Relation between the $2\nu\beta\beta$ and $0\nu\beta\beta$ nuclear matrix elements

TL;DR

This paper establishes a formal relation between the nuclear matrix elements of neutrinoless and two-neutrino double beta decay, based on their dependence on nucleon separation distance, highlighting challenges in accurately determining these matrix elements.

Contribution

It introduces a new formal relation linking $0 uetaeta$ and $2 uetaeta$ decay matrix elements through their integral representations.

Findings

Derived a relation connecting $M^{0 u}_{GT}$ and $M^{2 u}_{cl}$.

Discussed the challenges in accurately determining closure matrix elements.

Highlighted the dependence of matrix elements on nucleon separation distance.

Abstract

A formal relation between the GT part of the nuclear matrix elements $M^0\nu}_{GT}$ of $0\nu\beta\beta$ decay and the closure matrix elements $M^{2\nu}_{cl}$ of $2\nu\beta\beta$ decay is established. This relation is based on the integral representation of these quantities in terms of their dependence on the distance $r$ between the two nucleons undergoing transformation. We also discuss the difficulties in determining the correct values of the closure $2\nu\beta\beta$ decay matrix elements.