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CMS-PAS-EXO-21-002
Inclusive nonresonant multilepton probes of new phenomena at $\sqrt{s}= $ 13 TeV
Abstract: An inclusive search for nonresonant signatures of beyond the standard model phenomena in events with three or more charged leptons, including hadronic decays of 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 with the CMS detector at the LHC in 2016-2018. Events are categorized based on the charge and flavor multiplicities of the leptons, the multiplicity of b tagged jets, and various kinematic variables. Three scenarios of physics beyond the standard model are probed, viz. the pair production of type-III seesaw heavy fermions with arbitrary couplings to leptons of any flavor, vector-like leptons with couplings to tau leptons, and third generation leptoquarks with flavor-diagonal or cross-generational couplings involving top quarks and charged leptons. Optimal separation between signal and standard model background processes is achieved by the use of signal-specific boosted decision trees. No significant deviations from the background expectations are observed. Lower limits are set at 95% confidence level on the masses of type-III seesaw heavy fermions at 890 GeV for any branching fraction combination to standard model leptons. Scalar leptoquarks decaying exclusively to a top quark and a lepton of any flavor are excluded for masses below 1120 GeV. Doublet and singlet vector-like tau lepton extensions of standard model are excluded for masses below 1045 GeV and in mass range of 125-170 GeV, respectively. Detailed results are also presented to facilitate alternative theoretical interpretations.
Figures & Tables Summary Additional Figures References CMS Publications
Figures

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Figure 1:
Example processes illustrating production and decay of type-III seesaw heavy fermion pairs at the LHC that result in multilepton final states.

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Figure 1-a:
Example process illustrating production and decay of type-III seesaw heavy fermion pairs at the LHC that result in multilepton final states.

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Figure 1-b:
Example process illustrating production and decay of type-III seesaw heavy fermion pairs at the LHC that result in multilepton final states.

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Figure 2:
Example processes illustrating production and decay of doublet (left) and singlet (right) vector-like tau lepton pairs at the LHC that result in multilepton final states.

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Figure 2-a:
Example process illustrating production and decay of doublet vector-like tau lepton pairs at the LHC that result in multilepton final states.

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Figure 2-b:
Example process illustrating production and decay of singlet vector-like tau lepton pairs at the LHC that result in multilepton final states.

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Figure 3:
Example processes illustrating the production and decay of leptoquark pairs in pp collisions at the LHC that result in multilepton final states.

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Figure 3-a:
Example process illustrating the production and decay of leptoquark pairs in pp collisions at the LHC that result in multilepton final states.

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Figure 3-b:
Example process illustrating the production and decay of leptoquark pairs in pp collisions at the LHC that result in multilepton final states.

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Figure 4:
The distributions of $ {M_{\rm T}}$ in 3L OnZ CR, visible diboson $ {p_{\mathrm {T}}} $ in 4L ZZ CR, ${{p_{\mathrm {T}}} ^\text {miss}}$ in 2L1T MisID CR, and $ {H_{\mathrm {T}}} $ in 3L ttZ CR events. The rightmost bin contains the overflow events in each distribution. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions.

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Figure 4-a:
The distribution of $ {M_{\rm T}}$ in 3L OnZ CR events. The rightmost bin contains the overflow events in each distribution. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions.

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Figure 4-b:
The distribution of visible diboson $ {p_{\mathrm {T}}} $ in 4L ZZ CR events. The rightmost bin contains the overflow events in each distribution. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions.

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Figure 4-c:
The distribution of ${{p_{\mathrm {T}}} ^\text {miss}}$ in 2L1T MisID CR events. The rightmost bin contains the overflow events in each distribution. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions.

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Figure 4-d:
The distribution of $ {H_{\mathrm {T}}} $ in 3L ttZ CR events. The rightmost bin contains the overflow events in each distribution. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions.

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Figure 5:
Distributions of BDT score from the SS-M $\mathcal {B}_{\mathrm{e}}=\mathcal {B}_{\mu}=\mathcal {B}_{\tau}$ BDT are shown for the combined 3L OnZ, 3L Z$\gamma$, and 2L1T MisID CRs denoted as 3L+2L1T CR (left), and the 4L ZZ CR (right). The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions.

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Figure 5-a:
The distribution of the BDT score from the SS-M $\mathcal {B}_{\mathrm{e}}=\mathcal {B}_{\mu}=\mathcal {B}_{\tau}$ BDT is shown for the combined 3L OnZ, 3L Z$\gamma$, and 2L1T MisID CRs denoted as 3L+2L1T CR. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions.

