Perturbing away from the limit of exact degeneracy gives corrections to these expressions of O (( µ$_{S}$ − µ$_{D}$ ) /µ$_{D}$ ). Note we have assumed that there is no CP violation for simplicity. In order to apply these expressions to the MSSM one can make the identifications where we neglect terms of O (1 /M$_{2}$ ) for the Bino/Higgsino system and O (1 /M$_{1}$ ) for the Wino/Higgsino system. Explicitly making the substitutions for the MSSM we have and The neutralino mass matrix in the (˜ γ, ˜ Z, ˜ H$_{d}$, ˜ H$_{u}$ ) basis is given by Is it possible to generate a large SD/SI ratio by having DM which is only a mixture of photino and Higgsino? The Higgsino component is required for a non-trivial coupling to the Z 0 and an admixture of photino (and not Zino) will allow ( | Z$_{H}$$_{d}$ | 2 − | Z$_{H}$$_{u}$ | $^{2}$) = 0 without introducing Appendix C: No-go Theorem for photino-Higgsino DM M =      M$_{1}$ c 2 w + M$_{2}$ s 2 w ( M$_{1}$ − M$_{2}$ ) c$_{w}$ s$_{w}$ − m$_{Z}$ s$_{2}$$_{w}$ c$_{β}$ m$_{Z}$ s$_{2}$$_{w}$ s$_{β}$ ( M$_{1}$ − M$_{2}$ ) c$_{w}$ s$_{w}$ M$_{1}$ s 2 w + M$_{2}$ c 2 w m$_{Z}$ c$_{2}$$_{w}$ c$_{β}$ − m$_{Z}$ c$_{2}$$_{w}$ s$_{β}$ − m$_{Z}$ s$_{2}$$_{w}$ c$_{β}$ m$_{Z}$ c$_{2}$$_{w}$ c$_{β}$ 0 − µ m$_{Z}$ s$_{2}$$_{w}$ s$_{β}$ − m$_{Z}$ c$_{2}$$_{w}$ s$_{β}$ − µ 0      . | 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$_{1}$ → ∞ . (B.10) | 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$_{1}$ → ∞ , (B.9) SDM Bino/Higgsino Wino/Higgsino µ$_{S}$ M$_{1}$ M$_{2}$ µ$_{D}$ µ µ λ v − m$_{Z}$ s$_{w}$ c$_{β}$ m$_{Z}$ c$_{w}$ c$_{β}$ λ $^{′}$v − m$_{Z}$ s$_{w}$ s$_{β}$ m$_{Z}$ c$_{w}$ s$_{β}$ 28