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

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