Here D and ¯ D are a vector-like pair of SU (2) doublet fermions, S is an SU (2) singlet, h is the SM Higgs doublet, λ ( λ $^{′}$) is the Yukawa coupling which leads to the mixing between the D ( ¯ D ) and S , µ$_{D}$ is the vector-like mass for the D and ¯ D , and µ$_{S}$ is the Majorana mass for S . For the purposes of SD scattering it is sufficient to replace h by its vev, 〈 h 〉 ≡ v = 174 GeV. The exchange of the uneaten component of h leads to SI DD. In the case where S plays the role of the Bino, the values of λ and λ ′ are constrained by the supersymmetric relations to be λ v = − m$_{Z}$ s$_{w}$ c$_{β}$ and λ $^{′}$v = − m$_{Z}$ s$_{w}$ s$_{β}$ , while in the case where S is the Wino, the values of λ and λ ′ are constrained by the supersymmetric relations to be λ v = m$_{Z}$ c$_{w}$ c$_{β}$ and λ $^{′}$v = m$_{Z}$ c$_{w}$ s$_{β}$ . We now use this model to discuss the coupling of the Z 0 boson to the DM in the MSSM. In Appendix B we discuss the diagonalization of the 3 × 3 mixing matrix of the SDM. With appropriate substitutions, these expressions correspond to either Bino/Higgsino ( M$_{2}$ → ∞ ) and Wino/Higgsino ( M$_{1}$ → ∞ ) neutralinos. In these limits we can write down approximate expressions for the effective coupling of the DM to the Z $^{0}$. When there are no degeneracies between parameters in the neutralino mass matrix and m$_{Z}$ may be treated as a perturbation, we have (see [9] and Appendix B): The largest values of | Z$_{H}$$_{d}$ | 2 − | Z$_{H}$$_{u}$ | 2 do not occur in this limit. Instead, they are found when two parameters of the neutralino mass matrix are degenerate. The reason is simple: a degeneracy allows a large gaugino–Higgsino mixing in spite of the relative smallness of the off-diagonal entries of the neutralino mass matrix (proportional to m$_{Z}$ ). It should be said that there is no particular reason to believe that a precise degeneracy should occur, since µ and the gaugino masses are SUSY preserving and breaking respectively. However, since this case maximizes the possible signal at SD experiments, it is worth noting. In the presence of these degeneracies, we have (see Appendix B): Perturbing away from the limit of exact degeneracy gives corrections to these expressions of O (( M$_{i}$ − µ ) /µ ). Note that DM with a mixed Wino/Higgsino has a SD DD rate enhanced relative to a Bino/Higgsino admixture by the appropriate power of c$_{w}$/s$_{w}$ = 1 . 8. What is the largest obtainable SD cross section in the MSSM? A numerical scan yields ( σ SUSY SD ) < 6 × 10 − $^{3}$pb (General MSSM , Non − thermal DM) , (31) | Z$_{H}$$_{d}$ | 2 − | Z$_{H}$$_{u}$ | 2 < 0 . 4 ⇒ (30) | Z$_{H}$$_{d}$ | 2 − | Z$_{H}$$_{u}$ | 2 =    ( s$_{β}$ − c$_{β}$ ) s$_{w}$ m$_{Z}$ 2 √ 2 | µ | + ( s 2 $_{β}$− c 2 $_{β}$) s 2 $_{w}$m 2 Z 8 µ 2 for | M$_{1}$ | = | µ | > m$_{Z}$ , M$_{2}$ → ∞ ( s$_{β}$ − c$_{β}$ ) c$_{w}$ m$_{Z}$ 2 √ 2 | µ | + ( s 2 $_{β}$− c 2 $_{β}$) c 2 $_{w}$m 2 Z 8 µ 2 for | M$_{2}$ | = | µ | > m$_{Z}$ , M$_{1}$ → ∞ . (29) | Z$_{H}$$_{d}$ | 2 − | Z$_{H}$$_{u}$ | 2 =    c$_{2}$$_{β}$ s 2 $_{w}$m 2 Z µ $^{2}$− M 2 1 for | M$_{1}$ | , | µ | , | µ | − | M$_{1}$ | > m$_{Z}$ , M$_{2}$ → ∞ c$_{2}$$_{β}$ c 2 $_{w}$m 2 Z µ $^{2}$− M 2 for | M$_{2}$ | , | µ | , | µ | − | M$_{2}$ | > m$_{Z}$ , M$_{1}$ → ∞ . (28) 13