  Assuming that Dark Matter (DM) is made of fermions in the sub-GeV mass range
with interactions dominated by electromagnetic moments of higher order, such as
the electric and magnetic dipoles or the anapole moment, we show that direct
detection experiments searching for atomic ionisation events in xenon targets
can shed light on whether DM is a Dirac or Majorana particle. Specifically, we
find that between about 45 (120) and 610 (1700) signal events are required to
reject Majorana DM in favour of Dirac DM with a statistical significance
corresponding to 3 (5) standard deviations. The exact number of DM signal
events corresponding to a given significance depends on the relative size of
the anapole, magnetic dipole and electric dipole contributions to the expected
rate of DM-induced atomic ionisations under the Dirac hypothesis. Our
conclusions are based on Monte Carlo simulations and the likelihood ratio test.
While the use of asymptotic formulae for the latter is standard in many
applications, here it requires a non-trivial extension to the case where one of
the hypotheses lies on the boundary of the parameter space. Our results
constitute a solid proof of concept about the possibility of using direct
detection experiments to reject the Majorana DM hypothesis when the DM
interactions are dominated by higher-order electromagnetic moments.
