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, $m_\tildeτ$, in the 126$-$260 (906$-$425) GeV range for a proper decay length of 50 mm in the maximally mixed (mass-degenerate) scenario, while for $m_\tildeτ $ = 200 GeV, stau proper decay lengths are excluded in the range 21$-$94 (6$-$333) mm. These results improve the exclusion limits compared to previous searches, and extend the parameter space explored in the context of supersymmetry.
Distributions of $p_\text{T, j2}$ for data and the predicted background, in the signal region. The signal distributions expected in the maximally mixed scenario for a few representative sets of $(m_{\tilde{\tau}} [\text{GeV}], c\tau_{0} [\text{mm}])$ values are overlaid: (100, 10), (100, 50), (100, 100), (200, 10), (200, 50), (200, 100), (300, 10), (300, 50), and (300, 100). In bins where the observed yield is zero, the Garwood interval at 68% CL is shown as a positive uncertainty. The last bin includes the overflow.
Distributions of $p^\text{miss}_\text{T}$ for data and the predicted background, in the signal region. The signal distributions expected in the maximally mixed scenario for a few representative sets of $(m_{\tilde{\tau}} [\text{GeV}], c\tau_{0} [\text{mm}])$ values are overlaid: (100, 10), (100, 50), (100, 100), (200, 10), (200, 50), (200, 100), (300, 10), (300, 50), and (300, 100). In bins where the observed yield is zero, the Garwood interval at 68% CL is shown as a positive uncertainty. The last bin includes the overflow.
Distributions of $m_\text{T2}$ for data and the predicted background, in the signal region. The signal distributions expected in the maximally mixed scenario for a few representative sets of $(m_{\tilde{\tau}} [\text{GeV}], c\tau_{0} [\text{mm}])$ values are overlaid: (100, 10), (100, 50), (100, 100), (200, 10), (200, 50), (200, 100), (300, 10), (300, 50), and (300, 100). In bins where the observed yield is zero, the Garwood interval at 68% CL is shown as a positive uncertainty. The last bin includes the overflow.
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