Present Status of Nuclear Shell-Model Calculations of Neutrinoless Double-Beta Decay Matrix Elements

TL;DR

This paper reviews recent shell-model calculations of nuclear matrix elements crucial for neutrinoless double-beta decay, highlighting their sensitivity to model choices and implications for neutrino physics.

Contribution

It provides a comprehensive overview of the latest shell-model approaches and analyzes their dependence on model parameters for key nuclei.

Findings

Shell-model calculations vary significantly with model space choices.

Nuclear Hamiltonians influence the predicted matrix elements.

Results inform experimental searches for neutrinoless double-beta decay.

Abstract

Neutrinoless double beta decay searches are currently among the major foci of experimental physics. The observation of such a decay will have important implications in our understanding of the intrinsic nature of neutrinos and shed light on the limitations of the Standard Model. The rate of this process depends on both the unknown neutrino effective mass and the nuclear matrix element associated with the given neutrinoless double-beta decay transition. The latter can only be provided by theoretical calculations, hence the need of accurate theoretical predictions of the nuclear matrix element for the success of the experimental programs. This need drives the theoretical nuclear physics community to provide the most reliable calculations of the nuclear matrix elements. Among the various computational models adopted to solve the many-body nuclear problem, the shell model is widely considered as the basic framework of the microscopic description of the nucleus. Here, we review the most recent and advanced shell-model calculations of the nuclear matrix elements considering the light-neutrino-exchange channel for nuclei of experimental interest. We report the sensitivity of the theoretical calculations with respect to variations in the model spaces and the shell-model nuclear Hamiltonians.