed description of the bin numbers can be found in Table 3. 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_{\mathrm{S}} = $ 1.4 TeV, before the fit, is also overlaid.
png pdf	Figure 11: The 2L1T SR distributions of the advanced ${S_{\mathrm {T}}}$ table for the combined 2016-2018 data set. The detailed description of the bin numbers can be found in Table 4. 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_{\mathrm{S}} = $ 1.4 TeV, before the fit, is also overlaid.
png pdf	Figure 11-a: The 2L1T SR distributions of the advanced ${S_{\mathrm {T}}}$ table for the combined 2016-2018 data set. The detailed description of the bin numbers can be found in Table 4. 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_{\mathrm{S}} = $ 1.4 TeV, before the fit, is also overlaid.
png pdf	Figure 11-b: The 2L1T SR distributions of the advanced ${S_{\mathrm {T}}}$ table for the combined 2016-2018 data set. The detailed description of the bin numbers can be found in Table 4. 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_{\mathrm{S}} = $ 1.4 TeV, before the fit, is also overlaid.
png pdf	Figure 11-c: The 2L1T SR distributions of the advanced ${S_{\mathrm {T}}}$ table for the combined 2016-2018 data set. The detailed description of the bin numbers can be found in Table 4. 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_{\mathrm{S}} = $ 1.4 TeV, before the fit, is also overlaid.
png pdf	Figure 12: The 1L2T SR distribution of the advanced ${S_{\mathrm {T}}}$ table for the combined 2016-2018 data set. The detailed description of the bin numbers can be found in Table 5. 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_{\mathrm{S}} = $ 1.4 TeV, before the fit, is also overlaid. For this category, the signal yield is negligible and is not visible in the figure.
png pdf	Figure 13: The 4L, 3L1T, 2L2T and 1L3T SR distributions of the advanced ${S_{\mathrm {T}}}$ table for the combined 2016-2018 data set. The detailed description of the bin numbers can be found in Table 6. 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_{\mathrm{S}} = $ 1.4 TeV, before the fit, is also overlaid.
png pdf	Figure 13-a: The 4L, 3L1T, 2L2T and 1L3T SR distributions of the advanced ${S_{\mathrm {T}}}$ table for the combined 2016-2018 data set. The detailed description of the bin numbers can be found in Table 6. 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_{\mathrm{S}} = $ 1.4 TeV, before the fit, is also overlaid.
png pdf	Figure 13-b: The 4L, 3L1T, 2L2T and 1L3T SR distributions of the advanced ${S_{\mathrm {T}}}$ table for the combined 2016-2018 data set. The detailed description of the bin numbers can be found in Table 6. 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_{\mathrm{S}} = $ 1.4 TeV, before the fit, is also overlaid.
png pdf	Figure 13-c: The 4L, 3L1T, 2L2T and 1L3T SR distributions of the advanced ${S_{\mathrm {T}}}$ table for the combined 2016-2018 data set. The detailed description of the bin numbers can be found in Table 6. 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_{\mathrm{S}} = $ 1.4 TeV, before the fit, is also overlaid.
png pdf	Figure 14: The SS-M $\mathcal {B}_{\mathrm{e}}=\mathcal {B}_{\mu}=\mathcal {B}_{\tau}$ 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.
png pdf	Figure 14-a: The SS-M $\mathcal {B}_{\mathrm{e}}=\mathcal {B}_{\mu}=\mathcal {B}_{\tau}$ 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.
png pdf	Figure 14-b: The SS-M $\mathcal {B}_{\mathrm{e}}=\mathcal {B}_{\mu}=\mathcal {B}_{\tau}$ 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.
png pdf	Figure 15: The SS-H $\mathcal {B}_{\mathrm{e}}=\mathcal {B}_{\mu}=\mathcal {B}_{\tau}$ 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.
png pdf	Figure 15-a: The SS-H $\mathcal {B}_{\mathrm{e}}=\mathcal {B}_{\mu}=\mathcal {B}_{\tau}$ 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.
png pdf	Figure 15-b: The SS-H $\mathcal {B}_{\mathrm{e}}=\mathcal {B}_{\mu}=\mathcal {B}_{\tau}$ 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.
png pdf	Figure 16: The SS-M $\mathcal {B}_{\tau}=1$ 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 $\tau$ lepton for $m_{\Sigma} = $ 550 GeV, before the fit, is also overlaid.
png pdf	Figure 16-a: The SS-M $\mathcal {B}_{\tau}=1$ 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 $\tau$ lepton for $m_{\Sigma} = $ 550 GeV, before the fit, is also overlaid.
png pdf	Figure 16-b: The SS-M $\mathcal {B}_{\tau}=1$ 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 $\tau$ lepton for $m_{\Sigma} = $ 550 GeV, before the fit, is also overlaid.
png pdf	Figure 17: The SS-H $\mathcal {B}_{\tau}=1$ 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 $\tau$ lepton for $m_{\Sigma} = $ 850 GeV, before the fit, is also overlaid.
png pdf	Figure 17-a: The SS-H $\mathcal {B}_{\tau}=1$ 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 $\tau$ lepton for $m_{\Sigma} = $ 850 GeV, before the fit, is also overlaid.
