Determination of neutrino mass ordering in future $^{76}$Ge-based neutrinoless double-beta decay experiments

TL;DR

This paper evaluates the potential of $^{76}$Ge-based neutrinoless double-beta decay experiments to determine neutrino mass ordering, using Bayesian analysis to quantify experimental sensitivity and distinguish normal from inverted hierarchy.

Contribution

It provides the first quantitative assessment of experimental power to identify neutrino mass ordering in future $^{76}$Ge experiments using Bayesian methods.

Findings

Experiments can set lower limits on half-life of neutrinoless double-beta decay.

Bayesian analysis can distinguish mass orderings with moderate evidence.

Normal hierarchy detection is feasible if effective neutrino mass is below 0.01 eV.

Abstract

Motivated by recent intensive experimental efforts on searching for neutrinoless double-beta decays, we perform a detailed analysis of the physics potential of the experiments based on $^{76}\mathrm{Ge}$. Assuming no signals, current and future experiments could place a $90\%$ lower limit on the half life $T^{0\nu}_{1/2} \gtrsim 4\times 10^{26}~{\rm yr}$ and $T^{0\nu}_{1/2} \gtrsim 7\times 10^{27}~{\rm yr}$, respectively. Then, how to report an evidence for neutrinoless double-beta decays is addressed by following the Bayesian statistical approach. For the first time, we present a quantitative description of experimental power to distinguish between normal and inverted neutrino mass orderings. Taking an exposure of $10^{4}~{\rm kg}\cdot{\rm yr}$ and a background rate of $10^{-4}~{\rm counts}/({\rm keV}\cdot{\rm kg}\cdot{\rm yr})$, we find that a moderate evidence for normal neutrino mass ordering (i.e., with a Bayes factor ${\cal B}$ given by $\ln({\cal B}) \simeq 2.5$ or a probability about $92.3\%$ according to the Jeffreys scale) can be achieved if the true value of effective neutrino mass $m^{}_{\beta\beta}$ turns out to be below $0.01~{\rm eV}$.