Relativistic description of nuclear matrix elements in neutrinoless double-βdecay

Abstract

Background: Neutrinoless double-β (0νββ) decay is related to many fundamental concepts in nuclear and particle physics beyond the standard model. Currently there are many experiments searching for this weak process. An accurate knowledge of the nuclear matrix element for the 0νββ decay is essential for determining the effective neutrino mass once this process is eventually measured.Purpose: We report the first full relativistic description of the 0νββ decay matrix element based on a state-ofthe-art nuclear structure model. Methods:We adopt the full relativistic transition operators which are derived with the charge-changing nucleonic currents composed of the vector coupling, axial-vector coupling, pseudoscalar coupling, and weak-magnetism coupling terms. The wave functions for the initial and final nuclei are determined by the multireference covariant density functional theory (MR-CDFT) based on the point-coupling functional PC-PK1. Correlations beyond the mean field are introduced by configuration mixing of both angular momentum and particle number projected quadrupole deformed mean-field wave functions. Results:The low-energy spectra and electric quadrupole transitions in 150 Nd and its daughter nucleus 150 Sm are well reproduced by the MR-CDFT calculations. The 0νββ decay matrix elements for both the 0

Systematic study of nuclear matrix elements in neutrinoless double-βdecay with a beyond-mean-field covariant density functional theory

“…Moreover, shape fluctuation is shown to be significant in the light 0νββ candidate nuclei, the description of which is impossible with the approaches based on single-reference state [28,29,33]. This dynamic deformation effect (or shape mixing effect) could moderate the quenching effect from the static deformation on the NMEs [37], which is fully taken into account in the present multi-reference BMF-CDFT approach.…”

“…It is seen that the deformations of dominant configurations in the ground state of mother and daughter nuclei are somewhat different, as already discussed in Refs. [34,37]. This static deformation effect can quench the NME of 0νββ decay significantly in particular for the case where the deformations of the mother and daughter nuclei differ considerably from each other, such as 76 Ge-Se and 150 Nd-Sm.…”

“…More numerical details about the calculation of the NME within the BMF-CDFT have been introduced in Ref. [37].…”

“…With the ground-state wave functions |0 + I/F of the initial and final nuclei from the BMF-CDFT calculation, the NME M 0ν for the 0νββ-decay can be calculated straightforwardly as follows [18,37] …”

“…Detailed formulism and a proof-ofprinciple calculation for the 0νββ decay in 150 Nd have been described in Ref. [37].…”