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CMS-SUS-21-004 ; CERN-EP-2023-019
Search for top squark pair production in a final state with at least one hadronically decaying tau lepton in proton-proton collisions at $ \sqrt{s} = $ 13 TeV
JHEP 07 (2023) 110
Abstract: A search for pair production of the supersymmetric partner of the top quark, the top squark, in proton-proton collisions at $ \sqrt{s} = $ 13 TeV is presented in final states containing at least one hadronically decaying tau lepton and large missing transverse momentum. This final state is highly sensitive to scenarios of supersymmetry in which the decay of the top squark to tau leptons is enhanced. The search uses a data sample corresponding to an integrated luminosity of 138 fb$ ^{-1} $, which was recorded with the CMS detector during 2016-2018. No significant excess is observed with respect to the standard model predictions. Exclusion limits at 95% confidence level on the masses of the top squark and the lightest neutralino are presented under the assumptions of simplified models. The results probe top squark masses up to 1150 GeV for a nearly massless neutralino. This search covers a relatively less explored parameter space in the context of supersymmetry, and the exclusion limit is the most stringent to date for the model considered here.
Figures & Tables Summary References CMS Publications
Figures

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Figure 1:
Diagrams of top squark pair production in pp collisions at the LHC, and the decays that lead to final states with pairs of b quarks and tau leptons accompanied by neutrinos and LSPs, within the framework of SMS.

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Figure 1-a:
Diagram of top squark pair production in pp collisions at the LHC, and the decays that lead to a final state with pairs of b quarks and tau leptons accompanied by neutrinos and LSPs, within the framework of SMS.

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Figure 1-b:
Diagram of top squark pair production in pp collisions at the LHC, and the decays that lead to a final state with pairs of b quarks and tau leptons accompanied by neutrinos and LSPs, within the framework of SMS.

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Figure 1-c:
Diagram of top squark pair production in pp collisions at the LHC, and the decays that lead to a final state with pairs of b quarks and tau leptons accompanied by neutrinos and LSPs, within the framework of SMS.

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Figure 1-d:
Diagram of top squark pair production in pp collisions at the LHC, and the decays that lead to a final state with pairs of b quarks and tau leptons accompanied by neutrinos and LSPs, within the framework of SMS.

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Figure 2:
A graphical representation of the mass parameterization described in Eq. 1

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Figure 3:
Distributions of the search variables $ p_{\mathrm{T}}^\text{miss} $, $ m_{\mathrm{T2}} $, and $ H_{\mathrm{T}} $ after event selection described in Sec. 5 for data and predicted backgrounds, corresponding to the $ \tau_\mathrm{h}\tau_\mathrm{h} $ category. The histograms for the background processes are stacked, and the signal distributions expected for a few representative sets of model parameter values are overlaid: $ x = $ 0.5 and [$ m_{\tilde{\mathrm{t}}_{1}} $, $ m_{\tilde{\chi}_{1}^{0}} $] $=$ [300, 100], [500, 350], [800, 300], and [1000, 1] GeV. The lower panel indicates the ratio of the observed number of events to the total predicted number of background events. The shaded bands indicate the statistical and systematic uncertainties in the predicted backgrounds, added in quadrature.

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Figure 3-a:
Distribution of the search variable $ p_{\mathrm{T}}^\text{miss} $ after event selection described in Sec. 5 for data and predicted backgrounds, corresponding to the $ \tau_\mathrm{h}\tau_\mathrm{h} $ category. The histograms for the background processes are stacked, and the signal distributions expected for a few representative sets of model parameter values are overlaid: $ x = $ 0.5 and [$ m_{\tilde{\mathrm{t}}_{1}} $, $ m_{\tilde{\chi}_{1}^{0}} $] $=$ [300, 100], [500, 350], [800, 300], and [1000, 1] GeV. The lower panel indicates the ratio of the observed number of events to the total predicted number of background events. The shaded bands indicate the statistical and systematic uncertainties in the predicted backgrounds, added in quadrature.

