Measurements of differential cross-sections in four-lepton events in 13 TeV proton-proton collisions with the ATLAS detector

Measurements of four-lepton differential and integrated fiducial cross-sections in events with two same-flavour, opposite-charge electron or muon pairs are presented. The data correspond to 139~fb$^{-1}$ of $\sqrt{s}=13$ TeV proton-proton collisions, collected by the ATLAS detector during Run 2 of the Large Hadron Collider (2015-2018). The final-state has contributions from a number of interesting Standard Model processes that dominate in different four-lepton invariant mass regions, including single $Z$ boson production, Higgs boson production and on-shell $ZZ$ production, with a complex mix of interference terms, and possible contributions from beyond-the-Standard Model physics. The differential cross-sections include the four-lepton invariant mass inclusively, in slices of other kinematic variables, and in different lepton flavour categories. Also measured are di-lepton invariant masses, transverse momenta, and angular correlation variables, in four regions of four-lepton invariant mass, each dominated by different processes. The measurements are corrected for detector effects and are compared to state-of-the-art Standard Model calculations, which are found to be consistent with the data. The $Z\to 4\ell$ branching fraction is extracted, giving a value of $\left(4.41 \pm 0.30\right) \times 10^{-6}$. Constraints on a model based on a spontaneously broken B-L gauge symmetry are also evaluated.