New Viewpoint to CP-violation and Quark-mixing

The relation between CP-violation phase angle and the other three mixing angles in Cabibbo-Kobayashi-Maskawa matrix is postulated. This relation has a very definite geometry meaning. The numerical result coincides surprisingly with that extracting from the experiments. It can be further put to the more precise tests in the future. PACS number(s): 11.30.Er, 12.10.Ck, 13.25.+m New Viewpoint to CP-violation and Quark-mixing Although more than thirty years have passed after the discovery of CP violation [1], our understanding about CP violation [2-6] is still very poor. In the Standard Model (SM), CP violation is due to the presence of a phase angle in the Cabibbo-Kobayashi-Maskawa (CKM) matrix [7,8], this phase angle is independent of the other three mixing angles. Up to now, all the experimental results are well in agreement with the predictions of the SM. Nevertheless, the correctness of CKM mechanism is far from being proved. On the other hand, the SM which has nineteen free parameters is not so satisfactory. It is evident that the less free parameters, the less uncertainty. People are always like to find a concise theory. People have made an great effort to reduce the number of the free parameters in the SM. Fritzsch firstly noted that, there exists a certain relation between the ratios of quark masses and the weak interaction mixing angles [9,10]. But, no one has ever doubted that, whether the four angles presented in the CKM matrix have an intrinsic relation. People have been taking the four angles as independent, and thinking that to be naturelly for many years. But, maybe it is very surprising, we find that the CP violation phase angle and the other three mixing angles satisfy the following relation cos δ 2 = 1 + cosθ1 + cosθ2 + cosθ3 4cos θ1 2 cos θ2 2 cos θ3 2 (1) where θi (i = 1, 2, 3) are the mixing angles describing the quark-mixing among three generations in the weak interaction and corresponding to the ones in the standard KobayashiMaskawa parametrization matrix