Search for long-lived particles decaying to oppositely charged lepton pairs with the ATLAS experiment at $\sqrt{s} =$ 13 TeV

In this thesis, a search for new long-lived, massive particles decaying into oppositely charged $ee$, $e\mu$ or $\mu\mu$ pairs with the ATLAS experiment at the Large Hadron Collider is presented. The search is based on data of proton-proton collisions at a centre-of-mass energy of 13 TeV recorded in 2016, corresponding to an integrated luminosity of 32.8 fb$^{-1}$. The lepton pairs are required to form a common vertex within the inner tracking volume of the ATLAS detector, which is displaced from the primary collision vertex. The signal selection criteria suppress the background produced in collisions to a negligible level. High-energy cosmic-ray muons are the dominant source of the remaining background, which is estimated from the data to be 0.27 $\pm$ 0.17 events. No vertices with invariant mass greater than 12 GeV are observed, in agreement with the background expectation. The result is interpreted in a simplified supersymmetric model in which the lightest neutralino produced via squark-antisquark production is long-lived and decays to $\ell^{+}\ell^{\prime -}\nu$ ($\ell = e$, $\mu$) via R-parity violating couplings. Upper limits on the signal cross-section are derived for specific squark and neutralino masses and for neutralino lifetimes ($c\tau$) between 1 mm and 10 m.