A model-independent treatment of dark-matter particle elastic scattering has been developed, yielding the most general interaction for WIMP-nucleon low-energy scattering, and the resulting amplitude has been embedded in the nucleus, taking into accou
nt the selection rules imposed by parity and time-reversal. One finds that, in contrast to the usual spin-independent/spin-dependent (SI/SD) formulation, the resulting cross section contains six independent nuclear response functions, three of which are associated with possible velocity-dependent interactions. We find that current experiments are four orders of magnitude more sensitive to derivative couplings than is apparent in the standard SI/SD treatment, which necessarily associates such interactions with cross sections proportional to the square of the WIMP velocity relative to the nuclear center of mass.
The communitys reliance on simplified descriptions of WIMP-nucleus interactions reflects the absence of analysis tools that integrate general theories of dark matter with standard treatments of nuclear response functions. To bridge this gap, we have
constructed a public-domain Mathematica package for WIMP analyses based on our effective theory formulation. Script inputs are 1) the coefficients of the effective theory, through which one can characterize the low-energy consequences of arbitrary ultraviolet theories of WIMP interactions; and 2) one-body density matrices for commonly used targets, the most compact description of the relevant nuclear physics. The generality of the effective theory expansion guarantees that the script will remain relevant as new ultraviolet theories are explored; the use of density matrices to factor the nuclear physics from the particle physics will allow nuclear structure theorists to update the script as new calculations become available, independent of specific particle-physics contexts. The Mathematica package outputs the resulting response functions (and associated form factors) and also the differential event rate, once a galactic WIMP velocity profile is specified, and thus in its present form provides a complete framework for experimental analysis. The Mathematica script requires no a priori knowledge of the details of the non-relativistic effective field theory or nuclear physics, though the core concepts are reviewed here and in arXiv:1203.3542.
