Theoretical uncertainty for neutrinoless double-beta decay from chiral EFT

We study the neutrinoless double-beta decay of germanium 76 in a model that describes the parent and daughter nuclei as four valence nucleons on top of a germanium 72 core. The valence nucleons interact with each other via chiral nucleon-nucleon and three-nucleon interactions, while in-medium effects are modeled as an effective core-nucleon interaction. These interactions are fitted to reproduce neutron-proton phase shifts, deuteron binding energy, and the binding energies of the nuclei of interest as well as the energies of their first excited 0+ states. We employ Markov-chain Monte Carlo sampling to generate distributions for the low-energy constants of the chiral nucleon-nucleon contact interaction. The wave functions for the relevant ground states resulting from each set of parameters is employed to calculate the corresponding neutrinoless double-beta decay matrix element. The resulting distribution for the matrix element possesses a mode in good agreement with traditional shell-model calculations. The associated theoretical uncertainty comes from the interval with 95% degree-of-belief.