In this Thesis we investigate possible generalizations of the usual assumptions behind Dark Matter (DM) modeling in relation with detection experiments. In fact, while model independent analyses should in principle allow to investigate the DM problem in its full generality, strong assumptions are usually made in order to reduce it to a form that can be tackled with our limited tools and knowledge. Investigation of only a handful of possible interactions, or assumptions regarding the DM interaction with ordinary particles, might reveal themselves on the other hand as oversimplifications of the problem, preventing us to understand the true nature of Dark Matter. For instance, the present situation of DM direct searches is unclear, with potential DM signals detected by some experiments being excluded by others. Given the difficulties in accommodating the results of the various direct detection experiments within the standard scenario, a generalization of the usual assumptions is therefore in order.
After presenting the complete list (up to dimension six in mass) of interaction operators between a scalar DM and the Standard Model particles, we show that the phenomenon of quantum interference between some of these operators drastically changes the DM phenomenology in direct detection searches, respect to the one usually assumed. In fact, relaxing the customary assumption of equal DM-proton and DM-neutron interactions, it can be shown that several experiments that are found to disagree one with the other in the standard interpretation can find better agreement allowing for a certain degree of isospin violation. We propose quantum interference between exchange processes of two different interaction mediators as a concrete mechanism for obtaining isospin violation, and investigate which pairs of mediators could lead to viable interference.
In the last part of this Thesis we consider a DM particle featuring a magnetic dipole moment, thus interacting with the photon. This can be seen again as an application of the effective operators framework, as the magnetic moment operator arises at loop order or in composite DM models. The interesting feature of this interaction is that it is of long-range type, in contrast with the contact type that is usually assumed. The phenomenology of these two kinds of interaction is very different and in fact we show that magnetic moment DM can accommodate all present direct detection experiments, assuming a conservative estimate of the XENON100 low energy threshold.