Cabibbo-Kobayashi-Maskawa Matrix Unitarity Triangle and Geometry Origin of the Weak CP Phase

In this work, the postulation that weak CP phase originates in a certain geometry, is further discussed. According to this postulation, the weak CP phase is determined by three mixing angles. So, if we can determine experimentally three elements of the Cabibbo-KobayashiMaskawa (CKM) matrix, we can then determine the whole CKM matrix and correspondingly, the unitarity triangle. We find that the angle γ is about π/2, this is coincide with the relevant analysis. Some other predictions are given in this paper, the comparison of the predictions based on the postulation to the relevant experimental and theoretical results is listed. All the predictions are consistent with the present experimental results. PACS number(s): 11.30.Er, 12.10.Ck, 13.25.+m Cabibbo-Kobayashi-Maskawa Matrix Unitarity Triangle and Geometry Origin of the Weak CP Phase Quark mixing and CP violation [1-7] is one of the most interesting and important problem in weak interaction and the whole particle physics. Up to now, people do not know the real origin of CP violation. In the standard model, CP violation originates from a phase presenting in the CKM matrix [8-9]. Mathematically, a phase is permitted to present in the three by three unitarity matrix. But, few people have asked the question, what is the mathematical and physical meaning of the phase and how is it generated ? In the previous works [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 and contrast the predictions with the experimental results. Then, we can see that, if our postulation is reasonable. To make this paper selfcontained, let us repeat the previous discussion firstly. 1. 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 [10-11] and that given by Wolfenstein [12] etc. However, the original parametrization chosed by Kobayashi and Maskawa is more helpful to our understanding on the problem, it is [9]