Supersymmetry (SUSY) is a framework which extends the Standard Model (SM) of particle physics by the introduction of an additional broken space-time symmetry between fermions and bosons and predicts fermionic (bosonic) superpartners to the SM bosons (fermions). These additional particles provide elegant solutions to several outstanding problems with the SM, a mechanism to resolve the hierarchy problem through corrections to the Higgs mass, a natural dark matter candidate in the case of R-parity conserving SUSY through the lightest superpartner particle (LSP), and if realized at the TeV scale leads to gauge coupling unification at very high energy.SUSY is rich in viable models of new physics but evidence remains undetected by detector experiments. Simplified models using only a few parameters allow for ease of modeling and interpretation while retaining relevant first-order phenomenology of more general SUSY models. This dissertation presents a search for signs of new physics motivated by simplified SUSY models where the superpartners to the light-flavor charged leptons, sleptons (ℓ), and a bino-like LSP (𝜒01 ) are light compared to the other SUSY particles. The search selects final states containing 2 same-flavor oppositely-charged leptons and significant missing transverse energy (𝐸miss𝑇) in association with an initial state radiation (ISR) jet. The search uses 140 fb−1 of 𝑝𝑝 collision data at √𝑠 = 13 TeV recorded by the ATLAS detector between 2015 and 2018. The results of the search are generally consistent with the SM. The search extends sensitivity to a gap in exclusion in the 𝑚ℓ , 𝑚𝜒01 plane left behind by previous efforts, excluding models with 𝑚ℓ up to 350 GeV with mass splittings, Δ(𝑚ℓ, 𝑚𝜒01), between 2 GeV and 100 GeV.

Results are presented for a variety of SUSY Simplified Models at the 14 TeV LHC as well as a 33 and 100 TeV proton collider. Our focus is on models whose signals are driven by colored production. We present projections of the upper limit and discovery reach in the gluino-neutralino (for both light and heavy flavor decays), squark-neutralino, and gluino-squark Simplified Model planes. Depending on the model a jets + ETmiss, monojet, or same-sign di-lepton search is applied. The impact of pileup is explored. This study utilizes the Snowmass backgrounds and combined detector. Assuming 3000 fb-1 of integrated luminosity, a gluino that decays to light flavor quarks can be discovered below 2.3 TeV at the 14 TeV LHC and below 11 TeV at a 100 TeV machine. © The Authors.