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

We present a focused study of a predictive unified model whose measurable consequences are immediately relevant to early discovery prospects of supersymmetry at the LHC. ATLAS and CMS have released their analysis with 35~pb$^{-1}$ of data and the model class we discuss is consistent with this data. It is shown that with an increase in luminosity the LSP dark matter mass and the gluino mass can be inferred from simple observables such as kinematic edges in leptonic channels and peak values in effective mass distributions. Specifically, we consider cases in which the neutralino is of low mass and where the relic density consistent with WMAP observations arises via the exchange of Higgs bosons in unified supergravity models. The magnitudes of the gaugino masses are sharply limited to focused regions of the parameter space, and in particular the dark matter mass lies in the range $sim (50-65) ~rm GeV$ with an upper bound on the gluino mass of $575~{rm GeV}$, with a typical mass of $450~{rm GeV}$. We find that all model points in this paradigm are discoverable at the LHC at $sqrt s = 7 rm ~TeV$. We determine lower bounds on the entire sparticle spectrum in this model based on existing experimental constraints. In addition, we find the spin-independent cross section for neutralino scattering on nucleons to be generally in the range of $sigma^{rm SI}_{ a p} = 10^{-46 pm 1}~rm cm^2$ with much higher cross sections also possible. Thus direct detection experiments such as CDMS and XENON already constrain some of the allowed parameter space of the low mass gaugino models and further data will provide important cross-checks of the model assumptions in the near future.