Grand unified theories and the double beta-decay

Abstract

Grand Unified and the superstring theories suggest that the neutrino is a Majorana particle identical with its antiparticle. The same theories indicate that it has a small finite mass and that it also interacts by a right handed current. These properties can be tested by the neutrinoless double beta-decay. We show that due to the virtual intermediate neutrino in the neutrinoless double-beta decay the classification according to allowed, first forbidden and second forbidden transitions does not reflect anymore the strength of the transition probability. We show that the relativistic corrections to the nucleon wave functions contribute to the leading term to the double neutrinoless beta-decay. This term has never been calculated before. We apply the theory to the ⁷⁶Ge to ⁷⁶ Se transition. We use the new generation of microsopic many body wave function of the nucleus. This approach is called MONSTER and VAMPIR. The starting point of these nuclear structure calculation is the Hartree-Fock-Bogoliubov approach with projection on good proton and neutron number and on good angular momentum before the variation (VAMPIR). Short range correlations between the nucleons and the finite extention of the nucleons have been included. We show that the matrix elements due to the relativistic recoil corrections including weak magnetism are by a factor 200 larger than the contributions calculated up to now. This yields from the lower limit of the lifetime measured by Avignone to an upper limit for the right handedness of the weak interaction which is two orders of magnitude more stringent than previous results. This work yields for the neutrino mass m_V 2.4 eV, for the right handedness parameter η 6.8×10⁻⁸ and for the right handedness of the leptonic and the hadronic interaction λ 4.3×10⁻⁶.