CMSSUS21003 ; CERNEP2022254  
Search for top squarks in the fourbody decay mode with single lepton final states in protonproton collisions at $ \sqrt{s}= $ 13 TeV  
CMS Collaboration  
19 January 2023  
JHEP 06 (2023) 060  
Abstract: A search for the pair production of the lightest supersymmetric partner of the top quark, the top squark ($ \tilde{\mathrm{t}}_{1} $), is presented. The search targets the fourbody decay of the $ \tilde{\mathrm{t}}_{1} $, which is preferred when the mass difference between the top squark and the lightest supersymmetric particle is smaller than the mass of the W boson. This decay mode consists of a bottom quark, two other fermions, and the lightest neutralino ($ \tilde{\chi}_{1}^{0} $), which is assumed to be the lightest supersymmetric particle. The data correspond to an integrated luminosity of 138 fb$ ^{1} $ of protonproton collisions at a centerofmass energy of 13 TeV collected by the CMS experiment at the CERN LHC. Events are selected using the presence of a highmomentum jet, an electron or muon with low transverse momentum, and a significant missing transverse momentum. The signal is selected based on a multivariate approach that is optimized for the difference between $ m(\tilde{\mathrm{t}}_{1}) $ and $ m(\tilde{\chi}_{1}^{0}) $. The contribution from leading background processes is estimated from data. No significant excess is observed above the expectation from standard model processes. The results of this search exclude top squarks at 95% confidence level for masses up to 480 and 700 GeV for $ m(\tilde{\mathrm{t}}_{1})  m(\tilde{\chi}_{1}^{0}) = $ 10 and 80 GeV, respectively.  
Links: eprint arXiv:2301.08096 [hepex] (PDF) ; CDS record ; inSPIRE record ; Physics Briefing ; CADI line (restricted) ; 
Figures  
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Figure 1:
Diagram of top squark pair production $ \tilde{\mathrm{t}}_{1} {\overline{\tilde{\mathrm{t}}}}_{1} $ in pp collisions, with a fourbody decay of each top squark. 
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Figure 2:
Distributions of $ p_{\mathrm{T}}(\ell) $ (upper), $ p_{\mathrm{T}}^\text{miss} $ (middle), and $ N_{\text{jet}} $ (lower), after the preselection from 2017 (left) and 2018 (right) data (points) and simulation (colored histograms). The simulated distribution of two signal points are represented by colored lines, while not being stacked on the background distributions: $ ({m}(\tilde{\mathrm{t}}_{1}), {m}(\tilde{\chi}_{1}^{0})) = $ (500, 490) and (500, 420) GeV. The last bin in each plot includes the overflow events. The lower panels show the ratio of data to the sum of the simulated SM backgrounds. The shaded bands indicate only the statistical uncertainty in the simulation predictions. 
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Figure 2a:
Distributions of $ p_{\mathrm{T}}(\ell) $ (upper), $ p_{\mathrm{T}}^\text{miss} $ (middle), and $ N_{\text{jet}} $ (lower), after the preselection from 2017 (left) and 2018 (right) data (points) and simulation (colored histograms). The simulated distribution of two signal points are represented by colored lines, while not being stacked on the background distributions: $ ({m}(\tilde{\mathrm{t}}_{1}), {m}(\tilde{\chi}_{1}^{0})) = $ (500, 490) and (500, 420) GeV. The last bin in each plot includes the overflow events. The lower panels show the ratio of data to the sum of the simulated SM backgrounds. The shaded bands indicate only the statistical uncertainty in the simulation predictions. 
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Figure 2b:
Distributions of $ p_{\mathrm{T}}(\ell) $ (upper), $ p_{\mathrm{T}}^\text{miss} $ (middle), and $ N_{\text{jet}} $ (lower), after the preselection from 2017 (left) and 2018 (right) data (points) and simulation (colored histograms). The simulated distribution of two signal points are represented by colored lines, while not being stacked on the background distributions: $ ({m}(\tilde{\mathrm{t}}_{1}), {m}(\tilde{\chi}_{1}^{0})) = $ (500, 490) and (500, 420) GeV. The last bin in each plot includes the overflow events. The lower panels show the ratio of data to the sum of the simulated SM backgrounds. The shaded bands indicate only the statistical uncertainty in the simulation predictions. 
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Figure 2c:
Distributions of $ p_{\mathrm{T}}(\ell) $ (upper), $ p_{\mathrm{T}}^\text{miss} $ (middle), and $ N_{\text{jet}} $ (lower), after the preselection from 2017 (left) and 2018 (right) data (points) and simulation (colored histograms). The simulated distribution of two signal points are represented by colored lines, while not being stacked on the background distributions: $ ({m}(\tilde{\mathrm{t}}_{1}), {m}(\tilde{\chi}_{1}^{0})) = $ (500, 490) and (500, 420) GeV. The last bin in each plot includes the overflow events. The lower panels show the ratio of data to the sum of the simulated SM backgrounds. The shaded bands indicate only the statistical uncertainty in the simulation predictions. 
