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| CMS-PAS-EXO-24-020 | ||
| Search for the pair production of long-lived supersymmetric partners of the tau lepton in proton-proton collisions at $ \sqrt{s}= $ 13 TeV | ||
| CMS Collaboration | ||
| 2025-07-18 | ||
| Abstract: Gauge-mediated supersymmetry breaking models provide a strong motivation to search for a supersymmetric partner of the tau lepton (stau) with a macroscopic lifetime. Long-lived stau decays produce tau leptons that are displaced from the primary proton-proton interaction vertex, leading to unconventional signatures in the detector. This study presents the first search for the direct production of long-lived staus decaying within the tracker volume in proton-proton collisions at $ \sqrt{s} = $ 13 TeV, performed with a dedicated graph network-based identification algorithm for displaced tau leptons. The data sample used, corresponding to an integrated luminosity of 138 fb$ ^{-1} $, was recorded with the CMS experiment at the CERN LHC between 2016 and 2018. This search excludes at 95% confidence level stau masses in the 90-290 (90-450) GeV range for $ c\tau_{0} = $ 50 mm in the maximally mixed (mass degenerate) scenario, while for $ m_{\tilde{\tau}} = $ 200 GeV, stau proper lifetimes are excluded in the range 15-130 (5-390) mm. | ||
| Links: CDS record (PDF) ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Diagram of stau pair production in pp collisions at the CERN LHC, and the decay that leads to a final state with pairs of tau leptons accompanied by gravitinos. |
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Figure 2:
Distributions of the variables used to define the signal region for data and the predicted background: $ p_{\text{T,j2}} $ (upper left), $ p_{\mathrm{T}}^\text{miss} $ (upper right), and $ m_{\mathrm{T2}} $ (lower). The signal distributions expected in the maximally mixed scenario for a few representative sets of ($m_{\tilde{\tau}}$ [GeV], $ c\tau_{0}$ [mm]) values are overlaid: (100, 50), (100, 100), (200, 50), and (200, 100). In bins where the observed yield is zero, the Poissonian upper limit at 68% CL is shown as a positive uncertainty. 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. The last bin includes the overflow. |
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Figure 2-a:
Distributions of the variables used to define the signal region for data and the predicted background: $ p_{\text{T,j2}} $ (upper left), $ p_{\mathrm{T}}^\text{miss} $ (upper right), and $ m_{\mathrm{T2}} $ (lower). The signal distributions expected in the maximally mixed scenario for a few representative sets of ($m_{\tilde{\tau}}$ [GeV], $ c\tau_{0}$ [mm]) values are overlaid: (100, 50), (100, 100), (200, 50), and (200, 100). In bins where the observed yield is zero, the Poissonian upper limit at 68% CL is shown as a positive uncertainty. 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. The last bin includes the overflow. |
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Figure 2-b:
Distributions of the variables used to define the signal region for data and the predicted background: $ p_{\text{T,j2}} $ (upper left), $ p_{\mathrm{T}}^\text{miss} $ (upper right), and $ m_{\mathrm{T2}} $ (lower). The signal distributions expected in the maximally mixed scenario for a few representative sets of ($m_{\tilde{\tau}}$ [GeV], $ c\tau_{0}$ [mm]) values are overlaid: (100, 50), (100, 100), (200, 50), and (200, 100). In bins where the observed yield is zero, the Poissonian upper limit at 68% CL is shown as a positive uncertainty. 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. The last bin includes the overflow. |
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Figure 2-c:
Distributions of the variables used to define the signal region for data and the predicted background: $ p_{\text{T,j2}} $ (upper left), $ p_{\mathrm{T}}^\text{miss} $ (upper right), and $ m_{\mathrm{T2}} $ (lower). The signal distributions expected in the maximally mixed scenario for a few representative sets of ($m_{\tilde{\tau}}$ [GeV], $ c\tau_{0}$ [mm]) values are overlaid: (100, 50), (100, 100), (200, 50), and (200, 100). In bins where the observed yield is zero, the Poissonian upper limit at 68% CL is shown as a positive uncertainty. 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. The last bin includes the overflow. |
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Figure 3:
Observed and predicted event yields in the eight BRT1 bins as defined in Table 2. The signal yields expected in the maximally mixed scenario for a few representative sets of ($m_{\tilde{\tau}}$ [GeV], $c\tau_{0}$ [mm]) values are overlaid: (100, 50), (100, 100), (200, 50), and (200, 100). 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. |
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Figure 4:
Observed and predicted event yields in the eight SR bins as defined in Table 2. The signal yields expected in the maximally mixed scenario for a few representative sets of ($m_{\tilde{\tau}}$ [GeV], $ c\tau_{0}$ [mm]) values are overlaid: (100, 50), (100, 100), (200, 50), and (200, 100). In bins where the observed yield is zero, the Poissonian upper limit at 68% CL is shown as a positive uncertainty. 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 Section 8. |
