Can one measure nuclear matrix elements of neutrinoless double beta decay?

TL;DR

This paper proposes a method to measure the Fermi component of neutrinoless double beta decay nuclear matrix elements using charge-exchange reactions, aiding in model discrimination.

Contribution

It introduces a novel approach to reconstruct the total nuclear matrix element by measuring a small isospin-breaking Fermi matrix element, leveraging isospin conservation.

Findings

Reformulation of $M_{F}^{0 u}$ as an energy-weighted double Fermi transition

Potential to measure isospin-breaking Fermi matrix element experimentally

Method to discriminate between different nuclear structure models

Abstract

By making use of the isospin conservation by strong interaction, the Fermi $0\nu\beta\beta$ nuclear matrix element $M_{F}^{0\nu}$ is transformed to acquire the form of an energy-weighted double Fermi transition matrix element. This useful representation allows reconstruction of the total $M_{F}^{0\nu}$ provided a small isospin-breaking Fermi matrix element between the isobaric analog state in the intermediate nucleus and the ground state of the daughter nucleus could be measured, e.g. by charge-exchange reactions. Such a measurement could set a scale for the $0\nu\beta\beta$ nuclear matrix elements and help much to discriminate between different nuclear structure models in which calculated $M_{F}^{0\nu}$ may differ by as much as the factor of 5.