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Figure 3-b:
Distribution of the search variable $ m_{\mathrm{T2}} $ after event selection described in Sec. 5 for data and predicted backgrounds, corresponding to the $ \tau_\mathrm{h}\tau_\mathrm{h} $ category. The histograms for the background processes are stacked, and the signal distributions expected for a few representative sets of model parameter values are overlaid: $ x = $ 0.5 and [$ m_{\tilde{\mathrm{t}}_{1}} $, $ m_{\tilde{\chi}_{1}^{0}} $] $=$ [300, 100], [500, 350], [800, 300], and [1000, 1] GeV. The lower panel indicates the ratio of the observed number of events to the total predicted number of background events. The shaded bands indicate the statistical and systematic uncertainties in the predicted backgrounds, added in quadrature.

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Figure 3-c:
Distribution of the search variable $ H_{\mathrm{T}} $ after event selection described in Sec. 5 for data and predicted backgrounds, corresponding to the $ \tau_\mathrm{h}\tau_\mathrm{h} $ category. The histograms for the background processes are stacked, and the signal distributions expected for a few representative sets of model parameter values are overlaid: $ x = $ 0.5 and [$ m_{\tilde{\mathrm{t}}_{1}} $, $ m_{\tilde{\chi}_{1}^{0}} $] $=$ [300, 100], [500, 350], [800, 300], and [1000, 1] GeV. The lower panel indicates the ratio of the observed number of events to the total predicted number of background events. The shaded bands indicate the statistical and systematic uncertainties in the predicted backgrounds, added in quadrature.

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Figure 4:
Distributions of the search variables $ p_{\mathrm{T}}^\text{miss} $, $ m_{\mathrm{T2}} $, and $ S_{\mathrm{T}} $ after event selection described in Sec. 5 for data and predicted backgrounds, corresponding to the $ \mathrm{e}\tau_\mathrm{h} $ category. The histograms for the background processes are stacked, and the signal distributions expected for a few representative sets of model parameter values are overlaid: $ x = $ 0.5 and [$ m_{\tilde{\mathrm{t}}_{1}} $, $ m_{\tilde{\chi}_{1}^{0}} $] $=$ [300, 100], [500, 350], [800, 300], and [1000, 1] GeV. The lower panel indicates the ratio of the observed number of events to the total predicted number of background events. The shaded bands indicate the statistical and systematic uncertainties in the predicted backgrounds, added in quadrature.

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Figure 4-a:
Distribution of the search variable $ p_{\mathrm{T}}^\text{miss} $ after event selection described in Sec. 5 for data and predicted backgrounds, corresponding to the $ \mathrm{e}\tau_\mathrm{h} $ category. The histograms for the background processes are stacked, and the signal distributions expected for a few representative sets of model parameter values are overlaid: $ x = $ 0.5 and [$ m_{\tilde{\mathrm{t}}_{1}} $, $ m_{\tilde{\chi}_{1}^{0}} $] $=$ [300, 100], [500, 350], [800, 300], and [1000, 1] GeV. The lower panel indicates the ratio of the observed number of events to the total predicted number of background events. The shaded bands indicate the statistical and systematic uncertainties in the predicted backgrounds, added in quadrature.

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Figure 4-b:
Distribution of the search variable $ m_{\mathrm{T2}} $ after event selection described in Sec. 5 for data and predicted backgrounds, corresponding to the $ \mathrm{e}\tau_\mathrm{h} $ category. The histograms for the background processes are stacked, and the signal distributions expected for a few representative sets of model parameter values are overlaid: $ x = $ 0.5 and [$ m_{\tilde{\mathrm{t}}_{1}} $, $ m_{\tilde{\chi}_{1}^{0}} $] $=$ [300, 100], [500, 350], [800, 300], and [1000, 1] GeV. The lower panel indicates the ratio of the observed number of events to the total predicted number of background events. The shaded bands indicate the statistical and systematic uncertainties in the predicted backgrounds, added in quadrature.

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Figure 4-c:
Distribution of the search variable $ S_{\mathrm{T}} $ after event selection described in Sec. 5 for data and predicted backgrounds, corresponding to the $ \mathrm{e}\tau_\mathrm{h} $ category. The histograms for the background processes are stacked, and the signal distributions expected for a few representative sets of model parameter values are overlaid: $ x = $ 0.5 and [$ m_{\tilde{\mathrm{t}}_{1}} $, $ m_{\tilde{\chi}_{1}^{0}} $] $=$ [300, 100], [500, 350], [800, 300], and [1000, 1] GeV. The lower panel indicates the ratio of the observed number of events to the total predicted number of background events. The shaded bands indicate the statistical and systematic uncertainties in the predicted backgrounds, added in quadrature.

