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Search for long-lived particles using displaced vertices of oppositely charged leptons in 140 fb$^{-1}$ of pp collisions at $\sqrt{s} = 13$ TeV with the ATLAS detector

A search is presented for long-lived particles decaying into an oppositely charged lepton pair, $μ^{+}μ^{-}$, $e^{+}e^{-}$, or $e^{\pm}μ^{\mp}$, that form a vertex within the inner tracking system of the ATLAS detector at the Large Hadron Collider, displaced from the primary proton-proton interaction region. The analysis uses the 140 fb$^{-1}$ of Run-2 data collected at $\sqrt{s}=13$ TeV by the ATLAS experiment in 2015-2018. The results of the analysis are interpreted in the context of three benchmark models covering masses from 0.1 to 2.2 TeV and a range of mean proper lifetimes times the speed of light from 1 to 10000 mm. The first model is a generic $Z'$ boson pair-produced by a new heavy scalar, with the $Z'$ decaying into lepton pairs. The remaining two models are $R$-parity violating supersymmetric models in which the lightest neutralino $\tildeχ^{0}_{1}$ decays into $\ell^{+}\ell^{'-}ν$ ($\ell, \ell^{'} = e$, $μ$). The models differ by the mode of production of the $\tildeχ^{0}_{1}$, which can be produced via the decay of pairs of gluinos or of pairs of charginos and neutralinos ($\tildeχ_{1}^{\pm}\tildeχ_{1}^{0}$, $\tildeχ_{1}^{\pm}\tildeχ_{2}^{0}$, or $\tildeχ_{2}^{0}\tildeχ_{1}^{0}$). Although each benchmark sample includes pair-produced LLPs, only a single vertex is required to be reconstructed. No dilepton displaced vertex candidate is observed and the results are presented as upper limits on the production cross-sections. This analysis sets leading limits on the production cross-sections for multiple models, including parameter space that has never been directly probed.