Assessing the discovery potential of directional detection of Dark Matter

There is a worldwide effort toward the development of a large TPC (Time Projection Chamber) devoted to directional Dark Matter detection. All current projects are being designed to fulfill a unique goal : identifying weakly interacting massive particle (WIMP) as such by taking advantage of the expected direction dependence of WIMP-induced events toward the constellation Cygnus. However such proof of discovery requires a careful statistical data treatment. In this paper, the discovery potential of forthcoming directional detectors is adressed by using a frequentist approach based on the profile likelihood ratio test statistic. This allows us to estimate the expected significance of a Dark Matter detection. Moreover, using this powerful test statistic, it is possible to propagate astrophysical and experimental uncertainties in the determination of the discovery potential of a given directional detection experiment. This way, we found that a 30 kg.year CF$_4$ directional experiment could reach a 3$\sigma$ sensitivity at 90% C.L. down to $10^{-5}$ pb and $3.10^{-4}$ pb for the WIMP-proton axial cross section in the most optimistic and pessimistic scenario respectively.