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Figure 5:
Exclusion limits at 95% CL for the pair production of long-lived staus, displayed in the plane of $ m_{\tilde{\tau}} $ and $ c\tau_{0} $. The maximally mixed scenario is presented on the upper panel, and the mass degenerate scenario on the lower panel. The color axis represents the observed upper limit on the cross section. The signal cross sections are evaluated using NLO$ + $NLL calculations. The black (red) lines represent the observed (expected) limits on $ m_{\tilde{\tau}} $ and $ c\tau_{0} $ and enclose the region excluded at 95% CL. 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. The limits presented here have been obtained using an asymptotic approximation of the test statistic. |
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Figure 5-a:
Exclusion limits at 95% CL for the pair production of long-lived staus, displayed in the plane of $ m_{\tilde{\tau}} $ and $ c\tau_{0} $. The maximally mixed scenario is presented on the upper panel, and the mass degenerate scenario on the lower panel. The color axis represents the observed upper limit on the cross section. The signal cross sections are evaluated using NLO$ + $NLL calculations. The black (red) lines represent the observed (expected) limits on $ m_{\tilde{\tau}} $ and $ c\tau_{0} $ and enclose the region excluded at 95% CL. 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. The limits presented here have been obtained using an asymptotic approximation of the test statistic. |
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Figure 5-b:
Exclusion limits at 95% CL for the pair production of long-lived staus, displayed in the plane of $ m_{\tilde{\tau}} $ and $ c\tau_{0} $. The maximally mixed scenario is presented on the upper panel, and the mass degenerate scenario on the lower panel. The color axis represents the observed upper limit on the cross section. The signal cross sections are evaluated using NLO$ + $NLL calculations. The black (red) lines represent the observed (expected) limits on $ m_{\tilde{\tau}} $ and $ c\tau_{0} $ and enclose the region excluded at 95% CL. 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. The limits presented here have been obtained using an asymptotic approximation of the test statistic. |
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Figure 6:
Cross section upper limits at 95% CL for the pair production of long-lived staus in the maximally mixed scenario, as a function of $ m_{\tilde{\tau}} $, for $ c\tau_{0}= $ 10, 30, 50, 100, 200, and 300 mm (left to right, upper to lower). The inner (yellow) and outer (blue) bands indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis. The central values of the expected upper limits are denoted by the dashed black line. The solid black line represents the observed upper limits. The signal cross sections and uncertainties evaluated using NLO$ + $NLL calculations are shown as a red line and shaded band. The limits presented here have been obtained using an asymptotic approximation of the test statistic. |
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Figure 6-a:
Cross section upper limits at 95% CL for the pair production of long-lived staus in the maximally mixed scenario, as a function of $ m_{\tilde{\tau}} $, for $ c\tau_{0}= $ 10, 30, 50, 100, 200, and 300 mm (left to right, upper to lower). The inner (yellow) and outer (blue) bands indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis. The central values of the expected upper limits are denoted by the dashed black line. The solid black line represents the observed upper limits. The signal cross sections and uncertainties evaluated using NLO$ + $NLL calculations are shown as a red line and shaded band. The limits presented here have been obtained using an asymptotic approximation of the test statistic. |
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Figure 6-b:
Cross section upper limits at 95% CL for the pair production of long-lived staus in the maximally mixed scenario, as a function of $ m_{\tilde{\tau}} $, for $ c\tau_{0}= $ 10, 30, 50, 100, 200, and 300 mm (left to right, upper to lower). The inner (yellow) and outer (blue) bands indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis. The central values of the expected upper limits are denoted by the dashed black line. The solid black line represents the observed upper limits. The signal cross sections and uncertainties evaluated using NLO$ + $NLL calculations are shown as a red line and shaded band. The limits presented here have been obtained using an asymptotic approximation of the test statistic. |
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Figure 6-c:
Cross section upper limits at 95% CL for the pair production of long-lived staus in the maximally mixed scenario, as a function of $ m_{\tilde{\tau}} $, for $ c\tau_{0}= $ 10, 30, 50, 100, 200, and 300 mm (left to right, upper to lower). The inner (yellow) and outer (blue) bands indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis. The central values of the expected upper limits are denoted by the dashed black line. The solid black line represents the observed upper limits. The signal cross sections and uncertainties evaluated using NLO$ + $NLL calculations are shown as a red line and shaded band. The limits presented here have been obtained using an asymptotic approximation of the test statistic. |
