Weak nuclear decays deep-underground as a probe of axion dark matter

TL;DR

This paper proposes using the time modulation of weak nuclear decays to detect axion dark matter, developing a theoretical framework and analyzing existing data to set constraints, and suggesting new measurements for improved sensitivity.

Contribution

It introduces a theoretical model for decay rate modulation due to axion dark matter and applies it to existing data, proposing new experiments for enhanced detection capabilities.

Findings

Recast old decay data to constrain axion decay constant in specific mass range.

Predicted time variation of weak decay rates in response to oscillating axion background.

Proposed new measurement to extend sensitivity to higher axion masses.

Abstract

We investigate the time modulation of weak nuclear decays as a method to probe axion dark matter. To this end, we develop a theoretical framework to compute the $\theta$-dependence of weak nuclear decays, including electron capture and $\beta$ decay, which enables us to predict the time variation of weak radioactivity in response to an oscillating axion dark matter background. As an application, we recast old data sets, from the weak nuclear decays of ${^{40}\text{K}}$ and ${^{137}\text{Cs}}$ taken at the underground Gran Sasso Laboratory, in order to set constraints on the axion decay constant, specifically in the axion mass range from few $10^{-23}\;$eV up to $10^{-19}\;$eV. We finally propose a new measurement at the Gran Sasso Laboratory, based on the weak nuclear decay of ${^{40}\text{K}}$ via electron capture, in order to explore even shorter timescales, thus reaching sensitivities to axion masses up to $10^{-9}\;$eV.