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Neutrinoless Double Beta Decay in Gauge Theories

Neutrinoless double beta decay is a very important process both from the particle and nuclear physics point of view. Its observation will severely constrain the existing models and signal that the neutrinos are massive Majorana particles. From the elementary particle point of view it pops up in almost every model. In addition to the traditional mechanisms, like the neutrino mass, the admixture of right handed currents etc, it may occur due to the R-parity violating supersymmetric (SUSY) interactions. From the nuclear physics point of view it is challenging, because: 1) The relevant nuclei have complicated nuclear structure. 2) The energetically allowed transitions are exhaust a small part of all the strength. 3) One must cope with the short distance behavior of the transition operators, especially when the intermediate particles are heavy (eg in SUSY models). Thus novel effects, like the double beta decay of pions in flight between nucleons, have to be considered. 4) The intermediate momenta involved are about 100 MeV. Thus one has to take into account possible momentum dependent terms in the nucleon current. We find that, for the mass mechanism, such modifications of the nucleon current for light neutrinos reduce the nuclear matrix elements by about 25 per cent, almost regardless of the nuclear model. In the case of heavy neutrinos the effect is much larger and model dependent. Taking the above effects into account, the available nuclear matrix elements for the experimentally interesting nuclei A = 76, 82, 96, 100, 116, 128, 130, 136 and 150 and the experimental limits on the life times we have extracted new stringent limits on the average neutrino mass and on the R-parity violating coupling for various SUSY models.