Search for direct pair production of supersymmetric partners to the $\tau$ lepton in the all-hadronic final state at $\sqrt{s}=13~\mathrm{TeV}$

A search for the direct production of a pair of $\tau$ sleptons in proton-proton collisions at a center-of-mass energy of $13~\mathrm{TeV}$ is presented. The search is carried out in events with two $\tau$ leptons, each decaying to one or more hadrons and a neutrino. In addition to scenarios in which the $\tau$ sleptons decay promptly, the search also addresses scenarios in which the $\tau$ sleptons have macroscopic lifetimes, giving rise to displaced $\tau$ leptons. The data were collected with the CMS detector from 2016 to 2018, and correspond to an integrated luminosity of $137~\mathrm{fb}^{-1}$. No significant excess is seen in the observed event counts with respect to the standard model background expectation. Limits on pair production of both promptly decaying and long-lived $\tau$ sleptons are obtained in the framework of simplified models in which the $\tau$ slepton decays to a $\tau$ lepton and the lightest supersymmetric particle (LSP), which is assumed to be stable. In the case of purely left-handed $\tau$ slepton pair production, with a prompt decay to a $\tau$ lepton and a nearly massless LSP, $\tau$ slepton masses between 115 and $340~\mathrm{GeV}$ are excluded. In a scenario with macroscopic $\tau$ slepton decay lengths corresponding to $c\tau_{0}=0.1~\mathrm{mm}$, $\tau$ slepton masses between 150 and $220~\mathrm{GeV}$ are excluded for the case that the LSP is nearly massless.