The prediction for SD scattering is somewhat more robust to variation in the hadronic matrix elements than the SI case: the uncertainties in these values can lead to O (30%) variation in the SD cross section [35]. If the SD interaction is mediated by the Z 0 boson, then the coefficients d$_{q}$ are given by where Q$_{Z}$$_{−}$$_{DM}$ parametrizes the coupling of the DM to the Z 0 and c$_{w}$ ≡ cos θ$_{w}$ . For concreteness, (and since it is relevant for calculations of solar capture) when we quote values for SD scattering we will focus on the cross section off of protons. For SD scattering mediated by the Z $^{0}$, the neutron scattering is O (20%) smaller. The SD cross section is In the next section, we discuss the form that Q$_{Z}$$_{−}$$_{DM}$ takes in the MSSM. The best DM candidate in the MSSM is the lightest neutralino, which is an admixture of Bino ( ˜ B ), Wino ( ˜ W ), and the up and down-type Higgsinos ( ˜ H$_{u}$ and ˜ H$_{d}$ ). The stability of the lightest superpartner (LSP) is guaranteed by R -parity, which is introduced to avoid proton decay. The neutralino mass matrix is given by where M$_{1}$ is the Bino mass, M$_{2}$ is the Wino mass, µ is the Supersymmetric (SUSY) Higgs boson mass parameter, m$_{Z}$ is the Z 0 mass, β = arctan( v$_{u}$/v$_{d}$ ), v$_{u,d}$ are the up and down-type Higgs boson vevs, s$_{w}$ ≡ sin θ$_{w}$ , c$_{w}$ ≡ cos θ$_{w}$ , s$_{β}$ ≡ sin β , and c$_{β}$ ≡ cos β . The composition of the lightest neutralino, which we denote χ , is specified by χ ≡ Z$_{B}$ ˜ B + Z$_{W}$ ˜ W + Z$_{H}$$_{d}$ ˜ H$_{d}$ + Z$_{H}$$_{u}$ ˜ H$_{u}$. (18) M =      M$_{1}$ 0 − m$_{Z}$ s$_{w}$ c$_{β}$ m$_{Z}$ s$_{w}$ s$_{β}$ 0 M$_{2}$ m$_{Z}$ c$_{w}$ c$_{β}$ − m$_{Z}$ c$_{w}$ s$_{β}$ − m$_{Z}$ s$_{w}$ c$_{β}$ m$_{Z}$ c$_{w}$ c$_{β}$ 0 − µ m$_{Z}$ s$_{w}$ s$_{β}$ − m$_{Z}$ c$_{w}$ s$_{β}$ − µ 0      , σ$_{SD}$ ( χ p → χ p ) ≈ 4 × 10 − $^{4}$pb $^{(}$Q$_{Z}$$_{−}$$_{DM}$ 0 . 1 ) 2 (SD typical) . (17) d$_{q}$ = g 2 2 c 2 w T q 3 $^{(}$Q$_{Z}$$_{−}$$_{DM}$ 2 ) 1 m 2 Z , (16) III. DIRECT DETECTION OF NEUTRALINO DARK MATTER 8