Shell model calculations for neutrinoless double beta decay

The study of the neutrinoless double beta (0 νββ ) decay is of great interest because of its potential to provide us with information about the lepton number conservation and neutrino properties as the neutrinos character (are they Dirac or Majorana particles?) and their absolute mass. Since the 0 νββ decay has not yet been discovered experimentally, one can only extract limits of the absolute neutrino mass. For that, one needs accurate calculations of both nuclear matrix elements (NMEs) and phase space factors (PSFs) which appear in the theoretical lifetime expressions, corroborated with experimental lifetime limits. In this paper I first present recent shell model (ShM) calculations of the NMEs and PSFs for 0 νββ decay performed by our group, in the hypothesis that the mechanism of its occurrence is the exchange of light Majorana neutrinos between two nucleons inside the nucleus. Also, the consensus on the use of different nuclear structure ingredients/parameters in the computation of the NMEs is discussed. Then, I present new limits of the Majorana neutrino mass parameter derived from the analysis of 0 νββ decay of nine isotopes.