Readout strategies for directional dark matter detection beyond the neutrino background

16 pages, 12 figures, submitted to PRDInternational audienceThe 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 non-directional limit by several orders of magnitude. For high WIMP masses (around 100 GeV), the non-directional limit is overcome by a factor of a few. Furthermore we show that even for directional detectors which can only measure 1- or 2-dimensional projections of the 3-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 non-directional detectors