AI 中文总结
本文系统分类了模 $S_3$ 轻子味模型，发现 18 个 NO 和 19 个 IO 可行模型，其中 14 个同时满足两种排序，预测了绝对质量可观测量可区分排序。
AI 中文摘要
我们对一类经济的模 $S_3$ 轻子味模型进行了系统研究，该模型不扩大连续规范对称性，也不引入右手中微子或额外的 flavo 场。我们提供了由 $S_3$ 单态-双重态表示结构和允许的模权重分配所允许的所有不等价实现的完整分类。基于当前中微子振荡数据，我们使用贝叶斯模型比较和参数相关性分析，对正常排序（NO）和倒排序（IO）两种情形研究了其现象学可行性。我们确定了 18 个对 NO 可行的模型和 19 个对 IO 可行的模型，其中 14 个在两种排序下均满足实验约束。可行的模型成功容纳了当前的中微子振荡数据，同时为轻子 CP 破坏、马约拉纳相位以及探测绝对中微子质量尺度的可观测量提供了非平凡预测。在这些预测中，绝对质量可观测量为两种排序提供了最清晰的区分。在最佳拟合点，有效电子中微子质量（$m_\beta$）的预测范围在 NO 和 IO 之间完全不重叠，而中微子质量之和（$\sum_i m_i$）和有效马约拉纳质量（$m_{\beta\beta}$）的预测范围仅部分分离。IO 模型通常预测更高的绝对中微子质量尺度，因此受到宇宙学观测的更强约束，并且更容易被无中微子双贝塔衰变搜索所探测。我们的结果表明，尽管其场内容经济，模 $S_3$ 框架容纳了多种现象学上可行的轻子味实现，并具有实验可检验的预测。
英文摘要
We perform a systematic study of an economical class of modular $S_3$ lepton-flavor models without enlarging the continuous gauge symmetry or introducing right-handed neutrinos or additional flavon fields. We provide a complete classification of all inequivalent realizations allowed by the $S_3$ singlet--doublet representation structure and the admissible modular-weight assignments. Their phenomenological viability is investigated for both normal ordering (NO) and inverted ordering (IO) using Bayesian model comparison and parameter-correlation analysis based on current neutrino-oscillation data. We identify 18 viable models for NO and 19 for IO, with 14 satisfying the experimental constraints in both orderings. The viable models successfully accommodate current neutrino-oscillation data while yielding nontrivial predictions for leptonic CP violation, Majorana phases, and observables probing the absolute neutrino-mass scale. Among these predictions, the absolute-mass observables provide the clearest separation between the two orderings. At the best-fit points, the predicted ranges of the effective electron-neutrino mass ($m_β$) are completely disjoint between NO and IO, whereas those of the sum of neutrino masses ($\sum_i m_i$) and the effective Majorana mass ($m_{ββ}$) show only partial separation. The IO models generally predict a higher absolute neutrino-mass scale and are consequently more strongly constrained by cosmological observations and more accessible to neutrinoless double-beta-decay searches. Our results show that, despite its economical field content, the modular $S_3$ framework accommodates a diverse set of phenomenologically viable lepton-flavor realizations with experimentally testable predictions.
Comments33 pages, 10 figures, 15 tables
