  Accurate nuclear matrix elements (NMEs) for neutrinoless double beta decays
of candidate nuclei are important for the design and interpretation of future
experiments. Significant progress has been made in the modeling of these NMEs
from first principles. The NME for 48Ca shows a good agreement among three
different ab initio calculations starting from the same nuclear interaction
constructed within the chiral EFT and the same decay operator. These studies
open the door to ab initio calculations of the matrix elements for the decay of
heavier nuclei such as 76Ge, 130Te, and 136Xe. The ultimate goal is the
computation of NMEs in many-body calculations with controllable approximations,
using nuclear interactions and weak transition operators derived consistently
from chiral EFT. We are expecting more progress towards this goal in the near
future.
