Theoretical challenges in Double Beta Decay

The study of the double beta decay (DBD), particularly the neutrino less decay mode, is of great interest for testing the lepton number conservation (LNC) and getting information about neutrino properties, as the neutrinos character (Dirac or Majorana particles?), their absolute mass and hierarchy, etc. [1]-[2]. To make predictions of the DBD lifetimes and put constraints on the neutrino parameters, one needs accurate calculations of the nuclear matrix elements (NME) and phase space factors (PSF) entering the DBD lifetime expressions. In this paper I present recent calculations of these quantities, performed with approaches developed by our group. Then, I compare the theoretical predictions for the two-neutrino (2 v ) DBD lifetimes, for the most experimentally interesting nuclei, with the experimental ones, and comment on the reliability of the neutrinoless (0 v ) DBD calculations. (paper)