Impact of nuclear shell model uncertainties on silicon and germanium WIMP-nucleus limits

Abstract: Dark matter (DM) direct detection searches look for nuclear recoils as a result of weakly interacting massive particles (WIMPs) scattering off nuclei. Calculating the rate associated with this WIMP-nucleus elastic scattering process involves input from several components, which include the direct detection experimental response functions, the high energy physics content employed, the DM halo velocity distribution, and the target nuclear structure information. Uncertainties in any of these components can impact the interpretation of experimental signals, and affect analysis of rate predictions. In this work, we focus on the uncertainties present due to the nuclear structure modelling of silicon and germanium targets, where a comprehensive set of nuclear form factors are employed through a non-relativistic effective field theory (NREFT) formalism. We show that these uncertainties, obtained from large-scale shell model calculations, impact the nuclear form factors and thus experimental exclusion limits for a SuperCDMS-like experiment. The impact of high energy physics content (through particle physics coefficients) on the magnitude of the nuclear uncertainties is also explored for several WIMP-nucleus scattering responses. Non-negligible nuclear uncertainties are present for several direct detection nuclear responses, indicating that nuclear structure must be accounted for in experimental analysis and interpretation.