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Figure 2d:
Distributions of $ p_{\mathrm{T}}(\ell) $ (upper), $ p_{\mathrm{T}}^\text{miss} $ (middle), and $ N_{\text{jet}} $ (lower), after the preselection from 2017 (left) and 2018 (right) data (points) and simulation (colored histograms). The simulated distribution of two signal points are represented by colored lines, while not being stacked on the background distributions: $ ({m}(\tilde{\mathrm{t}}_{1}), {m}(\tilde{\chi}_{1}^{0})) = $ (500, 490) and (500, 420) GeV. The last bin in each plot includes the overflow events. The lower panels show the ratio of data to the sum of the simulated SM backgrounds. The shaded bands indicate only the statistical uncertainty in the simulation predictions. 
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Figure 2e:
Distributions of $ p_{\mathrm{T}}(\ell) $ (upper), $ p_{\mathrm{T}}^\text{miss} $ (middle), and $ N_{\text{jet}} $ (lower), after the preselection from 2017 (left) and 2018 (right) data (points) and simulation (colored histograms). The simulated distribution of two signal points are represented by colored lines, while not being stacked on the background distributions: $ ({m}(\tilde{\mathrm{t}}_{1}), {m}(\tilde{\chi}_{1}^{0})) = $ (500, 490) and (500, 420) GeV. The last bin in each plot includes the overflow events. The lower panels show the ratio of data to the sum of the simulated SM backgrounds. The shaded bands indicate only the statistical uncertainty in the simulation predictions. 
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Figure 2f:
Distributions of $ p_{\mathrm{T}}(\ell) $ (upper), $ p_{\mathrm{T}}^\text{miss} $ (middle), and $ N_{\text{jet}} $ (lower), after the preselection from 2017 (left) and 2018 (right) data (points) and simulation (colored histograms). The simulated distribution of two signal points are represented by colored lines, while not being stacked on the background distributions: $ ({m}(\tilde{\mathrm{t}}_{1}), {m}(\tilde{\chi}_{1}^{0})) = $ (500, 490) and (500, 420) GeV. The last bin in each plot includes the overflow events. The lower panels show the ratio of data to the sum of the simulated SM backgrounds. The shaded bands indicate only the statistical uncertainty in the simulation predictions. 
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Figure 3:
Simulated distributions of $ p_{\mathrm{T}}(\ell) $ (upper), $ p_{\mathrm{T}}^\text{miss} $ (middle), and $ N_{\text{jet}} $ (lower) after the preselection. The W+jets and $ \mathrm{t} \overline{\mathrm{t}} $ background distributions are shown as colored histograms, and the signal distributions by the solid lines. The total background distribution and the signal distributions are all normalized to unit area. On the left, the signal distributions are given for a top squark mass of 300 GeV and $ \Delta {m}= $ 10, 30, 50, and 80 GeV. On the right, the signal distributions are shown for four different $ ({m}(\tilde{\mathrm{t}}_{1}), {m}(\tilde{\chi}_{1}^{0})) $ values, all corresponding to the same $ \Delta {m}= $ 30 GeV. 
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Figure 3a:
Simulated distributions of $ p_{\mathrm{T}}(\ell) $ (upper), $ p_{\mathrm{T}}^\text{miss} $ (middle), and $ N_{\text{jet}} $ (lower) after the preselection. The W+jets and $ \mathrm{t} \overline{\mathrm{t}} $ background distributions are shown as colored histograms, and the signal distributions by the solid lines. The total background distribution and the signal distributions are all normalized to unit area. On the left, the signal distributions are given for a top squark mass of 300 GeV and $ \Delta {m}= $ 10, 30, 50, and 80 GeV. On the right, the signal distributions are shown for four different $ ({m}(\tilde{\mathrm{t}}_{1}), {m}(\tilde{\chi}_{1}^{0})) $ values, all corresponding to the same $ \Delta {m}= $ 30 GeV. 
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Figure 3b:
Simulated distributions of $ p_{\mathrm{T}}(\ell) $ (upper), $ p_{\mathrm{T}}^\text{miss} $ (middle), and $ N_{\text{jet}} $ (lower) after the preselection. The W+jets and $ \mathrm{t} \overline{\mathrm{t}} $ background distributions are shown as colored histograms, and the signal distributions by the solid lines. The total background distribution and the signal distributions are all normalized to unit area. On the left, the signal distributions are given for a top squark mass of 300 GeV and $ \Delta {m}= $ 10, 30, 50, and 80 GeV. On the right, the signal distributions are shown for four different $ ({m}(\tilde{\mathrm{t}}_{1}), {m}(\tilde{\chi}_{1}^{0})) $ values, all corresponding to the same $ \Delta {m}= $ 30 GeV. 
