Title: Fermion Masses and Mixing in Pati-Salam Unification with $S_3$ Modular Symmetry Show Chinese title

Title: 费米子质量和混合在具有 $S_3$ 模块对称性的Pati-Salam统一理论中

Abstract: Modular invariance has recently paved new promising directions in flavor model building. Motivated by this development, we present in this work the first implementation of the $S_3$ modular symmetry within the Pati-Salam unification framework, addressing the flavor structure of quarks and leptons. Assigning left- and right-handed matter fields as $S_3$ doublets or singlets, we propose three benchmark models that achieve compelling fits to sixteen observables including charged fermion mass ratios and flavor mixing parameters. Light neutrino masses arise via the type-I seesaw mechanism, and neutrino oscillation parameters are explored in light of the latest NuFIT-6.0 results. All models favor a normal neutrino mass ordering, with the atmospheric mixing angle lie in the lower octant. For models I and III, the effective Majorana mass $m_{\beta\beta}$ is within the reach of upcoming neutrinoless double-beta decay experiments, while it is too small to be detected in model II. Predicted leptonic CP-violating phases, the sum of active neutrino masses, and Majorana phases span wide but distinctive ranges, enabling future experiments to test and differentiate the proposed models. Show Chinese abstract

Abstract: 模不变性最近为味模型构建开辟了新的有前景的方向。受此发展的推动，我们在本文中首次在Pati-Salam大统一框架内实现了$S_3$模形式对称性，探讨了夸克和轻子的味结构。将左手和右手物质场分别指定为$S_3$双重态或单态，我们提出了三个基准模型，这些模型能够很好地拟合包括带电费米子质量比和味混合参数在内的十六个可观测量。轻中微子质量通过I型跷跷板机制产生，且在最新NuFIT-6.0结果的基础上探索了中微子振荡参数。所有模型都倾向于正常的中微子质量排序，并且大气混合角位于较低八分位。对于模型I和III，有效Majorana质量$m_{\beta\beta}$在即将到来的无中微子双贝塔衰变实验范围内，而在模型II中则太小而无法被检测到。预测的轻子CP破坏相位、活性中微子质量之和以及Majorana相位范围广泛但各具特色，使得未来的实验能够检验并区分所提出的模型。