Towards complete leading-order predictions for neutrinoless double β decay
Abstract
The amplitude for the neutrinoless double β (0ββ) 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 0ββ searches. Assuming that the 0ββ 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 work, we develop a method to estimate the numerical value of its coefficient in analogy to the Cottingham formula and validate the result by reproducing the charge-independence-breaking contribution to the nucleon-nucleon scattering lengths. Our central result, while derived in the MS scheme, is given in terms of the renormalized amplitude A(|p|,|p|), 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 0ββ decay.