Double beta decay and the SU(4) symmetry

Double beta decay without ν emission is a process which is of the upmost importance for determining the nature of the neutrino itself and fundamental interactions beyond the standard model. It may help to decide whether the neutrino is a massless particle, as assumed in the standard model, or a massive Majorana particle as occurring in some of its extensions. The study of double beta decay with ν emission may be helpful. In this paper, we describe an approach based on the SU(4) symmetry to successively the 2 ν and the 0 ν processes, and try to look at possible differences or similarities. The approach to double β decay followed here does not pretend to accurate predictions. It however leads to a natural explanation of 2 ν double beta decay amplitudes and allows one to reproduce some of the results obtained by different authors. With several respects, it could be improved, by considering for instance the effect of the single particle spin-orbit. (data)