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A search for long-lived particles decaying into hadrons and at least one muonis presented. The analysis selects events that pass a muon ormissing-transverse-momentum trigger and contain a displaced muon track and adisplaced vertex. The analyzed dataset of proton-proton collisions at $\sqrt{s}= 13$ TeV was collected with the ATLAS detector and corresponds to 136fb$^{-1}$. The search employs dedicated reconstruction techniques thatsignificantly increase the sensitivity to long-lived particle decays that occurin the ATLAS inner detector. Background estimates for Standard Model processesand instrumental effects are extracted from data. The observed event yields arecompatible with those expected from background processes. The results arepresented as limits at 95% confidence level on model-independent cross sectionsfor processes beyond the Standard Model, and interpreted as exclusion limits inscenarios with pair-production of long-lived top squarks that decay via a small$R$-parity-violating coupling into a quark and a muon. Top squarks with massesup to 1.7 TeV are excluded for a lifetime of 0.1 ns, and masses below 1.3 TeVare excluded for lifetimes between 0.01 ns and 30 ns.

physical review. d/physical review. d.

Search for long-lived, massive particles in events with a displaced  vertex and a muon with large impact parameter in $pp$ collisions at $\sqrt{s}  = 13$ TeV with the ATLAS detector