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CMS-EXO-24-020 ; CERN-EP-2025-296
Search for the pair production of long-lived supersymmetric partners of the tau lepton in proton-proton collisions at $ \sqrt{s}= $ 13 TeV
Submitted to the Journal of High Energy Physics
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 an unconventional signature. This paper presents a search for the direct production of long-lived staus decaying within the CMS tracker volume in proton-proton collisions at $ \sqrt{s}= $ 13 TeV, performed for the first time with an identification algorithm based on a graph neural network dedicated to displaced tau leptons. The data sample, 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, $ m_{\tilde{\tau}} $, in the 126-260 (90-425) GeV range for a proper decay length of 50$ \text{mm} $ in the maximally mixed (mass-degenerate) scenario, while for $ m_{\tilde{\tau}} = $ 200 GeV, stau proper decay lengths are excluded in the range 21-94 (6-333)$ \text{mm} $. These results improve the exclusion limits compared to previous searches, and extend the parameter space explored in the context of supersymmetry.
Figures & Tables Summary References CMS Publications
Figures

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Figure 1:
Diagram of stau pair production in pp collisions at the 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 DISTAU score for signal and background jets. The background jets are taken from simulated $ \mathrm{t} \overline{\mathrm{t}} $ events where both top quarks decay hadronically, while signal jets are sampled from four representative $ (m_{\tilde{\tau}} [{\text{GeV}}],\ c\tau_{0} [{\text{mm}}]) $ hypotheses: (200, 5), (200, 100), (400, 5), and (400, 100). Each distribution is normalized such that its integral is unity.

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Figure 3:
Distributions of DISTAU score for $ \tau_\mathrm{h}^\text{dis} $ probes in the $ \mu\tau_\mathrm{h} $ CR described in Section 4.2, for data and predicted SM processes, corresponding to the 2018 data-taking period. Here DY($ \mu\tau_\mathrm{h} $) represents events from the $ \mathrm{Z}/\gamma^{*}\to\tau\tau $ process, where one of the tau leptons decays to a muon and the other decays hadronically. Events from other decay modes of $ \mathrm{Z}/\gamma^{*} $ are denoted as DY(other). Processes denoted as ``Top quark'' comprise $ \mathrm{t} \overline{\mathrm{t}} $, single top, and \ttbarV, and other SM processes include events from diboson production. Uncertainties in the simulation are shown as a grey band and include only the statistical uncertainty in the number of simulated events. Simulation is not fully calibrated to describe data, as the distribution is shown to illustrate the general behavior of the classifier and is not directly used for the measurement of simulation-to-data correction factors. The results for the 2016 and 2017 data-taking periods are similar in behavior.

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Figure 4:
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 four representative sets of $ (m_{\tilde{\tau}} [{\text{GeV}}],\ c\tau_{0} [{\text{mm}}]) $ values are overlaid: (100, 50), (100, 100), (200, 50), and (200, 100). In bins where the observed yield is zero, the Garwood interval 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 4-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 four representative sets of $ (m_{\tilde{\tau}} [{\text{GeV}}],\ c\tau_{0} [{\text{mm}}]) $ values are overlaid: (100, 50), (100, 100), (200, 50), and (200, 100). In bins where the observed yield is zero, the Garwood interval 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 4-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 four representative sets of $ (m_{\tilde{\tau}} [{\text{GeV}}],\ c\tau_{0} [{\text{mm}}]) $ values are overlaid: (100, 50), (100, 100), (200, 50), and (200, 100). In bins where the observed yield is zero, the Garwood interval 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 4-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 four representative sets of $ (m_{\tilde{\tau}} [{\text{GeV}}],\ c\tau_{0} [{\text{mm}}]) $ values are overlaid: (100, 50), (100, 100), (200, 50), and (200, 100). In bins where the observed yield is zero, the Garwood interval 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 5:
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 four representative sets of $ (m_{\tilde{\tau}} [{ \text{GeV}}],\ c\tau_{0} [{ \text{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 6:
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 four representative sets of $ (m_{\tilde{\tau}} [{\text{GeV}}],\ c\tau_{0} [{\text{mm}}]) $ values are overlaid: (100, 50), (100, 100), (200, 50), and (200, 100). In bins where the observed yield is zero, the Garwood interval 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 prediction, added in quadrature. The predicted yields and uncertainties shown in the upper (lower) panel are before (after) the maximum likelihood fit to data under the background-only hypothesis, as described in Section 8.

