Abstract
The amplitude for the neutrinoless double () decay of the two-neutron system constitutes a key building block for nuclear-structure calculations of heavy nuclei employed in large-scale searches. Assuming that the process is mediated by a light-Majorana-neutrino exchange, a systematic analysis in chiral effective field theory shows that already at leading order a contact operator is required to ensure renormalizability. In this Letter, we develop a method to estimate the numerical value of its coefficient (in analogy to the Cottingham formula for electromagnetic contributions to hadron masses) and validate the result by reproducing the charge-independence-breaking contribution to the nucleon-nucleon scattering lengths. Our central result, while derived in dimensional regularization, is given in terms of the renormalized amplitude , matching to which will allow one to determine the contact-term contribution in regularization schemes employed in nuclear-structure calculations. Our results thus greatly reduce a crucial uncertainty in the interpretation of searches for decay.
- Received 23 December 2020
- Revised 11 March 2021
- Accepted 12 March 2021
DOI:https://doi.org/10.1103/PhysRevLett.126.172002
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