Shell Model Analysis of the Neutrinoless Double Beta Decay of $^{48}$Ca

TL;DR

This paper introduces a new shell model method to accurately compute the nuclear matrix elements for neutrinoless double beta decay of calcium-48, aiding in neutrino mass determination.

Contribution

A novel shell model approach for calculating nuclear matrix elements of $^{48}$Ca neutrinoless double beta decay, considering various physical parameters and interactions.

Findings

Dependence of NME on short-range correlations analyzed

Impact of intermediate state energies on NME studied

Finite-size effects and interaction choices evaluated

Abstract

The neutrinoless double beta ($0\nu\beta\beta$) decay process could provide crucial information to determine the absolute scale of the neutrino masses, and it is the only one that can establish whether neutrino is a Dirac or a Majorana particle. A key ingredient for extracting the absolute neutrino masses from $0\nu\beta\beta$ decay experiments is a precise knowledge of the nuclear matrix elements (NME) describing the half-life of this process. We developed a new shell model approach for computing the $0\nu\beta\beta$ decay NME, and we used it to analyze the $0\nu\beta\beta$ mode of $^{48}$Ca. The dependence of the NME on the short range correlations parameters, on the average energy of the intermediate states, on the finite-size cutoff parameters, and on the effective interaction used for the many-body calculations is discussed.