THE NEUTRINOLESS DOUBLE BETA DECAY AND THE NEUTRINO MASS

Neutrino less Double Beta Decay (0 nu beta beta) is presently the only known experiment to distinguish between Dirac neutrinos, different from their antiparticles, and Majorana neutrinos, identical with their antiparticles. In addition 0 nu beta beta allows to determine the absolute scale of the neutrino masses. This is not possible with neutrino oscillations. To determine the neutrino masses one must assume, that the light Majorana neutrino exchange is the leading mechanism for 0 nu beta beta and that the matrix element of this transition can be calculated reliably. The experimental 0 nu beta beta transition amplitude in this mechanism is a product of the light left handed effective Majorana neutrino mass and of this transition matrix element. The different methods, Quasi-particle Random Phase Approximation (QRPA), Shell Model (SM), Projected Hartree-Fock-Bogoliubov (PHFB) and Interacting Boson Model (IBM2) used in the literature and the reliability of the matrix elements in these approaches are reviewed. In the second part it is investigated how one can determine the leading mechanism or mechanisms from the data of the 0 nu beta beta decay in different nuclei. Explicit expressions are given for the transition matrix elements. It is shown that possible interference terms allow to test CP (Charge and Parity conjugation) violation.