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Figure 6-a:
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 four representative sets of $ (m_{\tilde{\tau}} [{\text{GeV}}],\ c\tau_{0} [{\text{mm}}]) $ values are overlaid: (100, 50), (100, 100), (200, 50), and (200, 100). In bins where the observed yield is zero, the Garwood interval 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 prediction, added in quadrature. The predicted yields and uncertainties shown in the upper (lower) panel are before (after) the maximum likelihood fit to data under the background-only hypothesis, as described in Section 8.

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Figure 6-b:
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 four representative sets of $ (m_{\tilde{\tau}} [{\text{GeV}}],\ c\tau_{0} [{\text{mm}}]) $ values are overlaid: (100, 50), (100, 100), (200, 50), and (200, 100). In bins where the observed yield is zero, the Garwood interval 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 prediction, added in quadrature. The predicted yields and uncertainties shown in the upper (lower) panel are before (after) the maximum likelihood fit to data under the background-only hypothesis, as described in Section 8.

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Figure 7:
Exclusion limits at 95% CL for the pair production of long-lived staus decaying to a $ \tau $ lepton and a nearly massless gravitino ($ m_\tilde{\mathrm{G}}= $ 1 GeV), displayed in the plane of $ m_{\tilde{\tau}} $ and $ c\tau_{0} $. The maximally mixed (mass-degenerate) scenario is presented in the upper (lower) panel. The color axis represents the observed upper limit on the cross section. The signal cross sections are evaluated using NLO$ + $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 (dotted) red lines indicate the region containing 68% (95%) of the distribution of limits expected under the background-only hypothesis accounting for experimental uncertainties ($ \sigma_\text{experiment} $). The red dotted line corresponding to ``Expected$ +2\sigma_\text{experiment} $" is not shown for the maximally mixed scenario, as it does not exclude any points in this plane. The dashed black lines show the change in the observed limit from the variation of the signal cross sections within their theoretical uncertainties ($ \sigma_\text{theory} $).

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Figure 7-a:
Exclusion limits at 95% CL for the pair production of long-lived staus decaying to a $ \tau $ lepton and a nearly massless gravitino ($ m_\tilde{\mathrm{G}}= $ 1 GeV), displayed in the plane of $ m_{\tilde{\tau}} $ and $ c\tau_{0} $. The maximally mixed (mass-degenerate) scenario is presented in the upper (lower) panel. The color axis represents the observed upper limit on the cross section. The signal cross sections are evaluated using NLO$ + $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 (dotted) red lines indicate the region containing 68% (95%) of the distribution of limits expected under the background-only hypothesis accounting for experimental uncertainties ($ \sigma_\text{experiment} $). The red dotted line corresponding to ``Expected$ +2\sigma_\text{experiment} $" is not shown for the maximally mixed scenario, as it does not exclude any points in this plane. The dashed black lines show the change in the observed limit from the variation of the signal cross sections within their theoretical uncertainties ($ \sigma_\text{theory} $).

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Figure 7-b:
Exclusion limits at 95% CL for the pair production of long-lived staus decaying to a $ \tau $ lepton and a nearly massless gravitino ($ m_\tilde{\mathrm{G}}= $ 1 GeV), displayed in the plane of $ m_{\tilde{\tau}} $ and $ c\tau_{0} $. The maximally mixed (mass-degenerate) scenario is presented in the upper (lower) panel. The color axis represents the observed upper limit on the cross section. The signal cross sections are evaluated using NLO$ + $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 (dotted) red lines indicate the region containing 68% (95%) of the distribution of limits expected under the background-only hypothesis accounting for experimental uncertainties ($ \sigma_\text{experiment} $). The red dotted line corresponding to ``Expected$ +2\sigma_\text{experiment} $" is not shown for the maximally mixed scenario, as it does not exclude any points in this plane. The dashed black lines show the change in the observed limit from the variation of the signal cross sections within their theoretical uncertainties ($ \sigma_\text{theory} $).

