There is a worldwide effort toward the development of a large 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 addressed 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 taking into account astrophysical and experimental uncertainties. We show that the energy threshold and the background contamination are key experimental issues for directional detection, while angular resolution and sense recognition efficiency only mildly affect the sensitivity and the energy resolution is unimportant. This way, we found that a 30 kg.year ${\mathrm{CF}}_4$ directional experiment could reach a $3\sigma$ sensitivity at 90% C.L. down to ${10}^{-5}\mathrm{pb}$ and ${3.10}^{-4}\mathrm{pb}$ for the WIMP-proton axial cross section in the most optimistic and pessimistic detector performance case, respectively.

• Received 27 October 2011

DOI:https://doi.org/10.1103/PhysRevD.85.035006