Can recoil direction separate dark matter from solar neutrinos?

In plain words

Solar neutrinos push nuclei away from the Sun, while dark matter pushes them along Earth's path through the galaxy. A detector that measures recoil directions could tell them apart, if it can track recoils only a few keV in energy.

Precise statement

In the neutrino fog, defined by O'Hare as the region where the discovery-limit index $n = -(d \ln \sigma / d \ln \mathrm{exposure})^{-1}$ exceeds 2, sensitivity grows slower than $1/\sqrt{\mathrm{exposure}}$. The question is the angular resolution, head-tail recognition efficiency and threshold (e.g., in a He:$\mathrm{SF_6}$ or $\mathrm{CF_4}$ gas time projection chamber) needed to restore n near 1 at WIMP masses 5-10 GeV and cross sections about one order of magnitude below the 8B fog boundary for the chosen target, and the exposure this requires.

What would settle it

Demonstrated head-tail sensitivity and angular resolution for few-keV nuclear recoils in a prototype, combined with a sensitivity calculation using the measured performance.

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