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Figure 8:
Cross section upper limits at 95% CL for the pair production of long-lived staus decaying to a $ \tau $ lepton and a nearly massless gravitino ($ m_\tilde{\mathrm{G}}= $ 1 GeV) in the maximally mixed scenario, as a function of $ m_{\tilde{\tau}} $, for $ c\tau_{0}= $ 10, 30, 50, 100, 200, and 300$ \text{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.

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Figure 8-a:
Cross section upper limits at 95% CL for the pair production of long-lived staus decaying to a $ \tau $ lepton and a nearly massless gravitino ($ m_\tilde{\mathrm{G}}= $ 1 GeV) in the maximally mixed scenario, as a function of $ m_{\tilde{\tau}} $, for $ c\tau_{0}= $ 10, 30, 50, 100, 200, and 300$ \text{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.

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Figure 8-b:
Cross section upper limits at 95% CL for the pair production of long-lived staus decaying to a $ \tau $ lepton and a nearly massless gravitino ($ m_\tilde{\mathrm{G}}= $ 1 GeV) in the maximally mixed scenario, as a function of $ m_{\tilde{\tau}} $, for $ c\tau_{0}= $ 10, 30, 50, 100, 200, and 300$ \text{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.

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Figure 8-c:
Cross section upper limits at 95% CL for the pair production of long-lived staus decaying to a $ \tau $ lepton and a nearly massless gravitino ($ m_\tilde{\mathrm{G}}= $ 1 GeV) in the maximally mixed scenario, as a function of $ m_{\tilde{\tau}} $, for $ c\tau_{0}= $ 10, 30, 50, 100, 200, and 300$ \text{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.

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Figure 8-d:
Cross section upper limits at 95% CL for the pair production of long-lived staus decaying to a $ \tau $ lepton and a nearly massless gravitino ($ m_\tilde{\mathrm{G}}= $ 1 GeV) in the maximally mixed scenario, as a function of $ m_{\tilde{\tau}} $, for $ c\tau_{0}= $ 10, 30, 50, 100, 200, and 300$ \text{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.

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Figure 8-e:
Cross section upper limits at 95% CL for the pair production of long-lived staus decaying to a $ \tau $ lepton and a nearly massless gravitino ($ m_\tilde{\mathrm{G}}= $ 1 GeV) in the maximally mixed scenario, as a function of $ m_{\tilde{\tau}} $, for $ c\tau_{0}= $ 10, 30, 50, 100, 200, and 300$ \text{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.

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Figure 8-f:
Cross section upper limits at 95% CL for the pair production of long-lived staus decaying to a $ \tau $ lepton and a nearly massless gravitino ($ m_\tilde{\mathrm{G}}= $ 1 GeV) in the maximally mixed scenario, as a function of $ m_{\tilde{\tau}} $, for $ c\tau_{0}= $ 10, 30, 50, 100, 200, and 300$ \text{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.

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Figure 9:
Cross section upper limits at 95% CL for the pair production of long-lived staus decaying to a $ \tau $ lepton and a nearly massless gravitino ($ m_\tilde{\mathrm{G}}= $ 1 GeV) in the mass-degenerate scenario, as a function of $ m_{\tilde{\tau}} $, for $ c\tau_{0}= $ 10, 30, 50, 100, 200, and 300$ \text{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.

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Figure 9-a:
Cross section upper limits at 95% CL for the pair production of long-lived staus decaying to a $ \tau $ lepton and a nearly massless gravitino ($ m_\tilde{\mathrm{G}}= $ 1 GeV) in the mass-degenerate scenario, as a function of $ m_{\tilde{\tau}} $, for $ c\tau_{0}= $ 10, 30, 50, 100, 200, and 300$ \text{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.

