Grand unification, the double beta decay and the Pauli principle

Theories which unify the electroweak and the strong: interaction prefer that the neutrino is a Majorana particle and therefore essentially identical with its own antiparticle. In such grand unified models the neutrino has also a finite mass and a slight right-handed weak interaction, since the model is left-right symmetric. These models have vector bosons mediating the left-and the right-handed weak interactions. If these models are correct, the neutrinoless double beta-decay is feasable. Although the neutrinoless double beta-decay has not been seed it is possible to extract from the lower limits of the lifetime upper limits for the effective electron-neutrino mass and for the effective mixing angle of the right-handed and the left-handed vector bosons mediating the weak interaction. One also can obtain an effective upper limit for the mass ratio of the light and the heavy vector bosons. A condition for obtaining reliable limits for these fundamental quantities from the measured lower limits of the half lifes of the 0 nu beta beta decay are that the nuclear matrix can be calculated correctly. These nuclear structure calculations can be tested by calculating the two neutrino double beta decay (2 nu beta beta) for which rye have experimental data and not only lower limits as for the 0 nu beta beta decay The 2 nu beta beta decay is dominated by the Gamow Teller (GT) transitions. The intermediate 1(+) states in the odd-odd mass nucleus are usually calculated within the Quasi-Particle Random Phase Approximation (QRPA). The QRPA treats Fermion pairs as bosons. This overestimates the ground state correlations and leads to the collaps of the 2 nu beta beta decay probability for the physical J(pi) = 1(+), T = 1 particle-particle interaction, We have extended the QRPA including: the Fermi commutation relations. One finds now agreement (in almost all cases) for the 2 nu beta beta decay probability This increases also the reliability of the conclusions extracted from the upper limits of the 0 nu beta beta decay for the neutrino mass, the left-right mixing angle and the lower limit for the mass of the "heavy" vector boson.