We propose a bottom-up approach that a structure of a high-energy physics is explored by accumulating existence proofs and/or no-go theorems in the standard model or its extension. As an illustration, we study fermion mass hierarchies based on an extension of the standard model with vector-like fermions. It is shown that a magnitude of elements of Yukawa coupling matrices can become $O(1)$ and a Yukawa coupling unification can be realized in a theory beyond the extended model, if vector-like fermions mix with three families. In this case, small Yukawa couplings in the standard model can be highly sensitive to a small variation of matrix elements, and it seems that the mass hierarchy occurs as a result of a fine tuning.

中文翻译：

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费米子质量等级的自下而上方法：类似矢量费米子的案例

我们提出了一种自下而上的方法，通过在标准模型或其扩展中积累存在证明和/或不通过定理来探索高能物理的结构。例如，我们研究了基于标准模型扩展的费米子质量层次结构，其中包含类矢量费米子。结果表明，如果类向量费米子与三族混合，汤川耦合矩阵的元素量级可以变为$O(1)$，并且可以在超出扩展模型的理论中实现汤川耦合统一。在这种情况下，标准模型中的小型 Yukawa 耦合可能对矩阵元素的微小变化高度敏感，并且质量层次似乎是微调的结果。