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Processes of the form $pp\to anything \to X_i X_j \to x\bar{x} + y\bar{y} (+\slashchar{E})$ are studied via a technique that may be viewed as an adaptationof time-honoured Dalitz plot analyses. $X_i$ and $X_j$ are new heavy states(with $i,j=1...n$), which may be identical or distinct; and $x\bar{x}$ and$y\bar{y}$ are necessarily distinct Standard Model (SM) fermion pairs whoseinvariant masses can be measured. A Dalitz-like plot of said invariant masses,$M(x\bar{x})$ {\it vs.$$} $M(y\bar{y})$, exhibits a topology connected to themasses and specific decay chains of $X_i$ and $X_j$. Aside from relativelyminor details, observed patterns consist of a collection of box and wedgeshapes. This collection is model-dependent: comparison of the observed patternto the possibilities for a specific model yields information on which newparticle pair combinations are actually being produced, information beyond thatextractable from conventional one-dimensional invariant mass distributions. Thetechnique is illustrated via application to the Minimal Supersymmetric StandardModel (MSSM) process $pp \to\tilde{g}\tilde{g},\tilde{g}\tilde{q},\tilde{q}\tilde{q} \to\widetilde{\chi}_i^0 \widetilde{\chi}_j^0 \to e^+ e^- + \mu^+ \mu^- (+\slashchar{E})$. Here the heavy states are neutralinos $\widetilde{\chi}_i^0$($i=2,3,4$) -- note $\widetilde{\chi}_1^0$ is excluded -- which are produced ingluino/squark ($\tilde{g}$/$\tilde{q}$) cascade decay chains. Even with fairlymodest expectations for the LHC performance during the first few years, thismethod still provides substantial insight into the neutralino mass spectrum andcouplings if gluino/squark masses are relatively low ($\simeq 400 \hbox{GeV}$).Comment: 28 pages, LaTeX, 7 figure

Pair-produced heavy particle topologies: MSSM neutralino properties at the LHC from gluino/squark cascade decays