In the absence of direct accelerator data to constrain particle models, and given existing astrophysical uncertainties associated with the phase space distribution of WIMP dark matter in our galactic halo, extracting information on fundamental particle microphysics from possible signals in underground direct detectors will be challenging. Given these challenges we explore the requirements for direct detection of dark matter experiments to extract information on fundamental particle physics interactions. In particular, using Bayesian methods, we explore the quantitative distinctions that allow differentiation between different non-relativistic effective operators, as a function of the number of detected events, for a variety of possible operators that might generate the detected distribution. Without a spinless target one cannot distinguish between spin-dependent and spin-independent interactions. In general, of order 50 events would be required to definitively determine that the fundamental dark matter scattering amplitude is momentum independent, even in the optimistic case of minimal detector backgrounds and no inelastic scattering contributions. This bound can be improved with reduced uncertainties in the dark matter velocity distribution.
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