Toward Complete Leading-Order Predictions for Neutrinoless Double $\ensuremath{\beta}$ Decay

Toward Complete Leading-Order Predictions for Neutrinoless Double $β$ Decay

Vincenzo Cirigliano, Wouter Dekens, Jordy de Vries, Martin Hoferichter, and Emanuele Mereghetti

Phys. Rev. Lett. 126, 172002 – Published 30 April 2021

Abstract

The amplitude for the neutrinoless double $β$ ( $0 ν β β$ ) decay of the two-neutron system $n n \to p p e^{-} e^{-}$ constitutes a key building block for nuclear-structure calculations of heavy nuclei employed in large-scale $0 ν β β$ searches. Assuming that the $0 ν β β$ 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 $A_{ν} (| p |, | p^{'} |)$ , 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 $0 ν β β$ decay.

Received 23 December 2020
Revised 11 March 2021
Accepted 12 March 2021

DOI:https://doi.org/10.1103/PhysRevLett.126.172002

Physics Subject Headings (PhySH)

Chiral perturbation theory Neutrinoless double beta decay Nucleon-nucleon interactions

Effective field theory

Particles & Fields

Authors & Affiliations

Vincenzo Cirigliano ¹, Wouter Dekens ², Jordy de Vries ^3,4,5,6, Martin Hoferichter ⁷, and Emanuele Mereghetti ¹

¹Los Alamos National Laboratory, Theoretical Division, Los Alamos, New Mexico 87545, USA
²Department of Physics, University of California at San Diego, La Jolla, California 92093, USA
³Department of Physics, Amherst Center for Fundamental Interactions, University of Massachusetts, Amherst, Massachusetts 01003, USA
⁴RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, New York 11973-5000, USA
⁵Institute for Theoretical Physics Amsterdam and Delta Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
⁶Nikhef, Theory Group, Science Park 105, 1098 XG, Amsterdam, The Netherlands
⁷Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, 3012 Bern, Switzerland