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Figure 5:
Distributions of the search variables $ p_{\mathrm{T}}^\text{miss} $, $ m_{\mathrm{T2}} $, and $ S_{\mathrm{T}} $ after event selection described in Sec. 5 for data and predicted backgrounds, corresponding to the $ \mu\tau_\mathrm{h} $ category. The histograms for the background processes are stacked, and the signal distributions expected for a few representative sets of model parameter values are overlaid: $ x = $ 0.5 and [$ m_{\tilde{\mathrm{t}}_{1}} $, $ m_{\tilde{\chi}_{1}^{0}} $] $=$ [300, 100], [500, 350], [800, 300], and [1000, 1] GeV. The lower panel indicates the ratio of the observed number of events to the total predicted number of background events. The shaded bands indicate the statistical and systematic uncertainties in the predicted backgrounds, added in quadrature.

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Figure 5-a:
Distribution of the search variable $ p_{\mathrm{T}}^\text{miss} $ after event selection described in Sec. 5 for data and predicted backgrounds, corresponding to the $ \mu\tau_\mathrm{h} $ category. The histograms for the background processes are stacked, and the signal distributions expected for a few representative sets of model parameter values are overlaid: $ x = $ 0.5 and [$ m_{\tilde{\mathrm{t}}_{1}} $, $ m_{\tilde{\chi}_{1}^{0}} $] $=$ [300, 100], [500, 350], [800, 300], and [1000, 1] GeV. The lower panel indicates the ratio of the observed number of events to the total predicted number of background events. The shaded bands indicate the statistical and systematic uncertainties in the predicted backgrounds, added in quadrature.

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Figure 5-b:
Distribution of the search variable $ m_{\mathrm{T2}} $ after event selection described in Sec. 5 for data and predicted backgrounds, corresponding to the $ \mu\tau_\mathrm{h} $ category. The histograms for the background processes are stacked, and the signal distributions expected for a few representative sets of model parameter values are overlaid: $ x = $ 0.5 and [$ m_{\tilde{\mathrm{t}}_{1}} $, $ m_{\tilde{\chi}_{1}^{0}} $] $=$ [300, 100], [500, 350], [800, 300], and [1000, 1] GeV. The lower panel indicates the ratio of the observed number of events to the total predicted number of background events. The shaded bands indicate the statistical and systematic uncertainties in the predicted backgrounds, added in quadrature.

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Figure 5-c:
Distribution of the search variable $ S_{\mathrm{T}} $ after event selection described in Sec. 5 for data and predicted backgrounds, corresponding to the $ \mu\tau_\mathrm{h} $ category. The histograms for the background processes are stacked, and the signal distributions expected for a few representative sets of model parameter values are overlaid: $ x = $ 0.5 and [$ m_{\tilde{\mathrm{t}}_{1}} $, $ m_{\tilde{\chi}_{1}^{0}} $] $=$ [300, 100], [500, 350], [800, 300], and [1000, 1] GeV. The lower panel indicates the ratio of the observed number of events to the total predicted number of background events. The shaded bands indicate the statistical and systematic uncertainties in the predicted backgrounds, added in quadrature.

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Figure 6:
The 15 signal regions defined in bins of $ p_{\mathrm{T}}^\text{miss} $, $ m_{\mathrm{T2}} $, and $ H_{\mathrm{T}} $. The bin boundaries for $ S_{\mathrm{T}} $ are the same as those for $ H_{\mathrm{T}} $.

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Figure 7:
The purities in top quarks, the scale factors $ \text{SF} $ from simulation to data, and the $ \text{SF}^{\mathrm{e}\mu} - \text{SF}^{\mu\mu} $ differences in the various bins (as defined in Fig. 6) of the top enriched CR, where the purity is estimated from simulation. The upper left, upper right, and lower subfigures correspond to 2016, 2017, and 2018 data, respectively. To mitigate the effect of statistical fluctuations, bins 14 and 15 are merged to provide the same SF in both bins for subsequent calculations.