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Figure 3c:
Simulated distributions of $ p_{\mathrm{T}}(\ell) $ (upper), $ p_{\mathrm{T}}^\text{miss} $ (middle), and $ N_{\text{jet}} $ (lower) after the preselection. The W+jets and $ \mathrm{t} \overline{\mathrm{t}} $ background distributions are shown as colored histograms, and the signal distributions by the solid lines. The total background distribution and the signal distributions are all normalized to unit area. On the left, the signal distributions are given for a top squark mass of 300 GeV and $ \Delta {m}= $ 10, 30, 50, and 80 GeV. On the right, the signal distributions are shown for four different $ ({m}(\tilde{\mathrm{t}}_{1}), {m}(\tilde{\chi}_{1}^{0})) $ values, all corresponding to the same $ \Delta {m}= $ 30 GeV. 
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Figure 3d:
Simulated distributions of $ p_{\mathrm{T}}(\ell) $ (upper), $ p_{\mathrm{T}}^\text{miss} $ (middle), and $ N_{\text{jet}} $ (lower) after the preselection. The W+jets and $ \mathrm{t} \overline{\mathrm{t}} $ background distributions are shown as colored histograms, and the signal distributions by the solid lines. The total background distribution and the signal distributions are all normalized to unit area. On the left, the signal distributions are given for a top squark mass of 300 GeV and $ \Delta {m}= $ 10, 30, 50, and 80 GeV. On the right, the signal distributions are shown for four different $ ({m}(\tilde{\mathrm{t}}_{1}), {m}(\tilde{\chi}_{1}^{0})) $ values, all corresponding to the same $ \Delta {m}= $ 30 GeV. 
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Figure 3e:
Simulated distributions of $ p_{\mathrm{T}}(\ell) $ (upper), $ p_{\mathrm{T}}^\text{miss} $ (middle), and $ N_{\text{jet}} $ (lower) after the preselection. The W+jets and $ \mathrm{t} \overline{\mathrm{t}} $ background distributions are shown as colored histograms, and the signal distributions by the solid lines. The total background distribution and the signal distributions are all normalized to unit area. On the left, the signal distributions are given for a top squark mass of 300 GeV and $ \Delta {m}= $ 10, 30, 50, and 80 GeV. On the right, the signal distributions are shown for four different $ ({m}(\tilde{\mathrm{t}}_{1}), {m}(\tilde{\chi}_{1}^{0})) $ values, all corresponding to the same $ \Delta {m}= $ 30 GeV. 
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Figure 3f:
Simulated distributions of $ p_{\mathrm{T}}(\ell) $ (upper), $ p_{\mathrm{T}}^\text{miss} $ (middle), and $ N_{\text{jet}} $ (lower) after the preselection. The W+jets and $ \mathrm{t} \overline{\mathrm{t}} $ background distributions are shown as colored histograms, and the signal distributions by the solid lines. The total background distribution and the signal distributions are all normalized to unit area. On the left, the signal distributions are given for a top squark mass of 300 GeV and $ \Delta {m}= $ 10, 30, 50, and 80 GeV. On the right, the signal distributions are shown for four different $ ({m}(\tilde{\mathrm{t}}_{1}), {m}(\tilde{\chi}_{1}^{0})) $ values, all corresponding to the same $ \Delta {m}= $ 30 GeV. 
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Figure 4:
BDT output distributions from data (points) and simulation (colored histograms) after the preselection in 10 GeV steps of $ \Delta {m} $ from 10 (upper left) to 80 (lower right) GeV for the 2017 data. The last bin corresponds to the SR. For each $ \Delta {m} $ value, the predicted signal distribution is shown by the solid red line for a representative $ ({m}(\tilde{\mathrm{t}}_{1}), {m}(\tilde{\chi}_{1}^{0})) $ point, unstacked from the histograms. The lower panels show the ratio of the data to the sum of the background predictions, with the vertical bars and shaded area giving only the statistical uncertainty in the data and the simulated background, respectively. 
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Figure 4a:
BDT output distributions from data (points) and simulation (colored histograms) after the preselection in 10 GeV steps of $ \Delta {m} $ from 10 (upper left) to 80 (lower right) GeV for the 2017 data. The last bin corresponds to the SR. For each $ \Delta {m} $ value, the predicted signal distribution is shown by the solid red line for a representative $ ({m}(\tilde{\mathrm{t}}_{1}), {m}(\tilde{\chi}_{1}^{0})) $ point, unstacked from the histograms. The lower panels show the ratio of the data to the sum of the background predictions, with the vertical bars and shaded area giving only the statistical uncertainty in the data and the simulated background, respectively. 
