Measurement of Charge and Light Yields for $^{127}$Xe L-Shell Electron Captures in Liquid Xenon

Dark matter searches using dual-phase xenon time-projection chambers (LXe-TPCs) rely on their ability to reject background electron recoils (ERs) while searching for signal-like nuclear recoils (NRs). ER response is typically calibrated using $\beta$-decay sources, such as tritium, but these calibrations do not characterize events accompanied by an atomic vacancy, as in solar neutrino scatters off inner shell electrons. Such events lead to emission of X-rays and Auger electrons, resulting in higher electron-ion recombination and thus a more NR-like response than inferred from $\beta$-decay calibration. We present a cross-calibration of tritium $\beta$-decays and $^{127}$Xe electron-capture decays (which produce inner-shell vacancies) in a small-scale LXe-TPC and give the most precise measurements to date of light and charge yields for the $^{127}$Xe L-shell electron-capture in liquid xenon. We observe a 6.9$\sigma$ (9.2$\sigma$) discrepancy in the L-shell capture response relative to tritium $\beta$-decays, measured at a drift field of 363 $\pm$ 14 V/cm (258 $\pm$ 13 V/cm), when compared to simulations tuned to reproduce the correct $\beta$-decay response. In dark matter searches, use of a background model that neglects this effect leads to overcoverage (higher limits) for background-only multi-kiloton-year exposures, but at a level much less than the 1-$\sigma$ experiment-to-experiment variation of the 90\% C.L. upper limit on the interaction rate of a 50 GeV/$c^2$ dark matter particle.