Novel approaches to calculate nuclear matrix elements for double beta decays

Neutrinoless double beta decay is a unique process that could reveal physics beyond the Standard Model of particle physics. If observed, it would prove that neutrinos are Majorana particles, and it could give information regarding the neutrino masses and their hierarchy, provided that reliable nuclear matrix elements (NME) can be obtained. The two-neutrino double beta decay is an associate process that is allowed by the Standard Model and it was observed for about ten nuclei. The NME associated with this decay mode could be even more difficult to calculate, but they can be directly related to the experimental half-lives, and they can be constrained using data from charge-exchange reactions. Here we offer a brief overview of the theoretical challenges associated with these two processes, emphasizing the tools necessary to reliably calculate the associated nuclear matrix elements. We also emphasize the role of the competing mechanisms that could contribute to the neutrinoless double beta decay half-life.