  The framework of non-relativistic effective field theory (NREFT) aims to
generalise the standard analysis of direct detection experiments in terms of
spin-dependent (SD) and spin-independent (SI) interactions. We show that a
number of NREFT operators lead to distinctive new directional signatures, such
as prominent ring-like features in the directional recoil rate, even for
relatively low mass WIMPs. We discuss these signatures and how they could
affect the interpretation of future results from directional detectors. We
demonstrate that considering a range of possible operators introduces a factor
of 2 uncertainty in the number of events required to confirm the median recoil
direction of the signal. Furthermore, using directional detection, it is
possible to distinguish the more general NREFT interactions from the standard
SI/SD interactions at the $2\sigma$ level with $\mathcal{O}(100-500)$ events.
In particular, we demonstrate that for certain NREFT operators, directional
sensitivity provides the only method of distinguishing them from these standard
operators, highlighting the importance of directional detectors in probing the
particle physics of dark matter.