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Figure 5-b:
The distribution of the BDT score from the SS-M $\mathcal {B}_{\mathrm{e}}=\mathcal {B}_{\mu}=\mathcal {B}_{\tau}$ BDT is shown for the 4L ZZ CR. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions.

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Figure 6:
SR distributions of the fundamental $ {L_{\rm T}+ {{p_{\mathrm {T}}} ^\text {miss}}}$ table scheme for the combined Run 2 dataset. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions. Expected SM background distributions and uncertainties are shown after fitting the data with the background-only hypothesis.

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Figure 6-a:
SR distributions of the fundamental $ {L_{\rm T}+ {{p_{\mathrm {T}}} ^\text {miss}}}$ table scheme for the combined Run 2 dataset. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions. Expected SM background distributions and uncertainties are shown after fitting the data with the background-only hypothesis.

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Figure 6-b:
SR distributions of the fundamental $ {L_{\rm T}+ {{p_{\mathrm {T}}} ^\text {miss}}}$ table scheme for the combined Run 2 dataset. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions. Expected SM background distributions and uncertainties are shown after fitting the data with the background-only hypothesis.

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Figure 6-c:
SR distributions of the fundamental $ {L_{\rm T}+ {{p_{\mathrm {T}}} ^\text {miss}}}$ table scheme for the combined Run 2 dataset. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions. Expected SM background distributions and uncertainties are shown after fitting the data with the background-only hypothesis.

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Figure 7:
SR distributions of the fundamental $ {S_{\rm T}}$ table scheme for the combined Run 2 dataset. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions. Expected SM background distributions and uncertainties are shown after fitting the data with the background-only hypothesis.

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Figure 7-a:
SR distributions of the fundamental $ {S_{\rm T}}$ table scheme for the combined Run 2 dataset. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions. Expected SM background distributions and uncertainties are shown after fitting the data with the background-only hypothesis.

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Figure 7-b:
SR distributions of the fundamental $ {S_{\rm T}}$ table scheme for the combined Run 2 dataset. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions. Expected SM background distributions and uncertainties are shown after fitting the data with the background-only hypothesis.

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Figure 7-c:
SR distributions of the fundamental $ {S_{\rm T}}$ table scheme for the combined Run 2 dataset. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions. Expected SM background distributions and uncertainties are shown after fitting the data with the background-only hypothesis.

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Figure 8:
3L SR distributions of the advanced table scheme for the combined Run 2 dataset. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions. Expected SM background distributions and uncertainties are shown after fitting the data with the background-only hypothesis.

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Figure 8-a:
3L SR distributions of the advanced table scheme for the combined Run 2 dataset. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions. Expected SM background distributions and uncertainties are shown after fitting the data with the background-only hypothesis.

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Figure 8-b:
3L SR distributions of the advanced table scheme for the combined Run 2 dataset. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions. Expected SM background distributions and uncertainties are shown after fitting the data with the background-only hypothesis.

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Figure 8-c:
3L SR distributions of the advanced table scheme for the combined Run 2 dataset. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions. Expected SM background distributions and uncertainties are shown after fitting the data with the background-only hypothesis.

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Figure 9:
2L1T SR distributions of the advanced table scheme for the combined Run 2 dataset. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions. Expected SM background distributions and uncertainties are shown after fitting the data with the background-only hypothesis.

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Figure 9-a:
2L1T SR distributions of the advanced table scheme for the combined Run 2 dataset. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions. Expected SM background distributions and uncertainties are shown after fitting the data with the background-only hypothesis.

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Figure 9-b:
2L1T SR distributions of the advanced table scheme for the combined Run 2 dataset. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions. Expected SM background distributions and uncertainties are shown after fitting the data with the background-only hypothesis.

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Figure 9-c:
2L1T SR distributions of the advanced table scheme for the combined Run 2 dataset. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions. Expected SM background distributions and uncertainties are shown after fitting the data with the background-only hypothesis.

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Figure 10:
1L2T SR distribution of the advanced table scheme for the combined Run 2 dataset. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions. Expected SM background distributions and uncertainties are shown after fitting the data with the background-only hypothesis.

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Figure 11:
4L, 3L1T, 2L2T and 1L3T SR distributions of the advanced table scheme for the combined Run 2 dataset. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions. Expected SM background distributions and uncertainties are shown after fitting the data with the background-only hypothesis.

