Improved calculations of beta decay backgrounds to new physics in liquid xenon detectors

TL;DR

This paper provides high-precision theoretical predictions for beta decay spectra of isotopes relevant to liquid xenon dark matter detectors, emphasizing nuclear structure effects and their impact on background estimations.

Contribution

It introduces improved calculations of beta decay spectra incorporating nuclear structure, atomic effects, and compares them to simpler models, highlighting their significance for dark matter experiments.

Findings

Nuclear structure effects significantly alter low-energy spectra.

Predicted event rate reductions of 12-23% compared to allowed transition models.

Emphasizes need for direct spectral measurements for accurate background modeling.

Abstract

We present high-precision theoretical predictions for the electron energy spectra for the ground-state to ground-state $\beta$ decays of $^{214}$Pb, $^{212}$Pb, and $^{85}$Kr most relevant to the background of liquid xenon dark matter detectors. The effects of nuclear structure on the spectral shapes are taken into account using large-scale shell model calculations. Final spectra also include atomic screening and exchange effects. The impact of nuclear structure effects on the $^{214}$Pb and $^{212}$Pb spectra below $\approx100$ keV, pertinent for several searches for new physics, are found to be comparatively larger than those from the atomic effects alone. We find that the full calculation for $^{214}$Pb ($^{212}$Pb) predicts 15.0-23.2% (12.1-19.0%) less event rate in a 1-15 keV energy region of interest compared to the spectrum calculated as an allowed transition when using values of the weak axial vector coupling in the range $g_{\rm A}=0.7-1.0$. The discrepancy highlights the importance of both a proper theoretical treatment and the need for direct measurements of these spectra for a thorough understanding of $\beta$ decay backgrounds in future experiments.