Gluon contribution to the dark matter direct detection

In this article we have calculated the spin-independent cross section of nucleon-dark matter scattering process at loop level, which is relevant to dark matter direct detection. Paying particular attention to the scattering of gluon with dark matter, which contributes as leading order in the perturbation, we have systematically evaluated loop diagrams with tracking the characteristic loop momentum which dominates in the loops. Here loop diagrams whose typical loop momentum scales are the masses of quarks and other heavier particles are separately presented. Then, we have properly taken into account each contribution to give the cross section. We assume that the dark matter is pure bino or wino in the supersymmetric models. The application to other models is straightforward.