png pdf	Figure 17-b: The SS-H $\mathcal {B}_{\tau}=1$ 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 $\tau$ lepton for $m_{\Sigma} = $ 850 GeV, before the fit, is also overlaid.
png pdf	Figure 18: The 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 $\tau$ lepton in the doublet scenario for $m_{{\tau ^{\prime}}} = $ 400 GeV, before the fit, is also overlaid.
png pdf	Figure 18-a: The 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 $\tau$ lepton in the doublet scenario for $m_{{\tau ^{\prime}}} = $ 400 GeV, before the fit, is also overlaid.
png pdf	Figure 18-b: The 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 $\tau$ lepton in the doublet scenario for $m_{{\tau ^{\prime}}} = $ 400 GeV, before the fit, is also overlaid.
png pdf	Figure 19: The 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 $\tau$ lepton in the doublet scenario for $m_{{\tau ^{\prime}}} = $ 900 GeV, before the fit, is also overlaid.
png pdf	Figure 19-a: The 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 $\tau$ lepton in the doublet scenario for $m_{{\tau ^{\prime}}} = $ 900 GeV, before the fit, is also overlaid.
png pdf	Figure 19-b: The 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 $\tau$ lepton in the doublet scenario for $m_{{\tau ^{\prime}}} = $ 900 GeV, before the fit, is also overlaid.
png pdf	Figure 20: The LQ-M $\mathcal {B}_{\tau}=1$ 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 $\tau$ lepton for $m_{\mathrm{S}} = $ 700 GeV, before the fit, is also overlaid.
png pdf	Figure 20-a: The LQ-M $\mathcal {B}_{\tau}=1$ 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 $\tau$ lepton for $m_{\mathrm{S}} = $ 700 GeV, before the fit, is also overlaid.
png pdf	Figure 20-b: The LQ-M $\mathcal {B}_{\tau}=1$ 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 $\tau$ lepton for $m_{\mathrm{S}} = $ 700 GeV, before the fit, is also overlaid.
png pdf	Figure 21: The LQ-H $\mathcal {B}_{\tau}=1$ 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 $\tau$ lepton for $m_{\mathrm{S}} = $ 1.2 TeV, before the fit, is also overlaid.
png pdf	Figure 21-a: The LQ-H $\mathcal {B}_{\tau}=1$ 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 $\tau$ lepton for $m_{\mathrm{S}} = $ 1.2 TeV, before the fit, is also overlaid.
png pdf	Figure 21-b: The LQ-H $\mathcal {B}_{\tau}=1$ 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 $\tau$ lepton for $m_{\mathrm{S}} = $ 1.2 TeV, before the fit, is also overlaid.
png pdf	Figure 22: The LQ-M $\mathcal {B}_{\mathrm{e}}+\mathcal {B}_{\mu}=1$ 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_{\mathrm{S}} = $ 700 GeV, before the fit, is also overlaid.
png pdf	Figure 22-a: The LQ-M $\mathcal {B}_{\mathrm{e}}+\mathcal {B}_{\mu}=1$ 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_{\mathrm{S}} = $ 700 GeV, before the fit, is also overlaid.
png pdf	Figure 22-b: The LQ-M $\mathcal {B}_{\mathrm{e}}+\mathcal {B}_{\mu}=1$ 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_{\mathrm{S}} = $ 700 GeV, before the fit, is also overlaid.
png pdf	Figure 23: The LQ-H $\mathcal {B}_{\mathrm{e}}+\mathcal {B}_{\mu}=1$ 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_{\mathrm{S}} = $ 1.4 TeV, before the fit, is also overlaid.
png pdf	Figure 23-a: The LQ-H $\mathcal {B}_{\mathrm{e}}+\mathcal {B}_{\mu}=1$ 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_{\mathrm{S}} = $ 1.4 TeV, before the fit, is also overlaid.
png pdf	Figure 23-b: The LQ-H $\mathcal {B}_{\mathrm{e}}+\mathcal {B}_{\mu}=1$ 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_{\mathrm{S}} = $ 1.4 TeV, before the fit, is also overlaid.
png pdf	Figure 24: 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 SS-M and the SS-H $\mathcal {B}_{\mathrm{e}}=\mathcal {B}_{\mu}=\mathcal {B}_{\tau}$ BDTs. To the left of the vertical dashed gray line, the limits are shown from the advanced ${S_{\mathrm {T}}}$ table, and to the right the limits are shown from the BDT regions.
png pdf	Figure 25: Observed (left) and expected (right) lower limits at 95% CL on the mass of the type-III seesaw fermions in the plane defined by $\mathcal {B}_{\mathrm{e}}$ and $\mathcal {B}_{\tau}$, with the constraint that $\mathcal {B}_{\mathrm{e}} + \mathcal {B}_{\mu} + \mathcal {B}_{\tau}=$ 1. These limits arise from the SS-H $\mathcal {B}_{\tau}=$ 1 BDT when $\mathcal {B}_{\tau} \ge $ 0.9, and by the SS-H $\mathcal {B}_{\mathrm{e}}=\mathcal {B}_{\mu}=\mathcal {B}_{\tau}$ BDT for the other decay branching fraction combinations.
