Cirigliano, VincenzoVincenzoCiriglianoDekens, WouterWouterDekensde Vries, JordyJordyde VriesHoferichter, MartinMartinHoferichterMereghetti, EmanueleEmanueleMereghetti2024-09-212024-09-212021-04-30https://boris-portal.unibe.ch/handle/20.500.12422/45591The amplitude for the neutrinoless double β (0νββ) 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 0νββ searches. Assuming that the 0νββ 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 Aν ðjpj; jp0 jÞ, 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 0νββ decay.en500 - Science::530 - Physicsarticle10.48350/1562342012.1160210.1103/PhysRevLett.126.172002