A coherent understanding of low-energy nuclear recoils in liquid xenon

Liquid xenon detectors such as XENON10 and XENON100 obtain a significant fraction of their sensitivity to light (less than or similar to 10GeV) particle dark matter by looking for nuclear recoils of only a few keV, just above the detector threshold. Yet in this energy regime a correct treatment of the detector threshold and resolution remains unclear. The energy dependence of the scintillation yield of liquid xenon for nuclear recoils also bears heavily on detector sensitivity, yet numerous measurements have not succeeded in obtaining concordant results. In this article we show that the ratio of detected ionization to scintillation can be leveraged to constrain the scintillation yield. We also present a rigorous treatment of liquid xenon detector threshold and energy resolution. Notably, the effective energy resolution differs significantly from a simple Poisson distribution. We conclude with a calculation of dark matter exclusion limits, and show that existing data from liquid xenon detectors strongly constrain recent interpretations of light dark matter.