  Searches for new physics often face unknown backgrounds, causing false
detections or weakened upper limits. This paper introduces the deficit hawk
technique, which mitigates unknown backgrounds by testing multiple options for
data cuts, such as fiducial volumes or energy thresholds. Combining the power
of likelihood ratios with the robustness of the interval-searching techniques,
deficit hawks could improve mean upper limits on new physics by a factor two
for experiments with partial or speculative background knowledge. Deficit hawks
are well-suited to analyses that use machine learning or other multidimensional
discrimination techniques, and can be extended to permit discoveries in regions
without unknown background.
