Three-nucleon lepton-number-violating potentials in chiral EFT and their matrix elements in light nuclei

We derive the three-nucleon neutrinoless double beta decay potential in $\Delta$-full chiral effective field theory through next-to-next-to-next-to leading order in Weinberg's power counting. The matrix elements of the resulting operators are computed in light nuclei using Variational Monte Carlo with wave functions constructed from the Norfolk family of nuclear interactions. We find that three-nucleon corrections induce a modest quenching of the total nuclear matrix elements. We discuss model dependencies and the potential impact of these corrections on the sensitivity of experimental programs to probe lepton number violating parameters. These results provide a benchmark of many-body methods capable of reaching heavier nuclei of experimental interest.