A search for new long-lived particles decaying to leptons using proton-proton collision data produced by the CERN LHC at $\sqrt{s}$ = 13 TeV is presented. Events are selected with two leptons (an electron and a muon, two electrons, or two muons) that both have transverse impact parameter values between 0.01 and 10 cm and are not required to form a common vertex. Data used for the analysis were collected with the CMS detector in 2016, 2017, and 2018, and correspond to an integrated luminosity of 118 (113) fb$^{-1}$ in the ee channel (e$\mu$ and $\mu\mu$ channels). The search is designed to be sensitive to a wide range of models with displaced e$\mu$, ee, and $\mu\mu$ final states. The results constrain several well-motivated models involving new long-lived particles that decay to displaced leptons. For some areas of the available phase space, these are the most stringent constraints to date.
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