Neutrinoless double beta decay from a modern perspective

Neutrinoless double beta decay is a very important process both from the particle and nuclear physics point of view. From the elementary particle point of view it pops up in almost every model. giving rise, among others, to the following mechanisms: a) The traditional contributions like the light neutrino mass mechanism . b) The exotic R-parity violating supersymmetric (SUSY) contributions. Similar considerations apply to its sister lepton and muon number violating muon to positron conversion. The observation of neutrinoless double beta decay will signal that the neutrinos are massive Majorana particles. For nuclear physics it is challenging, because: 1) The nuclei, which can undergo double beta decay, have complicated structure. 2) The energetically allowed transitions are suppressed. 3) One must cope with the short distance behavior of the transition operators. Thus novel effects (decay of pions in flight between nucleons etc) have to be considered. 4) One has to take into account possible momentum dependent terms of the nucleon current. For light neutrinos such modifications of the nucleon current reduce the nuclear matrix elements by about 25 per cent. In the case of heavy neutrino the effect is much larger and model dependent. With the above effects the nuclear matrix elements for all interesting nuclei A = 76, 82, 96, 100, 116, 128, 130, 136 and 150 are discussed. Some have been obtained in the shell model but most in QRPA. Thus we have extracted new limits on the various lepton violating parameters. We find an average neutrino mass of about 0.5eV and, for reasonable choices of the parameters of SUSY models, we get a stringent limit on the R-parity violating parameter less than 0.00068