arXiv 2411.033922024-11-05hep-ph

逆跷跷板机制与 $\mathbf{S}_{3}$ 味对称性

Inverse See-Saw Mechanism with $\mathbf{S}_{3}$ flavor symmetry

Juan Carlos Gómez-Izquierdo, Catalina Espinoza, Lucia E. Gutiérrez Luna, Myriam Mondragón

备注：: 37 pages, 10 figures, 3 tables

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AI总结：

本文在 B-L 规范模型中引入 S3⊗Z2 对称性实现逆跷跷板机制，研究其对轻子混合、CLFV 及无中微子双β衰变的影响，并拟合夸克质量矩阵。

摘要：

当前的 neutrino 实验为通过带电轻子味破坏过程和无中微子双β衰变来检验逆跷跷板机制提供了机会。受此启发，本文在 $B-L$ 规范模型中研究了 $\mathbf{S}_{3}\otimes \mathbf{Z}_{2}$ 离散对称性，其中活跃的轻中微子质量矩阵来源于上述机制。在此框架下，我们探讨了希格斯双重态的复真空期望值对费米子质量的影响，并在对汤川耦合的特定假设下，发现中微子混合由 Cobimaximal 模式控制，但来自带电轻子部门的显著偏差破坏了关于大气角（$45^{\circ}$）和狄拉克 CP 破坏相位（$-90^{\circ}$）的已知预言。此外，由于存在 TeV 尺度的重中微子，带电轻子味破坏（CLFV）和无中微子双β衰变获得了显著的贡献。我们得到了这些可观测量的解析公式，然后通过数值计算，对于正常和倒置质量顺序，能够很好地拟合轻子混合，然而，CLFV 的衰变分支比数值不利于倒置顺序。同时，对于 $m_{ee}$ 有效中微子质量，参数空间区域在正常和倒置顺序下均低于 GERDA 界限。另一方面，通过一个特定的基准点，发现夸克质量矩阵具有能够以高精度拟合 CKM 混合矩阵的结构。

英文摘要：

The current neutrino experiments provide an opportunity for testing the inverse see-saw mechanism through charged lepton flavor violating processes and neutrinoless double beta decay. Motivated by this, in this paper we study the $\mathbf{S}_{3}\otimes \mathbf{Z}_{2}$ discrete symmetry in the $B-L$ gauge model where the active light neutrino mass matrix comes from the aforementioned mechanism. In this framework, the effect of complex vacuum expectation values of the Higgs doublets on the fermion masses is explored and, under certain assumptions on the Yukawa couplings, we find that the neutrino mixing is controlled by the Cobimaximal pattern, but a sizeable deviation from the charged lepton sector breaks the well known predictions on the atmospheric angle ($45^{\circ}$) and the Dirac CP-violating phase ($-90^{\circ}$). In addition, due to the presence of heavy neutrinos at the $TeV$ scale, charged lepton flavor violation (CLFV) and neutrinoless double beta decay get notable contributions. Analytical formulae for these observables are obtained, and then a numerical calculation allows to fit quite well the lepton mixing for the normal and inverted hierarchies, however, the branching ratios decay values for CLFV disfavors the latter one. Along with this, the region of parameter space for the $m_{ee}$ effective neutrino mass lies below the GERDA bounds for both the normal and inverted hierarchies. On the other hand, with a particular benchmark, the quark mass matrices are found to have textures that allow to fit with great accuracy the CKM mixing matrix.

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