Grand unification, nuclear structure and the double beta-decay

Abstract

Unification of the electroweak and the strong interaction prefers 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 also left handed and right-handed vector bosons to mediate the weak interactions. If these models are correct the neutrinoless double beta-decay is feasable. Thus if one finds the neutrinoless double beta-decay one knows that the standard model can not be correct in which the neutrino is a Dirac particle and therefore different from its antiparticle. Although the neutrinoless double beta-decay has not been seen it is possible to extract from the lower limits of the lifetime against the double neutrinoless beta-decay 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. The extraction of this physical quantities from the data is made difficult due to the fact that the weak interaction must not be diagonal in the representation of the mass matrix of the six neutrinos requested by such left-right symmetric models. A condition for obtaining reliable limits for these fundamental quantities from the measured lower limits of the half lifes of the 0νββ decay are correct calculations of the nuclear matrix elements involved. These nuclear structure calculations can be tested by calculating the two neutrino double beta decay (2νββ) for which we have experimental data and not only lower limits as for the 0νββ decay. The 2νββ 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 Approcimation (QRPA). Since the proton-proton and neutron-neutron pairing correlations are treated in the BCS approach particle numbers are only conserved in average for the initial |0 i +〉 and the final vb0 f +〉 states. Particle number projection is used to improve on this point. Since QRPA with the physical particle-particle interaction from the Bonn potential is close to breakdown, where the excitation energy goes to zero, higher up to third order RPA is included, by allowing anharmonicities up to three bosons in the physical wave functions. Third order RPA which is the lowest order to allow modifications of the ground state correlations affect the results appreciably. Since the intermediate states are supperpositions of proton- neutron two quasi-particle states one expects that proton-neutron pairing affects these states. From the masses of the nuclei one can extract a proton-neutron (pn) pairing gap. Due to the finite basis and the inclusion of only T = 1 (and not also T = 0, J = 1) pn-pairing the bare Brückner matrix elements of the Bonn potential yield no pn-pairing gap in most nuclei. If one fits the experimental pn-pairing gap by renormalizing the pn J π = 0 + particle-particle Brückner matrix elements by a factor d pn ≈ 1.3 to 1.4 one obtains strong pn-pairing correlations, which reduce the GT strength. Since now part of the pn particle-particle correlations are already included in the BCS wave functions the 2νββ strength is reduced and the dependence on the 1 + particle-particle strength parameter g pp gets weaker. In heavier nuclei like 76Ge to 76Se this dependence on g pp of the second order GT matrix elements Σ α GT(0 i + → 1 α + → 0 f +) almost disappears. The upper limits derived from the neutrinoless double beta decay of 76Ge are for the effective neutrino mass 〈 m νe 〉≤ 0.88 eV, for the left-right mixing angle 〈 tgζ 〉≤ 1.55 × 10 −8 and for the mass ratio of the light over the heavy vector boson squared 〈 M 1 2 M 2 2 〉 ≤ 1.08 × 10 −6 .