Effective Theories for Dark Matter Nucleon Scattering

We reformulate the calculation of the dark matter-nucleon scattering cross sections based on the method of effective field theories. We assume that the scatterings are induced by the exchange of colored mediators, and construct the effective theories by integrating out the colored particles. All of the leading order matching conditions as well as the renormalization group equations are presented. We consider a Majorana fermion, and real scalar and vector bosons for the dark matter and show the results for each case. The treatment for the twist-2 operators is discussed in detail, and it is shown that the scale of evaluating their nucleon matrix elements does not have to be the hadronic scale. The effects of the QCD corrections are evaluated on the assumption that the masses of the colored mediators are much heavier than the electroweak scale. Our formulation is systematic and model-independent, and thus suitable to be implemented in numerical packages, such as micrOMEGAs and DarkSUSY.