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arXiv · 2610.28742

Radiative corrections to double-$β$ decay and their impact on experimental analyses

Jordy de Vries·Emanuele Mereghetti·Saad el Morabit·Stefan Sandner
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Abstract

We present a comprehensive study of the $\mathcal{O}(α)$ radiative corrections to two-neutrino and neutrinoless double-$β$ decay within a heavy-nucleus effective field theory. We compute all virtual and real-emission corrections for intermediate nuclear states of arbitrary excitation energy, including new closed-form expressions for the required one-loop integrals with heavy-nucleus propagators. For excitation energies large compared with the lepton energies, the corrections factorize into the tree-level rate times a universal double-weak Sirlin function, which differs substantially from the sum of two single-$β$ Sirlin functions used so far in the literature. We discuss the impact of the radiative corrections on the analysis of measured spectra in terms of ratios of nuclear matrix elements, $ξ_{31}$, and show that neglecting radiative corrections can significantly bias the extraction. Real-photon emission, not considered in previous analyses, plays a central role and the impact of radiative corrections depends crucially on the detector setup. We provide the photon spectrum, fully differential in the photon energy and direction, and recommend that experiments simulate the photon explicitly. For $0νββ$ decay, the radiative corrections increase the inclusive rate by about $5\%$, independently of the nuclear matrix elements or the neutrino Majorana mass.

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Jordy de Vries, Emanuele Mereghetti, Saad el Morabit, Stefan Sandner. 2026-10-20. Radiative corrections to double-$β$ decay and their impact on experimental analyses. https://arxiv.org/abs/2610.28742

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