Spectral shapes of forbidden argon β decays as background component for rare-event searches

Abstract

The spectral shape of the electrons from the two first-forbidden unique ${\beta }^{-}$ decays of 39Ar and 42Ar were calculated for the first time to the next-to-leading order. Especially the spectral shape of the 39Ar decay can be used to characterize this background component for dark matter searches based on argon. Alternatively, due to the low thresholds of these experiments, the spectral shape can be investigated over a wide energy range with high statistics and thus allow a sensitive comparison with the theoretical predictions, in particular at low electron energies where the shape of the computed β spectrum has a slight dependence on the value of the weak axial-vector coupling constant.