We present a model that gives a natural explanation to the charged lepton mass hierarchy and study the contributions to the electron and the muon $g-2$. In the model, we introduce lepton-flavor-dependent $U(1)_F$ symmetry and three additional Higgs doublets with $U(1)_F$ charges, to realize that each generation of charged leptons couples to one of the three additional Higgs doublets. The $U(1)_F$ symmetry is softly broken by $+1$ charges, and the smallness of the soft breaking naturally gives rise to the hierarchy of the Higgs VEVs, which then accounts for the charged lepton mass hierarchy. Since electron and muon couple to different scalar particles, each scalar contributes to the electron and the muon $g-2$ differently. We survey the space of parameters of the Higgs sector and find that there are sets of parameters that explain the muon $g-2$ discrepancy. On the other hand, we cannot find the parameter sets that can explain $g-2$ discrepancy within 2$\sigma$. Here the $U(1)_F$ symmetry suppresses charged lepton flavor violation.

中文翻译：

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介子和电子 g − 2 以及费米子质量等级的起源

我们提出了一个模型，该模型可以自然地解释带电轻子质量层次结构，并研究对电子和 μ 子 $g-2$ 的贡献。在模型中，我们引入了依赖于轻子风味的 $U(1)_F$ 对称性和三个额外的带有 $U(1)_F$ 电荷的 Higgs 双峰，以实现每一代带电轻子都与三个额外的 Higgs 中的一个耦合双峰。$U(1)_F$ 对称性被 $+1$ 电荷软破坏，软破坏的小自然会产生 Higgs VEV 的层次结构，然后解释带电轻子质量层次结构。由于电子和μ子耦合到不同的标量粒子，每个标量对电子和μ子$g-2$的贡献不同。我们调查了希格斯扇区的参数空间，发现有一组参数可以解释 μ 子 $g-2$ 的差异。另一方面，我们在 2$\sigma$ 中找不到可以解释 $g-2$ 差异的参数集。这里的 $U(1)_F$ 对称性抑制了带电轻子风味违规。