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

A search for long-lived particles giving rise to displaced decays with at least one muon is presented. The analysis selects events that pass a muon or missing transverse energy trigger and contain a displaced muon and a displaced vertex with at least three tracks and a vertex visible invariant mass of at least $20~\textrm{GeV}$. A data sample of $\sqrt{s} = 13~\textrm{TeV}$ proton-proton collisions collected by the ATLAS detector between $2016$ and $2018$, corresponding to a total integrated luminosity of $136~\textrm{fb}^{-1}$, is used for this search. The analysis employs dedicated reconstruction techniques that significantly increase the sensitivity to displaced 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. Results are presented as limits at $95\%$ confidence level on the model-independent cross section for processes beyond the Standard Model, and interpreted as exclusion limits on scenarios with pair-production of long-lived stop squarks that decay via a small $R$-parity violating coupling to a quark and a muon. Stop squarks with a lifetime of $0.1$ ns in these scenarios are excluded for masses up to $1.7~\textrm{TeV}$.