正态中微子族的强贝叶斯证据
Strong Bayesian Evidence for the Normal Neutrino Hierarchy
摘要：
三个中微子质量的配置可以有两种形式，称为正常和反向层次。我们计算贝叶斯证据与这两个层次结构。以前的研究发现了一个正常的层次结构，这是由宇宙学数据限制了可用的参数空间的不对称方式驱动的。在这里，我们确定了第二个不对称的存在，这是由中微子振荡的数据。通过结合对质量平方分裂的约束和对中微子质量总和的限制，即$Σm_ν< 0.13$ eV，并使用最小的质量信息先验，我们推断出42：1的几率有利于正常的层次结构，这在杰弗里斯尺度中被归类为“强”。我们将探讨这些几率如何在更高精度的宇宙学数据下演变，并讨论这一发现对中微子性质的影响。最后，推断个体质量为$m_1 = 3.80^{+26.2}_{-3.73} \, \text{meV}, m_2 = 8.8^{+18}_{-1.2} \, \text{meV}, m_3 = 50.4^{+5.8}_{-1.2} \, \text{meV}$（$95\%$可信区间）。
英文摘要：
The configuration of the three neutrino masses can take two forms, known as the normal and inverted hierarchies. We compute the Bayesian evidence associated with these two hierarchies. Previous studies found a mild preference for the normal hierarchy, and this was driven by the asymmetric manner in which cosmological data has confined the available parameter space. Here we identify the presence of a second asymmetry, which is imposed by data from neutrino oscillations. By combining constraints on the squared-mass splittings with the limit on the sum of neutrino masses of $Σm_ν< 0.13$ eV, and using a minimally informative prior on the masses, we infer odds of 42:1 in favour of the normal hierarchy, which is classified as "strong" in the Jeffreys' scale. We explore how these odds may evolve in light of higher precision cosmological data, and discuss the implications of this finding with regards to the nature of neutrinos. Finally the individual masses are inferred to be $m_1 = 3.80^{+26.2}_{-3.73} \, \text{meV}, m_2 = 8.8^{+18}_{-1.2} \, \text{meV}, m_3 = 50.4^{+5.8}_{-1.2} \, \text{meV}$ ($95\%$ credible intervals).
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