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A search for the direct production of a pair of $\tau$ sleptons, thesupersymmetric partners of $\tau$ leptons, is presented. Each $\tau$ slepton isassumed to decay to a $\tau$ lepton and the lightest supersymmetric particle(LSP), which is assumed to be stable and to not interact in the detector,leading to an imbalance in the total reconstructed transverse momentum. Thesearch is carried out in events identified as containing two $\tau$ leptons,each decaying to one or more hadrons and a neutrino, and significant transversemomentum imbalance. In addition to scenarios in which the $\tau$ sleptons decaypromptly, the search also addresses scenarios in which the $\tau$ sleptons havesufficiently long lifetimes to give rise to nonprompt $\tau$ leptons. The datawere collected in proton-proton collisions at a center-of-mass energy of 13 TeVat the CERN LHC with the CMS detector in 2016-2018, and correspond to anintegrated luminosity of 138 fb$^{-1}$. No significant excess is seen withrespect to standard model expectations. Upper limits on cross sections for thepair production of $\tau$ sleptons are obtained in the framework of simplifiedmodels. In a scenario in which the $\tau$ sleptons are superpartners ofleft-handed $\tau$ leptons, and each undergoes a prompt decay to a $\tau$lepton and a nearly massless LSP, $\tau$ slepton masses between 115 and 340 GeVare excluded. In a scenario in which the lifetime of the $\tau$ sleptonscorresponds to $c\tau_0$ = 0.1 mm, where $\tau_{0}$ represents the mean properlifetime of the $\tau$ slepton, masses between 150 and 220 GeV are excluded.

physical review. d/physical review. d.

Search for direct pair production of supersymmetric partners of $\tau$  leptons in the final state with two hadronically decaying $\tau$ leptons and  missing transverse momentum in proton-proton collisions at $\sqrt{s}$ = 13  TeV