The interpolating formula for the $0\nu\beta\beta$-decay half-life in the case of light and heavy neutrino mass mechanisms

TL;DR

This paper revisits an interpolating formula to estimate neutrinoless double beta decay half-lives across different neutrino mass mechanisms, showing its broad applicability and implications for distinguishing these mechanisms.

Contribution

The paper provides a mathematical justification for the interpolating formula's validity across nuclear models and analyzes conditions for mechanism dominance in $0 uetaeta$-decay.

Findings

The formula is valid for all known nuclear structure approaches.

The ratio of NMEs for light and heavy neutrinos is isotope-independent.

Distinguishing neutrino mass mechanisms via different nuclei is challenging.

Abstract

We revisit the "interpolating formula" proposed in our previous publication. It allows one to calculate the neutrinoless double beta decay ($0\nu\beta\beta$-decay) half-life for arbitrary neutrino mass without involvement of the complicated results for nuclear matrix elements (NME) obtained within specific nuclear structure models. The formula derives from the finding that the value of a properly normalized ratio of the NMEs for the light and heavy neutrino mass mechanisms weakly depends on isotope. From this fact it follows, in particular, that the light and heavy neutrino mass mechanisms can hardly be distinguished in a model independent way searching for $0\nu\beta\beta$-decay of different nuclei. Here we show that this formula holds for all the known nuclear structure approaches. We give a mathematical justification of our results examining analytical properties of the NMEs. We also consider several simplified benchmark scenarios within left-right symmetric models and analyze the conditions for the dominance of the light or heavy neutrino mass mechanisms in $0\nu\beta\beta$-decay.