AI 中文总结
本文研究基于D₅对称性的四希格斯模型，发现其在自发CP破坏框架下无法产生非块对角CKM矩阵，排除了用该模型解释CP破坏实验观测的可能。
AI 中文摘要
已知CP破坏发生在味物理中，且CKM矩阵为复矩阵。我们研究基于D₅对称性的四希格斯模型（four-Higgs model）的汤川 sector（Yukawa sector），为理解汤川 sector 中所有可能的CP破坏来源，系统分析了左手与右手夸克场在D₅群下所有可能的表示分配的影响。在施加非块对角CKM矩阵和无质量夸克的条件后，我们发现唯一可行的表示由一个D₅二重态和一个单态组成。在此情况下，夸克 sector 中出现两种不同类型的夸克质量模型。对于每个模型，我们向质量矩阵引入允许自发CP破坏（SCPV）的最一般真空。由于D₅对称性的特定结构，真空期望值（vevs）满足特定关系，使得对于两种夸克模型，上夸克和下夸克的质量平方矩阵（即M_d M_d^†和M_u M_u^†）可通过同一幺正变换同时块对角化，迫使CKM矩阵成为块对角，从而导致混合角和CP破坏消失。该结果排除了在SCPV框架下，用D₅ 4HDM解释实验观测的可能性。
英文摘要
It is known that CP violation occurs in flavor physics, and the CKM matrix is complex. We investigate the Yukawa sector of a four-Higgs model based on D_5 symmetry. To understand all possible sources of CP violation in the Yukawa sector, we systematically analyze the impact of all possible representation assignments of the left-handed and right-handed quark fields under the D_5 group. After imposing the conditions of non-block-diagonal CKM matrix and the absence of massless quarks, we find that the only viable representation consists of one D_5 doublet and one singlet. In this case, two distinct types of quark mass models emerge in the quark sector. For each model, we introduce the most general vacuum that allows spontaneous CP violation (SCPV) into the mass matrices. Due to the specific structure of the D_5 symmetry, the vacuum expectation values (vevs) satisfy particular relations such that, for both quark models, the up- and down-quark mass squared matrices (i.e., M_d M_d^\dagger and M_u M_u^\dagger) can be simultaneously block-diagonalized by the same unitary transformation, forcing the CKM matrix to be block-diagonal and thus yielding vanishing mixing angles and CP violation. This result rules out the possibility of explaining experimental observations within the D_5 4HDM under the SCPV framework.
