  We examine the dark matter interpretation of the modulation signal reported
by the DAMA experiment from the perspective of effective field theories
displaying Galilean invariance. We consider the most general effective coupling
leading to the elastic scattering of a dark matter particle with spin 0 or 1/2
off a nucleon, and we analyze the compatibility of the DAMA signal with the
null results from other direct detection experiments, as well as with the
non-observation of a high energy neutrino flux in the direction of the Sun from
dark matter annihilation. To this end, we develop a novel semi-analytical
approach for comparing experimental results in the high-dimensional parameter
space of the non-relativistic effective theory. Assuming the standard halo
model, we find a strong tension between the dark matter interpretation of the
DAMA modulation signal and the null result experiments. We also list possible
ways-out of this conclusion.
