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

The neutrinoless $\beta\beta$ ($0\nu\beta\beta$) 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 $0\nu\beta\beta$ 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 $0\nu\beta\beta$-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.