Theoretical status of the double beta decay

Abstract

The detection of the neutrinoless double beta decay would establish that the neutrino is a Majorana particle and it would allow to measure the absolute neutrino mass in the meV region. To extract from the neutrinoless double beta decay halflife the absolute neutrino mass, the transition matrix element is as important as the experimental data. The dramatic progress in the last years is reviewed to determine these transition matrix elements for the neutrinoless double beta decay. It is shown, that the values calculated in the Quasi-particle Random Phase Approach (QRPA) and the recent results in the interacting boson model agree with each other completely within the uncertainties of the theories, while the shell model yields values which in the region of 76Ge are by a factor ½ smaller than QRPA. Possible reasons for the differences and an experimental way of measuring the Fermi part for the neutrinoless double beta decay transition matrix elements are discussed. This would allow to determine experimentally which of the two approaches is the correct one. Finally we show that the renormalization parameter gpp, which multiplies the nucleon-nucleon interaction matrix elements can be overconstraint together with the axial charge gA in three nuclei, where the ground state of the intermediate nucleus in the double beta decay system is a 1+ state and apart of the 2νββ also the β− decay for the second leg and the electron capture (EC) in the first leg is measured. It is shown, that this overconstraint determination of gpp and gA leads to the same result for the transition matrix elements as when one adjusts gpp to the 2νββ alone.