Rare ${}^{40}\mathrm{K}$ Decay with Implications for Fundamental Physics and Geochronology

Potassium-40 is a widespread, naturally occurring isotope whose radioactivity impacts subatomic rare-event searches, nuclear structure theory, and estimated geological ages. A predicted electron-capture decay directly to the ground state of argon-40 has never been observed. The KDK (potassium decay) collaboration reports strong evidence of this rare decay mode. A blinded analysis reveals a nonzero ratio of intensities of ground-state electron-captures ($I_{{\mathrm{EC}}^0}$) over excited-state ones ($I_{{\mathrm{EC}}^{*}}$) of $I_{{\mathrm{EC}}^0}/I_{{\mathrm{EC}}^{*}}=0.0095\stackrel{\mathrm{stat}}{\pm }0.0022\stackrel{\mathrm{sys}}{\pm }0.0010$ (68% C.L.), with the null hypothesis rejected at $4\sigma$. In terms of branching ratio, this signal yields $I_{{\mathrm{EC}}^0}=0.098\%\stackrel{\mathrm{stat}}{\pm }0.023\%\stackrel{\mathrm{sys}}{\pm }0.010\%$, roughly half of the commonly used prediction, with consequences for various fields [L. Hariasz et al., companion paper, Phys. Rev. C 108, 014327 (2023)].

Figure 1

(a) Decay scheme of ${}^{40}\mathrm{K}$. The branching ratios and half-life were calculated from our determination of $I_{{\mathrm{EC}}^0}/I_{{\mathrm{EC}}^{*}}$ and from literature values for $T^{-}$ (partial half-life of the ${\beta }^{-}$ decay) and $T^{*}$ (partial half-life of ${\mathrm{EC}}^{*}$) [23]. The $\gamma$ transition energy is taken from [22], ${\mathrm{Q}}_{{\mathrm{EC}}^0}$ and $Q^{-}$ are taken from [24]. (b) Schematic of how the KDK experiment distinguishes ${\mathrm{EC}}^{*}$ from ${\mathrm{EC}}^0$ (not to scale).

Figure 2

SDD coincidence and anticoincidence spectra. Results of simultaneous fit to coincident (top) and anticoincident (bottom) SDD spectra at a $2\mathrm{\mu }\mathrm{s}$ coincidence window. Signal counts are shown in green. Various fluorescence peaks and an exponential background model are included. The total minimization has an associated goodness of fit of $p=0.4$.

Figure 3

The anticoincident x-ray signal region corresponding to Fig. 2, showing a fit assuming a null hypothesis of $\rho =0$ (dashed black) and an alternate fit with $\rho$ free (solid red), returning $\rho =I_{{\mathrm{EC}}^0}/I_{{\mathrm{EC}}^{*}}=0.0095\stackrel{\mathrm{stat}}{\pm }0.0022\stackrel{\mathrm{sys}}{\pm }0.0010$. A likelihood ratio test between the two hypotheses returns $p=2\times {10}^{-5}$ which is equivalent to a $4\sigma$ significance. For each bin count $o$ and associated fit value $e$ the residual is defined as $(o-e)/\sqrt{e}$.

Figure 4

Effect of updates to ${}^{40}\mathrm{K}$ decay scheme on geochronology. (a) Variation in $\mathrm{K}/\mathrm{Ar}$ age when adding the ${\mathrm{EC}}^0$ branch to commonly used reference decay constants [13] (Min, blue, dashed, errors from ${\mathrm{EC}}^0$ only) and to the ${\beta }^{-}$ and ${\mathrm{EC}}^{*}$ branches of a recent literature evaluation (Sec. 5.2 of [23], Kossert preevaluation, red, solid, all errors). In all cases $t_{\text{current}}$ represents time calculated using Min decay constants neglecting ${\mathrm{EC}}^0$. (b) Systematic change in $\mathrm{K}/\mathrm{Ar}$ age of the Fish Canyon sanidine reference material when ${\mathrm{EC}}^0$ is added to the previous decay constants and to those in [44]. (c) Updated ${}^{40}\mathrm{Ar}/{}^{39}\mathrm{Ar}$ age of the Acapulco meteorite using the decay constants and reference ages shown in (b). $\mathrm{Pb}/\mathrm{Pb}$ age is updated from [42]. All uncertainties correspond to a 68% confidence level.