png pdf	Figure 25-a: Observed (left) and expected (right) lower limits at 95% CL on the mass of the type-III seesaw fermions in the plane defined by $\mathcal {B}_{\mathrm{e}}$ and $\mathcal {B}_{\tau}$, with the constraint that $\mathcal {B}_{\mathrm{e}} + \mathcal {B}_{\mu} + \mathcal {B}_{\tau}=$ 1. These limits arise from the SS-H $\mathcal {B}_{\tau}=$ 1 BDT when $\mathcal {B}_{\tau} \ge $ 0.9, and by the SS-H $\mathcal {B}_{\mathrm{e}}=\mathcal {B}_{\mu}=\mathcal {B}_{\tau}$ BDT for the other decay branching fraction combinations.
png pdf	Figure 25-b: Observed (left) and expected (right) lower limits at 95% CL on the mass of the type-III seesaw fermions in the plane defined by $\mathcal {B}_{\mathrm{e}}$ and $\mathcal {B}_{\tau}$, with the constraint that $\mathcal {B}_{\mathrm{e}} + \mathcal {B}_{\mu} + \mathcal {B}_{\tau}=$ 1. These limits arise from the SS-H $\mathcal {B}_{\tau}=$ 1 BDT when $\mathcal {B}_{\tau} \ge $ 0.9, and by the SS-H $\mathcal {B}_{\mathrm{e}}=\mathcal {B}_{\mu}=\mathcal {B}_{\tau}$ BDT for the other decay branching fraction combinations.
png pdf	Figure 26: Observed and expected upper limits at 95% CL on the production cross section for the vector-like $\tau$ leptons: doublet model (left), and singlet model (right). For the doublet vector-like lepton model, to the left of the vertical dashed gray line, the limits are shown from the advanced ${S_{\mathrm {T}}}$ 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 ${S_{\mathrm {T}}}$ table for all masses.
png pdf	Figure 26-a: Observed and expected upper limits at 95% CL on the production cross section for the vector-like $\tau$ leptons: doublet model (left), and singlet model (right). For the doublet vector-like lepton model, to the left of the vertical dashed gray line, the limits are shown from the advanced ${S_{\mathrm {T}}}$ 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 ${S_{\mathrm {T}}}$ table for all masses.
png pdf	Figure 26-b: Observed and expected upper limits at 95% CL on the production cross section for the vector-like $\tau$ leptons: doublet model (left), and singlet model (right). For the doublet vector-like lepton model, to the left of the vertical dashed gray line, the limits are shown from the advanced ${S_{\mathrm {T}}}$ 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 ${S_{\mathrm {T}}}$ table for all masses.
png pdf	Figure 27: Observed and expected upper limits at 95% CL on the production cross section for the scalar leptoquarks: $\mathcal {B}_{\mathrm{e}}=$ 1 (upper left), $\mathcal {B}_{\mu}=$ 1 (upper right), and $\mathcal {B}_{\tau}=$ 1 (lower). In each figure, the limits to the left of the vertical dashed gray line are shown from the advanced ${S_{\mathrm {T}}}$ table, and to the right are shown from the BDT regions.
png pdf	Figure 27-a: Observed and expected upper limits at 95% CL on the production cross section for the scalar leptoquarks: $\mathcal {B}_{\mathrm{e}}=$ 1 (upper left), $\mathcal {B}_{\mu}=$ 1 (upper right), and $\mathcal {B}_{\tau}=$ 1 (lower). In each figure, the limits to the left of the vertical dashed gray line are shown from the advanced ${S_{\mathrm {T}}}$ table, and to the right are shown from the BDT regions.
png pdf	Figure 27-b: Observed and expected upper limits at 95% CL on the production cross section for the scalar leptoquarks: $\mathcal {B}_{\mathrm{e}}=$ 1 (upper left), $\mathcal {B}_{\mu}=$ 1 (upper right), and $\mathcal {B}_{\tau}=$ 1 (lower). In each figure, the limits to the left of the vertical dashed gray line are shown from the advanced ${S_{\mathrm {T}}}$ table, and to the right are shown from the BDT regions.
png pdf	Figure 27-c: Observed and expected upper limits at 95% CL on the production cross section for the scalar leptoquarks: $\mathcal {B}_{\mathrm{e}}=$ 1 (upper left), $\mathcal {B}_{\mu}=$ 1 (upper right), and $\mathcal {B}_{\tau}=$ 1 (lower). In each figure, the limits to the left of the vertical dashed gray line are shown from the advanced ${S_{\mathrm {T}}}$ table, and to the right are shown from the BDT regions.

