Neutrinoless double-beta decay of germanium 76 with uncertainty from chiral effective field theory

We study the neutrinoless double-beta decay of germanium 76 in a model that describes both parent and daughter nuclei as four valence nucleons on top of a germanium 72 core. The valence nucleons interact with each other via bare chiral nucleon-nucleon and three-nucleon interactions, while in-medium effects are modeled as a Woods-Saxon mean field. These interactions are fitted to reproduce neutron-proton phase shifts, the deuteron binding energy, and the binding energies of the nuclei of interest and energies of their first excited 0+ states. We employ Markov-chain Monte Carlo sampling to generate distributions for the low-energy constants (LECs) of the chiral nucleon-nucleon interaction. For each set of LECs we obtain the wave functions of the relevant nuclei and employ them to calculate the decay?s nuclear matrix element. The resulting distribution for the latter possesses a peak in good agreement with traditional shell-model calculations. The theoretical uncertainty associated to the distribution is taken as the corresponding interval with 95% degree-of-belief.