标题： 未来基于$^{76}$的无中微子双贝塔衰变实验中中微子质量顺序的确定 显示英文标题

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

摘要： 鉴于近期在寻找无中微子双β衰变方面的大量实验努力，我们对基于$^{76}\mathrm{Ge}$的实验的物理潜力进行了详细分析。 假设没有信号，当前和未来的实验可以分别对半衰期$T^{0\nu}_{1/2} \gtrsim 4\times 10^{26}~{\rm yr}$和$T^{0\nu}_{1/2} \gtrsim 7\times 10^{27}~{\rm yr}$置于$90\%$的下限。 然后，通过遵循贝叶斯统计方法来解决如何报告无中微子双β衰变的证据。 首次，我们提出了对实验能力的定量描述，以区分正常和倒置的中微子质量顺序。 在曝光量为$10^{4}~{\rm kg}\cdot{\rm yr}$且背景速率为$10^{-4}~{\rm counts}/({\rm keV}\cdot{\rm kg}\cdot{\rm yr})$的情况下，我们发现如果有效中微子质量$m^{}_{\beta\beta}$的真实值低于$0.01~{\rm eV}$，则可以获得中微子质量顺序的适度证据（即贝叶斯因子${\cal B}$，由$\ln({\cal B}) \simeq 2.5$给出，或根据 Jeffreys 标度约为$92.3\%$的概率）。 显示英文摘要

摘要： 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 $0.01~{\rm eV}$.