A search for long-lived particles decaying into hadrons is presented. The analysis uses 139 fb$^{-1}$ of $pp$ collision data collected at $\sqrt{s} = 13$ TeV by the ATLAS detector at the LHC using events that contain multiple energetic jets and a displaced vertex. The search employs dedicated reconstruction techniques that significantly increase the sensitivity to long-lived particles decaying in the ATLAS inner detector. Background estimates for Standard Model processes and instrumental effects are extracted from data. The observed event yields are compatible with those expected from background processes. The results are used to set limits at 95% confidence level on model-independent cross sections for processes beyond the Standard Model, and on scenarios with pair-production of supersymmetric particles with long-lived electroweakinos that decay via a small $R$-parity-violating coupling. The pair-production of electroweakinos with masses below 1.5 TeV is excluded for mean proper lifetimes in the range from 0.03 ns to 1 ns. When produced in the decay of $m(\tilde{g})=2.4$ TeV gluinos, electroweakinos with $m(\tilde\chi^0_1)=1.5$ TeV are excluded with lifetimes in the range of 0.02 ns to 4 ns.
A search for supersymmetry in events with large missing transverse momentum, jets, and at least one hadronically decaying $\tau$-lepton is presented. Two exclusive final states with either exactly one or at least two $\tau$-leptons are considered. The analysis is based on proton-proton collisions at $\sqrt{s}$ = 13 TeV corresponding to an integrated luminosity of 36.1 fb$^{-1}$ delivered by the Large Hadron Collider and recorded by the ATLAS detector in 2015 and 2016. No significant excess is observed over the Standard Model expectation. At 95% confidence level, model-independent upper limits on the cross section are set and exclusion limits are provided for two signal scenarios: a simplified model of gluino pair production with $\tau$-rich cascade decays, and a model with gauge-mediated supersymmetry breaking (GMSB). In the simplified model, gluino masses up to 2000 GeV are excluded for low values of the mass of the lightest supersymmetric particle (LSP), while LSP masses up to 1000 GeV are excluded for gluino masses around 1400 GeV. In the GMSB model, values of the supersymmetry-breaking scale are excluded below 110 TeV for all values of $\tan\beta$ in the range $2 \leq \tan\beta \leq 60$, and below 120 TeV for $\tan\beta>30$.
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