In this talk, I introduce Dark Matter(DM) direct detection in non-relativistic effective field theory. In particular, I discuss proton-philic spin-dependent inelastic Dark Matter (pSIDM), a scenario where Weakly Interacting Massive Particles (WIMP) upscatter inelastically to a heavier state and predominantly couple to the spin of protons, I will show that pSIDM can still provide a viable explanation of the observed DAMA modulation amplitude in compliance with the constraints from other experiments. provided that the WIMP velocity distribution departs from a standard Maxwellian.
I will then move on to discuss a generalization of pSIDM to the most general effective theory of a WIMP of spin 0, 1/2 or 1, including up to 14 effective WIMP-nucleus interaction terms. We take into account all the possible interferences among operators by studying the intersections among the ellipsoidal surfaces of constant signal of DAMA and other experiments in the space of the coupling constants of the effective theory We find that, compared to the elastic case, inelastic scattering partially relieves but does not eliminate the existing tension between the DAMA effect and the constraints from the null results of other experiments if we assume a standard Maxwellian velocity distribution in the Galaxy.. We also find that the residual tension between DAMA and other results is considerably more sensitive on the astrophysical parameters compared to the elastic case. In addition to that, we find that the configurations with the smallest tension can produce enough yearly modulation in some of the DAMA bins in compliance with the constraints from other experiments, but the ensuing shape of the modulation spectrum is too steep compared to the measured one.
The recent COSINE-100 bound, which uses the same target material as DAMA, is naturally evaded due to the large expected modulation fractions in the pSIDM scenario.