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The discovery of supersymmetry is one of the major goals of the currentexperiments at the Tevatron and in proposed experiments at the Large HadronCollider (LHC). However when sparticles are produced the signatures of theirproduction will to a significant degree depend on their hierarchical masspatterns. Here we investigate hierarchical mass patterns for the four lightestsparticles within one of the leading candidate theories - the SUGRA model.Specifically we analyze the hierarchies for the four lightest sparticles forthe mSUGRA as well as for a general class of supergravity unified modelsincluding nonuniversalities in the soft breaking sector. It is shown that outof nearly $10^4$ possibilities of sparticle mass hierarchies, only a smallnumber survives the rigorous constraints of radiative electroweak symmetrybreaking, relic density and other experimental constraints. The signature spaceof these mass patterns at the LHC is investigated using a large set of finalstates including multi-leptonic states, hadronically decaying $\tau$s, tagged$b$ jets and other hadronic jets. In all, we analyze more than 40 such leptonplus jet and missing energy signatures along with several kinematicalsignatures such as missing transverse momentum, effective mass, and invariantmass distributions of final state observables. It is shown that a compositeanalysis can produce significant discrimination among sparticle mass patternsallowing for a possible identification of the source of soft breaking. Whilethe analysis given is for supergravity models, the techniques used in theanalysis are applicable to wide class of models including string and branemodels.

Probing Supergravity Unified Theories at the Large Hadron Collider