The effective field theory of dark matter direct detection

Abstract

We extend and explore the general non-relativistic effective theory of dark\nmatter (DM) direct detection. We describe the basic non-relativistic building\nblocks of operators and discuss their symmetry properties, writing down all\nGalilean-invariant operators up to quadratic order in momentum transfer arising\nfrom exchange of particles of spin 1 or less. Any DM particle theory can be\ntranslated into the coefficients of an effective operator and any effective\noperator can be simply related to most general description of the nuclear\nresponse. We find several operators which lead to novel nuclear responses.\nThese responses differ significantly from the standard minimal WIMP cases in\ntheir relative coupling strengths to various elements, changing how the results\nfrom different experiments should be compared against each other. Response\nfunctions are evaluated for common DM targets - F, Na, Ge, I, and Xe - using\nstandard shell model techniques. We point out that each of the nuclear\nresponses is familiar from past studies of semi-leptonic electroweak\ninteractions, and thus potentially testable in weak interaction studies. We\nprovide tables of the full set of required matrix elements at finite momentum\ntransfer for a range of common elements, making a careful and fully\nmodel-independent analysis possible. Finally, we discuss embedding\nnon-relativistic effective theory operators into UV models of dark matter.\n