Tables
png pdf	Table 1: A summary of control regions for the irreducible SM processes Z$ \gamma $, WZ, $ {{\mathrm{t} {}\mathrm{\bar{t}}} }$Z, and ZZ, and for the misidentified lepton backgrounds. The ${{p_{\mathrm {T}}} ^\text {miss}}$, ${M_{\mathrm {T}}}$, the minimum 3L lepton ${p_{\mathrm {T}}}$ (${p_{\mathrm {T}}} ^{\mathrm {3}}$), and ${S_{\mathrm {T}}}$ are in units of GeV. The 3L OnZ CR is further split into 3L MisID e/$\mu $ CR, 3L WZ CR, and 3L $ {{\mathrm{t} {}\mathrm{\bar{t}}} }$Z CR.
png pdf	Table 2: Fundamental scheme of event categorization, as a function of lepton charge combinations and mass variables. The mass categorizations refer to masses of OSSF pairs if present, and of OSDF pairs otherwise, as explained in the text. For categorization purposes, all possible opposite-sign dielectron and dimuon pair masses in the event are considered, whereas only the largest mass in the event is considered for all other opposite-sign pairs. Only the dielectron and dimuon pairs are considered to tag events as OnZ. The 1L3T OSSF0 and OSSF1 events are combined into a single category. Disallowed categories are marked with "--''.
png pdf	Table 3: The binning of $ {L_{\mathrm {T}}} $+${{p_{\mathrm {T}}} ^\text {miss}}$ and ${S_{\mathrm {T}}}$ distributions for the fundamental scheme in the 3L channel, and the binning of ${S_{\mathrm {T}}}$ distribution for the advanced scheme in the 3L channel. The categorization is described in Table 2. The ranges, as well the ${{p_{\mathrm {T}}} ^\text {miss}}$ and $ {H_{\mathrm {T}}} $ requirements, are given in GeV. The first bins in the $ {L_{\mathrm {T}}} $+$ {{p_{\mathrm {T}}} ^\text {miss}}$ or ${S_{\mathrm {T}}}$ range contain the underflow, the last bins contain the overflow.
png pdf	Table 4: The binning of $ {L_{\mathrm {T}}} $+${{p_{\mathrm {T}}} ^\text {miss}}$ and ${S_{\mathrm {T}}}$ distributions for the fundamental scheme in the 2L1T channel, and the binning of ${S_{\mathrm {T}}}$ distribution for the advanced scheme in the 2L1T channel. The categorization is described in Table 2. The ranges, as well as the ${{p_{\mathrm {T}}} ^\text {miss}}$ and $ {H_{\mathrm {T}}} $ requirements, are given in GeV. The first bins in the $ {L_{\mathrm {T}}} $+${{p_{\mathrm {T}}} ^\text {miss}}$ or ${S_{\mathrm {T}}}$ range contain the underflow, and the last bins contain the overflow.
png pdf	Table 5: The binning of $ {L_{\mathrm {T}}} $+${{p_{\mathrm {T}}} ^\text {miss}}$ and ${S_{\mathrm {T}}}$ distributions for the fundamental scheme in the 1L2T channel, and the binning of ${S_{\mathrm {T}}}$ distribution for the advanced scheme in the 1L2T channel. The categorization is described in Table 2. The ranges, as well as the ${{p_{\mathrm {T}}} ^\text {miss}}$ and $ {H_{\mathrm {T}}} $ requirements, are given in GeV. The first bins in the $ {L_{\mathrm {T}}} $+${{p_{\mathrm {T}}} ^\text {miss}}$ or ${S_{\mathrm {T}}}$ range contain the underflow, and the last bins contain the overflow.
png pdf	Table 6: The binning of $ {L_{\mathrm {T}}} $+${{p_{\mathrm {T}}} ^\text {miss}}$ and ${S_{\mathrm {T}}}$ distributions for the fundamental scheme in the 4L, 3L1T, 2L2T, and 1L3T channels, and the binning of ${S_{\mathrm {T}}}$ distribution for the advanced scheme in the 4L, 3L1T, 2L2T, and 1L3T channels. The categorization is described in Table 2. The ranges, as well as the ${{p_{\mathrm {T}}} ^\text {miss}}$ and $ {H_{\mathrm {T}}} $ requirements, are given in GeV. The first bins in the $ {L_{\mathrm {T}}} $+${{p_{\mathrm {T}}} ^\text {miss}}$ or ${S_{\mathrm {T}}}$ range contain the underflow, and the last bins contain the overflow. For the 3L1T and 2L2T channels, multiple categories in the 1B or 2B selections are combined. These bins are marked with a single- or a double-dagger. For the 1L3T channel, all the b tag categories are combined and the corresponding bins are marked with an asterisk.
png pdf	Table 7: Input variables used for the BDTs trained for the various BSM models. Note that the indices $i,j$ run over the leptons of all flavors ($i,j=1,2,3,4$) in a given event. If a given variable is not defined in a given channel, the variable is set to a nonphysical default value for signal and background processes, and plays no role in training.
png pdf	Table 8: Signal mass points as used in the training of BDTs and the masses for which the specific trained BDT is applied in the SRs according to the best sensitivity. The labels \textit {L}, \textit {M}, and \textit {H} denote low, medium, and high mass ranges, respectively.
png pdf	Table 9: Sources, magnitudes, effective variations, and correlation properties of systematic uncertainties in the SRs. Uncertainty sources marked as "Yes'' in the Correlation column have their nuisance parameters correlated across the 3 years of data collection.

