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arXiv 2603.08071hep-ph
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Dirac CP相位的相位不变结构及混合矩阵单位性约束的基独立缩减

Rephasing invariant structure of Dirac CP phase and basis independent reduction of unitarity constraints for mixing matrices

Saitama University（埼玉大学）；Yokohama National University（横滨国立大学）

Masaki J. S. Yang

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10 pages
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AI总结：

本文研究了Dirac CP相位的相位不变结构及混合矩阵单位性约束的基独立缩减，提出了一种紧凑形式表达并实现了PDG参数化的相位不变表示。

摘要：

在本文中，我们探讨了在近似条件$U^{e}_{13} = 0$下Dirac CP相位$δ$的相位不变结构，其中中微子对角化矩阵$U^{e}$的1-3元素被忽略。进一步简化条件$U^{e}_{12} = 0$后，Dirac相位简化为紧凑形式$δ= δ^ν + \arg [ (U_{33}^e / U_{23}^{e}) - ( U_{33}^ν / U_{23}^ν) ] - \arg [ ( U_{33}^e / U_{23}^{e}) + (U_{23}^{ν*} / U_{33}^{ν*} ) ] $，并且有限的$U_{12}^{e}$的CP相位可以视为该紧凑形式的推广。这些结果涵盖了几乎所有夸克和轻子混合矩阵中CP相位的微扰计算，且与任何特定参数化无关。作为本文工作的第二个结果，我们推导了一个任意单位矩阵$V$的单位性约束的基独立缩减，通过使用反演公式消除元素$V_{21}, V_{22}, V_{31}, V_{32}$。应用显式的相位变换到此缩减中，得到PDG参数化中的相位不变表示，这允许将用PDG参数化表达的理论结果直接转换为相位不变量。

英文摘要：

In this paper, we explore rephasing invariant structures of the Dirac CP phase $δ$ under an approximation $U^{e}_{13} = 0$, where the 1-3 element of the diagonalization of charged leptons $U^{e}$ is neglected. With the further simplified condition $U^{e}_{12} = 0$, the Dirac phase reduces to a compact form $δ= δ^ν + \arg [ (U_{33}^e / U_{23}^{e}) - ( U_{33}^ν / U_{23}^ν) ] - \arg [ ( U_{33}^e / U_{23}^{e}) + (U_{23}^{ν*} / U_{33}^{ν*} ) ] $, and the CP phase for finite $U_{12}^{e}$ can be understood as a generalization of this compact form. These results encompass almost all perturbative calculations of the CP phases in quark and lepton mixing matrices with hierarchical masses of charged fermions, and are independent of any specific parametrization. As a second result of this work, we derive a basis independent reduction of the unitarity constraints for an arbitrary unitary matrix $V$ by eliminating the elements $V_{21}, V_{22}, V_{31}, V_{32}$ using the inversion formula. Applying the explicit rephasing transformation to this reduction yields a rephasing invariant representation of the PDG parametrization, which allows the translation of theoretical results expressed in the PDG parametrization directly into rephasing invariants.

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