Toward Complete Leading-Order Predictions for Neutrinoless Double β Decay

Cirigliano, Vincenzo; Dekens, Wouter; de Vries, Jordy; Hoferichter, Martin; Mereghetti, Emanuele (2021). Toward Complete Leading-Order Predictions for Neutrinoless Double β Decay. Physical review letters, 126(17) American Physical Society 10.1103/PhysRevLett.126.172002

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The 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.

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