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Figure 4b:
BDT output distributions from data (points) and simulation (colored histograms) after the preselection in 10 GeV steps of $ \Delta {m} $ from 10 (upper left) to 80 (lower right) GeV for the 2017 data. The last bin corresponds to the SR. For each $ \Delta {m} $ value, the predicted signal distribution is shown by the solid red line for a representative $ ({m}(\tilde{\mathrm{t}}_{1}), {m}(\tilde{\chi}_{1}^{0})) $ point, unstacked from the histograms. The lower panels show the ratio of the data to the sum of the background predictions, with the vertical bars and shaded area giving only the statistical uncertainty in the data and the simulated background, respectively. 
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Figure 4c:
BDT output distributions from data (points) and simulation (colored histograms) after the preselection in 10 GeV steps of $ \Delta {m} $ from 10 (upper left) to 80 (lower right) GeV for the 2017 data. The last bin corresponds to the SR. For each $ \Delta {m} $ value, the predicted signal distribution is shown by the solid red line for a representative $ ({m}(\tilde{\mathrm{t}}_{1}), {m}(\tilde{\chi}_{1}^{0})) $ point, unstacked from the histograms. The lower panels show the ratio of the data to the sum of the background predictions, with the vertical bars and shaded area giving only the statistical uncertainty in the data and the simulated background, respectively. 
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Figure 4d:
BDT output distributions from data (points) and simulation (colored histograms) after the preselection in 10 GeV steps of $ \Delta {m} $ from 10 (upper left) to 80 (lower right) GeV for the 2017 data. The last bin corresponds to the SR. For each $ \Delta {m} $ value, the predicted signal distribution is shown by the solid red line for a representative $ ({m}(\tilde{\mathrm{t}}_{1}), {m}(\tilde{\chi}_{1}^{0})) $ point, unstacked from the histograms. The lower panels show the ratio of the data to the sum of the background predictions, with the vertical bars and shaded area giving only the statistical uncertainty in the data and the simulated background, respectively. 
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Figure 4e:
BDT output distributions from data (points) and simulation (colored histograms) after the preselection in 10 GeV steps of $ \Delta {m} $ from 10 (upper left) to 80 (lower right) GeV for the 2017 data. The last bin corresponds to the SR. For each $ \Delta {m} $ value, the predicted signal distribution is shown by the solid red line for a representative $ ({m}(\tilde{\mathrm{t}}_{1}), {m}(\tilde{\chi}_{1}^{0})) $ point, unstacked from the histograms. The lower panels show the ratio of the data to the sum of the background predictions, with the vertical bars and shaded area giving only the statistical uncertainty in the data and the simulated background, respectively. 
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Figure 4f:
BDT output distributions from data (points) and simulation (colored histograms) after the preselection in 10 GeV steps of $ \Delta {m} $ from 10 (upper left) to 80 (lower right) GeV for the 2017 data. The last bin corresponds to the SR. For each $ \Delta {m} $ value, the predicted signal distribution is shown by the solid red line for a representative $ ({m}(\tilde{\mathrm{t}}_{1}), {m}(\tilde{\chi}_{1}^{0})) $ point, unstacked from the histograms. The lower panels show the ratio of the data to the sum of the background predictions, with the vertical bars and shaded area giving only the statistical uncertainty in the data and the simulated background, respectively. 
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Figure 4g:
BDT output distributions from data (points) and simulation (colored histograms) after the preselection in 10 GeV steps of $ \Delta {m} $ from 10 (upper left) to 80 (lower right) GeV for the 2017 data. The last bin corresponds to the SR. For each $ \Delta {m} $ value, the predicted signal distribution is shown by the solid red line for a representative $ ({m}(\tilde{\mathrm{t}}_{1}), {m}(\tilde{\chi}_{1}^{0})) $ point, unstacked from the histograms. The lower panels show the ratio of the data to the sum of the background predictions, with the vertical bars and shaded area giving only the statistical uncertainty in the data and the simulated background, respectively. 
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Figure 4h:
BDT output distributions from data (points) and simulation (colored histograms) after the preselection in 10 GeV steps of $ \Delta {m} $ from 10 (upper left) to 80 (lower right) GeV for the 2017 data. The last bin corresponds to the SR. For each $ \Delta {m} $ value, the predicted signal distribution is shown by the solid red line for a representative $ ({m}(\tilde{\mathrm{t}}_{1}), {m}(\tilde{\chi}_{1}^{0})) $ point, unstacked from the histograms. The lower panels show the ratio of the data to the sum of the background predictions, with the vertical bars and shaded area giving only the statistical uncertainty in the data and the simulated background, respectively. 
