Ab initio benchmarks of neutrinoless double beta decay in light nuclei with a chiral Hamiltonian

TL;DR

This paper presents ab initio calculations of nuclear matrix elements for neutrinoless double-beta decay in light nuclei, comparing different many-body methods to establish reliable benchmarks and uncertainties.

Contribution

It provides the first consistent ab initio benchmarks of NMEs for $0 uetaeta$ decay in light nuclei using multiple methods and chiral interactions, highlighting the agreement and discrepancies among approaches.

Findings

NMEs for $ riangle T=0$ are consistent within 10% across methods.

Discrepancies are larger for $ riangle T=2$ transitions in some nuclei.

The study demonstrates the importance of cross-method benchmarks for uncertainty quantification.

Abstract

We report ab initio benchmark calculations of nuclear matrix elements (NMEs) for neutrinoless double-beta ($0\nu\beta\beta$) decays in light nuclei with mass number ranging from $A=6$ to $A=22$. We use the transition operator derived from light-Majorana neutrino exchange and evaluate the NME with three different methods: two variants of in-medium similarity renormalization group (IMSRG) and importance-truncated no-core shell model (IT-NCSM). The same two-plus-three-nucleon interaction from chiral effective field theory is employed, and both isospin-conserving ($\Delta T=0$) and isospin-changing ($\Delta T=2$) transitions are studied. We compare our resulting ground-state energies and NMEs to those of recent ab initio no-core shell model and coupled-cluster calculations, also with the same inputs. We show that the NMEs of $\Delta T=0$ transitions are in good agreement among all calculations, at the level of 10%. For $\Delta T=2$, relative deviations are more significant in some nuclei. The comparison with the exact IT-NCSM result allows us to analyze these cases in detail, and indicates the next steps towards improving the IMSRG-based approaches. The present study clearly demonstrates the power of consistent cross-checks that are made possible by ab initio methodology. This capability is crucial for providing meaningful many-body uncertainties in the NMEs for the $0\nu\beta\beta$ decays in heavier candidate nuclei, where quasi-exact benchmarks are not available.