# A renormalized approach to neutrinoless double-beta decay

## TL;DR

This paper investigates neutrinoless double-beta decay using effective field theories, highlighting the necessity of a short-range operator in certain transitions and connecting it to electromagnetic effects, with ab initio calculations for specific isotopes.

## Contribution

It demonstrates the need for a short-range lepton-number-violating operator in neutrinoless double-beta decay at leading order within effective field theory frameworks.

## Key findings

- Short-range operator needed in spin-singlet S-wave transitions.
- Higher partial wave transitions depend only on long-range currents.
- Ab initio calculations performed for $^6$He and $^{12}$Be.

## Abstract

The process at the heart of neutrinoless double-beta decay, $nn \rightarrow p p\, e^- e^-$ induced by a light Majorana neutrino, is investigated in pionless and chiral effective field theory. We show in various regularization schemes the need to introduce a short-range lepton-number-violating operator at leading order, confirming earlier findings. We demonstrate that such a short-range operator is only needed in spin-singlet $S$-wave transitions, while leading-order transitions involving higher partial waves depend solely on long-range currents. Calculations are extended to include next-to-leading corrections in perturbation theory, where to this order no additional undetermined parameters appear. We establish a connection based on chiral symmetry between neutrinoless double-beta decay and nuclear charge-independence breaking induced by electromagnetism. Data on the latter confirm the need for a leading-order short-range operator, but do not allow for a full determination of the corresponding lepton-number-violating coupling. Using a crude estimate of this coupling, we perform ab initio calculations of the matrix elements for neutrinoless double-beta decay for $^6$He and $^{12}$Be. We speculate on the phenomenological impact of the leading short-range operator on the basis of these results.