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Figure 11-a:
4L, 3L1T, 2L2T and 1L3T SR distributions of the advanced table scheme for the combined Run 2 dataset. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions. Expected SM background distributions and uncertainties are shown after fitting the data with the background-only hypothesis.

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Figure 11-b:
4L, 3L1T, 2L2T and 1L3T SR distributions of the advanced table scheme for the combined Run 2 dataset. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions. Expected SM background distributions and uncertainties are shown after fitting the data with the background-only hypothesis.

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Figure 11-c:
4L, 3L1T, 2L2T and 1L3T SR distributions of the advanced table scheme for the combined Run 2 dataset. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions. Expected SM background distributions and uncertainties are shown after fitting the data with the background-only hypothesis.

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Figure 12:
SS-M $\mathcal {B}_{\mathrm{e}}=\mathcal {B}_{\mu}=\mathcal {B}_{\tau}$ BDT regions for the 3-lepton (top) and 4-lepton (bottom) channels for the combined Run 2 dataset. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions. Expected SM background distributions and uncertainties are shown after fitting the data with the background-only hypothesis.

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Figure 12-a:
SS-M $\mathcal {B}_{\mathrm{e}}=\mathcal {B}_{\mu}=\mathcal {B}_{\tau}$ BDT regions for the 3-lepton channel for the combined Run 2 dataset. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions. Expected SM background distributions and uncertainties are shown after fitting the data with the background-only hypothesis.

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Figure 12-b:
SS-M $\mathcal {B}_{\mathrm{e}}=\mathcal {B}_{\mu}=\mathcal {B}_{\tau}$ BDT regions for the 4-lepton channel for the combined Run 2 dataset. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions. Expected SM background distributions and uncertainties are shown after fitting the data with the background-only hypothesis.

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Figure 13:
SS-H $\mathcal {B}_{\mathrm{e}}=\mathcal {B}_{\mu}=\mathcal {B}_{\tau}$ BDT regions for the 3-lepton (top) and 4-lepton (bottom) channels for the combined Run 2 dataset. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions. Expected SM background distributions and uncertainties are shown after fitting the data with the background-only hypothesis.

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Figure 13-a:
SS-H $\mathcal {B}_{\mathrm{e}}=\mathcal {B}_{\mu}=\mathcal {B}_{\tau}$ BDT regions for the 3-lepton channel for the combined Run 2 dataset. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions. Expected SM background distributions and uncertainties are shown after fitting the data with the background-only hypothesis.

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Figure 13-b:
SS-H $\mathcal {B}_{\mathrm{e}}=\mathcal {B}_{\mu}=\mathcal {B}_{\tau}$ BDT regions for the 4-lepton channel for the combined Run 2 dataset. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions. Expected SM background distributions and uncertainties are shown after fitting the data with the background-only hypothesis.

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Figure 14:
SS-M $\mathcal {B}_{\tau}=$ 1 BDT regions for the 3-lepton (top) and 4-lepton (bottom) channels for the combined Run 2 dataset. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions. Expected SM background distributions and uncertainties are shown after fitting the data with the background-only hypothesis.

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Figure 14-a:
SS-M $\mathcal {B}_{\tau}=$ 1 BDT regions for the 3-lepton channel for the combined Run 2 dataset. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions. Expected SM background distributions and uncertainties are shown after fitting the data with the background-only hypothesis.

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Figure 14-b:
SS-M $\mathcal {B}_{\tau}=$ 1 BDT regions for the 4-lepton channel for the combined Run 2 dataset. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions. Expected SM background distributions and uncertainties are shown after fitting the data with the background-only hypothesis.

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Figure 15:
SS-H $\mathcal {B}_{\tau}=$ 1 BDT regions for the 3-lepton (top) and 4-lepton (bottom) channels for the combined Run 2 dataset. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions. Expected SM background distributions and uncertainties are shown after fitting the data with the background-only hypothesis.

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Figure 15-a:
SS-H $\mathcal {B}_{\tau}=$ 1 BDT regions for the 3-lepton channel for the combined Run 2 dataset. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions. Expected SM background distributions and uncertainties are shown after fitting the data with the background-only hypothesis.

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Figure 15-b:
SS-H $\mathcal {B}_{\tau}=$ 1 BDT regions for the 4-lepton channel for the combined Run 2 dataset. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions. Expected SM background distributions and uncertainties are shown after fitting the data with the background-only hypothesis.

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Figure 16:
VLL-M BDT regions for the 3-lepton (top) and 4-lepton (bottom) channels for the combined Run 2 dataset. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions. Expected SM background distributions and uncertainties are shown after fitting the data with the background-only hypothesis.

