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arXiv · 2012.11602

Towards complete leading-order predictions for neutrinoless double $β$ decay

Vincenzo Cirigliano·Wouter Dekens·Jordy de Vries·Martin Hoferichter·Emanuele Mereghetti
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Abstract

The amplitude for the neutrinoless double $β$ ($0νββ$) decay of the two-neutron system, $nn\to ppe^-e^-$, 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 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 $\overline{\text{MS}}$ scheme, is given in terms of the renormalized amplitude $\mathcal{A}_ν(|\mathbf{p}|,|\mathbf{p}^\prime|)$, 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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Vincenzo Cirigliano, Wouter Dekens, Jordy de Vries, Martin Hoferichter, Emanuele Mereghetti. 2021-04-30. Towards complete leading-order predictions for neutrinoless double $β$ decay. https://doi.org/10.1103/physrevlett.126.172002

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