Challenges for a reliable shell model description of the neutrinoless double beta decay matrix elements

Assuming that the neutrinos are Majorana particles and the neutrinoless double beta (0μββ) decay is observed, a reliable 0μββ matrix element is necessary to decide the neutrino mass hierarchy and the minimum neutrino mass. Many nuclear structure techniques, including the shell model, are presently used to calculate these matrix elements. In the last few years one could see a slow convergence of these results, but not yet at a level of 20 several shell model effective interactions and varying other parameters, finding results in a range that spans about 20In this contribution we describe challenges for obtaining reliable shell model 0μββ matrix elements, with emphasis to ⁷⁶Ge and ⁸²Se decays.