  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.
