Can we overcome the neutrino floor at high masses?

The neutrino floor is a barrier in the parameter space of weakly interacting massive particles (WIMPs) below which discovery is impeded due to an almost irreducible background of neutrinos. Directional gas time projection chambers could discriminate against solar neutrinos, relevant for WIMP masses $\lesssim$10 GeV. At higher masses $\gtrsim$100 GeV the floor is set by the background of atmospheric neutrinos. Probing below this part of the floor would require very large target exposures. Since gas-based detectors would be prohibitively large at this scale, we instead reevaluate the prospects for liquid noble experiments to probe below the neutrino floor. We combine all potential methods of subtracting the neutrino background to determine how much of this difficult to reach, but well-motivated, parameter space it is feasible to reach. Most notably, we quantify whether a proposed directional signal in xenon and argon experiments called "columnar recombination" can help in this task. We find that even if the strength of this effect is amplified beyond current experimental results, the quantity of directional information contained in the recombination signal is too low to realistically discriminate against the atmospheric neutrino background. Instead, benefiting from the refined measurements of neutrino fluxes by experiments such as DUNE and JUNO will be the most practical means to push direct WIMP searches below the neutrino floor. For an ultimate global coordination of xenon and argon experiments, we show that the neutrino floor is a surmountable barrier. The direct detection of 100 GeV-scale supersymmetric WIMPs may, eventually, be within reach.