Measuring the Unmeasured: Detecting the $^{40}$K Electron Capture Directly to the $^{40}$Ar Ground State with the KDK Experiment

$^{40}$K is a ubiquitous background for many low-energy physics experiments and for many low-energy exotic physics searches. But $^{40}$K has positive uses too, it forms the basis of K-Ar geochronological dating techniques and it allows study of a third-forbidden unique $\beta$-decay. The precision of $^{40}$K $\beta$-decay information is an important uncertainty in low energy exotic physics searches and is one of the limits on the K-Ar geochronology dating technique accuracy and precison. The $^{40}$K $\beta$-decay information uncertainty is dominated by one branch of the \textsuperscript{40}K decay that has never been experimentally measured, the electron capture decay directly to the ground state of $^{40}$Ar. This unknown decay path impacts the estimated amount of $^{40}$K based on the number of measured 1461 keV $\gamma$ rays at the few percent level and it affects the K-Ar geochronology dating technique at the same level. With data taken at Oak Ridge National Laboratory, this small decay branch was measured by the KDK (potassium decay) collaboration by integrating an X-ray detector into the Modular Total Absorption Spectrometer (MTAS). We report details of the technique used to measure this decay branch, the expected sensitivity, and the status of the analysis.