Contributions of different neutron pairs in different approaches for neutrinoless double beta decay

TL;DR

This paper compares various theoretical approaches for calculating neutrinoless double beta decay matrix elements, focusing on the roles of different neutron pair angular momenta and parities in each method.

Contribution

It provides a detailed comparison of how different models incorporate neutron pair angular momenta and parities in neutrinoless double beta decay calculations.

Findings

QRPA and Shell Model involve similar neutron pair angular momenta.

HFB is limited to even angular momenta like 0+, 2+, 4+.

IBM restricts to 0+ and 2+ nucleon pairs.

Abstract

The methods used till now to calculate the neutrinoless double beta decay matrix elements are: the Quasiparticle Random Phase Approximation (QRPA), the Shell Model (SM), the angular momentum projected Hartee-Fock-Bogoliubov approach (HFB) and the Interacting Boson Model (IBM). The different approaches are compared specifically concerning the the angular momenta and parities of the neutron pairs, which are changed into two protons by the $0\nu\beta\beta$ decay. The QRPA and SM involve about the same angular momentum and parity neutron pairs, while the HFB is restricted to $0^{+}, 2^{+}, 4^{+}, ...$, and IBM to $0^{+}$ and $2^{+}$ nucleon pairs. The differences in the seniority contributions for the QRPA and the SM are discussed.