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Figure 5:
BDT output distributions from data (points) and simulation (colored histograms) after the preselection in 10 GeV steps of $ \Delta {m} $ from 10 (upper left) to 80 (lower right) GeV for the 2018 data. The last bin corresponds to the SR. For each $ \Delta {m} $ value, the predicted signal distribution is shown by the solid red line for a representative $ ({m}(\tilde{\mathrm{t}}_{1}), {m}(\tilde{\chi}_{1}^{0})) $ point, unstacked from the histograms. The lower panels show the ratio of the data to the sum of the background predictions, with the vertical bars and shaded area giving only the statistical uncertainty in the data and the simulated background, respectively. 
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Figure 5a:
BDT output distributions from data (points) and simulation (colored histograms) after the preselection in 10 GeV steps of $ \Delta {m} $ from 10 (upper left) to 80 (lower right) GeV for the 2018 data. The last bin corresponds to the SR. For each $ \Delta {m} $ value, the predicted signal distribution is shown by the solid red line for a representative $ ({m}(\tilde{\mathrm{t}}_{1}), {m}(\tilde{\chi}_{1}^{0})) $ point, unstacked from the histograms. The lower panels show the ratio of the data to the sum of the background predictions, with the vertical bars and shaded area giving only the statistical uncertainty in the data and the simulated background, respectively. 
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Figure 5b:
BDT output distributions from data (points) and simulation (colored histograms) after the preselection in 10 GeV steps of $ \Delta {m} $ from 10 (upper left) to 80 (lower right) GeV for the 2018 data. The last bin corresponds to the SR. For each $ \Delta {m} $ value, the predicted signal distribution is shown by the solid red line for a representative $ ({m}(\tilde{\mathrm{t}}_{1}), {m}(\tilde{\chi}_{1}^{0})) $ point, unstacked from the histograms. The lower panels show the ratio of the data to the sum of the background predictions, with the vertical bars and shaded area giving only the statistical uncertainty in the data and the simulated background, respectively. 
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Figure 5c:
BDT output distributions from data (points) and simulation (colored histograms) after the preselection in 10 GeV steps of $ \Delta {m} $ from 10 (upper left) to 80 (lower right) GeV for the 2018 data. The last bin corresponds to the SR. For each $ \Delta {m} $ value, the predicted signal distribution is shown by the solid red line for a representative $ ({m}(\tilde{\mathrm{t}}_{1}), {m}(\tilde{\chi}_{1}^{0})) $ point, unstacked from the histograms. The lower panels show the ratio of the data to the sum of the background predictions, with the vertical bars and shaded area giving only the statistical uncertainty in the data and the simulated background, respectively. 
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Figure 5d:
BDT output distributions from data (points) and simulation (colored histograms) after the preselection in 10 GeV steps of $ \Delta {m} $ from 10 (upper left) to 80 (lower right) GeV for the 2018 data. The last bin corresponds to the SR. For each $ \Delta {m} $ value, the predicted signal distribution is shown by the solid red line for a representative $ ({m}(\tilde{\mathrm{t}}_{1}), {m}(\tilde{\chi}_{1}^{0})) $ point, unstacked from the histograms. The lower panels show the ratio of the data to the sum of the background predictions, with the vertical bars and shaded area giving only the statistical uncertainty in the data and the simulated background, respectively. 
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Figure 5e:
BDT output distributions from data (points) and simulation (colored histograms) after the preselection in 10 GeV steps of $ \Delta {m} $ from 10 (upper left) to 80 (lower right) GeV for the 2018 data. The last bin corresponds to the SR. For each $ \Delta {m} $ value, the predicted signal distribution is shown by the solid red line for a representative $ ({m}(\tilde{\mathrm{t}}_{1}), {m}(\tilde{\chi}_{1}^{0})) $ point, unstacked from the histograms. The lower panels show the ratio of the data to the sum of the background predictions, with the vertical bars and shaded area giving only the statistical uncertainty in the data and the simulated background, respectively. 
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Figure 5f:
BDT output distributions from data (points) and simulation (colored histograms) after the preselection in 10 GeV steps of $ \Delta {m} $ from 10 (upper left) to 80 (lower right) GeV for the 2018 data. The last bin corresponds to the SR. For each $ \Delta {m} $ value, the predicted signal distribution is shown by the solid red line for a representative $ ({m}(\tilde{\mathrm{t}}_{1}), {m}(\tilde{\chi}_{1}^{0})) $ point, unstacked from the histograms. The lower panels show the ratio of the data to the sum of the background predictions, with the vertical bars and shaded area giving only the statistical uncertainty in the data and the simulated background, respectively. 