Summary

A search has been performed for physics beyond the standard model (SM), using multilepton events in proton-proton collision data at $\sqrt{s} = $ 13 TeV, collected in 2016-2018 by the CMS experiment at the LHC, corresponding to an integrated luminosity of 138 fb$^{-1}$. The search is carried out in seven orthogonal channels based on the number of light leptons and hadronically decaying $\tau$ leptons. Three model-independent schemes are used to define signal regions for the search. In addition, for each model scenario considered, a boosted decision tree is used to define model-specific signal regions. In all cases, the observations are found to be consistent with the expectations from the SM processes. Constraints are set on the production cross section of a number of beyond the SM signal models predicting a variety of multilepton final states.

Type-III seesaw heavy fermions are excluded at 95% confidence level (CL) with masses below 980 GeV (expected 1060 GeV), assuming flavor-democratic mixings with SM leptons, and below 990 GeV (expected 1065 GeV), 1065 GeV (expected 1140 GeV), and 890 GeV (expected 880 GeV), assuming mixings exclusively with electron, muon, and $\tau$ lepton flavors, respectively. Lower limits on the masses of the heavy fermions are also presented for various decay branching fractions of the heavy fermions to the different SM lepton flavors. These are the most stringent constraints on the type-III seesaw heavy fermions to date.

In the vector-like lepton doublet model, vector-like $\tau$ leptons are excluded at 95% CL with masses below 1045 GeV, with an expected exclusion of 975 GeV. These are the most stringent constraints on the doublet model. For the singlet model, vector-like $\tau$ leptons are excluded in the mass range from 125 to 150 GeV, while the expected exclusion range is from 125 to 170 GeV. These are the first constraints from the LHC on the singlet model.

Scalar leptoquarks coupled to top quarks and individual lepton flavors are also probed. In the scenario with the leptoquark coupling to a top quark and a $\tau$ lepton, leptoquarks with masses below 1120 GeV are excluded at 95% CL (expected 1235 GeV). For the decay to a top quark and an electron, leptoquarks are excluded with masses below 1340 GeV (expected 1370 GeV), and for the decay into a top quark and a muon, masses below 1420 GeV (expected 1460 GeV) are excluded.

Additional Figures
png pdf	Additional Figure 1: The $ {p_{\mathrm {T}}} $ distribution of the trailing lepton in 3L MisID CR events. The rightmost bin contains the overflow events. 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.
png pdf	Additional Figure 2: The $S_{\rm T}$ distribution in 3L WZ CR events. The rightmost bin contains the overflow events. 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.
png pdf	Additional Figure 3: The $\Delta {R}_{\rm min}$ distribution in 3L Z$\gamma $ CR events. The rightmost bin contains the overflow events. 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.
png pdf	Additional Figure 4: The model independent fundamental table categories, as defined in Table 1 in the paper. 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.
png pdf	Additional Figure 5: The $N_{\rm b}$ distribution in 3L, 2L1T, and 1L2T events. The rightmost bin contains the overflow events. 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 scalar leptoquark coupled to a top quark and a $\tau$ lepton for $m_{S} = $ 1 TeV, before the fit, is also overlaid.
png pdf	Additional Figure 6: The $N_{\rm b}$ distribution in 4L, 3L1T, 2L2T, and 1L3T events. The rightmost bin contains the overflow events. 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 scalar leptoquark coupled to a top quark and a $\tau$ lepton for $m_{S} = $ 1 TeV, before the fit, is also overlaid.
png pdf	Additional Figure 7: The $N_{\rm b}$ distribution in 4L, 3L1T, 3L, 2L2T, 2L1T, 1L3T, and 1L2T events. The rightmost bin contains the overflow events. 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 scalar leptoquark coupled to a top quark and a $\tau$ lepton for $m_{S} = $ 1 TeV, before the fit, is also overlaid.
png pdf	Additional Figure 8: The $L_{\rm T}$ distribution in 3L, 2L1T, and 1L2T events. The rightmost bin contains the overflow events. 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 vector-like $\tau$ lepton in the doublet scenario for $m_{\tau ^{\prime}} = $ 1 TeV, before the fit, is also overlaid.
png pdf	Additional Figure 9: The $ {{p_{\mathrm {T}}} ^\text {miss}} $ distribution in 3L, 2L1T, and 1L2T events. The rightmost bin contains the overflow events. 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} = $ 1 TeV, before the fit, is also overlaid.
png pdf	Additional Figure 10: The $H_{\rm T}$ distribution in 3L, 2L1T, and 1L2T events. The rightmost bin contains the overflow events. 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 scalar leptoquark coupled to a top quark and a $\tau$ lepton for $m_{S} = $ 1 TeV, before the fit, is also overlaid.
png pdf	Additional Figure 11: The $M_{\rm OSSF}$ distribution in 3L and 2L1T events. The rightmost bin contains the overflow events. 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} = $ 1 TeV, before the fit, is also overlaid.
png pdf	Additional Figure 12: The invariant mass distribution of the opposite-sign different-flavor ($M_{\rm OSDF}$) light lepton pair in 3L and 2L1T events. The rightmost bin contains the overflow events. 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} = $ 1 TeV, before the fit, is also overlaid.
