DM–Nucleon Interaction

Abstract

Now that we know how to compute hadronic matrix elements of (some) quark and gluon operators, we remain with turning the Dark Matter–nucleon scattering amplitude $\mathscr {M}_N$ into a Dark Matter–nucleus cross section. To do so, we start by performing a non-relativistic expansion in powers of the Dark Matter–nucleon relative speed v, which allows to identify contributions from different types of non-relativistic interactions: some involving the nucleon spin, some involving the Dark Matter spin, some involving q, etc. In this chapter we first introduce the non-relativistic expansion for spin-0 and spin-1∕2 Dark Matter, then we show how to expand $\mathscr {M}_N$ and express the result in terms of 16 Galilean-invariant building blocks. We will then see in Chap. 5 how different non-relativistic interactions involve different nuclear properties and correspond to different nuclear responses and form factors.