A search for long-lived neutral particles decaying to oppositely charged lepton pairs in $pp$ collisions at $\sqrt{s}=13$ TeV with the ATLAS detector

A search for long-lived neutral massive particles decaying to an oppositely charged $\mu\mu$, $ee$, or $e\mu$ lepton pair is presented using 140 $\mathrm{fb}^{-1}$ of Run II proton-proton collision data at $\sqrt{s}=13$ TeV collected by the ATLAS detector at the LHC from 2015 to 2018. The lepton pairs must form a vertex within the inner tracking volume of the detector, displaced from the primary vertex, and have a dilepton mass greater than 12 GeV. These signal selections effectively suppress Standard Model backgrounds where the remaining background, from high-energy cosmic ray muons and randomly crossing charged particle tracks, are estimated using data-driven methods. %resulting in an essentially background free analysis The results are interpreted for a model where a generic $Z'$ is the long-lived particle, pair-produced from a new heavy scalar ($S$) and decaying to lepton pairs or pairs of fermionic dark matter ($\chi$). Generic detection efficiencies and upper limits on the cross section are also presented for resonances with a mass of 100-700 GeV and decay length ($c\tau$) of 100-1000 mm. Despite the pair-produced nature of the $Z'$ in the specific model interpretation, the analysis searches for a single displaced vertex, allowing the results to be reinterpreted for other Beyond the Standard Model theories.