Effective Operators for Dark Matter Interactions

The aim of this thesis is to determine possible interactions between the Standard Model with right-chiral neutrinos and a sector of dark matter composed of a real scalar, left- and right-chiral fermion and a vector particle, which are singlets of the Standard Model gauge group. In the introductory chapters we review the evidence for dark matter and methods of its detection. In the main part, we present the complete list of gauge singlet operators of dimension not greater than 4, that consist of the standard sector fields. We obtain also an analogous list for the dark matter particles. Using both of them, we find the possible interactions between the two sectors, firstly for the renormalizable theories, then within the effective theory framework with operators up to dimension 6, imposing the stability symmetry condition on each dark matter field. We consider the problem of generation for the effective operators in underlying, renormalizable gauge theory that includes the Standard Model. It is shown, which of the operators can be generated in tree-level approximation and which require a loop.