Soft Leptons, Hard Problems: Searches for the Electroweak Production of Supersymmetric Particles in Compressed Mass Spectra with the ATLAS Detector

Supersymmetry is an attractive extension of the Standard Model of particle physics that posits an additional spacetime symmetry relating fermions and bosons. Phenomenologically, supersymmetry predicts the existence of bosonic superpartners for each of the Standard Model fermions and vice versa. In doing so, many outstanding issues in particle physics can be solved, including the nature of dark matter, the hierarchy problem, and gauge coupling unification. This dissertation presents searches for the direct electroweak production of supersymmetric states within compressed mass spectra, which generically lead to soft particles in the final state. These searches use 139~$\mbox{fb\(^{-1}\)}$ of $\sqrt{s}=13$ TeV proton--proton collision data collected by the ATLAS experiment at the Large Hadron Collider between 2015 and 2018. Selected events contain two oppositely-charged, same-flavor leptons with low transverse momenta, missing transverse energy, and additional hadronic activity from initial-state radiation. No statistically significant deviations from the Standard Model predictions are observed in the data. The results are used to set limits on the masses of the supersymmetric states in the context of $R$-parity-conserving simplified models in which the lightest supersymmetric particle is a neutralino arising from nearly mass-degenerate decays of the lightest chargino, the second-to-lightest neutralino, or a slepton. These limits significantly extend existing constraints on well-motivated dark matter scenarios.