The observed pattern of fermion masses and mixing is an outstanding puzzle in particle physics, generally known as the . Over the years, guided by precision neutrino oscillation data, discrete flavor symmetries have often been used to explain the neutrino mixing parameters, which look very different from the quark sector. In this review, we discuss the application of non-Abelian finite groups to the theory of neutrino masses and mixing in the light of current and future neutrino oscillation data. We start with an overview of the neutrino mixing parameters, comparing different global fit results and limits on normal and inverted neutrino mass ordering schemes. Then, we discuss a general framework for implementing discrete family symmetries to explain neutrino masses and mixing. We discuss CP violation effects, giving an update of CP predictions for trimaximal models with nonzero reactor mixing angle and models with partial reflection symmetry, and constraining models with neutrino mass sum rules. The connection between texture zeros and discrete symmetries is also discussed. We summarize viable higher-order groups, which can explain the observed pattern of lepton mixing where the non-zero plays an important role. We also review the prospects of embedding finite discrete symmetries in the Grand Unified Theories and with extended Higgs fields. Models based on modular symmetry are also briefly discussed. A major part of the review is dedicated to the phenomenology of flavor symmetries and possible signatures in the current and future experiments at the intensity, energy, and cosmic frontiers. In this context, we discuss flavor symmetry implications for neutrinoless double beta decay, collider signals, leptogenesis, dark matter, as well as gravitational waves.

中文翻译：

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轻子质量的现象学以及与离散风味对称性的混合


观察到的费米子质量和混合模式是粒子物理学中的一个突出难题，通常被称为“费米子质量和混合”。多年来，在精确的中微子振荡数据的指导下，离散风味对称性经常被用来解释中微子混合参数，这些参数看起来与夸克扇区非常不同。在这篇综述中，我们根据当前和未来的中微子振荡数据讨论了非阿贝尔有限群在中微子质量和混合理论中的应用。我们首先概述中微子混合参数，比较不同的全局拟合结果以及正常和反中微子质量排序方案的限制。然后，我们讨论实现离散族对称性以解释中微子质量和混合的通用框架。我们讨论了 CP 破坏效应，更新了具有非零反应堆混合角的三极大模型和具有部分反射对称性的模型的 CP 预测，以及具有中微子质量和规则的约束模型。还讨论了纹理零点和离散对称性之间的联系。我们总结了可行的高阶群，这可以解释观察到的轻子混合模式，其中非零起着重要作用。我们还回顾了在大统一理论和扩展希格斯场中嵌入有限离散对称性的前景。还简要讨论了基于模对称的模型。这篇评论的主要部分致力于风味对称的现象学以及当前和未来在强度、能量和宇宙前沿的实验中可能的特征。在这种背景下，我们讨论了风味对称性对中微子双β衰变、对撞机信号、轻子发生、暗物质以及引力波的影响。