Toward Complete Leading-Order Predictions for Neutrinoless Double β Decay

The amplitude for the neutrinoless double beta (0 nu beta beta) decay of the two-neutron system nn -> ppe(-)e(-) constitutes a key building block for nuclear-structure calculations of heavy nuclei employed in large-scale 0 nu beta beta searches. Assuming that the 0 nu beta beta 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 renonnalizability. 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 A nu(vertical bar p vertical bar,vertical bar p'vertical bar), 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 0 nu beta beta decay.

Automated summary

This letter presents a systematic analysis of neutrinoless double beta decay using chiral effective field theory, proposing a method to estimate the numerical value of the exchange coefficient and validating the result by reproducing the charge-independence-breaking contribution to nucleon-nucleon scattering lengths. The central result, derived in dimensional regularization, greatly reduces a crucial uncertainty in the interpretation of searches for neutrinoless double beta decay.