Neutrinoless $ββ$ decay in the interacting boson model based on the nuclear energy density functionals

TL;DR

This study develops a microscopic IBM-2 framework grounded in nuclear EDF SCMF theory to predict neutrinoless double beta decay NMEs. By mapping SCMF deformation-energy surfaces onto the IBM-2 energy surface and formulating transition operators via generalized seniority, it produces $0\nu\beta\beta$ NMEs for ten candidate decays using both relativistic (DD-PC1) and nonrelativistic (D1M) EDF inputs, with closure assumed. The results, favoring GT-dominated NMEs and generally smaller than prior IBM-2 predictions, show sensitivity to EDF choice, Hamiltonian parameters, and mean-field minima, and align variably with other many-body methods. The analysis identifies key uncertainties and outlines future improvements, including Majorana terms and configuration mixing, to enhance predictive accuracy for experimental constraints on the neutrino mass. Overall, the approach enables systematic NME predictions for nuclei far from stability, contributing to the interpretation of next-generation $0\nu\beta\beta$ experiments.

Abstract

The neutrinoless $ββ$ ($0νββ$) decay nuclear matrix elements (NMEs) are calculated in the interacting boson model (IBM), which is based on the nuclear energy density functional (EDF) theory. The Hamiltonian of the IBM that gives rise to the energies and wave functions of the ground and excited states of $0νββ$ decay emitting isotopes and corresponding final nuclei is determined by mapping the self-consistent mean-field deformation-energy surface obtained with a given EDF onto the corresponding bosonic energy surface. The transition operators are formulated using the generalized seniority scheme, and the pair structure constants are determined by the inputs provided by the self-consistent calculations. The predicted values of the $0νββ$-decay NMEs with the nonrelativistic and relativistic EDFs are compared with those resulting from different many-body methods. Sensitivities of the predicted NMEs to the model parameters and assumptions are discussed.

Figures (14)

• Figure 1: Potential energy curves along the $\beta$ deformation for the even-even nuclei involved in the $0\nu\beta\beta$-decay processes, computed by the constrained SCMF methods within the RHB and within the HFB. The total mean-field energies are plotted with respect to the global minimum.
• Figure 2: Excitation energies of the $2^+_1$ and $4^+_1$ states in the (a), (c) parent and (b), (d) daughter even-even nuclei of the $0\nu\beta\beta$ decays, obtained from the mapped IBM-2 calculations that are based on the RHB and HFB SCMF models. Experimental data are taken from the Brookhaven National Nuclear Data Center data.
• Figure 3: Same as the caption to Fig. \ref{['fig:yrast']}, but for the $0^+_2$ and $2^+_2$ states.
• Figure 4: Calculated and experimental data$B(E2)$ values for low-lying states in parent nuclei.
• Figure 5: Same as the caption of Fig. \ref{['fig:be2_ee1']}, but for daughter nuclei.