when the squarks are heavy. This upper bound is largely a consequence of the LEP bounds on the chargino masses which force the mixing ∼ m$_{Z}$/µ to be less than one. Eq. (29) provides a good analytic understanding of this number – it comes within approximately 10% of this value. The deviation is due to mixing effects that occur away from the large M$_{1}$ limit. In many models of SUSY breaking the relation M$_{1}$/α$_{1}$ = M$_{2}$/α$_{2}$ = M$_{3}$/α$_{3}$ holds. We refer to this condition as unified gaugino masses. Because this is equivalent to M$_{2}$ ≈ 2 M$_{1}$ at the weak scale, the LSP is mostly Bino and Higgsino. In this case, Finally, for m$_{χ}$ > m$_{W}$ , a thermal relic density within ± 3 σ of the WMAP measurement implies an upper limit on the amount of Higgsino in the DM particle. Therefore, This result holds for the case with unified gaugino masses as well. Note that Eqs. (31), (33), and (35) all occur for a DM mass of O (80 GeV). To saturate the above bound ( i.e. maximize σ$_{SD}$ for thermal, well-tempered DM) requires a Bino/Higgsino mixture (recall that d$_{q}$ vanishes for a pure Higgsino), with a negligible Wino contribution. The largest values of SD DD occur when the DM has the largest Bino/Higgsino mixing which happens for the lowest values of the DM mass. As the mass of the DM increases, a larger component of Higgsino or Wino is needed for the DM to efficiently annihilate down to the correct relic density, which in turn typically leads to a decrease in σ$_{SD}$ . As shown in Fig. 2, there is a tight correlation between the SD cross section and the DM mass, in the decoupling limit when there is gaugino mass unification and a thermal relic abundance. For low masses, the neutralino is well-tempered for low masses and as m$_{χ}$ → O (1 TeV) the neutralino approaches a pure Higgsino. Examining Fig. 2, except for when the annihilation channel χχ → t ¯ opens, σ$_{SD}$ is a smooth, monotonically decreasing curve. An experiment sensitive to cross sections of O (10 − $^{4}$pb) will probe m$_{χ}$ ≲ 200 GeV. There is a spread in the points in this figure from the liberal range taken on the relic density constraint. For masses approaching O (1 TeV), there is additional extent from the variation in the Bino content of the neutralino and from contributions from squark exchange. For masses at 1 TeV, σ$_{SD}$ goes from 10 − $^{6}$pb → 0 for M$_{1}$ from 1300 GeV → ∞ . Note that the projected reach of a 1 ton version of COUPP is O (10 − $^{6}$) pb for m$_{χ}$ = 1 TeV [17], which would probe the entire range of SD cross sections for neutralinos excepting a nearly pure TeV Higgsino . 14 | Z$_{H}$$_{d}$ | 2 − | Z$_{H}$$_{u}$ | 2 < 0 . 24 ⇒ (34) ( σ SUSY SD )$_{thermal}$ < 2 × 10 − $^{3}$pb (General MSSM , Thermal DM) . (35) | Z$_{H}$$_{d}$ | 2 − | Z$_{H}$$_{u}$ | 2 < 0 . 32 ⇒ (32) ( σ SUSY SD ) < 4 × 10 − $^{3}$pb (Unified Gaugino Masses , Non − thermal DM) . (33)