Extended operator expansion method for neutrinoless double beta decay

Abstract

Reliable calculations of nuclear matrix elements are a prerequisite for the determination of the effective neutrino mass and other particle physics parameters from neutrinoless double beta decay. Here, the operator expansion method is improved by including Coulomb, tensor and central interactions simultaneously. Furthermore, the formalism of the OEM is extended to those matrix elements necessary to extract the right-handed parameters 〈λ 〉 and 〈η 〉 from 0νββ decay. OEM includes the dependence of the nuclear matrix elements on the intermediate states implicitly and can therefore be understood as a step beyond the closure approximation. Numerical studies are carried out for the isotope76Ge combining the OEM expressions with ground-state wave functions calculated within a proton-neutron quasiparticle Random Phase Approximation (pn-QRPA) model. The influence and relative importance of central, tensor and Coulomb interactions is investigated. Within the OEM, contributions from the Coulomb force are found to be negligible in 0νββ decay, while the tensor force leads to a moderate change of the results, of the order of (10–30)%, giving a better agreement between sets of calculations which employ different NN-interactions. Generally, results of the OEM+QRPA calculation are similar to previous calculations of 0νββ decay matrix elements, indicating that 0νββ decay is not sensitive to model approximations and might therefore be more accurately calculated than the strongly suppressed 2νββ decay matrix elements.