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Figure 5g:
BDT output distributions from data (points) and simulation (colored histograms) after the preselection in 10 GeV steps of $ \Delta {m} $ from 10 (upper left) to 80 (lower right) GeV for the 2018 data. The last bin corresponds to the SR. For each $ \Delta {m} $ value, the predicted signal distribution is shown by the solid red line for a representative $ ({m}(\tilde{\mathrm{t}}_{1}), {m}(\tilde{\chi}_{1}^{0})) $ point, unstacked from the histograms. The lower panels show the ratio of the data to the sum of the background predictions, with the vertical bars and shaded area giving only the statistical uncertainty in the data and the simulated background, respectively. 
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Figure 5h:
BDT output distributions from data (points) and simulation (colored histograms) after the preselection in 10 GeV steps of $ \Delta {m} $ from 10 (upper left) to 80 (lower right) GeV for the 2018 data. The last bin corresponds to the SR. For each $ \Delta {m} $ value, the predicted signal distribution is shown by the solid red line for a representative $ ({m}(\tilde{\mathrm{t}}_{1}), {m}(\tilde{\chi}_{1}^{0})) $ point, unstacked from the histograms. The lower panels show the ratio of the data to the sum of the background predictions, with the vertical bars and shaded area giving only the statistical uncertainty in the data and the simulated background, respectively. 
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Figure 6:
Distributions of $ p_{\mathrm{T}}(\ell) $ (upper) and BDT output for $ \Delta {m}= $ 10 GeV (lower) in the VR where 200 $ < p_{\mathrm{T}}^\text{miss} < $ 280 GeV, from 2017 (left) and 2018 (right) data (points) and simulation (colored histograms). The predicted signal distribution is shown by the solid red line for $ ({m}(\tilde{\mathrm{t}}_{1}), {m}(\tilde{\chi}_{1}^{0})) = $ (475, 465), unstacked from the histograms. The lower panels show the ratio of data to the sum of the simulated SM backgrounds. The shaded bands indicate only the statistical uncertainty in the simulation predictions. 
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Figure 6a:
Distributions of $ p_{\mathrm{T}}(\ell) $ (upper) and BDT output for $ \Delta {m}= $ 10 GeV (lower) in the VR where 200 $ < p_{\mathrm{T}}^\text{miss} < $ 280 GeV, from 2017 (left) and 2018 (right) data (points) and simulation (colored histograms). The predicted signal distribution is shown by the solid red line for $ ({m}(\tilde{\mathrm{t}}_{1}), {m}(\tilde{\chi}_{1}^{0})) = $ (475, 465), unstacked from the histograms. The lower panels show the ratio of data to the sum of the simulated SM backgrounds. The shaded bands indicate only the statistical uncertainty in the simulation predictions. 
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Figure 6b:
Distributions of $ p_{\mathrm{T}}(\ell) $ (upper) and BDT output for $ \Delta {m}= $ 10 GeV (lower) in the VR where 200 $ < p_{\mathrm{T}}^\text{miss} < $ 280 GeV, from 2017 (left) and 2018 (right) data (points) and simulation (colored histograms). The predicted signal distribution is shown by the solid red line for $ ({m}(\tilde{\mathrm{t}}_{1}), {m}(\tilde{\chi}_{1}^{0})) = $ (475, 465), unstacked from the histograms. The lower panels show the ratio of data to the sum of the simulated SM backgrounds. The shaded bands indicate only the statistical uncertainty in the simulation predictions. 
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Figure 6c:
Distributions of $ p_{\mathrm{T}}(\ell) $ (upper) and BDT output for $ \Delta {m}= $ 10 GeV (lower) in the VR where 200 $ < p_{\mathrm{T}}^\text{miss} < $ 280 GeV, from 2017 (left) and 2018 (right) data (points) and simulation (colored histograms). The predicted signal distribution is shown by the solid red line for $ ({m}(\tilde{\mathrm{t}}_{1}), {m}(\tilde{\chi}_{1}^{0})) = $ (475, 465), unstacked from the histograms. The lower panels show the ratio of data to the sum of the simulated SM backgrounds. The shaded bands indicate only the statistical uncertainty in the simulation predictions. 
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Figure 6d:
Distributions of $ p_{\mathrm{T}}(\ell) $ (upper) and BDT output for $ \Delta {m}= $ 10 GeV (lower) in the VR where 200 $ < p_{\mathrm{T}}^\text{miss} < $ 280 GeV, from 2017 (left) and 2018 (right) data (points) and simulation (colored histograms). The predicted signal distribution is shown by the solid red line for $ ({m}(\tilde{\mathrm{t}}_{1}), {m}(\tilde{\chi}_{1}^{0})) = $ (475, 465), unstacked from the histograms. The lower panels show the ratio of data to the sum of the simulated SM backgrounds. The shaded bands indicate only the statistical uncertainty in the simulation predictions. 