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Figure 16-a:
VLL-M BDT regions for the 3-lepton channel for the combined Run 2 dataset. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions. Expected SM background distributions and uncertainties are shown after fitting the data with the background-only hypothesis.

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Figure 16-b:
VLL-M BDT regions for the 4-lepton channel for the combined Run 2 dataset. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions. Expected SM background distributions and uncertainties are shown after fitting the data with the background-only hypothesis.

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Figure 17:
VLL-H BDT regions for the 3-lepton (top) and 4-lepton (bottom) channels for the combined Run 2 dataset. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions. Expected SM background distributions and uncertainties are shown after fitting the data with the background-only hypothesis.

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Figure 17-a:
VLL-H BDT regions for the 3-lepton channel for the combined Run 2 dataset. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions. Expected SM background distributions and uncertainties are shown after fitting the data with the background-only hypothesis.

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Figure 17-b:
VLL-H BDT regions for the 4-lepton channel for the combined Run 2 dataset. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions. Expected SM background distributions and uncertainties are shown after fitting the data with the background-only hypothesis.

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Figure 18:
LQ-M $\mathcal {B}_{\tau}=$ 1 BDT regions for the 3-lepton (top) and 4-lepton (bottom) channels for the combined Run 2 dataset. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions. Expected SM background distributions and uncertainties are shown after fitting the data with the background-only hypothesis.

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Figure 18-a:
LQ-M $\mathcal {B}_{\tau}=$ 1 BDT regions for the 3-lepton channel for the combined Run 2 dataset. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions. Expected SM background distributions and uncertainties are shown after fitting the data with the background-only hypothesis.

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Figure 18-b:
LQ-M $\mathcal {B}_{\tau}=$ 1 BDT regions for the 4-lepton channel for the combined Run 2 dataset. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions. Expected SM background distributions and uncertainties are shown after fitting the data with the background-only hypothesis.

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Figure 19:
LQ-H $\mathcal {B}_{\tau}=$ 1 BDT regions for the 3-lepton (top) and 4-lepton (bottom) channels for the combined Run 2 dataset. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions. Expected SM background distributions and uncertainties are shown after fitting the data with the background-only hypothesis.

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Figure 19-a:
LQ-H $\mathcal {B}_{\tau}=$ 1 BDT regions for the 4-lepton channel for the combined Run 2 dataset. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions. Expected SM background distributions and uncertainties are shown after fitting the data with the background-only hypothesis.

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Figure 19-b:
LQ-H $\mathcal {B}_{\tau}=$ 1 BDT regions for the 3-lepton (top) and 4-lepton (bottom) channels for the combined Run 2 dataset. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions. Expected SM background distributions and uncertainties are shown after fitting the data with the background-only hypothesis.

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Figure 20:
LQ-M $\mathcal {B}_{\mathrm{e}}+\mathcal {B}_{\mu}=$ 1 BDT regions for the 3-lepton (top) and 4-lepton (bottom) channels for the combined Run 2 dataset. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions. Expected SM background distributions and uncertainties are shown after fitting the data with the background-only hypothesis.

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Figure 20-a:
LQ-M $\mathcal {B}_{\mathrm{e}}+\mathcal {B}_{\mu}=$ 1 BDT regions for the 3-lepton channel for the combined Run 2 dataset. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions. Expected SM background distributions and uncertainties are shown after fitting the data with the background-only hypothesis.

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Figure 20-b:
LQ-M $\mathcal {B}_{\mathrm{e}}+\mathcal {B}_{\mu}=$ 1 BDT regions for the 4-lepton channel for the combined Run 2 dataset. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions. Expected SM background distributions and uncertainties are shown after fitting the data with the background-only hypothesis.

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Figure 21:
LQ-H $\mathcal {B}_{\mathrm{e}}+\mathcal {B}_{\mu}=$ 1 BDT regions for the 3-lepton (top) and 4-lepton (bottom) channels for the combined Run 2 dataset. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions. Expected SM background distributions and uncertainties are shown after fitting the data with the background-only hypothesis.

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Figure 21-a:
LQ-H $\mathcal {B}_{\mathrm{e}}+\mathcal {B}_{\mu}=$ 1 BDT regions for the 3-lepton channel for the combined Run 2 dataset. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions. Expected SM background distributions and uncertainties are shown after fitting the data with the background-only hypothesis.

