  A search for new physics with non-resonant signals in dielectron and dimuon
final states in the mass range above 2 TeV is presented. This is the first
search for non-resonant signals in dilepton final states at the LHC to use a
background estimate from the data. The data, corresponding to an integrated
luminosity of 139 fb$^{-1}$, were recorded by the ATLAS experiment in
proton-proton collisions at a center-of-mass energy of $\sqrt{s} = 13$ TeV
during Run 2 of the Large Hadron Collider. The benchmark signal signature is a
two-quark and two-lepton contact interaction, which would enhance the dilepton
event rate at the TeV mass scale. To model the contribution from background
processes a functional form is fit to the dilepton invariant-mass spectra in
data in a mass region below the region of interest. It is then extrapolated to
a high-mass signal region to obtain the expected background there. No
significant deviation from the expected background is observed in the data.
Upper limits at 95 % CL on the number of events and the visible cross-section
times branching fraction for processes involving new physics are provided.
Observed (expected) 95 % CL lower limits on the contact interaction energy
scale reach 35.8 (37.6) TeV.
