Readout strategies for directional dark matter detection beyond the neutrino background

The search for weakly interacting massive particles (WIMPs) by direct detection faces an encroaching background due to coherent neutrino-nucleus scattering. As the sensitivity of these experiments improves, the question of how to best distinguish a dark matter signal from neutrinos will become increasingly important. A proposed method of overcoming this so-called ``neutrino floor'' is to utilize the directional signature that both neutrino- and dark-matter-induced recoils possess. We show that directional experiments can indeed probe WIMP-nucleon cross sections below the neutrino floor with little loss in sensitivity due to the neutrino background. In particular we find at low WIMP masses (around 6 GeV) the discovery limits for directional detectors penetrate below the nondirectional limit by several orders of magnitude. For high WIMP masses (around 100 GeV), the nondirectional limit is overcome by a factor of a few. Furthermore we show that even for directional detectors which can only measure one- or two-dimensional projections of the three-dimensional recoil track, the discovery potential is only reduced by a factor of 3 at most. We also demonstrate that while the experimental limitations of directional detectors, such as sense recognition and finite angular resolution, have a detrimental effect on the discovery limits, it is still possible to overcome the ultimate neutrino background faced by nondirectional detectors.