Search for high-mass dilepton resonances using $139\,\mathrm{fb}^{-1}$ of $pp$ collision data collected at $\sqrt{s}=13\,\mathrm{TeV}$ with the ATLAS detector

A search for high-mass dielectron and dimuon resonances in the mass range of 250$\,$GeV to 6$\,$TeV is presented. The data were recorded by the ATLAS experiment in proton-proton collisions at a centre-of-mass energy of $\sqrt{s}=13\,$TeV during Run 2 of the Large Hadron Collider and correspond to an integrated luminosity of $139\,\mathrm{fb}^{-1}$. A functional form is fitted to the dilepton invariant-mass distribution to model the contribution from background processes, and a generic signal shape is used to determine the significance of observed deviations from this background estimate. No significant deviation is observed and upper limits are placed at the 95% confidence level on the fiducial cross-section times branching ratio for various resonance width hypotheses. The derived limits are shown to be applicable to spin-0, spin-1 and spin-2 signal hypotheses. For a set of benchmark models, the limits are converted into lower limits on the resonance mass and reach 4.5$\,$TeV for the E$_6$-motivated $Z'_{\psi}$ boson. Also presented are limits on Heavy Vector Triplet model couplings.