Second order beta-decay processes with and without neutrinos in the final state are key probes of nuclear physics and of the nature of neutrinos. Neutrinoful double-beta decay is the rarest Standard Model process that has been observed and provides a unique test of the understanding of weak nuclear interactions. Observation of neutrinoless double-beta decay would reveal that neutrinos are Majorana fermions and that lepton number conservation is violated in nature. While significant progress has been made in phenomenological approaches to understanding these processes, establishing a connection between these processes and the physics of the Standard Model and beyond is a critical task as it will provide input into the design and interpretation of future experiments. The strong-interaction contributions to double-beta decay processes are non-perturbative and can only be addressed systematically through a combination of lattice Quantum Chromoodynamics (LQCD) and nuclear many-body calculations. In this review, current efforts to establish the LQCD connection are discussed for both neutrinoful and neutrinoless double-beta decay. LQCD calculations of the hadronic contributions to the neutrinoful process $nn\to pp e^- e^- \bar\nu_e\bar\nu_e$ and to various neutrinoless pionic transitions are reviewed, and the connections of these calculations to the phenomenology of double-beta decay through the use of effective field theory (EFTs) is highlighted. At present, LQCD calculations are limited to small nuclear systems, and to pionic subsystems, and require matching to appropriate EFTs to have direct phenomenological impact. However, these calculations have already revealed qualitatively that there are terms in the EFTs that can only be constrained from double-beta decay processes themselves or using inputs from LQCD. Future prospects for direct calculations in larger nuclei are also discussed.

中文翻译：

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核双 β 衰变的晶格 QCD 输入

在终态有和没有中微子的二阶β衰变过程是核物理学和中微子性质的关键探测。中微子双β衰变是已观察到的最罕见的标准模型过程，它提供了对弱核相互作用理解的独特测试。对无中微子双β衰变的观察将揭示中微子是马约拉纳费米子，并且本质上违反了轻子数守恒。虽然在理解这些过程的现象学方法方面取得了重大进展，但在这些过程与标准模型物理及其他物理之间建立联系是一项关键任务，因为它将为未来实验的设计和解释提供输入。双β衰变过程的强相互作用贡献是非微扰的，只能通过晶格量子色动力学（LQCD）和核多体计算的组合来系统地解决。在这篇综述中，讨论了当前为有中微子和无中微子双 β 衰变建立 LQCD 连接的努力。回顾了对中微子过程 $nn\to pp e^- e^- \bar\nu_e\bar\nu_e$ 和各种无中微子离子跃迁的强子贡献的 LQCD 计算，以及这些计算与双重现象学的联系突出显示了通过使用有效场论 (EFT) 的β衰变。目前，LQCD 计算仅限于小型核系统和 pionic 子系统，并需要与适当的 EFT 匹配才能产生直接的现象学影响。然而，这些计算已经定性地揭示了 EFT 中的某些项只能受到双β 衰减过程本身或使用来自 LQCD 的输入的约束。还讨论了在更大的原子核中直接计算的未来前景。