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

A search for long-lived particles decaying into at least one muon and hadrons is presented. The analysis selects events that pass a muon or missing-transverse-momentum trigger and contain a displaced muon and a displaced vertex with at least three tracks and a visible invariant vertex mass of at least 20~GeV. The analyzed dataset of proton--proton collisions at $\sqrt{s} = 13$~TeV was collected with the ATLAS detector and corresponds to 136~fb$^{-1}$. The search employs dedicated reconstruction techniques that significantly increase the sensitivity to long-lived particle decays. Background estimates for Standard Model processes and instrumental effects are extracted entirely from data. The observed event yields are compatible with those expected from background processes. The results are presented as limits at 95\% confidence level on model-independent cross sections for processes beyond the Standard Model, and interpreted as exclusion limits on scenarios with pair-production of long-lived top squarks that decay via a small $R$-parity-violating coupling to a quark and a muon. Top squarks with masses up to 1.7~TeV are excluded for a lifetime of 0.1~ns, and masses below 1.3~TeV are excluded for all lifetimes between 0.01~ns and 30~ns.