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Figure 21-b:
LQ-H $\mathcal {B}_{\mathrm{e}}+\mathcal {B}_{\mu}=$ 1 BDT regions for the 4-lepton channel for the combined Run 2 dataset. The gray bands represent the sum of statistical and systematic uncertainties on the SM background predictions. Expected SM background distributions and uncertainties are shown after fitting the data with the background-only hypothesis.

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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 table schemes and the BDT regions of SS-M and SS-H $\mathcal {B}_{\mathrm{e}}=\mathcal {B}_{\mu}=\mathcal {B}_{\tau}$ BDT. To the left of the vertical dashed gray line, the limits are shown from the advanced $ {S_{\rm T}}$ table, and to the right the limits are shown from the BDT regions.

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Figure 23:
Observed (left) and expected (right) lower limits at 95% CL on the mass for 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.

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Figure 23-a:
Observed lower limits at 95% CL on the mass for 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.

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Figure 23-b:
Expected lower limits at 95% CL on the mass for 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.

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Figure 24:
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_{\rm 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_{\rm T}}$ table for all masses.

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Figure 24-a:
Observed and expected upper limits at 95% CL on the production cross section for the doublet vector-like tau lepton model. To the left of the vertical dashed gray line, the limits are shown from the advanced $ {S_{\rm T}}$ table, while to the right the limits are shown from the BDT regions.

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Figure 24-b:
Observed and expected upper limits at 95% CL on the production cross section for the singlet vector-like tau lepton model. The limit is shown from the advanced $ {S_{\rm T}}$ table for all masses.

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Figure 25:
Observed and expected upper limits at 95% CL on the production cross section for the scalar leptoquarks: $\mathcal {B}_{\mathrm{e}}=$ 1 coupling (upper left), $\mathcal {B}_{\mu}=$ 1 coupling (upper right), and $\mathcal {B}_{\tau}=$ 1 coupling (lower). In each figure, the limits to the left of the vertical dashed gray line are shown from the advanced $ {S_{\rm T}}$ table, and to the right are shown from the BDT regions.

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Figure 25-a:
Observed and expected upper limits at 95% CL on the production cross section for the scalar leptoquarks with $\mathcal {B}_{\mathrm{e}}=$ 1 coupling. The limits to the left of the vertical dashed gray line are shown from the advanced $ {S_{\rm T}}$ table, and to the right are shown from the BDT regions.

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Figure 25-b:
Observed and expected upper limits at 95% CL on the production cross section for the scalar leptoquarks with $\mathcal {B}_{\mu}=$ 1 coupling. The limits to the left of the vertical dashed gray line are shown from the advanced $ {S_{\rm T}}$ table, and to the right are shown from the BDT regions.

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Figure 25-c:
Observed and expected upper limits at 95% CL on the production cross section for the scalar leptoquarks with $\mathcal {B}_{\tau}=$ 1 coupling. The limits to the left of the vertical dashed gray line are shown from the advanced $ {S_{\rm T}}$ table, and to the right are shown from the BDT regions.
Tables

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Table 1:
Fundamental scheme of event categorization as a function of lepton charge and mass variables. The mass categorizations refer to masses of OSSF pairs if present, and of OSOF pairs otherwise. For categorization purposes, all possible dielectron and dimuon pair masses in the event are considered, whereas only the largest mass in the event in considered for all other pairs. Only the dielectron and dimuon pairs are considered to tag events as OnZ. Disallowed categories are marked with "$-$'', and categories marked with "*'' are inclusive of the unmarked ones in a given OSSF$n$ channel. The 1L3T OSSF0 and OSSF1 events are combined into a single category. Categories A3, A4, A9, A10, B4, and B10 have partially overlapping control region selections that are removed accordingly.

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Table 2:
The binning of $ {L_{\rm T}+ {{p_{\mathrm {T}}} ^\text {miss}}}$ or $ {S_{\rm T}}$ variable for fundamental and advanced table schemes in 3L channel based on categorization described in Table 1. The ranges, as well the $ {p_{\rm T}^{\rm miss}}$ and $ {H_{\mathrm {T}}} $ requirements, are given in GeV. The first bins in the $ {L_{\rm T}+ {{p_{\mathrm {T}}} ^\text {miss}}}$ or $ {S_{\rm T}}$ range contain the underflow, the last bins contain the overflow.