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Figure 9-b:
Cross section upper limits at 95% CL for the pair production of long-lived staus decaying to a $ \tau $ lepton and a nearly massless gravitino ($ m_\tilde{\mathrm{G}}= $ 1 GeV) in the mass-degenerate scenario, as a function of $ m_{\tilde{\tau}} $, for $ c\tau_{0}= $ 10, 30, 50, 100, 200, and 300$ \text{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.

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Figure 9-c:
Cross section upper limits at 95% CL for the pair production of long-lived staus decaying to a $ \tau $ lepton and a nearly massless gravitino ($ m_\tilde{\mathrm{G}}= $ 1 GeV) in the mass-degenerate scenario, as a function of $ m_{\tilde{\tau}} $, for $ c\tau_{0}= $ 10, 30, 50, 100, 200, and 300$ \text{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.

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Figure 9-d:
Cross section upper limits at 95% CL for the pair production of long-lived staus decaying to a $ \tau $ lepton and a nearly massless gravitino ($ m_\tilde{\mathrm{G}}= $ 1 GeV) in the mass-degenerate scenario, as a function of $ m_{\tilde{\tau}} $, for $ c\tau_{0}= $ 10, 30, 50, 100, 200, and 300$ \text{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.

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Figure 9-e:
Cross section upper limits at 95% CL for the pair production of long-lived staus decaying to a $ \tau $ lepton and a nearly massless gravitino ($ m_\tilde{\mathrm{G}}= $ 1 GeV) in the mass-degenerate scenario, as a function of $ m_{\tilde{\tau}} $, for $ c\tau_{0}= $ 10, 30, 50, 100, 200, and 300$ \text{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.

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Figure 9-f:
Cross section upper limits at 95% CL for the pair production of long-lived staus decaying to a $ \tau $ lepton and a nearly massless gravitino ($ m_\tilde{\mathrm{G}}= $ 1 GeV) in the mass-degenerate scenario, as a function of $ m_{\tilde{\tau}} $, for $ c\tau_{0}= $ 10, 30, 50, 100, 200, and 300$ \text{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.
Tables

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Table 1:
Signal and control region definitions.

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Table 2:
The $ p_{\text{T,j2}} $, $ p_{\mathrm{T}}^\text{miss} $, and $ m_{\mathrm{T2}} $ requirements for each of the eight analysis bins.

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Table 3:
Relative systematic uncertainties expressed as a percentage (%) of the signal and background yields in the SR, from various sources considered in this search, after 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 values 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 $ \text{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 in the eight SR bins, as defined in Table 2, are shown alongside the background yields obtained from the maximum likelihood fit to data under the background-only hypothesis and the number of events observed in the recorded data. All yields, except for the number of recorded events, are quoted with uncertainties obtained by adding statistical and systematic components in quadrature. Signal and predicted background uncertainties correspond to the prefit values, while the postfit background uncertainties are taken from the fit described in Section 8. In the header row, $ m_{\tilde{\tau}} $ and $ c\tau_{0} $ are in units of GeVns and $ \text{mm} $, respectively.
Summary
A search for the direct pair production of long-lived superpartners of the tau lepton (staus) has been performed in final states with two hadronically decaying tau leptons ($ \tau_\mathrm{h} $) using data collected by the CMS detector in 2016--2018, corresponding to an integrated luminosity of 138 fb$ ^{-1} $. The potentially 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} $ candidates. In the maximally mixed (mass-degenerate) scenario, stau masses, $ m_{\tilde{\tau}} $, in the 126-260 (90-425) GeV range are excluded for a proper decay length, $ c\tau_{0} $, of 50$ \text{mm} $, and stau proper decay lengths in the range 21-94 (6-333)$ \text{mm} $ are excluded for $ m_{\tilde{\tau}} = $ 200 GeV. The development of a dedicated algorithm targeting displaced $ \tau_\mathrm{h} $ signatures has led to a significant improvement in the experimental sensitivity. These results improve the exclusion limits compared to previous searches [33,34,35,36,37,38,39], and extend the parameter space explored in the context of supersymmetry.
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