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Knowledge of the ionization and scintillation responses of liquid xenon (LXe)to nuclear recoils is crucial for LXe-based dark matter experiments. Currentcalibrations carry large uncertainties in the low-energy region below $\sim3$keV$_nr$ where signals from dark matter particles of $<$10 GeV/c$^2$ masses areexpected. The coherent elastic neutrino-nucleus scattering (CE$\nu$NS) by solar$^8$B neutrinos also results in a continuum of nuclear recoil events below 3.0keV$_{nr}$ (99\% of events), which further complicates low-mass dark mattersearches in LXe experiments. In this paper, we describe a method to quantifythe uncertainties of low-energy LXe responses using published calibration data,followed by case studies to evaluate the impact of yield uncertainties on${^8}$B searches and low-mass dark matter sensitivity in a typical ton-scaleLXe experiment. We conclude that naively omitting yield uncertainties leads tooverly optimistic limits by factor $\sim2$ for a 6 GeV/c$^2$ WIMP mass. Futurenuclear recoil light yield calibrations could allow experiments to recover thissensitivity and also improve the accuracy of solar ${^8}$B flux measurements.

Nuclear recoil response of liquid xenon and its impact on solar 8B neutrino and dark matter searches