png pdf	Additional Figure 13: The invariant mass distribution of the opposite-sign same-flavor ($M_{\rm OSSF}$) tau lepton pair in 1L2T events. The rightmost bin contains the overflow events. 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 vector-like $\tau$ lepton in the doublet scenario for $m_{\tau ^{\prime}} = $ 1 TeV, before the fit, is also overlaid.
png pdf	Additional Figure 14: The invariant mass distribution of the opposite-sign same-flavor ($M_{\rm OSSF}$) tau lepton pair in 2L2T, 1L3T, and 1L2T events. The rightmost bin contains the overflow events. 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 vector-like $\tau$ lepton in the doublet scenario for $m_{\tau ^{\prime}} = $ 1 TeV, before the fit, is also overlaid.
png pdf	Additional Figure 15: The invariant mass distribution of the opposite-sign different-flavor ($M_{\rm OSDF}$) light lepton and tau lepton pair in 2L1T and 1L2T events. The rightmost bin contains the overflow events. 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 vector-like $\tau$ lepton in the doublet scenario for $m_{\tau ^{\prime}} = $ 1 TeV, before the fit, is also overlaid.
png pdf	Additional Figure 16: The $M_{\rm T}^{\textrm {1}}$ in 3L, 2L1T, and 1L2T events. The rightmost bin contains the overflow events. 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 scalar leptoquark coupled to a top quark and a $\tau$ lepton for $m_{S} = $ 1 TeV, before the fit, is also overlaid.
png pdf	Additional Figure 17: The $M_{\rm T}^{\textrm {12}}$ in 3L, 2L1T, and 1L2T events. The rightmost bin contains the overflow events. 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 vector-like $\tau$ lepton in the doublet scenario for $m_{\tau ^{\prime}} = $ 1 TeV, before the fit, is also overlaid.
png pdf	Additional Figure 18: The $M_{\rm T}^{\textrm {12}}$ in 4L, 3L1T, 2L2T, 2L1T, 1L3T, and 1L2T events. The rightmost bin contains the overflow events. 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 vector-like $\tau$ lepton in the doublet scenario for $m_{\tau ^{\prime}} = $ 1 TeV, before the fit, is also overlaid.
png pdf	Additional Figure 19: 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 fundamental $L_{\rm T}+ {{p_{\mathrm {T}}} ^\text {miss}} $ table.
png pdf	Additional Figure 20: 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 fundamental $S_{\rm T}$ table.
png pdf	Additional Figure 21: 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 advanced $S_{\rm T}$ table.
png pdf	Additional Figure 22: 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 SS ($\mathcal {B}_{\mathrm{e}}=\mathcal {B}_{\mu}=\mathcal {B}_{\tau}$) BDT regions.
png pdf	Additional Figure 23: Observed and expected upper limits at 95% CL on the production cross section for the type-III seesaw fermions in the $\mathcal {B}_{\mathrm{e}}=$ 1 scenario using the fundamental $L_{\rm T}+ {{p_{\mathrm {T}}} ^\text {miss}} $ table.
png pdf	Additional Figure 24: Observed and expected upper limits at 95% CL on the production cross section for the type-III seesaw fermions in the $\mathcal {B}_{\mathrm{e}}=$ 1 scenario using the fundamental $S_{\rm T}$ table.
png pdf	Additional Figure 25: Observed and expected upper limits at 95% CL on the production cross section for the type-III seesaw fermions in the $\mathcal {B}_{\mathrm{e}}=$ 1 scenario using the advanced $S_{\rm T}$ table.
png pdf	Additional Figure 26: Observed and expected upper limits at 95% CL on the production cross section for the type-III seesaw fermions in the $\mathcal {B}_{\mathrm{e}}=$ 1 scenario using the SS ($\mathcal {B}_{\mathrm{e}}=\mathcal {B}_{\mu}=\mathcal {B}_{\tau}$) BDT regions.
png pdf	Additional Figure 27: Observed and expected upper limits at 95% CL on the production cross section for the type-III seesaw fermions in the $\mathcal {B}_{\mu}=$ 1 scenario using the fundamental $L_{\rm T}+ {{p_{\mathrm {T}}} ^\text {miss}} $ table.
png pdf	Additional Figure 28: Observed and expected upper limits at 95% CL on the production cross section for the type-III seesaw fermions in the $\mathcal {B}_{\mu}=$ 1 scenario using the fundamental $S_{\rm T}$ table.
png pdf	Additional Figure 29: Observed and expected upper limits at 95% CL on the production cross section for the type-III seesaw fermions in the $\mathcal {B}_{\mu}=$ 1 scenario using the advanced $S_{\rm T}$ table.
png pdf	Additional Figure 30: Observed and expected upper limits at 95% CL on the production cross section for the type-III seesaw fermions in the $\mathcal {B}_{\mu}=$ 1 scenario using the SS ($\mathcal {B}_{\mathrm{e}}=\mathcal {B}_{\mu}=\mathcal {B}_{\tau}$) BDT regions.
