content_image/375346.jpg content_image/375345.jpg content_image/375344.jpg content_image/375342.jpg content_image/375343.jpg content_image/375341.jpg
## A. Spin Independent 

The operator responsible for SI DM-nucleus interactions is 

<img src='content_image/375346.jpg'>

where χ is the DM and q is a quark. Taking the expectation value of this operator between two nucleon states ( N = p (proton) or n (neutron)) determines the effective interaction of the DM with a nucleon, 

<img src='content_image/375345.jpg'>

where the nuclear matrix element f ( N ) Tq is determined in chiral perturbation theory from the pion nucleon-scattering sigma term. The coefficient of the effective DM-nucleon interaction, f$_{N}$ (¯ χ χ )( ¯ N N ), is given by 

<img src='content_image/375344.jpg'>

where f ( N ) TG = 1 − ∑ q = $_{u,d,s}$f ( N ) Tq and the h on c ( h ) q refers to Higgs boson exchange [31]. 

The nucleon-Higgs interaction is coherent over the nucleus [32] resulting in the well known A 2 enhancement for SI cross sections. To compare between experiments using different nuclei, the elastic scattering cross section is normalized to a per nucleon value [13]: 

<img src='content_image/375342.jpg'>

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

We use the DarkSUSY package for numerical analysis [33], so for analytic estimates we will use the same values for the nuclear matrix elements, namely 

<img src='content_image/375343.jpg'>

Since these values are derived from the pion nucleon scattering sigma term, their error bars are correlated. 

If the Higgs boson, h , that mediates the interaction between the DM and the nucleon is SM-like, the coefficients c$_{q}$ are given by 

<img src='content_image/375341.jpg'>