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Figure 6-d:
Cross section upper limits at 95% CL for the pair production of long-lived staus in the maximally mixed scenario, as a function of $ m_{\tilde{\tau}} $, for $ c\tau_{0}= $ 10, 30, 50, 100, 200, and 300 mm (left to right, upper to lower). The inner (yellow) and outer (blue) bands indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis. The central values of the expected upper limits are denoted by the dashed black line. The solid black line represents the observed upper limits. The signal cross sections and uncertainties evaluated using NLO$ + $NLL calculations are shown as a red line and shaded band. The limits presented here have been obtained using an asymptotic approximation of the test statistic. |
png pdf |
Figure 6-e:
Cross section upper limits at 95% CL for the pair production of long-lived staus in the maximally mixed scenario, as a function of $ m_{\tilde{\tau}} $, for $ c\tau_{0}= $ 10, 30, 50, 100, 200, and 300 mm (left to right, upper to lower). The inner (yellow) and outer (blue) bands indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis. The central values of the expected upper limits are denoted by the dashed black line. The solid black line represents the observed upper limits. The signal cross sections and uncertainties evaluated using NLO$ + $NLL calculations are shown as a red line and shaded band. The limits presented here have been obtained using an asymptotic approximation of the test statistic. |
png pdf |
Figure 6-f:
Cross section upper limits at 95% CL for the pair production of long-lived staus in the maximally mixed scenario, as a function of $ m_{\tilde{\tau}} $, for $ c\tau_{0}= $ 10, 30, 50, 100, 200, and 300 mm (left to right, upper to lower). The inner (yellow) and outer (blue) bands indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis. The central values of the expected upper limits are denoted by the dashed black line. The solid black line represents the observed upper limits. The signal cross sections and uncertainties evaluated using NLO$ + $NLL calculations are shown as a red line and shaded band. The limits presented here have been obtained using an asymptotic approximation of the test statistic. |
png pdf |
Figure 7:
Cross section upper limits at 95% CL for the pair production of long-lived staus in the mass degenerate scenario, as a function of $ m_{\tilde{\tau}} $, for $ c\tau_{0}= $ 10, 30, 50, 100, 200, and 300 mm (left to right, upper to lower). The inner (yellow) and outer (blue) bands indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis. The central values of the expected upper limits are denoted by the dashed black line. The solid black line represents the observed upper limits. The signal cross sections and uncertainties evaluated using NLO$ + $NLL calculations are shown as a red line and shaded band. The limits presented here have been obtained using an asymptotic approximation of the test statistic. |
png pdf |
Figure 7-a:
Cross section upper limits at 95% CL for the pair production of long-lived staus in the mass degenerate scenario, as a function of $ m_{\tilde{\tau}} $, for $ c\tau_{0}= $ 10, 30, 50, 100, 200, and 300 mm (left to right, upper to lower). The inner (yellow) and outer (blue) bands indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis. The central values of the expected upper limits are denoted by the dashed black line. The solid black line represents the observed upper limits. The signal cross sections and uncertainties evaluated using NLO$ + $NLL calculations are shown as a red line and shaded band. The limits presented here have been obtained using an asymptotic approximation of the test statistic. |
png pdf |
Figure 7-b:
Cross section upper limits at 95% CL for the pair production of long-lived staus in the mass degenerate scenario, as a function of $ m_{\tilde{\tau}} $, for $ c\tau_{0}= $ 10, 30, 50, 100, 200, and 300 mm (left to right, upper to lower). The inner (yellow) and outer (blue) bands indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis. The central values of the expected upper limits are denoted by the dashed black line. The solid black line represents the observed upper limits. The signal cross sections and uncertainties evaluated using NLO$ + $NLL calculations are shown as a red line and shaded band. The limits presented here have been obtained using an asymptotic approximation of the test statistic. |
png pdf |
Figure 7-c:
Cross section upper limits at 95% CL for the pair production of long-lived staus in the mass degenerate scenario, as a function of $ m_{\tilde{\tau}} $, for $ c\tau_{0}= $ 10, 30, 50, 100, 200, and 300 mm (left to right, upper to lower). The inner (yellow) and outer (blue) bands indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis. The central values of the expected upper limits are denoted by the dashed black line. The solid black line represents the observed upper limits. The signal cross sections and uncertainties evaluated using NLO$ + $NLL calculations are shown as a red line and shaded band. The limits presented here have been obtained using an asymptotic approximation of the test statistic. |
