Possible test of grand unification in the double beta decay

Abstract

The more successful grand unified theories predict that the neutrino is identical with its antiparticle and therefore is a Majorana neutrino which violates lepton number conservation. Such a neutrino should have a finite mass and also a small right handed weak interaction. If the double neutrinoless beta decay is observed with the full decay energy in the two electrons, it would establish that the electron neutrino is a Majorana particle. It is shown that the relativistic corrections of the nucleonic wave functions are essential for determining an upper limit of the right handedness from the measured lower limit of the life-time against the neutrinoless double beta decay. The upper limit for the right handedness of the weak interaction derived from the lower limit of the life-times against the neutrinoless beta decay is |〈 η〉| <1.8 × 10 −8 and the upper limit for the neutrino mass is |〈 m ν 〉| <1.9[ eV]. To test the nuclear structure part of the theory the double beta decay with two neutrinos is calculated and compared with the known experimental values. It is shown that it is important to take into account in the intermediate nucleus not only the particle-hole, but also the particle-particle interaction which acts destructively and reduces the double beta decay with two neutrinos by about a factor 1 100 and one obtains a reasonable agreement with the experimental measured data. Applying the same improved description to the β &+;-decay in proton rich nuclei, one can explain the long standing puzzle of the quenching of the Gamow-Teller strength in agreement with the data.