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Figure 7-a:
The purities in top quarks, the scale factors $ \text{SF} $ from simulation to data, and the $ \text{SF}^{\mathrm{e}\mu} - \text{SF}^{\mu\mu} $ differences in the various bins (as defined in Fig. 6) of the top enriched CR, where the purity is estimated from simulation.

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Figure 7-b:
The purities in top quarks, the scale factors $ \text{SF} $ from simulation to data, and the $ \text{SF}^{\mathrm{e}\mu} - \text{SF}^{\mu\mu} $ differences in the various bins (as defined in Fig. 6) of the top enriched CR, where the purity is estimated from simulation.

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Figure 7-c:
The purities in top quarks, the scale factors $ \text{SF} $ from simulation to data, and the $ \text{SF}^{\mathrm{e}\mu} - \text{SF}^{\mu\mu} $ differences in the various bins (as defined in Fig. 6) of the top enriched CR, where the purity is estimated from simulation.

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Figure 8:
Event yields in the 15 search bins as defined in Fig. 6, for the $ \tau_\mathrm{h}\tau_\mathrm{h} $ (upper), $ \mathrm{e}\tau_\mathrm{h} $ (lower left), and $ \mu\tau_\mathrm{h} $ (lower right) categories. The yields for the background processes are stacked, and those expected for a few representative sets of model parameter values are overlaid: $ x = $ 0.5 and [$ m_{\tilde{\mathrm{t}}_{1}} $, $ m_{\tilde{\chi}_{1}^{0}} $] $=$ [300, 100], [500, 350], [800, 300], and [1000, 1] GeV. The $ p_{\mathrm{T}}^\text{miss} $ and $ m_{\mathrm{T2}} $ bin definitions are shown in GeV. The lower panel indicates the ratio of the observed number of events to the total predicted number of background events in each bin. The shaded bands indicate the statistical and systematic uncertainties in the background, added in quadrature. The predicted yields and uncertainties shown here are prior to the maximum likelihood fit described in Sec. 8.

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Figure 8-a:
Event yields in the 15 search bins as defined in Fig. 6, for the $ \tau_\mathrm{h}\tau_\mathrm{h} $ category. The yields for the background processes are stacked, and those expected for a few representative sets of model parameter values are overlaid: $ x = $ 0.5 and [$ m_{\tilde{\mathrm{t}}_{1}} $, $ m_{\tilde{\chi}_{1}^{0}} $] $=$ [300, 100], [500, 350], [800, 300], and [1000, 1] GeV. The $ p_{\mathrm{T}}^\text{miss} $ and $ m_{\mathrm{T2}} $ bin definitions are shown in GeV. The lower panel indicates the ratio of the observed number of events to the total predicted number of background events in each bin. The shaded bands indicate the statistical and systematic uncertainties in the background, added in quadrature. The predicted yields and uncertainties shown here are prior to the maximum likelihood fit described in Sec. 8.

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Figure 8-b:
Event yields in the 15 search bins as defined in Fig. 6, for the $ \mathrm{e}\tau_\mathrm{h} $ category. The yields for the background processes are stacked, and those expected for a few representative sets of model parameter values are overlaid: $ x = $ 0.5 and [$ m_{\tilde{\mathrm{t}}_{1}} $, $ m_{\tilde{\chi}_{1}^{0}} $] $=$ [300, 100], [500, 350], [800, 300], and [1000, 1] GeV. The $ p_{\mathrm{T}}^\text{miss} $ and $ m_{\mathrm{T2}} $ bin definitions are shown in GeV. The lower panel indicates the ratio of the observed number of events to the total predicted number of background events in each bin. The shaded bands indicate the statistical and systematic uncertainties in the background, added in quadrature. The predicted yields and uncertainties shown here are prior to the maximum likelihood fit described in Sec. 8.

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Figure 8-c:
Event yields in the 15 search bins as defined in Fig. 6, for the $ \mu\tau_\mathrm{h} $ category. The yields for the background processes are stacked, and those expected for a few representative sets of model parameter values are overlaid: $ x = $ 0.5 and [$ m_{\tilde{\mathrm{t}}_{1}} $, $ m_{\tilde{\chi}_{1}^{0}} $] $=$ [300, 100], [500, 350], [800, 300], and [1000, 1] GeV. The $ p_{\mathrm{T}}^\text{miss} $ and $ m_{\mathrm{T2}} $ bin definitions are shown in GeV. The lower panel indicates the ratio of the observed number of events to the total predicted number of background events in each bin. The shaded bands indicate the statistical and systematic uncertainties in the background, added in quadrature. The predicted yields and uncertainties shown here are prior to the maximum likelihood fit described in Sec. 8.