png pdf	Additional Figure 31: Observed and expected upper limits at 95% CL on the production cross section for the type-III seesaw fermions in the $\mathcal {B}_{\tau}=$ 1 scenario using the fundamental $L_{\rm T}+ {{p_{\mathrm {T}}} ^\text {miss}} $ table.
png pdf	Additional Figure 32: Observed and expected upper limits at 95% CL on the production cross section for the type-III seesaw fermions in the $\mathcal {B}_{\tau}=$ 1 scenario using the fundamental $S_{\rm T}$ table.
png pdf	Additional Figure 33: Observed and expected upper limits at 95% CL on the production cross section for the type-III seesaw fermions in the $\mathcal {B}_{\tau}=$ 1 scenario using the advanced $S_{\rm T}$ table.
png pdf	Additional Figure 34: Observed and expected upper limits at 95% CL on the production cross section for the type-III seesaw fermions in the $\mathcal {B}_{\tau}=$ 1 scenario using the SS ($\mathcal {B}_{\tau}=$ 1) BDT regions.
png pdf	Additional Figure 35: Observed and expected upper limits at 95% CL on the production cross section for the vector-like tau leptons in the doublet model using the fundamental $L_{\rm T}+ {{p_{\mathrm {T}}} ^\text {miss}} $ table.
png pdf	Additional Figure 36: Observed and expected upper limits at 95% CL on the production cross section for the vector-like tau leptons in the doublet model using the fundamental $S_{\rm T}$ table.
png pdf	Additional Figure 37: Observed and expected upper limits at 95% CL on the production cross section for the vector-like tau leptons in the doublet model using the advanced $S_{\rm T}$ table.
png pdf	Additional Figure 38: Observed and expected upper limits at 95% CL on the production cross section for the vector-like tau leptons in the doublet model using the VLL BDT regions.
png pdf	Additional Figure 39: Observed and expected upper limits at 95% CL on the production cross section for the vector-like tau leptons in the singlet model using the fundamental $L_{\rm T}+ {{p_{\mathrm {T}}} ^\text {miss}} $ table.
png pdf	Additional Figure 40: Observed and expected upper limits at 95% CL on the production cross section for the vector-like tau leptons in the singlet model using the fundamental $S_{\rm T}$ table.
png pdf	Additional Figure 41: Observed and expected upper limits at 95% CL on the production cross section for the vector-like tau leptons in the singlet model using the advanced $S_{\rm T}$ table.
png pdf	Additional Figure 42: Observed and expected upper limits at 95% CL on the production cross section for the scalar leptoquarks with $\mathcal {B}_{\mathrm{e}}=$ 1 coupling using the fundamental $L_{\rm T}+ {{p_{\mathrm {T}}} ^\text {miss}} $ table.
png pdf	Additional Figure 43: Observed and expected upper limits at 95% CL on the production cross section for the scalar leptoquarks with $\mathcal {B}_{\mathrm{e}}=$ 1 coupling using the fundamental $S_{\rm T}$ table.
png pdf	Additional Figure 44: Observed and expected upper limits at 95% CL on the production cross section for the scalar leptoquarks with $\mathcal {B}_{\mathrm{e}}=$ 1 coupling using the advanced $S_{\rm T}$ table.
png pdf	Additional Figure 45: Observed and expected upper limits at 95% CL on the production cross section for the scalar leptoquarks with $\mathcal {B}_{\mathrm{e}}=$ 1 coupling using the LQ ($\mathcal {B}_{\mathrm{e}}+\mathcal {B}_{\mu}=$ 1) BDT regions.
png pdf	Additional Figure 46: Observed and expected upper limits at 95% CL on the production cross section for the scalar leptoquarks with $\mathcal {B}_{\mu}=$ 1 coupling using the fundamental $L_{\rm T}+ {{p_{\mathrm {T}}} ^\text {miss}} $ table.
png pdf	Additional Figure 47: Observed and expected upper limits at 95% CL on the production cross section for the scalar leptoquarks with $\mathcal {B}_{\mu}=$ 1 coupling using the fundamental $S_{\rm T}$ table.
png pdf	Additional Figure 48: Observed and expected upper limits at 95% CL on the production cross section for the scalar leptoquarks with $\mathcal {B}_{\mu}=$ 1 coupling using the advanced $S_{\rm T}$ table.
png pdf	Additional Figure 49: Observed and expected upper limits at 95% CL on the production cross section for the scalar leptoquarks with $\mathcal {B}_{\mu}=$ 1 coupling using the LQ ($\mathcal {B}_{\mathrm{e}}+\mathcal {B}_{\mu}=$ 1) regions.
png pdf	Additional Figure 50: Observed and expected upper limits at 95% CL on the production cross section for the scalar leptoquarks with $\mathcal {B}_{\tau}=$ 1 coupling using the fundamental $L_{\rm T}+ {{p_{\mathrm {T}}} ^\text {miss}} $ table.
png pdf	Additional Figure 51: Observed and expected upper limits at 95% CL on the production cross section for the scalar leptoquarks with $\mathcal {B}_{\tau}=$ 1 coupling using the fundamental $S_{\rm T}$ table.
