Landscape of Supersymmetric Particle Mass Hierarchies and their Signature Space at the CERN Large Hadron Collider

The minimal supersymmetric standard model with soft breaking has a large landscape of supersymmetric particle mass hierarchies. This number is reduced significantly in well-motivated scenarios such as minimal supergravity and alternatives. We carry out an analysis of the landscape for the first four lightest particles and identify at least 16 mass patterns, and provide benchmarks for each. We study the signature space for the patterns at the CERN Large Hadron Collider by analyzing the $\mathrm{\text{lepton}}+$ ($\mathrm{\text{jet}}\ge 2$) $+$ missing $P_T$ signals with 0, 1, 2, and 3 leptons. Correlations in missing $P_T$ are also analyzed. It is found that even with $10{\mathrm{fb}}^{-1}$ of data a significant discrimination among patterns emerges.