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 similar to(50-65) GeV with an upper bound on the gluino mass of 575 GeV, with a typical mass of 450 GeV. We find that all model points in this paradigm are discoverable at the LHC at root s = 7 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(SI)(chi 10p) = 10(-46 +/- 1) 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.