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 Lip in almost every model, giving rise, among others, to the following mechanisms: (a) The traditional contributions like the light neutrino mass mechanism as well as the j(L)-j(R) leptonic interference (lambda and eta terms). (b) The exotic R-parity violating supersymmetric (SUSY) contributions. In this scheme, the currents are only left handed and the intermediate particles normally are very heavy. There exists, however, the possibility of light intermediate neutrinos arising from the combination of V-A and P-S currents at the quark level. This leads to the same structure as the above lambda term. Similar considerations apply to its sister lepton and muon number violating muon to positron conversion in the presence of nuclei. Anyway, regardless of the dominant mechanism, the observation of neutrinoless double betas decay, which is the most important of the two from an experimental point of view, will severely constrain the existing models and will signal that the neutrinos are massive Majorana particles. From the nuclear physics point of view it is challenging, because: (1) The nuclei, which can undergo double beta decay, have a complicated nuclear structure. (2) The energetically allowed transitions are suppressed (exhaust a small part of the entire strength). (3) Since in some mechanisms the intermediate particles are very heavy, one must cope with the short distance behavior of the transition operators. Thus novel effects, like the double beta decay of pions in flight between nucleons, have to be considered. In SUSY models this mechanism is more important than the standard two nucleon mechanism. (4) The intermediate momenta involved are quite high (about 100 MeV/c). Thus, one has to take into account possible momentum-dependent terms of the nucleon current, like the modification of the axial current due to PCAC, weak magnetism terms, etc. We find that, for the mass mechanism, such modifications of the nucleon current for light neutrinos reduce the nuclear matrix elements by about 25%, almost regardless of the nuclear model. In the case of heavy neutrino the effect is much larger and model dependent. Taking the above effects into account the needed nuclear matrix elements have become available for all the experimentally interesting nuclei A = 76, 82, 96, 100, 116, 128, 130, 136 and 150. Some of them have been obtained in the large basis shell model but most of them in various versions of QRPA, Then using the best presently available experimental limits on the half-life of the 0nubetabeta-decay, we have extracted new limits on the various lepton violating parameters. In particular we find < 0.5 eV/c(2) and, for reasonable choices of tile parameters of SUSY models in the allowed SUSY parameter space, we get a stringent limit on tile R-parity violating parameter lambda(111)' < 0.68 x 10(-3). (C) 2001 Elsevier Science B.V. All rights reserved. [References: 215]
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