ar X iv : h ep - p h / 99 07 31 6 v 1 1 2 Ju l 1 99 9 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. From the elementary particle point of view it pops up in almost every model. In addition to the traditional mechanisms, like the light neutrino mass, λ and η terms etc we can have direct R-parity violating supersymmetric (SUSY) contributions. In any case its observation 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 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 M eV /c. 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%, 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 availabe nuclear matrix elements for the exper-136 and 150 and the presently available experimental limits on the half-life of the 0νββ-decay we have extracted the following