Short-range correlations for neutrinoless double-beta decay and low-momentum NN potentials

TL;DR

This paper investigates the impact of short-range correlations on neutrinoless double-beta decay nuclear matrix elements using a shell-model approach with renormalized low-momentum NN potentials, providing insights into the role of high-momentum components.

Contribution

It introduces a consistent renormalization of the neutrino potential using V-low-k derived from the CD-Bonn potential to study decay matrix elements across multiple isotopes.

Findings

Short-range correlations significantly affect decay matrix elements.

Renormalization reduces dependence on cutoff parameters.

Results align with other theoretical approaches.

Abstract

We approach the calculation of the nuclear matrix element of the neutrinoless double-beta decay process, considering the light-neutrino-exchange channel, by way of the realistic shell-model. In particular the focus of our work is spotted on the role of the short-range correlations, which should be taken into account because of the short-range repulsion of the realistic potentials. Our shell-model wave functions are calculated using an effective Hamiltonian derived from the high-precision CD-Bonn nucleon-nucleon potential, the latter renormalized by way of the so-called V-low-k approach. The renormalization procedure decouples the repulsive high-momentum component of the potential from the low-momentum ones by the introduction of a cutoff Lambda, and is employed to renormalize consistently the two-body neutrino potentials to calculate the nuclear matrix elements of candidates to this decay process in mass interval ranging from A=76 up to A=136. We study the dependence of the decay operator on the choice of the cutoff, and compare our results with other approaches that can be found in present literature.