Dark matter spin determination with directional direct detection
  experiments
  If the dark matter particle has spin 0, only two types of WIMP-nucleon
interaction can arise from the non-relativistic reduction of renormalisable
single-mediator models for dark matter-quark interactions. Based on this
crucial observation, we show that about 100 signal events at next generation
directional detection experiments can be enough to enable a $2\sigma$ rejection
of the spin 0 dark matter hypothesis in favour of alternative hypotheses where
the dark matter particle has spin 1/2 or 1. In this context directional
sensitivity is crucial, since anisotropy patterns in the sphere of nuclear
recoil directions depend on the spin of the dark matter particle. For
comparison, about 100 signal events are expected in a CF$_4$ detector operating
at a pressure of 30 torr with an exposure of approximately 26,000
cubic-meter-detector days for WIMPs of 100 GeV mass and a WIMP-Fluorine
scattering cross-section of 0.25 pb. Comparable exposures are within reach of
an array of cubic meter time projection chamber detectors.
