On the Geometry Origin of Weak CP Phase

In this work, the postulation that weak CP phase originates in a certain geometry, is further discussed. Some intrinsic and strict constraints on the mixing angles, weak CP phase, and the Wolfenstein’s parameters ρ and η are given by present data and the postulation itself. Especially, we predict 0.0076 ≤ |Vtd| ≤ 0.0093, 74.9 ≤ γ ≤ 75.7 when the corresponding inputs are at the 90% C. L.. The comparison of the predictions to the relevant experimental and theoretical results is listed. All the predictions coincide with the present experimental results and theoretical analysis very well. PACS number(s): 11.30.Er, 12.10.Ck, 13.25.+m Quark mixing and CP violation [1, 2, 3, 4, 5, 6, 7] is one of the most interesting and important problem in particle physics. Up to now, the origin of CP violation is not clear to us. In the standard model, CP violation originates from a phase which presents in the CKM matrix [8, 9]. Mathematically, (N−1)(N−2) 2 phases are permitted to present in N by N unitarity matrix in addition to N(N−1) 2 Euler angles. However, physics is always in favour of more concise theory. In the previous work [10], we have postulated that, the weak CP phase originates in a certain geometry. Here, we discuss further this issue. The central purpose is to make some predictions which can be tested by more precise data in B-factory in following few years. To make this paper selfcontained, we begin with describing our postulation firstly. 1. The Postulation A. CKM matrix in KM parametrization and SO(3) rotation There are many parametrization of the CKM matrix, such as the standard one advocated by the Particle Data Group [11, 12] and those given by Wolfenstein [13] etc. However, the original parametrization chosed by Kobayashi and Maskawa is more helpful to our understanding the problem, it is [9]