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Figure 7:
Distributions of $ p_{\mathrm{T}}^\text{miss} $ (upper) and BDT output for $ \Delta {m}= $ 60 GeV (lower) in the VR where $ p_{\mathrm{T}}(\ell) > $ 30 GeV, from 2017 (left) and 2018 (right) data (points) and simulation (colored histograms). The predicted signal distribution is shown by the solid red line for $ ({m}(\tilde{\mathrm{t}}_{1}), {m}(\tilde{\chi}_{1}^{0})) = $ (576, 516), unstacked from the histograms. The lower panels show the ratio of data to the sum of the simulated SM backgrounds. The shaded bands indicate only the statistical uncertainty in the simulation predictions. 
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Figure 7a:
Distributions of $ p_{\mathrm{T}}^\text{miss} $ (upper) and BDT output for $ \Delta {m}= $ 60 GeV (lower) in the VR where $ p_{\mathrm{T}}(\ell) > $ 30 GeV, from 2017 (left) and 2018 (right) data (points) and simulation (colored histograms). The predicted signal distribution is shown by the solid red line for $ ({m}(\tilde{\mathrm{t}}_{1}), {m}(\tilde{\chi}_{1}^{0})) = $ (576, 516), unstacked from the histograms. The lower panels show the ratio of data to the sum of the simulated SM backgrounds. The shaded bands indicate only the statistical uncertainty in the simulation predictions. 
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Figure 7b:
Distributions of $ p_{\mathrm{T}}^\text{miss} $ (upper) and BDT output for $ \Delta {m}= $ 60 GeV (lower) in the VR where $ p_{\mathrm{T}}(\ell) > $ 30 GeV, from 2017 (left) and 2018 (right) data (points) and simulation (colored histograms). The predicted signal distribution is shown by the solid red line for $ ({m}(\tilde{\mathrm{t}}_{1}), {m}(\tilde{\chi}_{1}^{0})) = $ (576, 516), unstacked from the histograms. The lower panels show the ratio of data to the sum of the simulated SM backgrounds. The shaded bands indicate only the statistical uncertainty in the simulation predictions. 
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Figure 7c:
Distributions of $ p_{\mathrm{T}}^\text{miss} $ (upper) and BDT output for $ \Delta {m}= $ 60 GeV (lower) in the VR where $ p_{\mathrm{T}}(\ell) > $ 30 GeV, from 2017 (left) and 2018 (right) data (points) and simulation (colored histograms). The predicted signal distribution is shown by the solid red line for $ ({m}(\tilde{\mathrm{t}}_{1}), {m}(\tilde{\chi}_{1}^{0})) = $ (576, 516), unstacked from the histograms. The lower panels show the ratio of data to the sum of the simulated SM backgrounds. The shaded bands indicate only the statistical uncertainty in the simulation predictions. 
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Figure 7d:
Distributions of $ p_{\mathrm{T}}^\text{miss} $ (upper) and BDT output for $ \Delta {m}= $ 60 GeV (lower) in the VR where $ p_{\mathrm{T}}(\ell) > $ 30 GeV, from 2017 (left) and 2018 (right) data (points) and simulation (colored histograms). The predicted signal distribution is shown by the solid red line for $ ({m}(\tilde{\mathrm{t}}_{1}), {m}(\tilde{\chi}_{1}^{0})) = $ (576, 516), unstacked from the histograms. The lower panels show the ratio of data to the sum of the simulated SM backgrounds. The shaded bands indicate only the statistical uncertainty in the simulation predictions. 
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Figure 8:
The observed yields in data (points) and the predicted background components (colored histograms) in the eight SRs for the 2017 data. The vertical bars on the points give the statistical uncertainty in the data. The hatched area shows the total uncertainty in the sum of the backgrounds. The expected yields for two signal points with $ ({m}(\tilde{\mathrm{t}}_{1}), {m}(\tilde{\chi}_{1}^{0})) = $ (500, 490) and (600, 520) GeV are also given by the lines, unstacked from the histograms. The lower panel shows the ratio of the number of observed events to the predicted total background. The vertical bars on the points give the statistical uncertainty in the ratio and the hatched area the total uncertainty. 
