Today dark matter is one of the most crucial problems in cosmology and particle physics. In this thesis, we firstreviw the existence of dark matter in the universe. Then, we will study a model for dark matterthat violates parity and CP symmetries. In this model, if dark matter decay into two photons, these photons own a net circular polarization. In order to study dark matter, one can measure this polarization. To begin with we introduce a model for this kind of dark matter decayinginto photons from a one-loop process. After this, by presenting a Lagrangian, the decay of dark matterinto polarized photons is calculated. Moreever also we consider one different model for dark matter in which thedivivative of dark matter field is coupled with fermions. For this special model, we calculate the amplitude of the interaction. We will show that for this model the calculation of the loop is divergent. Then fore we must renormalize.
