First observation of the ground-state electron-capture of $^{40}$K

Potassium-40 is a naturally-occurring isotope whose radioactivity impacts estimated geological ages spanning billions of years, nuclear structure theory, and subatomic rare-event searches -- including those for dark matter and neutrinoless double-beta decay. The decays of this long-lived isotope must be precisely known for its use as a geochronometer, and to account for its presence in low-background experiments. There are several known decay modes for potassium-40, but a predicted electron-capture decay directly to the ground state of argon-40 has never been observed. Though this decay impacts several fields, theoretical predictions span an order of magnitude. The KDK (potassium decay) collaboration reports on the first observation of this rare decay mode, using a novel combination of a low-threshold X-ray detector surrounded by a tonne-scale, high-efficiency $\gamma$-ray tagger at Oak Ridge National Laboratory. A blinded analysis reveals a distinctly non-zero ratio of intensities of ground-state electron-captures ($I_{\text{EC}^0}$) over excited-state ones ($I_{\text{EC}^*}$) of $I_{\text{EC}^0} / I_{\text{EC}^*} = 0.0095 \stackrel{\text{stat}}{\pm} 0.0022 \stackrel{\text{sys}}{\pm} 0.0010 $ (68% CL), with the null hypothesis rejected at 4$\sigma$. In terms of branching ratio, this unambiguous signal yields $ I_{\text{EC}^0} = 0.098 \% \stackrel{\text{stat}}{\pm}0.023\% \stackrel{\text{sys}}{\pm} 0.010 $, roughly half of the commonly used prediction. This first observation of a third-forbidden unique electron capture improves our understanding of low-energy backgrounds in dark-matter searches and has implications for nuclear-structure calculations. For example, a shell-model based theoretical estimate for the neutrinoless double-beta decay half-life of calcium-48 is increased by a factor of $7^{+3}_{-2}$. Implications are illustrated for Earth and solar system chronologies.