味盲原理：Gatto-Sartori-Tonin关系的对称方法
The flavor-blind principle: A symmetrical approach to the Gatto-Sartori-Tonin relation
摘要：
我们进行了系统的研究一般Gatto-Sartori-Tonin关系，$\tan^2θ_{ij}= m_i/m_j$。这种对费米子混合现象的研究使我们得到了在没有任何近似的情况下获得它所需的必要条件。我们首先考虑两个狄拉克费米子家族。利用群的层次性，得到了一个充要条件是存在一个具有$m_{11}=0$的正规矩阵.这个矩阵可以分解成两个不同的线性无关的贡献。这两个独立贡献的起源可以自然地用我们称之为味盲原理来解释。这一原则指出，汤川耦合要么是味盲的，要么被分解成几个服从不同排列对称的集合。在一般情况下，它示出的Yukawa矩阵的对称性的引入组如下的$n$费米子家庭的唯一顺序破缺$S_{nL}\otimes S_{nR} \rightarrow S_{(n-1)L}\otimes S_{(n-1)R} \rightarrow \cdots \rightarrow S_{2L}\otimes S_{2R} \rightarrow S_{2A}$。三个费米子家族的特殊情况解释了为什么我们最近提出的四个质量比参数化即使在没有分级质量的情况下也可以使用。
英文摘要：
We perform a systematic study of the generic Gatto-Sartori-Tonin relation, $\tan^2θ_{ij}= m_i/m_j$. This study of fermion mixing phenomena leads us to the necessary conditions that are needed in order to obtain it without any approximation. We begin by considering two Dirac fermion families. By means of the hierarchy in the masses, it is found that a sufficient and necessary condition is to have a normal matrix with $m_{11}=0$. This matrix can be decomposed into two different linearly independent contributions. The origin for such two independent contributions can be naturally explained by what we shall call the flavor-blind principle. This principle states that Yukawa couplings shall be either flavor-blind or decomposed into several sets obeying distinct permutation symmetries. In general, it is shown that the symmetry properties of the introduced set of Yukawa matrices follow for $n$ fermion families the unique sequential breaking $S_{nL}\otimes S_{nR} \rightarrow S_{(n-1)L}\otimes S_{(n-1)R} \rightarrow \cdots \rightarrow S_{2L}\otimes S_{2R} \rightarrow S_{2A}$. The particular case of three fermion families explains why the four mass ratios parametrization that we recently proposed can be used even in the case of no hierarchical masses.
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