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Figure 9:
The observed yields in data (points) and the predicted background components (colored histograms) in the eight SRs for the 2018 data. The vertical bars on the points give the statistical uncertainty in the data. The hatched area shows the total uncertainty in the sum of the backgrounds. The expected yields for two signal points with $ ({m}(\tilde{\mathrm{t}}_{1}), {m}(\tilde{\chi}_{1}^{0})) = $ (500, 490) and (600, 520) GeV are also given by the lines, unstacked from the histograms. The lower panel shows the ratio of the number of observed events to the predicted total background. The vertical bars on the points give the statistical uncertainty in the ratio and the hatched area the total uncertainty. 
png pdf 
Figure 10:
The 95% CL upper limits in the (m($ \tilde{\mathrm{t}}_{1} $), $ \Delta {m} $) plane on the cross section for the production and fourbody decay of the top squark using the combined 2016, 2017, and 2018 data. The color shading represents the observed upper limit for a given point in the plane, using the color scale to the right of the figure. The solid black and dashed red lines show the observed and expected 95% CL lower limits, respectively, on m($ \tilde{\mathrm{t}}_{1} $) as a function of $ \Delta {m} $. The thick lines give the central values of the limits. The corresponding thin lines represent the $ \pm $ 1 standard deviation ($ \sigma_{\text{theory}} $) variations in the limits due to the theoretical uncertainties in the case of the observed limits, and $ \pm $ 1 and 2 standard deviation ($ \sigma_{\text{experiment}} $) variations due to the experimental uncertainties in the case of the expected limits. 
Tables  
png pdf 
Table 1:
The relative systematic uncertainties in percent from the different sources in the signal and the total relative uncertainty in the W+jets, $ \mathrm{t} \overline{\mathrm{t}} $, and nonprompt background predictions, shown separately for the 2017 and 2018 data analysis. The ranges given are across the eight SRs. The ``$ \text{} $'' symbol means that a given source of uncertainty is not applicable. 
png pdf 
Table 2:
The predicted number of W+jets, $ \mathrm{t} \overline{\mathrm{t}} $, nonprompt, and other ($ N^\mathrm{SR} $(Other)) background events and their sum ($ N^\mathrm{SR} $(Total)), in the eight SRs for the 2017 and 2018 data analysis. The first 3 predicted yields are derived from data, while the yields of the other background processes come from simulation. The uncertainties shown are the quadratic sum of the statistical and systematic uncertainties given in Table 1 for all the background processes. The corresponding $ \Delta {m} $ and BDT output threshold values for each SR are displayed in the first and second columns, respectively, and the observed number of events in data is shown in the last column. 
Summary 
The results of a search for the direct pair production of top squarks in singlelepton final states are presented within a compressed scenario where $ R $ parity is conserved and the mass difference $ \Delta {m} = m(\tilde{\mathrm{t}}_{1})  m(\tilde{\chi}_{1}^{0}) $ between the lightest top squark ($ \tilde{\mathrm{t}}_{1} $) and the lightest supersymmetric particle, taken to be the lightest neutralino $ \tilde{\chi}_{1}^{0} $, does not exceed the W boson mass. The considered decay mode of the top squark is the prompt fourbody decay to $ \mathrm{b} \mathrm{f} \overline{\mathrm{f}}^{\,\prime} \tilde{\chi}_{1}^{0} $, where the fermions in the final state $ \mathrm{f} $ and $ \overline{\mathrm{f}}^{\,\prime} $ represent a charged lepton and its neutrino for the decay products of one $ \tilde{\mathrm{t}}_{1} $, and two quarks for the other top squark. The search is based on data collected from protonproton collisions at $ \sqrt{s}= $ 13 TeV, recorded with the CMS detector during the years 2016, 2017, and 2018, corresponding to an integrated luminosity of 138 fb$ ^{1} $. Events are selected containing a single lepton (electron or muon), at least one highmomentum jet, and significant missing transverse momentum. The analysis is based on a multivariate tool specifically trained for different $ \Delta {m} $ regions, thus adapting the signal selection to the evolution of the kinematical variables as a function of $ ({m}(\tilde{\mathrm{t}}_{1}), {m}(\tilde{\chi}_{1}^{0})) $. The dominant background processes are W+jets, $ \mathrm{t} \overline{\mathrm{t}} $, and events with nonprompt leptons, which are estimated using control regions in the data. The observed number of events is consistent with the predicted standard model backgrounds in all signal regions. Upper limits are set at the 95% confidence level on the $ \tilde{\mathrm{t}}_{1} {\overline{\tilde{\mathrm{t}}}}_{1} $ production cross section as a function of the $ \tilde{\mathrm{t}}_{1} $ and $ \tilde{\chi}_{1}^{0} $ masses, within the context of a simplified model. Assuming a 100% branching fraction in the fourbody decay mode, the search excludes top squark masses up to 480 and 700 GeV at $ \Delta {m} = $ 10 and 80 GeV, respectively. The results summarized in this paper are among the best limits to date on the top squark pair production cross section, where the top squark decays via the fourbody mode, and currently correspond to the most stringent limits for $ \Delta {m} < $ 30 GeV. 
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