Neutrinoless double-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>β</mml:mi></mml:math> decay: Combining quantum Monte Carlo and the nuclear shell model with the generalized contact formalism
R. Weiss, Pablo Soriano, Alessandro Lovato, J. Menéndez, R. B. Wiringa
Abstract
Neutrinoless double beta decay searches can determine the Majorana nature of neutrinos, the absolute neutrino mass, and provide invaluable insights on the matter dominance of the universe. However, the uncertainty in the nuclear matrix elements that govern the decay limits the physics reach of these experiments. We devise a novel framework based on the generalized contact formalism that combines the nuclear shell model and quantum Monte Carlo methods and compute the neutrinoless double-beta decay of nuclei used in the most advanced experiments, including $^{76}\mathrm{Ge}, ^{130}\mathrm{Te}$, and $^{136}\mathrm{Xe}$. Our results cover all relevant terms, including the leading-order short-range operator recognized recently. We validate our method in light nuclei by comparing against accurate variational Monte Carlo results. On heavy systems we obtain reduced nuclear matrix elements compared with previous calculations due to additional correlations captured by quantum Monte Carlo and introduced within the generalized contact formalism, suggesting longer decay half-lives than previously considered. On the other hand, we find an enhancement of the nuclear matrix elements due to the new short-range operator.