The neutrinoless double beta decay of ⁷⁶Ge, ⁸²Se, ⁸⁶Kr, ¹¹⁴Cd, ^{128, 130}Te and ^{134, 136}Xe in the framework of a relativistic quark confinement model

Abstract

The half-life of the 0⁺ → 0⁺ neutrinoless double beta decay is calculated for ⁷⁶Ge, ⁸²Se, ⁸⁶Kr, ¹¹⁴Cd, ^{128, 130}Te and ^{134, 136}Xe and the upper limit for the effective neutrino mass of 3.0 eV is deduced from available experimental data. In addition, the contribution of the right-handed charged weak currents to the effective weak hamiltonian is estimated. The relevant parameters attain the values |〈Λ〉| < 4.1 × 10⁻⁶ and |〈ν〉| < 6.6 × 10⁻⁸. The nucleonic weak current is treated starting from the current quark level and evaluating the quark current using relativistic quark wave functions obtained from a Dirac equation with a harmonic confinement potential. The nuclear matrix elements of the thus obtained effective weak operators are evaluated using the proton-neutron quasi-particle random phase approximation approach avoiding the use of closure and the accompanying singular neutrino potentials. The dependence of the decay half-life on the recoil effects and the p-wave contribution is analyzed. Detailed presentation of the theory is pursued.