png pdf	Additional Figure 52: Observed and expected upper limits at 95% CL on the production cross section for the scalar leptoquarks with $\mathcal {B}_{\tau}=$ 1 coupling using the advanced $S_{\rm T}$ table.
png pdf	Additional Figure 53: Observed and expected upper limits at 95% CL on the production cross section for the scalar leptoquarks with $\mathcal {B}_{\tau}=$ 1 coupling using the LQ ($\mathcal {B}_{\tau}=$ 1) regions.
png pdf	Additional Figure 54: The VLL-L BDT regions for the 3-lepton channel 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 $\tau$ lepton in the doublet scenario for $m_{\tau ^{\prime}} = $ 200 GeV, before the fit, is also overlaid.
png pdf	Additional Figure 55: The VLL-L BDT regions for the 4-lepton channel 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 $\tau$ lepton in the doublet scenario for $m_{\tau ^{\prime}} = $ 200 GeV, before the fit, is also overlaid.
png pdf	Additional Figure 56: The SS-VL $\mathcal {B}_{\mathrm{e}}=\mathcal {B}_{\mu}=\mathcal {B}_{\tau}$ BDT regions for the 3-lepton channel 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} = $ 100 GeV, before the fit, is also overlaid.
png pdf	Additional Figure 57: The SS-VL $\mathcal {B}_{\mathrm{e}}=\mathcal {B}_{\mu}=\mathcal {B}_{\tau}$ BDT regions for the 4-lepton channel 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} = $ 100 GeV, before the fit, is also overlaid.
png pdf	Additional Figure 58: The SS-L $\mathcal {B}_{\mathrm{e}}=\mathcal {B}_{\mu}=\mathcal {B}_{\tau}$ BDT regions for the 3-lepton channel 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} = $ 300 GeV, before the fit, is also overlaid.
png pdf	Additional Figure 59: The SS-L $\mathcal {B}_{\mathrm{e}}=\mathcal {B}_{\mu}=\mathcal {B}_{\tau}$ BDT regions for the 4-lepton channel 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} = $ 300 GeV, before the fit, is also overlaid.
png pdf	Additional Figure 60: The SS-VL $\mathcal {B}_{\tau}=$ 1 BDT regions for the 3-lepton channel 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 $\tau$ lepton for $m_{\Sigma} = $ 100 GeV, before the fit, is also overlaid.
png pdf	Additional Figure 61: The SS-VL $\mathcal {B}_{\tau}=$ 1 BDT regions for the 4-lepton channel 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 $\tau$ lepton for $m_{\Sigma} = $ 100 GeV, before the fit, is also overlaid.
png pdf	Additional Figure 62: The SS-L $\mathcal {B}_{\tau}=$ 1 BDT regions for the 3-lepton channel 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 $\tau$ lepton for $m_{\Sigma} = $ 300 GeV, before the fit, is also overlaid.
png pdf	Additional Figure 63: The SS-L $\mathcal {B}_{\tau}=$ 1 BDT regions for the 4-lepton channel 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 $\tau$ lepton for $m_{\Sigma} = $ 300 GeV, before the fit, is also overlaid.
png pdf	Additional Figure 64: The LQ-VL $\mathcal {B}_{\tau}=$ 1 BDT regions for the 3-lepton channel 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 $\tau$ lepton for $m_{S} = $ 200 GeV, before the fit, is also overlaid.
png pdf	Additional Figure 65: The LQ-VL $\mathcal {B}_{\tau}=$ 1 BDT regions for the 4-lepton channel 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 $\tau$ lepton for $m_{S} = $ 200 GeV, before the fit, is also overlaid.
png pdf	Additional Figure 66: The LQ-L $\mathcal {B}_{\tau}=$ 1 BDT regions for the 3-lepton channel 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 $\tau$ lepton for $m_{S} = $ 400 GeV, before the fit, is also overlaid.
png pdf	Additional Figure 67: The LQ-L $\mathcal {B}_{\tau}=$ 1 BDT regions for the 4-lepton channel 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 $\tau$ lepton for $m_{S} = $ 400 GeV, before the fit, is also overlaid.
png pdf	Additional Figure 68: The LQ-VL $\mathcal {B}_{\mathrm{e}}+\mathcal {B}_{\mu}=$ 1 BDT regions for the 3-lepton channel 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_{S} = $ 200 GeV, before the fit, is also overlaid.
png pdf	Additional Figure 69: The LQ-VL $\mathcal {B}_{\mathrm{e}}+\mathcal {B}_{\mu}=$ 1 BDT regions for the 4-lepton channel 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_{S} = $ 200 GeV, before the fit, is also overlaid.
png pdf	Additional Figure 70: The LQ-L $\mathcal {B}_{\mathrm{e}}+\mathcal {B}_{\mu}=$ 1 BDT regions for the 3-lepton channel 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_{S} = $ 400 GeV, before the fit, is also overlaid.
png pdf	Additional Figure 71: The LQ-L $\mathcal {B}_{\mathrm{e}}+\mathcal {B}_{\mu}=$ 1 BDT regions for the 4-lepton channel 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_{S} = $ 400 GeV, before the fit, is also overlaid.

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