Probing Supergravity Unified Theories at the Large Hadron Collider
  The discovery of supersymmetry is one of the major goals of the current experiments at the Tevatron and in proposed experiments at the Large Hadron Collider (LHC). However when sparticles are produced the signatures of their production will to a significant degree depend on their hierarchical mass patterns. Here we investigate hierarchical mass patterns for the four lightest sparticles within one of the leading candidate theories - the SUGRA model. Specifically we analyze the hierarchies for the four lightest sparticles for the mSUGRA as well as for a general class of supergravity unified models including nonuniversalities in the soft breaking sector. It is shown that out of nearly $10^4$ possibilities of sparticle mass hierarchies, only a small number survives the rigorous constraints of radiative electroweak symmetry breaking, relic density and other experimental constraints. The signature space of these mass patterns at the LHC is investigated using a large set of final states including multi-leptonic states, hadronically decaying $\tau$s, tagged $b$ jets and other hadronic jets. In all, we analyze more than 40 such lepton plus jet and missing energy signatures along with several kinematical signatures such as missing transverse momentum, effective mass, and invariant mass distributions of final state observables. It is shown that a composite analysis can produce significant discrimination among sparticle mass patterns allowing for a possible identification of the source of soft breaking. While the analysis given is for supergravity models, the techniques used in the analysis are applicable to wide class of models including string and brane models. 
Zuowei Liu