We examine the effect of nuclear response functions, as laid out in [Fitzpatrick et al, arXiv:1203.3542], on dark matter (DM) direct detection in the context of well-motivated UV completions, including electric and magnetic dipoles, anapole, spin-orbit, and pseudoscalar-mediated DM. Together, these encompass five of the six nuclear responses extracted from the non-relativistic effective theory of [Fitzpatrick et al, arXiv:1203.3542] (with the sixth difficult to UV complete), with two of the six combinations corresponding to standard spin-independent and -dependent responses. For constraints from existing direct detection experiments, we find that only the COUPP constraint, due to its heavy iodine target with large angular momentum and an unpaired spin, and its large energy range sensitivity, is substantially modified by the new responses compared to what would be inferred using the standard form factors to model the energy dependence of the response. For heavy targets such as xenon and germanium, the behavior of the new nuclear responses as recoil energy increases can be substantially different than that of the standard responses, but this has almost no impact on the constraints derived from experiments such as LUX, XENON100 and CDMS since the maximum nuclear recoil energy detected in these experiments is relatively low. We simulate mock data for 80 and 250 GeV DM candidates utilizing the new nuclear responses to highlight how they might affect a putative signal, and find the new responses are most important for momentum-suppressed interactions such as the magnetic dipole or pseudoscalar-mediated interaction when the target is relatively heavy (such as xenon and iodine).
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