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Figure 9:
Exclusion limits at 95% CL for the pair production of top squarks decaying to $ \tau_{\ell}\tau_\mathrm{h} $ or $ \tau_\mathrm{h}\tau_\mathrm{h} $ final states, displayed in the $ {m_{\tilde{\mathrm{t}}_{1}}}-m_{\tilde{\chi}_{1}^{0}} $ plane for $ x = $ 0.25 (upper left), 0.5 (upper right) and 0.75 (lower), as described in Eq. (1). Branching fractions are denoted by $ \mathit{B} $. The color axis represents the observed upper limit in the cross section, while the black (red) lines represent the observed (expected) upper mass limits. The signal cross sections are evaluated using NNLO$ + $NLL calculations. The solid lines represent the central values. The dashed red lines indicate the region containing 68% of the distribution of limits expected under the background-only hypothesis. The dashed black lines show the change in the observed limit due to variation of the signal cross sections within their theoretical uncertainties.

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Figure 9-a:
Exclusion limits at 95% CL for the pair production of top squarks decaying to $ \tau_{\ell}\tau_\mathrm{h} $ or $ \tau_\mathrm{h}\tau_\mathrm{h} $ final states, displayed in the $ {m_{\tilde{\mathrm{t}}_{1}}}-m_{\tilde{\chi}_{1}^{0}} $ plane for $ x = $ 0.25, as described in Eq. (1). Branching fractions are denoted by $ \mathit{B} $. The color axis represents the observed upper limit in the cross section, while the black (red) lines represent the observed (expected) upper mass limits. The signal cross sections are evaluated using NNLO$ + $NLL calculations. The solid lines represent the central values. The dashed red lines indicate the region containing 68% of the distribution of limits expected under the background-only hypothesis. The dashed black lines show the change in the observed limit due to variation of the signal cross sections within their theoretical uncertainties.

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Figure 9-b:
Exclusion limits at 95% CL for the pair production of top squarks decaying to $ \tau_{\ell}\tau_\mathrm{h} $ or $ \tau_\mathrm{h}\tau_\mathrm{h} $ final states, displayed in the $ {m_{\tilde{\mathrm{t}}_{1}}}-m_{\tilde{\chi}_{1}^{0}} $ plane for $ x = $ 0.5, as described in Eq. (1). Branching fractions are denoted by $ \mathit{B} $. The color axis represents the observed upper limit in the cross section, while the black (red) lines represent the observed (expected) upper mass limits. The signal cross sections are evaluated using NNLO$ + $NLL calculations. The solid lines represent the central values. The dashed red lines indicate the region containing 68% of the distribution of limits expected under the background-only hypothesis. The dashed black lines show the change in the observed limit due to variation of the signal cross sections within their theoretical uncertainties.

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Figure 9-c:
Exclusion limits at 95% CL for the pair production of top squarks decaying to $ \tau_{\ell}\tau_\mathrm{h} $ or $ \tau_\mathrm{h}\tau_\mathrm{h} $ final states, displayed in the $ {m_{\tilde{\mathrm{t}}_{1}}}-m_{\tilde{\chi}_{1}^{0}} $ plane for $ x = $ 0.75, as described in Eq. (1). Branching fractions are denoted by $ \mathit{B} $. The color axis represents the observed upper limit in the cross section, while the black (red) lines represent the observed (expected) upper mass limits. The signal cross sections are evaluated using NNLO$ + $NLL calculations. The solid lines represent the central values. The dashed red lines indicate the region containing 68% of the distribution of limits expected under the background-only hypothesis. The dashed black lines show the change in the observed limit due to variation of the signal cross sections within their theoretical uncertainties.
Tables

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Table 1:
Relative systematic uncertainties for the $ \tau_\mathrm{h}\tau_\mathrm{h} $ category from various sources in signal and background yields. These values are averages of the relative uncertainties in the different search regions, weighted by the yields in the respective bins. For the asymmetric uncertainties, the upper (lower) entry is the uncertainty due to the upward (downward) variation, which can be in the same direction as a result of taking the weighted average. In the header row, the top squark and LSP masses in GeV are indicated in parentheses. The uncertainty values shown here are prior to the maximum likelihood fit described in Sec. 8.

