Searches for Supersymmetry (SUSY) at the Large Hadron Collider

This paper provides an overview of supersymmetry (SUSY) and the ongoing efforts to detect SUSY particles at the Large Hadron Collider (LHC). SUSY proposes corresponding "sparticles" for each Standard Model particle, with the potential to resolve the hierarchy problem, identify dark matter, and unify forces at high energy scales. We explore the key observables central to SUSY searches at the LHC, such as effective mass ($M_{\text{eff}}$), scalar sum of transverse momenta ($H_T$), and stransverse mass ($M_{T2}$)--each of which is instrumental in distinguishing SUSY particles by their mass scales and decay characteristics. The paper also discusses the challenges of differentiating SUSY signals from Standard Model backgrounds, particularly in scenarios without significant missing transverse momentum ($E_T^{\text{miss}}$). A critical aspect of these searches is achieving high signal purity while effectively managing background detection. The LHC employs sophisticated detection techniques to enhance the signal-to-noise ratio--crucial for isolating genuine SUSY events from prevalent Standard Model processes such as multijet productions, gauge bosons with jets, and top quark pairs. Through this examination, the paper aims to illuminate the challenges and potential breakthroughs in SUSY searches, assessing their broader implications for fundamental physics.