发表机构
Department of Physics, Saitama University（埼玉大学物理系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究利用微扰奇异值分解，通过类似跷跷板过程对层次夸克质量矩阵进行对角化，推导CKM矩阵中CP相位\(\delta\)的近似表达式，还在特定基中得到相关不变量及与小林-益川参数化中CP相位的关系。
AI 中文摘要
本文通过对层次夸克质量矩阵\(m_{q}\)进行微扰奇异值分解，推导了CKM矩阵中CP相位\(\delta\)的近似表达式。对角化通过类似跷跷板的过程实现，即依次积分掉较重的世代，自然地得到用质量矩阵及其逆\(m_{q}^{-1}\)表示的混合矩阵。结果，在上型夸克质量矩阵为对角的基中，\(\delta\)简化为从下型质量矩阵及其逆构造的四阶不变量\(\delta \simeq \arg [ - m^{-1}_{d12} m_{d23}^{} / m^{-1}_{d11} m_{d13}^{} ]\)。此外，在小林-益川参数化中，CP相位同样在与不变量\(\delta_{\rm KM} \simeq \arg [ m^{-1}_{d13} m_{d33}^{} / m^{-1}_{d11} m_{d13}^{} ] \simeq \pi/2\)相同的基中表示。
英文摘要
In this paper, we derive approximate expressions for the CP phase $δ$ in the CKM matrix by a perturbative singular value decomposition for hierarchical mass matrices of quarks $m_{u,d}$. The diagonalization is achieved through a seesaw-like procedure in which the heavier generations are successively integrated out, naturally leading to mixing matrices expressed in terms of the mass matrices and their inverses $m_{u,d}^{-1}$. As a result, in the basis where the up-type quark mass matrix is diagonal, $δ$ is reduced to a fourth-order invariant $δ\simeq \arg [ - m^{-1}_{d12} m_{d23}^{} / m^{-1}_{d11} m_{d13}^{} ]$. Furthermore, in the Kobayashi--Maskawa parametrization, the CP phase is likewise expressed by an invariant $δ_{\rm KM} \simeq \arg [ m^{-1}_{d13} m_{d33}^{} / m^{-1}_{d11} m_{d13}^{} ] \simeq π/2$ in the same basis. Since the next-to-leading-order corrections are suppressed at second order in the perturbation, the accuracy of these expressions is typically of order $O(λ^{2}) \sim 4 \%$.
Comments9 pages, title is changed, some discussion is added