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Table 3:
The binning of $ {L_{\rm T}+ {{p_{\mathrm {T}}} ^\text {miss}}}$ or $ {S_{\rm T}}$ variable for fundamental and advanced table schemes in 2L1T channel based on categorization described in Table 1. The ranges, as well as the $ {p_{\rm T}^{\rm miss}}$ and $ {H_{\mathrm {T}}} $ requirements, are given in GeV. The first bins in the $ {L_{\rm T}+ {{p_{\mathrm {T}}} ^\text {miss}}}$ or $ {S_{\rm T}}$ range contain the underflow, and the last bins contain the overflow.

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Table 4:
The binning of $ {L_{\rm T}+ {{p_{\mathrm {T}}} ^\text {miss}}}$ or $ {S_{\rm T}}$ variable for fundamental and advanced table schemes in 1L2T channel based on categorization described in Table 1. The ranges, as well as the $ {p_{\rm T}^{\rm miss}}$ and $ {H_{\mathrm {T}}} $ requirements, are given in GeV. The first bins in the $ {L_{\rm T}+ {{p_{\mathrm {T}}} ^\text {miss}}}$ or $ {S_{\rm T}}$ range contain the underflow, and the last bins contain the overflow.

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Table 5:
The binning of $ {L_{\rm T}+ {{p_{\mathrm {T}}} ^\text {miss}}}$ or $ {S_{\rm T}}$ variable for fundamental and advanced table schemes in 4L, 3L1T, 2L2T and 1L3T channels based on categorization described in Table 1. The ranges, as well as the $ {p_{\rm T}^{\rm miss}}$ and $ {H_{\mathrm {T}}} $ requirements, are given in GeV. The first bins in the $ {L_{\rm T}+ {{p_{\mathrm {T}}} ^\text {miss}}}$ or $ {S_{\rm T}}$ range contain the underflow, and the last bins contain the overflow. For the 3L1T and 2L2T channels, multiple categories are combined in the 1 or $\geq $2 b tag selections. These bins are marked with dagger characters.

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Table 6:
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 non-physical default value for signal and background processes, and plays no role in training.

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Table 7:
Signal mass points as used in the trainings of BDTs and as used in the evaluation in the SRs according to the best sensitivity. The L, M, and H denote low, medium, and high mass ranges respectively.

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Table 8:
Sources, magnitudes, effective variations, and correlation model of systematic uncertainties in SRs. Uncertainty sources marked as "Yes'' under the correlation model have their nuisance parameters correlated across the 3 years of data collection.
Summary
A search has been performed for physics beyond the standard model, using multilepton events in 138 fb$^{-1}$ of pp collision data at $\sqrt{s} = $ 13 TeV, collected with the CMS detector using the LHC Run 2 dataset. The search is carried out in seven orthogonal channels based on the number of light leptons and hadronically decaying tau leptons. Three cut-based schemes are used to define SRs for the search. In addition, for each model scenario considered, a BDT is used to define model-specific SRs. In all cases, the observations are found to be consistent with the expectations from the standard model processes. Constraints are set on the production cross section of a number of BSM signal models predicting a variety of multilepton final states.

Type-III seesaw heavy fermions are excluded at 95% CL with masses below 980 GeV (expected 1060 GeV), assuming flavor-democratic mixings to SM leptons, and below 995 GeV (expected 1065 GeV), 1070 GeV (expected 1145 GeV), and 890 GeV (expected 885 GeV), assuming mixings exclusively with electron, muon, and tau 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 standard model lepton flavors. These are the strongest 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 (expected 975 GeV). These are the most stringent constraints on the doublet model. In the singlet model the expected exclusion mass range is 125-150 GeV, while the observed exclusion mass range is 125-170 GeV. These are the first LHC constraints on the singlet model.

Scalar leptoquarks coupling 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). Leptoquarks are excluded with masses below 1340 GeV (expected 1370 GeV) in the top-electron coupling scenario, and below 1420 GeV (expected 1460 GeV) in the top-muon scenario.
Additional Figures

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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 gray bands represent the sum of statistical and systematic uncertainties on the SM background prediction.

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Additional Figure 2:
The $S_{\rm T}$ distribution in 3L WZ CR events. The rightmost bin contains the overflow events. The gray bands represent the sum of statistical and systematic uncertainties on the SM background prediction.

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Additional Figure 3:
The $\Delta {R}_{\rm min}$ distribution in 3L Z$\gamma$ CR events. The rightmost bin contains the overflow events. The gray bands represent the sum of statistical and systematic uncertainties on the SM background prediction.

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Additional Figure 4:
The model independent fundamental table categories, as defined in Table 1. The gray bands represent the sum of statistical and systematic uncertainties on the SM background prediction.