png pdf |
Figure 7-d:
Cross section upper limits at 95% CL for the pair production of long-lived staus in the mass degenerate scenario, as a function of $ m_{\tilde{\tau}} $, for $ c\tau_{0}= $ 10, 30, 50, 100, 200, and 300 mm (left to right, upper to lower). The inner (yellow) and outer (blue) bands indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis. The central values of the expected upper limits are denoted by the dashed black line. The solid black line represents the observed upper limits. The signal cross sections and uncertainties evaluated using NLO$ + $NLL calculations are shown as a red line and shaded band. The limits presented here have been obtained using an asymptotic approximation of the test statistic. |
png pdf |
Figure 7-e:
Cross section upper limits at 95% CL for the pair production of long-lived staus in the mass degenerate scenario, as a function of $ m_{\tilde{\tau}} $, for $ c\tau_{0}= $ 10, 30, 50, 100, 200, and 300 mm (left to right, upper to lower). The inner (yellow) and outer (blue) bands indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis. The central values of the expected upper limits are denoted by the dashed black line. The solid black line represents the observed upper limits. The signal cross sections and uncertainties evaluated using NLO$ + $NLL calculations are shown as a red line and shaded band. The limits presented here have been obtained using an asymptotic approximation of the test statistic. |
png pdf |
Figure 7-f:
Cross section upper limits at 95% CL for the pair production of long-lived staus in the mass degenerate scenario, as a function of $ m_{\tilde{\tau}} $, for $ c\tau_{0}= $ 10, 30, 50, 100, 200, and 300 mm (left to right, upper to lower). The inner (yellow) and outer (blue) bands indicate the regions containing 68 and 95%, respectively, of the distribution of limits expected under the background-only hypothesis. The central values of the expected upper limits are denoted by the dashed black line. The solid black line represents the observed upper limits. The signal cross sections and uncertainties evaluated using NLO$ + $NLL calculations are shown as a red line and shaded band. The limits presented here have been obtained using an asymptotic approximation of the test statistic. |
| Tables | |
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Table 1:
Control and search region definitions. |
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Table 2:
The eight regions defined in bins of $ p_{\text{T,j2}} $, $ p_{\mathrm{T}}^\text{miss} $, and $ m_{\mathrm{T2}} $. |
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Table 3:
Relative systematic uncertainties in the signal and background yields in the SR, from various sources considered in this search, accounting for their correlations between the data-taking periods. The three values correspond to the minimum, median, and maximum values across the eight SR bins, as defined in Table 2. For cases where the minimum and maximum differ by less than 1%, only the median is shown. In the header row, $ m_{\tilde{\tau}} $ and $ c\tau_{0} $ are in units of GeV and mm, respectively. The uncertainty values shown here are prior to the maximum likelihood fit described in Section 8. |
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Table 4:
Predicted background and signal yields along with uncertainties in the eight SR bins, as defined in Table 2. In the header row, $ m_{\tilde{\tau}} $ and $ c\tau_{0} $ are in units of GeVns and mm, respectively. The number of events observed in the recorded data is also shown. The first uncertainty value listed is statistical, and the second is systematic. The yields and uncertainties are shown here prior to the maximum likelihood fit described in Section 8. |
| Summary |
| A search for the pair production of long-lived superpartners of the tau lepton (staus) has been performed in final states with two hadronically decaying tau leptons ($ \tau_\mathrm{h} $) using data collected by the CMS detector during 2016, 2017, and 2018, corresponding to an integrated luminosity of 138 fb$ ^{-1} $. The large background from misidentified jets in the fully hadronic final state is efficiently suppressed by the DISTAU neural network algorithm, specifically designed to identify displaced $ \tau_\mathrm{h} $. In the maximally mixed (mass degenerate) scenario, stau masses in the 90-290 (90-450) GeV range are excluded for $ c\tau_{0} = $ 50 mm, and for $ m_{\tilde{\tau}} = $ 200 GeV, stau proper lifetimes in the range 15-130 (5-390) mm are excluded. As shown by the exclusion limits, the introduction of a dedicated algorithm targeting displaced $ \tau_\mathrm{h} $ signatures led to a significant improvement in the experimental sensitivity. The results of this study significantly improve the exclusion limits compared to previous searches and extend the explored parameter space covered in the context of supersymmetry. |
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