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arXiv 2102.03050hep-phhep-th
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Dirac和Majorana费米子质量项的平移味对称性

A translational flavor symmetry in the mass terms of Dirac and Majorana fermions

Zhi-zhong Xing

备注：
15 pages. A proof is given to show that the translation of a massless neutrino field, which assures the Dirac equation to be invariant, is equivalent to the translational transformations of three neutrino flavor states in the flavor space as a consequence of flavor mixing. More discussions are added. Accepted for publication in JPG
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摘要：

要求一类具有相同电荷的基本狄拉克费米子或马约拉纳费米子的有效质量项在味空间中的平移变换$ψ^{}_{α\rm L (R)} \to ψ^{}_{α\rm L (R)} + n^{}_α z^{}_{ψ\rm L(R)}$下不变，其中$n^{}_α$和$z^{}_{ψ\rm L(R)}$分别代表味依赖复数和与费米子场反对易的常旋量场，我们证明了$n^{}_α$可以被识别为酉矩阵$U$的第$i$列中的元素$U^{}_{αi}$，该酉矩阵用于对角化相应的厄米或对称费米子质量矩阵$M^{}_ψ$，并且$m^{}_i = 0$相应地成立。我们发现反过来也是如此。既然带电轻子、上型夸克和下型夸克的质量谱都具有很强的层次性，并且目前的实验数据允许最轻的中微子是无质量的，我们认为第一家族费米子的零质量极限及其背后的平移味对称性应该是建立可行的费米子质量模型的自然起点。

英文摘要：

Requiring the effective mass term for a category of fundamental Dirac or Majorana fermions of the same electric charge to be invariant under the translational transformations $ψ^{}_{α\rm L (R)} \to ψ^{}_{α\rm L (R)} + n^{}_α z^{}_{ψ\rm L(R)}$ in the flavor space, where $n^{}_α$ and $z^{}_{ψ\rm L(R)}$ stand respectively for the flavor-dependent complex numbers and a constant spinor field anticommuting with the fermion fields, we show that $n^{}_α$ can be identified as the elements $U^{}_{αi}$ in the $i$-th column of the unitary matrix $U$ used to diagonalize the corresponding Hermitian or symmetric fermion mass matrix $M^{}_ψ$, and $m^{}_i = 0$ holds accordingly. We find that the reverse is also true. Now that the mass spectra of charged leptons, up- and down-type quarks are all strongly hierarchical and current experimental data allow the lightest neutrino to be massless, we argue that the zero mass limit for the first-family fermions and the translational flavor symmetry behind it should be a natural starting point for building viable fermion mass models.

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