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Table 2:
Relative systematic uncertainties for the $ \mathrm{e}\tau_\mathrm{h} $ category from various sources in signal and background yields. These values are averages of the relative uncertainties in the different search regions, weighted by the yields in the respective bins. For the asymmetric uncertainties, the upper (lower) entry is the uncertainty due to the upward (downward) variation, which can be in the same direction as a result of taking the weighted average. In the header row, the top squark and LSP masses in GeV are indicated in parentheses. The uncertainty values shown here are prior to the maximum likelihood fit described in Sec. 8.

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Table 3:
Relative systematic uncertainties for the $ \mu\tau_\mathrm{h} $ category from various sources in signal and background yields. These values are averages of the relative uncertainties in the different search regions, weighted by the yields in the respective bins. For the asymmetric uncertainties, the upper (lower) entry is the uncertainty due to the upward (downward) variation, which can be in the same direction as a result of taking the weighted average. In the header row, the top squark and LSP masses in GeV are indicated in parentheses. The uncertainty values shown here are prior to the maximum likelihood fit described in Sec. 8.

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Table 4:
Predicted background yields along with uncertainties for the $ \tau_\mathrm{h}\tau_\mathrm{h} $ category in the 15 search bins, as defined in Fig. 6. The number of events observed in data is also shown. The first uncertainty value listed is statistical and the second is systematic. The uncertainties smaller than 0.05 are listed as 0.0. The background yields and uncertainties shown here are prior to the maximum likelihood fit described in Sec. 8.

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Table 5:
Predicted background yields along with uncertainties for the $ \mathrm{e}\tau_\mathrm{h} $ category in the 15 search bins, as defined in Fig. 6. The number of events observed in data is also shown. The first uncertainty value listed is statistical and the second is systematic. The uncertainties smaller than 0.05 are listed as 0.0. The background yields and uncertainties shown here are prior to the maximum likelihood fit described in Sec. 8.

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Table 6:
Predicted background yields along with uncertainties for the $ \mu\tau_\mathrm{h} $ category in the 15 search bins, as defined in Fig. 6. The number of events observed in data is also shown. The first uncertainty value listed is statistical and the second is systematic. The uncertainties smaller than 0.05 are listed as 0.0. The background yields and uncertainties shown here are prior to the maximum likelihood fit described in Sec. 8.
Summary
Top squark pair production in final states with two tau leptons has been explored in data collected by the CMS detector during 2016, 2017, and 2018, corresponding to an integrated luminosity of 138 fb$ ^{-1} $. This search improves upon the previous publication [36] by analyzing the entirety of the Run 2 data, adding the $ \mathrm{e}\tau_\mathrm{h} $ and $ \mu\tau_\mathrm{h} $ final states, and utilizing improved algorithms for identifying hadronically decaying tau leptons and b quark jets. The dominant standard model backgrounds originate from top quark pair and single top quark production and processes where jets were misidentified as $ \tau_\mathrm{h} $ decays. Control regions in data are used to estimate these backgrounds, whereas other backgrounds are estimated using simulation. The simulated objects (leptons, jets, etc.) are corrected using scale factors to account for differences between their performance in simulation and collision data. No significant excess is observed, and exclusion limits on the top squark and lightest neutralino masses are set at 95% confidence level within the framework of simplified models where the top squark decays via a chargino to final states including tau leptons. A branching fraction of 50% is assumed for each of the two considered decay modes of the chargino, $ \tilde{\chi}_{1}^{+} \to \tilde{\tau}_{1}^{+}\nu_{\tau} $ and $ \tilde{\chi}_{1}^{+} \to \tau^{+}\tilde{\nu}_{{\tau}} $. These decay modes are motivated by high-$ \tan\beta $ and higgsino-like scenarios where decays to tau leptons are enhanced. In such models, top squark masses are excluded up to about 1150 GeV for a lightest supersymmetric particle (LSP) of mass 1 GeV, while LSP masses up to 450 GeV are excluded for a top squark mass of 900 GeV. These are the most stringent exclusion limits to date for the signal models considered in this study.
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