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

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 76Ge^{76}\mathrm{Ge}. Assuming no signals, current and future experiments could place a 90%90\% lower limit on the half life T1/20ν4×1026 yrT^{0\nu}_{1/2} \gtrsim 4\times 10^{26}~{\rm yr} and T1/20ν7×1027 yrT^{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 104 kgyr10^{4}~{\rm kg}\cdot{\rm yr} and a background rate of 104 counts/(keVkgyr)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 B{\cal B} given by ln(B)2.5\ln({\cal B}) \simeq 2.5 or a probability about 92.3%92.3\% according to the Jeffreys scale) can be achieved if the true value of effective neutrino mass mββm^{}_{\beta\beta} turns out to be below 0.01 eV0.01~{\rm eV}.Comment: 16 pages, 7 figures, the Jeffreys scale used, more discussions added, to appear in Phys. Rev.

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