content_image/361207.jpg content_image/361205.jpg content_image/361204.jpg content_image/361203.jpg content_image/361202.jpg content_image/361201.jpg
where y$_{q}$ ( y$_{χ}$ ) is the Yukawa coupling for the quark (DM) and m$_{h}$ is the Higgs mass. The per nucleon cross section is then 

<img src='content_image/361207.jpg'>

Estimates based on recent lattice simulations seem to favor smaller values for the nuclear matrix elements [34]. If these lattice results are correct, the dominant contribution to the SI scattering cross section would be due to the heavy quark content of the nucleon (since f ( N ) TG → 1 in the limit of small f ( N ) q ) and the coefficient in Eq. (10) would be replaced by 2 × 10 − 8 pb. In cases where c$_{d}$ ≫ c$_{u}$ , which can occur in models with multiple Higgs bosons such as the MSSM, then uncertainties in the f ( N ) Tq can lead to as much as an order of magnitude variation in σ$_{SI}$ ( χ N → χ N ) [35]. 

## B. Spin Dependent 

The operator responsible for SD DM-nucleus interactions is 

<img src='content_image/361205.jpg'>

Taking the expectation value of this operator between two nucleon states allows us to find the effective SD interaction of the DM with a nucleon ( N = p (proton) or n (neutron)), 

<img src='content_image/361204.jpg'>

where s ( N ) µ is the spin of the nucleon and the Δ q ( N ) are extracted from polarized deep elastic scattering. The coefficient of the effective DM-nucleon interaction, 2 a$_{N}$ (¯ χ γ $^{µ}$γ 5 χ )( ¯ N s ( N ) µ N ), is given by 

<img src='content_image/361203.jpg'>

The elastic scattering cross section quoted by the experiments is between the DM and a nucleon which is given by 

where m$_{r}$ is the reduced mass between the DM and a nucleon. 

<img src='content_image/361202.jpg'>

Again we follow DarkSUSY and use the following values for the SD calculations, 

<img src='content_image/361201.jpg'>

