The observation of neutrinoless double-beta ($0\nu \beta \beta$) decay would offer proof of lepton number violation, demonstrating that neutrinos are Majorana particles, while also helping us understand why there is more matter than antimatter in the Universe. If the decay is driven by the exchange of the three known light neutrinos, a discovery would, in addition, link the observed decay rate to the neutrino mass scale through a theoretical quantity known as the nuclear matrix element (NME). Accurate values of the NMEs for all nuclei considered for use in $0\nu \beta \beta$ experiments are therefore crucial for designing and interpreting those experiments. Here, we report the first comprehensive ab initio uncertainty quantification of the $0\nu \beta \beta$-decay NME, in the key nucleus ${}^{76}\mathrm{Ge}$. Our method employs nuclear strong and weak interactions derived within chiral effective field theory and recently developed many-body emulators. Our result, with a conservative treatment of uncertainty, is an NME of ${2.60}_{-1.36}^{+1.28}$, which, together with the best-existing half-life sensitivity and phase-space factor, sets an upper limit for effective neutrino mass of ${187}_{-62}^{+205}\mathrm{meV}$. The result is important for designing next-generation germanium detectors aiming to cover the entire inverted hierarchy region of neutrino masses.

中文翻译：

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Ge76 无中微子双贝塔衰变的从头算不确定性定量

无中微子双β的观测（$0\nu \beta \beta$）衰变将提供轻子数破坏的证据，证明中微子是马约拉纳粒子，同时也帮助我们理解为什么宇宙中物质多于反物质。如果衰变是由三个已知的轻中微子的交换驱动的，那么一项发现将通过称为核基质元素（NME）的理论量将观察到的衰变率与中微子质量尺度联系起来。考虑使用的所有核的 NME 的准确值$0\nu \beta \beta$因此，实验对于设计和解释这些实验至关重要。在这里，我们报告了第一个全面的从头开始不确定性量化$0\nu \beta \beta$-衰变NME，在关键核心${}^{76}锗$。我们的方法采用手性有效场理论和最近开发的多体模拟器中衍生的核强弱相互作用。通过对不确定性的保守处理，我们的结果是 NME${2.60}_{-1.36}^{+1.28}$，与现有的最佳半衰期灵敏度和相空间因子一起，设定了有效中微子质量的上限${187}_{-62}^{+205}\mathrm{兆伏}$。该结果对于设计旨在覆盖中微子质量的整个倒置层次结构区域的下一代锗探测器非常重要。