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Additional Figure 5:
The $N_{\rm b}$ distribution in 3L, 2L1T, and 1L2T events. The rightmost bin contains the overflow events. The gray bands represent the sum of statistical and systematic uncertainties on the SM background prediction.

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Additional Figure 6:
The $N_{\rm b}$ distribution in 4L, 3L1T, 2L2T, and 1L3T events. The rightmost bin contains the overflow events. The gray bands represent the sum of statistical and systematic uncertainties on the SM background prediction.

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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 gray bands represent the sum of statistical and systematic uncertainties on the SM background prediction.

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Additional Figure 8:
The $L_{\rm T}$ distribution in 3L, 2L1T, and 1L2T events. The rightmost bin contains the overflow events. The gray bands represent the sum of statistical and systematic uncertainties on the SM background prediction.

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Additional Figure 9:
The $L_{\rm T}$ distribution in 4L, 3L1T, 3L, 2L2T, 2L1T, 1L3T, and 1L2T events. The rightmost bin contains the overflow events. The gray bands represent the sum of statistical and systematic uncertainties on the SM background prediction.

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Additional Figure 10:
The $ {{p_{\mathrm {T}}} ^\text {miss}} $ distribution in 3L, 2L1T, and 1L2T events. The rightmost bin contains the overflow events. The gray bands represent the sum of statistical and systematic uncertainties on the SM background prediction.

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Additional Figure 11:
The $ {{p_{\mathrm {T}}} ^\text {miss}} $ distribution in 4L, 3L1T, 3L, 2L2T, 2L1T, 1L3T, and 1L2T events. The rightmost bin contains the overflow events. The gray bands represent the sum of statistical and systematic uncertainties on the SM background prediction.

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Additional Figure 12:
The $H_{\rm T}$ distribution in 3L, 2L1T, and 1L2T events. The rightmost bin contains the overflow events. The gray bands represent the sum of statistical and systematic uncertainties on the SM background prediction.

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Additional Figure 13:
The $H_{\rm T}$ distribution in 4L, 3L1T, 3L, 2L2T, 2L1T, 1L3T, and 1L2T events. The rightmost bin contains the overflow events. The gray bands represent the sum of statistical and systematic uncertainties on the SM background prediction.

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Additional Figure 14:
The $M_{\rm OSSF}$ distribution in 3L and 2L1T events. The rightmost bin contains the overflow events. The gray bands represent the sum of statistical and systematic uncertainties on the SM background prediction.

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Additional Figure 15:
The $M_{\rm OSSF}$ distribution in 4L, 3L1T, 3L, 2L2T, and 2L1T events. The rightmost bin contains the overflow events. The gray bands represent the sum of statistical and systematic uncertainties on the SM background prediction.

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Additional Figure 16:
The invariant mass distribution of the opposite-sign other-flavor ($M_{\rm OSOF}$) light lepton pair in 3L and 2L1T events. The rightmost bin contains the overflow events. The gray bands represent the sum of statistical and systematic uncertainties on the SM background prediction.

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Additional Figure 17:
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 gray bands represent the sum of statistical and systematic uncertainties on the SM background prediction.

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Additional Figure 18:
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 gray bands represent the sum of statistical and systematic uncertainties on the SM background prediction.

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Additional Figure 19:
The invariant mass distribution of the opposite-sign other-flavor ($M_{\rm OSOF}$) light lepton and tau lepton pair in 2L1T and 1L2T events. The rightmost bin contains the overflow events. The gray bands represent the sum of statistical and systematic uncertainties on the SM background prediction.

png pdf
Additional Figure 20:
The $M_{\rm T}^{\textrm {1}}$ in 3L, 2L1T, and 1L2T events. The rightmost bin contains the overflow events. The gray bands represent the sum of statistical and systematic uncertainties on the SM background prediction.

png pdf
Additional Figure 21:
The $M_{\rm T}^{\textrm {12}}$ in 3L, 2L1T, and 1L2T events. The rightmost bin contains the overflow events. The gray bands represent the sum of statistical and systematic uncertainties on the SM background prediction.

png pdf
Additional Figure 22:
The $M_{\rm T}^{\textrm {12}}$ in 4L, 3L1T, 2L2T, 2L1T, 1L3T, and 1L2T events. The rightmost bin contains the overflow events. The gray bands represent the sum of statistical and systematic uncertainties on the SM background prediction.

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 flavor-democratic scenario using the fundamental $L_{\rm T}+ {{p_{\mathrm {T}}} ^\text {miss}} $ table scheme.

