Search for events with a pair of displaced vertices from long-lived neutral particles decaying into hadronic jets in the ATLAS muon spectrometer in $pp$ collisions at $\sqrt{s}=13$ TeV

A search for events with two displaced vertices from long-lived particles (LLP) pairs using data collected by the ATLAS detector at the LHC is presented. This analysis uses 139~fb$^{-1}$ of proton--proton collision data at $\sqrt{s} = 13$ TeV recorded in 2015-2018. The search employs techniques for reconstructing vertices of LLPs decaying to jets in the muon spectrometer displaced between 3 m and 14 m with respect to the primary interaction vertex. The observed numbers of events are consistent with the expected background and limits for several benchmark signals are determined. For the SM-like Higgs boson with 125 GeV mass, branching fractions into neutral long-lived particles above 10% are excluded at 95% confidence level for LLP proper lifetimes ranging from 4 cm to 71.3 m. In addition, we present the first exclusion limits for the decay of LLPs to $t\overline{t}$ in the ATLAS muon spectrometer.