  We study prospects of dark-matter direct-detection searches for probing
non-relativistic effective theory for WIMP-baryon scattering. We simulate a
large set of noisy recoil-energy spectra for different scattering scenarios
(beyond the standard momentum-independent contact interaction), for Generation
2 and futuristic experiments. We analyze these simulations and quantify the
probability of successfully identifying the operator governing the scattering,
if a WIMP signal is observed. We find that the success rate depends on a
combination of factors: the WIMP mass, the mediator mass, the type of
interaction, and the experimental energy window. For example, for a 20 GeV
WIMP, Generation 2 is only likely to identify the right operator if the
interaction is Coulomb-like, and is unlikely to do so in any other case. For a
WIMP with a mass of 200 GeV or higher, success is almost guaranteed. We also
find that, regardless of the scattering model and the WIMP parameters, a single
Generation 2 experiment is unlikely to successfully discern the momentum
dependence of the underlying operator on its own, but prospects improve
drastically when experiments with different target materials and energy windows
are analyzed jointly. Furthermore, we examine the quality of parameter
estimation and degeneracies in the multi-dimensional parameter space of the
effective theory. We find in particular that the resulting WIMP mass estimates
can be severely biased if data are analyzed assuming the standard
(momentum-independent) operator while the actual operator has
momentum-dependence. Finally, we evaluate the ultimate reach of direct
detection, finding that the prospects for successful operator selection prior
to reaching the irreducible backgrounds are excellent, if the signal is just
below the current limits, but slim if Generation 2 does not report WIMP
detection.