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 flavor-democratic scenario using the fundamental $S_{\rm T}$ table scheme.

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 flavor-democratic scenario using the advanced $S_{\rm T}$ table scheme.

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 flavor-democratic 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 $\mathcal {B}_{{\mathrm {e}}}=$ 1 scenario using the fundamental $L_{\rm T}+ {{p_{\mathrm {T}}} ^\text {miss}} $ table scheme.

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 $\mathcal {B}_{{\mathrm {e}}}=$ 1 scenario using the fundamental $S_{\rm T}$ table scheme.

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 $\mathcal {B}_{{\mathrm {e}}}=$ 1 scenario using the advanced $S_{\rm T}$ table scheme.

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 $\mathcal {B}_{{\mathrm {e}}}=$ 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 $\mathcal {B}_{{\mu}}=$ 1 scenario using the fundamental $L_{\rm T}+ {{p_{\mathrm {T}}} ^\text {miss}} $ table scheme.

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 $\mathcal {B}_{{\mu}}=$ 1 scenario using the fundamental $S_{\rm T}$ table scheme.

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 $\mathcal {B}_{{\mu}}=$ 1 scenario using the advanced $S_{\rm T}$ table scheme.

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 $\mathcal {B}_{{\mu}}=$ 1 scenario using the SS ($\mathcal {B}_{{\mathrm {e}}}=\mathcal {B}_{{\mu}}=\mathcal {B}_{{\tau}}$) BDT regions.

png pdf
Additional Figure 35:
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 scheme.

png pdf
Additional Figure 36:
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 scheme.

png pdf
Additional Figure 37:
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 scheme.

png pdf
Additional Figure 38:
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 39:
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 scheme.

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 doublet model using the fundamental $S_{\rm T}$ table scheme.

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 doublet model using the advanced $S_{\rm T}$ table scheme.

png pdf
Additional Figure 42:
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 43:
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 scheme.

png pdf
Additional Figure 44:
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 scheme.

png pdf
Additional Figure 45:
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 scheme.

png pdf
Additional Figure 46:
Observed and expected upper limits at 95% CL on the production cross section for the scalar leptoquarks with $\mathcal {B}_{{\mathrm {e}}}=$ 1 coupling using the fundamental $L_{\rm T}+ {{p_{\mathrm {T}}} ^\text {miss}} $ table scheme.

png pdf
Additional Figure 47:
Observed and expected upper limits at 95% CL on the production cross section for the scalar leptoquarks with $\mathcal {B}_{{\mathrm {e}}}=$ 1 coupling using the fundamental $S_{\rm T}$ table scheme.

png pdf
Additional Figure 48:
Observed and expected upper limits at 95% CL on the production cross section for the scalar leptoquarks with $\mathcal {B}_{{\mathrm {e}}}=$ 1 coupling using the advanced $S_{\rm T}$ table scheme.

png pdf
Additional Figure 49:
Observed and expected upper limits at 95% CL on the production cross section for the scalar leptoquarks with $\mathcal {B}_{{\mathrm {e}}}=$ 1 coupling using the LQ ($\mathcal {B}_{{\mathrm {e}}}+\mathcal {B}_{{\mu}}=$ 1) BDT regions.

png pdf
Additional Figure 50:
Observed and expected upper limits at 95% CL on the production cross section for the scalar leptoquarks with $\mathcal {B}_{{\mu}}=$ 1 coupling using the fundamental $L_{\rm T}+ {{p_{\mathrm {T}}} ^\text {miss}} $ table scheme.

png pdf
Additional Figure 51:
Observed and expected upper limits at 95% CL on the production cross section for the scalar leptoquarks with $\mathcal {B}_{{\mu}}=$ 1 coupling using the fundamental $S_{\rm T}$ table scheme.

png pdf
Additional Figure 52:
Observed and expected upper limits at 95% CL on the production cross section for the scalar leptoquarks with $\mathcal {B}_{{\mu}}=$ 1 coupling using the advanced $S_{\rm T}$ table scheme.

png pdf
Additional Figure 53:
Observed and expected upper limits at 95% CL on the production cross section for the scalar leptoquarks with $\mathcal {B}_{{\mu}}=$ 1 coupling using the LQ ($\mathcal {B}_{{\mathrm {e}}}+\mathcal {B}_{{\mu}}=$ 1) regions.

png pdf
Additional Figure 54:
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 scheme.

png pdf
Additional Figure 55:
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 scheme.

png pdf
Additional Figure 56:
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 scheme.

png pdf
Additional Figure 57:
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.
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