9 v 1 1 6 D ec 1 99 8 Does Weak CP Phase Originate from a Certain Geometry ?

We further investigate the probability that, weak CP phase originates in a certain geometry. We find that our postulation on weak CP Phase gives strict constraints on angle γ in unitarity triangle DB and the element Vtd in Cabibbo-Kobayashi-Maskawa (CKM) matrix. The predicted |Vtd| is about 0.0086 and γ about 75.3 0 with the very narrow window respectively. These two parameters can be used to test our postulation precisely in near future. PACS number(s): 11.30.Er, 12.10.Ck, 13.25.+m Does Weak CP Phase Originate from a Certain Geometry ? As is well known, CP violation is one of the most important problem in particle physics [1-6]. People have been concerning it for more than thirty years. However, we still know little about it. With the runing of the B−factories, we expect to know more about it in near future. According to the standard CKM mechanism, CP violation originates from a phase presenting in the three by three quark mixing matrix [7-8]. Last winter, we have found that, the weak CP phase and the other three mixing angles in CKM matrix satisfy a certain geometry relation [9-10], so we postulated that, weak CP phase is a geometry phase. Although it is a ad hoc postulation, all the conclusions extracted from it are consistent with the present experimental results. Our postulation in the standard parametrization can be expressed as [10] sin δ13 = (1 + s12 + s23 + s13) √ 1− s 12 − s 23 − s 13 + 2s12s23s13 (1 + s12)(1 + s23)(1 + s13) (1) where sij and δ13 are the parameters in the standard parametrization [11-12] VKM = 