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We present a focused study of a predictive unified model whose measurableconsequences are immediately relevant to early discovery prospects ofsupersymmetry at the LHC. ATLAS and CMS have released their analysis with35~pb$^{-1}$ of data and the model class we discuss is consistent with thisdata. It is shown that with an increase in luminosity the LSP dark matter massand the gluino mass can be inferred from simple observables such as kinematicedges in leptonic channels and peak values in effective mass distributions.Specifically, we consider cases in which the neutralino is of low mass andwhere the relic density consistent with WMAP observations arises via theexchange of Higgs bosons in unified supergravity models. The magnitudes of thegaugino masses are sharply limited to focused regions of the parameter space,and in particular the dark matter mass lies in the range $\sim (50-65) ~\rmGeV$ with an upper bound on the gluino mass of $575~{\rm GeV}$, with a typicalmass of $450~{\rm GeV}$. We find that all model points in this paradigm arediscoverable at the LHC at $\sqrt s = 7 \rm ~TeV$. We determine lower bounds onthe entire sparticle spectrum in this model based on existing experimentalconstraints. In addition, we find the spin-independent cross section forneutralino scattering on nucleons to be generally in the range of $\sigma^{\rmSI}_{\na p} = 10^{-46 \pm 1}~\rm cm^2$ with much higher cross sections alsopossible. Thus direct detection experiments such as CDMS and XENON alreadyconstrain some of the allowed parameter space of the low mass gaugino modelsand further data will provide important cross-checks of the model assumptionsin the near future.

Predictive Signatures of Supersymmetry: Measuring the Dark Matter Mass and Gluino Mass with Early LHC data